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Figure 2.5.1 Danielle Bender, Public Hives.
Danielle Bender of Public Hives got into beekeeping because she saw the potential of bees being a “catalyst to people getting more engaged with their communities.” Public Hives promotes community pollinators by placing beehives in neighborhoods and parks in Miami, Florida.
A couple years ago in Miami, there was a big Zika virus scare. Danielle noticed that there was a lot of aerial spraying for Zika going on but residents – many of whom walked everywhere, were older, and didn’t have access to the Internet or TV – were not being informed. Danielle got curious about this, noting in her neighborhood where there once were a lot of bees, there were no longer. She also noticed that she didn’t see grasshoppers or any other bugs any more.
“Communication makes communities stronger,” thought Danielle, and through her observation that the bugs were disappearing, she asked, “How do we get community members to communicate with each other and share information?” And how could she help provide opportunities for wildlife and the environment to flourish in her community?
As a grant writer and arts administrator, Danielle proposed a project for a public space challenge where folks could generate ideas to make the community a better place to live in. Her proposal was to do beekeeping in public spaces even though she wasn’t a beekeeper at the time. She got her start in beekeeping after doing lots of research, attending beekeeper association meetings, and contacting different beekeepers in the area.
“Just the idea of being able to experience beekeeping and doing that in the middle of the city in an urban environment, meeting neighbors, that was the main motivation and it’s worked out.”
“People have been really enthusiastic about this [public space challenge] and they are really curious about bees. Super curious,” says Danielle.
Public Hives commissions artists to paint the outside of hives and provide interesting workshops. They take a broader arts approach to spreading knowledge about bees that they feel reaches more folks in the community than a strictly science-based approach would. For example, they provided one group workshop where architects from the University of Miami’s women in architecture program designed different bee hotels to support native pollinators and another where they brought in two musicians that do experimental noise music to set up an interactive experience where people could plug in headphones and listen to the noises coming out of the bees.
As people sign up for workshops on their website, Danielle and the folks at Public Hives ask them what kind of programming they’d want to see in the future.
Many of these workshops are pretty intimate with about 13 people per visit (although they are looking to make these a little smaller for the sake of the bees). Danielle has noticed that in such visits people who come are “usually all strangers.” She says, “Being in a situation where you are in a vulnerable position, you’re nervous, you’ve maybe never been around bees before, or you’re excited because you’ve always wanted to be around bees…That makes people want to talk to the people around them.”
The Miami community is curious. “They want to know where their food comes from, they want to know processes, they want to be involved, they want hands on, and allowing them to do that really makes them more enthusiastic about the process itself.”
This intentional community focus extends to the speakers and artists Public Hives chooses to give workshops and events. “We try to choose artists that either identify with the space, or live and work in the neighborhood,” says Danielle. For example, in the Little Haiti neighborhood, “We had an artist whose name is Serge Touissant. He does murals all over and we commissioned him to paint the hive,” says Danielle. “So when he painted the hives, they’re very recognizably his style of art, and my friend and her son (both Haitian) [recognized] Serge’s work.”
Employing local artists in beekeeping workshops helps connect the practice with the neighborhood “because an artist from that neighborhood painted it” (in the case of the hive painting projects). In general, this community approach helps in “demystifying bees to someone that may have had a bad perception about [bees].” Danielle loves that this project is “a full circle opportunity to…get people meeting, demystify bees, and give opportunities to artists and beekeepers that live in the area.”
Figure 2.5.2 Danielle Bender, Public Hives.
Public Hives also keeps it “local” whenever they host a honey harvesting workshop. They make sure that the demonstrations are led by a local beekeeper. They also center women and people of color when considering beekeepers to lead sessions, mentees, and artists. “Each beekeeper that leads a session is also simultaneously mentoring someone that may want to become a beekeeper. So, I make sure that any of the positions of someone leading a session is either led by women or POC.”
Danielle’s mission is to make sure this project goes beyond her as an individual “because that’s how things become stale, and that’s how people get burnt out.” Hence the emphasis on engaging the community on what kind of programming they would like to see and the focus on mentoring up and coming beekeepers to share in this wealth of knowledge, at places that naturally intersect for them.
“It’s just making sure that there’s room for other people to get involved.” | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.06%3A_Danielle_Bender-_Beekeeping_An_Artistic_Accessible_Approach.txt |
Figure 2.6.1 Julia Common (left), Sarah Common (right), Hives for Humanity
“The first time I put my hands in a hive I loved it,” says Julia Common of Hives for Humanity. Julia started beekeeping as a hobby at age 21, traveling with this hobby to England and Scotland. In 2012, when her daughter asked her to bring bees to the city of Vancouver, British Columbia, Canada, Julia became the Chief Beekeeper for Hives for Humanity, a 200 colony operation. Hives for Humanity is a non-profit organization providing mentorship-based programming for people to engage in therapeutic culture that surrounds the hive. In her daughter’s community in East Vancouver, there are houseless folks and people living with addictions. The organization’s core work is to use beekeeping as a therapeutic activity for these populations.
Julia started with two hives given to her by a researcher from Winnipeg, Manitoba, Canada and from there began her journey to learn beekeeping. By the time she started Hives for Humanity, she went from one hive to 75 to 150 to 250 to the current number of 200 full colonies and 75 nucs.
Her daughter Sarah who had been working with marginalized populations in the Downtown Eastside of Vancouver doing gardening work thought that beekeeping could provide places of respite for these populations. The introduction of the bees was well received. This area is fraught with drug addiction, homelessness, and unemployment but the community is strong. Sarah engages the community in beekeeping, gardening, candle making, and honey extraction. “They do all sorts of jobs to support the bees,” says Julia.
Vancouver is progressive with bees; pollinating corridors and parks abound and neonicotinoids are banned for use on plants. Vancouver’s winter is much milder and their growing season is longer. “Urban beekeeping is sweet because the bees have plenty to eat all the time,” says Julia. But, “the biggest challenge is that you do not want people to interfere with the bees.” So far, they’ve been lucky with minimal instances of people disturbing the bees.
Figure 2.6.2 Julia Common (center), Hives for Humanity
“Working for Hives for Humanity has changed how I do everything,” says Julia. “Everything that is happening to people is happening to the bees” – lack of nutrition, nowhere to live, chaos. Since moving from beekeeping as a hobby to a community service, Julia has focused on the parallels between human nature and bees, a connection she may not have made if she stayed in the country with her bees.
“Moving them around, making splits when they are not strong enough, over treating them, exposing them to monocultures where they get poor diet, and chemical exposure and miticides” – these are all problems she identifies in modern beekeeping but with the advantages of the climate in Vancouver mentioned above, Hives for Humanity is well poised to address them.
The community has enjoyed doing extraction and found satisfaction in tasting the honey from their bees and making salves or rolling candles in the winter. “Whenever I am with people I want them to have positive experiences with bees,” says Julia.
Hives for Humanity’s work of gardening, beekeeping and fostering connection to land and community, takes place on the unceded lands of the Musqueam, Tsleil-Waututh and Squamish Nations of the Coast Salish peoples. | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.07%3A_Julia_Common-_Apiculture_to_Community_Culture.txt |
Figure 2.7.1 Sarah Red-Laird, Bee Girl.
Sarah Red-Laird, founder and executive director of the Bee Girl organization, cannot think of a time that she wasn’t really into bees, honey, and beekeeping, though the fascination most likely began around the age of three when she got her first bee sting. Sarah became a beekeeper as an undergraduate student at the University of Montana where she did her senior thesis on beekeeping and Colony Collapse Disorder.
The Bee Girl organization’s mission is to educate and inspire communities to conserve bees, their flowers, and our countryside. She envisions a future where kids frolic in pastures of flowers, buzzing with bees, alongside profitable family farmers and ranchers. The organization’s programs primarily focus on both bee habitat conservation and kid’s education.
“There’s a huge need for beekeepers to talk to groups of kids and get kids excited about bees,” says Sarah. Every year Bee Girl teaches “Kids and Bees” workshops across the world, instructing and encouraging fellow beekeepers to bridge children’s fear to fascination by inviting them to learn about bees from an expert. She also partners with the American Beekeeping Federation, the Eastern Apicultural Society, the Farmers Union, and other nonprofit collaborators in her home town of Ashland, Oregon, to reach a few hundred kids each year with the motto: Love Your Bees.
Sarah has quite a presence in her Oregon community, consistently making appearances at local farming, beekeeping, and environmental events. She’s toured five countries, two Canadian provinces, and 20 states speaking on the topics of kids education and bee habitat conservation.
During the first few years of her organization’s founding, she taught evening beekeeping classes and a season-long hands-on beekeeping course. Now, however, she has moved on from teaching beekeeping to turn as much time and attention as she can to her “Regenerative Bee Pasture” project. This multi-pronged collaborative project aims to ensure there is an abundance and high diversity of bee-friendly flowers on as much of our agricultural landscapes as possible.
Starting with soil health, native bees and honey bees, and beekeepers will be the end beneficiaries of this project. As Regenerative Bee Pasture in Oregon grows, so will rural bee health.
Bee Girl has also advocated for urban bees. Beekeeping in Oregon has been legalized in every municipality in the southern region of the state. Sarah and the board of directors worked hard to legalize beekeeping in Ashland city limits in 2012. Since then, this ordinance has been used as a model for other municipalities to relax restrictions on beekeeping.
Despite the hard work of Bee Girl and other bee advocate groups, beekeepers still don’t have it easy. Looking back to her beekeeping educator days, Sarah says her beekeeping students didn’t realize “how much work, how much learning, and how much commitment there actually is [to keeping bees]. There is little or no room for mistakes, which is surprising. It’s a lot harder to keep bees than it is to have a cat or dog…or sometimes even a horse or chickens.”
Figure 2.7.2 Sarah Red-Laird, Bee Girl
Her primary advice to new beekeepers is to be wary of how incredibly important Varroa (and other pest/disease) management is. Secondly, she advises, “if you are not living in an area that has hundreds of acres of flowers blooming year round, you need to consider supplementarily feeding your bees…if there is not food out there for them, you need to help them out.”
Sarah takes a more holistic view of the larger picture of agriculture and soil management. She sees a need for a cultural shift in transitioning from an intensive, chemically dense system into a regenerative system. It’s tricky but “we just need more and more success stories on the ground of people showing how it really is ecologically beneficial to farm regeneratively and sustainably.” She continues, “It’s so much more beneficial for pollinators, and our own health, to build soil with flowering plants instead of with nozzles.” | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.08%3A_Sarah_Red-Laird-_Beekeeping_as_Part_of_the_Bigger_Picture-_Agriculture_and_Apiculture.txt |
Figure 2.8.1 Kristy Lynn Allen, The Beez Kneez
Kristy Lynn Allen, owner and founder of The Beez Kneez in Minneapolis, Minnesota first got introduced to beekeeping by way of her uncle, a commercial beekeeper. In an industry largely made up of white men, Kristy is carving her own path as a woman doing business in a way that feels right to her. “My partnerships are not based on geography but on relationships that are important to me,” she says. Regenerative in its own right, but not necessarily “the most efficient business model,” she says.
Kristy didn’t want to become a commercial beekeeper and so started her journey delivering honey on bicycles. Later down the line, Kristy joined up with an educator and together they started a Kickstarter to raise money for what is now the Beez Kneez LLC. Together they taught a beekeeping education program for awhile and then her partner moved on because she wanted to be a nonprofit while Kristy wanted to be a social enterprise to avoid having to continuously write grants. Kristy started a 14-week intensive beekeeping course called Camp Beez Kneez – which runs from April through October – under the guidance of another woman beekeeper for the first year of the program.
As folks participate in the camp throughout the year (and see how beekeeping is a lot more challenging than they anticipated), about half realize that beekeeping is too much for them and the other half are really into it. “It’s cool to watch those beekeepers and that community building,” says Kristy. “They take ownership over that particular hive, without the bees dying at the end of the year, and they get to see realistically what can happen.”
Kristy is proud of the model of city beekeeping she’s engaged in throughout the year because her program “forces those places I partner with to be very cautious of what they’re doing on their landscapes…universities planted way more forage, cut back on their treatments of lawns, even though they still do it, because our culture has a really hard time letting go of this green lawn situation.” While this model has its advantages, it’s hard to gauge why bee declines happen on campus – whether it’s crazy snowstorms or landscapers still treating lawns chemically. She feels bad for the bees that don’t make it through the seasons.
The Beez Kneez has about 150 production hives but a very small amount in the metro area. Kristy keeps only 20 hives on her farm on the border of Wisconsin and Minnesota. In addition to providing education to the community about the importance of bees, Kristy is searching for different angles to approach the bee issue, which “like all environmental issues, highlights how toxic our planet is.”
“As an activist, I’ve been trying to figure out ways to engage not just the people we preach to, but how do we hook ‘em?” says Kristy. During the first year of her campaign “Healthy Bees Healthy Lives,” the Beez Kneez hosted a competition inviting women chefs to a “Dandelion Honey Pastry Chef Challenge.” The competition would draw celebrities – chefs and entertainment alike – as a way to “hook” the community into paying attention to the bee issue. While pastries provided a good hook, Kristy acknowledges that there’s still a class issue within beekeeping because hosting fancy events alone to raise money doesn’t necessarily reach the populations who are typically underrepresented in the industry.
Figure 2.8.2 Kristy Lynn Allen, The Beez Kneez
It’s not just the fancy events Kristy struggles with, it’s the state meetings too and conducting business within a largely older white male crowd. Though she doesn’t “fit in” with this crowd or even understand things like how a Trump voter can love bees, she sees an opportunity to make connections across divides but it’s not an easy task. “The fact that we have the bees as a connection is huge [but] what do we do with all these angry white men? If we are really about building community, [how do we bridge that divide?]”
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• Kristy Lynn Allen © Kristy Lynn Allen is licensed under a All Rights Reserved license
• Kristy Lynn Allen inspects bee frame © Kristy Lynn Allen is licensed under a All Rights Reserved license | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.09%3A_Kristy_Lynn_Allen-_Carving_a_Different_Path_in_Beekeeping.txt |
Figure 2.9.1 Dr. Marla Spivak, Bee Squad
The Bee Squad in Minneapolis, Minnesota came about after a huge surge in backyard beekeeping in 2011/2012. At the time, there was no state apiary program and the Bee Squad was the only extension program. Dr. Marla Spivak at the University of Minnesota Bee Lab felt such a program was needed to help new beekeepers and educate them. The Bee Squad became part of the university lab.
This partnership “allows us to really focus on the education part and really focus on helping beekeepers and non-beekeepers in ways that are really attuned to what’s going on with the research and what really makes sense,” says Bridget Mendel Lee who works with Marla at the Bee Squad and the Bee Lab. “We are working with methods that really work for this climate and this particular region and this urban area in particular. And that’s always evolving.”
A major challenge of urban beekeeping in Minneapolis is “the density of beekeepers is really high and [so is] transmission of drift of mites, so we have to make sure the bees are well cared for,” says Marla.
Figure 2.9.2 Bridget Mendel-Lee, Bee Squad
The Bee Squad strongly advocates mite testing and so they sell mite kits (of powdered sugar, shaker, measuring scoop and instructions with pictures on how to use). “We really advocate for treatment according to where you are not just what we do in Minnesota,” says Bridget. “Because we are also talking to beekeepers who aren’t in our region.” The Bee Squad partnered with the University of Maryland and Michigan State to create an online platform where people can input their testing data and see what’s happening in their region.
Key to the Bee Squad’s reach is the various ways in which they partner with the community and with funders. The Bee Lab at the university was funded by state bonds, gifts, and donations. These came from all kinds of people in all kinds of income brackets, all of which made the difference. The Bee Squad was funded by folks that are also Bee Squad customers. “Many of our customers participate because they want to support the lab; and many donate far beyond the cost of the program.
Educating all supporters and customers helps “reach a lot of people at once by talking to large companies, but information spreads through family networks and neighborhoods, too.” Talking to people who start out hating bees, says Bridget, has been really interesting.
Figure 2.9.3 Dr. Marla Spivak (orange shirt) leads queen course, Bee Squad.
Like Kristy Lynn Allen of the Beez Kneez, Marla and Bridget find that bees have a reach beyond political affiliation and income status. “This is about bees and about changing our landscape on whatever level you want to take that,” says Marla.
“Our customers make a difference with huge amounts of funding; others with planting gardens, talking to neighbors, doing citizen science, or organizing educational opportunities for their communities.”
Bridget and Marla have seen the landscape of Minnesota change a lot since they started this project – more pollinator-friendly yards in Minneapolis and more political advocacy through groups like Pollinate Minnesota. Much like Kristy, the Bee Squad is carving their own path of a majority female-run operation with about 15-20 people on staff, most employed part-time. | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.10%3A_The_Bee_Squad-_Partnerships_in_Beekeeping.txt |
Figure 2.10.1 Stacey Vazquez (left) and Carolina Zuniga-Aisa (right), Island Bee Project
Stacey Vazquez is one half of the dynamic duo that runs Island Bee Project on Governors Island in New York City. Along with Carolina Zuniga-Aisa, Stacey manages the 7 hives on the island, which is also home to the GrowNYC garden program and the Earth Matter farm. Stacey and Carolina met at a beekeeping class at the Brooklyn Grange and became fast friends and co-bee nerds.
They started out working on Earth Matter’s (a compost learning center) farm for about two years and on their third year, the Trust for Governors Island contacted them to offer a dedicated space for their beekeeping. In 2019, Island Bee Project partnered with the Honeybee Conservancy and Stacey and Carolina moved again into the space they currently occupy.
In addition to providing education on honey bees, part of this partnership includes encouraging people to learn a bit more about the native bees that exist in New York as well. They continue collaborating with folks at the Brooklyn Grange and are always meeting new beekeepers in New York City. “I’m always super shocked at how small, yet huge that community is,” says Stacey.
And with the Honeybee Conservancy, the Island Bee Project works with some other beekeepers as well. “We’ve done some on-site fairs at community farms in the Bronx,” says Stacey, and in addition to all the education provided, they also support community through social media.
Like the other urban beekeepers interviewed, Stacey mentioned one of the challenges to beekeeping in the city is having enough forage for the bees. She recounted a story of one season where the bees went in search for something to eat that was not good for them – runoff from a nearby maraschino cherry factory. And they learned an important lesson that year to make sure the bees had sufficient food ever since.
Aside from that, there are many reasons why “New York City is an interesting place to keep bees,” says Stacey. People get creative with use of space. “We have friends that keep bees in cemetaries…on rooftops, backyards, and city parks. There’s room available but you really do have to seek it out.”
As self-proclaimed “lady beekeepers” with Latinx backgrounds, neither Stacey nor Carolina has had any big issues in the larger beekeeping community, but Stacey admits it is largely a “boys’ club” still. However, “there’s a big community of women and lady beekeepers in New York City [and that] community is building, but we were always really surprised when we went to conventions – it’s a pretty one kind of group deal.” While conventions have in the past consisted mostly of old white men, “they’re [often] farmers and it’s amazing talking to them,” says Stacey. “It’s always really cool hearing their stories and meet[ing] somebody who has like 40 years of beekeeping experience.”
At the first convention they went to in the Berkshires in western Massachusetts, “everybody from class [at the Brooklyn Grange] – city kids rented a car, we drove out there and when we got out in a big field…it was gorgeous…but when we walked in, we were definitely the most varied group there. At first, I’m pretty sure they were like, whoa, what are these folks doing here? What are these city kids doing here?”
“We definitely stuck out like sore thumbs. But at the end of the day, it was a great experience because everyone has the same goals in common and once people see that you’re really interested in this cause and helping bees and keeping them alive, people just kind of stop seeing what you are, they see who you are.”
Stacey thinks the beekeeper landscape is changing because “times change” and “I like to think this generation is becoming a little more conscious of what’s going on in their environment and things that need to change.” Stacey sees that “young people of all ethnicities and walks of life are really involved.”
And young people of all ages have taken interest in bees and beekeeping. “We love working with kids,” says Stacey. “When we do work with the Honeybee Conservancy, we go to different neighborhoods and talk to a whole class of kids.” One of the special things about this is when Stacey and Carolina talk to the kids about bees, they emphasize “how every job that they do is meant to help the hive as a whole. Everything is done for the greater good of the hive. It teaches children a less selfish view of how you should live your life even though you’re not a bee.” Kids learn that everybody has a job to do.
And beekeeping has become a family affair for one family that’s contacted them. A friend of a friend wanted to start a rooftop garden in her building and wanted to involve her two children (ages five and seven at the time) in the whole process. Stacey and Carolina split one of their hives, drove it over to Park Slope, Brooklyn, and the rest is history.
“We raised a beekeeping family in Brooklyn,” says Stacey. “They’re all beekeepers, and we still kind of mentor them when stuff goes on, if they have questions, and the mom comes out when we need volunteers and the kids come too. That was a really awesome thing [that] we taught a whole family how to keep bees.”
Figure 2.10.2 Stacey Vazquez, Island Bee Project
Stacey finds New York City a unique place to be a beekeeper. “It’s definitely a special community of people who want to cultivate a natural environment within the urban environment” and beekeeping is “not the first thing you think of somebody doing in the urban metropolis of the country.”
In terms of beekeeping philosophy, the Island Bee Project avoids chemical treatments, opting for natural intervention for Varroa mites, and “we try to keep it as minimally invasive as possible.” Like Alwyn of Oxx Beekeeping, Stacey and Carolina also use essential oils to keep mite count down and they also use formic acid.
Stacey mentioned a beekeeper in New Jersey who is raising “behaviorially hygienic bees” and this is something she hopes becomes a more mainstream practice “for people to be raising these kind of bees because they’ll either attack the varroa mites and bite their legs off so that they can’t attach to the bees, or they groom each other and take them off.”
“We’re aligned with the natural beekeeping philosophy,” says Stacey. “Our goal is definitely to get to a point where we don’t have to [treat them at all] but for sustainability reasons [minimally invasive and non-chemical treatments – and feeding – are needed so as] not to have to replace everything all the time.”
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• Stacey Vazquez and Carolina Zuniga-Aisa © Stacey Vazquez is licensed under a All Rights Reserved license
• Stacey Vazquez and youth group © Stacey Vazquez is licensed under a All Rights Reserved license | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.11%3A_Stacey_Vazquez-_Beekeeping_as_a_Family_%28and_Urban%29_Affair.txt |
Figure 2.11.1 Nicole Lindsey (left) and Timothy Jackson (right)
Timothy Jackson and Nicole Lindsey started Detroit Hives because they wanted to “find ways to bring communities together.” It all started with an article on the copious amounts of vacant lots in Detroit and a bad cold and cough.
In December 2016, Timothy had a bad cough and cold, tried various home remedies and all kinds of medications, but suffered from that cough for two months. A visit to a local convenience store and recommendation from someone working there led Timothy to discover the power of local, raw honey.
“For honey to do the trick, I thought what else could it do for me?” says Timothy. From the article on vacant lots to local, raw honey significantly helping end his longstanding cough, he and his girlfriend Nicole decided they wanted to get into their own honey production and use the plethora of vacant lots in the neighborhood to get it off the ground.
Detroit Hives now has 35 beehives in 9 locations in vacant lots and near community gardens. They’ve become bee ambassadors with the Honeybee Conservancy, based out of New York. They use their apiary to educate inner-city youth about bees and have mentored over 2,000 kids so far.
“We wanted to find ways to bring community together but also wanted to attract people to this neighborhood to see something special beyond the blight they usually see,” says Timothy. And since their story went viral, including a short documentary by Spruce Tone Films, Timothy and Nicole have inspired many other people of color to take on similar missions, not only locally but nationally and internationally (in Kenya and Ghana) as well.
“A lot of times people need to see something to know that it’s possible,” says Timothy. And, “we really are having fun.”
He and Nicole incorporate everything from their backgrounds into their beekeeping – advertising, photography, fraternity and sorority acknowledgment. “We embody everything we love and do in beekeeping,” says Timothy. And what they’re doing shows the community that science is involved, but so is art and creativity. They’re showing folks that this “doesn’t have to be done with a researcher with 300 years of experience.”
Education is a pivotal component of what Detroit Hives provides and they also work with local universities, including educational research with University of Detroit Mercy, and they’re working to help shape policy as well.
Figure 2.11.2 Timothy Jackson (center), Detroit Hives
“We don’t always have the opportunity to interact with nature in these urban environments,” says Timothy, but Detroit Hives is helping make that interaction more possible and more diverse in a state like Michigan which “is not the most diverse state for people of color in beekeeping.”
Timothy stressed the importance of supporting community gardens to help provide food security for the community.
Detroit has vacant lots in the thousands – blight and eyesores is what most people see, says Timothy, but turning these lots into bee farms is helping boost native bee populations and other pollinators. A boon to much of this unattended land is that it’s chemical pesticide-free and some areas abound with a “variety and diversity of native plants, including clover, dandelion, and chicory.”
These lots that many would pass by without a second glance – “the areas people are overlooking and looking down upon are our goldmine,” says Timothy. Honey bees are a conduit to speaking on larger issues, including “breaking race barriers,” he says. Honey bees are “the gateway drug to learning about other bugs, other people and gaining an appreciation for all living things.”
Media Attributions
• Timothy Jackson and Nicole Lindsey © Timothy Jackson is licensed under a All Rights Reserved license
• Timothy Jackson teaching about bees to young schoolchildren © Timothy Jackson is licensed under a All Rights Reserved license | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.12%3A_Timothy_Jackson-_Finding_the_Light_not_Blight-_Turning_Vacant_Lots_into_Bee_Farms.txt |
Figure 2.12.1 Eliese Watson, ABC Bees
Eliese Watson of ABC Bees in Alberta, Canada was 18 and working at a local gas station when a “tiny ancient old man came in” who turned out to be a beekeeper and offered her his bees. She turned him down at the time, but four years later, at a friend’s house, she met a rural beekeeper who had acquired the bees of this same old man after he died and this time she couldn’t refuse.
“From the first day I was beekeeping in those hives, I was stung and I was stuck on bees. And I never looked back,” says Eliese. That was in 2008.
Eliese offers mentorship programs in beekeeping free of charge, the only model like that in her area. Participants apply and are required to come once every two weeks for six hours and work the yard with Eliese. In her program, they learn how to make splits, how to raise queens naturally through the Miller method and grafting, and run two queen colonies. Eliese also teaches intermediate and advanced beekeeping that applies to treatment-free management and how to identify certain traits that are adaptable to illness in an apiary.
ABC Bees runs programs through charities and nonprofits and puts their hives in public places, including the largest urban farm in Canada called Grove Calgreen. ABC Bees has been on the farm since they opened in 2005. The farm runs a lot of kids camps and field days for the public so the community gets to engage with the bees there. ABC Bees also does a lot of outreach to children and people with disabilities and to people with intermediate and advanced skills in beekeeping looking to raise their own queens. The landscape of the beekeeping audience is also becoming more diverse than it once was, with a lot of refugees coming into Canada, especially from Syria. The climate in Northern Syria and Canada is similar and a lot of refugees are coming from an agrarian background. “You don’t have to speak English to understand how bees work,” says Eliese. “The bees there and the bees here are the same. You can beekeep anywhere, even with a language barrier.”
Alberta is the fifth largest honey producing region in the world, with an average yield per colony from 120-1260 pounds surplus. When Eliese first looked into beekeeping, there were less than 200 beekeepers in the whole province; the average beekeeper was over 50 and had over 16 years of experience, which meant there weren’t many resources or education around.
Starting from a grant, Eliese launched a project to bring in an educator to teach a beekeeping course for “true beginner beekeepers” in 2010 and the project was “explosive.” The workshop was so successful, that they continued to offer it and from there ABC Bees grew as the educational business it is today. ABC Bees’ focus on advocacy for legislation and municipal regulation of beekeeping came out of public demand.
Offering programming for beginners to the advanced, Eliese has focused on how to make sure the learning environment is as inclusive and exploratory as possible; a “space where everyone can feel comfortable and welcomed to say, ‘I don’t know, let’s find out.’” Eliese has found that at the commercial level of beekeeping, there’s a tension between each beekeeper thinking their way is the only right way and that any type of conversation is by default an argument. And on the research level, she’s found a polarity between researchers and scientists and beekeepers who work with bees every day. It’s a crazy world sometimes, “which is so funny”; a beekeeper could have a best friend who is also a beekeeper but “will manage things totally different,” says Eliese, “and they will openly argue and neither one of them will budge.”
The introduction of ABC Bees in Alberta “revolutionized beekeeping in this province,” says Eliese, “from being an elitist large-scale commercial operation where the only people who can keep bees are the people who come from a history or past who know the whole legacy of beekeeping, to now transitioning into hobby beekeepers or even people who are getting into beekeeping commercially, like myself.” Eliese has noticed a dramatic change in the industry with more beekeepers now than in 1986. There’s also the reality that bees and equipment are not allowed for import into Canada and so over 90% of beekeepers in Alberta have under nine hives.
Eliese sees an interesting contrast between beekeeping in larger densely populated places versus rural places and sometimes an ideology resemblant of a “God complex” in many urban beekeeping situations. She warns against keeping the dialogue to only focus on bees as a political statement and not include a balanced conversation about the actual health of the bees. For example, if you’re keeping bees and living in an environment where the natural landscape provides scarce food for bees, how are you keeping them healthy? How are you ensuring that just because you want to raise bees, you are also being responsible for taking care of them?
As a treatment-free beekeeper, it can be a challenge on either side of the coin, urban vs. rural, because in many rural settings where people come from a strong agrarian background, they may have a stronger affinity to agro chemical applications, says Eliese. “I breed treatment free stock” and because so many are used to chemical management, “I am a heretic in my own backyard.”
Figure 2.12.2 ABC Bees
While Eliese has not used chemical treatment in her bee management, she is not dogmatic in telling everyone to go treatment-free because “if a person is going to treat, I want to make sure they have as many resources as possible to do it as safely for themselves and the bees,” says Eliese. More important than preaching only chemical-free treatment, Eliese believes beekeepers should be making critical decisions based off the facts of their unique situations and “being accountable for the decisions you make in your operation.”
Most of Eliese’s public outreach encourages different communities to start their own bee clubs. “I really encourage a self-sufficiency model of leadership, and organic evolution of whatever their club desires,” says Eliese. “Kind of like a swarm, you give them all the resources they need to be viable but it’s up to them to actually drive.”
And for those starting up beekeeping as a hobby, Eliese recommends joining a community of beekeepers “to kind of mimic a hive because it can be extremely overwhelming to enter a box of insects that maybe want to kill you,” says Eliese. So it’s nice to go through that experience with someone else. | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.13%3A_Eliese_Watson-_Inclusivity_and_Room_to_Grow_in_Beekeeping.txt |
Figure 2.13.1 Alwyn “Oxx” Simeina, Oxx Beekeeping
Alwyn “Oxx” Simeina grew up eating raw honey in the U.S. Virgin Islands and has been chasing the taste of a particular “batch” of comb since Hurricane Hugo hit St. Croix and downed a tree that contained a hive within it. “I never could find [the taste again] but I keep trying,” says Oxx and from there, his desire to keep bees grew.
Oxx is a self-taught beekeeper and owner of Oxx Beekeeping in Kissimmee, Florida and he is a big proponent of chemical-free beekeeping. He started his self-education by attending seminars and joining a local beekeepers club and now he provides advice to his local community, including some of his former mentors.
Oxx first started beekeeping about five years ago. He says, “I couldn’t really find any mentors that looked like me,” because everyone in the beekeeping world were mostly older white men. “When I entered my first year, that’s when I decided to just read about [beekeeping] and the science about it, and my mentors were actually women.”
Today, Oxx has about 22 hives and provides classes and seminars to his community. As time progresses, he’s seeing a shift with more people of color and women expressing interest in becoming beekeepers. Kids in the community have expressed a particular affinity for the classes and “the whole concept of people actually taking care of the bees,” says Oxx. “And the smoker…they always get excited about that, I don’t know why.”
Figure 2.13.2 Alwyn “Oxx” Simeina (left), Oxx Beekeeping
Oxx’s approach to beekeeping is to be as natural as possible, encouraging people to study “the natural ways of the bee and imitate that [because] we’re already being unnatural by putting them in a box with frames.” In his hives, Oxx foregoes any chemical treatments and instead uses essential oils like lemongrass, oregano, eucalyptus, and lemon for mite control. He is also looking into the mycelium from mushrooms to help stop the spread of viruses from Varroa mites and hive beetles.
In his classes, he explains that when companies come to spray chemicals on the grass, the bees drink the chemically-treated water and get sick. Once people understand the process of this, participants tend to try not to use chemicals and instead go for non-chemical treatments like the water with soap method. Since offering classes, he’s seen a shift in people starting to grow gardens instead of just growing grass.
A major challenge to beekeeping in this urban area is when bees move into people’s houses due to loss of habitat, which is one of the things Oxx is working on in addition to providing classes and seminars. Oxx offers a service to come take care of bees in people’s yards — bee rescues — which can be a trying task. “A lot of times bees don’t survive because they’re in a stressful situation [like] trying to extract them out of a wall.” These are highly stressful situations for the bees, which can weaken them further when infected with pests.
For the future of beekeeping, Oxx really wants to see new beekeepers get away from the treatments. “I would love to see people get away from chemicals and all these treatments, giving the bees sugar water, and be more sustainable,” says Oxx. Oxx teaches beekeepers not to take all of the honey when extracting from the comb if they can help it, take a bit for yourself and leave a little bit of honey for the bees. “Let the bees enjoy their honey,” he says. | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.14%3A_Alwyn_Oxx_Simeina-_For_the_Love_of_Raw_Honey.txt |
Figure 2.14.1 Jasmine Joy, Beelieve Hawaii
Jasmine Joy started beekeeping when she was living on the North Shore of Oahu, Hawaii. She started working at Honey Girl Organics in 2011 because her best friend was working for the company that makes organic skin care with all products from the hive – beeswax, honey, propolis, and royal jelly. That friend eventually left and Jasmine took over the managerial duties of manufacturing the skin care line. She learned how to bee-keep and remove wild hives from homes through the company as well.
A year later, in 2012, Jasmine started Beelieve Hawaii, an organization that provides educational outreach, habitat restoration and honey bee rescue on the island of Oahu. In 2015, Jasmine became a partner of Hoa Aina O Makaha, a nonprofit which she describes as “not just a farm” but a “sacred sanctuary that is right next door to an elementary school.” By becoming a member of this farm, Jasmine got her start in teaching third graders about the life cycle of a honey bee, the different bees in the hive, and how bees communicate. The name of this program is called the Pollinator Program. About 100 kids participated in the program during its first year.
“Mindfulness is what really fuels my company, my mission, and what I believe,” says Jasmine. “[In] everything that my company does, mindfulness is embraced.” And Jasmine embraces beekeeping in many aspects of her life. Jasmine’s colleague studies the endangered Hawaii yellow-faced bee, Hylaeus, a species found only in Hawaii, and with him, she started a nonprofit called Bee Collective. Between Beelieve Hawaii and Bee Collective, Jasmine gets to work with children, young adults, and older adults on a regular basis.
Jasmine advises new beekeepers to find a mentor they respect who share the same values and energy. For those on an intermediate level, she advises seeking out a good place for an apiary and having two or more hives “which allows you to experience how each colony has a different personality and works as a superorganism,” says Jasmine.
For her own business, Jasmine is a treatment-free beekeeper. Below most of her hives, she keeps an “oil bottom board,” which is a tray you can pull out and pour mineral oil into. Above that is a sheet of mesh separating the bottom board from the hive box with holes only small enough that the African Small Hive Beetles can fall through. Another method of pest management Jasmine uses for mite control is organic powdered sugar. While she says it’s likely that every hive in Oahu has mites, responsible beekeepers should take care of their bees as best they can, “giving them the best environment that you can provide for them,” she says.
Figure 2.14.2 Jasmine Joy, Beelieve Hawaii
“I let my bees do their thing,” says Jasmine. “I have a real spiritual connection with them and I’m more of that kind of beekeeper – very intuitive.” If she observes a colony not doing well – that is not bringing in any nectar, not making comb for the queen to lay, Jasmine will concoct a “bee tea” for them with herbs, vitamins, and sugar water.
Beekeeping in Hawaii is unique because, as a tropical climate, there really is no “off season.” However, climate change is evident here as it is anywhere else. Typically, half of the year is hot and dry on Oahu, and the other half is cooler, wetter weather but Jasmine has seen the typical second swarm that ends in mid to late summer go all the way through to October. “My phone was ringing for wild swarms past the season, and other bee removalists are seeing this as well.”
In addition to climate change, Jasmine notes that beekeeping can get rather territorial. “The ways of the old patriarchy…of wanting to segregate from everybody and work alone…is falling apart.” On the one hand, she understands this from the perspective that beekeeping for her is “a very intimate time. It’s like my church.” But on the other hand, she acknowledges that “it’s important that [beekeepers] come together and teach each other different ways because we can all become better.” | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.15%3A_Jasmine_Joy-_The_Mindfulness_of_Beekeeping.txt |
Figure 2.15.1 Kirk Webster (second from left, standing)
When Kirk Webster finished high school in Vermont, he got into a toboggan accident that winter and while he was “moping around,” as he says, someone gave him “this little book about bees and beekeeping.” That spring he went back to the Mountain School in Vershire, Vermont and then to visit family in New Jersey where he met Myron Surmach, a beekeeper with about 30 hives at his house. And that’s how Kirk’s interest in beekeeping really sparked.
“I worked right here near where I live now with the Champlain Valley Apiaries,” says Kirk. “And I worked in Canada and Ontario for a beekeeper there, but then I was injured in that accident and my back was hurt pretty badly and I couldn’t do the heavy lifting of beekeeping.”
He took a little break and then ended up going to school on the West Coast and three years later, when he recovered and could do physical work again, he moved back to the East Coast and ended up in Concord, Massachusetts, where he started the apiary he has now. That was in the early ‘80s. Here he happened upon a few neglected beehives and volunteered to take care of them and the bees did really well, which rekindled his interest. Kirk’s beekeeping business started in Massachusetts and stayed there for four years, until he moved back up to Vermont.
Since Kirk became a full-time beekeeper, he’s operated under the landscape of the Varroa mite problem. His response to the crisis was different than most. Before becoming a beekeeper, he had a lot of exposure to organic farming and by “sheer serendipity” he met some of the “very first pioneers of the organic farming movement in North America who in turn had been inspired by the pioneers of organic farming in England.” In one way or another, Kirk tried to apply those sample principles to his beekeeping.
Kirk remembers a time when the American beekeeping community “used to be the one part of the agricultural community that was uniformly opposed to the pesticides and agricultural chemicals.” And then what felt to him “just like overnight, the beekeeping community became dependent on pesticides [because of the whole varroa mite problem].”
While Kirk’s methods seemed unconventional to some at first, he says he’s always tried to share any progress he’s made with the greater beekeeping community and the public, mostly through his writing. An unexpected side to the introduction of the varroa mite problem is that there are “grants out there in the millions” for honey bee research because “people realize the threat to our food supply,” says Kirk. “They really do care about the bees and being better,” but it’s a tough situation to be in because the agricultural science community is “really oriented around industrial agriculture and largely funded by it.” And often without any “huge interpretation by science,” any advice offered outside of the “official people who are paid to solve these problems…doesn’t look very good for them when people living in a barn somewhere in New England figure out a good solution.”
Much like Jasmine Joy, Kirk emphasizes the importance of focusing on the health of the bees. Kirk sees the “real existential threats to beekeeping [as] the poisoning of the environment and the loss of habitat for honey bees.” Looking at this broader picture, it “doesn’t matter how successful people are breeding bees that can coexist with varroa mites if the environment bees are living in [is] becoming more and more poisonous to them.”
Kirk has always gone the treatment-free method with his bees and he encourages new beekeepers to do the same, if they can. In addition to knowledge sharing, Kirk offers an eight-day workshop to a small group of folks to learn about the whole queen rearing cycle. Much like Jasmine, Kirk suggests new beekeepers find a good mentor and start off with more than one colony, especially because “almost nobody succeeds in keeping all their colonies alive every year.”
“Irrespective of what kind of stock you might have, just learning the basic process…the opportunities and possibilities from making your own new colonies…[goes a] really really long way toward…making sure you can have success,” says Kirk. He continues, “Splitting colonies and making new ones is helpful to both the parent colony and the new colonies in terms of their mite populations.” This practice enables you to take advantage of certain opportunities, like if you want to try a different stock from someone else.
Kirk recommends for any beekeeper, hobby or commercial, that producing their own replacement colonies is a crucial step. And if you end up with extra colonies you don’t need, “there’s just so many people in the Northeast who want bees and can’t get local bees,” that you could sell them or give them and “help out the community that way,” advises Kirk.
Figure 2.15.2 Kirk Webster
While Kirk goes treatment-free in his hives, he sees the frustration in the blanket advice of going treatment free for everyone especially for those beekeepers who only have one location. “Any queens that you raise will mate with other bees around you,” says Kirk and, “most of those bees are being treated…and haven’t been selected for mite resistance.” So, that’s definitely a challenge.
Kirk believes the “best thing any of us can do to help honey bees is to encourage and support organic farming any way that we can” because “the difference between organic farming and industrial agriculture is just like night and day for the bees.”
“We have to plant flowers along the road,” says Kirk and “when you start to have whole farms that are clean and healthy for the bees, that provides that much even if it’s not providing their entire foraging area.”
In general, Kirk sees a need to utilize honey bees as “indicators of the total health of an environment. So, I think we should focus more on that.” | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.16%3A_Kirk_Webster-_Looking_Organically_at_the_Broader_Landscape_of_Bee_Health.txt |
Figure 2.16.1 Michael Palmer, French Hill Apiaries
Michael Palmer’s beekeeping career started in 1974 when he took a beekeeping course and started off with just a couple hives from Bedford, Quebec, Canada. In 1979/1980, he bought a hundred hives from Better Bee and bought nucleus colonies (nucs) from a friend because back then, prices were pretty low. By 1982, he bought another hundred hives and was up to 200. During this period, he was working the fall, winter, and spring in the sugar woods and when he was done with that, he went to work in an orchard in New York state where they had 500 hives, which then put him at over 700 hives. Michael worked for them for four years and then bought their bees.
By 1992/1993 a few years after tracheal and Varroa mites became a huge problem, Michael lost a lot of his bees. In 1998, he went to visit Kirk Webster in Vermont and “that’s where the real change [was] for me,” says Michael, “to be able to raise my own [queens].” Michael says when you’re trying to run a commercial operation, you can’t spend all your money on something you can make, so his visit to Kirk Webster’s operation got him started on raising his own queens. From then on, he saw the quality increase.
Michael’s current setup includes a mating yard in the middle of about five to six of his apiaries where he gets his drones and where he tries to put good stock. Michael does not buy queens. “If I buy a queen or trade with someone, it’s for breeding purposes, not for production queens,” says Michael.
Since becoming a beekeeper, Michael has shared his nuc and queen rearing project information with everyone, largely through YouTube videos. He’s really pleased at how many people are now wintering nucleus colonies. He also feels fortunate in how much he gets to travel. “We go all over the world doing talks on bees and wintering nucs and raising queens,” says Michael. “Two weeks in New Zealand, three weeks in England…it’s pretty amazing [to] meet all the beekeepers and see what they do and their differences.”
Much like Brian and Jasmine, Michael has seen how beekeeping has “pulled [many a person] up out of the hole they were in [giving] them something to focus on.” He says beekeeping is “one of the best forms of meditation that you can have…the movement and the buzzing and everything else in the world disappears.” He continues, “It’s also like communion, both meditation and communion. It’s incredible.”
To new beekeepers, Michael suggests joining a bee club, getting a mentor, and keeping good records. “After that, it’s still a lot of experimenting and [hands on] learning” says Michael, which is why he emphasizes getting a good mentor.
Despite some beekeepers’ belief that feeding bees sugar is not healthy, Michael will tell anyone that “you can’t be afraid to feed sugar if they are starving.” And he also believes that as far as varroa mites go, it’s wonderful if some folks are not using treatments for mite control but that we must not “forget we are in a community here and when your colony crashes from varroa mites, it spreads varroa mites all over the neighborhood.”
Michael’s approach to beekeeping also differs from some of the other folks we’ve heard from in the sense that he says, “You can’t just walk away from your bees. It takes work. It takes investigation, it takes looking at them” on a least a regular basis of once a month or more. Michael is also skeptical of anyone trying to run a commercial operation and going completely treatment free and potentially losing 50-75% of their bees each year.
A major challenge nowadays is that “everyone wants to have bees,” says Michael, and a major concern he has with new beekeepers is when they are unaware of the potentially harmful and unresearched activity they can get into. For instance in buying used equipment, new beekeepers might not know what American Foulbrood disease is, and so they buy “old equipment out of a barn putting it out there, putting bees in it, [and] the colony dies of American Foulbrood.”
He thinks eventually we’ll find a healthy solution for widespread mite reduction. “Over time we are developing traits that are going to help,” says Michael. “So that’s the hope.” | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/02%3A_Interviews_From_the_Field/2.17%3A_Michael_Palmer-_Queen_Rearing_and_Other_Advice_for_New_Beekeepers.txt |
These practical tools are meant to support your beekeeping journey, and empower you to find, adapt or create the tools that work best for your practice. I use these tools in my own teaching and want you to have access to them too. Use these tools as you see fit, adapt them for your needs or use them to co-create new tools with your collaborators. Beekeeping is a practice best done in community so we can share ideas, resources and skills. Like all practices, we improve when we engage with the practice. We improve when we engage mindfully, plan our actions, reflect on what worked and try new strategies based on our learning. These tools invite you to do just that.
Thumbnail: www.pexels.com/photo/person-holding-fresh-honeycomb-2260933/
03: Tools and Resources for New Beekeepers
Download and print the Hive Inspection Sheet as a PDF. This worksheet was adapted from the work of Erin MacGregorForbes and Northeast Sustainable Agriculture Research and Education (NESARE).
Figure 3.1.1 Hive Inspection Sheet form page 1
Figure 3.1.2 Hive inspection sheet form page 2
3.02: Hive Management Journal
Download and print the Hive Management Journal as a PDF.
Figure 3.2.1 Hive Management Journal Page 1
Figure 3.2.2 Hive Management Journal Page 2
Figure 3.2.3 Hive Management Journal Page 3
Figure 3.2.4 Hive Management Journal Page 4
3.03: Apiary Action Plan
Download and print the Apiary Action Plan as a PDF.
Download and print the Apiary Action Plan Steps as a PDF.
Apiary Action Plan Guide created by Ang Röell, They Keep Bees, Winter 2020
Figure 3.3.1 Ang Roell holding beehive frame
In this activity, you will apply all you’ve learned in the field about biology, management and practice to create an Apiary Action Plan.
In this plan, you’ll consider and articulate details about your goals as an Apiculturist (beekeeper), set goals for your apiary, identify cost, think about siting new and mating yards, and make a decision about management / practice.
You will use the model to create an apiary expansion plan for how you will systemize your current apiary and expand upon the practices within it. This will include adding a queen rearing system or increase management plan, creating a calendar and record keeping system, and adapting a new management strategy or changing systems that are not working for you currently.
Figure 3.3.2 Dandelions
Step 1: Set A Holistic Goal for your Apiary
What is a holistic goal? (Source: Purple Pitch Fork)
The term “holistic goal” comes from a school of thought called Holistic Management. It is a three-part goal describing the quality of life desired, the forms of production to get there, and the future resource base that the forms of production depend on. Whether or not you practice Holistic Management, a written goal can be a powerful instrument for building understanding and cooperation in an apiary.
The power of Holistic Management process lies in the goal. Work that fulfills the commitment we have to ourselves, our families, our environment and our communities can only succeed in the context of a journey toward a holistic goal.
The holistic goal is a living document. In the journey of our lives, without knowing where we are going, we cannot know how to begin. A goal provides us with the knowledge we need to move with confidence, because with a goal: We know the direction to go (plan); We have a way to measure our progress (monitor); We can correct our course when things go wrong (control); We can get back on course when big things go wrong (replan). A goal doesn’t have to be beautiful. You don’t have to type it on the computer with four different fonts, bolded and italicized. The sentences don’t have to be complete. The motives don’t have to be lofty. The only requirement is that it works. The most challenging aspect of formulating a written holistic goal is actually doing it. The process has none of the instant gratification of chopping wood, extracting honey, or pulling weeds, (or even the gratification of financial or biological planning) but it guides and informs our decisions about how, when, and whether to do each of these tasks.
Figure 3.3.3 Goal Setting Framework slide
Your Holistic Goal Answers These Questions:
1. What do you want?
2. How will you get there?
3. What “being state” do you wish to bring to the project? What energy do you wish to bring to the work?
4. What are the needs of the project? What are the yields of your project?
5. How do they impact your close friends, family or collective, community, world?
6. Who/what are your allies/resources?
7. What knowledge do you bring?
8. What knowledge do you need? How will you acquire it?
9. What are your predators or impediments?
10. What relationship do you want with your bees? What impacts will your choices have on the bees, the greater ecology?
Figure 3.3.4 Apiary
Step 2: Creating a Plan to Start or Expand an Apiary
1. What do you need to expand an apiary? Make a list of all of the items you’ll need. What is your start-up cost?
OR What is your expansion cost?
2. Make a list of the items you need for: protective equipment, hive manipulation equipment and pieces of the hive. Outline the costs. How will you purchase these? Through which suppliers?
3. How many colonies will you start with or expand to? Why?
4. Discuss the pros and cons of 2 ways you could obtain bees to expand a beekeeping hobby or operation.
5. What size brood and honey super boxes would you use for expansion?
6. Will you customize any equipment? Which parts? How?
7. What would be advantages of customizing some of the requisite pieces of equipment?
Figure 3.3.5 Apiary
Step 3: Site the Apiary
1. Where will you establish your apiary or new yards?
2. Select a location in your area on which you’d like to site honey bees. Describe the best features of the site.
What might you do to overcome the most negative aspects of the site?
3. What infrastructure do you need in place to keep bees at this location?
4. What considerations of neighbors might take precedence over beekeeper’s point of view?
5. How will you approach neighbors and institutions to discuss apiary location?
6. How will you come to an agreement with neighbors about your practice (beekeeping) and their pesticide applications? How will you address fears/anxiety about having an apiary sited nearby?
Figure 3.3.6 Standing among beehives
Step 4: Managing the Apiary
1. Outline 1 season of management from April-November below. What tasks do you need to complete each month? Week?
2. How will you implement each step month-to-month?
3. When will you inspect?
4. What will you look for in Spring, Summer, Fall, Winter?
5. What is your treatment and/or manipulation plan? Why?
6. How did you decide upon this plan? Cite a minimum of 5 resources that informed this decision.
7. Where will you purchase your stock? How? Why?
8. How will you keep records? Count mites? When? What will inform your treatment decisions? Cite 2 resources for determining what threshold of mites should be present to determine treatment. | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/03%3A_Tools_and_Resources_for_New_Beekeepers/3.01%3A_Hive_Inspection_Sheet.txt |
First, ensure that the bees have enough honey stores to get through the winter, generally considered to be 60-90 lbs of capped honey (one deep or two mediums of wall-to-wall capped honey) in this area for a typical sized colony in standard Langstroth equipment; if your hives are still light in mid-September, feed them with 2:1 syrup (up until mid-October) to get them up to that weight. Mouse guards need to go on by early September.
Wrapping hives with black tar paper can help, but is not absolutely necessary (it’s also not a detriment); as someone said, it provides solar gain in the early spring, but has negligible insulation value. A wind break can also help, but is not necessary; a friend of mine uses sections of stockade fence that he bought at Home Depot; my hives are on the south side of a stand of red cedar trees, which provide a natural wind break.
Ventilation is key if you are using standard Langstroth equipment. It doesn’t have to be a lot – the standard notch in an inner cover is enough, even with a solid bottom board and a small lower entrance. Top insulation is critical, between the inner cover and the outer cover; otherwise the moisture in the air in the hive will condense inside the top, drip down on the bees and kill them; the ideal insulation is rigid foam insulation (1″ or 2″ thick) cut to the size of an inner cover; Homasote does not do the job. I alternatively use quilt boards, but they are a bit more complicated. The foam insulation and the notched inner cover accomplish; Michael Palmer, a highly respected commercial beekeeper in northern Vermont, demonstrates this set-up on YouTube in Keeping Bees in Frozen North America starting at about 54:40, though the entire presentation is worth watching.
Finally, I don’t want to reignite the debate about Varroa, but for anyone who might care, if you focus on the above steps and your colonies either abscond by late fall or don’t make it through the winter, you almost certainly will have lost them due to varroa and the viruses they vector. Randy Oliver describes this issue in Understanding Colony Buildup And Decline: Part 1 – Varroa and Late Season Collapse, which was published in the American Bee Journal. Monitor mites using an alcohol wash and consider your treatment options if the count is more than 3% at this time of year.
3.05: End of Year Beekeeping Evaluation
What Worked
This is the easiest and most fun question – what worked? Knowing what went well will help you to decide what to do next year. What went well or better than expected?
• Did a certain hive outperform the others?
• Did one yard produce more honey than the others?
• Did your colonies survive over winter?
• Was a particular Queen especially productive?
• Did you successfully split your hive(s)?
• Did you sell more honey at one market than another?
What Didn’t
Looking at our failures is never fun, but it helps us learn and grow. What did you do that didn’t go as well as planned?
• Did you use a certain feeder that leaked or ran out too fast?
• Did you not feed a colony that needed it?
• Did you pull honey too soon or too late?
• Did you wait too long for swarm management?
• Did you lose or kill a Queen?
• Did a hive get robbed out?
• Did you experience disease or pests?
• Did you keep a record or log?
This, of course, is not a full list of questions, just a few to help get you on the right track.
What Do I Want To Do Next Season?
What is something that you’d like to try next year?
• Did you read about a new technique you’d like to try?
• Do you want to experiment with a new hive style?
• Do you want to try new equipment?
• Do you want to dabble in Queen rearing?
• Do you want to collect swarms or cut-outs next spring?
• Do you want to sell Nucs or hives next year?
• Do you want to expand to new bee yards?
• Have you signed up for free insurance through the USDA?
3.06: The Beekeeper's Year
The Beekeeper’s Year: A Google Calendar – integrate into your existing Google calendar
Click on the image below for link to the PowerPoint version.
Figure 3.6.1 Beekeeper’s Year Field Guide cover. | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/03%3A_Tools_and_Resources_for_New_Beekeepers/3.04%3A_Wintering_Honey_Bees.txt |
Adapted from Boston Beekeepers Club/Beekeepers of Suffolk County & The Benevolent Bee Created for Organic Bee School 2014 (with some additions)
Free Online Manuals:
Beekeeping Basics: various resources available, some free, some with associated cost on this online catalogue
A Practical Manual of Beekeeping : UK; focuses on IPM; has section on going organic (p.264); written in a very accessible, personable way, yet also academic in content
Beyond Langstroth – Online Resources for Top Bar, Warre, Observation Hives:
Top Bar Hives:
Observation Hives:
Warre Hives:
Beekeeping Books:
Guides to Beekeeping:
The Idiot’s Guide to Beekeeping Dean Stiglitz & Ramona Herboldsheimer (2010)
Natural Beekeeping: Organic Approaches to Modern Apiculture Ross Conrad (2007)
The Practical Beekeeper: Beekeeping Naturally Michael Bush (2011): much of this material is available for free on his website
The Barefoot Beekeeper Phil Chandler: guide to Top Bar Hive construction and management (see website for lots more from Chandler)
The Thinking Beekeeper: A Guide to Natural Beekeeping in Top Bar Hives (2013) Christy Hemenway
Keeping Bees with a Smile: A Vision and Practice of Natural Apiculture (2013) Fedor Lazutin (Warre hive info)
The Beefriendly Beekeeper: A Sustainable Approach (2011) David Heaf (good resource for Warre hive tenders)
Observation Hives: How to Set Up, Maintain and Use a Window to the World of Honey Bees (1999) Thomas Webster & Dewey Caron
Traditional Focus:
Beekeeping Basics MAAREC (course book, purchase a PDF here )
The Beekeeper’s Handbook (a good go-to manual for pretty much anything, now in 4th ed.)
The Backyard Beekeeper: An Absolute Beginner’s Guide to Keeping Bees in Your Yard or Garden Kim Flottum (2010 revised edition): focus on all medium hive bodies
The ABC and XYZ of Bee Culture: An Encyclopedia of Beekeeping A. I. Root Company (look for old versions for more natural management)
Hive Management: A Seasonal Guide for Beekeepers Richard Bonney
Beekeeping: A Practical Guide Richard Bonney
New Complete Guide to Beekeeping Roger Morse
The Beekeeper’s Bible Richard Jones and Sharon Sweeney-Lynch
Beekeeping for Dummies Howland Blackston
Books That Take a Closer Look at Bees and Beekeeping:
Science/Behavior:
Honeybee Democracy Thomas Seeley (Cornell expert on swarming behavior) 2010
The Buzz About Bees: Biology of a Superorganism (information on bees biology, communication & more)
The Wisdom of the Hive: The Social Physiology of Honey Bee Colonies Thomas Seeley (1995)
Historical Science/Behavior:
The Dancing Bees: An Account of the Life and Senses of the Honey Bee Karl von Frisch (1953) – written by the first person to interpret the meaning of the waggle dance
Langstroth’s Hive and the Honey Bee: The Classic Beekeeper’s Manual L.L. Langstroth (1878) – written by the inventor of the Langstroth hive; more of a chapter book than a go-to manual
Art/Creative Portrayal of Factual Info:
The Pollinator’s Corridor Aaron Birk – graphic novel on restorative ecology
Other Books:
The Queen Must Die and Other Affairs of Bees and Men William Longgood – an ethnography of the beehive
Robbing the Bees: A Biography of Honey The Sweet Liquid Gold That Seduced the World Holley Bishop (2005)
Beeconomy: What Women and Bees Can Teach Us About Local Trade and the Global Market Tammy Horn (2011)
The Beekeepers’ Lament: How One Man and Half a Billion Honey Bees Help Feed America Hannah Nordhaus (2011)
Life of the Honeybee Heiderose & Andreas Fischer-Nagel – closeup photos, good for kids or educating
Journals:
Bee Culture published by A.I. Root Co.
American Bee Journal by Dadant Co. | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/03%3A_Tools_and_Resources_for_New_Beekeepers/3.07%3A_Resource_List.txt |
This resource was created by Morris Ostrofsky. I’ve included it here as a resource for people who want to explore queen rearing. Resources like this one, and the encouragement of “friend-tors” like Sam Comfort helped me take the plunge into rearing my own queens. Raising queens helped me develop a deeper understanding of the hive, and helped me shape my own beekeeping practice. Like anything on our learning edge, learning how to raise queens may make you question your skills, knowledge and understanding, but it will ultimately help you develop a deeper understanding of the hive’s rhythms.
The Graft-Free Queen Rearing document is also available for download as a PDF.
Figure 3.8.1 Honeybees
Many beekeepers reach a point in their beekeeping experience where they are comfortable with the basics and are seeking a new challenge. In an environment in which beekeepers have to deal with varroa and diseases and are dissatisfied with commercial queens there are reasons to raise your own queens. However, for many beekeepers the idea of grafting and producing their own queens is intimidating. The purpose of this paper is to offer four simple methods of queen rearing that do not require grafting. I will explain how a few high quality queens can be raised without special equipment or tools by a beekeeper with just a few years of beekeeping experience.
To quote Dr. C.L. Farrar, USDA Honey Bee Research Lab Leader, Madison, Wisconsin, “Below average queens living in a great environment will out perform a great queen living in a poor environment every time.” It is possible to create a great queen if they are well fed and raised in a bountiful environment.
In the last few years a common complaint I hear is the poor quality of queens that are available e.g., poorly mated. Another frequent complaint is the lack of acceptance. Not only is the acceptance track record poor but even when the queens are accepted, too many are superceded. The queens you purchased from half way across the country often do not perform as advertised in your own back yard. Locally produced queens are well adapted to your environment. To quote Kim Fottum, editor of Bee Culture magazine, “As Mark Twain might have said, ‘The difference between queens you buy and queens you raise yourself is almost always the difference between light and lightening.’”
Before describing various methods of graft free queen rearing, I would like to discuss some of the benefits of raising your own queens. One is genetics. Many beekeepers are wisely looking to genetics as a means of a long term solution to solving the problems associated with the exotic pests and diseases. When you raise your own queens, you can select for desirable traits e.g. disease resistance, hygienic behavior. Usually everyone has a favorite hive or knows a fellow beekeeper that has a hive with desirable traits. The queens in these hives are the cornerstone of improving an apiary.
Genetics is an excellent foundation. You can build on this foundation by controlling the conditions in which the queens are raised by selecting the genetic stock, using chemical free comb and ensuring that they are well fed as they develop.
Finally we all accept the fact the young queens are more productive and less likely to swarm. Having extra queens readily available means being prepared for emergencies; e.g. accidental death of the queen. Because of these reasons, many beekeepers want to take charge of the situation and raise their own queens. Most erroneously assume that grafting is the only way to accomplish this. However, this is not the case. There are multiple methods of graft-free queen rearing. Four methods are presented: Swarm cell, Nucleus, Miller and Hopkins. The reader can choose the method that best suits his/her comfort level and the number of queens desired.
Regardless of the method selected there are certain considerations that are common to all. Time of year is one. Spring and summer are the ideal times to raise queens. Food is available, the temperatures are correct for virgins to mate, and the bees’ natural inclination to propagate by producing new queens and swarming takes place. Fall is not the best time to raise new queens. There is less food available to produce a well fed queen. There are fewer nurse bees. Nor is there time for new queens to set up a hive with enough winter stores. But more importantly there are fewer drones available for mating.
Another consideration before venturing into queen rearing is preparation. Populations need to be strong; a decision needs to be made as to which will be the queen breeder (queen mother) and drone mother hives, and what additional equipment is needed. An adequate supply of protein supplements and feeding stimulants should also be on hand. A schedule should be made especially if the Hopkins or Miller methods are used.
All honey bees are not the same. As Charles Darwin correctly pointed out, “Within any population there are variations.” Case in point, look at your siblings; unless you have an identical twin, everyone is different. When selecting which hive(s) is to be used for your source of your breeder queens (AKA queen mother, queen mother hive), consider traits that are important to you. This is one of the areas where you have the most control of the quality of the new queens. There are a number of desirable traits you may wish to select for: gentleness, honey production, early build up, hygienic behavior, disease resistance, and good wintering ability. Your experience with your hive(s) will dictate which colony (colonies) you select as the queen mother hive.
Another decision you have to make is the number of queens you would like to produce. The most limiting factor in any queen rearing operation is the number of available mating boxes. This is an appropriate time to define mating box/nuc for the purpose of this paper. While mating boxes vary in size from as small as 2 full depth frames to 5 full depth frames, I use a standard 5 frame full depth nuc box with a follower board. Using this configuration means no special equipment is needed whether the nuc is used as a nuc or a mating box.
Graft free queen rearing requires between one and four hives depending on the method used. Each will be discussed separately with the corresponding method. At least one mating box/nuc is needed for every queen produced. Early on it will be necessary to decide the number of desired queens and prepare the appropriate number of mating box/nucs.
Overcrowding and better fed queen cells go hand in hand. Ideally the hives you raise queen cells in (cell builder hives) should be overcrowded with lots of young nurse bees. In fact the colony must be on the verge of swarming. To quote Sue Cobey (researcher at UC Davis), “Overcrowding is the secret of success.” The objective is numerous and well fed larvae. Feeding is the way to accomplish this objective. The quantity and quality of feeding greatly influences the quality of queens. This is one important way you can produce higher quality queens than those mass produced. “This is an important concept and must not be overlooked.” (Sue Cobey at OSBA 2012 conference) According to Sue Cobey well fed developing queens produce more eggs. Feeding the bees a pollen supplement is added insurance that the growing queens will have an adequate amount of protein. Use your favorite pollen supplement. Since you want a population that is booming, start feeding the potential cell builder hives about 2 months before you start raising queen cells.
A large drone population is needed in the cell builder hive(s) in addition to a large worker population. Drones do much more than serve as fodder for bee humor. They are an important, yet overlooked, part of the mating equation. It takes about 12 to 15 drones to mate with a virgin queen. Think of them as flying gametes.
To build and maintain the population of drone mother hives start feeding them a 1:1 sugar syrup solution with a feeding stimulant at least one month before starting to raise queen cells. Feeding needs to continue until the new queen has been mated. If the bees perceive a slow down in nectar flow; e.g. the feeding, they will stop drone production and also start removing developing drones from the hive. Drone production needs to continue right up to the time the queen is mated.
An additional method to increase the number of drones is the use of green plastic drone comb frames. The embossed cells are drone-sized; larger than the worker brood size. When the queen feels the larger sized cells, she lays an unfertilized egg which becomes a drone. When inserting these frames place them on the edge of the brood area between the pollen frame and the outer most brood frame at approximately the three or eight positions.
In most cases, two drone producing hives will be necessary for every hive that is producing queen cells. If there are other hives within a quarter to a half mile of your apiary, extra drone hives are not necessary. The exception to this is if you’re trying to improve genetics. In this case the best hives for producing drones (drone mothers), will be your own. The drone mother hives should be placed a half mile away from the mating boxes/nucs. The reason for moving your own drone mother hives away from your apiary is to avoid inbreeding between virgin queens and their brothers. Additionally you increase the likelihood of matings with selected drone stock. This is because the drones normally form their congregation areas closer to “home” than a half mile. The virgin queens typically fly further away from the home apiary and have a better chance to mate with the desired drones.
The Queen Development chart that follows illustrates the biological sequence of a queen’s development and mating and explains the “why” and “when” specific manipulations are performed. For example if you were to wait until day 17 to separate the queen cells in a cell builder, you would end up with a single queen. This is because on day 16 the first queen to emerge would dispatch all of her sisters. The beekeeper must be aware of the queen’s development sequence to successfully raise queens. The chart helps to visualize the process and is referenced as the methods are described.
Figure 3.8.2 Morris Ostrofsky’s queen development chart
Before any queen rearing project can be started, production activities have to be coordinated with seasonal and personal calendars. Seasonal conditions set the pace for raising queens. When the average temperature reaches 69 degrees F, the queen is able to go on her mating flight(s). For example in the southern Willamette Valley, the average temperature is 70 degrees F on June 1st. This is one degree warmer than the absolute minimum required for a virgin queen to mate. I use June 1st as the focal point for activities I schedule before and after this date. The timing of the mating flight(s) is critical and thus set the pace for the rest of the calendar. Because beekeeping is local, the date the temperature reaches 69 degrees F will vary as will specific calendars.
While most scheduling is flexible, some manipulations are less so. For example once 24-36 hour larvae are placed into the cell builder, the scheduling becomes more rigid. This is the point to make sure your personal schedule does not conflict with queen rearing activities. The Miller method, described later, will include an example of how useful a calendar is in organizing the sequence of steps for this or any other method.
Now that preparation common to all methods has been described, it is time to look at the specifics of the four methods of non-graft queen rearing. While raising queens is the objective, each uses a different approach. Although several of the steps are common to all, each will be presented as a stand alone process. Review each method and decide which is compatible with your goals and confidence level.
Swarm cell method: Ten to 15 quality queens can be produced from swarm cells. While a swarm cell situation can be created by stimulating a hive, the focus here is the situation where you did not plan for swarm (queen) cells but discover them during a hive inspection. You see that the workers have already built numerous, capped queen cells.
The Queen Development chart shows that the capped cells you are seeing are at least 8.5 days +/- .5 day old. How do we know this? This is because queen cells are capped over at about 8.5 days +/- .5 day. The presence of capped queen cells indicates that the old queen has already left with a swarm which usually leaves within a day before or after capping. Reduced population is also a clue. This can be confirmed by observing a reduced worker population in the hive and the fact that no eggs or very young brood are present.
Figure 3.8.3 Worker honey bees on comb
Although you did not actively work to produce these cells, many of the parameters for producing quality queens are present in this situation. The swarm cells have been produced in a hive that has survived winter, is prospering, and has a population that is healthy and vigorous enough to outgrow their home. These cells are well fed and made in a queen right hive.
Now that you have swarm cells, you have to decide how you want to proceed. You can re-queen the hive, make divisions (nucs) or produce mated queens in mating boxes. If you decide that you have enough hives and simply want to re-queen the mother hive, simply cut out all but one or two queen cells. Let the bees raise their own new queen.
To increase hive numbers you will use the queen cells to set up mating boxes/nucs. The goal is two queen cells per division. Sometimes a queen cell is empty and using two cells increases the likelihood of success.
The number of divisions or mating boxes will be largely dependent on the strength of the hive and the number of available queen cells. In an ideal situation you will find a few brood frames with a couple queen cells each. The frames could be used as is. But more often the queen cells are clustered with many on a single frame. In this case, the cells will have to be removed and distributed to maintain two queen cells per mating box/nuc.
Step 1: Decide how many queens/nucs you can produce after evaluating your resources; e.g. amount of brood, workers to care for the brood, queen cells and availability of mating boxes/nucs.
Step 2: Set up the nucleus hive or mating box using the original hive as the source of materials. If the resources of the mother (original) hive do not support the number of mating boxes/ nucs you choose to make, you can supplement using brood and workers from other hives.
Nucleus configuration:
• Three brood frames of capped brood with some cells that are emerging
• If the queen cells are located singly or in doubles on brood frames, simply include the brood frame with the queen cell(s)
• If the queen cells have been removed from mother hive frames, provide a space in the nucleus frames that are to receive the queen cells by cutting out a small portion of comb. The queen cells can then be placed in the space and fixed in place with a couple of tooth picks
• one frame of mostly pollen
• one frame of mostly honey
• enough workers to cover the brood and queen cells
Mating box configuration:
• one frame of mostly honey and pollen
• one brood frame with emerging brood
• 2 queen cells
• enough workers to cover the brood and queen cells
Figure 3.8.4 Honey bees on comb
Step 3: Leave one or two capped cells and at least a couple brood frames behind in the original hive. One of these remaining queen cells will become the new queen in the mother hive.
Step 4: Cut out well mottled queen cell(s) from the original hive. These cells should look roughly like the shell of a Virginia peanut. Remove some of the surrounding comb along with the queen cell to avoid damage the developing queen. The extra comb also provides a means to attach the cell to another frame. (See next photo) These cells will be used to set up the queenless mating boxes/nucs.
Figure 3.8.5 Queen cell surrounded by comb border
This photo illustrates placement of a queen cell in either a nuc or a mating box. Toothpicks were used to secure the queen cell onto the frame. Note the border of comb that surrounds the queen cell.
Step 5: If the nuc or mating box remains in the same yard as the mother hive, add an equal amount of bees to the nuc/mating box to compensate for the fact that the field bees will drift back to the original hive. Be sure the queen is not included when adding the extra bees.
Figure 3.8.5 Nuc
Step 6: Feed and reduce entrance. Before closing up the nuc, add a shim to create some space above the top bars and then add a protein patty. The nuc’s cover should have a 2 to 3 inch circular hole cut into the center. Place an inverted mason jar with 1:1 sugar syrup over the hole. The holes in the Mason jar lid should be 1/16 inch in diameter. Include a feed stimulant, such as Honey Bee Healthy, in the syrup. Cover the feeder with an empty box or bucket to protect the syrup from sunlight.
Step 7: Continue to feed the bees syrup for about two weeks. Since there are fewer field bees in the mating box/nuc than in an established hive, it is important to feed them even during a nectar flow. Use an entrance reducer to prevent robbing.
Step 8: Wait 3 weeks before opening the mating box/nuc. Since this method starts with queen cells, the waiting is less than with the nuc method. Waiting is the hardest part. But why do we wait? The primary reason is you do not want to lose the virgin queen. Looking at the Queen Development chart you can see that she has not been mated until day 20. Virgin queens are flighty and may get lost if they loft. I like to give her another 10 days to settle down and establish a brood pattern.
Step 9: Evaluate the results. You should find a laying queen with a good brood pattern. If this is the case, transfer the bees into a standard box. If you were not successful, return the frames to the original hive.
Nucleus method:
The Nucleus method produces a single queen and a new hive at the same time. Because it involves the fewest steps and can be done with a minimum of beekeeping experience, it is the easiest approach. It takes advantage of the bees’ emergency response to the lack of a queen. When the queenless nuc is set up, the bees will do the rest. Drones and the weather are important indicators that the conditions are right to raise a queen using the Nucleus method. Since drones are essential to produce even a single queen, their presence is one important indicator. When you start seeing drones on the landing board, it is time to start the Nucleus method. The weather is the second important factor. Virgin queens will not go on a mating flight if it is less than 69 degrees F. You need to be aware of when this critical temperature is likely to occur in your area.
I recommend using a five frame nuc box because it works well and is the most efficient use of brood pollen and honey. While the configuration is similar to that of the Swarm cell method nuc, there two differences between them. The most important is the use of a brood frame with eggs or 24 hour larvae. The other difference is that queen cells are not needed.
Step 1: Decide how many queens/nucs you can produce after evaluating your resources; e.g. amount of brood, workers to care for the brood, queen cells and availability of nuc boxes.
Step 2: Set up the nucleus hive using the original hive as the source of materials. If the resources of the mother (original) hive do not support the number of nucs you choose to make, you can supplement using brood and workers from other hives.
Nucleus configuration:
• One frame of mostly honey
• Two frames of emerging and capped brood
• One frame with eggs or 24 hour larvae (up to day 4 on Queen Development chart)
• one frame of mostly pollen
• enough workers to cover the brood and queen cells
Step 3: If the nuc remains in the same bee yard, brush an equal amount of bees into the nuc to compensate for the field bees drifting back to the original hive. Be sure the queen is not included when adding the extra bees.
Step 4: Feed and reduce entrance. Before closing up the nuc, add a shim to create some space above the top bars and then add a protein patty. The nuc’s cover should have a 2 to 3 inch circular hole cut into the center. Place an inverted mason jar with 1:1 sugar syrup over the hole. The holes in the Mason jar lid should be 1/16 inch in diameter. Include a feed stimulant, such as Honey Bee Healthy, in the syrup. Cover the feeder with an empty box or bucket to protect the syrup from sunlight.
Step 5: Continue to feed the bees syrup for about two weeks. Since there are fewer field bees in the nuc than in an established hive, it is important to feed them even during a nectar flow. Use an entrance reducer to prevent robbing.
Step 6: Wait at least a month before evaluating the results. Looking at queen development chart you can see that she has not been mated until day 20. Virgin queens are flighty and may get lost if they loft. I like to give her another 10 days to settle down and establish a brood pattern. You should find a laying queen with a good brood pattern. If this is the case, transfer the bees into a standard box. If you were not successful, return the frames to the original hive.
Miller Method
This method is named for Dr. C.C. Miller (1831-1920). One interesting fact is that his interest in beekeeping started after his wife, a complete novice, captured a swarm. Ultimately C. C. Miller gave up his medical practice and dedicated his life to raising queens. With the Miller method approximately nine queens can be produced. The following steps describe the Miller method to raise queens. An example of a calendar for the Miller method follows the steps.
Step 1: Decide how many queens you can produce after evaluating your resources; e.g. amount of brood, workers to care for the brood, queen cells and availability of mating boxes/nucs.
Step 2: Set up the mating boxes/nucs using the original hive as the source of materials. If the resources of the mother (original) hive do not support the number of mating boxes/nucs you choose to make, you can supplement using brood and workers from other hives.
Mating box configuration: (if raising nucs, refer to the Nucleus method for configuration)
• one frame of mostly honey and pollen
• one brood frame with capped and emerging brood
• 2 queen cells
• enough workers to cover the brood and queen cells
Figure 3.8.5 Miller frame
Step 3: Day 1: Construct and insert Miller frame
• Securely fasten four or five triangular shaped pieces of foundation to the top bar of an unwired full depth frame. The triangular shaped sections of foundation should measure approximately 3 inches wide at the top and taper to a point half way down toward the bottom bar. This is referred to as the Miller frame.
• Make sure the queen mother hive is level. The reason this is important is that bees will be building natural, unsupported comb. If the hive is not level, the comb will not be built within the frame.
• Re-arrange the frames to create a space in the center of the queen mother brood box. This is done by removing a little used frame on the outside edge of the brood box.
• Place the Miller frame in the created space.
Step 5: Day 7: (Six days after inserting the Miller frame in the queen mother hive.) Remove queen from the cell builder hive.
• The queen must be removed one day before moving the Miller frame from the queen mother hive to the cell builder hive. This queenless condition creates an emergency response and must exist if queen cells are to be raised. The bees respond to this emergency by quickly building queen cells.
• Store the queen temporarily in a small nuc. She will be returned to the cell builder hive at a later stage.
Step 6: Day 8: (The next day) Prepare the Miller frame and insert in the cell builder hive.
• Carefully remove the Miller frame while brushing off the bees. The frame must be held vertically because the unsupported comb can break and fall. The foundation will be drawn and a small amount of new comb will have been added. Young larvae and eggs should be seen at the margins of the comb. .
• Place the frame on a flat surface in an area with good lighting, high humidity and out of direct sunlight. The goal is to trim the comb back to the point of recently hatched larvae between 24- 36 hours old. (see photo) As a source of reference the larvae are close to the size of an unhatched egg as per the photo.
• Use a warm, sharp knife to trim off the lower margin of the empty comb and eggs.
Figure 3.8.6 Young larva
The yellow line in the photo below shows what the trim line might look like. Everything below it is removed.
Figure 3.8.7 Trim line of young larva cells
Figure 3.8.8 Larva cells indicating which cells to keep
• Destroy two thirds of the future queen cells left along the lower trim margin. This avoids having too many queen cells too close together. Squash two cells, keep the third, squash two and keep the third, etc.
Figure 3.8.9 Enlarged cells
• Enlarge the remaining cells containing the larvae by pushing the lower cell wall downward into a vertical position This simulates a queen cup and encourages the bees to build queen cells there.
• Transfer the prepared Miller frame into the center of the brood area in the now queenless cell builder hive.
Step 7: Feed and reduce entrance.
Before closing up the nuc, add a shim to create some space above the top bars and then add a protein patty. The nuc’s cover should have a 2 to 3 inch circular hole cut into the center. Place an inverted mason jar with 1:1 sugar syrup over the hole. The holes in the Mason jar lid should be 1/16 inch in diameter. Include a feed stimulant, such as Honey Bee Healthy, in the syrup. Cover the feeder with an empty box or bucket to protect the syrup from sunlight.
Figure 3.8.10 Queen cells on miller frame
Step 8: Day 18: (Ten days later) Prepare queen cells for mating boxes/nucs.
Remove queen cells from the Miller frame. These cells should look roughly like the shell of a Virginia peanut. Remove some of the surrounding comb along with the queen cell to avoid damage the developing queen. The extra comb also provides a means to attach the cell to another frame.
Step 9: Remove the queen cells and insert them into queenless mating boxes/nucs. (See Nucleus method for more detail.)
• Add enough workers to cover the brood and queen cells.
• Return the original queen to the cell builder hive or leave one or two queen cells to become the replacement queen.
Step 10: Feed and reduce entrance. Before closing up the nuc, add a shim to create some space above the top bars and then add a protein patty. The nuc’s cover should have a 2 to 3 inch circular hole cut into the center. Place an inverted mason jar with 1:1 sugar syrup over the hole. The holes in the Mason jar lid should be 1/16 inch in diameter. Include a feed stimulant, such as Honey Bee Healthy, in the syrup. Cover the feeder with an empty box or bucket to protect the syrup from sunlight.
Step 11: Continue to feed the mating box/nuc for two weeks.
Step: 12: Wait 3 weeks before checking the results. You should find a laying queen with a good brood pattern. If this is the case, transfer the bees into a standard box. If you were not successful, return the frames to the original hive.
Because the Miller method involves several steps and critical dates, a calendar is very useful to organize and coordinate your schedule with the queen rearing schedule. An example of a schedule follows.
Figure 3.8.11 Sample calendar pages
Figure 3.8.12 Queen rearing action plan
Hopkins Method
Isaac Hopkins described his method of raising queens in 1911. According to G.W. Hayes, “The Hopkins Method of Queen Rearing is as good as and probably better for us than when first introduced 80 plus years ago.” In the same May 1991 edition of The American Bee Journal he noted, “Believe me when I tell you that you can raise more quality queens than you can probably use yourself with virtually no specialized equipment or manipulation.” The usual number of queens raised is about 20 using the Hopkins method.
The Hopkins and Miller methods are similar. The primary difference between them is the orientation of the frame upon which the queen cells are built. With the Hopkins method the frame is horizontal.
Step 1: Decide how many queens/nucs you can produce after evaluating your resources; e.g. amount of brood, workers to care for the brood, queen cells and availability of mating boxes/nucs.
Step 2: Set up the mating boxes/nucs using the original hive as the source of materials. If the resources of the mother (original) hive do not support the number of nucs you choose to make, you can supplement using brood and workers from other hives.
Nucleus configuration:
• Three (3) brood frames of capped brood with some cells that are emerging
• If the queen cells are located singly or in doubles on brood frames, simply include the brood frame with the queen cell(s)
• If the queen cells have been removed from mother hive frames, provide a space in the nucleus frames that are to receive the queen cells by cutting out a small portion of comb. The queen cells can then be placed in the space and fixed in place with a couple of tooth picks.
• one (1) frame of mostly pollen
• one (1) frame of mostly honey
• enough workers to cover the brood and queen cells
Mating box configuration:
• one frame of mostly honey and pollen
• one brood frame with emerging brood
• 2 queen cells
• enough workers to cover the brood and queen cells
Figure 3.8.13 Closeup of foundation pin for Hopkins Frame
Step 3: Day 1: Construct the Hopkins frame and place in queen mother hive.
• Build an unwired frame with foundation held in place with foundation pins. This is the Hopkins frame.
Figure 3.8.14 Foundation pin in Hopkins Frame
Unwired frames need be used as this will make later queen cell removal easier.
• Re-arrange the frames to create a space in the center of the queen mother brood box. This is done by removing a little used frame on the outside edge of the brood box. Brush off the bees and place this frame in another hive.
• Place the Hopkins frame in the space created in the queen mother hive.
Step 4: Day 5: Remove queen from the cell builder hive.
• The queen must be removed one day before moving the Hopkins frame from the queen mother hive to the cell builder hive. This queenless condition creates an emergency response and must exist if queen cells are to be raised. The bees respond to this emergency by quickly building queen cells.
• Store the queen temporarily in a small nuc. She will be returned to the cell builder hive at a later stage.
Step 5: Day 6:
• Evaluate the Hopkins frame and look for the presence of 24-36 hour old larvae.
• Look at the Hopkins brood frame from the queen mother hive frame. Since day one the bees will have drawn out the foundation and the queen should have started laying eggs in the new comb.
• You should see drawn comb, eggs and 24-36 hour larvae. If you do not see larvae of this age, replace the frame and wait another day or two
• Look at both sides of the Hopkins frame and select the side containing the most 24 -36 hourold larvae.
Figure 3.8.15 Hopkins brood frame
• Cull surplus cells in the Hopkins frame.
• Place the selected side face up on a work surface in an area with good lighting, temperature around 80 F, humidity, and NO direct sunlight as this would kill the larvae.
• Reduce the number of potential queen cells from developing too close together (as shown) by destroying two rows of worker cells and leaving the third intact. This provides space to keep the finished queen cells from being damaged when they are removed from the frame.
Figure 3.8.16 Destroyed cells
• Start at the top of the frame. Use a hive tool and scrape the cells from one side of the comb to the other. Damage the cell clear down to the mid-rib. Within the row of remaining, intact cells, destroy two cells down to the mid-rib and leave every third intact. The red lines on the photo indicate the cells to be destroyed.
• Place a shim above the brood frames in the now queenless cell builder hive. It acts as support for the prepared Hopkins frame and provides space for the protein patty and for the bees to build queen cells.
• Divide the protein patty into quarters and place them in the inside corners of the shim and above the brood frame top bars.
• Place the prepared brood frame on top of the shim and close the hive with a telescoping cover.
• Place an inverted mason jar with 1:1 sugar syrup over the hole. The holes in the Mason jar lid should be 1/16 inch in diameter. Include a feed stimulant, such as Honey Bee Healthy, in the syrup. Cover the feeder with an empty box or bucket to protect the syrup from sunlight.
Step 6:Nine days after placing the Hopkins frame on top of the cell builder (approximately day 15) prepare and transfer the queen cells to queenless mating boxes/ nucs.
• Figure 3.8.17 Finished cells
Place the frame in a standing position with the top bar on top and the bottom bar resting on a secure surface. With a sharp, wet knife carefully cut the comb leaving a half inch border around each queen cell.
• Create a cavity the size of the queen cell and border comb in the frame to receive the cell.
• Gently press the border comb with the queen cell into this cavity. Do not press on the fragile queen cell itself. If needed, a tooth pick can be used for additional support. (See Nucleus method)
• Return the original queen to the cell builder hive or place one or two queen cells in the cell builder to become the replacement queen.
Step 7: Feed and reduce entrance. Before closing up the mating box/nuc, add a shim to create some space above the top bars and then add a protein patty. The nuc’s cover should have a 2 to 3 inch circular hole cut into the center. Place an inverted mason jar with 1:1 sugar syrup over the hole. The holes in the Mason jar lid should be 1/16 inch in diameter. Include a feed stimulant, such as Honey Bee Healthy, in the syrup. Cover the feeder with an empty box or bucket to protect the syrup from sunlight.
Step 8: Continue to feed the mating box/nuc for a couple weeks.
Step 9: Wait three weeks to check the results. You should find a laying queen with a good brood pattern. If this is the case, transfer the bees into a standard box. If you were not successful, return the frames to the original hive.
There are a number of ways to raise queens and to do it well. Four methods have been presented. While we beekeepers like to believe we are in control, we can not overlook the queen’s influence. Appropriately we will leave it to her to have the last word.
“…If any old farmer can keep and hive me,
Then any old drone may catch and wive me;
I’m sorry for creators who can not pair
On a gorgeous day in the upper air, I’m sorry for cows who have to boast
Of affairs they’ve had by parcel post,
I’m sorry for man with his plots and guile,
His test tube manner, his test tube smile;
I’ll multiple and I’ll increase as I always have- by mere caprice;
For I am a queen and I am a bee,
I’m devil-may-care and I’m fancy- free,
Love-in-air is the thing for me,
Oh, it’s simply rare In the beautiful air,
And I wish to state
That I will always mate with whatever drone I encounter”
“Song of the Queen Bee”
Poems and Sketches of E.B. White reproduced in Queen Rearing and Bee Breeding Harry H. Laidlaw Jr. and Robert E. Page, Jr.
Figure 3.8.18 Honey bees surrounding a queen bee
References:
Harry H. Laidlaw Jr. & Robert E. Page Jr. (First Edition 1997) Queen Rearing and Bee Breeding, Wicwas Press
Larry John Connor (2009) Queen Rearing Essentials, Wicwas Press
Kim Flottum (2011) Better Beekeeping, Quarry Books, pgs 81, 92
Mel Disselkoen (2008) I.M.N. System of Queen Rearing, Self published
G. W. Hayes Jr. (May 1991) The Hopkins Method of Queen Rearing, American Bee Journal
Roy Hendrickson (April 2011) Managing Varroa: Selecting for Resistance & Queen Rearing, American Bee Journal, pg. 349 | textbooks/bio/Ecology/Radicalize_the_Hive_(Roell)/03%3A_Tools_and_Resources_for_New_Beekeepers/3.08%3A_Graft-Free_Queen_Rearing_by_Morris_Ostrofsky.txt |
• 1.1: What is EvoDevo?
The fields of Development and Evolution cannot be truly separated. When we study Developmental Biology we are mostly looking at a fine-tuned mechanical and genetic process that has been selected on for eons. Not only can evolution select on the final product - a working, fertile adult - but also can act at each developmental stage. It is easy to see how evolution acts through natural selection on adults, but how can it act on development itself?
• 1.2: EvoDevo Case Study
One great example of the interconnectedness of evolution and development is the problem of scaling in flies. Briefly, there are closely related fly genera that vary widely in size but have very similar proportions. An outstanding question in evodevo is: how do flies change their scale by tweaking or changing developmental processes?
• 1.3: Briefly, Genetics
For the most part when we think about Molecular Genetics we are thinking about making functional proteins from a gene encoded in DNA, though some RNA is functional on its own. This happens via two highly-regulated processes: Transcription uses RNA polymerase to make a single stranded mRNA molecule from one strand of a double stranded DNA molecule. Translation uses the ribosome to make a peptide (part or all of a protein) from the mRNA .
• 1.E: Introduction to Evolutionary Developmental Biology (Exercises)
Discussion questions and assignments for Chapter 1
Thumbnail: Adult Drosophila melanogaster fruitfly. (CC SA-By 2.5 Generic; André Karwath aka Aka).
01: Introduction to Evolutionary Developmental Biology (EvoDevo)
Anomalies
Anomalies refer to anything outside the ordinary, for example conjoined twins or missing limbs. Even though we commonly think of developmental anomalies as inherently "bad", they are not fundamentally so. For example, the average height of an NBA player is 6'7". Although this is anomalous (only 0.045% or one in 2200 American men are this tall or taller), it is not considered at all detrimental to be this tall. If you are a Developmental Biologist, you relish natural variation as a window into developmental processes. For example, you might find out what an NBA player ate growing up, how tall his parents are, if he grew up in a rural area or the city, and compare these data to the data of an average American man. The differences between the two can help you generate hypotheses regarding the developmental processes leading to tall height.
Figure 1: The poster to the left shows an advertisement for a tall man, Franz Winklemeier, who toured Europe in the 1880s. Image from Wellcome Images CC BY 4.0
At a deeper level we also notice something more fundamentally interesting about a very tall (or very short) person. Most people who are quite tall or quite short (say a 4'7" woman), have bodily proportions that are nearly the same as someone of average height. For example, their arms aren't placed too low, their neck isn't particularly long, their legs reach all the way to the ground. In short, their body has been "scaled" to a larger or smaller size. This leads us to think that perhaps development itself is scalable. Surely the blueprints for building a very short person are not so different from the blueprints for building a very tall person. Our current understanding is that signals from growing body parts signal to each other to accomplish this task. The same signals build a short or tall body, but a tall body might undergo more cell division or longer periods of growth than a short body.
Cell division is an important developmental process. What are some other developmental processes?
Classical Developmental Biology relies on mutations (gene based) and teratogenic (environment based) anomalies to dissect processes like this. Not only can we compare "normal" anomalies like heights that fall two standard deviations from the average, but we can also look at more rare anomalies like conjoined twin tadpoles or a cyclopic (one eyed) mouse. Both of these anomalies have the bonus of being able to be created in the lab. In fact, we can create them using either genetics, or environmental insult (a teratogen).
The Evolution of Development or the Development of Evolution?
In a very real way, the fields of Development and Evolution cannot be truly separated. When we study Developmental Biology we are mostly looking at a fine-tuned mechanical and genetic process that has been selected on for eons. Not only can evolution select on the final product - a working, fertile adult - but it also can act at each developmental stage. It is easy to imagine how evolution acts through natural selection on adults, but how can it act on development itself?
Consider the useful but pesky fruit fly, Drosophila melanogaster. Unlike you and me, who have support from our society (family, friends, institutions), Drosophila are r-selected. They survive by mating frequently and producing massive amounts of offspring that they leave behind on rotting fruit. Selection on adult Drosophila includes things such as ability to fly, to find food, find mates, and evade fly swatters. But other selective pressures affect embryonic Drosophila. Since the ability to mate quickly and produce many offspring is such a strong selective pressure on this species, embryos have evolved rapid development in response. In fact, Drosophila undergo such unusual developmental patterning in order to accomplish this incredibly fast development (about 24 hours to hatch into a larva), that we can use them as a model to see how evolution can speed up normal developmental processes. Surprisingly, to me at least, speeding up development doesn't just mean that everything moves along more quickly. Instead, Drosophila and its relatives undergo a unique type of embryonic development called "long germ-band" development. Instead of developing by slowly elongating and adding new differentiated tissue to the posterior end of the body, as many animals do, long germ-band insects develop all at once - rapidly subdividing an undifferentiated field of cells into the many parts of the larval body.
How else could evolution affect developmental processes?
This example is a classic illustration of evolution acting on developmental processes. There are many other ways evolution acts on development, these are often related to the physical constraints experienced by a growing embryo. On the flip side, we can also think of evolution itself as being constrained by development. Although much of natural selection acts on adults, that adult body must be formed by developmental processes inherited from ancestors and influenced by the environment. This is a limit on the types of bodies that can be produced, even if selective pressures are strong. However, the average member of a species does not show us the extremes of what morphologies are possible given evolutionary and physical constraints. This is where it becomes important to look at anomalies and other variation. When we see that height is scalable, we can look at the evolution of height in the past (what pressures drove the Homo genus to become tall with Homo erectus and its descendants? for example), pressures on height in the present (for example locomoter issues with very short or very tall heights), as well as the development of height (length of puberty, environmental factors such as food and toxins, for example). By examining our very short and very tall people, we can see the outer limits of these evolutionary and developmental constraints. Likewise by looking at rare anomalies (for example people born without limbs) we can examine the limits of perturbing development and find out what is possible.
One great example of the interconnectedness of evolution and development is the problem of scaling in flies. Briefly, there are closely related fly genera that vary widely in size but have very similar proportions. An outstanding question in EvoDevo is: how do flies change their scale by tweaking or changing developmental processes? | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/01%3A_Introduction_to_Evolutionary_Developmental_Biology_(EvoDevo)/1.1%3A_What_is_EvoDevo%3F.txt |
When we look within a species we see tall and short (or large and small) individuals but they are all scaled more or less the same. For example, we don't generally see tall people with abnormally long necks or short people with abnormally short legs. As a general concept, we can say that this kind of scaling must be the result of cross-talk between different cells, tissues, and organs. For example, we might expect a growing bone to stretch muscle fibers and induce them to elongate. We might also expect a bone that grows long to also grow wide in proportion. However, the actual cellular and molecular mechanisms that perform this scaling are often somewhat mysterious. Here we are going to begin to examine a case of scaling in a group of super-manipulable animals - the dipterans.
Bicoid in dipterans: Drosophila
Dipterans are a type of fly, and this group includes the flies you are probably most familiar with - houseflies and Drosophila fruit flies. As was mentioned in the Introduction, these flies undergo extremely rapid development. This is likely selected for by their transient food sources. Moreover, their embryos and larvae lack protection and are a good source of nutrition for insectivorous predators.
One way to speed up development is to pattern the whole animal at the same time instead of patterning one end first, like we and many other animals do. Drosophila and relatives (often called the "higher dipterans") pattern their anterior and posterior ends at the same time. In fact, the oocyte (egg) is patterned before fertilization even occurs, with the "organizer" of anterior patterning (Bicoid) at one end and the "organizer" of posterior patterning (Nanos) at the other1,2. There are many more genes involved in this process, but we will mostly focus here on Bicoid since it has been the subject of intense study.
Both the Nanos and Bicoid organizers in Drosophila are proteins that are found in a concentration gradient. Bicoid has its highest concentration at the anterior end, while Nanos is highest at the posterior. Towards the middle of the embryo they are both present at only low concentrations (Figure 2)1,2,3,4 If you deplete Bicoid from a fly egg, you end up with a fly missing anterior (head) structures and an expanded abdomen. If you deplete Nanos, you end up with a fly missing posterior (abdominal) structures and an expanded head. Note that the tip of the head and the tail are patterned by two separate developmental mechanisms, but we are going to ignore this for now.
At this point, I am going to make our first foray into light molecular genetics. If you get a bit confused, please read Briefly, Genetics for some clarification.
When Christiane Nusslein-Volhard first made Bicoid mutants, she noticed a couple of interesting things. First, you need to make the moms mutant. This makes sense because it is maternal mRNA that gets pumped into the oocyte, so of course it is the mom's genotype that rules the embryo's morphology in this case. Second, even though she didn't have perfect evidence, she noticed that the Bicoid protein gradient looks like a diffusion gradient. A diffusion gradient is the pattern you get when something is diffusing freely from a point source (Figures 2,3,4). Imagine you are baking cookies, a visitor knocks on your door. As you open the door, they notice a faint but terrific smell coming from your house. They make small talk with you and slowly walk towards the source of the smell towards the kitchen. As they get closer to the oven the smell intensifies. You open the oven to take out the cookies, and your kitchen is flooded with the smell of cookie goodness. In this case the baking cookies in your oven are the point source and the smell has formed a diffusion gradient in your house, faintest at the front door and strongest in the kitchen. This mechanism for forming a gradient is called the "SSD model" for synthesis, solute, diffusion. However, in the case of Bicoid, this model has its critics, as we will discover in The Curious Case of Bicoid.
The Problem of Scaling in Dipterans
The SSD model looks good on paper, but there is a confounding fact about dipteran embryos that forces us to take a closer look at it. Dipteran embryos vary in size tremendously. Drosophila embryos are teensy-tiny, about a third to half a centimeter long. Housefly embryos, on the other hand, are a whopping 1.5 centimeters long. What does this mean for the SSD model? Imagine your point source in our cookie example: a delicious smell coming from your oven. Only now you are cooking in your University's dining hall. Someone walks into the dining hall, what is the likelihood that they are going to smell those cookies? Pretty low, unless they have a great sense of smell. The door is now way too far for detectable odor to reach by diffusion. Likewise, in a large Musca (housefly) embryo, the diffusion gradient would only reach 1/5 (or less!) as far down the embryo as the same diffusion gradient in a small Drosophila embryo (Figure 4). How do flies solve this problem? There are several possible solutions that we will consider in The Curious Case of Bicoid. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/01%3A_Introduction_to_Evolutionary_Developmental_Biology_(EvoDevo)/1.2%3A_EvoDevo_Case_Study.txt |
Some Basic Terms
DNA is a double stranded nucleic acid polymer that is the primary hereditary material in most living organisms. Each strand of DNA is made up of covalently bound nucleotides. Each nucleotide is made up of a sugar, a phosphate, and a nitrogenous base. The covalent bond between nucleotides occurs between the sugar of one nucleotide and the phosphate of the next. In DNA, there is a single type of sugar but 4 types of bases. These bases - adenine, thymine, cytosine, and guanine - give each nucleotide its name (abbreviated A, T, C, and G).
The two strands of DNA are bound together by hydrogen bonds between nitrogenous bases. Each nitrogenous base has a "complementary" base. A pairs with T, and C pairs with G. If we think of a DNA strand having an orientation of sugar-phosphate-sugar-phosphate-sugar-phosphate then the second strand of the molecule has an orientation of phosphate-sugar-phosphate-sugar-phosphate-sugar. We call this type of orientation anti-parallel and we refer to the two strands as reverse complements. Reverse complementarity refers both to their opposite orientation (reverse) and the A=T G=C bonding pattern (complement).
RNA has a similar structure, though it is typically found as a single strand. It is capable of forming double strands (or even more complex structures, for example tRNA) through hydrogen bonding with reverse complement sequences. It can hydrogen bond with itself or with other RNA molecules.
The Central Dogma of Molecular Biology
For the most part when we think about Molecular Genetics we are thinking about making functional proteins from a gene encoded in DNA, though some RNA is functional on its own.
The production of protein from a DNA code happens via two highly-regulated processes: Transcription uses RNA polymerase to make a single stranded mRNA molecule from one strand of a double stranded DNA molecule. Translation uses a ribosome to make a peptide (part or all of a protein) from the mRNA (Figure 1).
Quick side note because many people are confused by some of the terms that we use in genetics, evolution, and development. A gene refers to a piece of DNA that codes for RNA. This RNA is often an mRNA but can also be a tRNA, rRNA, snRNA, miRNA, or a different "non-coding" type of RNA. mRNA is RNA that codes for protein. Most of the time "gene expression" refers to the production of mRNAs and/or the proteins they code for. Gene expression is the process of using DNA to make a functional product. As you probably know, most of the cells in your body are genetically identical (more or less); they "share a genome." However, your cells have very different functions. These different functions are driven by different environments and different gene expression profiles - that is, the cells express different genes. For example, we might expect to find a lot of Myosin protein in muscle cells but a lot of Aquaporin protein in kidney cells.
The regulation of gene expression (epigenetics)
Gene expression gets regulated at three major levels (that can be subdivided into many many sublevels). Transcription itself can be regulated (we often refer to this as turning a gene "on" or "off"). Regulating transcription is the job of transcription factors, also known as "trans acting" factors. These are diffusible molecules, often proteins, that act in many different ways to turn up or down the rate of transcription of a particular gene. Some transcription factors bind directly to to cis-regulatory sequences, pieces of DNA usually near the coding region of a gene, and influence the ability of RNA polymerase to bind to the promoter of the gene. They can do this by directly interacting with proteins involved in RNA polymerase recruitment (for example TFIID and Mediator), or by changing the accessibility of the promoter (for example, physically blocking the promoter, adding or removing methyl groups, or interacting with histones and histone binding proteins). Some transcription factors bind to other transcription factors and affect their ability to bind DNA.
The second major level of gene expression regulation is translational regulation. This includes any kind of regulators that affect the amount of protein/peptide produced by a single mRNA molecule. There are two very well-studied ways that this happens. The first is through RNA interference (RNAi), which you may have heard of. RNAi uses short pieces of non-coding RNA that are exact or very close reverse-complements to part of an mRNA sequence. This targets the mRNA for destruction or blocks translation.1 The second well-studied way to regulate translation is through RNA binding proteins. These proteins will often bind to specific sequences found outside the protein-coding region in mRNAs. These regions are called the untranslated regions or "UTRs". Proteins that bind here can
1. Destabilize the mRNA, lowering translation levels.
2. Stabilize the mRNA, raising translation levels.
3. Localize the RNA to a specific part of the cell.
4. Block or inhibit the binding of translation factors, lowering translation levels.
5. Recruit translation factors, raising translation levels.2
The third and final major level of regulating gene expression is the post-translational level. This level encompasses most of what we think of as signal transduction pathways, or the protein-protein and protein-small-molecule interactions that affect protein stability and function. This can include both covalent modification of the protein (for example, phosphorylation, dephosphorylation, glycosylation, or proteolytic cleavage) as well as non-covalent modification (for example allosteric inhibition or activation, homo and heterodimer formation).3 If you aren't sure what these terms mean right now, that's ok - most of them we wont cover and those we do cover are easier to understand in context as you learn about signal transduction pathways.
1.E: Introduction to Evolutionary Developmental Biology (Exercises)
At-home assignment
Watch the YouTube video at youtu.be/ydqReeTV_vk (Evo-Devo Despacito) and respond to the following two prompts:
1) What is one thing mentioned in the video you already know about?
2) What is one thing mentioned in the video you would like to learn more about?
Discussion and Reading Guide Questions
The questions below were originally written for students reading Freaks Of Nature by Mark Blumberg and Endless Forms by Sean Carroll. However, the questions in bold are discussion questions that can be answered without these books.
The "Reading Guide" questions are appropriate for short homework answers and the "Discussion Guide" questions are appropriate for open in-class or online discussion.
Discussion Questions
1. How does studying anomalies help us understand how development and evolution work?
2. How does studying development give us insights into evolutionary biology?
3. What is the argument for DNA being only a part of the process of development?
4. Why is it that tinkering with an embryo can sometimes produce an animal that has anomalies that still can function integratively? Does tinkering always result in an integrated adult animal
5. What animals did you draw as a child? Do you still allow yourself to be awed and inspired by nature? What (if anything) has changed since your childhood?
6. If you had to go on a nature vacation anywhere, where would you go and why?
7. Why do we study evo-devo and what are the central questions in the field?
8. What evolutionary adaptations most interest you?
9. How do "just so" stories differ from the scientific process?
10. What are some examples of "building blocks" and modular design in animals?
11. Do you think that hopeful monsters are a way that evolution happens? Why or why not?
12. What does it mean that some anomalous characters are "discontinuous" rather than continuous?
13. What are puntuated equilibria? Are they real or an artifact?
14. What is the genetic toolkit and what is the toolkit paradox? How can we resolve this paradox?
15. How does the "gene centric" view of this book differ from Freaks?
16. Can you think of any exceptions to "Williston's Law"?
Freaks Reading Guide: Chapter One
1. What are evolutionary constraints?
2. What is teratology?
3. What is Developmental Systems Theory?
Endless Forms Reading Guide: Intro and Chapter One
1. How does studying an organism's development help us understand its evolutionary relationships?
2. What is regulatory DNA?
3. What is a developmental constraint?
4. In what ways can evolutionary changes in the development of an organism affect its morphology?
5. What are Hox genes, and what role do they play in evolution?
6. What are serial homologs?
7. What will be covered in the first and second halves of this book? What do you already know about?
8. Does ontogeny recapitulate phylogeny? Why or why not? | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/01%3A_Introduction_to_Evolutionary_Developmental_Biology_(EvoDevo)/1.3%3A_Briefly%2C_Genetics.txt |
Fertilization
For sexually reproducing species, the completion of fertilization marks the start of embryogenesis. You are already aware that species have different reproductive isolation mechanisms that prevent interspecific fertilization. In the case of sea urchins (links below) you will see that there are several steps that can mediate species-specific recognition. These include chemo-attractants (chemicals secreted by the egg that the sperm responds to) and sticky molecules held by the sperm (bindins) that only interact with the same species eggs.
The sperm-entry point is also significant in many species in that it marks the first break in egg symmetry. Imagine a fairly symmetric ball. Now draw a single dot on that ball, this dot is now a landmark. You can be opposite the dot, close to the dot, or right on the dot. The sperm-entry point, like the dot, acts as a landmark to break symmetry. It does so in at least two related ways, by donating a centrosome to the egg, and by triggering cytoskeletal rearrangements. The sperm centrosome, a tiny organelle that acts as a seed for microtubule formation, can act as an organizer of the spindle apparatus. By putting one side of the spindle near the sperm-entry point, it can define the axis of the first cleavage (Figure 1).
Additionally, the sperm-entry point can be a trigger for cytoskeletal shifting, including a process called cortical rotation, wherein the outer layer of the cell (the cortex) rotates relative to the inner cytoplasm. While cortical rotation is limited to a few species (that we know about), studying it has led to breakthroughs in EvoDevo and developmental biology in general.
Cortical rotation's significance as a symmetry breaking event is underlined when we see what happens if we prevent it. Brief treatments of frog (Xenopus laevis) fertilized eggs with agents that affect microtubule polymerization prevent cortical rotation and result in a "ventralized" embryo - that is, it has ventral structures but lacks dorsal structures including those that would build a spinal cord. We call an embryo like this a "belly piece." What is it about cortical rotation that turns a frog into a frog, rather than into a mass of belly tissue?
Cortical rotation as an EvoDevo example
Even though cortical rotation is a process found in only a few animal species, it is an example of several fundamental concepts in EvoDevo
1) Establishment of organizers. Organizers are parts of the embryo that produce signals that pattern nearby or distant tissues. In Drosophila, Bicoid mRNA marks the head organizer, for example. Depletion of Bicoid leads to headless flies, too much Bicoid leads to big-headed larvae. Later in the semester we will examine the ZPA organizer in vertebrate limbs.
Frogs have a Spemann-Mangold organizer (named after student Hilde Mangold and her advisor Hans Spemann who discovered and characterized it)2. Removal of the organizer tissue leads to a ball of belly tissue. Addition of an organizer to another location on the embryo leads to twinned tadpoles.
2) Induction of cellular differentiation. Many cells have a "default" path that they will follow over time if they are not given additional instructions. One of the main roles of an organizer is to make and send off those additional instructions. Organizers do this through cell-signaling molecules and gene regulation. The Bicoid example in Drosophila is an example of gene regulation. The frog example demonstrates both gene regulation and cell-signaling, as I will soon describe.
3) Development happens in 4D. Not only do we have to think about complex 3D objects when we are thinking about development, but we also need to consider time. Over the course of time, cells and parts of cells change their positions. This changes the "local environment" - changing the types of interactions that can happen. This will be more important in gastrulation, but we will see the start of it here in cortical rotation. In the case of cortical rotation, the rotation changes the locations of mRNAs and proteins. These will eventually be inherited by different cells and will give these cells starting instructions for differentiation. These cells will later change their position and, as they come into contact with new neighbors, will differentiate further and give out new instructions.
Sperm entry triggers changes in the egg cell
An unfertilized frog oocyte is not perfectly symmetrical. It has radial symmetry, that is you can stick a pin from top to bottom and it will be symmetric around the pin. However, the top and bottom sides differ. The bottom (vegetal pole) is enriched with dense yolk granules while the top (animal pole) is enriched with less dense cytoplasm and pigment. Similar animal/vegetal symmetry is seen in many species. Frog eggs are also asymmetric in that they are made of two layers. An outer cortex and an inner cell mass. The animal and vegetal poles differ in the mRNAs and proteins (see Briefly, Genetics for a refresher on molecular biology terms)3 and so do the inner and outer parts of the oocyte.
Sperm entry induces a change in the way cytoskeletal microtubules interact with each other. They go from being a loosely organized network across the cell to a parallel array with highest density in the cortex and at the cortex/inner cell mass border. These microtubules rotate the cortex relative to the inner cell mass, taking with them the asymetrically localized cortical determinants2. Because the pigmentation in the egg was unevently distributed, this creates a "grey crescent" where the vegetal cortex now lies over the animal inner cell mass (Figure 2)
The interaction between vegetal cortex molecular determinants and animal inner-cell mass molecular determinants makes this grey crescent unique compared to either the animal or vegetal pole of the fertilized egg. The grey crescent marks the future dorsal side of the frog. You can see now why elimination of cortical rotation or elimination of the molecular determinants that populate the grey crescent lead to ventralization of the frog. Duplication of the grey crescent, either through transplantation or genetic manipulation, leads to an extra dorsal axis and "twinning" of the frog.
In the next chapter, Cleavage and Gastrulation, we will examine the development and genetic of this organizer and think about the consequences of organizing tissues in evolution.
Further Reading: Developmental Biology
www.ncbi.nlm.nih.gov/books/NBK9983/
• Introduction to fertilization
• 1. Sperm and Egg
• 2. How do you do? Sperm and egg recognition
• 3. One sperm per egg: the cortical granule reaction
• 4. OPTIONAL: The activation of egg metabolism
• 5. OPTIONAL: Two become one, fusion of genetic material
• 6. Breaking symmetry: Rearrangement of the egg cytoplasm
• 7. Summary
02: Fertilization and Cortical Rotation
At-home assignment
Free response question:
A recent paper examines the effect IVF may be playing on human evolution. Look at one or two of the traits being selected on by IVF (Table 1). and think about the role IVF might be playing in future evolution of that trait. Is the effect of IVF large enough to drive significant human evolution?
Discussion Questions and Reading Guide
The questions below were originally written for students reading Freaks Of Nature by Mark Blumberg and Endless Forms by Sean Carroll. However, the questions in bold are discussion questions that can be answered without these books.
The "Reading Guide" questions are appropriate for short homework answers and the "Discussion Guide" questions are appropriate for open in-class or online discussion.
Reading Guide for "Further Reading"
1. What are the four major events of fertilization?
2. What are the parts of an animal sperm cell?
3. Where does the power for sperm propulsion come from?
4. How does an animal egg differ from a sperm cell?
5. What are the different layers of an egg cell?
6. What is polyspermy? How does an urchin egg prevent this?
7. What processes produce the first asymmetry in frog embryos?
Discussion Questions
1. What are some other mechanisms that reduce the rates of interspecific fertilization?
2. What selective pressures drive pre-zygotic barriers between species?
3. What is the significance of an egg packed with protein and mRNAs?
4. What are different ways eggs and zygotes protect themselves in different environments? Consider, for example, urchin eggs, chicken eggs, and mammalian eggs.
5. Why is it important for animal embryos to "break symmetry?
6. What is the connection between eugenics and evolution?
7. Why do we consider eugenics to be unethical?
8. What does it mean when we say that cells "express" a gene?
9. How are evolution and development linked as fields of study? What is the link between both and genetics?
10. How are evolution and development both affected by environmental interactions?
11. How does the Kirschner/Gerhart view of EvoDevo differ from the West-Eberhard view?
Freaks Reading Guide: Chapter Two
This chapter brings in the dimension of "time" into the picture. Two of the examples in this chapter are covered in this online text, Sonic Hedgehog and the Segmentation Cacade.
1. What is cyclopia? Is it genetically or environmentally induced?
2. What is induction and how does it relate to cyclopia?
3. What is eugenics?
4. What is the difference between teratogenesis and mutagenesis? Which of these are used by developmental biologists?
5. How can the same mutation produce different phenotypes?
6. What are the different types of twins?
7. What subjects in this chapter are you interested in following up on later in the semester? | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/02%3A_Fertilization_and_Cortical_Rotation/2.E%3A_Fertilization_and_Cortical_Rotation_%28Exercises%29.txt |
Thumbnail: The process of gastrulation. Gastrulation occurs when a blastula, made up of one layer, folds inward and enlarges to create a gastrula. A gastrula has 3 germ layers--the ectoderm, the mesoderm, and the endoderm. Some of the ectoderm cells from the blastula collapse inward and form the endoderm. The blastospore is the hole created in this action. Whether this blastospore develops into a mouth or an anus determines whether the organism is a protostome or a dueterostome. This diagram is color coded. Ectoderm, blue. Endoderm, green. Blastocoel (the yolk sack), yellow. Archenteron (the gut), purple. (Public Domain; Abigail Pyne).
03: Cleavage and Gastrulation
Models for Making a Gradient
Morphogenic gradients are incredibly important in development for patterning tissues. If a tissue is completely homogenous (every cell doing the same task) it cannot be complex and is often not resistant to environmental fluctuations. In the case of Bicoid in Drosophila, we are considering a morphogenic gradient that patterns the anteroposterior axis - as mentioned in the Introduction, too much Bicoid gives us a giant head and too little gives us no head at all. There are somewhere around 60 different genes that respond to various levels of Bicoid protein and one of the earliest to be discovered is Hunchback. Hunchback gives positional information to a fly embryo, it sharpens the boundary between the anterior and posterior of the fly. While the Bicoid protein gradient is very broad and resembles a diffusion gradient, the Hunchback gradient is sharp, with significantly different protein levels within 10 μm, or about 2 nuclei1.
Obviously the levels of Bicoid must matter tremendously since the Bicoid gradient and its readout (for example Hunchback levels) are incredibly precise. An early model for the observed Bicoid gradient in Drosophila is the SSD model (Synthesis, Solute, Diffusion), where a point source of Bicoid protein (translated from anterior bicoid mRNA) sets up the concentration gradient. The related SDD model (Synthesis, Diffusion, Degradation) incorporates degradation over time of Bicoid protein, keeping the gradient from reaching the posterior end of the embryo. Several other models have been proposed that would allow for fluctuation in embryo size but still lead to a correct Bicoid readout:
1. More mRNA/protein in larger embryos: This would extend the gradient out further in larger embryos.
2. Nuclear shuttling: The same as the SDD model, but Bicoid protein gets taken up by nuclei as it diffuses by them. Under this model, the more densely packed the nuclei are (smaller embryo) the more quickly the Bicoid protein gets pulled out of the syncytial cytoplasm. In larger embryos, the protein can diffuse farther.
3. ARTS model (Active mRNA, Transport, Synthesis): The cytoskeleton actively transports Bicoid mRNA to form an mRNA gradient that gets readout as a protein gradient as it is translated. In larger embryos, the cytoskeleton can transport the mRNA further.
4. mRNA diffusion and degradation: This is similar to the ARTS model, except that in this model Bicoid mRNA degrades over time to maintain an mRNA gradient. Larger flies could have lower degradation rates of Bicoid mRNA or faster transport.
5. Facilitated diffusion of protein. This is similar to the ARTS model, only it involves transport of Bicoid protein by the cytoskeleton. In this case, larger flies could have faster transport of Bicoid protein.
There is some evidence for and against each of these models, suggesting that the Bicoid protein gradient is likely maintained by a combination of these models. Additionally, Bicoid protein readout might be more complex than we think - multiple proteins could be affecting how Bicoid interacts with its targets.
Evidence for and against the models
Data from both Drosophila and other, larger, dipterans have provided evidence supporting each of the models listed above. Additional testing has falsified the predictions of some of the models, and that is the subject of this section. Below I describe each model and a test of that model, I also include a figure that illustrates what the model expects and what was actually observed. I recommend this type of super-reductionist figure to help summarize a large set of data, but we always need to keep in mind that it does not tell the whole story.
1. More protein model. An embryo can get more protein by increasing the amount of mRNA, increasing the rate of translation of that mRNA, or decreasing the rate of protein degradation. Supporting this is the finding that putting in extra copies of Bicoid (more mRNA and more protein) into a fruit fly increases the Bicoid gradient and the size of the head. To see if this is what flies with larger embryos do to make a larger gradient, researchers put Bicoid DNA, complete with cis-regulatory sites and UTRs, from large embryo flies (Calliphora) in Drosophila. They found that the Bicoid gene from large embryos did not make a longer gradient in Drosophila. Therefore, if there are any factors affecting the mRNA stability or protein degradation, they must be specific to the larger flies3.
2. Nuclear shuttling. Early experiments on this suggested that adding a nuclear localization signal to Bicoid protein made a shallower gradient3. Later experiments tested this by making Drosophila with a mutant version of Bicoid that did not accumulate in nuclei. If nuclear import made the Bicoid protein gradient steeper, then they would have seen a broader gradient after inhibiting nuclear import. However, they saw a fairly normal looking Bicoid protein gradient, arguing strongly against this model4.
3 and 4. mRNA gradient models. In both models 3 and 4, mRNA is actively transported around the cell by the cytoskeleton. This is in direct opposition to the SDD model, where Bicoid protein is translated from anteriorly-tethered Bicoid mRNA. In these two mRNA gradient models, the protein gradient is simply a "read-out" of the mRNA gradient. Evidence for these two models comes from careful measurement of Bicoid mRNA in developing embryos (Figure 2). These careful measurements show that Bicoid mRNA itself forms a gradient, and is not simply a point source5. Its movement is dependent on the cytoskeleton, if the cytoskeleton is disrupted, the mRNA gradient is also disrupted6. Evidence against this model comes from the finding that Bicoid protein at the posterior of the embryo is older than Bicoid protein at the anterior. If Bicoid mRNA diffuses towards the posterior to make a gradient, then Bicoid protein is made from that mRNA, we would expect to see younger Bicoid protein at the posterior and mixed age Bicoid protein at the anterior end. However, Durrieu et al found the opposite, suggesting that even though Bicoid mRNA may form a gradient, this is not the main determinant of the protein gradient7.
5. Facilitated protein diffusion. Disruption of the cytoskeleton by treating a Drosophila embryo with anti-actin or anti-microtubule drugs leads to disruption of the protein gradient. Since mRNA tethering at the Anterior pole is also dependent on microtubules, just disrupting the cytoskeleton wouldn't tell you whether it is mRNA transport or protein transport that leads to the protein gradient. One study used a funny trick - if you raise Drosophila embryos in low-oxygen (hypoxic) conditions, the Bicoid mRNA will stay at the anterior end even if microtubules are disrupted. This study found that Bicoid protein still forms a gradient even if Bicoid mRNA does not, and that this gradient is dependent on the cytoskeleton8.
A Model Emerges
Despite all of the seemingly contradictory data, a model is beginning to emerge that both explains the robustness of the Bicoid protein gradient and explains how the gradient itself can scale to larger or smaller bodies. First, Bicoid mRNA is mostly sequestered at the anterior end of the embryo, but also travels along the cortex (outer edge) of the embryo via microtubules. Bicoid protein is translated off of the Bicoid mRNA, with a higher amount of translation happening at the anterior end, where the concentration of Bicoid mRNA is higher. Some Bicoid protein is likely also translated off of the lower concentration Bicoid mRNA that has moved posteriorly via microtubules. This leads to a gradient of Bicoid protein that is slightly broader than what we would expect if there was a simple point source of Bicoid protein (i.e. translation from anterior pole Bicoid mRNA).
This protein gradient is also modified as Bicoid protein gets transported around the embryo by the cytoskeleton (via actin filaments and microtubules). In this way, there is control over the gradient by the cytoskeleton and by the proteins that mediate interaction between Bicoid (protein and mRNA) and the cytoskeleton. These mediating proteins may be sensitive to local Bicoid levels and may allow Bicoid to move more quickly or slowly depending on the anteroposterior position and the gradient level. For example, a large fly might have less Bicoid protein by diffusion at 15% of its length (EL) than a small fly does at 15% of its length. However, all of the Bicoid protein at 15% EL in the large fly can get taken up by the mediating proteins and moved posteriorly to broaden the gradient. On the other hand in a small fly, the larger amount of Bicoid protein at 15% EL could oversaturate the mediating protein and be transported less efficiently.
Additionally, Bicoid proteins from different species of fly are known to have slightly different properties, for example Bicoid from larger fly species such as Calliphora vicinia and Lucilia sericata are not able to completely rescue Drosophila Bicoid mutants3. These different properties could also play a role in protein-protein interactions involving the cytoskeleton. Finally, the mediating proteins between the species could also differ, some might bind to Bicoid more efficiently and/or move along the cytoskeleton more efficiently. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/03%3A_Cleavage_and_Gastrulation/3.1%3A_The_Curious_Case_of_Bicoid%3A%09Models_for_Making_a_Gradient-A_Model_Emerges.txt |
Cleavage
Cleavage stages of embryogenesis are typically very similar across animals. During cleavage a single cell embryo rapidly divides to form a ball of cells, called a blastula. This ball may be hollow inside, have a hollow region, or be fairly solid. Early cleavage stages are different from later cell divisions in that they quickly produce many very similar looking cells. If morphogens are asymmetrically distributed in the egg, then these cells can differentiate via autonomous specification even at early stages. Conditional specification typically begins to occur towards the end of cleavage stages when cell division slows down and cells begin to communicate more extensively with each other. Sometimes this is called the "mid-blastula transition" or MBT. The MBT demarcates the transition between using mostly maternal cell and fate determinants (RNAs and protein) to the embryo producing its own RNAs and proteins. One interesting experiment that shows the extent of this transition is to block transcription using the drugs alpha-amanitin or actinomycin D - two inhibitors of RNA polymerase action. If these drugs are applied to an early cleavage-stage embryo cleavages proceed normally, suggesting that developmental processes and cell division at this early stage are using maternally-derived factors already present in the embryo. If the drugs are applied to later-stage embryos development halts, suggesting that at this point zygotically derived transcripts are necessary for development and cell division. The timing of the MBT and the sorting of maternal proteins and RNAs into different cleavage-stage cells varies widely among different animals.
Read more details about Cleavage here, focus on any section you find interesting and especially figure 8.5. www.ncbi.nlm.nih.gov/books/NBK9992/#_A1678_
Gastrulation
Gastrulation refers to a time of great flux in animal embryos. During gastrulation the cells produced during cleavage begin to move relative to each other. As they move, they change their local environment and come into contact with new cells. This change in local environment means that the cells may a) be exposed to different extracellular morphogens and b) make contact with new cell-cell signaling partners. The movement of cells (Figure 3) over (epiboly), under (involution), between (intercalation), internally (invagination) or away from an epithelial sheet (ingression and delamination) creates layers of tissue. As the cells comprising these tissue layers encounter new morphogens and new signaling partners, they become specified as germ-layers.
The following video shows a live-frog embryo undergoing cleavage and gastrulation and also shows an animated internal view of how the cells move inside the embryo. Note the different kinds of movements. https://www.youtube.com/watch?v=riSA1mo86Kg
Changing Partners
As mentioned earlier, gastrulation performs two key functions in a developing animal embryo. First, it creates tissue layers (germ layers) from set of fairly homogenous cells. Second, it allows for new interactions between cells and places cells in new morphogenic positions. As cells change their partners over time, they become fated to a specific path. For example, compare a picture of a fate-map of a blastula-stage frog to the fate map of a gastrulated frog (Figure 4).
While the blastula-stage frog seems almost random in its mapping, the gastrulated frog has all of its tissues/organs in roughly adult positions. The blastula stage has not undergone extensive cell movements yet and the cells are largely unspecified. If cells are removed during the blastula stage, other cells will often be able to take on the fate of the missing cells. For example, identical twins develop from a single embryo that has "split" into two after multiple cell divisions. Rather than each half of the embryo making only half an animal when contact is broken between the two cell masses they each develop into an entire animal. One of my favorite sets of experiments of all time, the Spemann-Mangold organizer experiments, shows the extent to which cell-cell communication can rule development. Before I discuss that I would like to briefly summarize frog gastrulation (no offense to other animals, but they are my favorite gastrulators). A more in-depth look at frog gastrulation can be found here: www.ncbi.nlm.nih.gov/books/NBK10113/ and an interactive fate-map for Xenopus is available from https://www.xenbase.org/anatomy/static/xenbasefate.jsp
Frog Gastrulation and the Dorsal lip of the Blastopore
After fertilization and cortical rotation, the frog embryo is divided roughly into four quadrants. These are demarcated by the two major axes A/V (animal-vegetal) and D/V (dorsoventral). There is no Anteroposterior axis yet, this axis will be generated during gastrulation. https://www.youtube.com/watch?v=EPMgHMnwW28
Over the course of gastrulation, the red area (future mesoderm) in Figure 5 will involute under the blue area (future ectoderm) and extend to form a layer at the roof of the blastocoel (Figures 3 and 4). This involution occurs most extensively at the dorsal side of the embryo (the side opposite sperm entry), but also occurs along the rest of the "blastopore lip". To visualize the blastopore lip, open your mouth wide. Your lips represent mesoderm and the rest of your face represents ectoderm (sorry no endoderm in this one!). Use your lips to cover your teeth. This is physically similar to involution. Now imagine that your lips could grow thin and long and cover the inside of your mouth. This is how the mesodermal cells end up as a second layer under the ectoderm. Finally, begin to close your mouth. This is similar to epiboly - when the ectodermal cells move over the surface of the embryo to cover the mesoderm and endoderm.
To understand the role of the Spemann-Mangold organizer, you need to keep these movements in mind. In particular, you need to think about the dorsal lip of the blastopore, the place where involution first begins and happens most extensively. If you look at the Figure 4 fate map, you will notice that the dorsal mesoderm (the mesoderm at the dorsal lip of the blastopore) will become the notochord. These cells are the first mesodermal to internalize during epiboly. This block of cells will elongate and thin out to become a rod of mesodermal tissue that spans the length of the embryo. This will run along the anteroposterior axis, just like your spinal column runs along your anterioposterior axis. Additionally, protein signals from the notochord will help to pattern the rest of the embryo, as Hans Spemann and Hilde Mangold famously discovered. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/03%3A_Cleavage_and_Gastrulation/3.2%3A_Cell_Division_and_Movement%3A_Cleavage_-_Frog_Gastrulation_and_the_Dorsal_Lip_of_the_Blastopore.txt |
The Spemann-Mangold Organizer
Hans Spemann and his graduate student Hilde Mangold perfected a technique to do cross species transplantations of the dorsal blastopore lip to new locations in the host's body. Spemann had wondered for years what exactly the dorsal lip of the blastopore did. He knew it was important because if he sliced an embryo in two, the half that got the dorsal blastopore lip developed into an tadpole, while the other half developed into a "belly piece." He also knew that if he carefully divided the embryo down the middle of the dorsal lip of the blastopore, both halves would develop into a tadpole. One possibility was that a morphogenic signal emanated from the dorsal lip that caused cellular differentiation in a time gradient, such that the closest cells to the dorsal lip differentiate first. Without this signal, cells wouldn't differentiate. Spemann thought he had support for this hypothesis when he did transplantation experiments in newts. When he transplanted the dorsal lip from one newt to another, he got conjoined twin newts - suggesting that some signal from the dorsal lip was indeed patterning the main body axis12,13.
Soon Spemann revised his hypothesis, largely based on careful observation of gastrulating embryos and on the cross-species transplantation work by Mangold. Mangold took the blastopore lip from an unpigmented newt species and transplanted under the ventral ectoderm of an early gastrula pigmented newt from the same genus. In this way she was able to see which tadpole tissues came from the donor (the unpigmented newt) and which from the host (the pigmented newt). They found that only a tiny portion of the twinned tadpole tissue was unpigmented - the notochord (plus some additional cells here and there - the technique was not completely perfect). This meant two important things: 1) The dorsal lip of the blastopore develops into the notochord. 2) The notochord patterns the tissue around it to make the primary body axis15.
Gastrulation in Evolution
In general, gastrulation involves the involution and invagination of outer-layer cells to become internalized. Other outer layer cells epibolize to cover these internalizing cells. In this way, an embryo goes from a single cell type to multiple distinct cell layers. The place where this invagination or involution (where cells internalize) occur is called the blastopore. The blastopore can be a discrete "hole" in the embryo that elongates (called an archenteron) as in the case of sea urchins (Figure 7), or it can be a broad lip of cells that narrows as epibolizing cells expand as in frogs and snails (Figures 5 and 8).
How can two such different structures be compared and even homologized? We consider gastrulation and blastopore formation to be homologous across Planulozoa (the group containing most animals, Figure 9) for two main reasons:
1. Other multicellular organisms do not undergo the massive tissue rearrangements we see in animal development. In this way, gastrulation represents an animal (or at least a Planulozoa) synapomorphy.
2. There are commonalities between various modes of gastrulation. The initial site of gastrulation is nearly always opposite the site of polar body extrusion, on the vegetal pole of the animal11. And of course the end result of gastrulation - a tube with ectoderm lining the outside and endoderm lining the inside with mesoderm or mesenchyme in the middle - is clearly homologous among planulozoans.
3.E: Cleavage and Gastrulation (Exercises)
At-home assignment
Make an illustration (by hand or computer-aided) for one of the topics/concepts we covered this week. Please cite your sources.
Group assignment
Choose a Bicoid model to explain to the class. Your explanation should include:
1) The location of mRNA and protein in the embryo
2) Any factors that impact the location of mRNA and protein (e.g. degradation)
3) How this model could be used to explain scaling in higher Dipterans (i.e. how can you use this model to build a small or a large embryo?)
4) How the model was tested and whether it held up to the test
5) BONUS: other experiments that researchers could run to test the model and what their results would tell us.
Discussion Questions and Reading Guide
The questions below were originally written for students reading Freaks Of Nature by Mark Blumberg and Endless Forms by Sean Carroll. However, the questions in bold are discussion questions that can be answered without these books.
The "Reading Guide" questions are appropriate for short homework answers and the "Discussion Guide" questions are appropriate for open in-class or online discussion.
Chapter 2 and 3 of Endless Forms
Reading Guide
1. What is a morphogen? Give examples
2. What is a homeotic change?
3. What is polydactyly? Is it a homeotic change?
4. How does the lac-z operon help explain cell-type differentiation?
5. What is the central dogma of molecular biology? At which step is the lac-z operon regulated?
6. What are the two features of gene logic in bacteria?
7. What is a homeobox and how does it relate to homeotic transformations?
8. Homeoboxes are incredibly conserved between disparate animal species, what kind of selection is this?
9. What is a conserved function of Pax-6 genes?
10. What does the Distalless gene do in general?
11. What does the tinman gene do in general?
Discussion Guide
1. What experiments showed that the "dorsal lip of the blastopore" acts as an organizer tissue?
2. What are the general properties of an organizer?
3. Freaks discussed the importance of environment and plasticity in Chapters 1 and 2, how does Endless Forms' discussion of hopeful monsters contrast with this?
4. In homeotic fly mutants, the antennae/wing look fairly normal - why is it that we recognize them as normal structures in the wrong place?
5. How do cells get differentiated and why is it important?
6. Explain the lac-z operon using the terms "cis" and "trans"
7. What did Monod mean when he said "What is true for E. coli is also true for the elephant."?
8. What are some similarities between building a fruit fly and building a human?
9. What is similar between Tinman, Pax6, Dll, and Hox genes?
10. What is the "genetic toolkit" and what are it's implications for evolution? | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/03%3A_Cleavage_and_Gastrulation/3.3%3A_The_EvoDevo_of_the_Blastopore%3A_The_Spemann-Mangold_Organizer_-_Gastrulation_in_Evolution.txt |
We already began examining Developmental Genetics and and got a taste of the complexity of genetic interactions. For example, the Drosophila gene Bicoid is transcribed into mRNA in maternal cells and pumped into the embryo. There its expression is regulated by localization signals on the mRNA, as well as degradation and localization of the protein. Bicoid protein itself acts as both a regulator of transcription and translation of downstream genes. The end effect is an embryo with different genes expressed along the A/P axis.
Now we will take a step back and look at a broader picture of Developmental Genetics, from the point of view of signaling pathways. A signaling pathway allows cells to communicate with their external environment. In Developmental Biology, this is usually cell-cell interactions. These kinds of interactions are incredibly important because each cell needs to follow its own developmental trajectory in coordination with all the cells around it. For example, imagine a growing mammalian limb bud. Each cell in the limb bud needs to know if it is on the thumb or pinky side of the limb and how close to the body it is. Not only that, it also needs to know how long development has progressed. Imagine if an osteogenic cell started forming bone matrix early in limb development. It would not undergo enough cell divisions to make the correct number of osteoblasts, leading to too little bone and an animal with a malformed limb.
The Genetic Toolkit
(An introductory PDF can be found here: Rediscovering Biology www.learner.org/courses/biology/pdf/7_gendev.pdf)
One of the major findings of Evo-Devo is that organisms share a common set of genes to build their very diverse bodies. In particular, animals share a suite of "body plan" genes that perform similar functions in development. Mixing and matching different gene expression patterns across tissue and cell types seems to be the primary mechanism for generating the unique bodies we see in each animal phylum. Novel evolutionary features (like spines, feathers, chambered hearts, tentacles, etc) appear to rely on the reuse of toolkit genes at new times and places in development (see Endless Forms for more details). Below, we will start to take a look at the genetics behind this genetic toolkit - how do these genes interact with each other?
In Evo/Devo, there are two main ways we can think about genetic interactions, but since they are interconnected so we will consider both simultaneously. One is Signal Transduction Pathways, which have an external signal (in Developmental Biology this is usually a secreted protein) that is usually received by a cell-membrane receptor that only certain cells express. When the ligand (secreted protein) and receptor bind, this triggers a cascade of protein modifications that lead to transcriptional activation of downstream genes (Figure 1).
The second way Evo/Devo thinks about signaling is Gene Regulatory Networks (GRNs). This includes the signal transduction pathway and its downstream effects on gene expression. If we turn up the expression of one gene, what other genes does it affect? GRNs are often represented as wiring diagrams with arrows and bars showing the effect of proteins on the expression of downstream genes (Figure 2).
Figure 1: Generic signal transduction pathway. An extracellular ligand binds to a membrane-bound receptor triggering the activation of a signal tranduction cascade in the cytoplasm. This cascade may be simple (as in the case of the Notch pathway below) or very complex requiring multiple steps and types of input. The final step of the transduction cascade is translocation of a cytoplasmic transcription factor to the nucleus where it will activate or inhibit the transcription of a downstream gene. An editable svg file of this figure can be downloaded at https://scholarlycommons.pacific.edu/open-images/18/ Figure 2: Partial Gene Regulatory Network wiring diagram for the specification of skeleton-forming mesoderm in the sea urchin, Strongylocentrotus purpuratus. Each gene is represented by a horizontal line attached to an arrow of the same unique color. The horizontal line indicates the cis-regulatory region of the gene and the arrow indicates transcription of the mRNA coding region. Lines emanating from the mRNA coding region indicate how the protein product of the gene regulates other downstream genes. Inputs onto the cis-regulatory regions by the protein products of other genes may be activating (arrow) or inhibitory (bar). “Ubiq” is unknown activators expressed in all cells. Figure from Dylus et al1 Published under a CC BY 4.0 license. Figure has been cropped from original.
The big picture: Cell fates are progressively restricted as development proceeds
Over the course of development all organs, tissues, and cell-types must be specified. In animals this is accomplished by repeated fate restriction2. For example, the totipotent embryo undergoes several rounds of division to form a blastula (ball of cells). Some of these cells will take on a mesodermal fate. At this point, they can become any type of mesodermal cell. In some animals experiments have been performed to show that a generic mesodermal cell can be induced by its neighbors to develop into a huge variety of mesodermal cell types3. Over time, however, these mesodermal cells divide, undergo shape changes, migrate, and differentiate. As they receive signals from their environment (mostly the cells around them) they differentiate into more specific cell types. For example, Figure 3 shows a mesodermal cell differentiating into muscle, bone, and blood cells. As time progresses, different muscle progenitor (myogenic) cells will differentiate into different types of muscle, for example smooth and striated. Each of these cell-fate decisions is dependent on the gene expression pattern in the cell, which is dependent on the cell's history and its neighbors.
We call this type of progressive differentiation "hierarchical" with more generic cell types (like mesoderm, Figure 3) at the top of the hierarchy and more specific cell types (like neutrophils) at the bottom4. As development progresses, we move down the hierarchy. Development begin axis specification, these axes are soon read out into regions - for example head, trunk/abdomen, and tail. Within these different regions tissues get specified, first at the level of germ-layers and later at more specific levels. For example, ectoderm splits into neuroectoderm and epidermal ectoderm depending on the location of the tissue. Next, cell-types within the tissues are specified. For example, neuroectoderm can become neurons or glial cells. Both of these cell types later differentiate into the many specific types of neurons and glia. At this point, cells are more or less terminally differentiated - their adult fates are specified and they cannot return to pluripotent forms. However, most cells are still receptive to the environment and can respond to environmental signals even once they are terminally differentiated. We refer to this as cellular plasticity.
The GRN in Figure 2 mirrors this hierarchy, with early acting genes at the top specifying more general tissues and later acting genes at the bottom specifying specific cell types. However, it is important to note that the genes acting at these different hierarchical levels are reused at other levels of the hierarchy and in other developing tissues. In fact, core parts of GRNs and signal transduction pathways are reused throughout development and have different outputs depending on their context. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/04%3A_Genetic_Toolkit/4.1%3A_Introduction%3A_The_Big_Picture.txt |
Cell-cell communication: Signal transduction pathways
Signal transduction pathways couple external signals to changes in gene expression within a cell. That is, an external signal triggers a cascade of biochemical changes in the cell resulting in higher or lower transcription of a set of genes. Fewer than a dozen major signal transduction pathways commonly regulate animal development5,6. Here, we will focus on four of these named after their receptor or ligand: Notch, Hedgehog (Hh), TGF-b (also called Dpp or BMP), and Wnt (Figure 4). These signal transduction pathways act as switches for Gene Regulatory Networks (discussed below) which they turn on using different mechanisms. Two main factors affect what types of patterning and specification processes a particular Signal Transduction Pathway is good for.
First, how is the signal communicated? Does it use a long-range ligand (paracrine signaling), does it require cell-to-cell contact (juxtacrine signaling), or does the ligand act on the same cell it was secreted from (autocrine signaling)? Long-range paracrine pathways, like TGF-b and Wnt are great at forming gradients across a large tissue and are often used as early morphogens patterning body axes or multiple cell types across a tissue. Short-range paracrine pathways, like Hh, often act as morphogens on a smaller scale - fine-tuning regionalization patterns. Other factors modify the signaling range of these ligands, for example the amount of ligand secreted, neutralization by extracellular matrix proteins, the number of responsive cells, and whether responsive cells are expressing inhibitors or coactivators of the target genes6. Juxtacrine signals, like the Notch pathway, involve the association of two membrane-bound receptors. In the case of Notch, this is typically a Delta/Serrate/Lag-12 (DSL)-class ligand and a full length glycosylated Notch protein. The Notch pathway is often used in on/off cell-fate decisions, famously in lateral-inhibition where an "on" signal in one cell triggers an "off" signal in all the surrounding cells.
The second important factor governing the utility of a Signal Transduction Pathway is its regulation. Most pathways can be regulated to some extent by their downstream target genes either through negative or positive feedback. In negative feedback the downstream target genes eventually turn the pathway off. For example, a signaling pathway could increase the transcription of a pathway inhibitor. In positive feedback they downstream targets keep the pathway on. For example, a signaling pathway could increase the transcription of its own receptor. Thus, negative feedback is good for promoting a transient one-time signal, while positive feedback converts a transient signal into a permanent cell-fate decision. Pathways can also be regulated by each other and their output can be modified by local transcription factors, which can differ among cell types. This topic is covered more extensively in Three habits of highly effective signaling pathways. by Borolo and Posakony.
Within the cell: Gene regulatory networks
In the early 2000s, Eric Davidson and Isabelle Peter wrote a series of papers proposing a philosophical framework for understanding Gene Regulatory Networks (GRNs). In 2011 they wrote a seminal paper on the evolution of these networks. They defined three basic types of core genetic interaction that are used to specify cell-types:
1. kernels: these are evolutionarily inflexible interactions that specify a body part.
2. batteries: These are involved in cell or tissue differentiation and are more flexible evolutionarily than kernels.
3. plug-ins: these are small sub-circuits that get used in many different developmental contexts7.
As a mother to Lego enthusiasts, I use Lego kits as an analogy to understand this. A kernel would be specialized pieces that go together, like a pair of wheels and an axle. They specify a particular function and are inflexible in their interaction - one wheel must be snapped onto each side of the axle to make it useful. A "battery" is more flexible but still usually used for a similar set of purposes. An example of this would be a literal battery pack in a Lego kit - it is used to power movement but is flexible in that it can power many types of constructions. A plug-in is similar to standard bricks, these can be used to build whatever cuboid objects your imagination suggests In order to make fancy constructions, however, you also require kernels and batteries.
How do we link these types of interactions to a developing embryo? Peter and Davidson conceive of animal development as being alternating steps of patterning and specification7. Patterning is dividing up a body or a set of tissues into smaller parts. Specification is a fate choice for the cell or tissue that was patterned. In this conception, the body axes and germ layers are first defined using body patterning genetic networks. Next, each section of the body is specified: neuroectoderm, gut, pharyngeal arches (in chordates), circulatory system, etc. Then, another round of patterning of these specified units occurs - each body part now gets patterned along its own axes. For example, the tips of the fingers vs an elbow or the anterior vs. the posterior of the heart (Figure 5).8 | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/04%3A_Genetic_Toolkit/4.2%3A_Signaling_and_Fate_Restriction%3A_Cell-cell_communication_-_Within_the_cell.txt |
The system of Signal Transduction and GRNs is incredibly flexible. Even though there are conserved units (like kernels and signal transduction pathways) the way these conserved units are connected to each other can be diverse both within a developing embryo and between different species. As new interactions evolve, this can lead to novelty. For example, the yellow box in Figure 2 contains a GRN battery that is used in skeleton formation across echinoderm classes. In the sea urchin shown this has been reused to make a special larval skeleton derived from a group of cells called the micromeres1,8 Loss of features can also be correlated with changes to connections between the genes in GRNs. For example, the gene pitx1 is a switch for skeleton patterning (it is a transcription factor that controls a battery that patterns mesodermal tissues)9. Loss of a cis regulatory element that turns it on in pelvic regions leads to a reduced pelvis. This mutation is common in freshwater fish populations, where a smaller pelvis may be beneficial, but not in marine fish populations, where a more robust pelvis may be beneficial10 (Figure 6).
There are many more examples of GRN evolution leading to changes in body plan, and we will cover some of them later. But I would like to mention one final example that you are already familiar with. The Hox genes are an animal synapomorphy, that is they are unique to the animal evolutionary lineage and found in most animals. In animals where Hox genes have been genetically examined, Hox genes are often involved in the same process - early regionalization along the A/P axis. Different sets of Hox genes are turned on at different locations along the A/P axis of the animal body. Interestingly, this appears to be an ancient conserved kernel for body patterning since many diverse species exhibit the same patterning (Figure 7).
4.E: Genetic Toolkit Exercises
Journal Club
This week's reading is Three Habits of Highly Effective Signaling Pathways
Reading Guide Questions
Signaling flips a switch
1. What are the three habits of signaling pathways?
2. What is an SPRE and what is it's significance in signaling pathways?
3. What might be the purpose of experimentally activating a signaling pathway?
Activator Insufficiency
4. Define activator insufficiency and zones of competence
5. How do the authors explain the finding that SPREs are insufficient in vitro, but sufficient in cultured cells?
Cooperative Activation
6. What is a signal-independent activator?
7. What is the purpose of co-activators?
Default Repression
8. How do developing organisms solve the problem of leaky expression?
9. Compare two types of default repression and how signaling releases the repression
Functional/mechanistic/evolutionary considerations
10. What role does chromatin modification play in develpmental signal transduction cascades?
Class Discussion Questions
Signaling flips a switch
1. Chose one habit to illustrate with a drawing.
2. Explain how Notch, Wnt and Hh accomplish transcriptional switching.
Activator Insufficiency
3. What do the authors mean when they say that signaling pathways exhibit "selective transcriptional responsiveness of target genes to pathway activity."?
4. What ways can cells limit the activation of a target gene by an activated signaling pathway?
Cooperative Activation
5. What is a potential drawback to cooperative activation?
Default Repression
6. Illustrate the different types of default repression
7. Illustrate one example of default repression
Functional/mechanistic/evolutionary considerations
8. Explain Figure 5: how is it a summary of the output of signaling pathway habits?
9. Explain how Koide et al tested whether default repression is separate from activator insufficiency.
Group exercise
This HHMI activity explores the evolution of cis-regulatory elements. You can complete the exercise without watching the suggested movie (available on YouTube and the HHMI website).
Modeling the Regulatory Switches of the Pitx1 gene in Stickleback Fish | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/04%3A_Genetic_Toolkit/4.3%3A_EvoDevo%3A_How_does_this_all_evolve%3F.txt |
Broad Scale Regionalization: Hox Genes and the Segmentation Cascade
We already took a quick look at Hox genes, both in your readings and in the Genetic Toolkit section. Now we will put them into a broader Evo-Devo context by looking at a specific example of Hox patterning (following up the The curious case of Bicoid story) and by seeing evidence that regionalization by Hox genes is conserved across animals. Some cis-regulatory elements driving Hox gene expression patterns are also conserved. However, the earlier developmental events that set up Hox expression domains are not conserved across animals, they differ widely sometimes even within a phylum. For example, even though all arthropods are segmented in Drosophila segments are patterned simultaneously, while in some other insects and arthropods they arise one at a time. The conservation of the Hox pattern despite the variability of broader A/P pattern generation suggests that Hox patterning represents a developmental constraint in animal evolution. That is, once the Hox pattern evolved, it was so advantageous that it was mostly retained for millions of years of animal evolution.
We focus on Drosophila even though it is an odd case of simultaneous regionalization because it is very well-studied and easier to understand than many other model organisms. Our look at Drosophila A/P regionalization and patterning will illustrate three major concepts in Evo-Devo:
1. There are multiple ways to get to constrained developmental stages.
2. Much of development occurs by repeatedly dividing up tissues/regions and specifying them into more restricted fates.
3. Multiple gene expression outputs can overlie each other to give a cell/tissue its specific identity.
In cleavage and gastrulation, we looked at the idea of symmetry breaking in creating axes and germ layers in animals. We also saw that opposing Bicoid and Nanos protein gradients are able to specify the first anteroposterior regionalization in developing fruit flies. But if we think about an adult fly, they have many more anteroposterior regions than simply a head and a tail. For example, only some segments bear wings or legs, other bear eyes or antennae and others have genitalia or excretory organs. How does the developing fly "regionalize" - that is go from having two opposing anteroposterior gradients to having fine-scale anteroposterior patterning? To answer this, we will look at the developmental genetics of the segmentation cascade - the series of steps that divides the embryonic fly into finer and finer subdivisions.
The Drosophila Segmentation Cascade
Here I will very briefly summarize the segmentation cascade, for more details please visit The Origins of Anterior-Posterior Polarity
The segmentation cascade is hierarchical in both developmental time and regulation of gene expression. Maternal effect genes are expressed earliest and they regulate the gap genes. Gap genes are expressed next, acting with the maternal effect genes to regulate the pair-rule genes. Pair-rule genes and gap genes regulate the expression of the segment-polarity genes, which are expressed last (Figure 1).
Figure 1: The Drosophila segmentation cascade. Drosophila divides up its segments all at once, but most arthropods (an animals in general) grow from a posterior growth zone where anterior-most regions develop first. Consider what parts of this expression and specification hierarchy might be conserved across different modes of development and which parts could not be.
From "The evolution of developmental gene networks: lessons from comparative studies on holometabolous insects" Andrew Peel, 2008 in Philosophical Transactions of the Royal Society, B. Published under The Royal Society Academic Institution Single Site Licence DOI: 10.1098/rstb.2007.2244
Maternal effect genes: Bicoid, Nanos, Hunchback, and a handful of other Drosophila genes are known as "maternal effect" genes. This means that if you mutate them in a female fly, the mutant phenotype will be seen in her offspring. Since you already know that Bicoid and Nanos mRNAs are made by the mother's cells and pumped into the oocyte before fertilization it should be pretty clear why this is. The maternal effect genes set up broad anterior and posterior regions in the fruit fly as well as dorsal/ventral regions (which we will not cover here, though it's a pretty juicy story).
Gap genes: The maternal effect genes are transcription and translation factors that affect the expression of the gap genes. The gap genes are transcription factors that are expressed in broad strips along the A/P axis (Figure 2). They are called gap genes because if one is mutated it leads to a "gap" in the embryo - the larva will be missing a large portion of its body2.
Figure 2: Gap genes. Left panel shows mRNA expression of three Drosophila gap genes, from Wikimedia commons by user Celefin. This is a derivative of an original figure by Haecker A, Qi D, Lilja T, Moussian B, Andrioli LP, Luschnig S, Mannervik, M. DOI 10.1371/journal.pbio.0050145 published under a CC BY 2.5 license Right panel shows the effect of a homozygous Kruppel mutation in an embryo. Grey shapes are denticle bands (bristles) found in each abdominal segment. The Kruppel mutant has lost 6 of these bands, corresponding with Kruppel expression over the first 6 abdominal segments. Right panel by Amanda Lo and Ajna Rivera. An editable svg version of this figure is available at https://scholarlycommons.pacific.edu/open-images/24/
Pair-rule genes: Gap genes and maternal effect genes affect the expression of the pair-rule genes - which are each expressed either in odd or even segments2. These are particularly interesting because these genes bridge the gap between regionalization and modularity. They are expressed in a modular pattern, but get their input from a regionalization pattern. Genetically, this means that the expression of each of these genes is activated by multiple combinations of gap and maternal effect proteins. For example, the even-skipped gene is expressed in 7 stripes along the A/P axis. It has 4 major cis-regulatory enhancers that control this. One element controlling stripes 3 and 7 has binding sites for Hunchback and Knirps, both of which repress the expression driven by the 3+7 enhancer (Figure 2). This enhancer is activated by the ubiquitous (expressed everywhere) activator Zelda3. The element controlling stripe 2 is even more complex with binding sites for Bicoid, Hunchback, Caudal, Kruppel, and Knirps (Figure 3)4.
Segment polarity genes: Segment polarity genes are expressed in either the anterior or posterior of each segment and help to define segment boundaries as well as the A/P patterning of each segment (Figure 4). Like the pair-rule genes, these are expressed in stripes along the entire A/P axis, rather than in a regional pattern like Maternal Effect and Gap genes. The expression domains of the segment polarity genes are regulated largely by the pair-rule and gap genes.
Hox genes: Another Level of Regionalization
While the maternal effect genes and the gap genes regionalize the Drosophila embryo to some extent, the adult animal will have an even more regionalized body. The Hox gene pattern provides segment-level regionalization. It specifies where legs, wings, antennae, mouthparts, genitalia, and other unique structures will go (Figure 5). As you already know, most animals use the Hox genes to do A/P patterning and it's a bit of a mystery how and why so many diverse early developmental strategies coalesce onto the same A/P patterning, and then diverge into diverse body plans later in development.
How conserved is the Hox patterning? First, nearly all animals have Hox genes and many of them are syntenic - meaning that the order of the Hox genes is conserved along the chromosome. This is related to the regulation of the Hox genes, they have distal regulatory factors (one of which we will see later in Ectodermal Appendages) but also have proximal regulatory factors. In vertebrates, some genes in the cluster can share regulatory factors5. Because of this, gene order matters. An analogy is: if you share a car with your neighbor, you cannot move to a new neighborhood without losing access to the car. This sharing of elements is an evolutionary constraints that has resulted in the conservation of these regulatory factors and the preservation of synteny of the Hox genes. In invertebrate lineages, synteny may be preserved due to tight clustering of the genes with each other and their proximal cis regulatory elements5. Some species and lineages however, have lost this conserved synteny, notably the nematodes and the tunicates5. Despite these losses, synteny still seems to be the rule with at least some conservation of gene order found in most phyla examined, including the most basally branching Hox-containing phylum, the cnidarians6.
Cnidarians (such as jellies and sea anemones) are an interesting case in which to look at the Hox genes because while the Hox genes are known to be conserved A/P patterning elements, the cnidarians lack an A/P axis. How can they be missing something so important? Well it's because of how we define anterior and posterior. A standard definition is that anterior is towards the head and posterior is towards the tail. What about animals that don't have an obvious head? We count their mouth and any conglomeration of major sensory organs as the head end and keep moving along their long axis to the nearest tip of the body. Typically, along the long axis of the body, the tip nearest the mouth is the anterior end and the tip nearest the anus is the posterior end. Cnidarians, however, not only lack a head they also lack major sensory organs and a mouth. Instead they have a ring of tentacles (that can point up or down depending on the species) that surrounds a single opening that serves as a mouth and anus.
Many evolutionary scenarios have been proposed to homologize the cnidarian "radial" axis with the A/P and D/V bilaterian axes. Hox genes are one way to look at this. DuBuc et al6 found that cnidarian homologs of anterior Hox genes (red in Figures 6 and 7) are expressed at the oral end of an anemone (Cnidaria) embryo and cnidarian homologs of central/posterior Hox genes (blue/green in Figure 6) are expressed at the aboral end (the end opposite the mouth/anus). They also found that Wnt, a signal transduction gene involved in many developmental processes including anteroposterior specification, was expressed between the expression domains of Ax6,an anterior Hox gene, and Ax1, a posterior Hox gene | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/05%3A_Regionalization_and_Organizers/5.1%3A_Splitting_up_the_A/P_axis%3A_Beginning-Hox_Genes%2C_Another_Level_of_Regionalization.txt |
Animal development can be seen as a series of successive fate decisions where cells take internal and external (signals from other cells) information and use it to become progressively more specified. Regionalization refers to subdividing an existing embryo or tissue into smaller parts with unique fates. This can occur at a large scale, for example Bicoid and Nanos broadly regionalizing the embryo into anterior, middle, and posterior, or it can occur at a small scale, for example Shh regionalizing an autopod (hand) into thumb and pinky sides. Regionalization typically occurs in three main steps: First, a morphogen broadly patterns a tissue by forming a gradient. Next, this gradient is read out by a series of transcription and translation factors that turn the gradient into discrete domains of gene expression. Finally (or concurrently) the cells expressing these unique combinations of genes are fated and begin to exhibit different properties. This chapter first broadly examines examples of regionalization and specification and then considers the role of organizers in these processes.
• 5.1: Splitting up the A/P axis: Beginning-Hox Genes, Another Level of Regionalization
We already took a quick look at Hox genes, both in your readings and in the Genetic Toolkit section. Now we will put them into a broader Evo-Devo context by looking at a specific example of Hox patterning and by seeing evidence that regionalization by Hox genes is conserved across animals. Some cis-regulatory elements driving Hox gene expression patterns are also conserved. However, the earlier developmental events that set up Hox expression domains are not conserved across animals.
• 5.2: Organizers-Other Organizers
One of the most interesting things about building animal bodies is the diversity we see across and within bodies. Much of this differentiation is ruled by local organizers and master control genes.
• 5.S: Regionalization and Organizers (References)
05: Regionalization and Organizers
Organizers
One of the most interesting things about building animal bodies is the diversity we see across and within bodies. For example, even though the Hox gene patterning in fruit flies and mice is very similar, the end results (an adult mouse or an adult fly) are extremely different. We see intriguing diversity within bodies as well. For example, a thoracic segment in a fruit fly might express a single Hox gene across a segment, yet parts of this segment take on many different forms. Much of this differentiation is ruled by local organizers and master control genes. These are locally expressed genes that are often expressed in many segments in similar spots. Depending on the Hox gene expressed in that segment, they will activate different body parts. For example, we will look later on at wing master control genes -these genes build wings in thoracic segments and different structures, like gin traps, in other segments. The type of wing - elytra, haltere, flying wing, etc. is also dependent on the position of the segment in the body and the species it is expressed in. For example, dragonflies have two flying wings, while the first wing in a beetle is a protective elytron, and the second wing in a fly is a proprioceptive organ.
This type of programming is known as serial homology. We will be coming back to this concept later, but it is a conceptually important idea in Evo-Devo. Serial homologs are a special type of homolog wherein the same type of tissue expressing a core set of genetic regulators (an organizer) is found in multiple spots along a body axis. One easy to understand example of serial homologs are arms and legs. Developmentally, they are nearly identical for the first part of their growth, they only grow substantial differences later. They express the same core limb genes (as we will soon consider) and have the same bones, albeit in slightly different shapes. Serial homologs are incredibly important in our understanding of evolution because they are genetically "cheap," since they use the same core gene regulatory network, but they can provide novel functions -like tool use plus locomotion. The fate of a serial homolog often depends on the Hox genes that are expressed in the region of the serial homolog organizer.
Organizer outputs are not only affected by the Hox code, they can also themselves set up the Hox code (as in the case of Nanos and Bicoid) or can set up a different axis (like the dorsoventral axis of a frog or the anteroposterior axis of a limb). Now that you have a firm grasp of gene regulatory networks, we can take a closer look at a famous organizer we have already considered - the Spemann-Mangold organizer of the frog gastrula.
The genetics of the Spemann-Mangold organizer and the notochord
If you need a quick refresher on the Spemann-Mangold organizer, check out Cleavage and Gastrulation. Briefly, the Spemann-Mangold organizer is mesoderm found at the position of the grey crescent, the dorsal pole of the frog (or newt) embryo. This organizer, as it develops into the notochord, induces the formation of dorsal structures like the central nervous system and spine. Amphibians with an extra Spemann-Mangold organizer grow a second A/P axis (conjoined twin tadpoles) and amphibians missing a Spemann-Mangold organizer develop into a "belly piece."
Using genetics, we can explain two huge questions: 1) What causes the organizer to develop? and 2) How does it induce the formation of dorsal structures? The first step in organizer formation is cortical rotation itself, as shown in Figure 1 of Cortical Rotation. In cortical rotation, microtubules rotate the outer cortex of the fertilized egg relative to the inner mass. The vegetal pole has several localized proteins and mRNAs tethered to its cytoskeleton. In the inner mass this includes VegT and Vg17,8. The outer cortex has vegetally localized Dishevelled (Dsh) protein, a component of the Wnt pathway, which is transported towards the animal pole during cortical rotation9. The displacement of Dsh creates a new zone - a part of the embryo with Dsh, but no Vg1 or VegT (Figure 8)10. Dsh helps localize and stabilize b-catenin, the transcription factor of the canonical Wnt pathway. Now we have Vg1 and VegT at the vegetal pole and Dsh and b-catenin at the future dorsal end.
Figure 8: Genetics of the Spemann-Mangold organizer. Maternally derived proteins set up an Animal/Vegetal axis in the unfertilized egg, including VegT and Vg1 in the Vegetal pole inner cortex (orange). After fertilization, cortical rotation brings the Vegetal pole outer cortex protein Dishevelled (Dsh, green) into contact with the Animal inner cortex, driving the accumulation of b-catenin in dorsal cells. Vegetal pole proteins activate the expression of TGFb (BMP) and Nodal. Nodal converts the adjacent Nodal- cells into mesoderm (red), resulting in a stripe of mesoderm just above the vegetal pole. Meanwhile, b-catenin enhances Nodal expression in the dorsal-most part of the embryo - resulting in high Nodal expression in the dorsal vegetal inner cortex. This, plus b-catenin, drives the expression of organizer genes like Chordin and Noggin, while repressing ventral mesoderm fates like muscle. Chordin and Noggin specify the notochord, which will elongate and induce the dorsal ectoderm (all ectoderm is blue) that lies over it to become neurectoderm. BMP represses organizer activity on the ventral side of the embryo, in particular ventral ectoderm will form skin, not neurectoderm. The notochord itself has a leading (anterior) and lagging (posterior) edge which express different genes and will induce different parts of the central nervous system.
An editable svg file of this figure is available at https://scholarlycommons.pacific.edu/open-images/27/
As cleavage proceeds, VegT and Vg1 induce the expression of Nodal (specifically Xenopus nodal related protein or Xnr) in the vegetal-most cells. These cells will become the endoderm. Nodal, a homolog of TGFb, signals to nearby cells lacking Nodal (Nodal- cells), these cells will become the mesoderm. Nodal expression is also induced by b-catenin. This makes a gradient of Nodal that is higher at the dorsal side, where it is induced by VegT and Vg1 as well as b-catenin. While b-catenin is stabilized in a wide swath of dorsal tissue, Nodal expression is restricted to the vegetal side of the embryo where it is expressed all over, but highest where b-catenin is present (Figure 8). Where Nodal signaling meets mesodermal cells with high b-catenin, we see the expression of a new suite of genes - the organizer genes Chordin, Noggin, Frizzled, and more (Figure 8)11.
These organizer genes are transcription factors and members of signal transduction pathways. Some of them will specify the organizer mesoderm as "dorsal" (notochord and somites) and some of them will signal to the overlying ectoderm during gastrulation and specify it as "neural" rather than epidermal. The physical mechanics of this process are fascinating, and we can study them later if you are interested, but for now I will focus just on the genetics and briefly summarize the tissue movements. As you saw before, mesodermal organizer cells undergo involution at the dorsal lip of the blastopore and crawl along the overlying ectodermal cells to form a thick layer beneath them. Most of the mesoderm in the gastrulating embryo expresses BMP4, a TGFb family secreted protein. This BMP4 signals to the overlying ectoderm to become epidermis. However, the organizer expresses BMP4 antagonists, like Chordin and Noggin12. This causes the ectoderm above the organizer mesoderm to take on neural fates.
The organizer itself is not a homogenous structure, it is made up of several cell populations that express different signaling genes and transcription factors. For example, the leading edge of the organizer (the part that will invaginate first and become the anterior-most notochord) expresses a Wnt and BMP4 antagonist called Cerberus13. Cerberus and other leading edge genes specify the anteriormost portions of the notochord via gene regulatory networks that will ultimately lead to expression of forebrain gene Otx214 in the overlying ectoderm. Organizer cells trailing this leading edge express the secreted signaling molecule FGF, which drives the expression of midbrain gene Krox20 in the ectoderm above it. Both Otx2 and Krox20 help make the Hox gene expression pattern, along with other organizer genes expressed in an anteroposterior pattern in the notochord14. In this way, the notochord is able to direct the anteroposterior patterning of the neural tube (Figure 8).
Other Organizers
There are a multitude of other organizers in developmental biology and their fundamental properties give us insights into the genetics of evolution. They are specified by external factors, for example by the intersection of Nodal-adjacent and b-catenin expressing cells in the Spemann-Mangold organizer. They act on other tissues via secreted signaling molecules, for example chordin inhibiting BMP4 to specify neurectoderm. And their activity on other tissues can vary over time and/or space, for example the ability of the notochord to induce both anterior and posterior nervous system structures.
The notochord has a third organizing activity on the ectoderm (not to mention it's organizing activity on the mesoderm), this is patterning the D/V axis of the neural tube. During gastrulation, the ectoderm lying over the notochord responds to signals from it to fold up into a tube and sinks under the epidermis. This tube is polarized into the dorsal side (close to the overlying epidermis) and the ventral side (close to the notochord). A Shh signal from the notochord drives Shh secretion from the ventral side. This Shh gradient opposes a dorsal BMP (TGFb family) gradient initiated by epidermal signaling (Figure 9).
These two opposing gradients lead to gradients of active transcription factors responsive to these signal transduction pathways and the expression of genes with cis-regulatory elements responsive to these transcription factors (Figure 9)15. Le Dreu and Marti name 11 distinct domains identified by unique transcription factor expression and neuronal subtype15.
Another famous organizer is one that you encountered in Intro Bio: the tetrapod limb organizer. This is a two-part organizer, with a long thin swath of cells at the distal-most point of the limb expressing and secreting growth-promoting FGFs, and the posterior-most point of the limb expressing Sonic Hedgehog (Shh, Figure 10). The FGF portion of the limb is called the Apical Ectodermal Ridge. It is the signaling center that keeps the limb adding more distal elements onto the end. In this way, the more proximal elements, like the humerus and elbow, develop first. More distal elements, like forearm, wrist, and hands, get laid down later. Interestingly, this system seems to be on a timer, rather than being strictly spatially patterned. If cell-division is inhibited midway through arm development, radius, ulna, and humerus can be small or absent, with a normally proportioned hand and shoulder girdle. This looks somewhat similar to gap mutant in Drosophila, though the developmental mechanism is completely different.
Figure 10: The tetrapod limb organizer. The apical ectodermal ridge (AER, red) secretes FGFs that keep the underlying cells proliferating and maintain Shh signaling from the Zone of Polarizing Activity (ZPA, blue). The Shh protein secreted from ZPA cells forms a gradient along the A/P (thumb/pinky) axis of the limb. Low/no Shh specifies thumb and index finger fates, high Shh specifies pinky and ring finger fates. What happens if we add Shh to the other side of the developing limb? Image from wikimedia commons user Peteruetz under a CC BY-SA 3.0 license
The Shh signaling center is a true organizer. It not only secretes a signaling molecule like the AER, but this signaling molecule acts in a graded fashion. High levels of Shh result in the development of posterior elements of the limb, like the radius or pinky, while low levels result in the development of mid-elements, like the middle fingers, and absence of Shh leads to anterior elements, like the thumb.
In general, signal transduction and transcription factor cascades are responsible for much of the patterning of the developing embryo. This gives us a big hint as to how evolution can act on development to change adult morphology. Small changes in the amount or location of a morphogen can have big effects on the adult. The same "toolkit" of genes is conserved in evolution, but is also reused in many different contexts. For example Shh's role in patterning your Central Nervous System as well as your hands. This reuse of toolbox elements in new contexts gives them new functions - depending on the local activator and repressors found there, the signal transduction pathway genes available, as well as epigenetic chromosomal modifications already present. So far we have mainly focused on gradients and organizers in patterning, but in Patterns we will look at a couple of other ways to pattern an embryo. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/05%3A_Regionalization_and_Organizers/5.2%3A_Organizers-Other_Organizers.txt |
In Genetic Toolkit, we examined how gene expression (and cell fate) is determined by local activators and on/off signal transduction pathways. We considered "wiring diagrams" for understanding how master regulatory genes can affect a suite of downstream genes in competent cell types. In this module, we will take a brief look at how these switches can evolve taking both organismal complexity and genetic complexity into consideration.
06: Genetic Basis of Complexity
Mutations and selection
Evolution at the genetic level begins with mutations generating genetic variants. Variants can be selected for or against if they affect fitness and thus increase or decrease in frequency in a population. If there is no selection on the variant, we say it is "neutral". In this case, it is subject to genetic drift and will increase or decrease in frequency just by chance. Most mutations in animals are in intergenic regions, but some will naturally occur in genes. We usually think of these genic mutations as the ones most likely to be seen by selection. If we are looking over long-ish periods of evolutionary time, we will likely not see many mutations that reduce fitness since these should be weeded out by natural or sexual selection. Instead, we expect to see mutations that are:
1. neutral (no effect on fitness)
2. nearly neutral (very little effect on fitness)
3. buffered (invisible due to epistatic effects) or
4. positive (positive effect on fitness)
When we compare sequences of homologous genes (genes that come from the same common ancestral gene) we can run analyses to tell us whether the sequence is under "positive" or "purifying" selection. Genes under purifying selection have had mutations "purified" out. In this case, there is one "best" sequence and most species in a taxon will have very similar sequences of this gene. When mutations arise in the gene, the individuals carrying the mutations tend to have lowered fitness and will not produce many offspring carrying those mutations. Comparing the sequences of distantly related species we see fewer differences than we would expect to see by chance (or neutral genetic drift).
Genes under positive selection show the opposite - more differences in genetic sequence in a taxon than we would expect to see by chance. A positively selected gene has had a history of mutations that gave individuals higher fitness. These mutations were different in different lineages, giving rise to species with different sets of positively selected mutations. In summary, if most mutations in a gene will make it less functional and result in a negative effect on fitness, we might expect to see purifying selection on that gene (i.e. most mutations will be weeded out by natural selection, Figure 1). But if there are specific mutations that function better in different ecosystems, we might expect to see positive selection on that gene (i.e. different mutations will prevail in different environments).
To find out whether a gene is under positive or purifying selection, we compare the gene sequence across organisms. If one species or lineage has many functional changes in a gene compared to its relatives, we say that the gene is under positive selection. If there are very few functional changes between distantly related species, we say that the gene is under purifying selection. Under purifying selection new gene variants (alleles) tend to decrease fitness. This could be because the gene is already at peak fitness or because the gene affects multiple processes (pleiotropy).
The "background rate" of mutation over evolutionary time can be estimated by the accumulation of neutral (or nearly neutral) mutations. These are mutations that should not change the function of the gene. The easiest place to look for these are synonymous changes to the DNA sequence. Synonymous changes are mutations in protein-coding DNA that do not affect protein sequence. These are often in the third codon. Nonsynonymous changes can affect function by changing the protein sequence Because synonymous changes don't affect protein function, we can use them to estimate the rate of neutral drift.
In the example shown, mouse, human, and snail sequences in a protein coding region are compared. DNA sequence that is the same for all species is shown in red. Pairwise comparisons counting the number of mutations that result in a amino acid change (NS for nonsynonymous) are compared to the number of mutations that do not result in an amino acid change (S for synonymous). When the number of S changes is higher than the number of NS changes, the gene is likely under purifying selection. That is, the number of functional changes is much lower than the number of neutral changes. When the number of S changes is lower than the number of NS changes, the gene is likely under positive selection.
Mutation location in a gene
In the section above, we categorized mutations by their effect on the phenotype. We can also categorize mutations by their position within a gene. There can be mutations in a coding region or mutations in a cis-regulatory region (there can also be mutations in a "junk" region but we don't need to consider those here).
Cis-regulatory mutations can change the expression pattern of a gene and cause loss of expression, lowered expression, increased expression, or ectopic expression (expression in a new place and/or at a new time). If the gene mutated is a regulatory gene itself, this can also have downstream effects on the expression of its targets. Overall, cis-regulatory mutations can change the "cellular fingerprint," which is the suite of genes expressed in a certain cell that gives that cell its identity and function. This can change the way a cell "behaves", both in terms of its own anatomy and physiology as well as the way it interacts with the cells around it, potentially even changing their fate via cell-cell signaling.
Mutations in coding regions can change the structure and function of a protein or RNA. These changes can be strictly structural in that they affect cellular anatomy, physiology, and/or cell signaling. For example, a mutation in the functional protein Myoglobin can change how well a muscle cell stores oxygen. On the other hand, a mutation in the Wnt pathway receptor Frizzled can change whether a cell is responsive to Wnt signaling. The Frizzled mutation isn't just structural since it might also affect target gene expression, turning Wnt-pathway targets on or off in a new pattern.
Generating mutants
A third way to categorize mutations is by examining their physical effect on the genome - did the mutational event delete a large portion of the genome? Did it convert one nucleotide into another? The three main types of mutation we will consider are:
1. Point mutations: converting one nucleotide pair into another
2. Indels: Insertions and deletions that add or remove nucleotides from the genome. These can be caused by transposons, slippage during replication, or DNA repair enzymes.
3. Duplications: This is a specific type of insertion mutation that inserts a piece of existing genetic sequence into a new locus without removing it from the original locus.
Of these three, duplications and insertions can add genomic complexity. Here I am defining complexity as the number of unique parts in a system. Genomic complexity would be increased if we add in new genetic information. It seems straightforward to imagine a case where an increase in genomic complexity would result in an increase in organismal complexity. For example, we add in an extra gene for digesting amylose and we increase the amount of grain we can eat - diversifying our diet and making it more complex. However, we can also increase genomic complexity without increasing organismal complexity and we can even increase organismal complexity without increasing genomic complexity. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/06%3A_Genetic_Basis_of_Complexity/6.1%3A_Types_of_Selection%3A_Beginning_-_Generating_Mutants.txt |
Increasing genomic or organismal complexity
The case where we increase genomic complexity without a concomitant increase in organismal complexity is fairly elementary. An insertion mutation can add in new "junk" DNA to an intergenic region, or an intron that has no effect on phenotype. Likewise, a duplication mutation (a type of insertion) could duplicate a gene that simply does the exact same job as an existing gene. In both cases, genomic complexity is increased while organismal complexity stays the same.
Increasing organismal complexity without increasing genomic complexity is more interesting. In this case, a point mutation or a deletion affects cis regulatory regions or coding regions in a way that increases the function or expression of a gene product. For example, imagine amylase (an enzyme that digests amylose starches), which is normally expressed in the small intestine. Local activators are present all over the digestive system (including the stomach, mouth, and intestines), but a switch regulated by an signalling pathway is only activated in the small intestine. A series of point mutations in the cis-regulatory regions of amylase now create a novel local activator response element (Figure 2). In a way, this could be seen as an increase in genomic complexity because a new binding site was added, but seen from another point of view, the overall number of nucleotides remains the same. This novel cis regulatory region turns on amylase in the mouth, so now salivary glands produce amylase and starch digestion can begin earlier, diversifying the diet of the animal. In this case, the species has maintained the number of genes and the number of nucleotides in the genome but organismal complexity has increased due to an new cis regulatorysite (figure 2).
Exonic (coding) mutations can also increase complexity, without adding genes or nucleotides to the genome. For example, imagine a mammalian protein with two domains - a functional domain and a repressor domain. The repressor domain can be ubiquitinated to inhibit the protein under particular conditions. In this case, our protein is a leg organizer. The repressor domain is bound by Hox genes of the trunk, limiting leg organizer expression to the region anterior to the thoracic and posterior to the lumbar regions of the body. Along with other limits to expression, this results in an animal with two pairs of legs. A point mutation that converted a protein-coding codon to a stop codon (a nonsense mutation), at the end of the functional domain, would result in a protein missing the repressor domain. This would cause ectopic activation of leg organizer activity and (potentially) additional legs (Figure 2).
Increasing organismal and genomic complexity
Genomic complexity can be added, at the small or large-scale, and it can occur over cis-regulatory or coding regions. It can involve horizontal transfer from another genome or duplication of elements already present in the genome. Here, we will consider different ways to add genetic complexity and how they might affect organismal complexity. I will focus on duplication rather than horizontal transfer for simplicity but similar consequences can occur with horizontal transfer as well. Smaller scale duplications can occur via errors in DNA replication, errors in meiotic crossing over, or transposon insertion. Larger scale duplications can occur via errors in meiotic crossing over, transposon insertion, or whole chromosome duplication via missegregation of chromosomes during cell division.
Small scale duplications can duplicate a single functional domain (like a bHLH domain), a single coding sequence, a single gene, or a single cis-regulatory protein binding site. In the case of the cis-regulatory binding site, the initial mutation might increase or decrease expression in target cells. Additional point mutations in the binding site could optimize for binding of a related protein. This would have the effect of driving ectopic gene expression and potentially new function. If the new site binds to a new local activator, then ectopic gene expression can occur in cells that express these activators when they also have an activating signal transduction pathway turned on. The new site alternatively could be a Signal Pathway Response Element (SPRE) in which case it will turn on expression ectopically only when the initial local activators are present.
Duplicating a gene (or at least a coding region) can have one of three major effects: creation of a pseudogene, DDS (duplication, divergence, subfunctionalization), or DDN (duplication, divergence, neofunctionalization). Pseudogenes do not add organismal complexity, but subfunctionalization and neofunctionalization potentially can. Under both DDS and DDN, we see a release of purifying selection due to the redundant duplicate protein (or RNA). Under DDS, a potentially pleiotropic protein is duplicated and now each duplicate can optimize for a subset of the original functions. This can lead to higher fitness and/or increased organismal complexity. Under DDN, one of the two redundant copies randomly acquires a new function that can then be optimized, as it is not under pleiotropic constraints. This new function increases organismal complexity.
Larger-scale duplications can also occur over either cis-regulatory regions or protein-coding/gene regions. The duplication of an entire enhancer element could potentially affect transcription either by acting on gene expression directly or by binding to and sequestering transcription factors present in the cell. An enhancer element can also be inserted into a new genomic location via transposon insertion or errors in crossing-over. In this case we would expect ectopic gene expression driven by this new element.
Larger-scale duplications over multiple coding regions include the duplication of the Hox-genes. This leads to multiple Hox-clusters in a single animal. An ancient duplication of the Hox-cluster gave rise to the Hox and Parahox clusters. Hox genes act in regionalizing the anteroposterior axis, mostly by acting on the ectoderm and mesoderm, of animals while Parahox genes are generally involved in endoderrmal and central nervous system patterning. Further Hox duplications (as seen in the whole-genome vertebrate duplications) allowed Hox genes to pattern new axes - like the vertebrate limb axis. Likewise, release of pleiotropic constraints on duplicated nervous system patterning genes may have given rise to the neural crest in vertebrates. This "fourth germ layer" plays important roles in patterning craniofacial structures as well as our enteric nervous system, adrenal gland, and other complex structures.
6.E: Genetic Basis of Complexity Exercises
In-class Lab
One way to increase genetic complexity is to duplicate a protein-coding gene. The Ortholog/Paralog Mini Lab explores using bioinformatics to generate hypotheses of orthology and paralogy. You will need one computer (chromebook or tablets are fine) per group for this lab.
Other Reading
For a slightly different take on homology, orthology and paralogy, check out this Microbial Genetics chapter.
Homologs, Orthologs, and Paralogs | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/06%3A_Genetic_Basis_of_Complexity/6.2%3A_The_Evolution_of_Complexity%3A_Increasing_Genomic_or_Organismal_Complexity.txt |
We have already discussed how graded morphogens can give polarity to an embryo (e.g. Bicoid) or to a tissue (e.g. Shh and TGFbs). This covers much of developmental patterning. In this section I will summarize some other types of patterns that we see in development, both repeated patterns, like spots and stripes, as well as tissue shape and size patterning (called morphometrics). To start out, I will cover a simple mathematical model that has been used to help explain stripe and spot patterns that we see in many tissues. But it's important to keep in mind that 1) this is only a model and does not approach the true complexity of actual biological systems and 2) it does not explain all stripe and spot patterns - for example the Drosophila segmentation pattern, which is set up by graded morphogens.
• 7.1: Turing Patterns to Generate Stripes and Spots
The Turing "reaction-diffusion" model uses a two-protein system to generate a pattern of regularly-spaced spots, that can be converted to stripes with a third external force. In this model, there is one activating protein that activates both itself and an inhibitory protein, that only inhibits the activator. By itself, transient expression of the activating protein would only produce a pattern of "both proteins off" or "spot of inhibitor on".
• 7.2: A Turing-like Model for Generating Stripes in Digit Development (Rivera and Ramirez)
If you think about the growth of your limbs, you imagine a tiny tissue with a little bone (that will become the humerus or femur) growing right in the middle. This bone is specified early on by Sox9, a transcription factor also involved in sex-determination. As the tissue grows longer and wider, two parallel bones appear (the radius and ulna or the tibia and fibula). The tissue grows longer and wider still, and five parallel bones appear - the metacarpals and eventually phalanges.
• 7.3: Lateral Inhibition in Nervous System Patterning
Drosophila neuroblast formation differs in one very important way from a traditional Turing pattern - each neuroblast arises in isolation from other neuroblasts. This patterning is not over an entire tissue, but is super local, occuring only over a 6-7 cell cluster with only a single cell becoming a neuron.
• 7.4: Size and Shape
The final type of developmental patterning that evolution can act on is the size and shape of tissues or organs. These are generally considered "morphometric" scaling issues and are classified as "allometric" changes. Morphometrics is the study of how a continuous geometry (like the outer surface of a body) can be warped. Allometry studies this in the context of evolution and development.
• 7.E: Patterning Class Activity and Discussion
• 7.R: Patterning References
Thumbnail: An example of a natural Turing pattern on a giant pufferfish. (CC BY-SA 3.0).
07: Patterning
Alan Turing was a British mathematician who was a cryptographer and a pioneer in computer science. As a side hobby, he was also a theoretical biologist who developed algorithms to try to explain complex patterns using simple inputs and random fluctuation. His "reaction-diffusion" model uses a two-protein system to generate a pattern of regularly-spaced spots, that can be converted to stripes with a third external force. In this model, there is one activating protein that activates both itself and an inhibitory protein, that only inhibits the activator1. By itself, transient expression of the activating protein would only produce a pattern of "both proteins off" or "spot of inhibitor on" since the activator would activate the inhibitor, thus turning off the expression of the activator (Figure 1 case). Things get more interesting when the molecules can diffuse or be transported across the tissue. In this case, the activator gets randomly turned on and it begins to diffuse away from its point source, activating itself in nearby cells. At the same time, it activates the inhibitor, which also diffuses away from the point source, inhibiting the activator. Depending on the timing on activation and diffusion or transport, this can result in the formation of an expanding ring of activator expression (Figure 1 equal rates). To get spots, however, we need two more layers of complexity. First, there must be random fluctuations in expression that turn the activator on at low levels across a tissue. Second, the activator must diffuse more slowly than the inhibitor. In this case, random spots of activator can be stabilized when they are far enough away from each other. Each of the small spots activates the expression of activator (which does not diffuse away quickly) and inhibitor (which diffuses away too quickly to completely eliminate activator expression from the initial point source). This gradient of inhibitor diffusing from each spot keeps any nearby cells from making activator. The overall result of this is a regular pattern of spots (Figure 1 bottom and side panels). The exact patterning depends on the size and shape of the tissue, the speed of activator and inhibitor diffusion, as well as any other patterning elements that might be present.
Can Math Explain How Animals Get Their Patterns? How Alan Turing's Reaction-Diffusion Model Simulates Patterns in Nature
In a very long and narrow tissue, there is only one direction diffusion can occur and this converts the Turing spot pattern into a stripe pattern (Figure 2). Similar forces, like directional growth and a morphogenic gradient, can also convert the spot pattern into stripes2. Without an external force, the default should be spots or a meandering labrinthine pattern, depending on the properties of the activator and inhibitor. Hiscock and Megason propose four main ways to get a stripe pattern. Besides making diffusion more likely in one direction than another, a tissue can be subject to a "production gradient." This gradient is a protein or transcriptional/translational cofactor that causes higher gene expression of both the activator and inhibitor on one side of the tissue. Computational models predict that this type of gradient causes stripes to orient themselves perpendicular to the gradient (Figure 2)2. Stripes will orient parallel to a "parameter gradient," where the activating and inhibitory properties of the two proteins are higher at one end of the tissue than the other. This type of modification could be produced by a gradient of a protein or cofactor that binds to the activator and both prevents it from activating gene expression and from being inhibited by the inihbitor (Figure 2)2. Finally, the tissue can grow directionally. For example, your limbs developed largely by growing away from your body (distally), with a much slower rate of growth in other directions. This is due to the AER at the distal-most part of the limb bud causing cell proliferation underneath it. A computational model shows that a reaction-diffusion Turing model will generate stripes parallel to the direction of tissue growth (Figure 2)2. A minilab helps us explore these models further with an online tool. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/07%3A_Patterning/7.1%3A_Turing_Patterns_to_Generate_Stripes_and_Spots.txt |
Your limbs first begin growing as a small nubbin off your torso. As cells proliferate, a small rod of skeletal tissue begins to grow right in the middle. This will become the humerus or femur. This skeletal tissue is specified early on by Sox9, a transcription factor also involved in sex-determination. As the limb tissue grows longer and wider, two parallel bones appear (the radius and ulna or the tibia and fibula). The tissue grows longer and wider still, and five parallel bones appear - the metacarpals and eventually phalanges (Figure 3).
Figure 3: Parts of the Tetrapod Limb. Left panel is an image from wikimedia commons (Peteruetz) published under a CC BY-SA 3.0 license. Right panel shows a basic model of tetrapod limb development. As each cartilage condensation (blue, Sox9) forms, it becomes repressive to the formation of nearby condensations. The diffusion and strength of repression give a "wavelength" shown in purple, outside the wave, condensations can form (X-axis is proximal-distal axis and Y-axis is strength of repression). The yellow region is a region of instability (high concentration of FGFs from the Apical Ectodermal Ridge) where condensations cannot form. As the limb grows larger, there is room for more condensations with the same wavelength. An editable svg file of the right panel can be downloaded at https://scholarlycommons.pacific.edu/open-images/32/
An early model for limb development proposed that an inhibitory diffusable morphogen is made by the cartilage condensations (that will later become limb bones). In the early limb bud, this inhibitor can diffuse across the entire tiny tissue, so only one condensation is laid down forming the large bone of the stylopod. As the limb grows longer and wider, the inhibitor cannot reach high enough concentrations to cover the entire width of the limb bud and two condensations form (the parallel bones of the zeugopod) form. In the developing autopod, the tissue is wide enough to support 5 mutually-inhibitory condensations - the five digits of the foot or hand (Figure 3)16. Several Turing models can generate a stripe pattern like this including the Activator Inhibitor model and the Substrate Depletion model (Figure 4).
Figure 4: Two Turing models for digit stripes. The model on the left is an Activator Inhibitor Model where diffusible activator V activates itself as well as diffusible inhibitor W. Inhibitor W inhibits itself and activator V. The cs represent different interaction strengths.
The model on the right is a Substrate Depletion model, where diffusible activator X uses up (or inhibits) substrate Y. Thus substrate Y inhibits itself by activating it's own inhibitor. To test between these models, the expression of molecules thought to be involved in the process can be assayed. If the expression patterns are overlapping (graph on the left) then the Activator Inhibitor model is supported. If the expression patterns are complementary (graph on the right) then the Substrate Depletion model is supported.
Figure modified from original figures by Marcon et al, 201621 originally published under a CC BY 4.0 license
Experiments on proteins expressed in either the interdigit areas or digits provided support for the Substrate Depletion Model17. However, these experiments also showed that instead of single proteins, digit patterning is actually specified via several interacting signaling pathways. Bmp, Sox9, and Wnt form the core components of the patterning that generates the "wavelength" of digit distance. All three of these genes form expression gradients, with the highest Sox9 in the middle of the digits and the highest Bmp and Wnt in the interdigits (Figure 5)17. Bmp expressed in the interdigit areas represses itself but diffuses outward to activate Sox9 in the nearby cells (the future digits). Sox9 represses Bmp, ensuring Bmp is only expressed in the interdigits. Wnt ligands are ubiquitous, but its targets (including b-catenin) are only expressed in the interdigits. Loss of b-catenin results in an expansion of Sox9 expression and an expansion of b-catenin expression reduces Sox9 expression, suggesting that Wnt/b-catenin is a repressor of Sox919,20. These interactions give a model where the digits form in a regular pattern with a wavelength specified by the strength of the Bmp/Sox9/Wnt interactions and the ability of Bmp and Wnt to diffuse (Figure 5)17.
Figure 5: The Raspopovic et al.17 model for digit specification. Sox9, the primary digit marker, specifies cells to form skeletal condensations. It is expressed in the cells that will become digits in the autopod. In this model, Sox9 (blue) is the activator and it interacts with the BMP and Wnt signaling pathways. Autopods are shown as grey circles in the left column with color-coded expression patterns. Sox9 and Smad (purple, output of the BMP pathway) are expressed in the digits while BMP (green) and b-catenin (red, output of the Wnt pathway) are expressed in the interdigits.
The left column shows the Turing model for these interactions. The top model was originally proposed by Raspopovic et al17 and subsequently refined by Marcon et al21. The Marcon et al model maintains the centrality of Sox9, which represses its own expression outside the condensation. Sox 9 inhibits the Wnt pathway, which represses b-catenin and other target genes in the Sox9 zones. b-catenin represses Smad, which is a target of diffusible BMP signaling. The inhibitory action of Smad on BMP ensures that BMP is not active in the Smad-expressing cells, giving these two members of the BMP pathway complementary activation patterns.
The bottom right panel summarizes the output of the complex Marcon et al model.
Modified from Marcon et al21 originally published under a CC BY 4.0 license
An editable svg version of this figure can be dowloaded at: https://scholarlycommons.pacific.edu/open-images/33/
Figure 6: Modifying the wavelength. The paddle-shaped autopod should allow for additional condensation formation as it grows. This should lead to additional bones in the distal portion of the autopod or branching of existing condensations (top panel).
Hoxd13 mutants give phenotypes like the top panel suggesting that Hoxd13 modifies the wavelength of the Sox9 condensations. Hoxd13 diffuses from the Apical Ecodermal Ridge and forms a gradient (yellow). Where Hoxd13 levels are high, the wavelength (or interdigit space) is large. Where Hoxd13 levels are low, the wavelength is small. The modulation of Hoxd13 levels and/or its ability to regulate the wavelength results in unbranched digits17,18.
An editable svg version of this figure can be dowloaded at: https://scholarlycommons.pacific.edu/open-images/34/
But there's one big problem with this. Unlike the zeugopod and stylopod, the autopod is paddle-shaped. That means that it grows wide quickly during development, making a tissue that should support more cartilage condensations at the tip than near the wrist by the proposed model (Figure 6). This problem is solved by Hoxd13. Hoxd13 is a a Hox gene that helps pattern the hands, feet, unrinary tract, and reproductive organs. In the hands and feet (autopods) it is expressed in a gradient, with the highest levels near the Apical Ecodermal Ridge (AER) at the tip of the limb bud. Hoxd13 stabilizes the digit number in two ways. First, it acts as a "no patterning zone." In the region with highest Hoxd13, the expression of Sox9 is unstable and new condensations cannot form. Further away from the AER in an area of lower Hoxd13, new Sox9-driven condensations can form. Even further away from the AER, where there is no Hoxd13 expression, the existing condensations are stable. No new condensations will form even as the tissue grows wider. Hoxd13 also stabilizes digit number by increasing the ability of Sox9 to inhibit Bmp and Wnt. This has the effect of making the digit wavelength wider in the distal portion of the autopod, repressing the development of additional digits there (Figure 6)18. In Hoxd13 mouse mutants, the cartilage condensations of the autopod branch in the distal portions, following the natural wavelength of the Bmp/Sox9/Wnt interaction18.
Figure 7: Mutations in regulators of Sox9 expression. Sox9 is normally expressed in vertebrate skeletal elements (future bone and cartilage). On the left is the typical Sox9 expression pattern in the autopod. The middle column shows normal expression of three morphogens involved in Sox9 patterning in the autopod.
Hox13 (purple) comes from the AER and forms a gradient that is higher at the distal end and lower at the proximal end.
b-cat (beta-catenin, red) is highest between the digits (in the interdigits).
BMP (green) is highest everywhere except the skeletal elements, including in the interdigits.
Loss of function mutations in each of these genes reveal their function in tuning the Turing mechanism for digit formation. Hox13 normally establishes a longer Sox9 wavelength in the distal end of an autopod. Hox13 mutants exhibit the proximal wavelegth at the distal end - resulting in branched digits. b-cat normally prevents Sox9 from being expressed in the interdigits. b-cat mutants exhibit skeletal elements across the autopod. BMP normally causes the secretion of Smads, which cause the expression of Sox9 in cells not expressing BMP. BMP mutants result in a loss of skeletal elements. Figure by Desmond Ramirez
Dr. Desmond Ramirez, PhD is a Postdoctoral Fellow working in the Katz Lab at UMass, Amherst.
Learn more about his work at https://desmondramirez.wordpress.com/ | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/07%3A_Patterning/7.2%3A__A_Turing-like_Model_for_Generating_Stripes_in_Digit_Development.txt |
Not all cells in a nervous system can be neurons. In fact, in our own central nervous systems about half to 3/4 of the cells are glial cells3. In Drosophila, neural progenitor cells (neuroblasts) are only a portion of all the neurectoderm cells. These neuroblasts express proneural bHLH transcription factors including Achaete-Scute complex genes. The Achaete-Scute complex (Ac-Sc) is a cluster of 4 bHLH genes whose protein products form homo- and hetero-dimers to regulate the transcription of neuronal genes. Cells expressing Ac-Sc delaminate from the neurectoderm sheet and eventually give rise to neurons4. Before I summarize Turing pattern-like mechanism for neuroblast specification, I first want to mention that Drosophila neuroblast formation differs in one very important way from a traditional Turing pattern - each neuroblast arises in isolation from other neuroblasts. This patterning is not over an entire tissue but instead is super local, occurring only over a 6-7 cell cluster with only a single cell becoming a neuron (Figure 5)5.
After proneural cluster specification, random oscillations of Notch signaling pathway components occur until one cell randomly expresses higher levels of Delta, the Notch ligand. This activates Notch signaling in neighboring cells. The activation of the Notch signaling pathway causes the expression of Hes gene Enhancer-of-split, which is a repressor of the AcSc complex. AcSc normally increases the expression of Delta, but in these Notch positive cells where AcSc is off Delta levels begin to go down. In the neighboring Delta positive cell, there is no Notch signaling to turn off AcSc (because of the lack of Delta in all neighboring cells) and Delta levels remain high. In this way, one cell in the proneural cluster is Delta/AcSc positive and the neighboring cells are Notch/Hes positive6 (Figure 3). This system creates one Delta postitive cell in a field via lateral inhibition. In the Turing model, Delta would be the local activator and Notch would be the repressor. Delta activates its own expression by not turning off AcSc and activates Notch in neighboring cells. Unlike the Turing model, Notch and Delta do not need to diffuse for this to work, instead the signal itself is propagated by cell-cell signaling.
Graded morphogens, reaction-diffusion, and lateral inhibition are all ways to generate patterns that are either repeating (like spots and stripes) or polarize a tissue. If you have ever been to the beach or taken a physics course you know that another way to generate a repeating pattern is with an oscillator that outputs a wave function. If you haven't taken physics (or are rusty) the easiest way to think about waves and oscillators is to imagine holding a rope that is tied to a pole. As you move your arm up and down, you act as the oscillator, moving from the high position to the low position. The range of motion of your arm determines the height of the wave. You can make the waves move faster (with higher frequency) by moving your arm more quickly. The speed of the oscillator determines the speed at which the waves move. If your arm moves too slowly, the wave disintegrates quickly and never makes it to the wall.
Waves and oscillators also occur in biological systems. One of these is the segmentation oscillator in vertebrates. In this case gene expression of Notch pathway genes act as the oscillator. A "clock and wavefront" model has been proposed to describe segmental patterning in vertebrates. Segmentation of the mesoderm surrounding the notochord (the somites) occurs in an anterior to posterior fashion, with somites budding off a posterior zone of unsegmented mesoderm. As new somites bud off, old ones are pushed anteriorly, such that the anteriormost somites bud first. The "segmentation clock" is the oscillator in the pre-somitc mesoderm at the posterior of the animal. A "wave" of hes-class gene expression travels across the presomitic mesoderm (PSM). When it reaches the anterior-most point of the presomitic mesoderm it arrests and the tissue buds off the PSM. The marker telling the tissues when they are far enough anterior are opposing gradients of retinoic acid (RA) in the anterior and FGFs in the posterior. When a wave of hes expression reaches low/moderate levels of each gradient molecule, this signals the tissue to undergo somitogenesis (somite budding)7.
In the video above, Hes gene expression in the PSM is in blue and in the somites it is red. So the question you might be asking now is "How does Hes act as an oscillator but also travel in a wave?" The wave you are seeing in the video above is a wave of gene expression. The cells themselves move very little. Imagine a stadium full of people doing "the wave." If the wave takes 1 minute to get around the stadium, it can be propogated by a coordinated audience if each person raises their hands for 1 second every minute.
The people themselves aren't running around the stadium, rather they are "oscillating" between arms up and arms down. Similarly, in the PSM each cell is oscillating between Hes on and Hes off. Just like a stadium wave, cells are testing their local environment to coordinate with nearby cells. When the wave arrives at low levels of FGF and higher levels of RA it stops, just like a wave hitting a wall, and the cells with matching expression patterns bud off the PSM as a somite (Figure 6).
How does Hes act as an oscillator and how do cells coordinate with each other? We don't 100% know the answer to this, but there is a lot of evidence that Hes is a cell-intrinsic oscillator and the Notch pathway (controlling Hes expression) helps to coordinate neighboring cells. Hes genes are transcription factors and some Hes genes inhibit their own expression. When protein levels of Hes are high enough, transcription levels go down. These Hes mRNAs and proteins also have a short half life, so when transcription levels go down, they don't stay down for long. As the mRNA and proteins degrade, repression of Hes expression is released and mRNA is made again. Of course, this raises the level of Hes protein, which represses Hes expression. In this way Hes expression acts as an oscillator, as long as it maintains at least a low level of expression and degrades quickly. In mice, degradation of protein occurs within 20 minutes. Stable mutants that last for 30 minutes have dampened oscillatory behavior, just like raising and lowering your arm too slowly when making rope waves7. Oscillation is a intrinsic property of the cells, it can occur in cell culture after serum treatment, but this oscillation is uncoordinated between cells - after a few cycles where all cells show the same periodicity of oscillation, they begin to loose coordination and oscillate on their own wavelength8,9.
As you can see in the video above, cells in the presomitic mesoderm tend to have the same state of Hes oscillation as their neighbors. This is likely coordinated through the Notch signaling pathway. As we've already seen, the Notch pathway is a juxtacrine signaling pathway with cells next door to each other communicating through cell-membrane receptors. Once activated, Notch undergoes intramembrane cleavage and the cytoplasmic half travels to the nucleus where it releases repression on Su(H) class transcription factors to activate gene expression of effectors like the Hes genes (hairy/enhancer of split genes also called Her genes). By signaling to each other, the PSM cells may exerting positive feedback on their neighbors such that Notch-positive cells induce Notch signaling in next door cells10. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/07%3A_Patterning/7.3%3A_Lateral_Inhibition_in_Nervous_System_Patterning.txt |
The final type of developmental patterning that evolution can act on is the size and shape of tissues or organs. These are generally considered "morphometric" scaling issues and are classified as "allometric" changes. Morphometrics is the study of how a continuous geometry (like the outer surface of a body) can be warped. Allometry studies this in the context of evolution and development. One of the people who defined the field, D'arcy Wentworth Thompson, came up with morphometric changes that allow one known species of fish to be warped into another known species (Figure 7).
While the extent of the role that allometry plays in evolution isn't totally clear, we know from examples that it does play some role. It's easy to see this if we look around at related species. For example, hominid skulls are very alike and often differ in ways that are easily explained by small variations in developmental growth patterns. Extra or earlier cell proliferation here, less or later cell proliferation there. While we know many genetic markers of cell proliferation (for example cell-cycle regulator Cyclin D1) increase cell-proliferation, there are many different upstream activators of proliferation depending on tissue/cell-type and developmental stage. To begin to understand the role of allometry in evolution, researchers compare tissue growth and the regulators of that growth between fairly closely related species.
Two places where both the development and evolution of size and shape changes are fairly well understood are beak shapes in birds and elytra in beetles. One of the most famous examples of evolution is Darwin's Finches. This group of finches underwent an adaptive radiation on the Galapagos Islands beginning about 2.3 million years ago12. Since then, the finches have adapted to different island niches into 14 different species. Comparing beak morphology between these species uncovered two conserved allometric programs for changing cell proliferation patterns. In early development, beak width is regulated by levels of BMP4 - higher BMP4 means a deeper and wider beak. For example, ground finches have high BMP4 expression in a region that signals to the predominate skeletogenic region of the early beak - the pre-nasal cartilage (pnc)13. Likewise, high levels of calmodulin next to the pnc are associated with longer beaks, like the beaks of cactus finches (Figure 8).
Slightly later in development, an upper beak structure called the pre-maxillary bone (pmx) begins to grow. This will eventually form the parts of the upper beak that structurally and functionally differ between many bird species. This part of the beak also expresses different sets of genes in different beak shapes. TGFβ receptor type II (TGFβIIr), β-catenin, and Dickkopf-3 (Dkk3) are all signal transduction cascade genes that are expressed at much higher levels in the large ground finch beaks compared to smaller beaked finches. These three genes were expressed in broader domains in larger beaks than in smaller beaks when looking at all five species in the figure above (Figure 9)14.
These findings buoyed the idea that allometric growth can fuel rapid evolution by changing the scale of a particular feature. Changing the scale just refers to scaling something up or down, making it larger or smaller in one or all dimensions. For example a large square is simply a scaled-up version of a small square. A rectangle would be a square that has been scaled larger in one dimension but not the other. Researchers noticed right away that simply changing scaling of the upper beak could explain a lot of the variation in Geospiza and this could be explained by the coordinate system of genetics above (or even a simpler genetic system). However, scaling wasn't enough to explain the variation in other related finch species. To explain that variation, researchers found that both scaling and shearing had to be considered. Shearing refers to a geometric transformation like that seen in the fish example from Thompson et al. above. In a shear transformation, each point moves along x at a distance proportional to its y coordinate (or vice versa) giving a diagonal line from a straight line. Shearing plus scaling was enough to explain at least the length and depth axes of the finch beaks studied (Figure 10)
The next question to answer is how broadly applicable is this coordinate system for beak shape transformation? Increasing or decreasing the expression levels of these genes does change chick beak shape in the ways predicted by Mallarino et al.14. This information might lead us to predict that evolution would use this coordinate system to make the wide variety of beaks that we see in living and fossil birds. However, studies of non-Geospiza finches show that evolution is more variable than we might imagine. If we have time, we will discuss the paper: "Closely related bird species demonstrate flexibility between beak morphology and underlying developmental programs". | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/07%3A_Patterning/7.4%3A_Size_and_Shape.txt |
Assignment 1
Choose one of the stories from How the Snake Lost It's Legs. and summarize the information for the class.
End your summary with at least one "future directions" question for us to consider in class.
Assignment 2
The questions below were originally written for students reading Endless Forms by Sean Carroll. However, the questions in bold are discussion questions that can be answered without these books.
The "Reading Guide" questions are appropriate for short homework answers and the "Discussion Guide" questions are appropriate for open in-class or online discussion.
Discussion Questions
1. Do you think our "sense of wonder and beauty is diminshed or enhanced by scientific understanding?"
2. Why do we think it is "easy" for butterflies to evolve new wing patterns but less easy to evolve new biochemical pathways (like new pigments for example)?
3. What kinds of lab experiments can give us insight into butterfly wing Evo-Devo?
4. What is the difference between morphological convergence and genetic convergence?
5. What changes besides protein changes in MC1R could lead to changes in animal coloration?
6. Can convergent evolution of a trait be driven by different genetic mutations?
7. Why do we know more about coloration in fruit flies than in zebras and leopards?
8. Draw a butterfly wing with a maximum ground plan and one with fewer pattern elements.
9. What are three butterfly wing inventions?
10. How is Bicyclus an example of plasticity? What is the switch that regulates this plasticity?
11. Explain the genetics and selection driving melanism in rock pocket mice.
12. What is Bard's model for zebra striping?
Endless Forms Reading Guide: Chapter 8
1. What is Batesian mimicry?
2. What are the serial homologs in a butterfly wing?
3. What is a wing scale? Is it homologous or homoplasious to a fish scale?
4. What is an eyespot focus and why do we call it an organizer?
Endless Forms Reading Guide: Chapter 9
1. What is disruptive coloration?
2. What is melanin?
3. What genetic changes drive melanism? Are these cis-regulatory or exonic? Why don't they affect other developmental processes?
4. What is the significance of MC1R in humans?
5. What causes white spots on mammals?
6. What is fitness?
7. What is a selection coefficient?
8. Give two reasons why we might not see spotted mice in nature.
In-class Activity (Mini-Lab)
Reaction Diffusion Simulator
Note: If possible this is ideally run in a computer lab or with loaner laptops. Otherwise, ask students ahead of time to bring in at least one laptop per group. Students can follow the questions below or can be given minimal instructions and just "play" with the simulation.
In the Turing Model, the pattern is changed by adjusting the speed of diffusion, the strength of interaction, and the rate of degradation. In the Grey-Scott model simulation, the feed rate is related to the speed of diffusion and the death rate is related to the rate of degredation.
1. To see the a "boring" pattern, choose a feed rate of 0.006 and a death rate of 0.028. Click anywhere on the canvas.
2. Choose the present "Solitons" and click anywhere on the canvas. This feed/death rate combination produces a field of equally spaced spots. How does this relate to the Turing model?
3. Adjust the feed rate to 0.02 and the death rate to 0.058, how does this affect the spot pattern you saw in Solitons?
4. Can you adjust the feed and death rates to produce stripes?
5. What happens if you click on the canvas while a pattern is being generated. What would this represent biologically?
6. What kinds of biochemical/molecular properties might affect feed and death rates?
Suggested Journal Club Paper
Closely related bird species demonstrate flexibility between beak morphology and underlying developmental programs.
7.R: Patterning References
Further Reading
Elytra evolution. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/07%3A_Patterning/7.E%3A_Patterning_Class_Activity_and_Discussion.txt |
• 8.1: What is an Evolutionary Novelty?
A novelty as a new structure or property of an organism that allows it to perform a new function, thus opening a new "adaptive zone". In this reckoning, a novelty allows an organism to exploit a new ecological resource and should lead to an adaptive radiation.
• 8.2: Case Study - The Evolution of Insect Wings
Insect wings are an incredibly important novelty associated with the radiation of the insects into one of the most diverse clades on the planet. They occupy land, water, and air and eat almost every food source imaginable. While their origin seems almost "out of the blue," careful developmental and paleontological studies have revealed key insights into their evolutionary history.
• 8.E: Novelty Discussion
• 8.S: Novelty (Summary)
08: Novelty
For discrete objects and characters it is easy to see what is new or novel. For example, if I went skydiving, that would be a novel experience for me since I've never been skydiving before. If we put a human on Mars, that would be a novel scientific undertaking for the human race. However, evolution often does not work with discrete characters, instead lines are blurred and fuzzy. For example, we might think of bat wings as a novelty in vertebrates since they are a synapomorphy (shared, derived, defining character) in the bat lineage. Bats invented something new - membranous wings. However, it could also be argued that this is simply a "functional innovation," that is, an elaboration of an existing structure to perform a new function. In this sense, bat wings are simply elongated forelimbs with some extra skin. So what counts as a novelty, exactly? To be direct about it, there really isn't one single definition that can be defended. The confusion seems to stem from our own biases regarding the characters we find interesting and "novel," like feathers, hands, and faces, which all had different evolutionary origins and trajectories.
Given that there isn't a single agreed upon definition of novelty, probably due to the fact that evolution doesn't follow strict patterns, how can we think about this subject at all? In 1963, Ernst Mayr, one of the founders of modern Evolutionary Biology defined a novelty as a new structure or property of an organism that allows it to perform a new function, thus opening a new "adaptive zone". In this reckoning, a novelty allows an organism to exploit a new ecological resource and should lead to an adaptive radiation1. A major flaw in this definition, however, was pointed out in 2008 by Massimo Pigliucci. He noted that some "novelties", like the mammalian inner ear, didn't lead to adaptive radiations and thus wouldn't fall under this definition2. We can broaden the definition to include any character that is unique to a taxon3, however it defies credulity to consider a character like an extra bristle on a crustacean antenna as an evolutionary novelty. Pigliucci combines these two definitions to say that novelties are unique characters that define a taxon that also have a novel function in their ecosystem. This means that they don't necessarily lead to an adaptive radiation, but they still do increase fitness compared to the ancestral state2. I personally like this definition in that it gives us two clear things to look for in a novelty: 1) It's actually new and 2) It does something for the organism. However, this definition is pretty broad and fuzzy. Under it flight feathers in birds, a novelty that allowed them to take to the skies and inhabit the most remote spots on earth, are placed at the same level as a functional protein mutation in a bacterium that gives it 10% greater capacity to digest pesticides.
What is an adaptive radiation?
An adaptive radiation is the rapid evolution of a lineage to fill multiple open ecological niches. One of the most famous adaptive radiations is the evolution of the Galapagos Finches (also called "Darwin's Finches"). When an ancestral population of finches reached the Galapagos Islands the islands had no other similar species with which to compete. The multiple open niches, like feeding on flowering cacti, hard seeds, small seeds, and insects, imposed disruptive selection on the birds. That is, finches with beaks better adapted to eating insects were selected for as were finches with beaks better adapted to eating hard seeds. Finches with intermediate phenotypes (mediocre at eating either food source) were selected against. Over long periods of time, this led to speciation of the finches into at least 12 distinct species each exploiting a slightly different food resource.
Image From "Voyage of the Beagle", Public Domain
One of the luminaries in the field of evolutionary novelty, Gunter Wagner, has created a definition of novelty that can help to direct research programs. His definition is more functional and specific than other definitions. By his reckoning there are two types of novelties:
• Type I, a new body part that is not strictly homologous to other body parts and
• Type II, a novel variant on a body part that allows for a new function.
A Type II novelty would include the evolution of fins in marine mammals - this is just a reconfiguration of an existing body part. In the case of Type II novelties the homology to ancestral body parts is clear, in a Type I it shouldn't be4. By this definition, we have to decide what we consider to be compelling novelty and what we consider to be compelling evidence. For example, we might decide that mammary glands - derived from hair glands - are novel since we personally feel they have enough differences from hair glands to be independent evolutionary units, but decide that the shiny scales of garfish (ganoid scales) are too similar to standard fish scales to count. In the latter case, we ignore the novel compounds that create the shininess.
Wagner has addressed the problem of using our own perspective to decide what counts as a novelty or not by defining novelties as being associated with novel core Gene-Regulatory-Networks (GRNs). Positional information can vary between species (see the Bicoid example!) but this evolutionarily variable positional information is read out by an evolutionarily stable core-GRN. This core-GRN specifies the tissue by activating "realizer-genes", sometimes called "structural genes". These are the genes that do the business of giving an organ it's functional properties. This realizer-gene output, like the positional information, is also changeable. The realizer-genes can be modified by adaptations to local environments4,5. Since the core-GRN is the stable component of the genetics underlying the development of the novel organ, a novel core-GRN thus is associated with a truly novel organ.
While I truly like this definition because of its simplicity - to understand how novelty arises we just go after those novel core-GRNs that define the novelty - it does have its weaknesses. A technical weakness is that we cannot be sure of the genes that make up a GRN with our current technology. For example, it's easily possible to miss a gene when sequencing transcriptomes, or for plastic developmental programs to compensate for a gene we CRISPR out of the genome. A more philosophical weakness is that in our own hubris it is very easy to shift the boundaries of what we consider to be the core-GRN and equally easy to ignore evidence of the same or similar core-GRNs in clearly non-homologous tissues (like the Notch/Hes interaction being a core-GRN in non-homologous segmentation in some annelids, arthropods, and vertebrates). That said, there does appear to be mounting evidence that, at least in some cases, we can associate a novel organ with a novel core-GRN4.
For now, we will try taking the best of all these definitions to examine some interesting characters that have evolved in various groups. We can even try to define them as novel (or not) by these definitions. We will look at comparative developmental biology and genetics of several key "innovations" (a term that has to do with function rather that distinctiveness). In this chapter, we will look at one ectodermal novelty, insect wings. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/08%3A_Novelty/8.1%3A_What_is_an_Evolutionary_Novelty%3F.txt |
Insect wings are an incredibly important novelty associated with the radiation of the insects into one of the most diverse clades on the planet. They occupy land, water, and air and eat almost every food source imaginable. While their origin seems almost "out of the blue," careful developmental and paleontological studies have revealed key insights into their evolutionary history. Unlike insect legs, which form on the ventral side of the body, wings are dorsal appendages. This alone suggests a separate evolutionary origin from legs since they are not serially homologous. But, like legs, wings are found only on the thoracic segments - suggesting that Hox genes limit the expression of wing organizer genes. The insect body plan has three thoracic segments - T1, T2, and T3. Of these, only T2 and T3 build wings. In Drosophila, the T3 wings are reduced and form tiny halteres, which are proprioceptive organs. In beetles like Tribolium, which has been the focus of several wing development studies, the T2 wing forms an elytron (plural: elytra), a hard protective covering (Figure 1).
The Hox gene Scr represses wing development in T1, lowering Scr expresssion in Tribolium beetles gives an extra T1 outgrowth that resembles an elytron6. Looking more closely at the T1 tissue that forms the extra elytron in Scr- beetles, researchers in the Tomoyasu lab found that it is made up of two separate tissues, both of which normally express a gene called Vestigial6. Vestigial is normally expressed in early wing tissues (called "wing discs") but is also expressed in a few other tissues in the insect body. The Tomoyasu lab was very intrigued by the fact that two non-wing Vestigial expressing tissues were repressed from coming together to form a wing by Scr. These two tissues are called the pleural plate (the ventral-most tissue, referred to as "pleural") and the carinated margin (the dorsal-most tissue, referred to as "tergal"). The Tomoyasu lab hypothesized that wings evolved from these two body wall tissues fusing together and growing out of the body (Figure 2). Some evidence from this comes from comparing insects to crustaceans (Note here that I use "crustacean" to refer to all non-insect pancrustaceans but "crustacean" is not a true evolutionary clade).
Insects and crustaceans form a monophyletic clade called Pancrustacea and they share the same overall body plan. However, insects have derived limbs that are similar across the clade, while crustaceans in general have much more diversity. Ancestrally, pancrustaceans were marine organisms and had branched limbs, with one branch forming structures like gills. Insects obviously don't use gills, since they live on land and not in water, so the gill-forming structures in crustaceans are thought to form the pleural plates in insects. If the Tomoyasu hypothesis is correct, then insects have an ancestral gill forming structure joining up with a portion of the dorsal body wall (tergal location) to form a new appendage - the wing (Figure 2).
The Tomoyasu lab garnered more evidence for this when they looked for other serial homologs of wing tissue in abdominal segments. They found repeated Vestigial gene expression in dorsal body wall structures called "gin traps". These are defensive structures found in Tribolium pupae but disappear by adulthood. They express other wing-specifying genes like Vestigial, Apterous (Ap) Nubbin, and Disheveled (Dsh). Interestingly, they are formed on the abdomen, a part of the body in insects that is famous for not growing limbs. The lab also found a second tissue that expresses wing-specifying genes, the ventral carinated margin (Figures 1 and 2). The lab used the wing and gin-trap marker Nubbin to follow the development of both the carinated margin and the gin trap7.
When the researchers experimentally lowered levels of abdominal Hox genes Ubx and AbdA, they found that instead of gin traps, they got a fusion of the two Nubbin-expressing tissues. This fused tissue later formed a wing-like outgrowth in an abdominal segment (Figure 3). This suggest an evolutionary scenario wherein the pancrustacean ancestor had two Vestigal/Nubbin expressing tissues in its abdominal and thoracic segments. The tergal tissue would become part of the body wall and the pleural tissue would join the ventral legs to become the gill-branch. When insects moved to land, however, the gill-forming tissue was up for grabs since gills were no longer selected for. In the abdomen, the gill-forming tissue becomes part of the body wall, but in the thorax, it fuses with the Vestigial/Nubbin expressing tergal tissue to form wings. In the abdomen, where wing formation is suppressed, the tergal Vestigial/Nubbin tissue is free to take on a new fate. In the case of Tribolium, it forms a defensive structure in the abdomen, the pupal gin-traps (Figures 3 and Figure 4). In the thorax it forms the carinated margin. In this way, the wings are a novelty, but can also be thought of as serial homologs to the pleural plates+carinated margin in the thorax as well as to the gin-trap+pleural tissue in the abdomen.
Variations on a theme
Case study: bat wings
Brand new stuff:
Case study: placenta
8.E: Novelty Discussion
What counts as novelty?
(Note: This is intended as an online Discussion Board homework, it could also be modified for use in a classroom discussion)
Todd Oakley (an expert in the genetic basis of novel features in evolution) sparked an interesting Twitter and Amazon book review discussion on how to define novelty.
Please read his blog post linked here and discuss the following questions with your classmates:
1. How would you define novelty?
2. Is there a fundamental difference between microevolution and macroevolution?
3. Do you agree with McShea and Brandon's rule of macroevolution (that complexity and diversity increase unless opposed)? Why or why not?
4. What does Dr. Oakley mean when he says that novelty happens at the macroevolutionary scale but not at the microevolutionary scale? | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/08%3A_Novelty/8.2%3A_Case_Study_-_The_Evolution_of_Insect_Wings.txt |
Evolvability has emerged as the connection between population-level evolution and macroevolution. Although both of these processes are fundamentally the same (both occurring through mutation, drift, and selection), they happen at such different scales that we typically use very different tools and mindsets to study each of them. For example, population-level evolution is often modeled with Hardy-Weinberg related equations examining the fitness and prevalence of particular alleles. On the other hand, we typically study macroevolutionary change by comparing distinct species using the fossil record and molecular genetics. The question is, then, how do we go from here to there? How do these micro-level processes eventually result in macro-level patterns? Evolvability is one useful way to approach this. A population is "evolvable" if it can cope with changing environments via adaptation. That is, if genetic mutations in the population have a good chance of increasing fitness.
While at the surface level, this seems simplistic, we can follow it to deeper levels to see how the evolvability of a population affects developmental processes whose evolution underlies macroevolutionary changes. Gerhart and Kirschner tackle this in their paper the Theory of Facilitated Variation. In this paper they identify major routes by which developmental genetic changes can "facilitate" (or help increase) phenotypic variation without compromising fitness (i.e. they increase evolvability).
These routes, termed weak regulatory linkage, exploratory processes, and compartmentation, are summarized below:
Ability to engage in weak regulatory linkage
Linkage occurs between processes that are connected to each other or to the same specific conditions. For example, when you are cold you shiver and get goosebumps. These two processes are connected to each other via a condition (cold) and also via the sympathetic nervous system. Likewise, developmental processes can be linked via shared gene regulatory networks and/or via shared regulatory components (for example genes that are expressed in response to the same transcription factor, or signal transduction pathways that respond to the same signaling molecule).
Weak regulatory linkage refers to linked processes that are regulated by simple inputs that do not provide much information to the processes. We have seen examples of this in Habits of Highly Effective Signalling Pathways, where a transcription factor releases repression on a set of downstream genes. These genes self-activate via local activators as soon as the inhibition is released suggesting there could potentially be multiple ways to de-inhibit them. This is considered weak regulatory linkage because the regulation by the transcription factor is "weak." When local activators are present, the default for the process is "on". The transcription factor is only needed to release inhibition. Once this inhibition is released, a cascade of gene expression can occur, resulting in a complex process with large developmental or physiological consequences. In this way a complex process can be turned off or turned on in new places with small-scale regulatory changes. For example, the transcription factor expression can be turned up or down, or other proteins can act to modify the ability of the transcription factor to bind to its target DNA.
In general, weak regulatory linkage occurs when a simple signal can trigger multiple complex processes depending on the cellular context. Gerhart and Kirschner note that this increases the plasticity of a system since small changes to the regulatory factors (transcription factors for example) can change the functional output of a complex system. The complex system itself is largely self-regulating, requiring only a trigger from the regulatory factors. In this way, development can occur more slowly or more quickly in certain conditions, choices between two tissue states (e.g. gonad type) can be modified by environmental factors, etc.
Exploratory processes
Exploratory processes are search and find processes like following a chemical cue gradient to a point source. We see this type of process in development when we examine how axons form during neurogenesis and how vasculature arises to feed organs and tissues. We see it in adults in the vertebrate adaptive immune system and foraging behavior in chemically-guided organisms like ants. We say that this type of process shows robustness because it adapts quickly to local environmental changes. For example, with strict XY grid patterning of vasculature, growth over developmental time would need to be under strict control and size/shape variance in organs would not be tolerated. Small blood vessels, however, do not grow due to a coordinate system, rather they grow based on a "supply and demand" system with outgrowths to regions of low oxygen. Cells secrete a protein signal (VEGF) when they are low on oxygen, promoting blood vessel growth towards them2.
Exploratory processes are also adaptable over evolutionary time since they allow for size and shape variance. This is important within populations, where individuals may vary in size or shape. But it is also important over longer periods of evolutionary time as these flexible patterning processes will form a useable system based on their simple set of rules for growth. For example, transplanted leg discs in insects become innervated as do ectopic limbs in chick embryos3,4. In this way, exploratory processes facilitate evolution by helping to build a viable body when other morphological components have evolved into more fit conformations.
Compartmentation
In plants, the ability to separate the the light reactions from the Calvin Cycle of photosynthesis either temporally (as in CAM plants) or spatially (as in C4 plants) has lead to incredible success and diversity in these plant types as they are no longer reliant on keeping their stomata open during the hottest and dryest (but also sunniest) parts of the day. In our own cells, we can see compartmentalization of our mitochondria, with the intermembrane space about 10 times more acidic than the lumen. This allows for the proton motive force to be concentrated and also protects the pH of the rest of the cell. Our cells also physically separate cell-cell signaling from transcriptional regulation - allowing modification of signaling pathways dependent on cell history (development) and environment.
When one compartment of an organism (or cell) can act semi-independently of another, we expect higher variation. That is, each compartment can run its developmental program via activation and inhibition of specific GRNs without disrupting the development of other compartments. In this way, gene expression changes that affect only one or a few compartments might be limited in effect. Evolution thus may be able to act on compartments individually, as long as these are expression changes like transcript number, protein isoforms, or post-translational modification. Protein-coding mutations, on the other hand, could potentially act on many compartments at once. Evolution can potentially act on individual compartments via gene expression changes, while exploratory processes can maintain the robustness of signaling and nutrient pathways across the entire body.
Evolvability in animals relies on two competing types of development:
1. Processes resistant to evolutionary change. These include exploratory processes that use external signals to find the most efficient or most effective morphology, leading to retention of the process of. But these can also include processes that are conserved over long evolutionary periods of time due to physical or genetic constraints.
2. Changable processes. These include processes that change over time because they are either compartmentalized or are co-opted onto other robust developmental programs. Compartmentation (a process resistant to change) allows for physical separation of developmental processes, and weak regulatory linkage allows for co-option of processes to new times and places (for example compartments).
In this way, evolutionary change happens on a background of robust processes. Some of these robust processes are malleable in developmental time (like vascularization), while others are constraints - limiting what is possible in a particular evolutionary lineage. One example we have already considered is tetrapod limb evolution. While there are physical and genetic constraints on this limiting the number of bone condensations per developmental section, these constraints also create compartments - the stylopod, zeugopod, and autopod as well as the 5 digits. Size variation and adaptations to the compartments is supported by robust exploratory processes, linking bone development to supporting musculature, vasculature, and innervation.
Further Reading
Deep homology (genetic constraints): https://www.sdbonline.org/sites/fly/lewhelddeep/deephomology.htm
Bauplans (developmental constraints): https://evolution-outreach.springeropen.com/articles/10.1007/s12052-012-0424-z
Genetics is modulated by environment, this modulation can be short-lived (like getting a tan) or long-lived (like getting insulin-resistant diabetes). It can even span generations (thrifty epigenotype). How does this "plasticity" arise in genetics and how does this change how evolution works?
http://science.sciencemag.org/content/357/6350/eaan0221.long: If you get your 23andme genotype done, it will only tell you what your risk is for certain disease and disorders. Why can't we be sure? | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/09%3A_Evolvability_and_Plasticity.txt |
This section examines the evolution and development of specific novel traits including ectodermal appendages (like hair and sweat glands), lactose tolerance in adults, and eyespots in butterflies (thumbnail image).
Several of these sections were written by students as they took Evolutionary Developmental Biology as part of their final projects.
10: Case Studies
Ectodermal appendages are organs associated with the skin like feathers and hair. We typically only call vertebrate skin elaborations "ectodermal appendages" even though other animal groups have skin organs (like glands) as well. In this section we will just focus on the vertebrate appendages with a special focus on the mammary glands. Details on this as well as a summary of the development of other skin organs can be found here: Mechanisms of ectodermal organogenesis.
Ectodermal appendages (or organs) have common developmental patterning and are thought to have a common evolutionary organ as well, with co-option of elements from different appendage types occurring frequently. These appendages are first obvious as a thickening of the epidermis to form a "placode." This is followed by cellular proliferation of the epidermis and condensation of underlying mesenchymal cells of the dermis to form a bud with a thick mesenchymal base. The ectodermally derived bud can now undergo one of multiple trajectories, which it chooses based on signals from the mesoderm - the mesenchyme of the dermis as well as the somitic mesoderm (Figure 1). We roughly classify these appendages into two main groups: the oral appendages, including teeth and salivary glands, and the skin appendages, including feathers, scales, hair, mammary glands, sweat glands, and oil glands.
Early on, scientists noticed something interesting - once an ectodermal placode was in place, it could be induced to form one of many tissues. For example, mammary bud mesenchyme can stimulate the formation of mammary glands in dorsal epithelium2. One interesting experiment showed that mouse dental mesenchyme could even induce teeth in chick oral epithelium, despite the fact that birds do not ordinarily grow teeth3. As discussed earlier, ectodermal appendage development follows the trajectory of general to specific (Figure 2) with the early placodes being less specified than later buds.
Evolution and Diversity of Tetrapod Skin Appendages
Fishes have their own amazing and diverse skin appendages including the "lateral line" organs that detect electrical fields, pressure and water flow changes4. However, here we will focus on the ectodermal appendages of the tetrapods with a focus on the mammary glands of Mammalia. The ancestral tetrapod is hypothesized to have had mucus glands in its skin, similar to those in living amphibians. These mucus glands keep the skin moist and prevent the internal parts of the animal from drying out. Additionally, mucus glands and other skin glands are used by brooding modern amphibians to keep their eggshell-less eggs from drying out in terrestrial ecosystems and may have played a similar role in early tetrapods (Figure 3).
About 350 million years ago, one group of tetrapods, the Amniota, evolved a new type of skin protein that prevented their skin from drying out: keratin. All amniotes (including mammals, birds, lizards, etc) have alpha-keratin and the sauropsids (birds and other reptiles) additionally have beta-keratin, which they use to build feathers and scales. Unlike egg-laying mammals, sauropsids have calcified eggshells which reduce water loss. The egg-laying mammals (the monotremes like platypus), have parchment shelled eggs that can dry out quickly. This is thought to be the ancestral condition for the group containing the mammals, the synapsids, and glandular skin secretions from the brooding parent (like mucus secretions in salamanders) are thought to have helped prevent egg desiccation in ancestral synapsids including mammals5.
The ancestral mammal thus inherited glandular skin that was multifunctional: it likely secreted oil, sweat, and other dilute secretions (possibly a form of sweat) to keep it's eggs hydrated. We can get some hints as to how these skin glands diversified into multiple ectodermal appendages by comparing the three living clades of mammmals the egg-laying monotremes, the therian marsupials, and the therian placentals (also known as the eutherians). Mammals have four main types of skin glands, these are the wax producing glands of the ear (which we will ignore for now, the sebaceous glands that produce oil, the sweat glands, and the mammary glands. The last three of these glands have special anatomical relationships with each other. A typical hair follicle is associated with a sebaceous gland and can also be associated with an apocrine sweat gland. The mammary glands in some species are associated with a hair follicle as well as a sebaceous gland. This has led to the hypothesis that mammary glands are at least partly derived from apocrine sweat glands (Figure 4).
Figure 4: Comparison of mammalian skin glands. The APSU (apo-pilosebaceous unit) is a common type of skin gland found in the armpit and groin of humans. It consists of a sebaceous gland, a hair follicle, and an apocrine sweat gland. Apocrine glands secrete by pinching off part of a secretory cell and releasing it into the duct. This is very different from typical (eccrine) sweat gland that secrete by exocytosis and are found all over the skin of humans. The MPSU (mammolobular-pilosebaceous unit) is thought to be a derived APSU with apocrine mammolobular secretory cells replacing the sweat-gland cells. A mammary gland contains one or more MPSUs and a nipple (in most cases, though some mammals like monotremes lack nipples).
Overview of mammary gland development
Despite the diversity in their final forms, mammary glands develop along largely similar pathways across mammals. As shown in Figure 1, they are induced by underlying mesenchyme and other signals to form two parallel mammary lines, which are likely induced by the Gli3-induced secretion of FGF10 by a subset of the somitic mesoderm, driving the expression of Wnt10b in the overlying ectoderm and specifying mammary cell fate6. Monotremes retain mammary lines as patches of milk-secreting cells. Cross-talk between the epidermis and dermis (mesenchymal) generate a mammary bud, which grows downward into the mesenchyme to form a mammary sprout. In therians, the mammary buds and sprouts receive BMP4 signaling from the underlying mesenchyme to continue to prevent them from taking the default hair-follicle fate6. In other parts of the skin, Noggin and Shh inhibit BMP4 and allow the default hair fate6. The epithelial mammary buds express PTHrP (Parathyroid Hormone related Peptide), which activates its receptor in the mesenchyme to induce condensation and differentiation of the growing mammary primary sprout. Thus there is cross-talk between the epidermis and dermis (mesenchyme) to generate the mammary bud and induce growth into the primary sprout. In some placental mammals like mice the primary sprout grows deeply into hypodermal fat tissue where it begins to branch into alveolar glandular tissue. In other mammals it branches more shallowly into secondary sprouts, which themselves branch into alveolar glandular tissue8.
Where did the hair go?
If mammary glands evolved from hair follicles and their associated glands, what happened to the hair? While many placental mammals have aereolar hair (Figure 5), most do not have hair associated with the part of the nipple that secretes milk. Additionally, no placental mammals examined develop a hair follicle during or before formation of a mammary sprout. I will get back to the placental mammal issue in a moment, but first I'd like to spend a little time looking at our hairy-aerola cousins.
Monotremes, those basally branching mammals, do maintain hair association with mammary glands (Figure 4). Oftedal proposes that this is the ancestral mammalian case and that mammary hairs, rather than a nipple, have a dual use: they not only wick milk from skin glands into the mouth of an infant, but they also wick moist secretions onto dessication-prone eggs. The evolution of internal embryonic development and live-birth in the therian mammals changed the evolutionary pressure on the milk-producing glands. They lost the selective pressure to keep eggs hydrated and instead were selected on solely for nourishment of infants. This may have driven the milk ducts to condense and flow into a single nipple per mammary gland, rather than a dispersed hair patch (Figure 6)5,8.
Evidence from mammary gland development in therian mammals lends some support to this hypothesis. In marsupials, early mammary gland development proceeds as a physically condensed version of monotreme development. In monotremes, a single mammary primary sprout develops into a hair follicle, a sebaceous gland, and mammary secretory and ductal cells (the multi-component MPSU). In marsupials, a single primary sprout forms multiple MPSUs, each with its own hair follicle, sebaceous gland, and mammary cells. However, the hair follicles eventually atrophy and die, leaving behind a large pocket into which milk and sebum can empty (Figure 4)8. Placental mammals (eutherians), like us, are more variable. Eutherians can make one or many primary sprouts per mammary bulb and (as mentioned above) may make or lack secondary sprouts. Species without secondary sprouts do not have hair follicles and sebaceous associated with growing mammary glands, but species with secondary sprouts do. This includes humans and horses. Our MPSU hair follicles and sebaceous glands atrophy and die during embryogenesis so we are left with an MPSU made of a single component: the mammary alveoli and ducts8.
By comparing the development of the mammary glands of these different groups, Oftedal and Dhouailly have proposed a scenario for mammary gland evolution by co-option and heterochrony. Briefly, mammary glands use existing skin placode developmental mechanisms to begin to form, in particular the existing patterning used by the apo-pilosebaceous glands, then switch to a program of branching morphogenesis (a developmental patterning mechanism found in the kidney, lungs, and salivary glands in tetrapods but also in bird feathers and insect tracheal development). This creates the ductal tree of the mammary gland as the apocrine portion of the apo-pilosebaceous unit, instead of a sweat gland8. The origin of the overlying nipple is still unclear but is developmentally induced by the developing mammary gland.
The genetics of mammary gland evolution: co-option and novelty
Earlier, I briefly discussed the fate choice that skin makes between hair and mammary gland - turning on BMP4 signaling in mesenchymal cells via FGF10 signaling from part of the somitic mesoderm turns off the default hair program and turns on the mammary program. FGF/Wnt/BMP interactions are used in forming other skin in overlying ectoderm is used in patterning other skin appendages and may be a general cassette for ectodermal patterning9. In this way, mammary glands placode and bud formation are likely driven by similar signaling as other ectodermal appendages with some modifications. Once the mammary placode/bud begins to grow, it expresses a common epidermal organ gene: PTHrP. PTHrP has a more ancestral function in vertebrates in endochondrial bone formation and tooth eruption. As teeth are an ectodermal epithelial structure, it is likely that PTHrP's role in mammary gland development was coopted from tooth development. Evidence for co-option of tooth genes comes from another gene family key in tooth development -the calcium binding protein ODAM. ODAM was duplicated during tetrapod evolution to form the caseins, the calcium transport proteins in milk10.
FGF10 and Wnt10b are not the only players in mammary specification. Several Hox genes are implicated in ectodermal organ specification, with Hoxc8 initiating mouse mammary placode development and Hoxb3, b6, b9, d9, d10, and d8, among others, expressed during later development, including during postnatal mammary development11,12. Of these, Hoxd9 and d8 are most commonly expressed in mouse mammary bulbs. These two genes are also involved in both limb and hair development in mice.
While Hoxd9 and d8 are located next to each other on the chromosome and largely regulated by two giant cis-regulatory elements HoxD-T-DOM and HoxD-C-DOM, they do not exhibit completely identical patterns of expression, suggesting that there are specific regulators that act differentialy on their individual promoters. Recently, scientists in the Beccari lab in Geneva dissected the regulatory elements driving Hox d8 and d9 expression and found how they managed to go from being expressed in the limb and hair to being expressed in the mammary bulb. While Hoxd8 mammary bulb expression depended on a 13kb local enhancer region, the Hoxd9 mammary bulb expression depended on distant cis regulatory regions in T-DOM12.
The Hoxd9 mammary bulb cis regulatory element is particularly intriguing because it seems to partly rely on the existing cis regulatory elements that drive limb expression of Hoxd9. Limb expression is driven by cis regulatory elements within T-DOM and during limb development, a giant 1500 kb region of the chromosome folds over to contact Hoxd9. The mammary bud enhancer for Hoxd9 is also found within this 1500 kb region, and it is thought that this enhancer takes advantage of the attraction between the limb bud enhancer and the Hox cluster to get access to Hoxd9 during mammary bulb development (Figure 7)12. Taken together, this begins to paint a picture of the evolution of mammary placodes and bulbs - they use existing transcription factor and patterning genes in new combinations. At least one of the genes involved gets expressed in the developing mammary tissue by co-opting and modifying existing enhancer elements.
Once the embryonic mammary glands are built, they still need to secrete milk. While the similarities between milk-producing glands and apocrine sweat glands are obvious at anatomical and developmental levels, the content of the two substances produced is substantially different. One milk product, the caseins, is made from mutated ODAM tooth protein (see above). The major protein essential in processing the fat droplets found in milk, XOR, is usually an antimicrobial protein but plays a second role in milk biosynthesis. This is a clear case of heterotopy (expression of a gene in a new domain). Lysozyme took both paths - it was coopted from the immune system as an antimicrobial protein in the mammary glands, and it also underwent a gene duplication to form a whey protein used to lactose13. Even though milk composition is complex and varies from species to species (even within species as an infant gets older), we can trace the evolutionary history of these components and see how evolution could have acted to produce this secretion. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/10%3A_Case_Studies/10.1%3A_Case_Study_-_Ectodermal_Appendages.txt |
Birds are in the class Aves. They evolved from theropod dinosaurs and the first fossil bird discovered was Archaeopteryx. A few characteristics that make an animal a bird include wings, toothless beaks, and feathers. Bird feet have four digits but these can can be arranged in different ways. The most common digit arrangement is three in the front and one in the back as seen in perching birds and raptors like the Savanna Hawk (Figure 1). The difference between the perching food and the raptor foot is not in the digit layout but in the claws. In the raptor foot, the claws are more curved. They can also have two in the front and two in the back as seen with the grasping bird in the image. Another variation in bird feet is webbed digits which occur in swimming birds like ducks.
There are a few different digit arrangements commonly seen in bird feet (Figure 2) . This most-common arrangement is called anisodactyly. It is where digits 2, 3,and 4 face anteriorly and the hallux faces posteriorly (Figure 2). Syndactyl feet have the same arrangement as anisodactyl, but digits 2, 3, and 4 are encased by skin, this is seen in kingfisher feet (Figure1). There are also more extreme cases of webbing, especially in ducks and other water-fowl. A zygodactyl foot is when two digits, 2 and 3, are facing anteriorly and they other two digits, 1 and 4 are facing posteriorly, one example of this is in cuckoos and owls (Figure 1). A heterodactyl foot is similar to a zygodactyl foot but digits 3 and 4 face anteriorly and digits 1 and 2 face posteriorly, this foot is very rare and only seen in trogons (Figure 1). And finally a pamprodactyl foot is when digits 1 and 4 can rotate so that all four digits can face anteriorly. Mousebirds and swifts are famous for their pamprodactyl feet (Figure 2). When their digits face the same way, swifts (not pictured) are able to use them as hooks.
Figure 2: Digit arrangements in bird feet. Top panel shows line drawings of bird feet from Bothelo et al, 2015. Used with permission. Bottom panel shows a "footprint" of each of the different types of feet with digits numbered. Bottom panel from Wikimedia commons (Darekk2) and originally published under a CC-BY-SA 3.0 license.
Birds arose from therapod dinosaurs with 4 toed feet (Figure 3). The anisodactyl foot formed when the hallux was rotated posteriorly. It also used to be slightly elevated and smaller than the other digits. It is now no longer elevated and longer than the second digit. This resulted in digits 2, 3, and 4 facing anteriorly and digit 1 posteriorly as shown in the previous images. This is a modified version of the ancestral foot with few changes. The zygodactyl foot formed when both digits 1 and 4 rotated posteriorly (Figure 4). This is a more drastic change than the anisodactyl foot.
Figure 3: The evolution of digit morphology. Left panel: Homologous digits are color coded. Forelimbs are on the right and Hindlimbs are on the left. Most vertebrates have five digits on each autopod, but the reptile lineage shows asymmetric digit loss. Birds, like Archaeopteryx and chick (Gallus gallus) have four digits on their hindlimbs and three in their wings. Within the bird lineage different digit arrangements have evolved. Image from Vargas et al, 2008 published under a CC BY license. Right panel: the evolution of digit arrangements within the bird lineage. The order in which each type of dactyly evolved is unknown and at least one has evolved multiple times. Figure by Jessica Niccum, Alexis Amador, and Ajna Rivera
Botelho et al (2014) examined the development of the zygodactyl foot seen in birds like budgies. In this study, they found that in the beginning stages, budgerigars had similar development to that of a chicken (which has anisodactyl feet). Unlike chickens, however, after about 35 hours, the fourth digit rotated medio- laterally. After 36 hours, the fourth digit became flexed resembling a semi-zygodactyl foot, like owls have. After 37 hours, the fourth digit further rotated to resemble zygodactyl foot orientation (Figure 4). This suggests that digit rotation near the end of foot development is responsible for the evolution of zygodactyly, and zygodactyl feet do not grow digits in a new location. Because of this late-stage difference, the researchers examined the possibility that muscle formation and activation was responsible for digit rotation.
Figure 4: Development of a zygodactyl foot. A. External anatomy of a developing budgerigar foot at successive stages (HHXX). B. Skeletal structures in budgerigar foot development, cartilage is stained blue and bones are red. C. TrA is trochlea accessoria, the distal tip of metatarsal 4 The hook shape seen at HH38 is characteristic of zygodactyl birds. D. Diagram of the change in digit 4 orientation during development. Figure from Botehlo et al 2014. Used with permission.
Much of the development of various digit conformations is tied to the development of muscle formation and activation in the early stages. In anisodactyl feet, both EBDIV and ABDIV (extensor and adductor brevis muscles) are well developed. In zygodactyly such as budgies, however, the EBDIV is almost completely absent. The researchers found that the EBDIV becomes reduced when it separates from the other muscles in zygodactyl feet. The ABDIV, however, is well developed. The ABDIV causes the flexion of the 4th digit. This flexion combined with the constraint from EBDIV results in the zygodactyl orientation (Figures 4 and 5).
Figure 5: Anisodactyl vs. zygodactyl foot development. A. Shows the development of a quail foot while B. Shows the development of a budgerigar foot.
Brown is antibody staining against myosin2, which is found in muscles. Arrows point out the musculus extensor brevis digiti 4, which degenerates in the budgerigar and allows the musculus abductor digiti 4 to pull the fourth digit medio-laterally.
Figure from Botelho et al, 2014. Used with permission.
To our knowledge, development of other bird hindlimb digit confirmations haven’t been studied. Based on what we know about anisodactyl and zygodactyl foot development, we hypothesize a similar evolutionary and developmental trajectory for heterodactyl feet. The Heterodactyl foot looks similar to the Zygodactyl foot but digit 2 is rotated instead of digit 4. We think the development could be the same as the Zygodactyl foot but the muscular changes affect the 2nd digit. Trogon birds have heterodactyl feet (Figures1 and 2). They have two digits anteriorly, digits 3 and 4, and two posteriorly, digits 1 and 2.
Syndactyl feet, like those of kingfishers (Figure 1) have fusion of two digits via webbing. Under this webbing, they have the same digit conformation as anisodactyl feet. Research on bat wings has shown that the webbing between the digits is due to expression of a Bmp antagonist. In other animals like mice, Bmps cause the death of the interdigital mesenchyme. So, a Bmp antagonist in syndactyl birds could potentially prevent the apoptosis of the mesenchyme surrounding the digits, leading to syndactyl feet. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/10%3A_Case_Studies/10.2%3A_Bird_Dactyly.txt |
Butterfly wing patterns are organized along Ground Plans, which are compartments for different intervein pattern elements (Figure 1). These pattern elements include eyespots, ellipses, and midlines. The Ground plan, at least for nymphalids, has three symmetry bands: the basal system closest to the body, the central system, the border system, and the margin, which is farthest from the body. Eyespots occur the border band. Eyespots serve a role in predator avoidance and sexual signaling. They come in different sizes, shapes, numbers, and colors (Figure 5). They can also differ within a species based off geography, season, and sex. There are three stages of eyespot development: establishment of eyespot foci in late larval wings, establishment of color rings in early pupae, and pigment synthesis in late pupae.
Figure 1: Blue Morpho Groundplan by Kinsei Imada. Veins are in blue and pigment spots are in white. Colored regions indicate clonal boundaries. Cells within a clonal boundary are thought to come from the same "mother" cell. Clonal boundaries were estimated by comparing gynandromorphic butterflies to wild type butterflies. Gynandromorphic butterflies have some male cells and some female cells. Cells from a male "mother cell" will all be male and cells from a female "mother cell" will all be female. Since male and female cells have different pigment patterns, gynandromorphic butterflies allow us to figure out clonal boundaries.
Stages of eyespot development
Establishment of eyespot foci in late larval wings is the first stage of eyespot development. The location of eyespot foci are determined by the genes Antennapedia (Antp), Notch (N), and Distalless (Dll) in Bicyclus anynana. These interact with the transcription factor Spalt. Distalless has different functions in different butterflies. In B. anynana, it promotes eyespot development but in Junonia coenia and Vanessa cardui, two other nymphalid butterflies, it represses it, suggesting that evolution may act even at early stages of eyespot development. Establishment of eyespot foci occurs in four steps: margin and intervein expression, midline patterning, focal determination, and focal maturation.
Notch functions in defining dorsal-ventral boundaries, it defines intervein tissue through lateral inhibition with its ligand Delta. Notch upregulation followed by the activation of Distalless is an early event for the development of eyespots. Notch is upregulated in discrete focal pattern and Distalless is upregulated in intervein midlines (Figure 2). Notch expression tends to increase over time because of a positive feedback mechanism. The focal Notch upregulation precedes Distalless activation with lag time of 1.5 stages which is about 12-24 hours.
Figure 2: Gene expression pre-patterns eyespots. Antennapedia (green) and Notch (yellow) are expressed in foci corresponding to eyespots. Dll (red) and Notch are expressed in intervein midlines. Dll is additionally expressed in the wing margin. Figure from Saenko et al, 2011 under a CC BY 2.0 license.
Figure 2 shows the spatial and temporal patterns of Antp, Notch and Distalless in late last instar wing marginal discs of three different butterflies. It shows that there is a perfect correlation between presence of eyespots and late last instar Notch and Distalless focal expression. In genetic experiments, researchers reduced levels of Notch or Distalless, which reduced or eliminates two specific eyespots in the hindwing.
Establishment of color rings is the second step of eyespot development. There is currently no confirmed model, but the most popular theory is that there is a morphogenic gradient coming from the eyespot foci. Epidermal scale cells at different distances respond to signal using transcription factors called Engrailed and Spalt. This stage occurs during pupal development. Though not confirmed how this happens, research shows that the expression of both Distalless and Spalt corresponds with adult black scales, and the expression of both Distalless and Engrailed corresponds with gold scales.
Pigment synthesis is the third step of butterfly eyespot development. Figure 4 shows the biochemical pathway of pigment synthesis in B. anynana. As mentioned before, Spalt and Distalless corresponded to black scales, and Engrailed and Distalless corresponded to gold scales. Melanin biosynthesis pathways allow for the pigmentation of these eyespots.
Figure 4: Melanin biosynthesis pathways for pigment synthesis in B. anynana. Figure from Matsuoka et al, 2018 and published under a CC BY 4.0 license.
There are five products of melanin biosynthetic pathways, dopa-melanin, dopamine-melanin, pheomelanin, NBAD, and NADA. Dopa-melanin and dopamine-melanin (the eumelanins) are black and brown pigments, respectively. Pheomelanin is a reddish-yellow pigment, NBAD sclerotin has a yellow color, and NADA sclerotin is colorless. Black scales have a combination of dopa-melanin and dopamine-melanin, which are black and brown pigments. Gold scales have a combination of pheomelanin, dopamine-melanin, and NBAD sclerotin, which are reddish-yellow, brown, and yellow pigments.
Plasticity in eyespot development
Bicyclus anynana eyespots vary in size based on season. Environmental temperature during larval and pupal stages of development leads to changes in ecdysone hormone levels, which regulates eyespot size. This plasticity has likely evolved due to seasonal predation. During the wet season, B. anynana have higher levels of ecdysone and larger eyespots, which help them avoid predation. During the dry season, ecdysone levels drop as do eyespot sizes. Hindwing eyespots display higher levels of plasticity in overall size, center size, and center brightness than forewing eyespots, since the ecdysone receptors in hindwing eyespots are much more sensitive than those in forewing eyespots. The result of this is that slight changes in ecdysone levels affect hindwing eyespot development in a much higher degree than forewing eyespot development.
The evolution of eyespots
Eyespots are present in Nymphalidae. They have convergently evolved in butterflies and moths. In butterflies, they first originated along the dorsal midline, as dorsal fin, then appeared as a pair of anterior pectoral fins, and finally in a more posterior region of the body as pelvic fins. Eyespots replaced the simpler pattern elements that already existed at those locations. The simple colored spot became a multicolored and multi-ringed eyespot.
Figure 5: A hypothesis for the evolution of eyespots. Novel features (gene expression, gene networks, and morphological features) are marked where they evolved along the lepidopteran lineage. This hypothesis posits the co-option of discal-cell eyespots (as seen in saturniid butterflies) into border spots and border eyespots following the invention of Spalt regulation of melanin production in scales. Figure from Monteiro et al, 2006 originally published under a CC BY-2.0 license.
The three selective pressures on eyespots are camouflage, anti-predatory defense, and sexual display. Eyespots are a form of camouflage because they look like vertebrate eyes. The selective pressure of anti-predatory defense and sexual display are often at odds with each other, Bicyclus species overcome this with signal partitioning. Signal partitioning is when visual signals are separated to different parts of the body, and signal displays are restricted to appropriate spatio-temporal conditions. Bicyclus species do this by folding their wings, which hides the dorsal wing surface and exposes the ventral wing surface. To deal with the selective pressure of anti-predatory defense, eyespots are generally on the border of the wing. They are far from the body, so the predators attack the wing instead of the body, allowing the butterfly to escape. Anti-predatory defense places huge selective pressure on large ventral eyespots on the forewing and hindwing because to scare off potential predators, Bicyclus species fold their wings. By exposing the ventral wing surface, there is selection for larger ventral eyespots. On the other hand, during sexual display, males open up their wings to expose the dorsal wing surface. Females prefer intact dorsal forewing eyespots in B. anynana, since it indicates that the eyespots have UV reflective pupils. Sexual display thus select for more intact dorsal forewing eyespots. Figure 6 shows the differences in ventral and dorsal wing surfaces in four different Bicyclus species. Ventral wing surfaces are shown on the left, and dorsal wing surfaces are shown on the right. Ventral eyespots are much bigger than the dorsal eyespots, which shows that signal partitioning does occur with anti-predatory defense selecting for larger ventral eyespots and sexual display selecting for more intact dorsal forewing eyespots. Dorsal and forewing characters are also more likely to change through evolutionary time compared to ventral and hindwing characters because mate selection is a stronger selection pressure than anti-predatory defense.
Figure 6: Ventral and dorsal eyespots in four different Bicyclus species. Ventral forewings and hindwings are shown on the left, and dorsal forewings and hindwings are shown on the right. Figure from Oliver et al, 2009. Used with permission. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/10%3A_Case_Studies/10.3%3A_Butterfly_Wing_Spots.txt |
Think for a minute about how many people you know are lactose intolerant. While most people think in terms of lactose intolerance, evolutionarily, lactose intolerance is the ancestral state. In mammals, the ability to digest lactose has been selected for in infants. In humans, some people also have the ability to digest lactose as an adult. This is called "lactose persistence."There are four different forms of lactase "deficiency": primary, secondary, developmental, and congenital. Primary lactase deficiency is the loss of lactase from childhood into adulthood, this is common among humans with about 70% of the world's adult population unable to digest lactose. Secondary lactase deficiency is the loss of lactose digestion due to injury to the body (most commonly, the intestines). Developmental deficiency is the lack of lactase due to premature birth, and congenital is the lack of lactase from birth onward. The focus of this article will be on primary lactase deficiency.
Lactose tolerance
Lactose tolerance considers the presence of lactase within the small intestine. It is located on the brush border of the small intestine enterocyte. Lactase is an enzyme that is responsible for breaking up lactose into glucose and galactose, which would be used for glycolysis and energy production in the body. However if lactase is absent in the small intestine, lactose ends up being processed in the large intestine, allowing bacteria to consume it, produce gases and acid, causing traditional symptoms of lactose intolerance such as bloating, flatulence, and diarrhea (Figure 1).
Understanding the genetics of lactase persistence is vital to knowing how it is inherited between populations. Lactose intolerance is inherited in an autosomal recessive pattern, that means that one copy of the lactase persistence allele is enough to confer the ability to digest lactose as an adult. The lactose enzyme is encoded by the LCT gene. This gene has a set of protein-binding regions that help regulate it's expression. On the same chromosome is the MCM6 gene, encoding a helicase. Within MCM6 is an additional enhancer region for the LCT gene. Mutations in this enhancer region can confer lactase persistence. The common mutations are named after their distance upstream of the LCT start codon and the nucleotide at that location: -13907*G, -13910*T, -13915*G, -14009*G, and -14010*C.
Figure 3: A common mutation in a lactase enhancer region. The -13910 mutation creates a binding site for the transcription factor Oct1. Oct 1 can form a complex with HNF1⍺, a transcription factor with a binding site just upstream of the LCT coding region. This binding bends the DNA and helps to initiate transcription of LCT. This mutation allows lactase to be produced past childhood and into adulthood, allowing consumption and processing of lactose without repercussions to the body.
The evolution and development of lactose intolerance
Lactose intolerance usually begins between childhood and early adulthood. It is measured by comparing sucrase and lactase concentrations in small intestine biopsies. Sucrase processes sucrose (table sugar) in the small intestine and is present throughout a persons lifetime, it's concentration is used to normalize lactase concentration. Figure 3 compares lactase:sucrose concentration in different age groups. In infancy, lactase and sucrase levels are around the same concentrations in most individuals, indicating that there is an abundant amount of lactase present. This is vital during infancy as babies require milk from their mothers for nutrition and energy. At older ages, lactase levels slowly wane compared to sucrase. This is the period where children are weaning off their mother’s milk and will no longer need the lactase to digest this source of lactose. In children 5-17 years old, there is a wide spread of lactase concentrations, with many individuals exhibiting very low levels. In many people, the body has turned off the transcription and formation of lactase as it is no longer naturally needed to digest mother's milk. While the exact mechanisms pertaining this change in expression is not known, it is possible that epigenetic modifications are affecting the MCM6 gene. This data is important in demonstrating that humans naturally lose lactose persistence as they grow out of infancy, similar to other mammals.
Figure 4: Lactase concentration over time. Distribution of sucrose:lactose concentration in four different age groups. The ratios are shown along the x axis and the numbers of individuals in each class are on the y-axis. All four histograms are to the same scale along the x axes, although the y axes are on different scales. The scale of the end of the xaxis is condensed from the position marked (6.5 and above); the highest ratio group contains all with ratios above 20. In our previous studies, ratios of >10 have been considered diagnostic of lactase nonpersistence. This figure is from Wang et al, 1998 and is used with permission.
Lactase persistence has evolved several times in humans (see Table to the left from Silanikove et al, 2015, published under a CC BY 4.0 license. This is associated with ruminant domestication. Not all populations with domestic ruminants (for example sheep and goats in Southern Europe and water buffalos and yaks in Asia) have high rates of lactose tolerance, however. This may be due to the prevelance of cheese, yogurt, and butter production in these populations. Cheese, yogurt, and butter are all low in lactose. The convergent evolution of lactase persistence has been driven by different mutations in enhancer regions. The most common is the European 13910*T mutation (Figure 3). This mutation is seen at the highest levels in Northern Europe and at lower levels in Southern Europe, Africa and the Middle East (Figure 5). The spread of the mutation is thought to be due to migration of populations from the North. However, it is suspected that the population in India is due to the British colonizing and reproducing with the Indian population. Other mutations (Figure 5) are more regionally localized and are all thought to be associated with pastoralism (livestock domestication).
Future directions
As of right now, there’s no complete hypothesis for the development of lactase persistence. It's commonly thought that persistence evolved due to a change in food preservation and diet. Especially seen for the 13910*T mutation, a change in climate may have favored adaptations for changes in diet. As people migrated North from the Fertile Crescent, the climate got colder, presenting an environment not suitable for growth of some of their crops. However, the colder environment allowed for further preservation of milk from domesticated cows. The lack of available food and the readily resource of milk favored people who had the ability to digest milk. Milk is nutritious in proteins, fats, and sugars, giving people additional calories and nutrients.
Most data on lactase persistence is from the Old World where populations are more homogenous. However in the New World, populations found in the USA and Latin America may be more diverse, with many people of mixed racial descent. This presents the possibility of developing some form of tolerance no longer on a binary scale but more on a gradient. It is possible that while some populations would still become intolerant as adults, the period of childhood tolerance could be longer than current data shows. This research will not only guide people into further understanding their ability to process lactose, but also allows people to be more aware of how their current diet might affect the genes and traits they pass on. | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/10%3A_Case_Studies/10.4%3A_Lactase_Persistence.txt |
For this assignment you will turn in your alignment, your tree, the names of a pair of orthologs, the names of a pair of paralogs, and a short description of the significance of the gene you chose. Additionally, you will have an "Appendix" with notes on the steps (if anything happened at a step that was not described in the instructions, if you noticed anything interesting).
INSTRUCTIONS
Getting your set of sequences
1. Get your “bait” sequences.
1. Go to Uniprot and type in YFG name + a model species (for example if you are interested in centipede genes ultimately, you would put in Drosophila). Read a bit about your gene and scroll down to FASTA. Click on this and it will take you to the FASTA formatted protein sequence.
1. If there is more than one “version” of YFG for that species, get the FASTA for all of them - they are likely homologs. For example, looking at Dlx (the Distalless in vertebrates) I find 5 version in humans. So I would get the FASTA for each of these. Put these all in the same text document.
2. Get your “model” sequences. Follow the same instructions for your other two (or three) models. If you are having trouble selecting your models, you can ask me for help! Add these to the FASTA text document.
3. Get your “test” sequences
1. Blast your “bait” sequence in NCBI blastp. Limit your search to your test species, it helps if you know the scientific name (Wikipedia has these). Choose the sequences with an evalue less than 1e-10. If there are too many, just pick the top 5. If there aren’t any with an evalue this low, pick the top 3. Add these to the FASTA text document.
4. Get your “outgroup” sequence
1. This should be a sequence that is similar to but not homologous to YFG. To find one, go back to UniProt and click on BLAST. Paste in your bait sequence and choose the UniRef50 database from the pulldown menu and click run. Wait.
2. Scroll down the results list until you start seeing gene names that differ from YFG. Click on a high scoring one of these and get the FASTA sequence, add this to your FASTA text document at the very top.
Making your tree
The next step is to align your sequences and make a tree. Aligning sequences places the most similar parts of each sequence in vertical columns. It makes it easier to visually see whether the sequences are really very similar or not so much. You can also sometimes see things like conserved domains in an alignment. The other useful thing about alignments is that they can be used to score similarity by statistical algorithms. These programs use alignments to infer phylogenetic relationships.
1. Paste your FASTA formatted sequence into https://www.ebi.ac.uk/Tools/msa/muscle/ and choose Pearson/FASTA as your output. The output is important because we need an output file that the next program can read.
2. The results page has a bunch of different options. Save the basic text version and then click around to visualize your alignment in different ways. Do you see anything interesting? Any patterns?
3. Upload this “alignment file” to http://iqtree.cibiv.univie.ac.at. and click submit job. IQtree by default will test different models of molecular evolution on your data and see which one fits. We aren’t going to use super fancy models, so we don’t need to add in things like a gamma distribution or free rate heterogeneity. As IQtree runs you can ponder the difference between paralogs and orthologs and/or start writing up a description of your gene and what happened at each step you did to find out about it’s genetic complexity in your non-model organism.
Sample output by Hyung Joo Kim and Kinsei Imada
This tree seeks to find out whether the Drosophila Distalless-family gene INDY (I'm Not Dead Yet) has a homolog in a related insect, Folsomia candida (FOLCA).
Human paralogs are boxed in red. The closest relative in this tree to Drosophila INDY (XP_009059854.1) is a molluscan gene (orthologs boxed in red). The FOLCA gene falls within the same clade as Drosophila INDY, suggesting that it might be an INDY homolog.
In blue are human and Drosophila representatives of an ancestral gene duplication event.
2: Comparative Vertebrate Anatomy Observations
In this lab, you will consider the morphological processes of evolution and development by examining developing vertebrate embryos.
Before you start please adjust your oculars so you can see two full circles, you may need to slightly adjust how far your eyes are from the microscope.. This can take 5-10 minutes so be patient.
Please choose one of the following:
1. Chick or Frog embryo, single stage (you will “reconstruct” the 3D morphology by comparing sections of a single embryo).
2. Chick or Frog embryo across time (you will “reconstruct” development by examining different stages)
3. Chick and Frog comparisons (you will compare Chick and Frog morphology at a similar developmental timepoint)
Take some time to get acquainted with your slides and your microscope. Make sure you can see through both oculars and you are focusing up and down for each section.
Start to make a few sketches of what you see on plain white paper. Practice drawing the features that stand out to you and seem salient. You may use the books provided, online resources, or people in the classroom for help in figuring out different features.
Note: I offer an extra credit for an art piece based on sketches (examples below) and provide watercolors, watercolor paper, and colored pencils for the students. I grade it on detail, quality, and overall aesthetics.
Resources:
Early Frog Development
Late Frog Development
Chick Development
Sections of a chick embryo at five stages by Kristina Vu
Frog vs. Chick comparative embryology during late-organogenesis by Yongjin Byun | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/80%3A_Mini-Labs/1%3A_Ortholog/Paralog_Lab.txt |
Butterfly Wings Lab
Nipam Patel, the author of the picture below, is interested in using gynandromorphic Morpho butterflies to understand wing development in insects. Much of his research focuses on developmental mechanisms of boundary formation across evolution. Boundary formation (like we see in brain lamination or in segmentation) is a key process in compartmentalizing an embryo. As we read before, compartmentalization can increase evolvability by separating cellular functions and reducing pleiotropy.
In Figure 1, a series of Blue Morpho butterflies is pictured. The top left butterfly is a wild-type male and the top center butterfly is a wild-type female. All of the rest of the butterflies are gynandromorphic with some male cells and some female cells in their wings. We will use these natural sports to make a hypothesis about boundary formation in butterfly wings.
Genetic mosaics and eyespots
Genetic mosaics are classical models for studying developmental processes. Mutations in key developmental genes often results in early embryonic lethality. Sometimes, a genetic mosaic organism can be generated that has only a small subset of cells or a single tissue/organ that exhibits the mutation. In these cases, the role of the gene in just that tissue or organ can be studied much later in development1. Drosophila wing compartments and the finding that the transcription factor Engrailed is involved in boundary formation were both discovered using genetic mosaics2,3. Drosophila wings tend to be fairly simple in terms of wing vein patterning and pigmentation, compared to butterfly wings (see Figure 3 below). However both wings undergo very similar early development and share a basic "ground plan", the set of instructions that both defines the major regions of the wing (veins and margin) as well as sets the boundaries for the initiation of color pattern elements4. These pigmented pattern elements (notably eyespots) can be repeated across the wing with each element exhibiting a similar morphology due to similar developmental patterning5. Because of this, eyespots are considered to be serial homologs like limbs or ectodermal appendages.
Color elements are a useful assessor of boundaries since they are easy to see and vary both within a population and between species. Since the color elements are serially homologous, a single wing offers multiple opportunities to observe the effect of boundaries on pattern formation. By creating or finding genetic mosaics that exhibit abnormal wing patterning, we can start to understand how compartments both restrict individual phenotypic variance (by providing a ground plan) and allow for greater population variance (by reducing inductive effects).
The wing ground plan
The wing ground plan develops along 3 axes: the D/V axis (the front and the back of the wing), the A/P axis (the top/bottom axis on the figures below), and the proximal-distal axis. For this lab, we will only consider the dorsal sides of the wings. Each side (dorsal or ventral) is patterned on a warped X-Y coordinate grid with the veins making up the horizontal boundaries and a series of bands (colored in Figure 2) making up the ventral boundaries.
Figure 2: The nymphalid ground plan
The vertical boundaries of the nymphalid ground plan were first proposed by Fred Nijhout to explain color variation in the Nymphalidae, a large group of spectacularly patterned butterflies6. These bands, from distal to proximal, are the wing margin (red), the border band (orange), the central band (yellow), and the basal band (green). The horizontal boundaries are formed by the wing veins. The intervein region within a band is a compartment called a "cell" where pattern formation can be initiated semi-independently from other cells6.
In the last 3 decades as gene expression, gene sequencing, and genetic manipulation techniques have become more reliable, a wealth of knowledge regarding butterfly wing patterning has emerged. For example, Abbassi and Marcus (2017) define a new developmental compartment boundary shared between butterflies and Drosophila (named Far-Posterior) based on genetic mosaic and gynandromorph data (Figure 3)
Lab instructions
1. Using Figure 1 above, draw the Blue Morpho ground plan. Write up a short justification for your ground plan based on the picture and the information
2. Do you think this ground plan is homologous to the Drosophila and V. braziliensis ground plans? Why or why not?
3. Imagine you are a butterfly researcher trying to justify a collecting trip to an exotic location to collect butterflies. How would you pitch your research to the greater scientific/heathcare community?
Class Discussion Readings and Questions
Read an overview of tetragametism(genetic gynandromorphism)
Read a case study of a genetic "gynandromorphic" human , you can skip the Materials, Methods, and Results sections, please focus on the Introduction, Case Report, and Discussion.
Choose one or more of the questions below to answer
1. What is gynandromorphism, how can we tell when an organism is gynandromorphic? How did doctors know that a phenotypically normal girl was gynandromorphic (in the third reading)?
2. Why do scientists and doctors seek out gynandromorphic individuals to study? How are they useful for understanding biology? Can scientists create gynandromorphs or other types of mosaic/chimeric animals?
3. What are the different mechanisms that can give a 46XY/46XX karyotype in an amniocentesis? Be sure to describe both the false positive as well as different developmental mechanisms for generating true positives.
4. Gynandromorphic (46XX/46XY) humans often have abnormal genitalia and gonads that are either a mix of ovarian and testicular tissue (called ovotestes) or one ovary and one testis. What information does this give us regarding the development of gonads and genitalia in humans?
Reaction Diffusion Simulator
Reaction Diffusion Simulator
Note: If possible this is ideally run in a computer lab or with loaner laptops. Otherwise, ask students ahead of time to bring in at least one laptop per group. Students can follow the questions below or can be given minimal instructions and just "play" with the simulation.
In the Turing Model, the pattern is changed by adjusting the speed of diffusion, the strength of interaction, and the rate of degradation. In the Grey-Scott model simulation, the feed rate is related to the speed of diffusion and the death rate is related to the rate of degredation.
1. To see the a "boring" pattern, choose a feed rate of 0.006 and a death rate of 0.028. Click anywhere on the canvas.
2. Choose the present "Solitons" and click anywhere on the canvas. This feed/death rate combination produces a field of equally spaced spots. How does this relate to the Turing model?
3. Adjust the feed rate to 0.02 and the death rate to 0.058, how does this affect the spot pattern you saw in Solitons?
4. Can you adjust the feed and death rates to produce stripes?
5. What happens if you click on the canvas while a pattern is being generated. What would this represent biologically?
6. What kinds of biochemical/molecular properties might affect feed and death rates? | textbooks/bio/Evolutionary_Developmental_Biology/Evolutionary_Developmental_Biology_(Rivera)/80%3A_Mini-Labs/3._Butterfly_Wings_Lab%3A_Boundaries_and_Pattern_Formation.txt |
History of Earth is split in multiple intervals, and some of them are listed in the clock and chart below. These classifications, however, do not reflect well the stages of evolution. This is why in this chapter, the history of life is described from the palaeoecological point of view which reflects milestones of organic world development.
01: The Really Short History of Life
In the strict sense, origin of life does not belong to biology. In addition, biologists were long fought for the impossibility of a spontaneous generation of life (which was a common belief from Medieval times to the end of 19 century). One of the founders of genetics, Timofeev-Resovsky, when he was asked about his point of view on the origin of life, often joked that “he was too small these times, and do not remember anything”.
However, contemporary biology can guess something about these times. Of course, such guesses are no more than theories based on common scientific principles, actuality and parsimony.
First, Earth was very different. For example, the atmosphere had no oxygen; it was much closer to the atmosphere of Venus than to the atmosphere of contemporary Earth and contained numerous chemicals which are now poisonous for most life (like CS2) or HCN). However, by the end of Archean first oxygen appears in the atmosphere, and in early Proterozoic, it started to accumulate rapidly. The process is called the “oxygen revolution,” and it had many consequences. But what the reason for oxygenation was nothing else than the appearance of first photosynthetic organisms, most likely cyanobacteria.
Second, the first traces of life on Earth are suspiciously close to the time of Earth origin (4,540 mya)— molecular clock place LUCA about 4,000 mya, and recently found first traces of cyanobacteria are 3,700 mya. Altogether, life on Earth was most of the time of its existence!
Third, first living things were most likely prokaryotes (Monera, bacteria). These could be both photosynthetic (cyanobacteria) and chemotrophic bacteria, as evidenced from isotope analysis of Isua sedimentary rocks in Greenland, and now also from the presence of stromatolites, the traces of cyanobacteria in the same place.
What was the first living thing? It has a name LUCA, Last Universal Common Ancestor, but only a little could be estimated about its other features. It was probably a cell with DNA/RNA/proteins stream, like all current living things. Unclear is how this stream appeared and how it happened that it was embedded into the cell. One of the helpful ideas is “RNA world”, speculation about times when no DNA yet exist, and even proteins did not function properly, but RNAs already worked as an information source as well as biological machines. Another possibility is that lipid globules, some other organic molecular and water formed coacervates, small droplets in which these RNAs could dwell. If this happened, then resulted structure could be called “proto-cell”.
1.02: Prokaryotic World
Most of the Proterozoic prokaryotes (Monera) dominated the living world. Typical landscape these times was high, almost vertical rocks and shallow plains, which should be covered with the tide for dozens of kilometers. This is because there were no terrestrial organisms decreasing erosion. Ocean was low oxygenated; only water surface contained oxygen.
In those conditions, ancestor of eukaryotes appeared. First eukaryotes could probably remain contemporary heterotrophic Excavata (Fig. 2.2.3) like Jacoba, but there are no fossils of this kind. However, there is a number of fossils which could be treated as algae, photosynthetic protists. These fossils remind contemporary red and green algae (Fig 2.2.9, the bottom row). It is possible that some other Proterozoic fossils (acritarchs) belong to other protist groups, for example, unicellular Dinozoa (Fig. 2.2.8).
Ecosystems of these times were similar to Archean and mostly consisted of cyano- and other bacteria, and represented now by stromatolites. No one can say anything about terrestrial life in Proterozoic, but it possible that Monera dominated there as well.
At the end of middle Neoproproterozoic, continents of Earth joined in one big continent Rodinia; this triggered the most powerful glaciation in history, “snowball Earth”, Cryogenian glaciation.
1.03: The Rise of Nonskeletal Fauna
This mentioned above glaciation possibly, in turn, triggered the evolution of Earth, because, in the Ediacaran period (the last period of Proterozoic), animals and other multi-cellular organism appear. There are three most unusual things about Ediacarian ecosystems. First, they were filled with creatures as similar to contemporary life as would (not yet discovered) extra-terrestrial life be. In other words, they (like Pteridinium, see Fig. 2.2.30) had no similarity with the recent fauna and flora. Second, all these Ediacaran creatures were soft, nonskeletal. This last fact is even more striking because, in the next period (Cambrian), almost all animals and even algae had skeletal parts.
There were different types of ecosystems in Neoproterozoic. However, in essence, they all consisted of these soft creatures (it is not easy to say what they were, animals, plants of colonial protists). They thrived for about 90 million years and then suddenly declined (some left-overs existed in Cambrian, though). This decline is the third bizarre thing. Weird because later ecosystems almost always left descendants, even famous dinosaurs went extinct but left the great group of birds, their direct “offspring”.
Why they went extinct, it is not clear. Several factors could be blamed: oxidization of ocean, the appearance of macroscopic carnivores, increased transparency of water. The last could relate with two first by means of pellet production. Many recent small plankton invertebrates pack their feces in granules (pellets), which speedily fall to the ocean bottom. In Ediacaran, there was probably no pellet production, and therefore ocean water was mostly muddy. When first pellet producers appear, water start to be increasingly more transparent, which raised oxygen production by algae and, as the next step, allowed more and bigger animals to exist. Bigger plankton animals mean that it starts to be rewarding to hunt them (remember ecological pyramid). These hunters were probably first macroscopic carnivores, which caused the end of Ediacaran’s “soft life”.
After Ediacaran great extinction (this is the first documented great extinction), one can observe the rise of very different creatures, small, skeletal Cambrian organisms. They appear insignificant diversity and represent many current phyla of animals. This is called “Cambrian revolution”, or “Cambrian explosion” (see below). | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/01%3A_The_Really_Short_History_of_Life/1.01%3A_Origin_of_Life.txt |
This happened during the Cambrian and Ordovician periods, which jointly continued for almost 100 million years. Most of this time the Earth climate was relatively warm, but continents were concentrated in the Southern hemisphere. At the end of Ordovician, Africa hit the South Pole, and this resulted in a serious glaciation.
The sea, in large degree, prevailed over the land and thus created exceptionally favorable conditions for the development of marine communities, which in this epoch became finally similar to what we see around now. For some groups, there was not “enough space” in the sea, and, as a consequence, the colonization of land from higher organisms started.
At this time, all main types and even classes of invertebrates and vertebrates and terrestrial plants already existed. Stromatolites went to the “background” of ecosystems and were replaced with other builders of bioherms (reef-like organic structures) like archaeocyaths (Fig. 2.2.13, group probably close to the sponges) and calcareous red and green algae. Archaeocyaths went extinct at the end of the Ordovician, but calcareous algae have survived.
In Cambrian, there was a great variety of different groups of animals, usually small size and with a skeleton of different types (phosphate, calcareous, organic): that was a consequence of “skeletal revolution”. some of them were crawlers, some swimmers, and some burrowers.
Among the seafloor bilaterians, trilobites (an extinct group of arthropods) dominated, there were also many other groups of arthropods and lobopods (intermediates between ecdysozoan nematode-like “worms” and arthropods), plus various spiralians, namely brachiopods and mollusks (Fig. 2.2.21, 2.2.22) including cephalopods which played the role of pelagic predators, preceding sea scorpions and armored fish. There were also plenty of echinoderms, mostly sea lilies and many other, now extinct, classes (Fig. 2.2.15). First jawless fishes (Fig. 2.2.17, top row) were also the part of pelagic life.
It can be assumed that at this time started the mass “exodus” of invertebrates to the land. Perhaps, there was already some soil fauna, consisting of nematodes, small arthropods, and other similar organisms.
Green algae were gradually replaced red algae in communities. For some of them, like for some invertebrates, there was “not enough space” in the ocean, and they proceeded to conquer the land. The living conditions outside of the ocean were much more stringent for plants than for the animals, so the process of adaptation took a long time. The first land plants are known from the Ordovician; they probably were liverworts (Fig. 2.2.10, top left). Land conquest for plants was concerted with the development of symbiosis with mycorrhizal fungi (Fig. 2.2.5). Apparently, among the first terrestrial photosynthetic organisms were symbioses, both with a predominant fungus and predominant alga. The first gave rise to the lichens, who took the most extreme habitats, and the second to the contemporary terrestrial plants.
Terrestrial plants had to solve many problems. There were, in particular, water supply (so they developed vascular system), gas exchange (acquired stomata), competition for light (body began to grow vertically with the help of supportive tissues), and spore dispersal (diploid stage, sporophyte, began to form sporangia on a long stalk containing spores covered with thick envelope).
A serious plant problem was also in the optimization of the life cycle. Putative ancestors of land plants, charophyte green algae, did not have any sporophyte as their zygote proceeds to meiosis almost immediately after fertilization. New sporophyte could arise in connection with the need to disperse the spores from plants growing in the shallow water, where the wind acted as the most efficient dispersal agent. First, sporophytes served likely only for the storage of the haploid spores, but later most of the gametophyte functions were transferred to the sporophyte.
It is important to note also that the colonization of the land by plants was to happen after the formation of soil, the process involved bacteria, fungi, and invertebrates. Furthermore, the term “colonization of land” is not accurate since the actual land in the usual sense in those days did not exist; it was, in fact, huge, often completely flooded this wetlands-sea bottom space, interspersed with rock formations; there were no permanent freshwater. We can say that animals and plants made the land themselves, stopping erosion that once ruled the earth’s surface. Land type familiar to us was formed slowly; we can, for example, assume that until Jurassic watersheds were completely devoid of vegetation.
1.05: First Life on Land
This epoch (spans Silurian and Devonian periods) began more than 440 million years ago and took about 85 million years. The Earth’s climate was gradually warmer, starting with a small glaciation of Gondwana (the South Pole was in Brazil), climatic situation slowly reversed, and during the Devonian period, the world was dominated by abnormally high temperatures and extremely high ocean level. This time was ended with Caledonian orogeny, the result of proto-North America and proto-Europe collision, when mountains of Scandinavia, Scotland, and eastern North America have risen.
On land, there was a radiation (i.e., evolution in different directions) of terrestrial plants. There were already several biomes: bog communities, semi-aquatic ecosystems, and more dry plant associations with domination of mosses. Once the plants have “learned” how to make chemicals that make their cell walls much stronger (lignin and suberin), they started to make “skyscrapers” to escape competition for the light; this allowed them to grow up to the almost unlimited height. By the end of epoch, first forests appeared, which consisted of marattioid ferns (Fig. 2.2.11, middle left), giant horsetails, mosses, and first seed plants.
Origin of seed was most likely connected with the origin of trees. Ancestors of the seed plants (it is possible that they were close to modern tongue ferns, Fig. 2.2.11) were among the first plants to acquire the cambium, “stem-cell” tissue, and, consequently, the ability of the secondary thickening their trunk. After that, growth in height was virtually unrestricted. But there was another problem: the huge ecological gap between the giant sporophyte and minuscule, short-lived gametophyte dramatically reduced protection capabilities of the sporophyte and the overall plants’ viability (a similar thing happened with dinosaurs in the Late Cretaceous).
Seed plants solved the problem and found the room for gametophyte right on the sporophyte. However, this change required plenty of coordination in the development (e.g., pollination), and initially, seed plants (like contemporary ginkgo, Fig. 2.2.12, top left, and cycads) were not much better than their sporic competitors.
At the seas, predatory vertebrates, armored fish “pushed” the old dominants, chelicerates (Fig. 2.2.26, bottom right) into the land. The last group became first terrestrial predators. There was already plenty of prey in the terrestrial fauna, in particular, millipedes and wingless proto-insects (Fig. 2.2.29, the middle). The last group (in order to escape predators) was likely forced to migrate to live on trees, and true insects appeared in the next epoch.
Shallow-water communities were dominated by advanced fish groups. The most important were ancestors of terrestrial vertebrates, lobe-finned fish (Fig. 2.2.17, 4th from top). These predatory animals, probably in order to “catch up” with the retreating water (as the tides at that time apparently extended for kilometers into the “land”), and also in the search for more food, started to develop adaptations to the terrestrial lifestyle. At the end of the epoch, they “made” organisms similar to modern amphibians, labyrinthodonts. They had many characters of terrestrial animals but likely spent most of their life in water. | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/01%3A_The_Really_Short_History_of_Life/1.04%3A_Filling_Marine_Ecosystems.txt |
This epoch took about 60 millions of years and is often described as the kind of tropical world, with warm and humid climate, plenty of CO2 in the atmosphere, and the predominance of ferns. In fact, in the world at that time, the climate was quite variable. For example, the Arctic continent Angarida (or “Siberia”, it corresponds with recent East Siberia) had really cold and dry climate. In contrast, the Euro-North-America was on the equator and had a tropical climate.
However, there was a little carbon dioxide and lots of oxygen; in fact, much more oxygen then it was on the whole history of Earth, both earlier and later. One of the proofs is an existence of giant palaeodictyopteroidean insects, some of them had more than a meter wingspan! As insects depend on the tracheal system for ventilation, it is safe to guess that there were plant of oxygen in the atmosphere to supply these big bodies.
The raise of oxygen is probably explained with appearance of forest biomes. Accumulation of coal is also related, the more carbon accumulated, the less should go into CO2.
These Carboniferous forests were dominated with primitive woody ferns, tree-like horsetails, and basal seed plants (they have quite misleading name “seed ferns” but in fact, belonged to groups which now include ginkgo and cycads). There were also related to conifers (cordaites and, finally, woody lycophytes which now exist only as small water quillworts (Isoëtes).
Forests of this epoch were peculiar, and more similar to mangroves then to “normal” forests. They were systematically flooded with the tides and surf waves, and at the same time, decomposition of organic matter was slow (as there were no phytophagous insects and little fungi). Consequently, the bottom of such forest was probably covered with mud. This mud was threaded with numerous rhizomes of woody lycophytes.
They, as many other trees of these times, had imperfect thickening, and sooner or later would break and fall. Besides, sporic trees had no control over their microscopic gametophytes, and this resulted in periodical outbursts when many young plants of the same age started to compete and eliminate each other. All of these factors add to the existing mess, and lower levels of these forests were literally inundated with large size wood litter.
This was the primary ground of the origin of reptiles and flying insects. These two groups could origin “together”, as elements of the one food chain also included trees. At the beginning of their evolution, many insect groups probably feed on generative organs of plants. Then dragonflies formed the first flying predators, and as the response, cockroaches and crickets went into the litter layer.
Some amphibians slowly evolved toward feeding on terrestrial invertebrates (like insects, slugs, and millipedes), and as a consequence, developed the full independence from water. This independence required substantial restructuring of the organization, in particular, the improvement of the respiratory system, skin, fertilization, and embryogenesis. Together, these changes resulted in the appearance of a new group, reptiles.
Seas in this epoch were dominated by mollusks, primitive arthropods, cartilaginous, and lobe-finned fishes.
1.07: Pangea and Great Extinction
At the end of the Carboniferous period, there have been several important events. Firstly, all Earth continents collided in a single continent Pangea. Second, an active mountain-building started; this orogeny formed Urals, Altai, the Caucasus, Atlas, Ardennes. Then part of Pangaea (namely, Australia) “drove” to the South Pole, thus started the Great glaciation. Temperatures on Earth were thus even lower than it is now, in the epoch of Great Cenozoic glaciation.
Interesting is that these processes were not strongly affected the evolution of the biosphere, at least in the beginning. Of course, there are were new types of vegetation, conifer forests, savannas, and deserts. Three ferns declined, cycads (rare now) appeared. However, the fauna has not changed. The role of reptiles increased significantly, many of them were insectivorous, and some reptiles (synapsids) started to acquire characters of the future mammals. Amphibian stegocephalians have still thrived. Higher insects (insects with metamorphosis) were close to modern Hymenoptera and lived on conifers, and they played an essential role in the further evolution of the seed. In a forest, litter lived multiple herbivorous and predatory cockroach-like insects.
Reptile metabolism is entirely compatible with water life, so in Permian, some reptilian groups “returned” to water (this process continued in Mesozoic): there were marine, fish-eating mesosaurs, and freshwater hippo-like pareiasaurs.
At the end of the Permian period, about 270 million years ago, glaciation stopped. However, orogeny intensified, half of Siberiawere covered with volcanic lava (famous Siberian Traps). That event probably was the reason for the great extinction of marine life: trilobites did not survive Permian, as well as 40% of cephalopods, 50% echinoderms, 90% brachiopods, and bryozoans, almost all corals and so on. More or less happily escaped were only sponges and bivalvians. However, some groups appeared first at this time, for example, contemporary bony fishes and decapod crustaceans. | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/01%3A_The_Really_Short_History_of_Life/1.06%3A_Coal_and_Mud_Forests.txt |
In the Triassic and early Jurassic, Pangea begins to disintegrate. The Atlantic Ocean (which still grows) opened. The climate was warm at first but very dry, and by the end of the era, it gradually became more convenient to the terrestrial life.
Among the seed plants, there appeared more advanced groups like bennettites, which participate in making savanna type vegetation (without grasses, though, the role of grasses was likely played with ferns, mosses, and lichens). Seeds of many plants were protected by scales or were embedded in an almost closed cupula. Seed protection was the “answer” of seed plants to the appearance of numerous phytophagous insect groups. Some other groups of insects began to adapt to the pollination of seed plants; this was an additional factor to facilitate the growing of seed covers.
Reptilians were still dominated but gradually replaced with various groups of archosauromorphs, the most advanced reptiles by that time, able to move very quickly, typically using only two legs.
Simultaneously run there were processes of “mammalization” and “avification” of reptiles. Ancestors of mammals were now in a small dimensional class and became insectivorous; this is because small herbivorous reptiles were simply physiologically impossible. Plant food is not very nutritional, and reptile feeding apparatus was unable to extract enough calories to support small, presumably more active animal. Giant herbivorous reptiles have less relative surface and therefore need fewer calories. Only turtles are an exception because of their “super-protection”, which however has closed all further ways to improve the organization.
Ancestors of mammals were animals of the size of a hedgehog or less; they continued to improve their dental system, the thermal insulation system, and increase the size of the brain. The result was the emergence of first the first true mammals.
Among “true” reptiles, dinosaurs (birds’ancestors), crocodiles, and pterosaurs (which dominate the air for the next 70 million years) have appeared.
In the seas, there are first diatom algae, that stimulated the zooplankton, and in turn, cephalopods, which dominated throughout the Mesozoic. Also, to replace the extinct by this time mesosaurs, appeared new groups of marine reptiles, for example, notosaurs and molluscivorous placodonts.
1.09: Jurassic Park- World of Reptiles
The climate on Earth in this epoch (Jurassic and Early Cretaceous) approached the optimum, the split of the continental plates led to its humidification. A new flourishing of fauna and flora began. The sea strongly prevailed over the land, even high continental platforms such as the Russian and North African, were flooded.
The abundance of phytoplankton and zooplankton caused the thrive of marine fauna, including sponges, corals, bivalve mollusks (who took an active part in the construction of bioherms), echinoderms, etc. Ichthyosaurs and plesiosaurs were the most abundant marine predators.
Interestingly that in fossil deposits, pregnant females of ichthyosaurs are often found. Therefore, the ichthyosaurs were not only viviparous but also gave birth in conditions that “promoted” fossilization. The reason is they likely could not give birth as modern cetaceans: a tail up, this was not allowed with their vertical (like in fish, but not like in cetaceans) caudal fin. Then it seems that they were forced to give birth in shallow water, probably forming large groups (like modern seals).
On land, there were forests similar to the recent temperate taiga, composed mainly of representatives of the ginkgo class. Many of them were technically also angiosperms as their seeds were well protected by additional covers. These forests were mostly inhabited by insects, and primitive mammals hunted for them.
In open spaces, savanna forests were maintained (as modern grasslands exist only due to the constant pressure of ungulates) by giant herbivorous dinosaurs, replacing all the other groups with size of a modern cow and bigger. There also lived numerous predatory dinosaurs, both large and small bird-like insectivorous forms.
Flight of ancient birds was still very imperfect. The ancestors of birds needed feathers mainly for thermal insulation, and the flight occurred from the jumping movements required to catch flying insects. There is no much difference between archosauromorph reptiles and birds; in fact, flying is the only radical difference of birds.
The other group of flying archosaurs, pterosaurs, dominated the water and land borders. Ancestors of pterosaurs were fish-eating animals, and their flight arose as an adaptation to catching prey from the water. | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/01%3A_The_Really_Short_History_of_Life/1.08%3A_Renovation_of_the_Terrestrial_Life.txt |
Cretaceous and Paleogene periods are usually referred to as different eras. However, here we join them in one epoch, as the development of the biosphere between the Cretaceous and the Paleogene did not change its direction.
The climate on Earth at that time was generally favorable for life, at in the end of the Cretaceous period, one of an absolute maximum of temperatures on Earth was observed. Continents gradually acquired current positions and outlines. Alpine orogeny began, then Andes and the Rocky Mountains arose, and then the Himalayas.
The main event of this epoch was the Aptian revolution. At the very end of the Lower Cretaceous almost simultaneously appeared those groups of animals and plants which are dominant to this day: flowering plants, polypod ferns, placental mammals, higher (tailless) birds, social insects (bees, ants and termites), butterflies, and higher bony fishes.
The origin of flowering plants for a long time was considered enigmatic. However, they do not radically differ from the rest of the seed plants: neither double fertilization nor protection of ovaries, much less the presence of a flower are unique attributes of flowering plants.
On the other hand, recent studies of both fossil and modern flowering plants indicate that the first flowering plants were herbaceous perennials, and some of them even aquatic. It is possible that during the previous epochs, some smaller primitive “gymnosperms”, so-called “seed ferns” gradually acquired a herbaceous appearance, together with the capacity for easy vegetative reproduction (“partiality”), and a much shorter and more optimized life cycle. In the same direction, many other groups of seed plants were evolved, pushing each other’s evolution, but the ancestors of flowering plants were the first to achieve this level.
Flowering plants colonized the land quickly, first at herbaceous stories where ferns and mosses could not compete with them (and there were no other seed plants, too). Then secondary woody flowering trees were formed, and apparently, they began to interfere with the woody “gymnosperms”. By the end of the era, angiosperms forced out all other plants (except conifers) on the periphery of the ecosystems. As the climate gradually differentiated (becoming colder in high latitudes and warmer in the lower latitudes), tropical forests arose (they did not exist from the Carboniferous period).
An important event in the middle of the Upper Cretaceous was the occurrence of graminoids (grass-like plants). Capable of firmly retaining captured territory, they began to play an increasing role in communities.
The leaf litter of flowering plants, which is much copious than that of other seed plants (remember their fast life cycle), dramatically changed the carbon regime of freshwater ecosystems. Most of the oligotrophic (as modern sphagnum bogs) places have become mesotrophic or eutrophic, rich in organic substances. This is associated with strong changes in the fauna of insects (the emergence of higher forms of Diptera and beetles), and in turn, associated with the previous event the emergence of numerous insectivorous lizards, as well as with the radiation of tailed amphibians. Another consequence was probably a change of the outflow of some elements to the sea, possibly having an influence on the further development of the marine communities.
In the seas, various crocodiles, hampsosaurs, and giant mosasaur lizards dominated, and then extinct, likely due to the rapid radiation of fast-swimming higher bony fishes. At the end of the era, cetaceans appeared. Cephalopods began to decline, but the role of gastropods and bivalves significantly increased.
Extinction of dinosaurs is usually called the main event of this era. It must be said, however, that many dinosaur groups died out much earlier than the end of the Cretaceous, and many faded gradually, so Cretaceous extinction was only the “last stroke” of their decline.
On the other hand, the often-named exogenous causes of extinction (meteorite, etc.) do not explain why it touched practically only dinosaurs and had little effect on the evolution of the other tetrapods, insects and plants. In most of Earth history, exogenous influences cannot be firmly tied to any evolutionary event, for example, the time of the appearance of the largest meteorite craters of the Phanerozoic cannot be associated with any extinction.
One of the endogenous causes of extinction was the appearance of a predator capable of feeding on small and medium-sized prey (Rautian’s hypothesis). The fact is that before the Cretaceous period, the animals of the small-sized class were represented only by insectivorous forms. However, gradually improving the dental apparatus, some mammals finally switched to plant food. These improvements finally led to the emergence of predatory forms capable of feeding on these herbivorous mammals. (Note that insectivorous animals of small size could not serve as regular food for any predator according to the law of the ecological pyramid.)
Since such a predator (they could be small predatory lizards, snakes, birds, and other mammals that appeared in this era) could not be specialized only in one kind of prey, it was necessarily the main enemy of small offspring of giant dinosaurs.
The other point is that the average size of adult dinosaurs increased dramatically by the end of the Cretaceous (this is the typical race of arms between prey and predator), but young dinosaurs simply could not be large! Dinosaur eggs had an upper limit of size because they (1) must be warmed to the center and also (2) be reasonably easy to hatch.
So small carnivores added much pressure to the gradual extinction of herbivorous, and after them, large predatory dinosaurs. Small dinosaurs evolve into birds, and whoever was left, did not have any significant advantages over mammals and birds, and therefore lost in the competition.
It is curious that the extinction of large predatory forms led to a kind of “vacuum” in terrestrial communities, and the most unexpected groups pretended to be predators before the advent of real predatory mammals (at the end of epoch): there were terrestrial crocodiles, giant predatory birds, and carnivorous ungulates.
Pterosaurs evolved into more and more large forms, and at the end of the era, they were unable to withstand competition with increasingly better flying birds. However, the first flying mammals appeared: bats, whose flight arose, perhaps, as a means to save themselves from tree-ridden predators. Bats and birds safely divided the habitat, which is why they co-exist today.
Winning groups started extensive radiation. In the described epoch, several hundreds of order-level groups of mammals, birds and bony fishes appeared, and the most orders of flowering plants.
1.11: Last Great Glaciation
Movements of continents in this epoch led to very adverse consequences. Panama and Suez isthmus closed, Antarctica gradually shifted to the area of the South Pole, and the northern continents surrounded the Arctic region as a ring. Everything now was ready for new Great Glaciation.
Life in the seas has not changed much. At the beginning of the epoch, due to the dryer climate and the progressive development of herbivorous mammals, grasslands were extensively expanded. These areas were inhabited by a fauna in which various proboscis, ungulates, rodents, and predatory mammals dominated.
One of the most curious episodes of this era was the Great Inter-American Exchange, the result of the formation of the Panama Isthmus. South America, isolated so far from all other continents (like Australia now), experienced the invasion of more advanced North American groups. Some South American animals have successfully withstood this onslaught and even advanced far to the north (opossums, armadillos, porcupines). However, the more significant part of the South American fauna went extinct.
After the formation of the glaciers, the rich Antarctic fauna and flora also died out, the last remnants (refugia) of which are now in the remnants of flooded Zealandia continent: now islands New Zealand, Lord Howe, and New Caledonia.
The advent of the glacier led to the formation of another type of community, arctic steppe: tundra, which advanced or retreated along with the ice.
The final accord of the development of the biosphere in this era was the appearance (most likely in East Africa) of representatives of the species Homo sapiens L. | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/01%3A_The_Really_Short_History_of_Life/1.10%3A_The_Rise_of_Contemporary_Ecosystems.txt |
Treemaps placed above are alternatives to dendrograms (“phylogeny trees”) and classification lists (“classifs”). Please remember that this is only one of ways to represent hierarchical, tree-like data. All three approaches are generally equivalent.
2.02: Illustrations
Below, all black and white illustrations were provided by Georgij Vinogradov and Michail Boldumanu.
3.01: Foundations of Science
Principle of Actuality
It states that current geologic processes, occurring at the same rates observed today, in the same manner, account for all of Earth’s geological features. The central argument of this principle is “The present is the key to the past.”
Occam’s razor
The principle of simplicity is the central theme of father William of Occam’s (ca. 1300) approach, so much so that this principle has come to be known as “Occam’s Razor.” Occam used his principle to eliminate unnecessary hypotheses and favor shortest explanation (which nowadays is called most parsimonous).
Principle of Falsification
The principle of falsification by sir Karl Popper defined as "A theory is falsifiable ... if there exists at least one ... statement[s] which [is] forbidden by it". An example of non-falsifiable hypothesis could be the Russel’s teapot: “If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes.”
Null and Alternative Hypothesis
Ronald Fisher, British statistician and geneticist formulated an approach of two rival hypotheses: null hypothesis and the alternative hypothesis. If being tested with alternative hypothesis, it is failed-to-reject if the null hypothesis is rejected based on statistical evidence.
3.02: Few Drops of Geology
Geological Time
Stratigraphy refers to the natural and cultural soil layers that make up an archaeological deposit. The notion is tied up with 19th-century geologist Charles Lyell, who stated that because of natural forces, soils found deeply buried will have been laid down earlier—and therefore be older—than the soils found on top. The age of rock layers are determined by fossils using relative dating and absolute dating. If there are same fossils in more than one layers, these layers have the same age The majority of the time fossils are dated using relative dating techniques. Using relative dating the fossil is compared to something for which an age is already known.
Absolute dating is used to determine a precise age of a rock or fossil through radiometric dating methods. Radioactive minerals occur in rocks and fossils are almost a geological clock. Radioactive isotopes break down at a constant rate over time through radioactive decay. By measuring the ratio of the amount of the stable isotope to the amount of the radioactive isotope, an age can be determined.
Origin of Earth
Pierre-Simone Laplace reached the conclusion that the stability of the Solar system would best be accounted for by a process of evolving from chaos. Laplace suggested that:
1. The Sun was originally a giant cloud of gas or nebulae that rotated evenly.
2. The gas contracted due to cooling and gravity.
3. This forced the gas to rotate faster, just as an ice skater rotates faster when his extended arms are drawn onto his chest.
4. This faster rotation would throw off a rim of gas, which following cooling, would condense into a planet.
5. This process would he repeated several times to produce all the planets.
6. The asteroids between Mars and Jupiter were caused by rings which failed to condense properly.
7. The remaining gas ball left in the centre became the Sun.
It is frequently accepted nowadays that in addition to the above processes, Earth underwent the heating stage and at some point likely became a “lava ball”, and then cooling stage when water start to condense and make primary ocean. Also, geology and astronomical features of Moon suggest that this body originated from Earth on the some very early stage of Solar system evolution.
Structure of Earth
The Earth consists of concentric layers, core, mantle and crust. Core is in the center and is the hottest part of the Earth. It is solid and possibly made up of metals with temperatures of up to 5,500°C. Mantle is the widest section of the Earth. It has a thickness of approximately 2,900 km. The mantle is made up of semi-liquid magma. Crust is the outer layer of the Earth. It is a thin layer up to 60 km deep. The crust is made up of tectonic plates, which are in constant motion. Earthquakes and volcanoes are most likely to occur at plate boundaries.
Everything in Earth can be placed into one of four major subsystems: lithosphere (land), hydrosphere (water), biosphere (living things), and atmosphere (air). Earth is the only known planet that has a layer of water.
The differentiation of Earth body finally resulted in developing of lighter gas layer on the surface (primary atmosphere), initially very thin and relatively cold. Therefore, water vapour were condensed into primary ocean (primary hydrosphere). According to the principle of actuality, it should be close to today’s volcanic gases 15% of CO\(_2\), plus CH\(_4\) (methane), NH\(_3\) (ammonia), H\(_2\)S, SO\(_2\) and different “acidic smokes” like HCl.
Plate Tectonics
Alfred Wegener is best known as the creator of the theory of continental drift by hypothesizing in 1912 that the continents are slowly gliding around the Earth. According to Wegener, in the beginning of Mesozoic era, there were two large continents, Gondwana and Laurasia which were separated by Tethys Ocean. Gondwana was one of Earth broke up around 180 000 years ago. Moreover, in Permian period, all continents where united in one as Pangaea, which was surrounded by one big ocean.
Mantle is the thickest Earth layer but it slowly moves. Mantle convection breaks the lithosphere into plates and continues to move them around Earth surface. These plates might move alongside each other, move by, and even collide with each other. As a result, oceans basins may open, it may move continents, create mountains, and cause earthquakes. Continents will keep changing their positions due to mantle convection.
Hotspots are the living proofs of mantle convection. In the United States, there are two locations which are considered hotspots: Yellowstone and Hawaii. A hotspot is a place where the intense heat of the outer core radiates through the mantle. The most amazing fact about them is that whereas ocean (Hawaii) or continental (Yellowstone) plates move on, these hotspots stay in place! This is why in the past, Yellowstone was located westward, and Hawaiian volcanoes northward. | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/02%3A_Diversity_of_Life/2.01%3A_Diversity_maps.txt |
To understand life, a basic knowledge of chemistry is needed. This includes atoms (and its components like protons, neutrons and electrons), atomic weight, isotopes, elements, the periodic table, chemical bonds (ionic, covalent, and hydrogen), valence, molecules, and molecular weight:
Atoms
The smallest unit of matter undividable by chemical means. An atom is made up of two main parts: a nucleus vibrating in the centre, and a virtual cloud of electrons spinning around in zones at different distances from the nucleus (not to be confused with the cell nuclei). When atoms interact, its less like the bumping of balls and more a matter of attraction and repulsion; at atomic levels, mass is much less an important consideration than charges, which are electrical: positive, negative, or neutral (balanced).
Protons
Stable elementary particles having the smallest known positive charge, found in the nuclei of all elements. The proton mass is less than that of a neutron. A proton is the nucleus of the light hydrogen atom, i.e., the hydrogen ion.
Neutrons
Like protons but neutral charge and also located in the nucleus.
Radioactive
decay occurs in unstable atomic nuclei—that is, ones that do not have enough binding energy to hold the nucleus together due to an excess of either protons or neutrons.
Electrons
determine how atoms will interact. Located on the outside of the nucleus known as the outer shell and has a negative charge that determines what type of change it has.
Atomic weight
is the average of the masses of naturally-occurring isotopes.
Isotopes
each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons.
Periodic table of elements
The periodic table we use today is based on the one devised and published by Dmitri Mendeleev in 1869. The periodic table of the chemical elements displays the organization of matter.
Chemical bonds
are attractive forces between the atoms.
Valence
A typical number of chemical bonds in this element. For example, nitrogen (N) has valence 3 and therefore usually makes three bonds.
Molecules
Molecules form when two or more atoms form chemical bonds with each other.
Molecular weight
calculated as a sum of atomic weights.
Covalent bonds
When two atoms bind in one molecule, there are two variants possible. Non-polar bond is when electrons are equally shared between atoms. Polar bond is when one of atoms attract electrons more than another, and therefore becomes partly negative while the second—partly positive.
Ionic bonds
Ionic bonding is the complete transfer of some electron(s) between atoms and is a type of chemical bond that generates two oppositely charged ions.
It is essential to know that protons have a charge of $+1$, neutrons have no charge, and electrons have a charge of $-1$. The atomic weight is equal to the weight of protons and neutrons. Isotopes have the same number of protons but different number of neutrons; some isotopes are unstable (radioactive).
One of the most outstanding molecules is water. Theoretically, water should boil at much lower temperature, but it boils at 100$^\circ$C just because of the hydrogen bonds sealing water molecules. These bonds arise because a water molecule is polar: hydrogens are slightly positively charged, and oxygen is slightly negatively charged.
Another important concept related to water is acidity. If in a solution of water, the molecule takes out proton (H$^+$), it is an acid. One example of this would be hydrochloric acid (HCl) which dissociates into H$^+$ and Cl$^-$. If the molecule takes out OH$^-$ (hydroxide ion), this is a base. An example of this would be sodium hydroxide (NaOH) which dissociates into Na$^+$ and hydroxide ion.
To plan chemical reactions properly, we need to know about molar mass and molar concentration. Molar mass is a gram equivalent of molecular mass. This means that (for example) the molecular mass of salt (NaCl) is $23 + 35$, which equals 58. Consequently, one mole of salt is 58 grams. One mole of any matter (of molecular structure) always contains $6.02214078 \times 10^{23}$ molecules (Avogadro’s number).
The density of a dissolved substance is the concentration. If in 1 liter of distilled water, 58 grams of salt are diluted, we have 1M (one molar) concentration of salt. Concentration will not change if we take any amount of this liquid (spoon, drop, or half liter).
Depending on the concentration of protons in a substance, a solution can be very acidic. The acidity of a solution can be determined via pH. For example, if the concentration of protons is 0.1 M ($1 \times 10^{-1}$, which 0.1 grams of protons in 1 liter of water), this is an extremely acidic solution. The pH of it is just 1 (the negative logarithm, or negative degree of ten of protons concentration). Another example is distilled water. The concentration of protons there equals $1 \times 10^{-7}$ M, and therefore pH of distilled water is 7. Distilled water is much less acidic because water molecules dissociate rarely.
When two or more carbon atoms are connected, they form a carbon skeleton. All organic molecules are made of some organic skeleton. Apart from C, elements participate in organic molecules (biogenic elements) are H, O, N, P, and S. These six elements make four types of biomolecules: (1) lipids—hydrophobic organic molecules which do not easily dissolve in water; (2) carbohydrates or sugars, such as glucose (raisins contain lots of glucose) and fructose (honey); by definition, carbohydrates have multiple $-$OH group, there are also polymeric carbohydrates (polysaccharides) like cellulose and starch; (3) amino acids (components of proteins) which always contain N, C, O and H; and (4) nucleotides combined from carbon cycle with nitrogen (heterocycle), sugar, and phosphoric acid; polymeric nucleotides are nucleic acids such as DNA and RNA.
On the next page is the most important thing for everyone who need to learn chemistry (and yes, you need to): periodic table. It was invented by Dmitry Mendeleev in 1869 and updated since, mostly by adding newly discovered and/or synthesized elements. Note that Roman numerals were added to standard table to show numbers of main groups. | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/03%3A_Life_Stories/3.03%3A_Chemistry_of_Life.txt |
There are two basic features of all Earth life (and we do not actually know any other Life):
1. Semi-permeable membranes:
Most of living cells surrounded by oily cover which consists of two layers made of lipids and embedded there proteins. These membranes allow some molecules (e.g., gases or lipids) to go through, but most molecules only enter “with permission”, under the tight control of membrane proteins.
2. DNA $\rightarrow$ RNA $\rightarrow$ proteins:
That sequence is called transcription (first arrow) and translation (second arrow). DNA stores information in form of nucleotide sequence, then fragments of DNA are copying into RNA (transcription). RNA, in turn, controls protein synthesis (translation). This is sometimes called the “central dogma of molecular biology”.
3.05: How to Be the Cell
Most simple, prokaryotic cell should perform several essential duties in order to survive. These are:
1. Obtaining energy. In all living world, the energy is accumulated in the form of ATP molecules. To make ATP, there are three most common ways:
Phototrophy
Energy from the light of Sun.
Organotrophy
Energy from burning of organic molecules, either slow (fermentation), or fast (respiration).
Lithotrophy
Energy from inorganic chemical reactions (“rocks”).
2. Obtaining building blocks (monomers which are using to built polymers like nucleic acids, proteins and polysaccharides). The principal monomer in the living world is glucose. From glucose, it is possible to chemically create everything else (of course, one must add nitrogen and phosphorous when needed). There are two principal ways to obtain monomers:
Autotrophy
Make monomers from carbon dioxide.
Heterotrophy
Take monomers from somebody else’s organic molecules.
There are six possible combinations of these above processes. For example, what we called “photosynthesis” is in fact photoautotrophy. Prokaryotes are famous because they have all six combinations at work.
3. Multiply. There are always three steps:
1. Duplicate DNA. As it is a double spiral, one must unwind it, and then build the antisymmetric copy of each chain in accordance with a simple complement rule—each nucleotide make hydrogen bond only with one nucleotide of other type:
A T
T A
G C
C G
2. Split duplicated DNA.
3. Split the rest of the cell.
Prokaryotic DNA is small and circular, optimized for the speedy duplication and division. Consequently, prokaryotes multiply with alarming speed.
4. Make proteins. This process involves transcription ans translation. As proteins are “working machines” of the cell and DNA is an “instruction book”, there must be the way to transfer this information from DNA to proteins. It usually involves RNA which serves as temporary “blueprints” for proteins:
1. DNA and RNA each contains four types of nucleotides, this is an alphabet.
2. With help of enzymes, pieces of DNA responsible for one protein (gene) copied into RNA. Rules are almost the same as for DNA duplication above, but T from DNA is replaced in RNA with U.
3. The sequence of nucleotides is a language in which every tree nucleotides mean one amino acid.
4. Ribosomes translate trios of nucleotides (triplets) into amino acids and make proteins. They do it in accordance with genetic code:
Genetic code. All amino acids designated with shortcuts.
U C A G
U UUU Phe
UUC Phe
UUA Leu
UUG Leu
UCU Ser
UCC Ser
UCA Ser
UCG Ser
UAU Tyr
UAC Tyr
UAA STOP
UAG STOP
UGU Cys
UGC Cys
UGA STOP
UGG Trp
U
C
A
G
C CUU Leu
CUC Leu
CUA Leu
CUG Leu
CCU Pro
CCC Pro
CCA Pro
CCG Pro
CAU His
CAC His
CAA Gln
CAG Gln
CGU Arg
CGC Arg
CGA Arg
CGG Arg
U
C
A
G
A AUU Ile
AUC Ile
AUA Ile
AUG Met
ACU Thr
ACC Thr
ACA Thr
ACG Thr
AAU Asn
AAC Asn
AAA Lys
AAG Lys
AGU Ser
AGC Ser
AGA Arg
AGG Arg
U
C
A
G
G GUU Val
GUC Val
GUA Val
GUG Val
GCU Ala
GCC Ala
GCA Ala
GCG Ala
GAU Asp
GAC Asp
GAA Glu
GAG Glu
GGU Gly
GGC Gly
GGA Gly
GGG Gly
U
C
A
G
5. Make sex. To evolve, organisms must diversify first, natural selection works only if there is an initial diversity. There are two ways to diversify:
1. Mutations which are simply mistakes in DNA. Majority of mutations are bad, and many are lethal. The probability to obtain useful mutation is comparable with probability to mend your cell phone using hammer.
2. Recombinations are much safer, they increase diversity but unable to create novelties. In addition, recombinations serve also as a way to discard bad genes from the “gene pool” of population because from time to time, two or more bad genes meet together in one genotype and this combination becomes lethal.
Prokaryotes developed bacterial conjugation when two cell exchange parts of their DNA, this facilitates recombination. In bacterial world, recombination is possible not only within one population, but sometimes also between different species, this is called horizontal gene transfer. | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/03%3A_Life_Stories/3.04%3A_Very_Basic_Features_of_Life.txt |
This small section will schematically describe structures of two cells, cell of eukaryote, and cell of prokaryote.
Cell of eukaryote, second-order cell: 1 nucleus, 2 nuclear envelope, 3 nuclear pore, 4 DNA = chromatin = chromosomes, 5 ribosomes (black), 6 ER, 7 AG, 8 vesicles, 9 vacuole (big vesicle), 10 mitochondria (surrounded with double membrane), 11 mitochondrial DNA, 12 chloroplast (surrounded with double membrane), 13 chloroplast DNA, 14 cytoskeleton (brown), 15 phagocytosis (caught in the middle of process), 16 cytoplasm, 17 cell membrane, 18 eukaryotic flagella.
Prokaryotic cell, cell of Monera, is much smaller, much more rigid and much simpler. Labels not provided because there is not much to label, and what is available, was already shown in the eukaryote. Except the cell wall which is outside of the cell membrane (some eukaryotes have cell wall though), and prokaryotic flagella (right bottom corner) which is just a molecule of protein:
3.07: Ecological Interactions- Two-Species Model
Two-species model allows to describe how two theoretical species might influence each other. For example, Species I may facilitate Species II: it means that if biomass (sum of weight) of Species I increases, biomass of Species II also increases (\(+\) interaction). There are also \(+\) and \(0\) interactions. Two species and three signs make six combinations:
+ 0 -
+ mutualism commensalism1 exploitation2
0 ... neutralism amensalism
- ... ... interference3
\(^1\) Includes phoresy (transportation), inquilinism (housing) and “sponging”.
\(^2\) Includes predation, parasitism and phytophagy.
\(^3\) Includes competition, allelopathy and aggression.
Mutualism
It sometimes called “symbiosis”. Two different species collaborate to make each other life better. One of the most striking example is lichenes which is algae-fungus mutualism.
Commensalism
Remember “Finding Nemo”? Clown fish lives inside actinia. This type of commensalism is called “housing”. Another example is suckerfish and shark, this is phoresy. Sponging happens when scavengers feed on what is left after the bigger carnivore meal.
Exploitation
This is the most severe interaction. Predation kills, but parasitism or phytophagy (the only difference is that second uses plants) do not.
Neutralism
Rare. Philosophically, everything is connected in nature, and if Species I and II live together, they usually interact, somehow.
Amensalism
This happens when suppressing organism is, for example, much bigger then the “partner”. Big trees often suppress all surrounding smaller plants.
Interference
Competition happens when Species I and II share same ecological niche, have similar requirements. Gause’s Principle says that sooner or later, one of them wins and another looses. Allelopathy is a mediated competition, typically through some chemicals like antibiotics. Most advanced (but least pleasant) is the direct aggression when individuals of one species physically eliminate the other one.
3.08: How to become an animal
Three driving forces of eukaryotic evolution:
• Prey and predator interactions
• Surface and volume
• Ecological pyramid (Fig. 3.8.1).
finally resulted in appearance of animals and plants. But these two groups originated differently.
Animals belong to the highest level of the pyramid of life (Fig. 3.8.2). They not only multi-cellular but also multi-tissued creatures. It is easy to become multicellular, enough is not to split cells completely after mitosis. And the big advantage is immediately feel: size.
To make a big body, it is much easier to join several cells then grow one cell. Explanation lays (as well as explanation of many other biology phenomena) in the surface/volume paradox: the more is the volume, the less is relative surface, and this is often bad. Multiplication of cells allows to be big without decreasing relative surface. And being big is a good idea for many living things, especially for plants (the more is the size, the more intensive is photosynthesis) and for prey in general (the bigger is prey, the more chances to survive after contact with predator).
But this is not working out of the box for active hunters like animals’ ancestors! To move, they need also the tight coordination between cells, and to eat, they need altruistic cells which feed other cells. Consequently, first animals (like phagocytella: Fig. 3.9.1) must acquire have at least two tissues: (1) surface cells, adapted to motion, likely flagellate, and (2) cells located in deeper layers, adapted to digestion, probably amoeba-like. This evolution could go through several stages:
• Blastaea: not the animal yet. Volvox, Proterospongia.
• Phagocytella. Two tissues: kinoblast and phagocytoblast. Trichoplax.
• Gastraea (jellyfish without “bells and whistles”). Three tissues: ectoderm, entoderm and mesoderm. Closed gut.
What about communication, circulation, gas exchange etc.? If the first animal was small enough, all of these will run without specialized tissues, via diffusion, cell contacts and so on. But when size grows, the surface/volume paradox dictates that new and new tissue and organ appear. And size surely will grow because there is a constant race of arms between prey and predator, and between different predators.
3.09: How to be an animal
More organized, bigger animal has multiple needs, and therefore, multiple tissues and organs (Fig. 3.9.2):
• locomotion: appendages, skin-muscular bag (A), fins;
• support: many types of skeleton (endoskeleton, chitinous exoskeleton, shells, skin plates) and hydrostatic skeleton based on body cavities filled with liquid (A + K + M);
• feeding and excretion: mouth, anus, intestines, pharynx (G), stomach (J), digestion glands (like liver, I) etc.;
• osmoregulation: simple nephridia (C) and complicated kidneys;
• gas exchange: external gills (B), internal lungs and tracheas;
• circulation: open (M) or closed blood system with hear(s) (L);
• reception: eyes (D), mechanical sensors (ears, hairs), chemical sensors (nose) and many others;
• communication: neural cells (neurons), nerves (groups of neurons) (F), ganglia (E) and brain (masses of neurons);
• reproduction: sexual organs filled with sexual cells (N), male and female, separately or together, and fertilization “tools”. | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/03%3A_Life_Stories/3.06%3A_Overview_of_the_Cell.txt |
From Georges Cuvier times, highest animal groups (phyla) are understood as different body plans (Fig. 3.10.2).
There are some important animal phyla with notes about their body plans. Note that most of mentioned characters do not belong to the 100% of phylum species. As biology is a science of exceptions, this is normal. The following table lists many of animal phyla and also classes of chordates. Look also on “split pyramid” scheme (Fig. 3.10.1).
Subregnum Spongia: no symmetry
Phylum 1. Porifera: sitting filtrators with skeletal spicules (H)
Subregnum Cnidaria: radial symmetry, stinging cells
Phylum 2. Anthozoa: sitting, colonial, with skeleton (I)
Phylum 3. Medusozoa: swimming, solitary, soft (A)
Subregnum Bilateria: bilateral symmetry, likely originated from crawling habit
Infraregnum Deuterostomia: with specific embryogenesis
Phylum 4. Echinodermata: small-plate exoskeleton, secondary radial, water-vascular appendages (E)
Phylum 5. Chordata: head and tail, gills in pharynx, axial skeleton (B)
Subphylum Vertebrata: vertebral column
Pisces: fish-like, gills
Classis 2. Chondrichtyes: cartilaginous, live in ocean
3. Actinopterygii: boned, rayed fins
4. Dipnoi: boned, thick fins, gills and lungs
Tetrapoda: four legs
Superclassis Anamnia: water eggs
Superclassis Amniota: terrestrial eggs
Classis 6. Reptilia: no feathers, four-pedal
7. Aves: feathers, bipedal
8. Mammalia: grinding jaws, fur, milk
Infraregnum Protostomia: specific embryogenesis
Superphylum Spiralia: worms, mollusks and alike
Phylum 6. Mollusca: shell, body straight (F)
Phylum 7. Lophophorata: shell and alike, body curved (J)
Phylum 8. Annelida: naked, segmented (G)
Superphylum Ecdysozoa: molting, with chitinous cuticle
Phylum 9. Nemathelminthes: worms with bending motion and primary cavity (C)
Phylum 10. Arthropoda: both body and appendages segmented (D)
Classis 1. Chelicerata: spiders, ticks, mites, scorpions
2. Malacostraca: crabs, lobsters, shrimp
3. Hexapoda: insects and alike
3.11.01: Syngamy and meiosis
• Syngamy if one of safest mechanisms of recombination
• Continuous syngamy is not good
• Meiosis is the counterpart of syngamy
• The simplest way to make meiosis is to split paired (homologous) chromosomes between two daughter cells, and then immediately (without S-phase) split duplicated DNA; thus meiosis has two divisions
3.11.02: Male and female
In syngamy, there are always two partners. They could be superficially almost identical—only genotypes and some surface chemistry differ. Two dangers are here: to mate with same genotype (then why to mate?) or mate with other species (which could result in broken genotype). To improve partner recognition, there are many mechanisms.
One is based simply on size. If one is bigger, then smaller one is presumably the good partner. From this point, smaller cell is called male, and bigger called female.
Now, females could invest in storage (and bigger size) whereas males invest in numbers. This strategy will dramatically improve fertilization and also allows to select better males. It results in big, non-motile female cells and small, fast-moving, numerous male cells. Here females called oocytes (or egg cells) and males—spermatozoa.
The ultimate step could be non-motile males too, but this is not frequent because they will need the external help for the fertilization. These non-motile male cells (spermatia) exist in red algae, sponges, crustaceans and flowering plants.
3.11.03: Mendels theory explanations and corrections
• In crossings, he often used two different variants of one character: two genotype variants (alleles, paralogs) of one gene which control two variants of one phenotype
• “Factors” (genes) are paired in plant but separated in gametes: because of meiosis
• One “factor” is dominant: one variant is working DNA, the other is not
• Different characters are separating between gametes independently: this is how anaphase I of meiosis goes
• This is because different characters are located in different places: i.e., in different pairs of chromosomes
• If genes are located in the same chromosome, they are linked and will not be inherited independently
• However, linkage could be broken in crossing-over (it runs in prophase I of meiosis)
• Sometimes, sex is determined with chromosome set: one gender has the pair where chromosomes are non-equal
3.11.04: Anaphase I and recombinants
Imagine that parent is fully heterozygous, like in Mendel’s first generation. It has red flowers (Rr) and long stems (Ll), the whole genotype is then “RrLl”.
There are two possibilities in the anaphase I:
1. Either “R-chromosome” and “L-chromosome” come together to one pole (consequently, “l-chromosome” and “r-chromosome” to other pole)
2. Or “R-chromosome” + “l-chromosome” come one way, and “r-chromosome” + “L-chromosome” another way
Each variant has 1/2 (50%) probability, like in throwing a coin.
Four gamete types are possible:
1. RL
2. rl
3. Rl
4. rL
Four gametes give 16 combinations (phenotypes are short-stemmed, long-stemmed, white-flowered and red-flowered):
RL rl Rl rL
RL RRLL RrLl RRLl RrLL
rl RrLl rrll Rrll rrLl
Rl RRLl Rrll RRll RrLl
rL RrLL rrLl RrLl rrLL
(Please count proportions to see that it is really 9:3:3:1.)
As R and L are dominant, only four phenotypes appear, and two of them are recombinants, phenotypes unlike parents. | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/03%3A_Life_Stories/3.10%3A_Animalia-_body_plans_phyla_and_classes.txt |
• The following factors “pushed” plants on land:
1. Availability of light
2. Temperature-gases conflict
3. Increased competition in shallow waters
• Two first tissues:
1. isolating/ventilating compound epidermis
2. photosynthetic/storage ground tissue were response to desiccation.
• Epidermis could be developed in advance as adaptation to spore delivery.
• Next stages:
1. supportive tissues to solve “Manhattan problem”
2. vascular tissues to transport water and sugars
3. branching
4. absorption tissues (or mycorrhiza) for water uptake
3.12.02: Life cycles
This is a short list of terms associated with life cycles:
• mitosis, meiosis (R!), syngamy (Y!)
• vegetative reproduction (cloning), sexual reproduction and asexual reproduction
• result of syngamy: zygote; participant of syngamy: gamete
• smaller gamete: male, bigger gamete: female; movable male gamete: spermatozoon (sperm), motionless female gamete: oocyte (egg cell)
• result of meiosis: spores
• haplont (plants: gametophyte) and diplont (plants: sporophyte)
• sporic life cycle (like in plants), gametic life cycle (like in animals) and sporic (only protists)
• sporic: gametophyte dominance (mosses) and sporophyte dominance (ferns and seed plants)
Note that Mendel “saw” genes mixed, segregated and then immediately mixed/recombined again, whereas in the life cycle of unicellular eukaryote, they are segregated, then mixed/recombined and immediately segregated again.
This is because for multicellular organism, diploid condition is better. Since not all genes are strictly dominant, then (1) diploids are broader adapted, due to two variants of gene; (2) if one copy breaks (mutation), the other still works. Diploid condition is also a handy tool to effectively segregate homozygous lethal mutations.
Syngamy is a cheapest and safest way to mix genes within population. After syngamy, the most natural step for unicellular organism is to return DNA amount back to normal, reduce it through the meiosis (of course, genes do not unmix). However, if the organism is multicellular, there is a choice because (a) they already have the developmental program allowing them to exist as stable group of cells and (b) diploid is better. So, while some of multicellular life head to meiosis, zygote of many others proceeds to diplont.
Diplont is a body of diploid cells. It still “keeps in mind” that at some point, meiosis will be required, but this could be postponed for now. Main goal for the diplont is to grow its multicellular body and (if this is reasonable), clone itself with vegetative reproduction.
Then, when time came, meiosis occurs and resulted in 4 cells. They are haploid. Here is the second choice. These new cells could proceed back to syngamy, like in animals and some protists; but in other protists and plants, these cells (now they are called spores) will grow into haplont.
Haplont is a body of haploid cells. Again, it “remembers” that at some point, syngamy will be required, but at the moment, it enjoys multicellular life which could be superficially very similar to diplont.
Finally, some cells of haplont become gametes which go to sexual reproduction, syngamy. Life cycle is now completed.
3.12.03: Three phyla of plants
As animal phyla differ by body plans, plant phyla differ with life cycles. Plants started from green algal ancestors which have no diplont, only zygote was diploid in their life cycle. But diplont is better! So plants gradually increased the diploid stage (plant’s diplont is called sporophyte) and reduced haploid (gametophyte). And they still did not reach the animal (gametic) shortcut of the life cycle, even in most advanced plants there is small gametophyte of few cells. One of reasons is that plants do not move, and young sporophyte always starts its life on the mother gametophyte.
Mosses have sporophyte which is adapted only for spore dispersal. Gametophyte is then a main photosynthetic stage which makes most of photosynthesis and therefore need to be big. However, it cannot grow big! This is because for the fertilization, it needs water. Therefore, mosses could not be larger then the maximal level of water.
To overcome the restriction, stages role must reverse. Ferns did that, and their gametophyte is really small and adapted only for fertilization. This works pretty well but only if the plant body is relatively small.
Trees capable to secondary growth (that is, thickening of stem with special “stem cells”) will experience the ecological conflict between ephemeral, minuscule gametophyte and giant stable sporophyte. Whatever efforts sporophyte employs, result is unpredictable. Birth control, so needed for large organisms, is impossible. One solution is not to grow so big.
Another solution is much more complicated. They need to reduce gametophyte even more and place it on sporophyte. And also invent the new way of bringing males to female because between tree crowns, the old-fashioned water fertilization is obviously not possible. To make this new way (it called pollination), some other external agents must be employed. First was a wind, and the second came out of the clever trick to convert enemies into friends: insects.
Still, result was really cumbersome and the whole life cycle became much slower than in ferns, it could span years! The only way was to optimize and optimize it, until in flowering plants, it starts to be comparable and even faster then in two other phyla. | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/03%3A_Life_Stories/3.12%3A_Plant_stories/3.12.01%3A_Plants_and_plants.txt |
On the next page, see the map of “ideal continent” representing the Earth landmasses, ocean currents, climates and ecoregions (according to Rjabchikov, 1960).
Next few pages are filled with schematic maps of four real continents. However, these maps are simplified to the extreme in order to show the most important ecological and geographical features of the each continent.
4.02: Architectural Models of Tropical Trees- Illustrated Key
Tropical landscape is full of trees. They rarely flower or bear fruits, and often have very similar leaves. However, shapes and structures of trunks and crowns (so similar in temperate regions) are seriously different in tropics. If you want to know tropics better, you should learn these architectural models.
The following key is based on Halle, Oldeman and Thomlinson (1978) “Tropical Trees and Forests” (pp.84–97).
1. Stem strictly unbranched (Monoaxial trees) ...... 2.
— Stems branched, sometimes apparently unbranched in Chamberlain’s model (polyaxial trees) ...... 3.
2. Inflorescence terminal ...... Holttum’s model.
Monocotyledon: Corypha umbraculifera (Talipot palm—Palmae). Dicotyledon: Sohnreyia excelsa (Rutaceae).
— Inflorescences lateral ...... Corner’s model.
(a) Growth continuous:
Monocotyledon: Cocos nucifera (coconut palm—Palmae), Elaeis guineensis (African oil palm—Palmae). Dicotyledon: Carica papaya (papaya—Caricaceae).
(b) Growth rhythmic:
Gymnosperm: Female Cycas circinalis (Cycadaceae). Dicotyledon: Trichoscypha ferntginea (Anacardiaceae).
3(1). Vegetative axes all equivalent, homogenous (not partly trunk, partly branch), most often orthotropic and modular ...... 4.
— Vegetative axes not equivalent (homogenous, heterogenous or mixed but always clear difference between trunk and branches) ...... 7.
4. Basitony, i.e., branches at the base of the module, commonly subterranean, growth usually continuous, axes either hapaxanthic or pleonanthic ...... Tomlinson’s model.
(a) Hapaxanthy, i.e., each module determinate, terminating in an inflorescence:
Monocotyledon: Musa cv. sapientum (banana—Musaceae). Dicotyledon: Lobelia gibberoa (Lobeliaceae).
(b) Pleonanthy, i.e., each module not determinate, with lateral inflorescences
Monocotyledon: Phoenix dactylifera (date palm—Palmae).
— Acrotony, i.e., branches not at the base but distal on the axis ...... 5.
5. Dichotomous branching by equal division of apical meristem ...... Schoute’s model.
Monocotyledons:
Vegetative axes orthotropic: Hyphaene thebaica (doum palm—Palmae).
Vegetative axes plagiotropic: Nypa fruticans (nipa palm—Palmae)
— Axillary branching, without dichotomy ...... 6.
6. One branch per module only; sympodium one-dimensional, linear, monocaulous, apparently unbranched, modules hapaxanthic, i.e., inflorescences terminal ...... Chamberlain’s model.
Gymnosperm: Male Cycas circinalis (Cycadaceae). Monocotyledon: Cordyline indivisa (Agavaceae). Dicotyledon: Talisia mollis (Sapindaceae).
— Two or more branches per module; sympodium three-dimensional, nonlinear, clearly branched; inflorescences terminal ...... Leeuwenberg’s model.
Monocotyledon: Dracaena draco (dragon tree—Agavaceae). Dicotyledon: Ricinus communis (castor-bean), Manihot esculenta (cassava), both Euphorbiaceae.
7(3). Vegetative axes heterogeneous, i.e., differentiated into orthotropic and plagiotropic axes or complexes of axes ...... 8.
— Vegetative axes homogeneous, i.e., either all orthotropic or all mixed ...... 18.
8. Basitonic (basal) branching producing new (usually subterranean) trunks ...... McClure’s model.
Monocotyledon: Bambusa arundinacea (bamboo—Gramineae / Bambusoideae). Dicotyledon: Polygonum cuspidatum (Polygonaceae).
— Acrotonic (distal) branching in trunk formation (never subterranean) ...... 9.
9. Modular construction, at least of plagiotropic branches; modules generally with functional (sometimes with more or less aborted) terminal inflorescences ...... 10.
— Construction not modular; inflorescences often lateral but always lacking any influence on main principles of architecture ...... 13.
10. Growth in height sympodial, modular ...... 11.
— Growth in height monopodial, modular construction restricted to branches ...... 12.
11. Modules initially equal, all apparently branches, but later unequal, one becoming a trunk ...... Koriba’s model.
Dicotyledon: Hura crepitans (sand-box tree—Euphorbiaceae).
— Modules unequal from the start, trunk module appearing later than branch modules, both quite distinct ...... Prevost’s model.
Dicotyledon: Euphorbia pulcherrima (poinsettia—Euphorbiaceae), Alstonia boonei (emien—Apocynaceae).
12(10). Monopodial growth in height rhythmic ...... Fagerlind’s model.
Dicotyledon: Cornus alternifolius (dogwood—Cornaceae), Fagraea crenulata (Loganiaceae), Magnolia grandiflora (Magnoliaceae):
— Monopodial growth in height continuous ...... Petit’s model.
Dicotyledon: Gossypium spp. (cottons—Malvaceae).
13(9). Trunk a sympodium of orthotropic axes (branches either monopodial or sympodial, but never plagiotropic by apposition) ...... Nozeran’s model.
Dicotyledon: Theobroma cacao (cocoa—Sterculiaceae).
— Trunk an orthotropic monopodium ...... 14.
14. Trunk with rhythmic growth and branching ...... 15.
— Trunk with continuous or diffuse growth and branching ...... 16.
15. Branches plagiotropic by apposition ...... Aubreville’s model.
Dicotyledon: Terminalia catappa (sea-almond—Combretaceae).
Theoretical Model II defined as an architecture resulting from growth of a meristem producing a sympodial modular trunk, with tiers of branches also modular and plagiotropic by apposition, has still not been recognized in a known example. It would occur here, next to Aubreville’s model from which it differs in its sympodial trunk.
— Branches plagiotropic but never by apposition, monopodial or sympodial by substitution ...... Massart’s model.
Gymnosperms: Araucaria heterophylla (Norfolk Island pine—Araucariaceae). Dicotyledon: Ceiba pentandra (kapok—Bombacaceae), Myristica fragrans (nutmeg—Myristicaceae).
16(14). Branches plagiotropic but never by apposition, monopodial or sympodial by substitution ...... 17.
— Branches plagiotropic by apposition ...... Theoretical model I.
Dicotyledon: Euphorbia sp. (Euphorbiaceae)
17. Branches long-lived, not resembling a compound leaf ...... Roux’s model.
Dicotyledon: Coffea arabica (coffee—Rubiaceae), Bertholletia excelsa (Brazil nut—Lecythidaceae).
— Branches short-lived, phyllomorphic, i.e., resembling a compound leaf ...... Cook’s model.
Dicotyledon: Castilla elastica (Ceara rubber tree—Moraceae)
18(7). Vegetative axes all orthotropic ...... 19.
— Vegetative axes all mixed ...... 22.
19. Inflorescences terminal, i.e., branches sympodial and, sometimes in the periphery of the crown, apparently modular ...... 20.
— Inflorescences lateral, i.e., branches monopodial ...... 21.
20. Trunk with rhythmic growth in height ...... Scarrone’s model.
Monocotyledon: Pandanus vandamii (Pandanaceae). Dicotyledon: Mangifera indica (mango—Anacardiaceae).
— Trunk with continuous growth in height ...... Stone’s model.
Monocotyledon: Pandanus pulcher (Pandanaceae). Dicotyledon: Mikania cordata (Compositae)
21(19). Trunk with rhythmic growth in height ...... Rauh’s model.
Gymnosperm: Pinus caribaea (Honduran pine—Pinaceae). Dicotyledon: Hevea brasiliensis (Para rubber tree—Euphorbiaceae).
— Trunk with continuous growth in height ...... Attims’model.
Dicotyledon: Rhizophora racemosa (Rhizophoraceae)
22(18). Axes clearly mixed by primary growth, at first (proximally) orthotropic, later (distally) plagiotropic ...... Mangenot’s model.
Dicotyledon: Strychnos variabilis (Loganiaceae).
— Axes apparently mixed by secondary changes ...... 22.
23. Axes all orthotropic, secondarily bending (probably by gravity) ...... Champagnat’s model.
Dicotyledon: Bougainvillea glabra (Nyctaginaceae).
— Axes all plagiotropic, secondarily becoming erect, most often after leaf-fall ...... Troll’s model.
Dicotyledon: Annona muricata (custard apple—Annonaceae), Averrhoa carambola (carambola—Oxalidaceae), Delonix regia (poinciana—Leguminosae / Caesalpinioideae)
(a) Trunk a monopodium (e.g., Cleistopholis patens—Annonaceae):
(b) Trunk a sympodium (e.g., Parinari excelsa—Rosaceae):
Some woody vines do not conform with known tree models, e.g. Triphyophyllum pellalum, Ancistrocladus abbreviatus and Hedera helix: | textbooks/bio/Evolutionary_Developmental_Biology/Key_to_the_Diversity_and_History_of_Life_(Shipunov)/04%3A_Geography_of_Life/4.01%3A_Ideal_continent_and_real_continents.txt |
• 1.1: Introduction
There is, perhaps, no more evocative symbol of this grand view of evolution over deep time than the tree of life. This branching phylogenetic tree connects all living things through a series of splitting events to a single common ancestor. Recent research has dramatically increased our knowledge of the shape and form of this tree. The tree of life is a rich treasure-trove of information, telling us how species are related to one another, and how life has evolved.
• 1.2: The roots of comparative methods
The comparative approaches in this book stem from and bring together three main fields: population and quantitative genetics, paleontology, and phylogenetics.
• 1.3: A brief Introduction to Phylogenetic Trees
The difficulty of building phylogenies is currently reflected in the challenge of reconstructing the tree of life. Some parts of the tree of life are still unresolved even with the tremendous amounts of genomic data that are now available. Accordingly, scientists have devoted a focused effort to solving this difficult problem. There are now a large number of fast and efficient computer programs aimed solely at reconstructing phylogenetic trees.
• 1.4: What we can (and can’t) learn about evolutionary history from living species
• 1.5: Overview of the book
Some methods for analyzing comparative data – such as those for estimating patterns of speciation and extinction through time – require an ultrametric phylogenetic tree. Other approaches model trait evolution, and thus require data on the traits of species that are included in the phylogenetic tree. The methods also differ as to whether or not they require the phylogenetic tree to be complete –e.g., to include every living species descended from a certain ancestor.
• 1.S: A Macroevolutionary Research Program (Summary)
01: A Macroevolutionary Research Program
Evolution is happening all around us. In many cases – lately, due to technological advances in molecular biology – scientists can now describe the evolutionary process in exquisite detail. For example, we know exactly which genes change in frequency from one generation to the next as mice and lizards evolve a white color to match the pale sands of their novel habitats (Rosenblum et al. 2010). We understand the genetics, development, and biomechanical processes that link changes in a Galapagos finches’ diet to the shape of their bill (Abzhanov et al. 2004). And, in some cases, we can watch as one species splits to become two (for example, Rolshausen et al. 2009).
Detailed studies of evolution over short time-scales have been incredibly fruitful and important for our understanding of biology. But evolutionary biologists have always wanted more than this. Evolution strikes a chord in society because it aims to tell us how we, along with all the other living things that we know about, came to be. This story stretches back some 4 billion years in time. It includes all of the drama that one could possibly want – sex, death, great blooms of life and global catastrophes. It has had “winners” and “losers,” groups that wildly diversified, others that expanded then crashed to extinction, as well as species that have hung on in basically the same form for hundreds of millions of years.
There is, perhaps, no more evocative symbol of this grand view of evolution over deep time than the tree of life (Figure 1.1; Rosindell and Harmon 2012). This branching phylogenetic tree connects all living things through a series of splitting events to a single common ancestor. Recent research has dramatically increased our knowledge of the shape and form of this tree. The tree of life is a rich treasure-trove of information, telling us how species are related to one another, which groups are exceptionally diverse or depauperate, and how life has evolved, formed new species, and spread over the globe. Our knowledge of the tree of life, still incomplete but advancing every day, promises to transform our understanding of evolution at the grandest scale (Baum and Smith 2012).
Figure 1.1. A small section of the tree of life showing the relationships among tetrapods, from OneZoom (Rosindell and Harmon 2012). This image can be reused under a CC-BY-4.0 license.
Knowing the evolutionary processes that operate over the course of a few generations, even in great detail, does not automatically give insight into why the tree of life is shaped the way that it is. At the same time, it seems reasonable to hypothesize that the same processes that we can observe now - natural selection, genetic drift, migration, sexual selection, and so on - have been occurring for the last four billion years or so along the branches of the tree. A major challenge for evolutionary biology, then, comes in connecting our knowledge of the mechanisms of evolution with broad-scale patterns seen in the tree of life. This “tree thinking” is what we will explore here.
In this book, I describe methods to connect evolutionary processes to broad-scale patterns in the tree of life. I focus mainly – but not exclusively – on phylogenetic comparative methods. Comparative methods combine biology, mathematics, and computer science to learn about a wide variety of topics in evolution using phylogenetic trees and other associated data (see Harvey and Pagel 1991 for an early review). For example, we can find out which processes must have been common, and which rare, across clades in the tree of life; whether evolution has proceeded differently in some lineages compared to others; and whether the evolutionary potential that we see playing out in real time is sufficient to explain the diversity of life on earth, or whether we might need additional processes that may come into play only very rarely or over very long timescales, like adaptive radiation or species selection.
This introductory chapter has three sections. First, I lay out the background and context for this book, highlighting the role that I hope it will play for readers. Second, I include some background material on phylogenies - both what they are, and how they are constructed. This is necessary information that leads into the methods presented in the remainder of the chapters of the book; interested readers can also read Felsenstein (Felsenstein 2004), which includes much more detail. Finally, I briefly outline the book’s remaining chapters. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/01%3A_A_Macroevolutionary_Research_Program/1.01%3A_Introduction.txt |
The comparative approaches in this book stem from and bring together three main fields: population and quantitative genetics, paleontology, and phylogenetics. I will provide a very brief discussion of how these three fields motivate the models and hypotheses in this book (see Pennell and Harmon 2013 for a more comprehensive review).
The fields of population and quantitative genetics include models of how gene frequencies and trait values change through time. These models lie at the core of evolutionary biology, and relate closely to a number of approaches in comparative methods. Population genetics tends to focus on allele frequencies, while quantitative genetics focuses on traits and their heritability; however, genomics has begun to blur this distinction a bit. Both population and quantitative genetics approaches have their roots in the modern synthesis, especially the work of Fisher (1930) and Wright (1984), but both have been greatly elaborated since then (Falconer et al. 1996; see Lynch and Walsh 1998; Rice 2004). Although population and quantitative genetic approaches most commonly focus on change over one or a few generations, they have been applied to macroevolution with great benefit. For example, Lande (1976) provided quantitative genetic predictions for trait evolution over many generations using Brownian motion and Ornstein-Uhlenbeck models (see Chapter 3). Lynch (1990) later showed that these models predict long-term rates of evolution that are actually too fast; that is, variation among species is too small compared to what we know about the potential of selection and drift (or, even, drift alone!) to change traits. This is, by the way, a great example of the importance of macroevolutionary research from a deep-time perspective. Given the regular observation of strong selection in natural populations, who would have guessed that long-term patterns of divergence are actually less than we would expect, even considering only genetic drift (see also Uyeda et al. 2011)?
Paleontology has, for obvious reasons, focused on macroevolutionary models as an explanation for the distribution of species and traits in the fossil record. Almost all of the key questions that I tackle in this book are also of primary interest to paleontologists - and comparative methods has an especially close relationship to paleobiology, the quantitative mathematical side of paleontology (Valentine 1996; Benton and Harper 2013). For example, a surprising number of the macroevolutionary models and concepts in use today stem from quantitative approaches to paleobiology by Raup and colleagues in the 1970s and 1980s (e.g. Raup et al. 1973; Raup 1985). Many of the models that I will use in this book – for example, birth-death models for the formation and extinction of species – were first applied to macroevolution by paleobiologists.
Finally, comparative methods has deep roots in phylogenetics. In fact, many modern phylogenetic approaches to macroevolution can be traced to Felsenstein’s (1985) paper introducing independent contrasts. This paper was unique in three main ways. First, Felsenstein’s paper was written in a remarkably clear way, and convinced scientists from a range of disciplines of the necessity and value of placing their comparative work in a phylogenetic context. Second, the method of phylogenetic independent contrasts was computationally fast and straightforward to interpret. And finally, Felsenstein’s work suggested a way to connect the previous two topics, quantitative genetics and paleobiology, using math. I discuss independent contrasts, which continue to find new applications, in great detail later in the book. Felsenstein (1985) spawned a whole industry of quantitative approaches that apply models from population and quantitative genetics, paleobiology, and ecology to data that includes a phylogenetic tree.
More than twenty-five years ago, “The Comparative Method in Evolutionary Biology,” by Harvey and Pagel (1991) synthesized the new field of comparative methods into a single coherent framework. Even reading this book nearly 25 years later one can still feel the excitement and potential unlocked by a suite of new methods that use phylogenetic trees to understand macroevolution. But in the time since Harvey and Pagel (1991), the field of comparative methods has exploded – especially in the past decade. Much of this progress was, I think, directly inspired by Harvey and Pagel’s book, which went beyond review and advocated a model-based approach for comparative biology. My wildest hope is that my book can serve a similar purpose.
My goals in writing this book, then, are three-fold. First, to provide a general introduction to the mathematical models and statistical approaches that form the core of comparative methods; second, to give just enough detail on statistical machinery to help biologists understand how to tailor comparative methods to their particular questions of interest, and to help biologists get started in developing their own new methods; and finally, to suggest some ideas for how comparative methods might progress over the next few years. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/01%3A_A_Macroevolutionary_Research_Program/1.02%3A_The_roots_of_comparative_methods.txt |
It is hard work to reconstruct a phylogenetic tree. This point has been made many times (for example, see Felsenstein 2004), but bears repeating here. There are an enormous number of ways to connect a set of species by a phylogenetic tree – and the number of possible trees grows extremely quickly with the number of species. For example, there are about 5 × 1038 ways to build a phylogenetic tree1 of 30 species, which is many times larger than the number of stars in the universe. Additionally, the mathematical problem of reconstructing trees in an optimal way from species’ traits is an example of a problem that is “NP-complete,” a class of problems that include some of the most computationally difficult in the world. Building phylogenies is difficult.
The difficulty of building phylogenies is currently reflected in the challenge of reconstructing the tree of life. Some parts of the tree of life are still unresolved even with the tremendous amounts of genomic data that are now available. Accordingly, scientists have devoted a focused effort to solving this difficult problem. There are now a large number of fast and efficient computer programs aimed solely at reconstructing phylogenetic trees (e.g. MrBayes: Ronquist and Huelsenbeck 2003; BEAST: Drummond and Rambaut 2007). Consequently, the number of well-resolved phylogenetic trees available is also increasing rapidly. As we begin to fill in the gaps of the tree of life, we are developing a much clearer idea of the patterns of evolution that have happened over the past 4.5 billion years on Earth.
A core reason that phylogenetic trees are difficult to reconstruct is that they are information-rich2. A single tree contains detailed information about the patterns and timing of evolutionary branching events through a group’s history. Each branch in a tree tells us about common ancestry of a clade of species, and the start time, end time, and branch length tell us about the timing of speciation events in the past. If we combine a phylogenetic tree with some trait data – for example, mean body size for each species in a genus of mammals – then we can obtain even more information about the evolutionary history of a section of the tree of life.
The most common methods for reconstructing phylogenetic trees use data on species’ genes and/or traits. The core information about phylogenetic relatedness of species is carried in shared derived characters; that is, characters that have evolved new states that are shared among all of the species in a clade and not found in the close relatives of that clade. For example, mammals have many shared derived characters, including hair, mammary glands, and specialized inner ear bones.
Phylogenetic trees are often constructed based on genetic (or genomic) data using modern computer algorithms. Several methods can be used to build trees, like parsimony, maximum likelihood, and Bayesian analyses (see Chapter 2). These methods all have distinct assumptions and can give different results. In fact, even within a given statistical framework, different software packages (e.g. MrBayes and BEAST, mentioned above, are both Bayesian approaches) can give different results for phylogenetic analyses of the same data. The details of phylogenetic tree reconstruction are beyond the scope of this book. Interested readers can read “Inferring Phylogenies” (Felsenstein 2004), “Computational Molecular Evolution” (Yang 2006), or other sources for more information.
For many current comparative methods, we take a phylogenetic tree for a group of species as a given – that is, we assume that the tree is known without error. This assumption is almost never justified. There are many reasons why phylogenetic trees are estimated with error. For example, estimating branch lengths from a few genes is difficult, and the branch lengths that we estimate should be viewed as uncertain. As another example, trees that show the relationships among genes (gene trees) are not always the same as trees that show the relationships among species (species trees). Because of this, the best comparative methods recognize that phylogenetic trees are always estimated with some amount of uncertainty, both in terms of topology and branch lengths, and incorporate that uncertainty into the analysis. I will describe some methods to accomplish this in later chapters.
How do we make sense of the massive amounts of information contained in large phylogenetic trees? The definition of “large” can vary, but we already have trees with tens of thousands of tips, and I think we can anticipate trees with millions of tips in the very near future. These trees are too large to comfortably fit into a human brain. Current tricks for dealing with trees – like banks of computer monitors or long, taped-together printouts – are inefficient and will not work for the huge phylogenetic trees of the future. We need techniques that will allow us to take large phylogenetic trees and extract useful information from them. This information includes, but is not limited to, estimating rates of speciation, extinction, and trait evolution; testing hypotheses about the mode of evolution in a group; identifying adaptive radiations, key innovations, and other macroevolutionary explanations for diversity; and many other things. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/01%3A_A_Macroevolutionary_Research_Program/1.03%3A_A_brief_Introduction_to_Phylogenetic_Trees.txt |
Traditionally, scientists have used fossils to quantify rates and patterns of evolution through long periods of time (sometimes called “macroevolution”). These approaches have been tremendously informative. We now have a detailed picture of the evolutionary dynamics of many groups, from hominids to crocodilians. In some cases, very detailed fossil records of some types of organisms – for example, marine invertebrates – have allowed quantitative tests of particular evolutionary models.
Fossils are particularly good at showing how species diversity and morphological characters change through time. For example, if one has a sequence of fossils with known times of occurrence, one can reconstruct patterns of species diversity through time. A classic example of this is Sepkoski’s (1984) reconstruction of the diversity of marine invertebrates over the past 600 million years. One can also quantify the traits of those fossils and measure how they change across various time intervals (e.g. Foote 1997). In some groups, we can make plots of changes in lineage and trait diversity simultaneously (Figure 1.2). Fossils are the only evidence we have for evolutionary lineages that have gone extinct, and they provide valuable direct evidence about evolutionary dynamics in the past.
However, fossil-based approaches face some challenges. The first is that the fossil record is incomplete. This is a well-known phenomenon, identified by Darwin himself (although many new fossils continue to be found). The fossil record is incomplete in some very particular ways that can sometimes hamper our ability to study evolutionary processes using fossils alone. One example is that fossils are rare or absent from some classical examples of adaptive radiation on islands. For example, the entire fossil record of Caribbean anoles, a well-known adaptive radiation of lizards, consists of less than ten specimens preserved in amber (Losos 2009). We similarly lack fossils for other adaptive radiations like African cichlids and Darwin’s finches. The absence of fossils in these groups limits our ability to directly study the early stages of adaptive radiation. Another limitation of the fossil record relates to species and speciation. It is very difficult to identify and classify species in the fossil record – even more difficult than it is to do so for living species. It is hard to tell species apart, and particularly difficult to pin down the exact time when new species split off from their close relatives. In fact, most studies of fossil diversity focus on higher taxonomic groups like genera, families, or orders (see, e.g., Sepkoski 1984). These studies have been immensely valuable but it can be difficult to connect these results to what we know about living species. In fact, it is species (and not genera, families, or orders) that form the basic units of almost all evolutionary studies. So, fossils have great value but also suffer from some particular limitations.
Phylogenetic trees represent a rich source of complementary information about the dynamics of species formation through time. Phylogenetic approaches provide a useful complement to fossils because their limitations are very different from the limitations of the fossil record. For example, one can often include all of the living species in a group when creating a phylogenetic tree. Additionally, one can use information from detailed systematic and taxonomic studies to identify species, rather than face the ambiguity inherent when using fossils. Phylogenetic trees provide a distinct source of information about evolutionary change that is complementary to approaches based on fossils. However, phylogenetic trees do not provide all of the answers. In particular, there are certain problems that comparative data alone simply cannot address. The most prominent of these, which I will return to later, are reconstructing traits of particular ancestors (ancestral state reconstruction; Losos 2011) and distinguishing between certain types of models where the tempo of evolution changes through time (Slater et al. 2012). Some authors have argued that extinction, as well, cannot be detected in the shape of a phylogenetic tree (Rabosky 2010). I will argue against this point of view in Chapter 11, but extinction still remains a tricky problem when one is limited to samples from a single time interval (the present day). Phylogenetic trees provide a rich source of information about the past, but we should be mindful of their limitations (Alroy 1999).
Perhaps the best approach would combine fossil and phylogenetic data directly. Paleontologists studying fossils and neontologists studying phylogenetic trees share a common set of mathematical models. This means that, at some point, the two fields can merge, and both types of information can be combined to study evolutionary patterns in a cohesive and integrative way. However, surprisingly little work has so far been done in this area (but see Slater et al. 2012, Heath et al. (2014)). | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/01%3A_A_Macroevolutionary_Research_Program/1.04%3A_What_we_can_%28and_can%E2%80%99t%29_learn_about_evolutionary_history_from_living_species.txt |
In this book, I outline statistical procedures for analyzing comparative data. Some methods – such as those for estimating patterns of speciation and extinction through time – require an ultrametric phylogenetic tree. Other approaches model trait evolution, and thus require data on the traits of species that are included in the phylogenetic tree. The methods also differ as to whether or not they require the phylogenetic tree to be complete – that is, to include every living species descended from a certain ancestor – or can accommodate a smaller sample of the living species.
The book begins with a general discussion of model-fitting approaches to statistics (Chapter 2), with a particular focus on maximum likelihood and Bayesian approaches. In Chapters 3-9, I describe models of character evolution. I discuss approaches to simulating and analyzing the evolution of these characters on a tree. Chapters 10-12 focus on models of diversification, which describe patterns of speciation and extinction through time. I describe methods that allow us to simulate and fit these models to comparative data. Chapter 13 covers combined analyses of both character evolution and lineage diversification. Finally, in Chapter 14 I discuss what we have learned so far about evolution from these approaches, and what we are likely to learn in the future.
There are a number of computer software tools that can be used to carry out the methods described here. In this book, I focus on the statistical software environment R. For each chapter, my course website, in progress, provides sample R code that can be used to carry out all described analyses. I hope that this R code will allow further development of this language for comparative analyses. However, it is possible to carry out the algorithms we describe using other computer software or programming languages (e.g. Arbor, http://www.arborworkflows.com).
Statistical comparative methods represent a promising future for evolutionary studies, especially as our knowledge of the tree of life expands. I hope that the methods described in this book can serve as a Rosetta stone that will help us read the tree of life as it is being built.
1.0S: 1.S: A Macroevolutionary Research Program (Summary)
Footnotes
1: This calculation gives the number of distinct tree shapes (ignoring branch lengths) that are fully bifurcating – that is, each species has two descendants - and rooted.
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2: Another difficulty is that the "tree" of life may not look much like a tree due to hybridization, introgression, and other non-branching processes. These issues are currently barely addressed by comparative methods (but see Bastide et al. 2018), and rarely in this book as well! We leave that as a pressing future problem that has only begun to be solved.
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References
Abzhanov, A., M. Protas, B. R. Grant, P. R. Grant, and C. J. Tabin. 2004. Bmp4 and morphological variation of beaks in Darwin’s finches. Science 305:1462–1465.
Alroy, J. 1999. The fossil record of North American mammals: Evidence for a Paleocene evolutionary radiation. Syst. Biol. 48:107–118.
Bastide, P., C. Solís-Lemus, R. Kriebel, K. W. Sparks, and C. Ané. 2018. Phylogenetic comparative methods on phylogenetic networks with reticulations. Syst. Biol.
Baum, D. A., and S. D. Smith. 2012. Tree thinking: An introduction to phylogenetic biology. in Tree thinking: An introduction to phylogenetic biology.
Benton, M., and D. A. T. Harper. 2013. Introduction to paleobiology and the fossil record. John Wiley & Sons.
Drummond, A. J., and A. Rambaut. 2007. BEAST: Bayesian evolutionary analysis by sampling trees. BMC Evol. Biol. 7:214.
Falconer, D. S., T. F. C. Mackay, and R. Frankham. 1996. Introduction to quantitative genetics (4th edn). Trends Genet. 12:280. [Amsterdam, The Netherlands: Elsevier Science Publishers (Biomedical Division)], c1985-.
Felsenstein, J. 2004. Inferring phylogenies. Sinauer Associates, Inc., Sunderland, MA.
Felsenstein, J. 1985. Phylogenies and the comparative method. Am. Nat. 125:1–15.
Fisher, R. A. 1930. The genetical theory of natural selection: A complete variorum edition. Oxford University Press.
Foote, M. 1997. The evolution of morphological diversity. Annu. Rev. Ecol. Syst. 28:129–152.
Harvey, P. H., and M. D. Pagel. 1991. The comparative method in evolutionary biology. Oxford University Press.
Heath, T. A., J. P. Huelsenbeck, and T. Stadler. 2014. The fossilized birth–death process for coherent calibration of divergence-time estimates. Proc. Natl. Acad. Sci. U. S. A. 111:E2957–E2966. National Academy of Sciences.
Lande, R. 1976. Natural selection and random genetic drift in phenotypic evolution. Evolution 30:314–334.
Losos, J. 2009. Lizards in an evolutionary tree: Ecology and adaptive radiation of anoles. University of California Press.
Losos, J. B. 2011. Seeing the forest for the trees: The limitations of phylogenies in comparative biology. Am. Nat. 177:709–727.
Lynch, M. 1990. The rate of morphological evolution in mammals from the standpoint of the neutral expectation. Am. Nat. 136:727–741.
Lynch, M., and B. Walsh. 1998. Genetics and analysis of quantitative traits. Sinauer Sunderland, MA.
Pennell, M. W., and L. J. Harmon. 2013. An integrative view of phylogenetic comparative methods: Connections to population genetics, community ecology, and paleobiology. Ann. N. Y. Acad. Sci. 1289:90–105.
Rabosky, D. L. 2010. Extinction rates should not be estimated from molecular phylogenies. Evolution 64:1816–1824.
Raup, D. M. 1985. Mathematical models of cladogenesis. Paleobiology 11:42–52.
Raup, D. M., S. J. Gould, T. J. M. Schopf, and D. S. Simberloff. 1973. Stochastic models of phylogeny and the evolution of diversity. J. Geol. 81:525–542.
Rice, S. H. 2004. Evolutionary theory. Sinauer, Sunderland, MA.
Rolshausen, G., G. Segelbacher, K. A. Hobson, and H. M. Schaefer. 2009. Contemporary evolution of reproductive isolation and phenotypic divergence in sympatry along a migratory divide. Curr. Biol. 19:2097–2101.
Ronquist, F., and J. P. Huelsenbeck. 2003. MrBayes 3: Bayesian phylogenetic inference under mixed models. Bioinformatics 19:1572–1574.
Rosenblum, E. B., H. Römpler, T. Schöneberg, and H. E. Hoekstra. 2010. Molecular and functional basis of phenotypic convergence in white lizards at White Sands. Proc. Natl. Acad. Sci. U. S. A. 107:2113–2117.
Rosindell, J., and L. J. Harmon. 2012. OneZoom: A fractal explorer for the tree of life. PLoS Biol. 10:e1001406.
Sepkoski, J. J. 1984. A kinetic model of phanerozoic taxonomic diversity. III. Post-Paleozoic families and mass extinctions. Paleobiology 10:246–267.
Slater, G. J., L. J. Harmon, and M. E. Alfaro. 2012. Integrating fossils with molecular phylogenies improves inference of trait evolution. Evolution 66:3931–3944.
Uyeda, J. C., T. F. Hansen, S. J. Arnold, and J. Pienaar. 2011. The million-year wait for macroevolutionary bursts. Proc. Natl. Acad. Sci. U. S. A. 108:15908–15913.
Valentine, J. W. 1996. Evolutionary paleobiology. University of Chicago Press.
Wright, S. 1984. Evolution and the genetics of populations, Volume 1: Genetic and biometric foundations. University of Chicago Press.
Yang, Z. 2006. Computational molecular evolution. Oxford University Press. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/01%3A_A_Macroevolutionary_Research_Program/1.05%3A_Overview_of_the_book.txt |
This text is about constructing and testing mathematical models of evolution. In my view the best comparative approaches have two features. First, the most useful methods emphasize parameter estimation over test statistics and P-values. Ideal methods fit models that we care about and estimate parameters that have a clear biological interpretation. To be useful, methods must also recognize and quantify uncertainty in our parameter estimates. Second, many useful methods involve model selection, the process of using data to objectively select the best model from a set of possibilities. When we use a model selection approach, we take advantage of the fact that patterns in empirical data sets will reject some models as implausible and support the predictions of others. This sort of approach can be a nice way to connect the results of a statistical analysis to a particular biological question.
• 2.1: Introduction
Evolution is the product of a thousand stories. Individual organisms are born, reproduce, and die. The net result of these individual life stories over broad spans of time is evolution. At first glance, it might seem impossible to model this process over more than one or two generations. And yet scientific progress relies on creating simple models and confronting them with data. How can we evaluate models that consider evolution over millions of generations?
• 2.2: Standard Statistical Hypothesis Testing
Standard hypothesis testing approaches focus almost entirely on rejecting null hypotheses. In the framework (usually referred to as the frequentist approach to statistics) one first defines a null hypothesis. This null hypothesis represents your expectation if some pattern, such as a difference among groups, is not present, or if some process of interest were not occurring.
• 2.3: Maximum Likelihood
Likelihood is defined as the probability, given a model and a set of parameter values, of obtaining a particular set of data. That is, given a mathematical description of the world, what is the probability that we would see the actual data that we have collected? To calculate a likelihood, we have to consider a particular model that may have generated the data. That model will almost always have parameter values that need to be specified. We can refer to this specified model as a hypothesis, H.
• 2.4: Bayesian Statistics
Recent years have seen tremendous growth of Bayesian approaches in reconstructing phylogenetic trees and estimating their branch lengths. Although there are currently only a few Bayesian comparative methods, their number will certainly grow as comparative biologists try to solve more complex problems.
• 2.5: AIC versus Bayes
When you compare Bayes factors, you assume that one of the models you are considering is actually the true model that generated your data, and calculate posterior probabilities based on that assumption. By contrast, AIC assumes that reality is more complex than any of your models, and you are trying to identify the model that most efficiently captures the information in your data. So even though both techniques are carrying out model selection, the basic philosophy of how these models differ.
• 2.6: Models and Comparative Methods
One theme in the book is that I emphasize fitting models to data and estimating parameters. I think that this approach is very useful for the future of the field of comparative statistics for three main reasons. First, it is flexible; one can easily compare a wide range of competing models to your data. Second, it is extendable; one can create new models and automatically fit them into a preexisting framework for data analysis. Finally, it is powerful.
• 2.S: Fitting Statistical Models to Data (Summary)
02: Fitting Statistical Models to Data
Evolution is the product of a thousand stories. Individual organisms are born, reproduce, and die. The net result of these individual life stories over broad spans of time is evolution. At first glance, it might seem impossible to model this process over more than one or two generations. And yet scientific progress relies on creating simple models and confronting them with data. How can we evaluate models that consider evolution over millions of generations?
There is a solution: we can rely on the properties of large numbers to create simple models that represent, in broad brushstrokes, the types of changes that take place over evolutionary time. We can then compare these models to data in ways that will allow us to gain insights into evolution.
This book is about constructing and testing mathematical models of evolution. In my view the best comparative approaches have two features. First, the most useful methods emphasize parameter estimation over test statistics and P-values. Ideal methods fit models that we care about and estimate parameters that have a clear biological interpretation. To be useful, methods must also recognize and quantify uncertainty in our parameter estimates. Second, many useful methods involve model selection, the process of using data to objectively select the best model from a set of possibilities. When we use a model selection approach, we take advantage of the fact that patterns in empirical data sets will reject some models as implausible and support the predictions of others. This sort of approach can be a nice way to connect the results of a statistical analysis to a particular biological question.
In this chapter, I will first give a brief overview of standard hypothesis testing in the context of phylogenetic comparative methods. However, standard hypothesis testing can be limited in complex, real-world situations, such as those encountered commonly in comparative biology. I will then review two other statistical approaches, maximum likelihood and Bayesian analysis, that are often more useful for comparative methods. This latter discussion will cover both parameter estimation and model selection.
All of the basic statistical approaches presented here will be applied to evolutionary problems in later chapters. It can be hard to understand abstract statistical concepts without examples. So, throughout this part of the chapter, I will refer back to a simple example.
A common simple example in statistics involves flipping coins. To fit with the theme of this book, however, I will change this to flipping a lizard (needless to say, do not try this at home!). Suppose you have a lizard with two sides, “heads” and “tails.” You want to flip the lizard to help make decisions in your life. However, you do not know if this is a fair lizard, where the probability of obtaining heads is 0.5, or not. Perhaps, for example, lizards have a cat-like ability to right themselves when flipped. As an experiment, you flip the lizard 100 times, and obtain heads 63 of those times. Thus, 63 heads out of 100 lizard flips is your data; we will use model comparisons to try to see what these data tell us about models of lizard flipping. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/02%3A_Fitting_Statistical_Models_to_Data/2.01%3A_Introduction.txt |
Standard hypothesis testing approaches focus almost entirely on rejecting null hypotheses. In the framework (usually referred to as the frequentist approach to statistics) one first defines a null hypothesis. This null hypothesis represents your expectation if some pattern, such as a difference among groups, is not present, or if some process of interest were not occurring. For example, perhaps you are interested in comparing the mean body size of two species of lizards, an anole and a gecko. Our null hypothesis would be that the two species do not differ in body size. The alternative, which one can conclude by rejecting that null hypothesis, is that one species is larger than the other. Another example might involve investigating two variables, like body size and leg length, across a set of lizard species1. Here the null hypothesis would be that there is no relationship between body size and leg length. The alternative hypothesis, which again represents the situation where the phenomenon of interest is actually occurring, is that there is a relationship with body size and leg length. For frequentist approaches, the alternative hypothesis is always the negation of the null hypothesis; as you will see below, other approaches allow one to compare the fit of a set of models without this restriction and choose the best amongst them.
The next step is to define a test statistic, some way of measuring the patterns in the data. In the two examples above, we would consider test statistics that measure the difference in mean body size among our two species of lizards, or the slope of the relationship between body size and leg length, respectively. One can then compare the value of this test statistic in the data to the expectation of this test statistic under the null hypothesis. The relationship between the test statistic and its expectation under the null hypothesis is captured by a P-value. The P-value is the probability of obtaining a test statistic at least as extreme as the actual test statistic in the case where the null hypothesis is true. You can think of the P-value as a measure of how probable it is that you would obtain your data in a universe where the null hypothesis is true. In other words, the P-value measures how probable it is under the null hypothesis that you would obtain a test statistic at least as extreme as what you see in the data. In particular, if the P-value is very large, say P = 0.94, then it is extremely likely that your data are compatible with this null hypothesis.
If the test statistic is very different from what one would expect under the null hypothesis, then the P-value will be small. This means that we are unlikely to obtain the test statistic seen in the data if the null hypothesis were true. In that case, we reject the null hypothesis as long as P is less than some value chosen in advance. This value is the significance threshold, α, and is almost always set to α = 0.05. By contrast, if that probability is large, then there is nothing “special” about your data, at least from the standpoint of your null hypothesis. The test statistic is within the range expected under the null hypothesis, and we fail to reject that null hypothesis. Note the careful language here – in a standard frequentist framework, you never accept the null hypothesis, you simply fail to reject it.
Getting back to our lizard-flipping example, we can use a frequentist approach. In this case, our particular example has a name; this is a binomial test, which assesses whether a given event with two outcomes has a certain probability of success. In this case, we are interested in testing the null hypothesis that our lizard is a fair flipper; that is, that the probability of heads pH = 0.5. The binomial test uses the number of “successes” (we will use the number of heads, H = 63) as a test statistic. We then ask whether this test statistic is either much larger or much smaller than we might expect under our null hypothesis. So, our null hypothesis is that pH = 0.5; our alternative, then, is that pH takes some other value: pH ≠ 0.5.
To carry out the test, we first need to consider how many "successes" we should expect if the null hypothesis were true. We consider the distribution of our test statistic (the number of heads) under our null hypothesis (pH = 0.5). This distribution is a binomial distribution (Figure 2.1).
We can use the known probabilities of the binomial distribution to calculate our P-value. We want to know the probability of obtaining a result at least as extreme as our data when drawing from a binomial distribution with parameters p = 0.5 and n = 100. We calculate the area of this distribution that lies to the right of 63. This area, P = 0.003, can be obtained either from a table, from statistical software, or by using a relatively simple calculation. The value, 0.003, represents the probability of obtaining at least 63 heads out of 100 trials with pH = 0.5. This number is the P-value from our binomial test. Because we only calculated the area of our null distribution in one tail (in this case, the right, where values are greater than or equal to 63), then this is actually a one-tailed test, and we are only considering part of our null hypothesis where pH > 0.5. Such an approach might be suitable in some cases, but more typically we need to multiply this number by 2 to get a two-tailed test; thus, P = 0.006. This two-tailed P-value of 0.006 includes the possibility of results as extreme as our test statistic in either direction, either too many or too few heads. Since P < 0.05, our chosen α value, we reject the null hypothesis, and conclude that we have an unfair lizard.
In biology, null hypotheses play a critical role in many statistical analyses. So why not end this chapter now? One issue is that biological null hypotheses are almost always uninteresting. They often describe the situation where patterns in the data occur only by chance. However, if you are comparing living species to each other, there are almost always some differences between them. In fact, for biology, null hypotheses are quite often obviously false. For example, two different species living in different habitats are not identical, and if we measure them enough we will discover this fact. From this point of view, both outcomes of a standard hypothesis test are unenlightening. One either rejects a silly hypothesis that was probably known to be false from the start, or one “fails to reject” this null hypothesis2. There is much more information to be gained by estimating parameter values and carrying out model selection in a likelihood or Bayesian framework, as we will see below. Still, frequentist statistical approaches are common, have their place in our toolbox, and will come up in several sections of this book.
One key concept in standard hypothesis testing is the idea of statistical error. Statistical errors come in two flavors: type I and type II errors. Type I errors occur when the null hypothesis is true but the investigator mistakenly rejects it. Standard hypothesis testing controls type I errors using a parameter, α, which defines the accepted rate of type I errors. For example, if α = 0.05, one should expect to commit a type I error about 5% of the time. When multiple standard hypothesis tests are carried out, investigators often “correct” their P-values using Bonferroni correction. If you do this, then there is only a 5% chance of a single type I error across all of the tests being considered. This singular focus on type I errors, however, has a cost. One can also commit type II errors, when the null hypothesis is false but one fails to reject it. The rate of type II errors in statistical tests can be extremely high. While statisticians do take care to create approaches that have high power, traditional hypothesis testing usually fixes type I errors at 5% while type II error rates remain unknown. There are simple ways to calculate type II error rates (e.g. power analyses) but these are only rarely carried out. Furthermore, Bonferroni correction dramatically increases the type II error rate. This is important because – as stated by Perneger (1998) – “… type II errors are no less false than type I errors.” This extreme emphasis on controlling type I errors at the expense of type II errors is, to me, the main weakness of the frequentist approach3.
I will cover some examples of the frequentist approach in this book, mainly when discussing traditional methods like phylogenetic independent contrasts (PICs). Also, one of the model selection approaches used frequently in this book, likelihood ratio tests, rely on a standard frequentist set-up with null and alternative hypotheses.
However, there are two good reasons to look for better ways to do comparative statistics. First, as stated above, standard methods rely on testing null hypotheses that – for evolutionary questions - are usually very likely, a priori, to be false. For a relevant example, consider a study comparing the rate of speciation between two clades of carnivores. The null hypothesis is that the two clades have exactly equal rates of speciation – which is almost certainly false, although we might question how different the two rates might be. Second, in my opinion, standard frequentist methods place too much emphasis on P-values and not enough on the size of statistical effects. A small P-value could reflect either a large effect or very large sample sizes or both.
In summary, frequentist statistical methods are common in comparative statistics but can be limiting. I will discuss these methods often in this book, mainly due to their prevalent use in the field. At the same time, we will look for alternatives whenever possible. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/02%3A_Fitting_Statistical_Models_to_Data/2.02%3A_Standard_Statistical_Hypothesis_Testing.txt |
Section 2.3a: What is a likelihood?
Since all of the approaches described in the remainer of this chapter involve calculating likelihoods, I will first briefly describe this concept. A good general review of likelihood is Edwards (1992). Likelihood is defined as the probability, given a model and a set of parameter values, of obtaining a particular set of data. That is, given a mathematical description of the world, what is the probability that we would see the actual data that we have collected?
To calculate a likelihood, we have to consider a particular model that may have generated the data. That model will almost always have parameter values that need to be specified. We can refer to this specified model (with particular parameter values) as a hypothesis, H. The likelihood is then:
$L(H|D)=Pr(D|H) \label{2.1}$
Here, L and Pr stand for likelihood and probability, D for the data, and H for the hypothesis, which again includes both the model being considered and a set of parameter values. The | symbol stands for “given,” so equation 2.1 can be read as “the likelihood of the hypothesis given the data is equal to the probability of the data given the hypothesis.” In other words, the likelihood represents the probability under a given model and parameter values that we would obtain the data that we actually see.
For any given model, using different parameter values will generally change the likelihood. As you might guess, we favor parameter values that give us the highest probability of obtaining the data that we see. One way to estimate parameters from data, then, is by finding the parameter values that maximize the likelihood; that is, the parameter values that give the highest likelihood, and the highest probability of obtaining the data. These estimates are then referred to as maximum likelihood (ML) estimates. In an ML framework, we suppose that the hypothesis that has the best fit to the data is the one that has the highest probability of having generated that data.
For the example above, we need to calculate the likelihood as the probability of obtaining heads 63 out of 100 lizard flips, given some model of lizard flipping. In general, we can write the likelihood for any combination of H “successes” (flips that give heads) out of n trials. We will also have one parameter, pH, which will represent the probability of “success,” that is, the probability that any one flip comes up heads. We can calculate the likelihood of our data using the binomial theorem:
$L(H|D)=Pr(D|p)= {n \choose H} p_H^H (1-p_H)^{n-H} \label{2.2}$
In the example given, n = 100 and H = 63, so:
$L(H|D)= {100 \choose 63} p_H^{63} (1-p_H)^{37} \label{2.3}$
We can make a plot of the likelihood, L, as a function of pH (Figure 2.2). When we do this, we see that the maximum likelihood value of pH, which we can call $\hat{p}_H$, is at $\hat{p}_H = 0.63$. This is the “brute force” approach to finding the maximum likelihood: try many different values of the parameters and pick the one with the highest likelihood. We can do this much more efficiently using numerical methods as described in later chapters in this book.
We could also have obtained the maximum likelihood estimate for pH through differentiation. This problem is much easier if we work with the ln-likelihood rather than the likelihood itself (note that whatever value of pH that maximizes the likelihood will also maximize the ln-likelihood, because the log function is strictly increasing). So:
$\ln{L} = \ln{n \choose H} + H \ln{p_H}+ (n-H)\ln{(1-p_H)} \label{2.4}$
Note that the natural log (ln) transformation changes our equation from a power function to a linear function that is easy to solve. We can differentiate:
$\frac{d \ln{L}}{dp_H} = \frac{H}{p_H} - \frac{(n-H)}{(1-p_H)}\label{2.5}$
The maximum of the likelihood represents a peak, which we can find by setting the derivative $\frac{d \ln{L}}{dp_H}$ to zero. We then find the value of pH that solves that equation, which will be our estimate $\hat{p}_H$. So we have:
$\begin{array}{lcl} \frac{H}{\hat{p}_H} - \frac{n-H}{1-\hat{p}_H} & = & 0\ \frac{H}{\hat{p}_H} & = & \frac{n-H}{1-\hat{p}_H}\ H (1-\hat{p}_H) & = & \hat{p}_H (n-H)\ H-H\hat{p}_H & = & n\hat{p}_H-H\hat{p}_H\ H & = & n\hat{p}_H\ \hat{p}_H &=& H / n\ \end{array} \label{2.6}$
Notice that, for our simple example, H/n = 63/100 = 0.63, which is exactly equal to the maximum likelihood from figure 2.2.
Maximum likelihood estimates have many desirable statistical properties. It is worth noting, however, that they will not always return accurate parameter estimates, even when the data is generated under the actual model we are considering. In fact, ML parameters can sometimes be biased. To understand what this means, we need to formally introduce two new concepts: bias and precision. Imagine that we were to simulate datasets under some model A with parameter a. For each simulation, we then used ML to estimate the parameter $\hat{a}$ for the simulated data. The precision of our ML estimate tells us how different, on average, each of our estimated parameters $\hat{a}_i$ are from one another. Precise estimates are estimated with less uncertainty. Bias, on the other hand, measures how close our estimates $\hat{a}_i$ are to the true value a. If our ML parameter estimate is biased, then the average of the $\hat{a}_i$ will differ from the true value a. It is not uncommon for ML estimates to be biased in a way that depends on sample size, so that the estimates get closer to the truth as sample size increases, but can be quite far off in a particular direction when the number of data points is small compared to the number of parameters being estimated.
In our example of lizard flipping, we estimated a parameter value of $\hat{p}_H = 0.63$. For the particular case of estimating the parameter of a binomial distribution, our ML estimate is known to be unbiased. And this estimate is different from 0.5 – which was our expectation under the null hypothesis. So is this lizard fair? Or, alternatively, can we reject the null hypothesis that pH = 0.5? To evaluate this, we need to use model selection.
Section 2.3b: The likelihood ratio test
Model selection involves comparing a set of potential models and using some criterion to select the one that provides the “best” explanation of the data. Different approaches define “best” in different ways. I will first discuss the simplest, but also the most limited, of these techniques, the likelihood ratio test. Likelihood ratio tests can only be used in one particular situation: to compare two models where one of the models is a special case of the other. This means that model A is exactly equivalent to the more complex model B with parameters restricted to certain values. We can always identify the simpler model as the model with fewer parameters. For example, perhaps model B has parameters x, y, and z that can take on any values. Model A is the same as model B but with parameter z fixed at 0. That is, A is the special case of B when parameter z = 0. This is sometimes described as model A is nested within model B, since every possible version of model A is equal to a certain case of model B, but model B also includes more possibilities.
For likelihood ratio tests, the null hypothesis is always the simpler of the two models. We compare the data to what we would expect if the simpler (null) model were correct.
For example, consider again our example of flipping a lizard. One model is that the lizard is “fair:” that is, that the probability of heads is equal to 1/2. A different model might be that the probability of heads is some other value p, which could be 1/2, 1/3, or any other value between 0 and 1. Here, the latter (complex) model has one additional parameter, pH, compared to the former (simple) model; the simple model is a special case of the complex model when pH = 1/2.
For such nested models, one can calculate the likelihood ratio test statistic as
$\Delta = 2 \cdot \ln{\frac{L_1}{L_2}} = 2 \cdot (\ln{L_1}-\ln{L_2}) \label{2.7}$
Here, Δ is the likelihood ratio test statistic, L2 the likelihood of the more complex (parameter rich) model, and L1 the likelihood of the simpler model. Since the models are nested, the likelihood of the complex model will always be greater than or equal to the likelihood of the simple model. This is a direct consequence of the fact that the models are nested. If we find a particular likelihood for the simpler model, we can always find a likelihood equal to that for the complex model by setting the parameters so that the complex model is equivalent to the simple model. So the maximum likelihood for the complex model will either be that value, or some higher value that we can find through searching the parameter space. This means that the test statistic Δ will never be negative. In fact, if you ever obtain a negative likelihood ratio test statistic, something has gone wrong – either your calculations are wrong, or you have not actually found ML solutions, or the models are not actually nested.
To carry out a statistical test comparing the two models, we compare the test statistic Δ to its expectation under the null hypothesis. When sample sizes are large, the null distribution of the likelihood ratio test statistic follows a chi-squared (χ2) distribution with degrees of freedom equal to the difference in the number of parameters between the two models. This means that if the simpler hypothesis were true, and one carried out this test many times on large independent datasets, the test statistic would approximately follow this χ2 distribution. To reject the simpler (null) model, then, one compares the test statistic with a critical value derived from the appropriate χ2 distribution. If the test statistic is larger than the critical value, one rejects the null hypothesis. Otherwise, we fail to reject the null hypothesis. In this case, we only need to consider one tail of the χ2 test, as every deviation from the null model will push us towards higher Δ values and towards the right tail of the distribution.
For the lizard flip example above, we can calculate the ln-likelihood under a hypothesis of pH = 0.5 as:
$\begin{array}{lcl} \ln{L_1} &=& \ln{\left(\frac{100}{63}\right)} + 63 \cdot \ln{0.5} + (100-63) \cdot \ln{(1-0.5)} \nonumber \ \ln{L_1} &=& -5.92\nonumber\ \end{array} \label{2.8}$
We can compare this to the likelihood of our maximum-likelihood estimate :
$\begin{array}{lcl} \ln{L_2} &=& \ln{\left(\frac{100}{63}\right)} + 63 \cdot \ln{0.63} + (100-63) \cdot \ln{(1-0.63)} \nonumber \ \ln{L_2} &=& -2.50\nonumber \end{array} \label{2.9}$
We then calculate the likelihood ratio test statistic:
$\begin{array}{lcl} \Delta &=& 2 \cdot (\ln{L_2}-\ln{L_1}) \nonumber \ \Delta &=& 2 \cdot (-2.50 - -5.92) \nonumber \ \Delta &=& 6.84\nonumber \end{array} \label{2.10}$
If we compare this to a χ2 distribution with one d.f., we find that P = 0.009. Because this P-value is less than the threshold of 0.05, we reject the null hypothesis, and support the alternative. We conclude that this is not a fair lizard. As you might expect, this result is consistent with our answer from the binomial test in the previous section. However, the approaches are mathematically different, so the two P-values are not identical.
Although described above in terms of two competing hypotheses, likelihood ratio tests can be applied to more complex situations with more than two competing models. For example, if all of the models form a sequence of increasing complexity, with each model a special case of the next more complex model, one can compare each pair of hypotheses in sequence, stopping the first time the test statistic is non-significant. Alternatively, in some cases, hypotheses can be placed in a bifurcating choice tree, and one can proceed from simple to complex models down a particular path of paired comparisons of nested models. This approach is commonly used to select models of DNA sequence evolution (Posada and Crandall 1998).
Section 2.3c: The Akaike Information Criterion (AIC)
You might have noticed that the likelihood ratio test described above has some limitations. Especially for models involving more than one parameter, approaches based on likelihood ratio tests can only do so much. For example, one can compare a series of models, some of which are nested within others, using an ordered series of likelihood ratio tests. However, results will often depend strongly on the order in which tests are carried out. Furthermore, often we want to compare models that are not nested, as required by likelihood ratio tests. For these reasons, another approach, based on the Akaike Information Criterion (AIC), can be useful.
The AIC value for a particular model is a simple function of the likelihood L and the number of parameters k:
$AIC = 2k − 2\ln L \label{2.11}$
This function balances the likelihood of the model and the number of parameters estimated in the process of fitting the model to the data. One can think of the AIC criterion as identifying the model that provides the most efficient way to describe patterns in the data with few parameters. However, this shorthand description of AIC does not capture the actual mathematical and philosophical justification for equation (2.11). In fact, this equation is not arbitrary; instead, its exact trade-off between parameter numbers and log-likelihood difference comes from information theory (for more information, see Burnham and Anderson 2003, Akaike (1998)).
The AIC equation (2.11) above is only valid for quite large sample sizes relative to the number of parameters being estimated (for n samples and k parameters, n/k > 40). Most empirical data sets include fewer than 40 independent data points per parameter, so a small sample size correction should be employed:
$AIC_C = AIC + \frac{2k(k+1)}{n-k-1} \label{2.12}$
This correction penalizes models that have small sample sizes relative to the number of parameters; that is, models where there are nearly as many parameters as data points. As noted by Burnham and Anderson (2003), this correction has little effect if sample sizes are large, and so provides a robust way to correct for possible bias in data sets of any size. I recommend always using the small sample size correction when calculating AIC values.
To select among models, one can then compare their AICc scores, and choose the model with the smallest value. It is easier to make comparisons in AICc scores between models by calculating the difference, ΔAICc. For example, if you are comparing a set of models, you can calculate ΔAICc for model i as:
$ΔAIC_{c_i} = AIC_{c_i} − AIC_{c_{min}} \label{2.13}$
where AICci is the AICc score for model i and AICcmin is the minimum AICc score across all of the models.
As a broad rule of thumb for comparing AIC values, any model with a ΔAICci of less than four is roughly equivalent to the model with the lowest AICc value. Models with ΔAICci between 4 and 8 have little support in the data, while any model with a ΔAICci greater than 10 can safely be ignored.
Additionally, one can calculate the relative support for each model using Akaike weights. The weight for model i compared to a set of competing models is calculated as:
$w_i = \frac{e^{-\Delta AIC_{c_i}/2}}{\sum_i{e^{-\Delta AIC_{c_i}/2}}} \label{2.14}$
The weights for all models under consideration sum to 1, so the wi for each model can be viewed as an estimate of the level of support for that model in the data compared to the other models being considered.
Returning to our example of lizard flipping, we can calculate AICc scores for our two models as follows:
$\begin{array}{lcl} AIC_1 &=& 2 k_1 - 2 ln{L_1} = 2 \cdot 0 - 2 \cdot -5.92 \\ AIC_1 &=& 11.8 \\ AIC_2 &=& 2 k_2 - 2 ln{L_2} = 2 \cdot 1 - 2 \cdot -2.50 \\ AIC_2 &=& 7.0 \\ \end{array} \label{2.15}$
Our example is a bit unusual in that model one has no estimated parameters; this happens sometimes but is not typical for biological applications. We can correct these values for our sample size, which in this case is n = 100 lizard flips:
$\begin{array}{lcl} AIC_{c_1} &=& AIC_1 + \frac{2 k_1 (k_1 + 1)}{n - k_1 - 1} \\ AIC_{c_1} &=& 11.8 + \frac{2 \cdot 0 (0 + 1)}{100-0-1} \\ AIC_{c_1} &=& 11.8 \\ AIC_{c_2} &=& AIC_2 + \frac{2 k_2 (k_2 + 1)}{n - k_2 - 1} \\ AIC_{c_2} &=& 7.0 + \frac{2 \cdot 1 (1 + 1)}{100-1-1} \\ AIC_{c_2} &=& 7.0 \\ \end{array} \label{2.16}$
Notice that, in this particular case, the correction did not affect our AIC values, at least to one decimal place. This is because the sample size is large relative to the number of parameters. Note that model 2 has the smallest AICc score and is thus the model that is best supported by the data. Noting this, we can now convert these AICc scores to a relative scale:
$\begin{array}{lcl} \Delta AIC_{c_1} &=& AIC_{c_1}-AIC{c_{min}} \\ &=& 11.8-7.0 \\ &=& 4.8 \\ \end{array} \label{2.17}$
$\begin{array}{lcl} \Delta AIC_{c_2} &=& AIC_{c_2}-AIC{c_{min}} \\ &=& 7.0-7.0 \\ &=& 0 \\ \end{array}$
Note that the ΔAICci for model 1 is greater than four, suggesting that this model (the “fair” lizard) has little support in the data. This is again consistent with all of the results that we've obtained so far using both the binomial test and the likelihood ratio test. Finally, we can use the relative AICc scores to calculate Akaike weights:
$\begin{array}{lcl} \sum_i{e^{-\Delta_i/2}} &=& e^{-\Delta_1/2} + e^{-\Delta_2/2} \\ &=& e^{-4.8/2} + e^{-0/2} \\ &=& 0.09 + 1 \\ &=& 1.09 \\ \end{array} \label{2.18}$
$\begin{array}{lcl} w_1 &=& \frac{e^{-\Delta AIC_{c_1}/2}}{\sum_i{e^{-\Delta AIC_{c_i}/2}}} \\ &=& \frac{0.09}{1.09} \\ &=& 0.08 \end{array}$
$\begin{array}{lcl} w_2 &=& \frac{e^{-\Delta AIC_{c_2}/2}}{\sum_i{e^{-\Delta AIC_{c_i}/2}}} \\ &=& \frac{1.00}{1.09} \\ &=& 0.92 \end{array}$
Our results are again consistent with the results of the likelihood ratio test. The relative likelihood of an unfair lizard is 0.92, and we can be quite confident that our lizard is not a fair flipper.
AIC weights are also useful for another purpose: we can use them to get model-averaged parameter estimates. These are parameter estimates that are combined across different models proportional to the support for those models. As a thought example, imagine that we are considering two models, A and B, for a particular dataset. Both model A and model B have the same parameter p, and this is the parameter we are particularly interested in. In other words, we do not know which model is the best model for our data, but what we really need is a good estimate of p. We can do that using model averaging. If model A has a high AIC weight, then the model-averaged parameter estimate for p will be very close to our estimate of p under model A; however, if both models have about equal support then the parameter estimate will be close to the average of the two different estimates. Model averaging can be very useful in cases where there is a lot of uncertainty in model choice for models that share parameters of interest. Sometimes the models themselves are not of interest, but need to be considered as possibilities; in this case, model averaging lets us estimate parameters in a way that is not as strongly dependent on our choice of models. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/02%3A_Fitting_Statistical_Models_to_Data/2.03%3A_Maximum_Likelihood.txt |
Recent years have seen tremendous growth of Bayesian approaches in reconstructing phylogenetic trees and estimating their branch lengths. Although there are currently only a few Bayesian comparative methods, their number will certainly grow as comparative biologists try to solve more complex problems. In a Bayesian framework, the quantity of interest is the posterior probability, calculated using Bayes' theorem:
$Pr(H|D) = \dfrac{Pr(D|H) \cdot Pr(H)}{Pr(D)} \label{2.19}$
The benefit of Bayesian approaches is that they allow us to estimate the probability that the hypothesis is true given the observed data, $Pr(H|D)$. This is really the sort of probability that most people have in mind when they are thinking about the goals of their study. However, Bayes theorem also reveals a cost of this approach. Along with the likelihood, $Pr(D|H)$, one must also incorporate prior knowledge about the probability that any given hypothesis is true - Pr(H). This represents the prior belief that a hypothesis is true, even before consideration of the data at hand. This prior probability must be explicitly quantified in all Bayesian statistical analyses. In practice, scientists often seek to use “uninformative” priors that have little influence on the posterior distribution - although even the term "uninformative" can be confusing, because the prior is an integral part of a Bayesian analysis. The term $Pr(D)$ is also an important part of Bayes theorem, and can be calculated as the probability of obtaining the data integrated over the prior distributions of the parameters:
$Pr(D)=∫_HPr(H|D)Pr(H)dH \label{2.20}$
However, $Pr(D)$ is constant when comparing the fit of different models for a given data set and thus has no influence on Bayesian model selection under most circumstances (and all the examples in this book).
In our example of lizard flipping, we can do an analysis in a Bayesian framework. For model 1, there are no free parameters. Because of this, $Pr(H)=1$ and $Pr(D|H)=P(D)$, so that $Pr(H|D)=1$. This may seem strange but what the result means is that our data has no influence on the structure of the model. We do not learn anything about a model with no free parameters by collecting data!
If we consider model 2 above, the parameter pH must be estimated. We can set a uniform prior between 0 and 1 for pH, so that f(pH)=1 for all pH in the interval [0,1]. We can also write this as “our prior for $p_h$ is U(0,1)”. Then:
$Pr(H|D) = \frac{Pr(D|H) \cdot Pr(H)}{Pr(D)} = \frac{P(H|p_H,N) f(p_H)}{\displaystyle \int_{0}^{1} P(H|p_H,N) f(p_h) dp_H} \label{2.21}$
Next we note that $Pr(D|H)$ is the likelihood of our data given the model, which is already stated above as Equation \ref{2.2}. Plugging this into our equation, we have:
$Pr(H|D) = \frac{\binom{N}{H} p_H^H (1-p_H)^{N-H}}{\displaystyle \int_{0}^{1} \binom{N}{H} p_H^H (1-p_H)^{N-H} dp_H} \label{2.22}$
This ugly equation actually simplifies to a beta distribution, which can be expressed more simply as:
$Pr(H|D) = \frac{(N+1)!}{H!(N-H)!} p_H^H (1-p_H)^{N-H} \label{2.23}$
We can compare this posterior distribution of our parameter estimate, pH, given the data, to our uniform prior (Figure 2.3). If you inspect this plot, you see that the posterior distribution is very different from the prior – that is, the data have changed our view of the values that parameters should take. Again, this result is qualitatively consistent with both the frequentist and ML approaches described above. In this case, we can see from the posterior distribution that we can be quite confident that our parameter pH is not 0.5.
As you can see from this example, Bayes theorem lets us combine our prior belief about parameter values with the information from the data in order to obtain a posterior. These posterior distributions are very easy to interpret, as they express the probability of the model parameters given our data. However, that clarity comes at a cost of requiring an explicit prior. Later in the book we will learn how to use this feature of Bayesian statistics to our advantage when we actually do have some prior knowledge about parameter values.
Figure 2.3. Bayesian prior (dotted line) and posterior (solid line) distributions for lizard flipping. Image by the author, can be reused under a CC-BY-4.0 license.
Section 2.4b: Bayesian MCMC
The other main tool in the toolbox of Bayesian comparative methods is the use of Markov-chain Monte Carlo (MCMC) tools to calculate posterior probabilities. MCMC techniques use an algorithm that uses a “chain” of calculations to sample the posterior distribution. MCMC requires calculation of likelihoods but not complicated mathematics (e.g. integration of probability distributions, as in Equation \ref{2.22}, and so represents a more flexible approach to Bayesian computation. Frequently, the integrals in Equation \ref{2.21} are intractable, so that the most efficient way to fit Bayesian models is by using MCMC. Also, setting up an MCMC is, in my experience, easier than people expect!
An MCMC analysis requires that one constructs and samples from a Markov chain. A Markov chain is a random process that changes from one state to another with certain probabilities that depend only on the current state of the system, and not what has come before. A simple example of a Markov chain is the movement of a playing piece in the game Chutes and Ladders; the position of the piece moves from one square to another following probabilities given by the dice and the layout of the game board. The movement of the piece from any square on the board does not depend on how the piece got to that square.
Some Markov chains have an equilibrium distribution, which is a stable probability distribution of the model’s states after the chain has run for a very long time. For Bayesian analysis, we use a technique called a Metropolis-Hasting algorithm to construct a special Markov chain that has an equilibrium distribution that is the same as the Bayesian posterior distribution of our statistical model. Then, using a random simulation on this chain (this is the Markov-chain Monte Carlo, MCMC), we can sample from the posterior distribution of our model.
In simpler terms: we use a set of well-defined rules. These rules let us walk around parameter space, at each step deciding whether to accept or reject the next proposed move. Because of some mathematical proofs that are beyond the scope of this chapter, these rules guarantee that we will eventually be accepting samples from the Bayesian posterior distribution - which is what we seek.
The following algorithm uses a Metropolis-Hastings algorithm to carry out a Bayesian MCMC analysis with one free parameter.
Metropolis-Hastings algorithm
1. Get a starting parameter value.
• Sample a starting parameter value, p0, from the prior distribution.
2. Starting with i = 1, propose a new parameter for generation i.
• Given the current parameter value, p, select a new proposed parameter value, p′, using the proposal density Q(p′|p).
3. Calculate three ratios.
• a. The prior odds ratio. This is the ratio of the probability of drawing the parameter values p and p′ from the prior. $R_{prior} = \frac{P(p')}{P(p)} \label{2.24}$
• b. The proposal density ratio. This is the ratio of probability of proposals going from p to p′ and the reverse. Often, we purposefully construct a proposal density that is symmetrical. When we do that, Q(p′|p)=Q(p|p′) and a2 = 1, simplifying the calculations . $R_{proposal} = \frac{Q(p'|p)}{Q(p|p')} \label{2.25}$
• c. The likelihood ratio. This is the ratio of probabilities of the data given the two different parameter values. $R_{likelihood} = \frac{L(p'|D)}{L(p|D)} = \frac{P(D|p')}{P(D|p)} \label{2.26}$
4. Multiply. Find the product of the prior odds, proposal density ratio, and the likelihood ratio.$R_{accept} = R_{prior} ⋅ R_{proposal} ⋅ R_{likelihood} \label{2.27}$
5. Accept or reject. Draw a random number x from a uniform distribution between 0 and 1. If x < Raccept, accept the proposed value of p′ ( pi = p′); otherwise reject, and retain the current value p ( pi = p).
6. Repeat. Repeat steps 2-5 a large number of times.
Carrying out these steps, one obtains a set of parameter values, pi, where i is from 1 to the total number of generations in the MCMC. Typically, the chain has a “burn-in” period at the beginning. This is the time before the chain has reached a stationary distribution, and can be observed when parameter values show trends through time and the likelihood for models has yet to plateau. If you eliminate this “burn-in” period, then, as discussed above, each step in the chain is a sample from the posterior distribution. We can summarize the posterior distributions of the model parameters in a variety of ways; for example, by calculating means, 95% confidence intervals, or histograms.
We can apply this algorithm to our coin-flipping example. We will consider the same prior distribution, U(0, 1), for the parameter p. We will also define a proposal density, Q(p′|p) U(p − ϵ, p + ϵ). That is, we will add or subtract a small number ( ϵ ≤ 0.01) to generate proposed values of p′ given p.
To start the algorithm, we draw a value of p from the prior. Let’s say for illustrative purposes that the value we draw is 0.60. This becomes our current parameter estimate. For step two, we propose a new value, p′, by drawing from our proposal distribution. We can use ϵ = 0.01 so the proposal distribution becomes U(0.59, 0.61). Let’s suppose that our new proposed value p′=0.595.
We then calculate our three ratios. Here things are simpler than you might have expected for two reasons. First, recall that our prior probability distribution is U(0, 1). The density of this distribution is a constant (1.0) for all values of p and p′. Because of this, the prior odds ratio for this example is always:
$R_{prior} = \frac{P(p')}{P(p)} = \frac{1}{1} = 1 \label{2.28}$
Similarly, because our proposal distribution is symmetrical, Q(p′|p)=Q(p|p′) and Rproposal = 1. That means that we only need to calculate the likelihood ratio, Rlikelihood for p and p′. We can do this by plugging our values for p (or p′) into Equation \ref{2.2}:
$P(D|p) = {N \choose H} p^H (1-p)^{N-H} = {100 \choose 63} 0.6^63 (1-0.6)^{100-63} = 0.068 \label{2.29}$
Likewise,
$P(D|p') = {N \choose H} p'^H (1-p')^{N-H} = {100 \choose 63} 0.595^63 (1-0.595)^{100-63} = 0.064 \label{2.30}$
The likelihood ratio is then:
$R_{likelihood} = \frac{P(D|p')}{P(D|p)} = \frac{0.064}{0.068} = 0.94 \label{2.31}$
We can now calculate Raccept = Rprior ⋅ Rproposal ⋅ Rlikelihood = 1 ⋅ 1 ⋅ 0.94 = 0.94. We next choose a random number between 0 and 1 – say that we draw x = 0.34. We then notice that our random number x is less than or equal to Raccept, so we accept the proposed value of p′. If the random number that we drew were greater than 0.94, we would reject the proposed value, and keep our original parameter value p = 0.60 going into the next generation.
If we repeat this procedure a large number of times, we will obtain a long chain of values of p. You can see the results of such a run in Figure 2.4. In panel A, I have plotted the likelihoods for each successive value of p. You can see that the likelihoods increase for the first ~1000 or so generations, then reach a plateau around lnL = −3. Panel B shows a plot of the values of p, which rapidly converge to a stable distribution around p = 0.63. We can also plot a histogram of these posterior estimates of p. In panel C, I have done that – but with a twist. Because the MCMC algorithm creates a series of parameter estimates, these numbers show autocorrelation – that is, each estimate is similar to estimates that come just before and just after. This autocorrelation can cause problems for data analysis. The simplest solution is to subsample these values, picking only, say, one value every 100 generations. That is what I have done in the histogram in panel C. This panel also includes the analytic posterior distribution that we calculated above – notice how well our Metropolis-Hastings algorithm did in reconstructing this distribution! For comparative methods in general, analytic posterior distributions are difficult or impossible to construct, so approximation using MCMC is very common.
This simple example glosses over some of the details of MCMC algorithms, but we will get into those details later, and there are many other books that treat this topic in great depth (e.g. Christensen et al. 2010). The point is that we can solve some of the challenges involved in Bayesian statistics using numerical “tricks” like MCMC, that exploit the power of modern computers to fit models and estimate model parameters.
Section 2.4c: Bayes factors
Now that we know how to use data and a prior to calculate a posterior distribution, we can move to the topic of Bayesian model selection. We already learned one general method for model selection using AIC. We can also do model selection in a Bayesian framework. The simplest way is to calculate and then compare the posterior probabilities for a set of models under consideration. One can do this by calculating Bayes factors:
$B_{12} = \frac{Pr(D|H_1)}{Pr(D|H_2)} \label{2.32}$
Bayes factors are ratios of the marginal likelihoods P(D|H) of two competing models. They represent the probability of the data averaged over the posterior distribution of parameter estimates. It is important to note that these marginal likelihoods are different from the likelihoods used above for AIC model comparison in an important way. With AIC and other related tests, we calculate the likelihoods for a given model and a particular set of parameter values – in the coin flipping example, the likelihood for model 2 when pH = 0.63. By contrast, Bayes factors’ marginal likelihoods give the probability of the data averaged over all possible parameter values for a model, weighted by their prior probability.
Because of the use of marginal likelihoods, Bayes factor allows us to do model selection in a way that accounts for uncertainty in our parameter estimates – again, though, at the cost of requiring explicit prior probabilities for all model parameters. Such comparisons can be quite different from likelihood ratio tests or comparisons of AICc scores. Bayes factors represent model comparisons that integrate over all possible parameter values rather than comparing the fit of models only at the parameter values that best fit the data. In other words, AICc scores compare the fit of two models given particular estimated values for all of the parameters in each of the models. By contrast, Bayes factors make a comparison between two models that accounts for uncertainty in their parameter estimates. This will make the biggest difference when some parameters of one or both models have relatively wide uncertainty. If all parameters can be estimated with precision, results from both approaches should be similar.
Calculation of Bayes factors can be quite complicated, requiring integration across probability distributions. In the case of our coin-flipping problem, we have already done that to obtain the beta distribution in Equation \ref{2.22. We can then calculate Bayes factors to compare the fit of two competing models. Let’s compare the two models for coin flipping considered above: model 1, where pH = 0.5, and model 2, where pH = 0.63. Then:
$\begin{array}{lcl} Pr(D|H_1) &=& \binom{100}{63} 0.5^{0.63} (1-0.5)^{100-63} \\ &=& 0.00270 \\ Pr(D|H_2) &=& \int_{p=0}^{1} \binom{100}{63} p^{63} (1-p)^{100-63} \\ &=& \binom{100}{63} \beta (38,64) \\ &=& 0.0099 \\ B_{12} &=& \frac{0.0099}{0.00270} \\ &=& 3.67 \\ \end{array} \label{2.33}$
In the above example, β(x, y) is the Beta function. Our calculations show that the Bayes factor is 3.67 in favor of model 2 compared to model 1. This is typically interpreted as substantial (but not decisive) evidence in favor of model 2. Again, we can be reasonably confident that our lizard is not a fair flipper.
In the lizard flipping example we can calculate Bayes factors exactly because we know the solution to the integral in Equation \ref{2.33. However, if we don’t know how to solve this equation (a typical situation in comparative methods), we can still approximate Bayes factors from our MCMC runs. Methods to do this, including arrogance sampling and stepping stone models (Xie et al. 2011; Perrakis et al. 2014), are complex and beyond the scope of this book. However, one common method for approximating Bayes Factors involves calculating the harmonic mean of the likelihoods over the MCMC chain for each model. The ratio of these two likelihoods is then used as an approximation of the Bayes factor (Newton and Raftery 1994). Unfortunately, this method is extremely unreliable, and probably should never be used (see Neal 2008 for more details). | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/02%3A_Fitting_Statistical_Models_to_Data/2.04%3A_Bayesian_Statistics.txt |
Before I conclude this section, I want to highlight another difference in the way that AIC and Bayes approaches deal with model complexity. This relates to a subtle philosophical distinction that is controversial among statisticians themselves so I will only sketch out the main point; see a real statistics book like Burnham and Anderson (2003) or Gelman et al. (2013) for further details. When you compare Bayes factors, you assume that one of the models you are considering is actually the true model that generated your data, and calculate posterior probabilities based on that assumption. By contrast, AIC assumes that reality is more complex than any of your models, and you are trying to identify the model that most efficiently captures the information in your data. That is, even though both techniques are carrying out model selection, the basic philosophy of how these models are being considered is very different: choosing the best of several simplified models of reality, or choosing the correct model from a set of alternatives.
The debate between Bayesian and likelihood-based approaches often centers around the use of priors in Bayesian statistics, but the distinction between models and “reality” is also important. More specifically, it is hard to imagine a case in comparative biology where one would be justified in the Bayesian assumption that one has identified the true model that generated the data. This also explains why AIC-based approaches typically select more complex models than Bayesian approaches. In an AIC framework, one assumes that reality is very complex and that models are approximations; the goal is to figure out how much added model complexity is required to efficiently explain the data. In cases where the data are actually generated under a very simple model, AIC may err in favor of overly complex models. By contrast, Bayesian analyses assume that one of the models being considered is correct. This type of analysis will typically behave appropriately when the data are generated under a simple model, but may be unpredictable when data are generated by processes that are not considered by any of the models. However, Bayesian methods account for uncertainty much better than AIC methods, and uncertainty is a fundamental aspect of phylogenetic comparative methods.
In summary, Bayesian approaches are useful tools for comparative biology, especially when combined with MCMC computational techniques. They require specification of a prior distribution and assume that the “true” model is among those being considered, both of which can be drawbacks in some situations. A Bayesian framework also allows us to much more easily account for phylogenetic uncertainty in comparative analysis. Many comparative biologists are pragmatic, and use whatever methods are available to analyze their data. This is a reasonable approach but one should remember the assumptions that underlie any statistical result.
2.06: Models and Comparative Methods
For the rest of this book I will introduce several models that can be applied to evolutionary data. I will discuss how to simulate evolutionary processes under these models, how to compare data to these models, and how to use model selection to discriminate amongst them. In each section, I will describe standard statistical tests (when available) along with ML and Bayesian approaches.
One theme in the book is that I emphasize fitting models to data and estimating parameters. I think that this approach is very useful for the future of the field of comparative statistics for three main reasons. First, it is flexible; one can easily compare a wide range of competing models to your data. Second, it is extendable; one can create new models and automatically fit them into a preexisting framework for data analysis. Finally, it is powerful; a model fitting approach allows us to construct comparative tests that relate directly to particular biological hypotheses.
2.0S: 2.S: Fitting Statistical Models to Data (Summary)
Footnotes
1: I assume here that you have little interest in organisms other than lizards.
back to main text
2: And, often, concludes that we just "need more data" to get the answer that we want.
back to main text
3: Especially in fields like genomics where multiple testing and massive Bonferroni corrections are common; one can only wonder at the legions of type II errors that are made under such circumstances.
back to main text
References
Akaike, H. 1998. Information theory and an extension of the maximum likelihood principle. Pp. 199–213 in E. Parzen, K. Tanabe, and G. Kitagawa, eds. Selected papers of Hirotugu Akaike. Springer New York, New York, NY.
Burnham, K. P., and D. R. Anderson. 2003. Model selection and multimodel inference: A practical information theoretic approach. Springer Science & Business Media.
Edwards, A. W. F. 1992. Likelihood. Johns Hopkins University Press, Baltimore.
Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2013. Bayesian data analysis, third edition. Chapman; Hall/CRC.
Neal, R. 2008. The harmonic mean of the likelihood: Worst Monte Carlo method ever. Radford Neal’s blog.
Newton, M. A., and A. E. Raftery. 1994. Approximate Bayesian inference with the weighted likelihood bootstrap. J. R. Stat. Soc. Series B Stat. Methodol. 56:3–48.
Perneger, T. V. 1998. What’s wrong with Bonferroni adjustments. BMJ 316:1236–1238.
Perrakis, K., I. Ntzoufras, and E. G. Tsionas. 2014. On the use of marginal posteriors in marginal likelihood estimation via importance sampling. Comput. Stat. Data Anal. 77:54–69.
Posada, D., and K. A. Crandall. 1998. MODELTEST: Testing the model of DNA substitution. Bioinformatics 14:817–818.
Xie, W., P. O. Lewis, Y. Fan, L. Kuo, and M.-H. Chen. 2011. Improving marginal likelihood estimation for Bayesian phylogenetic model selection. Syst. Biol. 60:150–160. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/02%3A_Fitting_Statistical_Models_to_Data/2.05%3A_AIC_versus_Bayes.txt |
This chapter introduces Brownian motion as a model of trait evolution. I first connected Brownian motion to a model of neutral genetic drift for traits that have no effect on fitness. However, as I demonstrated, Brownian motion can result from a variety of other models, some of which include natural selection. For example, traits will follow Brownian motion under selection is if the strength and direction of selection varies randomly through time. In other words, testing for a Brownian motion model with your data tells you nothing about whether or not the trait is under selection.
• 3.1: Introduction to Brownian Motion
Imagine that you want to use statistical approaches to understand how traits change through time. This requires an exact mathematical specification of how evolution takes place. Obviously there are a wide variety of models of trait evolution, from simple to complex. e.g., creating a model where a trait starts with a certain value and has some constant probability of changing in any unit of time or an alternative model that is more detailed and explicit and considers a large set of individuals.
• 3.2: Properties of Brownian Motion
We can use Brownian motion to model the evolution of a continuously valued trait through time. Brownian motion is an example of a “random walk” model because the trait value changes randomly, in both direction and distance, over any time interval. The statistical process of Brownian motion was originally invented to describe the motion of particles suspended in a fluid.
• 3.3: Simple Quantitative Genetics Models for Brownian Motion
• 3.4: Brownian Motion on a Phylogenetic Tree
We can use the basic properties of Brownian motion model to figure out what will happen when characters evolve under this model on the branches of a phylogenetic tree.
• 3.5: Multivariate Brownian motion
The Brownian motion model we described above was for a single character. However, we often want to consider more than one character at once. This requires the use of multivariate models. The situation is more complex than the univariate case – but not much! In this section I will derive the expectation for a set of (potentially correlated) traits evolving together under a multivariate Brownian motion model.
• 3.6: Simulating Brownian motion on trees
To simulate Brownian motion evolution on trees, we use the three properties of the model described above. For each branch on the tree, we can draw from a normal distribution (for a single trait) or a multivariate normal distribution (for more than one trait) to determine the evolution that occurs on that branch. We can then add these evolutionary changes together to obtain character states at every node and tip of the tree.
• 3.S: Introduction to Brownian Motion (Summary)
03: Introduction to Brownian Motion
Squamates, the group that includes snakes and lizards, is exceptionally diverse. Since sharing a common ancestor between 150 and 210 million years ago (Hedges and Kumar 2009), squamates have diversified to include species that are very large and very small; herbivores and carnivores; species with legs and species that are legless. How did that diversity of species’ traits evolve? How did these characters first come to be, and how rapidly did they change to explain the diversity that we see on earth today? In this chapter, we will begin to discuss models for the evolution of species’ traits.
Imagine that you want to use statistical approaches to understand how traits change through time. To do that, you need to have an exact mathematical specification of how evolution takes place. Obviously there are a wide variety of models of trait evolution, from simple to complex. For example, you might create a model where a trait starts with a certain value and has some constant probability of changing in any unit of time. Alternatively, you might make a model that is more detailed and explicit, and considers a large set of individuals in a population. You could assign genotypes to each individual and allow the population to evolve through reproduction and natural selection.
In this chapter – and in comparative methods as a whole – the models we will consider will be much closer to the first of these two models. However, there are still important connections between these simple models and more realistic models of trait evolution (see chapter five).
In the next six chapters, I will discuss models for two different types of characters. In this chapter and chapters four, five, and six, I will consider traits that follow continuous distributions – that is, traits that can have real-numbered values. For example, body mass in kilograms is a continuous character. I will discuss the most commonly used model for these continuous characters, Brownian motion, in this chapter and the next, while chapter five covers analyses of multivariate Brownian motion. We will go beyond Brownian motion in chapter six. In chapter seven and the chapters that immediately follow, I will cover discrete characters, characters that can occupy one of a number of distinct character states (for example, species of squamates can either be legless or have legs). | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/03%3A_Introduction_to_Brownian_Motion/3.01%3A_Introduction_to_Brownian_Motion.txt |
We can use Brownian motion to model the evolution of a continuously valued trait through time. Brownian motion is an example of a “random walk” model because the trait value changes randomly, in both direction and distance, over any time interval. The statistical process of Brownian motion was originally invented to describe the motion of particles suspended in a fluid. To me this is a bit hard to picture, but the logic applies equally well to the movement of a large ball over a crowd in a stadium. When the ball is over the crowd, people push on it from many directions. The sum of these many small forces determine the movement of the ball. Again, the movement of the ball can be modeled using Brownian motion 1.
The core idea of this example is that the motion of the object is due to the sum of a large number of very small, random forces. This idea is a key part of biological models of evolution under Brownian motion. It is worth mentioning that even though Brownian motion involves change that has a strong random component, it is incorrect to equate Brownian motion models with models of pure genetic drift (as explained in more detail below).
Brownian motion is a popular model in comparative biology because it captures the way traits might evolve under a reasonably wide range of scenarios. However, perhaps the main reason for the dominance of Brownian motion as a model is that it has some very convenient statistical properties that allow relatively simple analyses and calculations on trees. I will use some simple simulations to show how the Brownian motion model behaves. I will then list the three critical statistical properties of Brownian motion, and explain how we can use these properties to apply Brownian motion models to phylogenetic comparative trees.
When we model evolution using Brownian motion, we are typically discussing the dynamics of the mean character value, which we will denote as $\bar{z}$, in a population. That is, we imagine that you can measure a sample of the individuals in a population and estimate the mean average trait value. We will denote the mean trait value at some time t as $\bar{z}(t)$. We can model the mean trait value through time with a Brownian motion process.
Brownian motion models can be completely described by two parameters. The first is the starting value of the population mean trait, $\bar{z}(0)$. This is the mean trait value that is seen in the ancestral population at the start of the simulation, before any trait change occurs. The second parameter of Brownian motion is the evolutionary rate parameter, σ2. This parameter determines how fast traits will randomly walk through time.
At the core of Brownian motion is the normal distribution. You might know that a normal distribution can be described by two parameters, the mean and variance. Under Brownian motion, changes in trait values over any interval of time are always drawn from a normal distribution with mean 0 and variance proportional to the product of the rate of evolution and the length of time (variance = σ2t). As I will show later, we can simulate change under Brownian motion model by drawing from normal distributions. Another way to say this more simply is that we can always describe how much change to expect under Brownian motion using normal distributions. These normal distributions for expected changes have a mean of zero and get wider as the time interval we consider gets longer.
A few simulations will illustrate the behavior of Brownian motion. Figure 3.1 shows sets of Brownian motion run over three different time periods (t = 100, 500, and 1000) with the same starting value $\bar{z}(0) = 0$ and rate parameter σ2 = 1. Each panel of the figure shows 100 simulations of the process over that time period. You can see that the tip values look like normal distributions. Furthermore, the variance among separate runs of the process increases linearly with time. This variance among runs is greatest over the longest time intervals. It is this variance, the variation among many independent runs of the same evolutionary process, that we will consider throughout the next section.
Imagine that we run a Brownian motion process over a given time interval many times, and save the trait values at the end of each of these simulations. We can then create a statistical distribution of these character states. It might not be obvious from figure 3.1, but the distributions of possible character states at any time point in a Brownian walk is normal. This is illustrated in figure 3.2, which shows the distribution of traits from 100,000 simulations with σ2 = 1 and t = 100. The tip characters from all of these simulations follow a normal distribution with mean equal to the starting value, $\bar{z}(0) = 0$, and a variance of σ2t = 100.
Figure 3.3 shows how rate parameter σ2 affects the rate of spread of Brownian walks. The panels show sets of 100 Brownian motion simulations run over 1000 time units for σ2 = 1 (Panel A), σ2 = 5 (Panel B), and σ2 = 25 (Panel C). You can see that simulations with a higher rate parameter create a larger spread of trait values among simulations over the same amount of time.
If we let $\bar{z}(t)$ be the value of our character at time t, then we can derive three main properties of Brownian motion. I will list all three, then explain each in turn.
1. $E[\bar{z}(t)] = \bar{z}(0)$
2. Each successive interval of the “walk” is independent
3. $\bar{z}(t) \sim N(\bar{z}(0),\sigma^2 t)$
First, $E[\bar{z}(t)] = \bar{z}(0)$. This means that the expected value of the character at any time t is equal to the value of the character at time zero. Here the expected value refers to the mean of $\bar{z}(t)$ over many replicates. The intuitive meaning of this equation is that Brownian motion has no “trends,” and wanders equally in both positive and negative directions. If you take the mean of a large number of simulations of Brownian motion over any time interval, you will likely get a value close to $\bar{z}(0)$; as you increase the sample size, this mean will tend to get closer and closer to $\bar{z}(0)$.
Second, each successive interval of the “walk” is independent. Brownian motion is a process in continuous time, and so time does not have discrete “steps.” However, if you sample the process from time 0 to time t, and then again at time t + Δt, the change that occurs over these two intervals will be independent of one another. This is true of any two non-overlapping intervals sampled from a Brownian walk. It is worth noting that only the changes are independent, and that the value of the walk at time t + Δt – which we can write as $\bar{z}(t+\Delta t)$ - is not independent of the value of the walk at time t, $\bar{z}(t)$. But the differences between successive steps [e.g. $\bar{z}(t)-\bar{z}(0)$ and $\bar{z}(t+\Delta t) - \bar{z}(t)$] are independent of each other and of $\bar{z}(0)$.
Finally, $\bar{z}(t) \sim N(\bar{z}(0),\sigma^2 t)$.That is, the value of $\bar{z}(t)$ is drawn from a normal distribution with mean $\bar{z}(0)$ and variance σ2t. As we noted above, the parameter σ2 is important for Brownian motion models, as it describes the rate at which the process wanders through trait space. The overall variance of the process is that rate times the amount of time that has elapsed. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/03%3A_Introduction_to_Brownian_Motion/3.02%3A_Properties_of_Brownian_Motion.txt |
Brownian motion under Genetic Drift
The simplest way to obtain Brownian evolution of characters is when evolutionary change is neutral, with traits changing only due to genetic drift (e.g. Lande 1976). To show this, we will create a simple model. We will assume that a character is influenced by many genes, each of small effect, and that the value of the character does not affect fitness. Finally, we assume that mutations are random and have small effects on the character, as specified below. These assumptions probably seem unrealistic, especially if you are thinking of a trait like the body size of a lizard! But we will see later that we can also derive Brownian motion under other models, some of which involve selection.
Consider the mean value of this trait, $\bar{z}$, in a population with an effective population size of Ne (this is technically the variance effective population )2. Since there is no selection, the phenotypic character will change due only to mutations and genetic drift. We can model this process in a number of ways, but the simplest uses an "infinite alleles" model. Under this model, mutations occur randomly and have random phenotypic effects. We assume that mutations are drawn at random from a distribution with mean 0 and mutational variance σm2. This model assumes that the number of alleles is so large that there is effectively no chance of mutations happening to the same allele more than once - hence, "infinite alleles." The alleles in the population then change in frequency through time due to genetic drift. Drift and mutation together, then, determine the dynamics of the mean trait through time.
If we were to simulate this infinite alleles model many times, we would have a set of evolved populations. These populations would, on average, have the same mean trait value, but would differ from each other. Let’s try to derive how, exactly, these populations3 evolve.
If we consider a population evolving under this model, it is not difficult to show that the expected population phenotype after any amount of time is equal to the starting phenotype. This is because the phenotypes don’t matter for survival or reproduction, and mutations are assumed to be random and symmetrical. Thus,
$E[\bar{z}(t)] = \bar{z}(0) \label{3.1}$
Note that this equation already matches the first property of Brownian motion.
Next, we need to also consider the variance of these mean phenotypes, which we will call the between-population phenotypic variance (σB2). Importantly, σB2 is the same quantity we earlier described as the “variance” of traits over time – that is, the variance of mean trait values across many independent “runs” of evolutionary change over a certain time period.
To calculate σB2, we need to consider variation within our model populations. Because of our simplifying assumptions, we can focus solely on additive genetic variance within each population at some time t, which we can denote as σa2. Additive genetic variance measures the total amount of genetic variation that acts additively (i.e. the contributions of each allele add together to predict the final phenotype). This excludes genetic variation involving interacions between alleles, such as dominance and epistasis (see Lynch and Walsh 1998 for a more detailed discussion). Additive genetic variance in a population will change over time due to genetic drift (which tends to decrease σa2) and mutational input (which tends to increase σa2). We can model the expected value of σa2 from one generation to the next as (Clayton and Robertson 1955; Lande 1979, 1980):
$E[\sigma_a^2 (t+1)]=(1-\frac{1}{2 N_e})E[\sigma_a^2 (t)]+\sigma_m^2 \label{3.2}$
where t is the elapsed time in generations, Ne is the effective population size, and σm2 is the mutational variance. There are two parts to this equation. The first, $(1-\frac{1}{2 N_e})E[\sigma_a^2 (t)]$, shows the decrease in additive genetic variance each generation due to genetic drift. The rate of decrease depends on effective population size, Ne, and the current level of additive variation. The second part of the equation describes how additive genetic variance increases due to new mutations (σm2) each generation.
If we assume that we know the starting value at time 0, σaStart2, we can calculate the expected additive genetic variance at any time t as:
$E[\sigma_a^2 (t)]={(1-\frac{1}{2 N_e})}^t [\sigma_{aStart}^2 - 2 N_e \sigma_m^2 ]+ 2 N_e \sigma_m^2 \label{3.3}$
Note that the first term in the above equation, ${(1-\frac{1}{2 N_e})}^t$, goes to zero as t becomes large. This means that additive genetic variation in the evolving populations will eventually reach an equilibrium between genetic drift and new mutations, so that additive genetic variation stops changing from one generation to the next. We can find this equilibrium by taking the limit of Equation \ref{3.3} as t becomes large.
$\lim_{t → ∞}E[σ_a^2(t)] = 2N_eσ_m^2 \label{3.4}$
Thus the equilibrium genetic variance depends on both population size and mutational input.
We can now derive the between-population phenotypic variance at time t, σB2(t). We will assume that σa2 is at equilibrium and thus constant (equation 3.4). Mean trait values in independently evolving populations will diverge from one another. Skipping some calculus, after some time period t has elapsed, the expected among-population variance will be (from Lande 1976):
$\sigma_B^2 (t)=\frac{t \sigma_a^2}{N_e} \label{3.5}$
Substituting the equilibrium value of σa2 from equation 3.4 into equation 3.5 gives (Lande 1979, 1980):
$\sigma_B^2 (t)=\frac{t \sigma_a^2}{N_e} = \frac{t \cdot 2 N_e \sigma_m^2}{N_e} = 2 t \sigma_m^2 \label{3.6}$
Thie equation states that the variation among two diverging populations depends on twice the time since they have diverged and the rate of mutational input. Notice that for this model, the amount of variation among populations is independent of both the starting state of the populations and their effective population size. This model predicts, then, that long-term rates of evolution are dominated by the supply of new mutations to a population.
Even though we had to make particular specific assumptions for that derivation, Lynch and Hill (1986) show that Equation \ref{3.6} is a general result that holds under a range of models, even those that include dominance, linkage, nonrandom mating, and other processes. Equation \ref{3.6} is somewhat useful, but we cannot often measure the mutational variance σm2 for any natural populations (but see Turelli 1984). By contrast, we sometimes do know the heritability of a particular trait. Heritability describes the proportion of total phenotypic variation within a population (σw2) that is due to additive genetic effects (σa2):
$h^2=\frac{\sigma_a^2}{\sigma_w^2}.$
We can calculate the expected trait heritability for the infinite alleles model at mutational equilibrium. Substituting Equation \ref{3.4}, we find that:
$h^2 = \frac{2 N_e \sigma_m^2}{\sigma_w^2} \label{3.7}$
So that:
$\sigma_m^2 = \frac{h^2 \sigma_w^2}{2 N_e} \label{3.8}$
Here, h2 is heritability, Ne the effective population size, and σw2 the within-population phenotypic variance, which differs from σa2 because it includes all sources of variation within populations, including both non-additive genetic effects and environmental effects. Substituting this expression for σw2 into Equation \ref{3.6}, we have:
$\sigma_B^2 (t) = 2 \sigma_m^2 t = \frac{h^2 \sigma_w^2 t}{N_e} \label{3.9}$
So, after some time interval t, the mean phenotype of a population has an expected value equal to the starting value, and a variance that depends positively on time, heritability, and trait variance, and negatively on effective population size.
To derive this result, we had to make particular assumptions about normality of new mutations that might seem quite unrealistic. It is worth noting that if phenotypes are affected by enough mutations, the central limit theorem guarantees that the distribution of phenotypes within populations will be normal – no matter what the underlying distribution of those mutations might be. We also had to assume that traits are neutral, a more dubious assumption that we relax below - where we will also show that there are other ways to get Brownian motion evolution than just genetic drift!
Note, finally, that this quantitative genetics model predicts that traits will evolve under a Brownian motion model. Thus, our quantitative genetics model has the same statistical properties of Brownian motion. We only need to translate one parameter: σ2 = h2σw2/Ne4.
Brownian Motion under Selection
We have shown that it is possible to relate a Brownian motion model directly to a quantitative genetics model of drift. In fact, there is some temptation to equate the two, and conclude that traits that evolve like Brownian motion are not under selection. However, this is incorrect. More specifically, an observation that a trait is evolving as expected under Brownian motion is not equivalent to saying that that trait is not under selection. This is because characters can also evolve as a Brownian walk even if there is strong selection – as long as selection acts in particular ways that maintain the properties of the Brownian motion model.
In general, the path followed by population mean trait values under mutation, selection, and drift depend on the particular way in which these processes occur. A variety of such models are considered by Hansen and Martins (1996). They identify three very different models that include selection where mean traits still evolve under an approximately Brownian model. Here I present univariate versions of the Hansen-Martins models, for simplicity; consult the original paper for multivariate versions. Note that all of these models require that the strength of selection is relatively weak, or else genetic variation of the character will be depleted by selection over time and the dynamics of trait evolution will change.
One model assumes that populations evolve due to directional selection, but the strength and direction of selection varies randomly from one generation to the next. We model selection each generation as being drawn from a normal distribution with mean 0 and variance σs2. Similar to our drift model, populations will again evolve under Brownian motion. However, in this case the Brownian motion parameters have a different interpretation:
$\sigma_B^2=(\frac{h^2 \sigma_W^2}{N_e} +\sigma_s^2)t \label{3.10}$
In the particular case where variation in selection is much greater than variation due to drift, then:
$σ_B^2 ≈ σ_s^2 \label{3.11}$
That is, when selection is (on average) much stronger than drift, the rate of evolution is completely dominated by the selection term. This is not that far fetched, as many studies have shown selection in the wild that is both stronger than drift and commonly changing in both direction and magnitude from one generation to the next.
In a second model, Hansen and Martins (1996) consider a population subject to strong stabilizing selection for a particular optimal value, but where the position of the optimum itself changes randomly according to a Brownian motion process. In this case, population means can again be described by Brownian motion, but now the rate parameter reflects movement of the optimum rather than the action of mutation and drift. Specifically, if we describe movement of the optimum by a Brownian rate parameter σE2, then:
$σ_B^2 ≈ σ_E^2 \label{3.12}$
To obtain this result we must assume that there is at least a little bit of stabilizing selection (at least on the order of 1/tij where tij is the number of generations separating pairs of populations; Hansen and Martins 1996).
Again in this case, the population is under strong selection in any one generation, but long-term patterns of trait change can be described by Brownian motion. The rate of the random walk is totally determined by the action of selection rather than drift.
The important take-home point from both of these models is that the pattern of trait evolution through time under this model still follows a Brownian motion model, even though changes are dominated by selection and not drift. In other words, Brownian motion evolution does not imply that characters are not under selection!
Finally, Hansen and Martins (1996) consider the situation where populations evolve following a trend. In this case, we get evolution that is different from Brownian motion, but shares some key attributes. Consider a population under constant directional selection, s, so that:
$E[\bar{z}(t+1)]=\bar{z}(t) + h^2 s \label{3.13}$
The variance among populations due to genetic drift after a single generation is then:
$\sigma_B^2 = \frac{h^2 \sigma_w^2}{N_e} \label{3.14}$
Over some longer period of time, traits will evolve so that they have expected mean trait value that is normal with mean:
$E[\bar{z}(t)]=t \cdot (h^2 s) \label{3.15}$
We can also calculate variance among species as:
$\sigma_B^2(t) = \frac{h^2 \sigma_w^2 t}{N_e} \label{3.16}$
Note that the variance of this process is exactly identical to the variance among populations in a pure drift model (equation 3.9). Selection only changes the expectation for the species mean (of course, we assume that variation within populations and heritability are constant, which will only be true if selection is quite weak). Furthermore, with comparative methods, we are often considering a set of species and their traits in the present day, in which case they will all have experienced the same amount of evolutionary time (t) and have the same expected trait value. In fact, equations \ref{3.14} and \ref{3.16} are exactly the same as what we would expect under a pure-drift model in the same population, but starting with a trait value equal to $\bar{z}(0) = t \cdot (h^2 s)$. That is, from the perspective of data only on living species, these two pure drift and linear selection models are statistically indistinguishable. The implications of this are striking: we can never find evidence for trends in evolution studying only living species (Slater et al. 2012).
In summary, we can describe three very different ways that traits might evolve under Brownian motion – pure drift, randomly varying selection, and varying stabilizing selection – and one model, constant directional selection, which creates patterns among extant species that are indistinguishable from Brownian motion. And there are more possible models out there that predict the same patterns. One can never tell these models apart by evaluating the qualitative pattern of evolution across species - they all predict the same pattern of Brownian motion evolution. The details differ, in that the models have Brownian motion rate parameters that differ from one another and relate to measurable quantities like population size and the strength of selection. Only by knowing something about these parameters can we distinguish among these possible scenarios.
You might notice that none of these “Brownian” models are particularly detailed, especially for modeling evolution over long time scales. You might even complain that these models are unrealistic. It is hard to imagine a case where a trait might be influenced only by random mutations of small effect over many alleles, or where selection would act in a truly random way from one generation to the next for millions of years. And you would be right! However, there are tremendous statistical benefits to using Brownian models for comparative analyses. Many of the results derived in this book, for example, are simple under Brownian motion but much more complex and different under other models. And it is also the case that some (but not all) methods are robust to modest violations of Brownian motion, in the same way that many standard statistical analyses are robust to minor variations of the assumptions of normality. In any case, we will proceed with models based on Brownian motion, keeping in mind these important caveats. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/03%3A_Introduction_to_Brownian_Motion/3.03%3A_Simple_Quantitative_Genetics_Models_for_Brownian_Motion.txt |
We can use the basic properties of Brownian motion model to figure out what will happen when characters evolve under this model on the branches of a phylogenetic tree. First, consider evolution along a single branch with length t1 (Figure 3.4A). In this case, we can model simple Brownian motion over time t1 and denote the starting value as $\bar{z}(0)$. If we evolve with some rate parameter σB2, then:
$E[\bar{z}(t)] \sim N(\bar{z}(0), \sigma_B^2 t_1) \label{3.17}$
Now consider a small section of a phylogenetic tree including two species and an ancestral stem branch (Figure 3.4B). Assume a character evolves on that tree under Brownian motion, again with starting value $\bar{z}(0)$ and rate parameter σB2. First consider species a. The mean trait in that species $\bar{x}_a$ evolves under Brownian motion from the ancestor to species a over a total time of t1 + t2. Thus,
$\bar{x}_a \sim N[\bar{z}(0), \sigma_B^2 (t_1+t_2)] \label{3.18}$
Similarly for species b, over a total time of t1 + t3
$\bar{x}_b \sim N[\bar{z}(0),\sigma_B^2 (t_1+t_3)] \label{3.19}$
However, $\bar{x}_a$ and $\bar{x}_b$ are not independent of each other. Instead, the two species share one branch in common (branch 1). Each tip trait value can be thought of as an ancestral value plus the sum of two evolutionary changes: one (from branch 1) that is shared between the two species and one that is unique (branch 2 for species a and branch 3 for species b). In this case, mean trait values $\bar{x}_a$ and $\bar{x}_b$ will share similarity due to their shared evolutionary history. We can describe this similarity by calculating the covariance between the traits of species a and b. We note that:
$\begin{array}{lcr} \bar{x}_a = \Delta \bar{x}_1 + \Delta \bar{x}_2\ \bar{x}_b = \Delta \bar{x}_1 + \Delta \bar{x}_3\ \end{array} \label{3.20}$
Where $\Delta \bar{x}_1$, $\Delta \bar{x}_2$, and $\Delta \bar{x}_3$ represent evolution along the three branches in the tree, are all normally distributed with mean zero and variances σ2t1, σ2t2, and σ2t3, respectively. $\bar{x}_a$ and $\bar{x}_b$ are sums of normal random variables and are themselves normal. The covariance of these two terms is simply the variance of their shared term:
$cov(\bar{x}_a,\bar{x}_b)=var(\Delta \bar{x}_1)=\sigma_B^2 t_1 \label{3.21}$
It is also worth noting that we can describe the trait values for the two species as a single draw from a multivariate normal distribution. Each trait has the same expected value, $\bar{z}(0)$, and the two traits have a variance-covariance matrix:
$\begin{bmatrix} \sigma^2 (t_1 + t_2) & \sigma^2 t_1 \ \sigma^2 t_1 & \sigma^2 (t_1 + t_3) \ \end{bmatrix} = \sigma^2 \begin{bmatrix} t_1 + t_2 & t_1 \ t_1 & t_1 + t_3 \ \end{bmatrix} = \sigma^2 \mathbf{C} \label{3.22}$
The matrix C in Equation \ref{3.22} is commonly encountered in comparative biology, and will come up again in this book. We will call this matrix the phylogenetic variance-covariance matrix. This matrix has a special structure. For phylogenetic trees with n species, this is an n × n matrix, with each row and column corresponding to one of the n taxa in the tree. Along the diagonal are the total distances of each taxon from the root of the tree, while the off-diagonal elements are the total branch lengths shared by particular pairs of taxa. For example, C(1, 2) and C(2, 1) – which are equal because the matrix C is always symmetric – is the shared phylogenetic path length between the species in the first row – here, species a - and the species in the second row – here, species b. Under Brownian motion, these shared path lengths are proportional to the phylogenetic covariances of trait values. A full example of a phylogenetic variance-covariance matrix for a small tree is shown in Figure 3.5. This multivariate normal distribution completely describes the expected statistical distribution of traits on the tips of a phylogenetic tree if the traits evolve according to a Brownian motion model. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/03%3A_Introduction_to_Brownian_Motion/3.04%3A_Brownian_Motion_on_a_Phylogenetic_Tree.txt |
The Brownian motion model we described above was for a single character. However, we often want to consider more than one character at once. This requires the use of multivariate models. The situation is more complex than the univariate case – but not much! In this section I will derive the expectation for a set of (potentially correlated) traits evolving together under a multivariate Brownian motion model.
Character values across species can covary because of phylogenetic relationships, because different characters tend to evolve together, or both. Fortunately, we can generalize the model described above to deal with both of these types of covariation. To do this, we must combine two variance-covariance matrices. The first one, C, we have already seen; it describes the variances and covariances across species for single traits due to shared evolutionary history along the branches of a phylogentic tree. The second variance-covariance matrix, which we can call R, describes the variances and covariances across traits due to their tendencies to evolve together. For example, if a species of lizard gets larger due to the action of natural selection, then many of its other traits, like head and limb size, will get larger too due to allometry. The diagonal entries of the matrix R will provide our estimates of σi2, the net rate of evolution, for each trait, while off-diagonal elements, σij, represent evolutionary covariances between pairs of traits. We will denote number of species as n and the number of traits as m, so that C is n × n and R is m × m.
Our multivariate model of evolution has parameters that can be described by an m × 1 vector, a, containing the starting values for each trait – $\bar{z}_1(0)$, $\bar{z}_2(0)$, and so on, up to $\bar{z}_m(0)$, and an m × m matrix, R, described above. This model has m parameters for a and m ⋅ (m + 1)/2 parameters for R, for a total of m ⋅ (m + 3)/2 parameters.
Under our multivariate Brownian motion model, the joint distribution of all traits across all species still follows a multivariate normal distribution. We find the variance-covariance matrix that describes all characters across all species by combining the two matrices R and C into a single large matrix using the Kroeneker product:
$\textbf{V} = \textbf{R} ⊗ \textbf{C} \label{3.23}$
This matrix V is n ⋅ m × n ⋅ m, and describes the variances and covariances of all traits across all species.
We can return to our example of evolution along a single branch (Figure 3.4a). Imagine that we have two characters that are evolving under a multivariate Brownian motion model. We state the parameters of the model as:
$\begin{array}{lcr} \mathbf{a} = \begin{bmatrix} \bar{z}_1(0) \ \bar{z}_2(0) \ \end{bmatrix} \ \mathbf{R} = \begin{bmatrix} \sigma_1^2 & \sigma_{12} \ \sigma_{12} & \sigma_2^2 \ \end{bmatrix} \ \end{array} \label{3.24}$
For a single branch, C = [t1], so:
$\mathbf{V} = \mathbf{R} \otimes \mathbf{C} = \begin{bmatrix} \sigma_1^2 & \sigma_{12} \ \sigma_{12} & \sigma_2^2 \ \end{bmatrix} \otimes [t_1] = \begin{bmatrix} \sigma_1^2 t_1 & \sigma_{12} t_1 \ \sigma_{12} t_1 & \sigma_2^2 t_1 \ \end{bmatrix} \label{3.25}$
The two traits follow a multivariate normal distribution with mean a and variance-covariance matrix V.
For the simple tree in figure 3.4b,
\begin{align} \mathbf{V} &= \mathbf{R} \otimes \mathbf{C} \[5pt] &= \begin{bmatrix} \sigma_1^2 & \sigma_{12} \ \sigma_{12} & \sigma_2^2 \ \end{bmatrix} \otimes \begin{bmatrix} t_1+t_2 & t_1 \ t_1 & t_1+t_3 \ \end{bmatrix} \[5pt] &= \begin{bmatrix} \sigma_1^2 (t_1+t_2) & \sigma_{12} (t_1+t_2) & \sigma_1^2 t_1 & \sigma_{12} t_1 \ \sigma_{12} (t_1+t_2) & \sigma_2^2 (t_1+t_2) & \sigma_{12} t_1 & \sigma_2^2 t_1 \ \sigma_1^2 t_1 & \sigma_{12} t_1 & \sigma_1^2 (t_1+t_3) & \sigma_{12} (t_1+t_3) \ \sigma_{12} t_1 & \sigma_2^2 t_1 & \sigma_{12} (t_1+t_3) & \sigma_2^2 (t_1+t_3) \ \end{bmatrix} \ \end{align} \label{3.26}
Thus, the four trait values (two traits for two species) are drawn from a multivariate normal distribution with mean
$a=[\bar{z}_1(0), \bar{z}_1(0), \bar{z}_2(0), \bar{z}_2(0)]$
and the variance-covariance matrix shown above.
Both univariate and multivariate Brownian motion models result in traits that follow multivariate normal distributions. This is statistically convenient, and in part explains the popularity of Brownian models in comparative biology.
3.06: Simulating Brownian motion on trees
To simulate Brownian motion evolution on trees, we use the three properties of the model described above. For each branch on the tree, we can draw from a normal distribution (for a single trait) or a multivariate normal distribution (for more than one trait) to determine the evolution that occurs on that branch. We can then add these evolutionary changes together to obtain character states at every node and tip of the tree.
I will illustrate one such simulation for the simple tree depicted in figure 3.4b. We first set the ancestral character state to be $\bar{z}(0)$, which will then be the expected value for all the nodes and tips in the tree. This tree has three branches, so we draw three values from normal distributions. These normal distributions have mean zero and variances that are given by the rate of evolution and the branch length of the tree, as stated in equation 3.1. Note that we are modeling changes on these branches, so even if $\bar{z}(0) \neq 0$ the values for changes on branches are drawn from a distribution with a mean of zero. In the case of the tree in Figure 3.1, x1 ∼ N(0, σ2t1). Similarly, x2 ∼ N(0, σ2t2) and x3 ∼ N(0, σ2t3). If I set σ2 = 1 for the purposes of this example, I might obtain x1 = −1.6, x2 = 0.1, and x3 = −0.3. These values represent the evolutionary changes that occur along branches in the simulation. To calculate trait values for species, we add: xa = θ + x1 + x2 = 0 − 1.6 + 0.1 = −1.5, and xb = θ + x1 + x3 = 0 − 1.6 + −0.3 = −1.9.
This simulation algorithm works fine but is actually more complicated than it needs to be, especially for large trees. We already know that xa and xb come from a multivariate normal distribution with known mean vector and variance-covariance matrix. So, as a simple alternative, we can simply draw a vector from this distribution, and our tip values will have exactly the same statistical properties as if they were simulated on a phylogenetic tree. These two methods for simulating character evolution on trees are exactly equivalent to one another. In our small example, this alternative is not too much simpler than just adding the branches - but in some circumstances it is much easier to draw from a multivariate normal distribution. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/03%3A_Introduction_to_Brownian_Motion/3.05%3A_Multivariate_Brownian_motion.txt |
In this chapter, I introduced Brownian motion as a model of trait evolution. I first connected Brownian motion to a model of neutral genetic drift for traits that have no effect on fitness. However, as I demonstrated, Brownian motion can result from a variety of other models, some of which include natural selection. For example, traits will follow Brownian motion under selection is if the strength and direction of selection varies randomly through time. In other words, testing for a Brownian motion model with your data tells you nothing about whether or not the trait is under selection.
There is one general feature of all models that evolve in a Brownian way: they involve the action of a large number of very small “forces” pushing on characters. No matter the particular distribution of these small effects or even what causes them, if you add together enough of them you will obtain a normal distribution of outcomes and, sometimes, be able to model this process using Brownian motion. The main restriction might be the unbounded nature of Brownian motion – species are expected to become more and more different through time, without any limit, which must be unrealistic over very long time scales. We will deal with this issue in later chapters.
In summary, Brownian motion is mathematically tractable, and has convenient statistical properties. There are also some circumstances under which one would expect traits to evolve under a Brownian model. However, as we will see later in the book, one should view Brownian motion as an assumption that might not hold for real data sets.
Footnotes
1: More formally, the ball will move in two-dimensional Brownian motion, which describe movement both across and up and down the stadium rows. But if you consider just the movement in one direction - say, the distance of the ball from the field - then this is a simple single dimensional Brownian motion process as described here.
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2: Variance effective population size is the effective population size of a model population with random mating, no substructure, and constant population size that would have quantitative genetic properties equal to our actual population. All of this is a bit beyond the scope of this book (but see Templeton 2006). But writing Ne instead of N allows us to develop the model without worrying about all of the extra assumptions we would have to make about how individuals mate and how populations are distributed over time and space.
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3: In this book, we will typically consider variation among species rather than populations. However, we will also always assume that species are made up of one population, and so we can apply the same mathematical equations across species in a phylogenetic tree.
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4: In some cases in the literature, the magnitude of trait change is expressed in within-population phenotypic standard deviations, $\sqrt{\sigma_w^2}$, per generation (Estes and Arnold 2007; e.g. Harmon et al. 2010). In that case, since dividing a random normal deviate by x is equivalent to dividing its variance by x2, we have σ2 = h2/Ne.
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References
Clayton, G., and A. Robertson. 1955. Mutation and quantitative variation. Am. Nat. 89:151–158.
Estes, S., and S. J. Arnold. 2007. Resolving the paradox of stasis: Models with stabilizing selection explain evolutionary divergence on all timescales. Am. Nat. 169:227–244.
Hansen, T. F., and E. P. Martins. 1996. Translating between microevolutionary process and macroevolutionary patterns: The correlation structure of interspecific data. Evolution 50:1404–1417.
Harmon, L. J., J. B. Losos, T. Jonathan Davies, R. G. Gillespie, J. L. Gittleman, W. Bryan Jennings, K. H. Kozak, M. A. McPeek, F. Moreno-Roark, T. J. Near, and Others. 2010. Early bursts of body size and shape evolution are rare in comparative data. Evolution 64:2385–2396.
Hedges, B. S., and S. Kumar. 2009. The timetree of life. Oxford University Press, Oxford.
Lande, R. 1976. Natural selection and random genetic drift in phenotypic evolution. Evolution 30:314–334.
Lande, R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain:body size allometry. Evolution 33:402–416.
Lande, R. 1980. Sexual dimorphism, sexual selection, and adaptation in polygenic characters. Evolution 34:292–305.
Lynch, M., and W. G. Hill. 1986. Phenotypic evolution by neutral mutation. Evolution 40:915–935.
Lynch, M., and B. Walsh. 1998. Genetics and analysis of quantitative traits. Sinauer Sunderland, MA.
Slater, G. J., L. J. Harmon, and M. E. Alfaro. 2012. Integrating fossils with molecular phylogenies improves inference of trait evolution. Evolution 66:3931–3944. Blackwell Publishing Inc.
Templeton, A. R. 2006. Population genetics and microevolutionary theory. John Wiley & Sons.
Turelli, M. 1984. Heritable genetic variation via mutation-selection balance: Lerch’s zeta meets the abdominal bristle. Theor. Popul. Biol. 25:138–193. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/03%3A_Introduction_to_Brownian_Motion/3.0S%3A_3.S%3A_Introduction_to_Brownian_Motion_%28Summary%29.txt |
By fitting a Brownian motion model to phylogenetic comparative data, one can estimate the rate of evolution of a single character. In this chapter, I demonstrated three approaches to estimating that rate: PICs, maximum likelihood, and Bayesian MCMC. In the next chapter, we will discuss other models of evolution that can be fit to continuous characters on trees.
• 4.1: Introduction
Mammals come in a wide variety of shapes and sizes. Body size is important as a biological variable because it predicts so many other aspect of an animal’s life, from the physiology of heat exchange to the biomechanics of locomotion. Thus, the rate at which body size evolves is of great interest among mammalian biologists. Throughout this chapter, I will discuss the evolution of body size across different species of mammals. The data I will analyze is taken from Garland (1992).
• 4.2: Estimating Rates using Independent Contrasts
The information required to estimate evolutionary rates is efficiently summarized in the early (but still useful) phylogenetic comparative method of independent contrasts (Felsenstein 1985). Independent contrasts summarize the amount of character change across each node in the tree, and can be used to estimate the rate of character change across a phylogeny. There is also a simple mathematical relationship between contrasts and maximum-likelihood rate estimates that I will discuss below.
• 4.3: Estimating rates using maximum likelihood
We can also estimate the evolutionary rate by finding the maximum-likelihood parameter values for a Brownian motion model fit to our data. Recall that ML parameter values are those that maximize the likelihood of the data given our model (see Chapter 2).
• 4.4: Bayesian approach to evolutionary rates
Finally, we can also use a Bayesian approach to fit Brownian motion models to data and to estimate the rate of evolution. This approach differs from the ML approach in that we will use explicit priors for parameter values, and then run an MCMC to estimate posterior distributions of parameter estimates. To do this, we will modify the basic algorithm for Bayesian MCMC.
• 4.5: Summary
04: Fitting Brownian Motion
Mammals come in a wide variety of shapes and sizes. Some species are incredibly tiny. For example, the bumblebee bat, weighing in at 2 g, competes for the title of smallest mammal with the slightly lighter (but also slightly longer) Etruscan shrew (Hill 1974). Other species are huge, as anyone who has encountered a blue whale knows. Body size is important as a biological variable because it predicts so many other aspect of an animal’s life, from the physiology of heat exchange to the biomechanics of locomotion. Thus, the rate at which body size evolves is of great interest among mammalian biologists. Throughout this chapter, I will discuss the evolution of body size across different species of mammals. The data I will analyze is taken from Garland (1992).
Sometimes one might be interested in calculating the rate of evolution of a particular character like body size in a certain clade, say, mammals. You have a phylogenetic tree with branch lengths that are proportional to time, and data on the phenotypes of species on the tips of that tree. It is usually a good idea to log-transform your data if they involve a measurement from a living thing (see Box 4.1, below). If we assume that the character has been evolving under a Brownian motion model, we have two parameters to estimate: $\bar{z}(0)$, the starting value for the Brownian motion model – equivalent to the ancestral state of the character at the root of the tree – and σ2, the diffusion rate of the character. It is this latter parameter that is commonly considered as the rate of evolution for comparative approaches1.
Box 4.1: Biology under the log
One general rule for continuous traits in biology is to carry out a log-transformation (usually natural log, base e, denoted ln) of your data before undertaking any analysis. This also applies to comparative data. There are two main reasons for this, one statistical and the other biological. The statistical reason is that many methods assume that variables follow normal distributions. One can observe that, in general, measurements of species' traits have a distribution that is skewed to the right. A log-transformation will often result in trait distributions that are closer to normal. But why is this the case? The answer is related to the biological reason for log-transformation. When you log transform a variable, the new scale for that variable is a ratio scale, so that a certain differences between points reflects a constant ratio of the two numbers represented by the points. So, for example, if any two numbers are separated by 0.693 units on a natural log scale, one will be exactly two times the other. Ratio scales make sense for living things because it is usually percentage changes rather than absolute changes that matter. For example, a change in body size of 1 mm might matter a lot for a termite, but be irrelevant for an elephant; whereas a change in body size of 50% might be expected to matter for them both. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/04%3A_Fitting_Brownian_Motion/4.01%3A_Introduction.txt |
The information required to estimate evolutionary rates is efficiently summarized in the early (but still useful) phylogenetic comparative method of independent contrasts (Felsenstein 1985). Independent contrasts summarize the amount of character change across each node in the tree, and can be used to estimate the rate of character change across a phylogeny. There is also a simple mathematical relationship between contrasts and maximum-likelihood rate estimates that I will discuss below.
We can understand the basic idea behind independent contrasts if we think about the branches in the phylogenetic tree as the historical “pathways” of evolution. Each branch on the tree represents a lineage that was alive at some time in the history of the Earth, and during that time experienced some amount of evolutionary change. We can imagine trying to measure that change initially by comparing sister taxa. We can compare the trait values of the two sister taxa by finding the difference in their trait values, and then compare that to the total amount of time they have had to evolve that difference. By doing this for all sister taxa in the tree, we will get an estimate of the average rate of character evolution ( 4.1A). But what about deeper nodes in the tree? We could use other non-sister species pairs, but then we would be counting some branches in the tree of life more than once (Figure 4.1B). Instead, we use a “pruning algorithm,” (Felsenstein 1985, Felsenstein (2004)) chopping off pairs of sister taxa to create a smaller tree (Figure 4.1C). Eventually, all of the nodes in the tree will be trimmed off – and the algorithm will finish. Independent contrasts provides a way to generalize the approach of comparing sister taxa so that we can quantify the rate of evolution throughout the whole tree.
A more precise algorithm describing how Phylogenetic Independent Contrasts (PICs) are calculated is provided in Box 4.2, below (from Felsenstein 1985). Each contrast can be described as an estimate of the direction and amount of evolutionary change across the nodes in the tree. PICs are calculated from the tips of the tree towards the root, as differences between trait values at the tips of the tree and/or calculated average values at internal nodes. The differences themselves are sometimes called “raw contrasts” (Felsenstein 1985). These raw contrasts will all be statistically independent of each other under a wide range of evolutionary models. In fact, as long as each lineage in a phylogenetic tree evolves independently of every other lineage, regardless of the evolutionary model, the raw contrasts will be independent of each other. However, people almost never use raw contrasts because they are not identically distributed; each raw contrast has a different expected distribution that depends on the model of evolution and the branch lengths of the tree. In particular, under Brownian motion we expect more change on longer branches of the tree. Felsenstein (1985) divided the raw contrasts by their expected standard deviation under a Brownian motion model, resulting in standardized contrasts. These standardized contrasts are, under a BM model, both independent and identically distributed, and can be used in a variety of statistical tests. Note that we must assume a Brownian motion model in order to standardize the contrasts; results derived from the contrasts, then, depend on this Brownian motion assumption.
Box 4.2: Algorithm for Phylogenetic Independent Contrasts
One can calculate PICs using the algorithm from Felsenstein (1985). I reproduce this algorithm below. Keep in mind that this is an iterative algorithm – you repeat the five steps below once for each contrast, or n − 1 times over the whole tree (see Figure 4.1C as an example).
1. Find two tips on the phylogeny that are adjacent (say nodes i and j) and have a common ancestor, say node k. Note that the choice of which node is i and which is j is arbitrary. As you will see, we will have to account for this “arbitrary direction” property of PICs in any analyses where we use them to do certian analyses!
2. Compute the raw contrast, the difference between their two tip values:$c_{ij} = x_i − x_j \label{4.1}$
• Under a Brownian motion model, cij has expectation zero and variance proportional to vi + vj.
1. Calculate the standardized contrast by dividing the raw contrast by its variance $s_{ij} = \frac{c_{ij}}{v_i + v_j} = \frac{x_i - x_j}{v_i + v_j} \label{4.2}\[ • Under a Brownian motion model, this contrast follows a normal distribution with mean zero and variance equal to the Brownian motion rate parameter σ2. 1. Remove the two tips from the tree, leaving behind only the ancestor k, which now becomes a tip. Assign it the character value: \[ x_k = \frac{(1/v_i)x_i+(1/v_j)x_j}{1/v_1+1/v_j} \label{4.3}\[ • It is worth noting that xk is a weighted average of xi and xj, but does not represent an ancestral state reconstruction, since the value is only influenced by species that descend directly from that node and not other relatives. 2. Lengthen the branch below node k by increasing its length from vk to vk + vivj/(vi + vj). This accounts for the uncertainty in assigning a value to xk. As mentioned above, we can apply the algorithm of independent contrasts to learn something about rates of body size evolution in mammals. We have a phylogenetic tree with branch lengths as well as body mass estimates for 49 species (Figure 4.2). If we ln-transform mass and then apply the method above to our data on mammal body size, we obtain a set of 48 standardized contrasts. A histogram of these contrasts is shown as Figure 4.2 (data from from Garland 1992). Figure 4.2. Histogram of PICs for ln-transformed mammal body mass on a phylogenetic tree with branch lengths in millions of years (data from Garland 1992). Image by the author, can be reused under a CC-BY-4.0 license. Note that each contrast is an amount of change, xi − xj, divided by a branch length, vi + vj, which is a measure of time. Thus, PICs from a single trait can be used to estimate σ2, the rate of evolution under a Brownian model. The PIC estimate of the evolutionary rate is: \[ \hat{\sigma}_{PIC}^2 = \frac{\sum{s_{ij}^2}}{n-1} \label{4.4}$
That is, the PIC estimate of the evolutionary rate is the average of the n − 1 squared contrasts. This sum is taken over all sij, the standardized independent contrast across all (i, j) pairs of sister branches in the phylogenetic tree. For a fully bifurcating tree with n tips, there are exactly n − 1 such pairs. If you are statistically savvy, you might note that this formula looks a bit like a variance. In fact, if we state that the contrasts have a mean of 0 (which they must because Brownian motion has no overall trends), then this is a formula to estimate the variance of the contrasts.
If we calculate the mean sum of squared contrasts for the mammal body mass data, we obtain a rate estimate of $\hat{\sigma}_{PIC}^2$ = 0.09. We can put this into words: if we simulated mammalian body mass evolution under this model, we would expect the variance across replicated runs to increase by 0.09 per million years. Or, in more concrete terms, if we think about two lineages diverging from one another for a million years, we can draw changes in ln-body mass for both of them from a normal distribution with a variance of 0.09. Their difference, then, which is the amount of expected divergence, will be normal with a variance of 2 ⋅ 0.09 = 0.18. Thus, with 95% confidence, we can expect the two species to differ maximally by two standard deviations of this distribution, $2 \cdot \sqrt{0.18} = 0.85$. Since we are on a log scale, this amount of change corresponds to a factor of e2.68 = 2.3, meaning that one species will commonly be about twice as large (or small) as the other after just one million years. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/04%3A_Fitting_Brownian_Motion/4.02%3A_Estimating_Rates_using_Independent_Contrasts.txt |
We can also estimate the evolutionary rate by finding the maximum-likelihood parameter values for a Brownian motion model fit to our data. Recall that ML parameter values are those that maximize the likelihood of the data given our model (see Chapter 2).
We already know that under a Brownian motion model, tip character states are drawn from a multivariate normal distribution with a variance-covariance matrix, C, that is calculated based on the branch lengths and topology of the phylogenetic tree (see Chapter 3). We can calculate the likelihood of obtaining the data under our Brownian motion model using a standard formula for the likelihood of drawing from a multivariate normal distribution:
$L(\mathbf{x} | \bar{z}(0), \sigma^2, \mathbf{C}) = \frac {e^{-1/2 (\mathbf{x}-\bar{z}(0) \mathbf{1})^\intercal (\sigma^2 \mathbf{C})^{-1} (\mathbf{x}-\bar{z}(0) \mathbf{1})}} {\sqrt{(2 \pi)^n det(\sigma^2 \mathbf{C})}} \label{4.5}$
Here, our model parameters are σ2 and $\bar{z}(0)$, the root trait value. x is an n × 1 vector of trait values for the n tip species in the tree, with species in the same order as C, and 1 is an n × 1 column vector of ones. Note that (σ2C)−1 is the matrix inverse of the matrix σ2C
As an example, with the mammal data, we can calculate the likelihood for a model with parameter values σ2 = 1 and $\bar{z}(0) = 0$. We need to work with ln-likelihoods (lnL), both because the value here is so small and to facilitate future calculations, so:
$lnL(\mathbf{x} | \bar{z}(0), \sigma^2, \mathbf{C}) = -116.2.$
To find the ML estimates of our model parameters, we need to find the parameter values that maximize that function. One (not very efficient) way to do this is to calculate the likelihood across a wide range of parameter values. One can then visualize the resulting likelihood surface and identify the maximum of the likelihood function. For example, the likelihood surface for the mammal body size data given a Brownian motion model is shown in Figure 4.3. Note that this surface has a peak around σ2 = 0.09 and $\bar{z}(0) = 4$. Inspecting the matrix of ML values, we find the highest ln-likelihood (-78.05) at σ2 = 0.089 and $\bar{z}(0) = 4.65$.
The calculation described above is inefficient, because we have to calculate likelihoods at a wide range of parameter values that are far from the optimum. A better strategy involves the use of optimization algorithms, a well-developed field of mathematical analysis (Nocedal and Wright 2006). These algorithms differ in their details, but we can illustrate how they work with a general example. Imagine that you are near Mt. St. Helens, and you are tasked with finding the peak of that mountain. It is foggy, but you can see the area around your feet and have an accurate altimeter. One strategy is to simply look at the slope of the mountain where you are standing, and climb uphill. If the slope is steep, you probably still are far from the top, and should climb fast; if the slope is shallow, you might be near the top of the mountain. It may seem obvious that this will get you to a local peak, but perhaps not the highest peak of Mt. St. Helens. Mathematical optimization schemes have this potential difficulty as well, but use some tricks to jump around in parameter space and try to find the overall highest peak as they climb. Details of actual optimization algorithms are beyond the scope of this book; for more information, see Nocedal and Wright (2006).
One simple example is based on Newton’s method of optimization [as implemented, for example, by the r function nlm()]. We can use this algorithm to quickly find accurate ML estimates2.
Using optimization algorithms we find a ML solution at $\hat{\sigma}_{ML}^2 = 0.08804487$ and $\hat{\bar{z}}(0) = 4.640571$, with lnL = −78.04942. Importantly, the solution can be found with only 10 likelihood calculations; this is the value of good optimization algorithms. I have plotted the path through parameter space taken by Newton’s method when searching for the optimum in Figure 4.4. Notice two things: first, that the function starts at some point and heads uphill on the likelihood surface until an optimum is found; and second, that this calculation requires many fewer steps (and much less time) than calculating the likelihood for a wide range of parameter values.
Using an optimization algorithm also has the added benefit of providing (approximate) confidence intervals for parameter values based on the Hessian of the likelihood surface. This approach assumes that the shape of the likelihood surface in the immediate vicinity of the peak can be approximated by a quadratic function, and uses the curvature of that function, as determined by the Hessian, to approximate the standard errors of parameter values (Burnham and Anderson 2003). If the surface is strongly peaked, the SEs will be small, while if the surface is very broad, the SEs will be large. For example, the likelihood surface around the ML values for mammal body size evolution has a Hessian of:
$H = \begin{bmatrix} -314.6 & -0.0026\ -0.0026 & -0.99 \ \end{bmatrix} \label{4.6}$
This gives standard errors of 0.13 (for $\hat{\sigma}_{ML}^2$) and 0.72 [for $\hat{\bar{z}}(0)$]. If we assume the error around these estimates is approximately normal, we can create confidence estimates by adding and subtracting twice the standard error. We then obtain 95% CIs of 0.06 − 0.11 (for $\hat{\sigma}_{ML}^2$) and 3.22 − 6.06 [for $\hat{\bar{z}}(0)$].
The danger in optimization algorithms is that one can sometimes get stuck on local peaks. More elaborate algorithms repeated for multiple starting points can help solve this problem, but are not needed for simple Brownian motion on a tree as considered here. Numerical optimization is a difficult problem in phylogenetic comparative methods, especially for software developers.
In the particular case of fitting Brownian motion to trees, it turns out that even our fast algorithm for optimization was unnecessary. In this case, the maximum-likelihood estimate for each of these two parameters can be calculated analytically (O’Meara et al. 2006).
$\hat{\bar{z}}(0) = (\mathbf{1}^\intercal \mathbf{C}^{-1} \mathbf{1})^{-1} (\mathbf{1}^\intercal \mathbf{C}^{-1} \mathbf{x}) \label{4.7}$
and:
$\hat{\sigma}_{ML}^2 = \frac {(\mathbf{x} - \hat{\bar{z}}(0) \mathbf{1})^\intercal \mathbf{C}^{-1} (\mathbf{x} - \hat{\bar{z}}(0) \mathbf{1})} {n} \label{4.8}$
where n is the number of taxa in the tree, C is the n × n variance-covariance matrix under Brownian motion for tip characters given the phylogenetic tree, x is an n × 1 vector of trait values for tip species in the tree, 1 is an n × 1 column vector of ones, $\hat{\bar{z}}(0)$ is the estimated root state for the character, and $\hat{\sigma}_{ML}^2$ is the estimated net rate of evolution.
Applying this approach to mammal body size, we obtain estimates that are exactly the same as our results from numeric optimization: $\hat{\sigma}_{ML}^2 = 0.088$ and $\hat{\bar{z}}(0) = 4.64$.
Equation (4.8) is biased, and will consistently estimate rates of evolution that are a little too small; an unbiased version based on restricted maximum likelihood (REML) and used by Garland (1992) and others is:
$\hat{\sigma}_{REML}^2 = \frac {(\mathbf{x} - \hat{\bar{z}}(0) \mathbf{1})^\intercal \mathbf{C}^{-1} (\mathbf{x} - \hat{\bar{z}}(0) \mathbf{1})}{n-1} \label{4.9}$
This correction changes our estimate of the rate of body size in mammals from $\hat{\sigma}_{ML}^2 = 0.088$ to $\hat{\sigma}_{REML}^2 = 0.090$. Equation \ref{4.8} is exactly identical to the estimated rate of evolution calculated using the average squared independent contrast, described above; that is, $\hat{\sigma}_{PIC}^2 = \hat{\sigma}_{REML}^2$. In fact, PICs are a formulation of a REML model. The “restricted” part of REML refers to the fact that these methods calculate likelihoods based on a transformed set of data where the effect of nuisance parameters has been removed. In this case, the nuisance parameter is the estimated root state $\hat{\bar{z}}(0)$ 3.
For the mammal body size example, we can further explore the difference between REML and ML in terms of statistical confidence intervals using likelihoods based on the contrasts. We assume, again, that the contrasts are all drawn from a normal distribution with mean 0 and unknown variance. If we again use Newton’s method for optimization, we find a maximum REML log-likelihood of -10.3 at $\hat{\sigma}_{REML}^2 = 0.090$. This returns a 1 × 1 matrix for the Hessian with a value of 2957.8, corresponding to a SE of 0.018. This slightly larger SE corresponds to 95% CI for $\hat{\sigma}_{REML}^2$ of 0.05 − 0.13.
In the context of comparative methods, REML has two main advantages. First, PICs treat the root state of the tree as a nuisance parameter. We typically have very little information about this root state, so that can be an advantage of the REML approach. Second, PICs are easy to calculate for very large phylogenetic trees because they do not require the construction (or inversion!) of any large variance-covariance matrices. This is important for big phylogenetic trees. Imagine that we had a phylogenetic tree of all vertebrates (~60,000 species) and wanted to calculate the rate of body size evolution. To use standard maximum likelihood, we have to calculate C, a matrix with 60, 000 × 60, 000 = 3.6 billion entries, and invert it to calculate C−1. To calculate PICs, by contrast, we only have to carry out on the order of 120,000 operations. Thankfully, there are now pruning algorithms to quickly calculate likelihoods for large trees under a variety of different models (see, e.g., FitzJohn 2012; Freckleton 2012; and Ho and Ané 2014). | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/04%3A_Fitting_Brownian_Motion/4.03%3A_Estimating_rates_using_maximum_likelihood.txt |
Finally, we can also use a Bayesian approach to fit Brownian motion models to data and to estimate the rate of evolution. This approach differs from the ML approach in that we will use explicit priors for parameter values, and then run an MCMC to estimate posterior distributions of parameter estimates. To do this, we will modify the basic algorithm for Bayesian MCMC (see Chapter 2) as follows:
1. Sample a set of starting parameter values, σ2 and $\bar{z}(0)$ from their prior distributions. For this example, we can set our prior distribution as uniform between 0 and 0.5 for σ2 and uniform from 0 to 10 for $\bar{z}(0)$.
2. Given the current parameter values, select new proposed parameter values using the proposal density Q(p′|p). For both parameter values, we will use a uniform proposal density with width wp, so that: (eq. 4.10)
$Q(p'|p) \sim U(p-\frac{w_p}{2}, p+\frac{w_p}{2})$
3. Calculate three ratios:
• The prior odds ratio, Rprior. This is the ratio of the probability of drawing the parameter values p and p’ from the prior. Since our priors are uniform, this is always 1.
• The proposal density ratio, Rproposal. This is the ratio of probability of proposals going from p to p’ and the reverse. We have already declared a symmetrical proposal density, so that Q(p′|p)=Q(p|p′) and Rproposal = 1.
• The likelihood ratio, Rlikelihood. This is the ratio of probabilities of the data given the two different parameter values. We can calculate these probabilities from equation 4.5 above. (eq. 4.11)
$R_{likelihood} = \frac{L(p'|D)}{L(p|D)} = \frac{P(D|p')}{P(D|p)}$
4. Find the acceptance ratio, Raccept, which is product of the prior odds, proposal density ratio, and the likelihood ratio. In this case, both the prior odds and proposal density ratios are 1, so Raccept = Rlikelihood.
5. Draw a random number x from a uniform distribution between 0 and 1. If x < Raccept, accept the proposed value of both parameters; otherwise reject, and retain the current value of the two parameters.
6. Repeat steps 2-5 a large number of times.
Using the mammal body size data, I ran an MCMC with 10,000 generations, discarding the first 1000 as burn-in. Sampling every 10 generations, I obtain parameter estimates of $\hat{\sigma}_{bayes}^2 = 0.10$ (95% credible interval: 0.066 − 0.15) and $\hat{\bar{z}}(0) = 3.5$ (95% credible interval: 2.3 − 5.3; Figure 4.5).
Note that the parameter estimates from all three approaches (REML, ML, and Bayesian) were similar. Even the confidence/credible intervals varied a little bit but were of about the same size in all three cases. All of the approaches above are mathematically related and should, in general, return similar results. One might place higher value on the Bayesian credible intervals over confidence intervals from the Hessian of the likelihood surface, for two reasons: first, the Hessian leads to an estimate of the CI under certain conditions that may or may not be true for your analysis; and second, Bayesian credible intervals reflect overall uncertainty better than ML confidence intervals (see chapter 2).
4.05: Summary
By fitting a Brownian motion model to phylogenetic comparative data, one can estimate the rate of evolution of a single character. In this chapter, I demonstrated three approaches to estimating that rate: PICs, maximum likelihood, and Bayesian MCMC. In the next chapter, we will discuss other models of evolution that can be fit to continuous characters on trees.
Footnotes
1: Throughout this chapter, when I say "rate" I will mean the Brownian motion parameter σ2. This is a little different from “traditional” estimates of evolutionary rate, like those estimated by paleontologists. For example, one might have measurements of trait in a series of fossils representing an evolutionary lineage sampled at different time periods. By calculating the amount of change over a given time interval, one can estimate an evolutionary rate. These rates can be expressed as Darwins (defined as the log-difference in trait values divided by time in years) or Haldanes (defined as the difference in trait values scaled by their standard deviations divided by time in generations). Both types of rates have been calculated from both fossil data and contemporary time-series data on evolution from both islands and lab experiments. Such rates best capture evolutionary trends, where the mean value of a trait is changing in a consistent way through time (for more information see review in Harmon 2014). Rates estimated by Brownian motion are a different type of “rate”, and some care must be taken to compare the two (see, e.g., Gingerich 1983).
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2: Note that there are more complicated optimization algorithms that are useful for more difficult problems in comparative methods. In the case presented here, where the surface is smooth and has a single peak, almost any algorithm will work.
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3:PICs are a transformation of the original data in which all information about the root state has been removed; our idea of what that root state might be has no effect on calculations using PICs. One can calculate the likelihood for the PIC REML method by assuming all of the standardized PICs are drawn from a normal distribution (eq. 4.5) with mean 0 and variance $\hat{\sigma}_{REML}^2$ (eq. 4.8). Alternatively, one can estimate the variance of the PICs directly, keeping in mind that one must use a mean of zero (eq. 4.4). These two methods give exactly the same results.
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References
Burnham, K. P., and D. R. Anderson. 2003. Model selection and multimodel inference: A practical information theoretic approach. Springer Science & Business Media.
Felsenstein, J. 2004. Inferring phylogenies. Sinauer Associates, Inc., Sunderland, MA.
Felsenstein, J. 1985. Phylogenies and the comparative method. Am. Nat. 125:1–15.
FitzJohn, R. G. 2012. Diversitree: Comparative phylogenetic analyses of diversification in R. Methods Ecol. Evol. 3:1084–1092.
Freckleton, R. P. 2012. Fast likelihood calculations for comparative analyses. Methods Ecol. Evol. 3:940–947.
Garland, T., Jr. 1992. Rate tests for phenotypic evolution using phylogenetically independent contrasts. Am. Nat. 140:509–519.
Gingerich, P. D. 1983. Rates of evolution: Effects of time and temporal scaling. Science 222:159–161.
Harmon, L. J. 2014. Macroevolutionary rates. in The Princeton guide to evolution. Princeton University Press.
Hill, J. E. 1974. A new family, genus and species of bat (mammalia, chiroptera) from thailand. British Museum (Natural History).
Ho, L. S. T., and C. Ané. 2014. A linear-time algorithm for Gaussian and non-Gaussian trait evolution models. Syst. Biol. 63:397–408.
Nocedal, J., and S. Wright. 2006. Numerical optimization. Springer Science & Business Media.
O’Meara, B. C., C. Ané, M. J. Sanderson, and P. C. Wainwright. 2006. Testing for different rates of continuous trait evolution using likelihood. Evolution 60:922–933. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/04%3A_Fitting_Brownian_Motion/4.04%3A_Bayesian_approach_to_evolutionary_rates.txt |
In this chapter, we will use the example of home range size, which is the area where an animal carries out its day-to-day activities. We will again use data from Garland (1992) and test for a relationship between body size and the size of a mammal’s home range. I will describe methods for using empirical data to estimate the parameters of multivariate Brownian motion models. I will then describe a model-fitting approach to test for evolutionary correlations. This model fitting approach is simple but not commonly used. Finally, I will review two common statistical approaches to test for evolutionary correlations, phylogenetic independent contrasts and phylogenetic generalized least squares, and describe their relationship to model-fitting approaches.
05: Multivariate Brownian Motion
As discussed in Chapter 4, body size is one of the most important traits of an animal. Body size has a close relationship to almost all of an animal’s ecological interactions, from whether it is a predator or prey to its metabolic rate. If that is true, we should be able to use body size to predict other traits that might be related through shared evolutionary processes. We need to understand how the evolution of body size is correlated with other species’ characteristics.
A wide variety of hypotheses can be framed as tests of correlations between continuously varying traits across species. For example, is the body size of a species related to its metabolic rate? How does the head length of a species relate to overall size, and do deviations from this relationship relate to an animal’s diet? These questions and others like them are of interest to evolutionary biologists because they allow us to test hypotheses about the factors in influencing character evolution over long time scales. These types of approaches allow us to answer some of the classic “why” questions in biology. Why are elephants so large? Why do some species of crocodilians have longer heads than others? If we find a correlation between two characters, we might suspect that there is a causal relationship between our two variables of interest - or perhaps that both of our measured variables share a common cause.
In this chapter, we will use the example of home range size, which is the area where an animal carries out its day-to-day activities. We will again use data from Garland (1992) and test for a relationship between body size and the size of a mammal’s home range. I will describe methods for using empirical data to estimate the parameters of multivariate Brownian motion models. I will then describe a model-fitting approach to test for evolutionary correlations. This model fitting approach is simple but not commonly used. Finally, I will review two common statistical approaches to test for evolutionary correlations, phylogenetic independent contrasts and phylogenetic generalized least squares, and describe their relationship to model-fitting approaches.
5.02: What is evolutionary correlation?
There is sometimes a bit of confusion among beginners as to what, exactly, we are doing when we carry out a comparative method, especially when testing for character correlations. Common language that comparative methods “control for phylogeny” or “remove the phylogeny from the data” is not necessarily enlightening or even always accurate. Another common suggestion is that species are not statistically independent and that we must account for that with comparative methods. While accurate, I still don’t think this statement fully captures the tree-thinking perspective enabled by comparative methods. In this section, I will use the particular example of correlated evolution to try to illustrate the power of comparative methods and how they differ from standard statistical approaches that do not use phylogenies.
In statistics, two variables can be correlated with one another. We might refer to this as a standard correlation. When two traits are correlated, it means that given the value of one trait – say, body size in mammals – one can predict the value of another – like home range area. Correlations can be positive (large values of x are associated with large values of y) or negative (large values of x are associated with small values of y). A surprisingly wide variety of hypotheses in biology can be tested by evaluating correlations between characters.
In comparative biology, we are often interested more specifically in evolutionary correlations. Evolutionary correlations occur when two traits tend to evolve together due to processes like mutation, genetic drift, or natural selection. If there is an evolutionary correlation between two characters, it means that we can predict the magnitude and direction of changes in one character given knowledge of evolutionary changes in another. Just like standard correlations, evolutionary correlations can be positive (increases in trait x are associated with increases in y) or negative (decreases in x are associated with increases in y).
We can now contrast standard correlations, testing the relationships between trait values across a set of species, with evolutionary correlations - where evolutionary changes in two traits are related to each other. This is a key distinction, because phylogenetic relatedness alone can lead to a relationship between two variables that are not, in fact, evolving together (Figure 5.1; also see Felsenstein 1985). In such cases, standard correlations will, correctly, tell us that one can predict the value of trait y by knowing the value of trait x, at least among extant species; but we would be misled if we tried to make any evolutionary causal inference from this pattern. In the example of Figure 5.1, we can only predict x from y because the value of trait x tells us which clade the species belongs to, which, in turn, allows reasonable prediction of y. In fact, this is a classical example of a case where correlation is not causation: the two variables are only correlated with one another because both are related to phylogeny.
If we want to test hypotheses about trait evolution, we should specifically test evolutionary correlations1. If we find a relationship among the independent contrasts for two characters, for example, then we can infer that changes in each character are related to changes in the other – an inference that is much closer to most biological hypotheses about why characters might be related. In this case, then, we can think of statistical comparative methods as focused on disentangling patterns due to phylogenetic relatedness from patterns due to traits evolving in a correlated manner. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/05%3A_Multivariate_Brownian_Motion/5.01%3A_Introduction_to_Multivariate_Brownian_Motion.txt |
We can model the evolution of multiple (potentially correlated) continuous characters using a multivariate Brownian motion model. This model is similar to univariate Brownian motion (see chapter 3), but can model the evolution of many characters at the same time. As with univariate Brownian motion, trait values change randomly in both direction and distance over any time interval. Here, though, these changes are drawn from multivariate normal distributions2. Multivariate Brownian motion can encompass the situation where each character evolves independently of one another, but can also describe situations where characters evolve in a correlated way.
We can describe multivariate Brownian motion with a set of parameters that are described by a, a vector of phylogenetic means for a set of r characters:
(eq. 5.1)
$\mathbf{a} = \begin{bmatrix} \bar{z}_1 (0) & \bar{z}_2 (0) & \dots & \bar{z}_r (0)\ \end{bmatrix}$
This vector represents the starting point in r-dimensional space for our random walk. In the context of comparative methods, this is the character measurements for the lineage at the root of the tree. Additionally, we have an evolutionary rate matrix R:
(eq. 5.2)
$\mathbf{R} = \begin{bmatrix} \sigma_1^2 & \sigma_{21} & \dots & \sigma_{n1}\ \sigma_{21} & \sigma_2^2 & \dots & \vdots\ \vdots & \vdots & \ddots & \vdots\ \sigma_{1n} & \dots & \dots & \sigma_{rn}^2\ \end{bmatrix}$
Here, the rate parameter for each axis (σi2) is along the matrix diagonal. Off-diagonal elements represent evolutionary covariances between pairs of axes (note that σij = σji). It is worth noting that each individual character evolves under a Brownian motion process. Covariances among characters, though, potentially make this model distinct from one where each character evolves independently of all the others (Figure 5.2).
When you have data for multiple continuous characters across many species along with a phylogenetic tree, you can fit a multivariate Brownian motion model to the data, as discussed in Chapter 3.
To calculate the likelihood, we can use the fact that, under our multivariate Brownian motion model, the joint distribution of all traits across all species has a multivariate normal distribution. Following Chapter 3, we find the variance-covariance matrix that describes that model by combining the two matrices R and C into a single large matrix using the Kroeneker product:
(eq. 5.3)
V = R ⊗ C
This matrix V is nr × nr. We can then substitute V for C in equation (4.5) to calculate the likelihood:
(eq. 5.4)
$L(\mathbf{x}_{nr} | \mathbf{a}, \mathbf{R}, \mathbf{C}) = \frac {e^{-1/2 (\mathbf{x}_{nr}- \mathbf{D} \cdot \mathbf{a})^\intercal (\mathbf{V})^{-1} (\mathbf{x}_nr-\mathbf{D} \cdot \mathbf{a})}} {\sqrt{(2 \pi)^{nm} det(\mathbf{V})}}$
Here D is an nr × r design matrix where each element Dij is 1 if (j − 1)⋅n < i ≤ j ⋅ n and 0 otherwise. xnr is a single vector with all trait values for all species, listed so that the first n elements in the vector are trait 1, the next n are for trait 2, and so on:
(eq. 5.5)
$\mathbf{x}_{nr} = \begin{bmatrix} x_{11} & x_{12} & \dots & x_{1n} & x_{21} & \dots & x_{nr}\ \end{bmatrix}$
We can find the value of the likelihood at its maximum by calculating L(xnr|a, R, C) using eq. 5.4 and an optimization routine to find the MLE.
Alternatively, one can calculate this MLE solution directly. Equations for estimating $\hat{\mathbf{a}}$ (the estimated vector of phylogenetic means for all characters) and $\hat{\mathbf{R}}$ (the estimated evolutionary rate matrix) are (Revell and Harmon 2008, Hohenlohe and Arnold (2008)):
(eq. 5.6)
$\hat{\mathbf{a}} = [(\mathbf{1}^\intercal \mathbf{C}^{-1} \mathbf{1})^{-1}(\mathbf{1}^\intercal \mathbf{C}^{-1} \mathbf{X})]^\intercal$
(eq. 5.7)
$\hat{\mathbf{R}} = \frac{(\mathbf{X} - \mathbf{1} \mathbf{\hat{a}})^\intercal \mathbf{C}^{-1} (\mathbf{X} - \mathbf{1} \mathbf{\hat{a}})}{n}$
Note here that we use X to denote the n (species) × r (traits) matrix of all traits across all species. Note the similarity between these multivariate equations (5.6 and 5.7) and their univariate equivalents (equations 4.6 and 4.7). | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/05%3A_Multivariate_Brownian_Motion/5.03%3A_Modeling_the_evolution_of_correlated_characters.txt |
There are many ways to test for evolutionary correlations between two characters. Traditional methods like PICs and PGLS work great for testing evolutionary regression, which is very similar to testing for evolutionary correlations. However, when using those methods the connection to actual models of character evolution can remain opaque. Thus, I will first present approaches to test for correlated evolution based on model selection using AIC and Bayesian analysis. I will then return to “standard” methods for evolutionary regression at the end of the chapter.
Section 5.4a: Testing for character correlations using maximum likelihood and AIC
To test for an evolutionary correlation between two characters, we are really interested in the elements in the matrix R. For two characters, x and y, R can be written as:
(eq. 5.8)
$\mathbf{R} = \begin{bmatrix} \sigma_x^2 & \sigma_{xy} \ \sigma_{xy} & \sigma_y^2 \ \end{bmatrix}$
We are interested in the parameter σxy - the evolutionary covariance - and whether it is equal to zero (no correlation) or not. One simple way to test this hypothesis is to set up two competing hypotheses and compare them to each other. One hypothesis (H1) is that the traits evolve independently of each other, and another (H2) that the traits evolve with some covariance σxy. We can write these two rate matrices as:
(eq. 5.9)
$\begin{array}{lcr} \mathbf{R}_{H_1} = \begin{bmatrix} \sigma_x^2 & 0 \ 0 & \sigma_y^2 \ \end{bmatrix} & \mathbf{R}_{H_2} = \begin{bmatrix} \sigma_x^2 & \sigma_{xy} \ \sigma_{xy} & \sigma_y^2 \ \end{bmatrix}\ \end{array}$
We can calculate an ML estimate of the parameters in RH2 using equation 5.4. The maximum likelihood estimate of RH1 can be obtained by noting that, if character evolution is independent across all characters, then both σx2 and σy2 can be obtained by treating each character separately and using equations from chapter 3 to solve for each. It turns out that the ML estimates for σx2 and σy2 are always exactly the same for H1 and H2.
To compare these two models, we calculate the likelihood of each using equation 5.4. We can then compare these two likelihoods using either a likelihood ratio test or by comparing AICc scores (see chapter 2).
For the mammal example, we can consider the two traits of (ln-transformed) body size and home range size (Garland 1992). These two characters have a positive correlation using standard regression analysis (r = 0.27), and a linear regression is significant (P = 0.0001; Figure 5.3). If we fit a multivariate Brownian motion model to these data, considering home range as trait 1 and body mass as trait 2, we obtain the following parameter estimates:
(eq. 5.10)
$\begin{array}{cc} \hat{\mathbf{a}}_{H_2} = \begin{bmatrix} 2.54 \ 4.64 \ \end{bmatrix} & \hat{\mathbf{R}}_{H_2} = \begin{bmatrix} 0.24 & 0.10 \ 0.10 & 0.09 \ \end{bmatrix}\ \end{array}$
Note the positive off-diagonal element in the estimated R matrix, suggesting a positive evolutionary correlation between these two traits. This model corresponds to hypothesis 2 above, and has a log-likelihood of lnL = −164.0. If we fit a model with no correlation between the two traits, we obtain:
(eq. 5.11)
$\begin{array}{cc} \hat{\mathbf{a}}_{H_1} = \begin{bmatrix} 2.54 \ 4.64 \ \end{bmatrix} & \hat{\mathbf{R}}_{H_1} = \begin{bmatrix} 0.24 & 0 \ 0 & 0.09 \ \end{bmatrix}\ \end{array}$
It is worth noting again that only the estimates of the evolutionary correlation were affected by this model restriction; all other parameter estimates remain the same. This model has a smaller (more negative) log-likelihood of lnL = −180.5.
A likelihood ratio test gives Δ = 33.0, and P < <0.001, rejecting the null hypothesis. The difference in AICc scores is 30.9, and the Akaike weight for model 2 is effectively 1.0. All ways of comparing these two models give strong support for hypothesis 2. We can conclude that there is an evolutionary correlation between body mass and home range size in mammals. What this means in evolutionary terms is that, across mammals, evolutionary changes in body mass tend to positively covary with changes in home range.
Section 5.4b: Testing for character correlations using Bayesian model selection
We can also implement a Bayesian approach to testing for the correlated evolution of two characters. The simplest way to do this is just to use the standard algorithm for Bayesian MCMC to fit a correlated model to the two characters. We can modify the algorithm presented in chapter 2 as follows:
1. Sample a set of starting parameter values σx2, σy2, σxy, $\bar{z}_1(0)$, and $\bar{z}_2 (0)$ from prior distributions. For this example, we can set our prior distribution as uniform between 0 and 1 for σx2 and σy2, uniform from -1 to +1 for σxy, uniform from 1 to 9 for $\bar{z}_1(0)$ (lnMass), and -3 to 5 for $\bar{z}_1(0)$ (lnHomerange).
2. Given the current parameter values, select new proposed parameter values using the proposal density Q(p′|p). Here, for all five parameter values, we will use a uniform proposal density with width 0.2, so that Q(p′|p)∼U(p − 0.1, p + 0.1).
3. Calculate three ratios:
• The prior odds ratio, Rprior. This is the ratio of the probability of drawing the parameter values p and p’ from the prior. Since our priors are uniform, Rprior = 1.
• The proposal density ratio, Rproposal. This is the ratio of probability of proposals going from p to p’ and the reverse. Our proposal density is symmetrical, so that Q(p′|p)=Q(p|p′) and Rproposal = 1.
• The likelihood ratio, Rlikelihood. This is the ratio of probabilities of the data given the two different parameter values. We can calculate these probabilities from equation 5.6 above (eq. 5.12).
$R_{likelihood} = \frac{L(p'|D)}{L(p|D)} = \frac{P(D|p')}{P(D|p)} \[ 1. Find Raccept, the product of the prior odds, proposal density ratio, and the likelihood ratio. In this case, both the prior odds and proposal density ratios are 1, so Raccept = Rlikelihood. 2. Draw a random number x from a uniform distribution between 0 and 1. If x < Raccept, accept the proposed value of all parameters; otherwise reject, and retain the current parameter values. 3. Repeat steps 2-5 a large number of times. We can then inspect the posterior distribution for the parameter is significantly greater than (or less than) zero. As an example, I ran this MCMC for 100,000 generations, discarding the first 10,000 generations as burn-in. I then sampled the posterior distribution every 100 generations, and obtained the following parameter estimates: \hat{\sigma}_x^2 = 0.26 [95% credible interval (CI): 0.18 - 0.38], \hat{\sigma}_y^2 = 0.10 (95% CI: 0.06 -0.15), and \hat{\sigma}_{xy} = 0.11 (95% CI: 0.06 - 0.17; see Figure 5.4). These results are comparable to our ML estimates. Furthermore, the 95% CI for σxy does not overlap with 0; in fact, none of the 901 posterior samples of σxy are less than zero. Again, we can conclude with confidence that there is an evolutionary correlation between these two characters. Section 5.5c: Testing for character correlations using traditional approaches (PIC, PGLS) The approach outlined above, which tests for an evolutionary correlation among characters using model selection, is not typically applied in the comparative biology literature. Instead, most tests of character correlation rely on phylogenetic regression using one of two methods: phylogenetic independent contrasts (PICs) and phylogenetic general least squares (PGLS). PGLS is actually mathematically identical to PICs in the simple case described here, and more flexible than PICs for other models and types of characters. Here I will review both PICs and PGLS and explain how they work and how they relate to the models described above. Phylogenetic independent contrasts can be used to carry out a regression test for the relationship between two different characters. To do this, one calculates standardized PICs for trait x and trait y. One then uses standard linear regression forced through the origin to test for a relationship between these two sets of PICs. It is necessary to force the regression through the origin because the direction of subtraction of contrasts across any node in the tree is arbitrary; a reflection of all of the contrasts across both axes simultaneously should have no effect on the analyses3. For mammal homerange and body mass, a PIC regression test shows a significant correlation between the two traits (P < <0.0001; Figure 5.5). There is one drawback to PIC regression analysis, though – one does not recover an estimate of the intercept of the regression of y on x – that is, the value of y one would expect when x = 0. The easiest way to get this parameter estimate is to instead use Phylogenetic Generalized Least Squares (PGLS). PGLS uses the common statistical machinery of generalized least squares, and applies it to phylogenetic comparative data. In normal generalized least squares, one constructs a model of the relationship between y and x, as: (eq. 5.13) y = XDb + ϵ Here, y is an n × 1 vector of trait values and b is a vector of unknown regression coefficients that must be estimated from the data. XD is a design matrix including the traits that one wishes to test for a correlation with y and – if the model includes an intercept – a column of 1s. To test for correlations, we use: (eq. 5.14) \[ \mathbf{X_D} = \begin{bmatrix} 1 & x_1 \ 1 & x_2 \ \dots & \dots \ 1 & x_n \ \end{bmatrix}$
In the case of one predictor and one response variable, b is 2 × 1 and the resulting model can be used to test correlations between two characters. However, XD could also be multivariate, and can include more than one character that might be related to y. This allows us to carry out the equivalent of multiple regression in a phylogenetic context. Finally, ϵ are the residuals – the difference between the y-values predicted by the model and their actual values. In traditional regression, one assumes that the residuals are all normally distributed with the same variance. By contrast, with GLS, one assumes that the residuals might not be independent of each other; instead, they are multivariate normal with expected mean zero and some variance-covariance matrix Ω.
In the case of Brownian motion, we can model the residuals as having variances and covariances that follow the structure of the phylogenetic tree. In other words, we can substitute our phylogenetic variance-covariance matrix C as the matrix Ω. We can then carry out standard GLS analyses to estimate model parameters:
(eq. 5.15)
$\hat{\mathbf{b}} = (\mathbf{X}_D ^ \intercal \mathbf{\Omega}^{-1} \mathbf{X}_D ^ \intercal)^{-1} \mathbf{X}_D ^ \intercal \mathbf{\Omega}^{-1} \mathbf{y} = (\mathbf{X}_D ^ \intercal \mathbf{C}^{-1} \mathbf{X}_D ^ \intercal)^{-1} \mathbf{X}_D ^ \intercal \mathbf{C}^{-1} \mathbf{y}$
The first term in $\hat{\mathbf{b}}$ is the phylogenetic mean $\bar{z}(0)$. The other term in $\hat{\mathbf{b}}$ will be an estimate for the slope of the relationship between y and x, the calculation of which statistically controls for the effect of phylogenetic relationships.
Applying PGLS to mammal body mass and home range results in an identical estimate of the slope and P-value as we obtain using independent contrasts. PGLS also returns an estimate of the intercept of this relationship, which cannot be obtained from the PICs.
Of course, another difference is that PICs and PGLS use regression, while the approach outlined above tests for a correlation. These two types of statistical tests are different. Correlation tests for a relationship between x and y, while regression tries to find the best way to predict y from x. For correlation, it does not matter which variable we call x and which we call y. However, in regression we will get a different slope if we predict y given x instead of predicting x given y. The model that is assumed by phylogenetic regression models is also different from the model above, where we assumed that the two characters evolve under a correlated Brownian motion model. By contrast, PGLS (and, implicitly, PICs) assume that the deviations of each species from the regression line evolve under a Brownian motion model. We can imagine, for example, that species can freely slide along the regression line, but that evolving around that line can be captured by a normal Brownian model. Another way to think about a PGLS model is that we are treating x as a fixed property of species. The deviation of y from what is predicted by x is what evolves under a Brownian motion model. If this seems strange, that’s because it is! There are other, more complex models for modeling the correlated evolution of two characters that make assumptions that are more evolutionarily realistic (e.g. Hansen 1997); we will return to this topic later in the book. At the same time, PGLS is a well-used method for evolutionary regression, and is undoubtedly useful despite its somewhat strange assumptions.
PGLS analysis, as described above, assumes that we can model the error structure of our linear model as evolving under a Brownian motion model. However, one can change the structure of the error variance-covariance matrix to reflect other models of evolution, such as Ornstein-Uhlenbeck. We return to this topic in a later chapter.
5.05: Multivariate Brownian Motion (Summary)
There are at least four methods for testing for an evolutionary correlation between continuous characters: likelihood ratio test, AIC model selection, PICs, and PGLS. These four methods as presented all make the same assumptions about the data and, therefore, have quite similar statistical properties. For example, if we simulate data under a multivariate Brownian motion model, both PICs and PGLS have appropriate Type I error rates and very similar power. Any of these are good choices for testing for the presence of an evolutionary correlation in your data.
Section 5.7: Footnotes
1: We might also want to carry out linear regression, which is related to correlation analysis but distinct. We will show examples of phylogenetic regression at the end of this chapter.
back to main text
2: Although the joint distribution of all species for a single trait is multivariate normal (see previous chapters), individual changes along a particular branch of a tree are univariate.
back to main text
3: Another way to think about regression through the origin is to think of pairs of contrasts across any node in the tree as two-dimensional vectors. Calculating a vector correlation is equivalent to calculating a regression forced through the origin.
back to main text
References
Felsenstein, J. 1985. Phylogenies and the comparative method. Am. Nat. 125:1–15.
Garland, T., Jr. 1992. Rate tests for phenotypic evolution using phylogenetically independent contrasts. Am. Nat. 140:509–519.
Hansen, T. F. 1997. Stabilizing selection and the comparative analysis of adaptation. Evolution 51:1341–1351.
Hohenlohe, P. A., and S. J. Arnold. 2008. MIPoD: A hypothesis-testing framework for microevolutionary inference from patterns of divergence. Am. Nat. 171:366–385.
Revell, L. J., and L. J. Harmon. 2008. Testing quantitative genetic hypotheses about the evolutionary rate matrix for continuous characters. Evol. Ecol. Res. 10:311–331. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/05%3A_Multivariate_Brownian_Motion/5.04%3A_Testing_for_evolutionary_correlations.txt |
This chapter consider four ways that comparative methods can move beyond simple Brownian motion models: by transforming the variance-covariance matrix describing trait covariation among species, by incorporating variation in rates of evolution, by accounting for evolutionary constraints, and by modeling adaptive radiation and ecological opportunity. It should be apparent that the models listed here do not span the complete range of possibilities, and so my list is not meant to be comprehensive. Instead, I hope that readers will view these as examples, and that future researchers will add to this list and enrich the set of models that we can fit to comparative data.
• 6.1: Introduction to Non-Brownian Motion
Brownian motion is very commonly used in comparative biology: in fact, a large number of comparative methods that researchers use for continuous traits assumes that traits evolve under a Brownian motion model. The scope of other models beyond Brownian motion that we can use to model continuous trait data on trees is somewhat limited. However, more and more methods are being developed that break free of this limitation, moving the field beyond Brownian motion.
• 6.2: Transforming the evolutionary variance-covariance matrix
There are three Pagel tree transformations (lambda: λ, delta: δ, and kappa: κ). I will describe each of them along with common methods for fitting Pagel models under ML, AIC, and Bayesian frameworks. Pagel’s three transformations can also be related to evolutionary processes, although those relationships are sometimes vague compared to approaches based on explicit evolutionary models rather than tree transformations (see below for more comments on this distinction).
• 6.3: Variation in rates of trait evolution across clades
There are several methods that one can use to test for differences in the rate of evolution across clades. First, one can compare the magnitude of independent contrasts across clades; second, one can use model comparison approaches to compare the fit of single- and multiple-rate models to data on trees; and third, one can use a Bayesian approach combined with reversible-jump machinery to try to find the places on the tree where rate shifts have occurred. I will explain each of these methods in t
• 6.4: Non-Brownian evolution under stabilizing selection
We can also consider the case where a trait evolves under the influence of stabilizing selection. Assume that a trait has some optimal value, and that when the population mean differs from the optimum the population will experience selection towards the optimum. As I will show below, when traits evolve under stabilizing selection with a constant optimum, the pattern of traits through time can be described using an Ornstein-Uhlenbeck (OU) model.
• 6.5: Early Burst Models
According to Simpson, species enter new adaptive zones in one of three ways: dispersal to a new area, extinction of competitors, or the evolution of a new trait or set of traits that allow them to interact with the environment in a new way. One idea is that we could detect the presence of adaptive radiations by looking for bursts of trait evolution deep in the tree. If we can identify clades that might be adaptive radiations, we can uncover this “early burst” pattern of trait evolution.
• 6.6: Peak Shift Models
One can imagine a scenario where species evolve on an adaptive landscape with many peaks; usually, populations stay on a single peak and phenotypes do not change, but occasionally a population will transition from one peak to another. We can either assume that these changes occur at random times, defining an average interval between peak shifts, or we can associate shifts with other traits that we map on the phylogenetic tree.
• 6.7: Appendix - Deriving an OU model under stabilizing selection
• 6.S: Beyond Brownian Motion (Summary)
06: Beyond Brownian Motion
Detailed studies of contemporary evolution have revealed a rich variety of processes that influence how traits evolve through time. Consider the famous studies of Darwin’s finches, Geospiza, in the Galapagos islands carried out by Peter and Rosemary Grant, among others (e.g. Grant and Grant 2011). These studies have documented the action of natural selection on traits from one generation to the next. One can see very clearly how changes in climate – especially the amount of rainfall – affect the availability of different types of seeds (Grant and Grant 2002). These changing resources in turn affect which individuals survive within the population. When natural selection acts on traits that can be inherited from parents to offspring, those traits evolve.
One can obtain a dataset of morphological traits, including measurements of body and beak size and shape, along with a phylogenetic tree for several species of Darwin’s finches. Imagine that you have the goal of analyzing the tempo and mode of morphological evolution across these species of finch. We can start by fitting a Brownian motion model to these data. However, a Brownian model (which, as we learned in Chapter 3, corresponds to a few simple scenarios of trait evolution) hardly seems realistic for a group of finches known to be under strong and predictable directional selection.
Brownian motion is very commonly used in comparative biology: in fact, a large number of comparative methods that researchers use for continuous traits assumes that traits evolve under a Brownian motion model. The scope of other models beyond Brownian motion that we can use to model continuous trait data on trees is somewhat limited. However, more and more methods are being developed that break free of this limitation, moving the field beyond Brownian motion. In this chapter I will discuss these approaches and what they can tell us about evolution. I will also describe how moving beyond Brownian motion can point the way forward for statistical comparative methods.
In this chapter, I will consider four ways that comparative methods can move beyond simple Brownian motion models: by transforming the variance-covariance matrix describing trait covariation among species, by incorporating variation in rates of evolution, by accounting for evolutionary constraints, and by modeling adaptive radiation and ecological opportunity. It should be apparent that the models listed here do not span the complete range of possibilities, and so my list is not meant to be comprehensive. Instead, I hope that readers will view these as examples, and that future researchers will add to this list and enrich the set of models that we can fit to comparative data. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/06%3A_Beyond_Brownian_Motion/6.01%3A_Introduction_to_Non-Brownian_Motion.txt |
In 1999, Mark Pagel introduced three statistical models that allow one to test whether data deviates from a constant-rate process evolving on a phylogenetic tree (Pagel 1999a,b)1. Each of these three models is a statistical transformation of the elements of the phylogenetic variance-covariance matrix, C, that we first encountered in Chapter 3. All three can also be thought of as a transformation of the branch lengths of the tree, which adds a more intuitive understanding of the statistical properties of the tree transformations (Figure 6.1). We can transform the tree and then simulate characters under a Brownian motion model on the transformed tree, generating very different patterns than if they had been simulated on the starting tree.
There are three Pagel tree transformations (lambda: λ, delta: δ, and kappa: κ). I will describe each of them along with common methods for fitting Pagel models under ML, AIC, and Bayesian frameworks. Pagel’s three transformations can also be related to evolutionary processes, although those relationships are sometimes vague compared to approaches based on explicit evolutionary models rather than tree transformations (see below for more comments on this distinction).
Perhaps the most commonly used Pagel tree transformation is λ. When using λ, one multiplies all off-diagonal elements in the phylogenetic variance-covariance matrix by the value of λ, restricted to values of 0 ≤ λ ≤ 1. The diagonal elements remain unchanged. So, if the original matrix for r species is:
$\mathbf{C_o} = \begin{bmatrix} \sigma_1^2 & \sigma_{12} & \dots & \sigma_{1r}\ \sigma_{21} & \sigma_2^2 & \dots & \sigma_{2r}\ \vdots & \vdots & \ddots & \vdots\ \sigma_{r1} & \sigma_{r2} & \dots & \sigma_{r}^2\ \end{bmatrix} \label{6.1}$
Then the transformed matrix will be:
$\mathbf{C_\lambda} = \begin{bmatrix} \sigma_1^2 & \lambda \cdot \sigma_{12} & \dots & \lambda \cdot \sigma_{1r}\ \lambda \cdot \sigma_{21} & \sigma_2^2 & \dots & \lambda \cdot \sigma_{2r}\ \vdots & \vdots & \ddots & \vdots\ \lambda \cdot \sigma_{r1} & \lambda \cdot \sigma_{r2} & \dots & \sigma_{r}^2\ \end{bmatrix} \label{6.2}$
In terms of branch length transformations, λ compresses internal branches while leaving the tip branches of the tree unaffected (Figure 6.1). λ can range from 1 (no transformation) to 0 (which results in a complete star phylogeny, with all tip branches equal in length and all internal branches of length 0). One can in principle use some values of λ greater than one on most variance-covariance matrices, although many values of λ > 1 result in matrices that are not valid variance-covariance matrices and/or do not correspond with any phylogenetic tree transformation. For this reason I recommend that λ be limited to values between 0 and 1.
λ is often used to measure the “phylogenetic signal” in comparative data. This makes intuitive sense, as λ scales the tree between a constant-rates model (λ = 1) to one where every species is statistically independent of every other species in the tree (λ = 0). Statistically, this can be very useful information. However, there is some danger is in attributing a statistical result – either phylogenetic signal or not – to any particular biological process. For example, phylogenetic signal is sometimes called a “phylogenetic constraint.” But one way to obtain a high phylogenetic signal (λ near 1) is to evolve traits under a Brownian motion model, which involves completely unconstrained character evolution. Likewise, a lack of phylogenetic signal – which might be called “low phylogenetic constraint” – results from an OU model with a high α parameter (see below), which is a model where trait evolution away from the optimal value is, in fact, highly constrained. Revell et al. (2008) show a broad range of circumstances that can lead to patterns of high or low phylogenetic signal, and caution against over-interpretation of results from analyses of phylogenetic signal, like Pagel’s λ. Also worth noting is that statistical estimates of λ under a ML model tend to be clustered near 0 and 1 regardless of the true value, and AIC model selection can tend to prefer models with λ ≠ 0 even when data is simulated under Brownian motion (Boettiger et al. 2012).
Pagel’s δ is designed to capture variation in rates of evolution through time. Under the δ transformation, all elements of the phylogenetic variance-covariance matrix are raised to the power δ, assumed to be positive. So, if our original C matrix is given above (equation 6.1), then the δ-transformed version will be:
$\mathbf{C_\delta} = \begin{bmatrix} (\sigma_1^2)^\delta & (\sigma_{12})^\delta & \dots & (\sigma_{1r})^\delta\ (\sigma_{21})^\delta & (\sigma_2^2)^\delta & \dots & (\sigma_{2r})^\delta\ \vdots & \vdots & \ddots & \vdots\ (\sigma_{r1})^\delta & (\sigma_{r2})^\delta & \dots & (\sigma_{r}^2)^\delta\ \end{bmatrix} \label{6.3}$
Since these elements represent the heights of nodes in the phylogenetic tree, then δ can also be viewed as a transformation of phylogenetic node heights. When δ is one, the tree is unchanged and one still has a constant-rate Brownian motion process; when δ is less than 1, node heights are reduced, but deeper branches in the tree are reduced less than shallower branches (Figure 6.1). This effectively represents a model where the rate of evolution slows through time. By contrast, δ > 1 stretches the shallower branches in the tree more than the deep branches, mimicking a model where the rate of evolution speeds up through time. There is a close connection between the δ model, the ACDC model (Blomberg et al. 2003), and Harmon et al.’s (2010) early burst model [see also Uyeda and Harmon (2014), especially the appendix).
Finally, the κ transformation is sometimes used to capture patterns of “speciational” change in trees. In the κ model, one raises all of the branch lengths in the tree by the power κ (we require that κ ≥ 0). This has a complicated effect on the phylogenetic variance-covariance matrix, as the effect that this transformation has on each covariance element depends on both the value of κ and the number of branches that extend from the root of the tree to the most recent common ancestor of each pair of species. So, if our original C matrix is given by Equation \ref{6.1}, the transformed version will be:
$\begin{array}{l} \mathbf{C_o} = \ \left(\begin{smallmatrix} b_{1,1}^k + b_{1,2}^k \dots + b_{1,d_1}^k & b_{1-2,1}^k + b_{1-2,2}^k \dots + b_{1-2,d_{1-2}}^k & \dots & b_{1-r,1}^k + b_{1-r,2}^k \dots + b_{1-r,d_{1-r}}^k \ b_{2-1,1}^k + b_{2-1,2}^k \dots + b_{2-1,d_{1-2}}^k & b_{2,1}^k + b_{2,2}^k \dots + b_{2,d_2}^k & \dots & b_{2-r,1}^k + b_{2-r,2}^k \dots + b_{2-r,d_{2-r}}^k \ \vdots & \vdots & \ddots & \vdots\ b_{r-1,1}^k + b_{r-1,2}^k \dots + b_{r-1,d_{1-r}}^k & b_{r-2,1}^k + b_{r-2,2}^k \dots + b_{r-2,d_{1-2}}^k & \dots & b_{r,1}^k + b_{r,2}^k \dots + b_{r,d_{r}}^k \ \end{smallmatrix}\right) \ \end{array} \label{6.4}$
where bx, y is the branch length of the branch that is the most recent common ancestor of taxa x and y, while dx, y is the total number of branches that one encounters traversing the path from the root to the most recent common ancestor of the species pair specified by x, y (or to the tip x if just one taxon is specified). Needless to say, this transformation is easier to understand as a transformation of the tree branches themselves rather than of the associated variance-covariance matrix.
When the κ parameter is one, the tree is unchanged and one still has a constant-rate Brownian motion process; when κ = 0, all branch lengths are one. κ values in between these two extremes represent intermediates (Figure 6.1). κ is often interpreted in terms of a model where character change is more or less concentrated at speciation events. For this interpretation to be valid, we have to assume that the phylogenetic tree, as given, includes all (or even most) of the speciation events in the history of the clade. The problem with this assumption is that speciation events are almost certainly missing due to sampling: perhaps some living species from the clade have not been sampled, or species that are part of the clade have gone extinct before the present day and are thus not sampled. There are much better ways of estimating speciational models that can account for these issues in sampling (e.g. Bokma 2008; Goldberg and Igić 2012); these newer methods should be preferred over Pagel’s κ for testing for a speciational pattern in trait data.
There are two main ways to assess the fit of the three Pagel-style models to data. First, one can use ML to estimate parameters and likelihood ratio tests (or AICc scores) to compare the fit of various models. Each represents a three parameter model: one additional parameter added to the two parameters already needed to describe single-rate Brownian motion. As mentioned above, simulation studies suggest that this can sometimes lead to overconfidence, at least for the λ model. Sometimes researchers will compare the fit of a particular model (e.g. λ) with models where that parameter is fixed at its two extreme values (0 or 1; this is not possible with δ). Second, one can use Bayesian methods to estimate posterior distributions of parameter values, then inspect those distributions to see if they overlap with values of interest (say, 0 or 1).
We can apply these three Pagel models to the mammal body size data discussed in chapter 5, comparing the AICc scores for Brownian motion to that from the three transformations. We obtain the following results:
Model Parameter estimates lnL AICc
Brownian motion σ2 = 0.088, θ = 4.64 -78.0 160.4
lambda σ2 = 0.085, θ = 4.64, λ = 1.0 -78.0 162.6
delta σ2 = 0.063, θ = 4.60, δ = 1.5 -77.7 162.0
kappa σ2 = 0.170, θ = 4.64, κ = 0.66 -77.3 161.1
Note that Brownian motion is the preferred model with the lowest AICc score, but also that all four AICc scores are within 3 units – meaning that we cannot easily distinguish among them using our mammal data. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/06%3A_Beyond_Brownian_Motion/6.02%3A_Transforming_the_evolutionary_variance-covariance_matrix.txt |
One assumption of Brownian motion is that the rate of change (σ2) is constant, both through time and across lineages. However, some of the most interesting hypotheses in evolution relate to differences in the rates of character change across clades. For example, key innovations are evolutionary events that open up new areas of niche space to evolving clades (Hunter 1998; reviewed in Alfaro 2013). This new niche space is an ecological opportunity that can then be filled by newly evolved species (Yoder et al. 2010). If this were happening in a clade, we might expect that rates of trait evolution would be elevated following the acquisition of the key innovation (Yoder et al. 2010).
There are several methods that one can use to test for differences in the rate of evolution across clades. First, one can compare the magnitude of independent contrasts across clades; second, one can use model comparison approaches to compare the fit of single- and multiple-rate models to data on trees; and third, one can use a Bayesian approach combined with reversible-jump machinery to try to find the places on the tree where rate shifts have occurred. I will explain each of these methods in turn.
Rate tests using phylogenetic independent contrasts
One of the earliest methods developed to compare rates across clades is to compare the magnitude of independent contrasts calculated in each clade (e.g. Garland 1992). To do this, one first calculates standardized independent contrasts, separating those contrasts that are calculated within each clade of interest. As we noted in Chapter 5, these contrasts have arbitrary sign (positive or negative) but if they are squared, represent independent estimates of the Brownian motion rate parameter (σ2). Basically, when rates of evolution are high, we should see large independent contrasts in that part of the tree (Garland 1992).
In his original description of this approach, Garland (1992) proposed using a statistical test to compare the absolute value of contrasts between clades (or between a single clade and the rest of the phylogenetic tree). In particular, Garland (1992) suggests using a t-test, as long as the absolute value of independent contrasts are approximately normally distributed. However, under a Brownian motion model, the contrasts themselves – but not the absolute values of the contrasts – should be approximately normal, so it is quite likely that absolute values of contrasts will strongly violate the assumptions of a t-test.
In fact, if we try this test on mammal body size, contrasting the two major clades in the tree (carnivores versus non-carnivores, Figure 6.2A), there looks to be a small difference in the absolute value of contrasts (Figure 6.2B). A t-test is not significant (Welch two-sample t-test P = 0.42), but we also can see that the distribution of PIC absolute values is strongly skewed (Figure 6.2C).
There are other simple options that might work better in general. For example, one could also compare the magnitudes of the squared contrasts, although these are also not expected to follow a normal distribution. Alternatively, we can again follow Garland’s (1992) suggestion and use a Mann-Whitney U-test, the nonparametric equivalent of a t-test, on the absolute values of the contrasts. Since Mann-Whitney U tests use ranks instead of values, this approach will not be sensitive to the fact that the absolute values of contrasts are not normal. If the P-value is significant for this test then we have evidence that the rate of evolution is greater in one part of the tree than another.
In the case of mammals, a Mann-Whitney U test also shows no significant differences in rates of evolution between carnivores and other mammals (W = 251, P = 0.70).
Rate tests using maximum likelihood and AIC
One can also carry out rate comparisons using a model-selection framework (O’Meara et al. 2006; Thomas et al. 2006). To do this, we can fit single- and multiple-rate Brownian motion models to a phylogenetic tree, then compare them using a model selection method like AICc. For example, in the example above, we tested whether or not one subclade in the mammal tree (carnivores) has a very different rate of body size evolution than the rest of the clade. We can use an ML-based model selection method to compare the fit of a single-rate model to a model where the evolutionary rate in carnivores is different from the rest of the clade, and use this test evaluate the support for that hypothesis.
This test requires the likelihood for a multi-rate Brownian motion model on a phylogenetic tree. We can derive such an equation following the approach presented in Chapter 4. Recall that the likelihood equations for (constant-rate) Brownian motion use a phylogenetic variance-covariance matrix, C, that is based on the branch lengths and topology of the tree. For single-rate Brownian motion, the elements in C are derived from the branch lengths in the tree. Traits are drawn from a multivariate normal distribution with variance-covariance matrix:
$\textbf{V}_{H_1} = σ^2\textbf{C}_{tree} \label{6.5}$
One simple way to fit a multi-rate Brownian motion model is to construct separate C matrices, one for each rate category in the tree. For example, imagine that most of a clade evolves under a Brownian motion model with rate σ12, but one clade in the tree evolves at a different (higher or lower) rate, σ22. One can construct two C matrices: the first matrix, C1, includes branches that evolve under rate σ12, while the second, C2, includes only branches that evolve under rate σ22. Since all branches in the tree are included in one of these two categories, it will be true that Ctree = C1 + C2. For any particular values of these two rates, traits are drawn from a multivariate normal distribution with variance-covariance matrix:
$\textbf{V}_{H_2} = σ_1^2\textbf{C}_1 + σ_2^2\textbf{C}_2 \label{6.6}$
We can now treat this as a model comparison-problem, contrasting H1: traits on the tree evolved under a constant-rate Brownian motion model, with H2: traits on the tree evolved under a multi-rate Brownian motion model. Note that H1 is a special case of H2 when σ12 = σ22; that is, these two models are nested and can be compared using a likelihood ratio test. Of course, one can also compare the two models using AICc.
For the mammal body size example, you might recall our ML single-rate Brownian motion model (σ2 = 0.088, $\bar{z}(0) = 4.64$, lnL = −78.0, AICc = 160.4). We can compare that to the fit of a model where carnivores get their own rate parameter (σc2) that might differ from that of the rest of the tree (σo2). Fitting that model, we find the following maximum likelihood parameter estimates: $\hat{\sigma}_c^2 = 0.068$, $\hat{\sigma}_o^2 = 0.01$, $\hat{\bar{z}}(0) = 4.51$). Carnivores do appear to be evolving more rapidly. However, the fit of this model is not substantially better than the single-rate Brownian motion (lnL = −77.6, AICc = 162.3).
There is one complication, which is how to deal with the actual branch along which the rate shift is thought to have occurred. O’Meara et al. (2006) describe “censored” and “noncensored” versions of their test, which differ in whether or not branches where rate shifts actually occur are included in the calculation. In the censored version of the test, O’Meara et al. (2006) omit the branch where we think a shift occurred, while in the noncensored version O’Meara et al. (2006) include that branch in one of the two rate categories (this is what I did in the example above, adding the stem branch of carnivores in the “non-carnivore” category). One could also specify where, exactly, the rate shift occurred along the branch in question, placing part of the branch in each of the two rate categories as appropriate. However, since we typically have little information about what happened on particular branches in a phylogenetic tree, results from these two approaches are not very different – unless, as stated by O’Meara et al. (2006), unusual evolutionary processes have occurred on the branch in question.
A similar approach was described by Thomas et al. (2006) but considers differences across clades to include changes in any of the two parameters of a Brownian motion model (σ2, $\bar{z}(0)$, or both). Remember that $\bar{z}(0)$ is the expected mean of species within a clade under a Brownian motion, but also represents the starting value of the trait at time zero. Allowing $\bar{z}(0)$ to vary across clades effectively allows different clades to have different “starting points” in phenotype space. In the case of comparing a monophyletic subclade to the rest of a tree, Thomas et al.’s (2006) approach is equivalent to the “censored” test described above. However, one drawback to both the Thomas et al. (2006) approach and the “censored” test is that, because clades each have their own mean, we no longer can tie the model that we fit using likelihood to any particular evolutionary process. Mathematically, changing $\bar{z}(0)$ in a subclade postulates that the trait value changed somehow along the branch leading to that clade, but we do not specify the way that the trait changed – the change could have been gradual or instantaneous, and no amount or pattern of change is more or less likely than anything else. Of course, one can describe evolutionary scenarios that might act like this process - but we begin to lose any potential tie to explicit evolutionary processes.
Rate tests using Bayesian MCMC
It is also possible to carry out this test in a Bayesian MCMC framework. The simplest way to do that would be to fit model H2 above, that traits on the tree evolved under a multi-rate Brownian motion model, in a Bayesian framework. We can then specify prior distributions and sample the three model parameters ($\bar{z}(0)$, σ12, and σ22) through our MCMC. At the end of our analysis, we will have posterior distributions for the three model parameters. We can test whether rates differ among clades by calculating a posterior distribution for the composite parameter σdiff2 = σ12 − σ22. The proportion of the posterior distribution for σdiff2 that is positive or negative gives the posterior probability that σ12 is greater or less than σ22, respectively.
Perhaps, though, researchers are unsure of where, exactly, the rate shift might have occurred, and want to incorporate some uncertainty in their analysis. In some cases, rate shifts are thought to be associated with some other discrete character, such as living on land (state 0) or in the water (1). In such cases, one way to proceed is to use stochastic character mapping (see Chapter 8) to map state changes for the discrete character on the tree, and then run an analysis where rates of evolution of the continuous character of interest depend on the mapping of our discrete states. This protocol is described most fully by Revell (2013), who also points out that rate estimates are biased to be more similar when the discrete character evolves quickly.
It is even possible to explore variation in Brownian rates without invoking particular a priori hypotheses about where the rates might change along branches in a tree. These methods rely on reversible-jump MCMC, a Bayesian statistical technique that allows one to consider a large number of models, all with different numbers of parameters, in a single Bayesian analysis. In this case, we consider models where each branch in the tree can potentially have its own Brownian rate parameter. By constraining sets of these rate parameters to be equal to one another, we can specify a huge number of models for rate variation across trees. The reversible-jump machinery, which is beyond the scope of this book, allows us to generate a posterior distribution that spans this large set of models where rates vary along branches in a phylogenetic tree (see Eastman et al. 2011 for details). | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/06%3A_Beyond_Brownian_Motion/6.03%3A_Variation_in_rates_of_trait_evolution_across_clades.txt |
We can also consider the case where a trait evolves under the influence of stabilizing selection. Assume that a trait has some optimal value, and that when the population mean differs from the optimum the population will experience selection towards the optimum (Figure 6.3). As I will show below, when traits evolve under stabilizing selection with a constant optimum, the pattern of traits through time can be described using an Ornstein-Uhlenbeck (OU) model. It is worth mentioning, though, that this is only one (of many!) models that follow an OU process over long time scales. In other words, even though this model can be described by OU, we cannot make inferences the other direction and claim that OU means that our population is under constant stabilizing selection. In fact, we will see later that we can almost always rule this simple version of the OU model out over long time scales by looking at the actual parameter values of the model compared to what we know about species’ population sizes and trait heritabilities.
We can follow the modeling approach from chapter 3 to derive the expected distribution of species’ traits on a tree under stabilizing selection. The derivation is a bit long and complicated, so I have moved it to an appendix of this chapter. For now, all you need to know is that we can write down the likelihood of an OU model on a phylogenetic tree (see equation 6.58-6.60, below).
We can fit an OU model to data in a similar way to how we fit BM models in the previous chapters. For any given parameters ($\bar{z}_0$, σ2, α, and θ) and a phylogenetic tree with branch lengths, one can calculate an expected vector of species means and a species variance-covariance matrix. One then uses the likelihood equation for a multivariate normal distribution to calculate the likelihood of this model. This likelihood can then be used for parameter estimation in either a ML or a Bayesian framework.
We can illustrate how this works by fitting an OU model to the mammal body size data that we have been discussing. Using ML, we obtain parameter estimates $\hat{\bar{z}}_0 = 4.60$, $\hat{\sigma}^2 = 0.10$, $\hat{\alpha} = 0.0082$, and $\hat{\theta} = 4.60$. This model has a lnL of -77.6, a little higher than BM, but an AICc score of 161.2, worse than BM. We still prefer Brownian motion for these data. Over many datasets, though, OU models fit better than Brownian motion (see Harmon et al. 2010; Pennell and Harmon 2013).
6.05: Early Burst Models
Adaptive radiations are a slippery idea. Many definitions have been proposed, some of which contradict one another (reviewed in Yoder et al. 2010). Despite some core disagreement about the concept of adaptive radiations, many discussions of the phenomenon center around the idea of “ecological opportunity.” Perhaps adaptive radiations begin when lineages gain access to some previously unexploited area of niche space. These lineages begin diversifying rapidly, forming many and varied new species. At some point, though, one would expect that the ecological opportunity would be “used up,” so that species would go back to diversifying at their normal, background rates (Yoder et al. 2010). These ideas connect to Simpson’s description of evolution in adaptive zones. According to Simpson (1945), species enter new adaptive zones in one of three ways: dispersal to a new area, extinction of competitors, or the evolution of a new trait or set of traits that allow them to interact with the environment in a new way.
One idea, then, is that we could detect the presence of adaptive radiations by looking for bursts of trait evolution deep in the tree. If we can identify clades, like Darwin’s finches, for example, that might be adaptive radiations, we should be able to uncover this “early burst” pattern of trait evolution.
The simplest way to model an early burst of evolution in a continuous trait is to use a time-varying Brownian motion model. Imagine that species in a clade evolved under a Brownian motion model, but one where the Brownian rate parameter (σ2) slowed through time. In particular, we can follow Harmon et al. (2010) and define the rate parameter as a function of time, as:
$σ^2(t)=σ_0^2e^{bt} \label{6.7}$
We describe the rate of decay of the rate using the parameter b, which must be negative to fit our idea of adaptive radiations. The rate of evolution will slow through time, and will decay more quickly if the absolute value of b is large.
This model also generates a multivariate normal distribution of tip values. Harmon et al. (2010) followed Blomberg's "ACDC" model (2003) to write equations for the means and variances of tips on a tree under this model, which are:
$\begin{array}{l} \mu_i(t) = \bar{z}_0 \ V_i(t) = \sigma_0^2 \frac{e^{b T_i}-1}{b} V_{ij}(t) = \sigma_0^2 \frac{e^{b s_{ij}}-1}{b} \end{array} \label{6.8}$
Again, we can generate a vector of means and a variance-covariance matrix for this model given parameter values ($\bar{z}_0$, σ2, and b) and a phylogenetic tree. We can then use the multivariate normal probability distribution function to calculate a likelihood, which we can then use in a ML or Bayesian statistical framework.
For mammal body size, the early burst model does not explain patterns of body size evolution, at least for the data considered here ($\hat{\bar{z}}_0 = 4.64$, $\hat{\sigma}^2 = 0.088$, $\hat{b} = -0.000001$, lnL = −78.0, AICc = 162.6).
6.06: Peak Shift Models
A second model considered by Hansen and Martins (1996) describes the circumstance where traits change in a punctuated manner. One can imagine a scenario where species evolve on an adaptive landscape with many peaks; usually, populations stay on a single peak and phenotypes do not change, but occasionally a population will transition from one peak to another. We can either assume that these changes occur at random times, defining an average interval between peak shifts, or we can associate shifts with other traits that we map on the phylogenetic tree (for example, major geographic dispersal or vicariance events, or the evolution of certain traits).
We have developed peak shift models by integrating OU models and reversible-jump MCMC (Uyeda and Harmon 2014). The mathematics of this model are beyond the scope of this book, but follow closely from the description of the multi-rate Brownian motion model described in the section “variation in rates of trait evolution across clades,” above. In this case, when we change model parameters, we move among OU regimes, and can alter the OU model parameters σ2 or α. The approach can be used to either identify parts of the tree that are evolving in separate regimes or to test particular hypotheses about the drivers of evolution. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/06%3A_Beyond_Brownian_Motion/6.04%3A_Non-Brownian_evolution_under_stabilizing_selection.txt |
We can first consider the evolution of the trait on the “stem” branch, before the divergence of species A and B. We model stabilizing selection with a single optimal trait value, located at θ. An example of such a surface is plotted as Figure 6.3. We can describe fitness of an individual with phenotype z as:
$W = e^{−γ(z − θ)^2} \label{6.11}$
We have introduced a new variable, $γ$, which captures the curvature of the selection surface. To simplify the calculations, we will assume that stabilizing selection is weak, so that γ is small.
We can use a Taylor expansion of this function to approximate Equation \ref{6.7} using a polynomial. Our assumption that $γ$ is small means that we can ignore terms of order higher than γ2:
$W = 1 − γ(z − θ)^2 \label{6.12}$
This makes good sense, since a quadratic equation is a good approximation of the shape of a normal distribution near its peak. The mean fitness in the population is then:
\begin{align} \bar{W} &= E[W] = E[1 - \gamma (z - \theta)^2] \ &= E[1 - \gamma (z^2 - 2 z \theta + \theta^2)] \ &= 1 - \gamma (E[z^2] - E[2 z \theta] + E[\theta^2]) \ &= 1 - \gamma (\bar{z}^2 - V_z - 2 \bar{z} \theta + \theta ^2) \end{align} \label{6.13}
We can find the rate of change of fitness with respect to changes in the trait mean by taking the derivative of (6.9) with respect to $\bar{z}$:
$\frac{\partial \bar{W}}{\partial \bar{z}} = -2 \gamma \bar{z} + 2 \gamma \theta = 2 \gamma (\theta - \bar{z}) \label{6.14}$
We can now use Lande’s (1976) equation for the dynamics of the population mean through time for a trait under selection:
$\Delta \bar{z} = \frac{G}{\bar{W}} \frac{\partial \bar{W}}{\partial \bar{z}} \label{6.15}$
Substituting Equations \ref{6.9} and \ref{6.10} into Equation \ref{6.11}, we have:
$\Delta \bar{z} = \frac{G}{\bar{W}} \frac{\partial \bar{W}}{\partial \bar{z}} = \frac{G}{1 - \gamma (\bar{z}^2 - V_z - 2 \bar{z} \theta + \theta ^2)} 2 \gamma (\theta - \bar{z}) \label{6.16}$
Then, simplifying further with another Taylor expansion, we obtain:
$\bar{z}' = \bar{z} + 2 G \gamma (\theta - \bar{z}) + \delta \label{6.17}$
Here, $\bar{z}$ is the species’ trait value in the previous generation and $\bar{z}'$ in the next, while G is the additive genetic variance in the population, γ the curvature of the selection surface, θ the optimal trait value, and δ a random component capturing the effect of genetic drift. We can find the expected mean of the trait over time by taking the expectation of this equation:
$E[\bar{z}'] = \mu_z' = \mu_z + 2 G \gamma (\theta - \mu_z) \label{6.18}$
We can then solve this differential equations given the starting condition $\mu_z(0) = \bar{z}(0)$. Doing so, we obtain:
$\mu_z(t) = \theta + e^{-2 G t \gamma} (\bar{z}(0)-\theta) \label{6.19}$
We can take a similar approach to calculate the expected variance of trait values across replicates. We use a standard expression for variance:
$\begin{array}{l} V_z' = E[\bar{z}'^2] + E[\bar{z}']^2 \ V_z' = E[(\bar{z} + 2 G \gamma (\theta - \bar{z}) + \delta)^2] - E[\bar{z} + 2 G \gamma (\theta - \bar{z}) + \delta]^2 \ V_z' = G/n + (1 - 2 G \gamma)^2 V_z \ \end{array} \label{6.20}$
If we assume that stabilizing selection is weak, we can simplify the above expression using a Taylor series expansion:
$V_z' = G/n + (1 - 4 G \gamma) V_z \label{6.23}$
We can then solve this differential equation with starting point Vz(0)=0:
$V_z(t) = \frac{e^{-4 G t \gamma}-1}{4 n \gamma} \label{6.24}$
Equations \ref{6.15} and \ref{6.20} are equivalent to a standard stochastic model for constrained random walks called an Ornstein-Uhlenbeck process. Typical Ornstein-Uhlenbeck processes have four parameters: the starting value ($\bar{z}(0)$), the optimum ( θ), the drift parameter ( σ2), and a parameter describing the strength of constraints ( α). In our parameterization, $\bar{z}(0)$ and θ are as given, α = 2G, and σ2 = G/n.
We now need to know how OU models behave when considered along the branches of a phylogenetic tree. In the simplest case, we can describe the joint distribution of two species, A and B, descended from a common ancestor, z. Using equation 6.17, expressions for trait values of species A and B are:
$\begin{array}{l} \bar{a}' = \bar{a} + 2 G \gamma (\theta - \bar{a}) + \delta \ \bar{b}' = \bar{b} + 2 G \gamma (\theta - \bar{b}) + \delta \ \end{array} \label{6.25}$
Expected values of these two equations give equations for the means, using equation 6.19:
$\begin{array}{l} \mu_a' = \mu_a + 2 G \gamma (\theta - \mu_a) \ \mu_b' = \mu_b + 2 G \gamma (\theta - \mu_b) \ \end{array} \label{6.27}$
We can solve this system of differential equations, given starting conditions $\mu_a(0)=\bar{a}_0$ and $\mu_b(0)=\bar{b}_0$:
$\begin{array}{l} \mu_a'(t) = \theta + e^{-2 G t \gamma} (\bar{a}_0 - \theta) \ \mu_b'(t) = \theta + e^{-2 G t \gamma} (\bar{b}_0 - \theta) \ \end{array} \label{6.29}$
However, we can also note that the starting value for both a and b is the same as the ending value for species z on the root branch of the tree. If we denote the length of that branch as t1 then:
$E[\bar{a}_0] = E[\bar{b}_0] = E[\bar{z}(t_1)] = e^{-2 G t_1 \gamma} (\bar{z}_0 - \theta) \label{6.31}$
Substituting this into equations (6.25-26):
$\begin{array}{l} \mu_a'(t) = \theta + e^{-2 G \gamma (t_1 + t)} (\bar{z}_0 - \theta) \ \mu_b'(t) = \theta + e^{-2 G \gamma (t_1 + t)} (\bar{z}_0 - \theta) \ \end{array} \label{6.32}\[ Equations We can calculate the expected variance across replicates of species A and B, as above: \[ \begin{array}{l} V_a' = E[\bar{a}'^2] + E[\bar{a}']^2 \ V_a' = E[(\bar{a} + 2 G \gamma (\theta - \bar{a}) + \delta)^2] + E[\bar{a} + 2 G \gamma (\theta - \bar{a}) + \delta]^2 \ V_a' = G / n + (1 - 2 G \gamma)^2 V_a \ \end{array} \label{6.34}$
Similarly,
$\begin{array}{l} V_b' = E[\bar{b}'^2] + E[\bar{b}']^2 \ V_b' = G / n + (1 - 2 G \gamma)^2 V_b \ \end{array} \label{6.37}$
Again we can assume that stabilizing selection is weak, and simplify these expressions using a Taylor series expansion:
$\begin{array}{l} V_a' = G / n + (1 - 4 G \gamma) V_a \ V_b' = G / n + (1 - 4 G \gamma) V_b \ \end{array} \label{6.39}$
We have a third term to consider, the covariance between species A and B due to their shared ancestry. We can use a standard expression for covariance to set up a third differential equation:
$\begin{array}{l} V_{ab}' = E[\bar{a}' \bar{b}'] + E[\bar{a}'] E[\bar{b}'] \ V_{ab}' = E[(\bar{a} + 2 G \gamma (\theta - \bar{a}) + \delta)(\bar{b} + 2 G \gamma (\theta - \bar{b}) + \delta)] + E[\bar{a} \ + 2 G \gamma (\theta - \bar{a}) + \delta] E[\bar{a} + 2 G \gamma (\theta - \bar{a}) + \delta] \ V_{ab}' = V_{ab} (1 - 2 G \gamma)^2 \end{array} \label{6.41}$
We again use a Taylor series expansion to simplify:
$V_{ab}′= − 4V_{ab}Gγ \label{6.44}$
Note that under this model the covariance between A and B decreases through time following their divergence from a common ancestor.
We now have a system of three differential equations. Setting initial conditions Va(0)=Va0, Vb(0)=Vb0, and Vab(0)=Vab0, we solve to obtain:
$\begin{array}{l} V_a(t) = \frac{1 - e^{-4 G \gamma t}}{4 n \gamma} + V_{a0} \ V_b(t) = \frac{1 - e^{-4 G \gamma t}}{4 n \gamma} + V_{b0} \ V_{ab}(t) = V_{ab0} e^{-4 G \gamma t} \ \end{array} \label{6.45}$
We can further specify the starting conditions by noting that both the variance of A and B and their covariance have an initial value given by the variance of z at time t1:
$V_{a0} = V_{ab0} = V_{ab0} = V_z(t_1) = \frac{e^{-4 G \gamma t_1}-1}{4 n \gamma} \label{6.48}$
Substituting 6.44 into 6.41-43, we obtain:
$\begin{array}{l} V_a(t) = \frac{e^{-4 G \gamma (t_1 + t)} -1}{4 n \gamma} \ V_b(t) = \frac{e^{-4 G \gamma (t_1 + t)} -1}{4 n \gamma} \ V_{ab}(t) = \frac{e^{-4 G \gamma t} -e^{-4 G \gamma (t_1 + t)}}{4 n \gamma} \ \end{array} \label{6.49}$
Under this model, the trait values follow a multivariate normal distribution; one can calculate that all of the other moments of this distribution are zero. Thus, the set of means, variances, and covariances completely describes the distribution of A and B. Also, as γ goes to zero, the selection surface becomes flatter and flatter. Thus at the limit as γ approaches 0, these equations are equal to those for Brownian motion (see Chapter 4).
This quantitative genetic formulation – which follows Lande (1976) – is different from the typical parameterization of the OU model for comparative methods. We can obtain the “normal” OU equations by substituting α = 2Gγ and σ2 = G/n:
$\begin{array}{l} V_a(t) = \frac{\sigma^2}{2 \alpha} (e^{-2 \alpha (t_1 + t)} - 1) \ V_b(t) = \frac{\sigma^2}{2 \alpha} (e^{-2 \alpha (t_1 + t)} - 1) \ V_ab(t) = \frac{\sigma^2}{2 \alpha} e^{-2 \alpha t} (1-e^{-2 \alpha t_1}) \ \end{array} \label{6.52}$
These equations are mathematically equivalent to the equations in Butler et al. (2004) applied to a phylogenetic tree with two species.
We can easily generalize this approach to a full phylogenetic tree with $n$ taxa. In that case, the $n$ species trait values will all be drawn from a multivariate normal distribution. The mean trait value for species i is then:
$\mu_i(t) = \theta + e^{-2 G \gamma T_i}(\bar{z}_0 - \theta) \label{6.55}$
Here Ti represents the total branch length separating that species from the root of the tree. The variance of species i is:
$V_i(t) = \frac{e^{-4 G \gamma T_i} - 1}{4 n \gamma} \label{6.56}$
Finally, the covariance between species i and j is:
$V_{ij}(t) = \frac{e^{-4 G \gamma (T_i - s_{ij})}-e^{-4 G \gamma T_i}}{4 n \gamma} \label{6.57}$
Note that the above equation is only true when Ti = Tj – which is only true for all i and j if the tree is ultrametric. We can substitute the normal OU parameters, α and σ2, into these equations:
$\begin{array}{l} \mu_i(t) = \theta + e^{- \alpha T_i}(\bar{z}_0 - \theta) \ V_i(t) = \frac{\sigma^2}{2 \alpha} e^{-2 \alpha T_i} - 1 \ V_{ij}(t) = \frac{\sigma^2}{2 \alpha} (e^{-2 \alpha (T_i - s_{ij})}-e^{-2 \alpha T_i}) \ \end{array} \label{6.58}$ | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/06%3A_Beyond_Brownian_Motion/6.07%3A_Appendix_-_Deriving_an_OU_model_under_stabilizing_selection.txt |
In this chapter, I have described a few models that represent alternatives to Brownian motion, which is still the dominant model of trait evolution used in the literature. These examples really represent the beginnings of a whole set of models that one might fit to biological data. The best applications of this type of approach, I think, are in testing particular biologically motivated hypotheses using comparative data.
Section 6.9: Footnotes
1: Pagel's original models were initially focused on discrete characters, but - as he later pointed out - apply equally well to continuous characters.
back to main text
References
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Blomberg, S. P., T. Garland Jr, and A. R. Ives. 2003. Testing for phylogenetic signal in comparative data: Behavioral traits are more labile. Evolution 57:717–745.
Boettiger, C., G. Coop, and P. Ralph. 2012. Is your phylogeny informative? Measuring the power of comparative methods. Evolution 66:2240–2251.
Bokma, F. 2008. Detection of “punctuated equilibrium” by Bayesian estimation of speciation and extinction rates, ancestral character states, and rates of anagenetic and cladogenetic evolution on a molecular phylogeny. Evolution 62:2718–2726. Blackwell Publishing Inc.
Eastman, J. M., M. E. Alfaro, P. Joyce, A. L. Hipp, and L. J. Harmon. 2011. A novel comparative method for identifying shifts in the rate of character evolution on trees. Evolution 65:3578–3589.
Garland, T., Jr. 1992. Rate tests for phenotypic evolution using phylogenetically independent contrasts. Am. Nat. 140:509–519.
Goldberg, E. E., and B. Igić. 2012. Tempo and mode in plant breeding system evolution. Evolution 66:3701–3709. Wiley Online Library.
Grant, P. R., and B. R. Grant. 2002. Unpredictable evolution in a 30-year study of Darwin’s finches. Science 296:707–711.
Grant, P. R., and R. B. Grant. 2011. How and why species multiply: The radiation of Darwin’s finches. Princeton University Press.
Hansen, T. F., and E. P. Martins. 1996. Translating between microevolutionary process and macroevolutionary patterns: The correlation structure of interspecific data. Evolution 50:1404–1417.
Harmon, L. J., J. B. Losos, T. Jonathan Davies, R. G. Gillespie, J. L. Gittleman, W. Bryan Jennings, K. H. Kozak, M. A. McPeek, F. Moreno-Roark, T. J. Near, and Others. 2010. Early bursts of body size and shape evolution are rare in comparative data. Evolution 64:2385–2396.
Hunter, J. P. 1998. Key innovations and the ecology of macroevolution. Trends Ecol. Evol. 13:31–36.
Lande, R. 1976. Natural selection and random genetic drift in phenotypic evolution. Evolution 30:314–334.
O’Meara, B. C., C. Ané, M. J. Sanderson, and P. C. Wainwright. 2006. Testing for different rates of continuous trait evolution using likelihood. Evolution 60:922–933.
Pagel, M. 1999a. Inferring the historical patterns of biological evolution. Nature 401:877–884.
Pagel, M. 1999b. The maximum likelihood approach to reconstructing ancestral character states of discrete characters on phylogenies. Syst. Biol. 48:612–622.
Pennell, M. W., and L. J. Harmon. 2013. An integrative view of phylogenetic comparative methods: Connections to population genetics, community ecology, and paleobiology. Ann. N. Y. Acad. Sci. 1289:90–105.
Revell, L. J. 2013. Two new graphical methods for mapping trait evolution on phylogenies. Methods Ecol. Evol. 4:754–759.
Revell, L. J., L. J. Harmon, and D. C. Collar. 2008. Phylogenetic signal, evolutionary process, and rate. Syst. Biol. 57:591–601.
Simpson, G. G. 1945. Tempo and mode in evolution. Trans. N. Y. Acad. Sci. 8:45–60.
Thomas, G. H., R. P. Freckleton, and T. Székely. 2006. Comparative analyses of the influence of developmental mode on phenotypic diversification rates in shorebirds. Proc. Biol. Sci. 273:1619–1624.
Uyeda, J. C., and L. J. Harmon. 2014. A novel bayesian method for inferring and interpreting the dynamics of adaptive landscapes from phylogenetic comparative data. Syst. Biol. 63:902–918. sysbio.oxfordjournals.org.
Yoder, J. B., E. Clancey, S. Des Roches, J. M. Eastman, L. Gentry, W. Godsoe, T. J. Hagey, D. Jochimsen, B. P. Oswald, J. Robertson, and Others. 2010. Ecological opportunity and the origin of adaptive radiations. J. Evol. Biol. 23:1581–1596. Blackwell Publishing Ltd. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/06%3A_Beyond_Brownian_Motion/6.0S%3A_6.S%3A_Beyond_Brownian_Motion_%28Summary%29.txt |
This chapter describes the Mk model, which can be used to describe the evolution of discrete characters that have a set number of fixed states. We can also elaborate on the Mk model to allow more complex models of discrete character evolution (the extended-Mk model). These models can all be used to simulate the evolution of discrete characters on trees.
07: Models of Discrete Character Evolution
R markdown to recreate analyses
Squamates, the clade that includes all living species of lizards, are well known for their diversity. From the gigantic Komodo dragon of Indonesia (Figure 7.1A, Varanus komodoensis) to tiny leaf chameleons of Madagascar (Figure 7.1B, Brookesia), squamates span an impressive range of form and ecological niche use (Vitt et al. 2003; Pianka et al. 2017). Even the snakes (Figure 7.1C and D), extraordinarily diverse in their own right (~3,500 species), are actually a clade that is nested within squamates (Streicher and Wiens 2017). The squamate lineage that is ancestral to snakes became limbless about 170 million years ago (see Hedges et al. 2006) – and also underwent a suite of changes to their head shape, digestive tract, and other traits associated with their limbless lifestyle. In other words, snakes are lizards – highly modified lizards, but lizards nonetheless. And snakes are not the only limbless lineage of squamates. In fact, lineages within squamates have lost their limbs over and over again through their history (e.g. Figure 7.1E and F), with some estimates that squamates have lost their limbs at least 26 times in the past 240 million years (Brandley et al. 2008).
Limblessness is an example of a discrete trait – a trait that can occupy one of a set of distinct character states. Analyzing the evolution of discrete traits requires a different modeling approach than what we used for continuous traits. In this chapter, I will discuss the Mk model (Lewis 2001), which is a general approach to modeling the evolution of discrete traits on trees. Fitting this model to comparative data will help us understand the evolution of traits like limblessness where species can be placed into one of a number of discrete character states.
7.02: Modeling the evolution of discrete states
So far, we have only dealt with continuously varying characters. However, many characters of interest to biologists are best defined as characters with a set number of fixed states. For limblessness in squamates, each species is either legless (state 0) or not (state 1; actually, there are some species that might be considered “intermediate” Brandley et al. 2008, but we will ignore those for now). We might have particular questions about the evolution of limblessness in squamates. For example, how many times this character has changed in the evolutionary history of squamates? How often does limblessness evolve? Do limbs ever re-evolve? Is the evolution of limblessness related to some other aspect of the lives of these reptiles?
We will consider discrete characters where each species might exhibit one of k states. (In the limbless example above, k = 2). For characters with more than two states, there is a key distinction between ordered and unordered characters. Ordered characters can be placed in an order so that transitions only occur between adjacent states. For example, I might include “intermediate” species that are somewhere in between limbed and limbless – for example, the “mermaid skinks” (Sirenoscincus) from Madagascar, so called because they lack hind limbs (Figure 7.2, Moch and Senter 2011). An ordered model might only allow transitions between limbless and intermediate, and intermediate and limbed; it would be impossible under such a model to go directly from limbed to limbless without first becoming intermediate. For unordered characters, any state can change into any other state. In this chapter, I will focus mainly on unordered characters; we will return to ordered characters later in the book.
Most work on the evolution of discrete characters on phylogenetic trees has focused on the evolution of gene or protein sequences. Gene sequences are made up of four character states (A, C, T, and G for DNA). Models of sequence evolution allow transitions among all of these states at certain rates, and may allow transition rates to vary across sites, among clades, or through time. There are a huge number of named models that have been applied to this problem (e.g. Jukes-Cantor, JC; General Time-Reversible, GTR; and many more, Yang 2006), and a battery of statistical approaches are available to fit these models to data (e.g. Posada 2008).
Any discrete character can be modeled in a similar way as gene sequences. When considering phenotypic characters, we should keep in mind two main differences from the analysis of DNA sequences. First, arbitrary discrete characters may have any number of states (beyond the four associated with DNA sequence data). Second, characters are typically analyzed independently rather than combining long sets of characters and assuming that they share the same model of change. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/07%3A_Models_of_Discrete_Character_Evolution/7.01%3A_Limblessness_as_a_discrete_trait.txt |
The most basic model for discrete character evolution is called the Mk model. First developed for trait data by Pagel (1994; although the name Mk comes from Lewis 2001). The Mk model is a direct analogue of the Jukes-Cantor (JC) model for sequence evolution. The model applies to a discrete character having k unordered states. Such a character might have k = 2, k = 3, or even more states. Evolution involves changing between these k states (Figure 7.3).
The basic version of the Mk model assumes that transitions among these states follow a Markov process. This means that the probability of changing from one state to another depends only on the current state, and not on what has come before. For example, it makes no difference if a lineage has just evolved the trait of “feathers,” or whether they have had feathers for millions of years – the probability of evolving a different character state is the same in both cases. The basic Mk model also assumes that every state is equally likely to change to any other state.
For the basic Mk model, we can denote the instantaneous rate of change between states using the parameter q. In general, qij is called the instantaneous rate between character states i and j. It is defined as the limit of the rate measured over very short time intervals1.
Again, for the basic Mk model, instantaneous rates between all pairs of characters are equal; that is, qij = qmn for all i ≠ j and m ≠ n.
We can summarize general Markov models for discrete characters using a transition rate matrix (Lewis 2001):
$\mathbf{Q} = \begin{bmatrix} -d_1 & q_{12} & \dots & q_{1k} \ q_{21} & -d_2 & \dots & q_{2k} \ \vdots & \vdots & \ddots & \vdots\ q_{k1} & q{k2} & \dots & -d_k \ \end{bmatrix} \label{7.1}$
Note that the instantaneous rates are only entered into the off-diagonal parts of the matrix. Along the diagonal, these matrices always have a set of negative numbers. For any Q matrix, the sum of all the elements in each row is zero – a necessary condition for a transition rate matrix. Because of this, each negative number has a value, di, equal to the sum of all of the other numbers in the row. For example,
$d_1 = \sum_{i=2}^{k} q_{1i} \label{7.2}$
For a two-state Mk model, k = 2 and rates are symmetric so that q12 = q21. In this case, we can write the transition rate matrix as:
$\mathbf{Q} = \begin{bmatrix} -q & q \ q & -q \ \end{bmatrix} \label{7.3}$
Likewise, for k = 3, the transition rate matrix is:
$\mathbf{Q} = \begin{bmatrix} -2 q & q & q\ q & -2 q & q\ q & q & -2 q\ \end{bmatrix} \label{7.4}$
In general, the k-state transition matrix for a basic Mk model is:
$\mathbf{Q} = \begin{bmatrix} 1-k & 1 & \dots & 1\ 1 & 1-k & \dots & 1\ \vdots & \vdots & \ddots & \vdots\ 1 & 1 & \dots & 1\ \end{bmatrix} \label{7.5}$
Once we have this transition rate matrix, we can calculate the probability distribution of trait states after any time interval t using the equation (Lewis 2001):
$\textbf{P}(t)=e^{\textbf{Q}t} \label{7.6}$
This equation looks simple, but calculating P(t) involves matrix exponentiation – raising e to a power defined by a matrix. This calculation is substantially different from raising e to the power defined by each element of a matrix2. The result is a matrix, P, of transition probabilities. Each element in this matrix (pij) gives the probability that starting in state i you will end up in state j over that time interval t. For the standard Mk model, there is a general solution to this equation:
$\begin{array}{l} p_{ii}(t) = \frac{1}{k} + \frac{k-1}{k} e^{-kqt} \ p_{ij}(t) = \frac{1}{k} - \frac{1}{k} e^{-kqt} \ \end{array} \label{7.7}$
In particular, when k = 2,
$\begin{array}{l} p_{ii}(t) = \frac{1}{k} + \frac{k-1}{k} e^{-kqt} = \frac{1}{2} + \frac{2-1}{2}e^{-2qt}=\frac{1+e^{-2qt}}{2} \ p_{ij}(t) = \frac{1}{k} - \frac{1}{k} e^{-kqt} = \frac{1}{2} - \frac{1}{2}e^{-2qt}=\frac{1-e^{-2qt}}{2} \ \end{array} \label{7.8}$
If we consider what happens when time gets very large in these equations, we see an interesting pattern. Any term that has et in it gets closer and closer to zero as t increases. Because of this, for all values of k, each pij(t) converges to a constant value, 1/k. This is the stationary distribution of character states, π, defined as the equilibrium frequency of character states if the process is run many times for a long enough time period. In general, the stationary distribution of an Mk model is:
$\pi = \begin{bmatrix} 1/k & 1/k & \dots & 1/k\ \end{bmatrix} \label{7.9}$
In the case of $k = 2$,
$\pi = \begin{bmatrix} 1/2 & 1/2 \ \end{bmatrix} \label{7.10}$ | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/07%3A_Models_of_Discrete_Character_Evolution/7.03%3A_The_Mk_Model.txt |
The Mk model assumes that transitions among all possible character states occur at the same rate. However, that may not be a valid assumption. For example, it is often supposed that it is easier to lose a complex character than to gain one. We might want to fit models that allow for such asymmetries in rates.
For models of DNA sequence evolution there are a wide range of models allowing different rates between distinct types of nucleotides (Yang 2006). Unequal rates are usually incorporated into the Mk model in two ways. First, one can consider the symmetric model (SYM; Paradis et al. 2004). In the symmetric model, the rate of change between any two character states is the same forwards as it is backwards (that is, rates of change are symmetric; qij = qji). The rate for a particular pair of states might differ from other pairs of character states. Note that when k = 2 the symmetric model is identical to the basic Mk model. The rate matrix for this model has as many free rate parameters as there are pairs of character states:
(eq. 7.11)
$p = \frac{k(k-1)}{2}$
However, in general symmetric models will not have stationary distributions where all character states occur at equal frequencies, as noted above for the Mk model. We can account for these uneven frequencies by adding additional parameters to our model:
(eq. 7.12)
$\pi_{SYM} = \begin{bmatrix} \pi_1 & \pi_2 & \dots & 1 - \sum_{i=1}^{n-1} \pi_i \end{bmatrix}$
Note that we only have to specify n − 1 equilibrium frequencies, since we know that they all sum to one. We have added n − 1 new parameters, for a total number of parameters:
(eq. 7.13)
$p = \frac{k(k-1)}{2} + n-1$
To obtain a Q-matrix for this model, we combine the information from both the relative transition rates and equilibrium frequencies:
(eq. 7.14)
$\mathbf{Q} = \begin{bmatrix} \cdot & r_1 & \dots & r_{n-1} \ r_1 & \cdot & \dots & \vdots \ \vdots & \vdots & \cdot & r_{k(k-1)/2} \ r_{n-1} & \dots & r_{k(k-1)/2} & \cdot \ \end{bmatrix} \begin{bmatrix} \pi_1 & 0 & 0 & 0 \ 0 & \pi_2 & 0 & 0 \ 0 & 0 & \ddots & 0 \ 0 & 0 & 0 & \pi_n \ \end{bmatrix}$
In this equation I have left the diagonal of the first matrix as dots. The final Q-matrix must have all rows sum to one, so one can adjust the values of that matrix after the multiplication step.
In the case of a two-state model, for example, we can create a model where the forward rate is double the backward rate, and the equilibrium frequency of character one is 0.75. Then:
(eq. 7.15)
$\mathbf{Q} = \begin{bmatrix} \cdot & 1 \ 2 & \cdot \ \end{bmatrix} \begin{bmatrix} 0.75 & 0 \ 0 & 0.25 \ \end{bmatrix} = \begin{bmatrix} \cdot & 0.25 \ 1.5 & \cdot \ \end{bmatrix} = \begin{bmatrix} -0.25 & 0.25 \ 1.5 & -1.5 \ \end{bmatrix}$
It is worth noting that this approach of setting parameters that define equilibrium state frequences, although borrowed from molecular evolution, is not completely standard in the comparative methods literature. One also sees equilibrium frequencies treated as a fixed property of the model, and assumed to be either equal across states or tied directly to the parameters in the Q-matrix.
The second common extension of the Mk model is called the all-rates-different model (ARD; Paradis et al. 2004). In this model every possible type of transition can have a different rate. There are thus k(k − 1) free rate parameters for this model, and again n − 1 parameters to specify the equilibrium frequencies of the character states.
The same algorithm can be used to calculate the likelihood for both of these extended Mk models (SYM and ARD). These models have more parameters than the standard Mk. To find maximum likelihood solutions, we must optimize the likelihood across the entire set of unknown parameters (see Chapter 7). | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/07%3A_Models_of_Discrete_Character_Evolution/7.04%3A_The_Extended_Mk_Model.txt |
We can also use the equations above to simulate evolution under an Mk or extended-Mk model on a tree (Felsenstein 2004). To do this, we simulate character evolution on each branch of the tree, starting at the root and progressing towards the tips. At speciation, we assume that both daughter species inherit the character state of their parental species immediately following speciation, and then evolve independently after that. At the end of the simulation, we will obtain a set of character states, one for each tip in the tree. The distribution of character states will depend on the shape of the phylogenetic tree (both its topology and branch lengths) along with the parameters of our model of character evolution.
We first draw a beginning character state at the root of the tree. There are several common ways to do this. For example, we can either draw from the stationary distribution or from one where each character state is equally likely. In the case of the standard Mk model, these are the same. For example, if we are simulating evolution under Mk with k = 2, then state 0 and 1 each have a probability of 1/2 at the root. We can draw the root state from a binomial distribution with pstate0 = 0.5.
Once we have a character state for the root, we then simulate evolution along each branch in the tree. We start with the (usually two) branches descending from the root. We then proceed up the tree, branch by branch, until we get to the tips.
We can understand this algorithm perfectly well by thinking about what happens on each branch of the tree, and then extending that algorithm to all of the branches (as described above). For each branch, we first calculate P(t), the transition probability matrix, given the length of the branch and our model of evolution as summarized by Q and the branch length t. We then focus on the row of P(t) that corresponds to the character state at the beginning of the branch. For example, let’s consider a basic two-state Mk model with q = 0.5. We will call the states 0 and 1. We can calculate P(t) for a branch with length t = 3 as:
(eq. 7.16)
$\mathbf{P}(t) = e^{\mathbf{Q} t} = exp( \begin{bmatrix} -0.5 & 0.5 \ 0.5 & -0.5 \ \end{bmatrix} \cdot 3) = \begin{bmatrix} 0.525 & 0.475 \ 0.475 & 0.525 \ \end{bmatrix}$
If we had started with character state 0 at the beginning of this branch, we would focus on the first row of this matrix. We want to end up at state 0 with probability 0.525 and change to state 1 with probability 0.475. We again draw a uniform random deviate u, and choose state 0 if 0 ≤ u < 0.525 and state 1 if 0.525 ≤ u < 1. If we started with a different character state, we would use a different row in the matrix. If this is an internal branch in the tree, then both daughter species inherit the character state that we chose immediately following speciation – but might diverge soon after! By repeating this along every branch in the tree, we obtain a set of character states at the tips of the tree. This is then the output of our simulation.
Two additional details here are worth noting. First, the procedure for simulating characters under the extended-Mk model are identical to those above, except that the calculation of matrix exponentials is more complicated than in the standard Mk model. Second, if you are simulating a character with more than two states, then the procedure for drawing a random number is slightly different3.
We can apply this approach to simulate the evolution of limblessness in squamates. Below, I present the results of three such simulations. These simulations are a little different than what I describe above because they consider all changes in the tree, rather than just character states at nodes and tips; but the model (and the principal) is the same. You can see that the model leaves an imprint on the pattern of changes in the tree, and you can imagine that one might be able to reconstruct the model using a phylogenetic comparative approach. Of course, typically we know only the tip states, and have to reconstruct changes along branches in the tree. We will discuss parameter estimation for the Mk and extended-Mk models in the next chapter.
7.06: R Markdown to Recreate Analyses
R markdown to recreate analyses
Reading in the data files
First we read in the data files.
``````sqTree<-read.tree(text=getURL("https://raw.githubusercontent.com/lukejharmon/pcm/master/datafiles/squamate.phy"))
plot(sqTree)``````
``sqData<-read.csv(text=getURL("https://raw.githubusercontent.com/lukejharmon/pcm/master/datafiles/brandley_table.csv"))``
Simulate binary character on tree
This code generates plots like Figure 7.4
``````qMatrix<-cbind(c(-1, 1), c(1, -1))*0.001
sh_slow<-sim.history(sqTree, qMatrix, anc="1")``````
``## Done simulation(s).``
``plotSimmap(sh_slow, pts=F, ftype="off")``
``````## no colors provided. using the following legend:
## 1 2
## "black" "red"``````
``add.simmap.legend(leg=c("limbed", "limbless"), colors=c("black", "red"), x=0.024, y =23, prompt=F)``
``````qMatrix<-cbind(c(-1, 1), c(1, -1))*0.01
sh_fast<-sim.history(sqTree, qMatrix, anc="1")``````
``## Done simulation(s).``
``plotSimmap(sh_fast, pts=F, ftype="off")``
``````## no colors provided. using the following legend:
## 1 2
## "black" "red"``````
``````qMatrix<-cbind(c(-0.02, 0.02), c(0.005, -0.005))
sh_asy<-sim.history(sqTree, qMatrix, anc="1")``````
``````## Note - the rate of substitution from i->j should be given by Q[j,i].
## Done simulation(s).``````
``plotSimmap(sh_asy, pts=F, ftype="off")``
``````## no colors provided. using the following legend:
## 1 2
## "black" "red"``````
Find the limbless species
Brandley et al.’s data has limb measurements. We will get our discrete character by counting species with zero-length fore- and hind limbs as limbless. This is different from the original analysis in Brandley et al., which counts things like spurs as “limbs” - and so our results might differ from theirs a bit.
``````limbless<-as.numeric(sqData[,"FLL"]==0 & sqData[,"HLL"]==0)
sum(limbless)``````
``## [1] 51``
``````# get names that match
nn<-sqData[,1]
nn2<-sub(" ", "_", nn)
names(limbless)<-nn2``````
Fit Mk model
We can fit a symmetric Mk model to these data using both likelihood and MCMC
``````# likelihood
td<-treedata(sqTree, limbless)``````
``````## Warning in treedata(sqTree, limbless): The following tips were not found in 'phy' and were dropped from 'data':
## Gonatodes_albogularis
## Lepidophyma_flavimaculatum
## Trachyboa_boulengeri``````
``````dModel<-fitDiscrete(td\$phy, td\$data)
# MCMC
mk_diversitree<-make.mk2(force.ultrametric(td\$phy), td\$data[,1])
simplemk<-constrain(mk_diversitree, q01~q10)
er_bayes<-mcmc(simplemk, x.init=0.1, nsteps=10000, w=0.01)``````
``````## 1: {0.0189} -> -141.93605
## 2: {0.0162} -> -135.45732`````` | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/07%3A_Models_of_Discrete_Character_Evolution/7.05%3A_Simulating_the_Mk_model_on_a_tree.txt |
In this chapter I have described the Mk model, which can be used to describe the evolution of discrete characters that have a set number of fixed states. We can also elaborate on the Mk model to allow more complex models of discrete character evolution (the extended-Mk model). These models can all be used to simulate the evolution of discrete characters on trees.
In summary, the Mk and extended Mk model are general models that one can use for the evolution of discrete characters. In the next chapter, I will show how to fit these models to data and use them to test evolutionary hypotheses.
Section 7.7: Footnotes
1: Imagine that you calculate a rate of character change by counting the number of changes of state of a character over some time interval, t. You can calculate the rate of change as nchanges/t. The instantaneous rate is the value that this rate approaches as t gets smaller and smaller so that the time interval is nearly zero.
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2: I will not cover the details of matrix exponentiation here – interested readers should see Yang (2006) for details – but the calculations are not trivial.
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3: One still obtains the relevant row from P(t) and draws a uniform random deviate u. Imagine that we have a ten-state character with states 0 - 9. We start at state 0 at the beginning of the simulation. Again using q = 0.5 and t = 3, we find that:
(eq. 7.17)
$\begin{array}{l} p_{ii}(t) = \frac{1}{k} + \frac{k-1}{k} e^{-kqt} = \frac{1}{10}+\frac{9}{10}e^{-2 \cdot 0.5 \cdot 3} = 0.145\ p_{ij}(t) = \frac{1}{k} - \frac{1}{k} e^{-kqt} \frac{1}{10} - \frac{1}{10}e^{-2 \cdot 0.5 \cdot 3} = 0.095\ \end{array}$
We focus on the first row of P(t), which has elements:
$\begin{bmatrix} 0.145 & 0.095 & 0.095 & 0.095 & 0.095 & 0.095 & 0.095 & 0.095 & 0.095 & 0.095 \ \end{bmatrix}$
We calculate the cumulative sum of these elements, adding them together so that each number represents the sum of itself and all preceding elements in the vector:
$\begin{bmatrix} 0.145 & 0.240 & 0.335 & 0.430 & 0.525 & 0.620 & 0.715 & 0.810 & 0.905 & 1.000 \ \end{bmatrix}$
Now we compare u to the numbers in this cumulative sum vector. We select the smallest element that is still strictly larger than u, and assign this character state for the end of the branch. For example, if u = 0.475, the 5th element, 0.525, is the smallest number that is still greater than u. This corresponds to character state 4, which we assign to the end of the branch. This last procedure is a numerical trick. Imagine that we have a line segment with length 1. The cumulative sum vector breaks the unit line into segments, each of which is exactly as long as the probability of each event in the set. One then just draws a random number between 0 and 1 using a uniform distribution. The segment that contains this random number is our event.
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References
Brandley, M. C., J. P. Huelsenbeck, and J. J. Wiens. 2008. Rates and patterns in the evolution of snake-like body form in squamate reptiles: Evidence for repeated re-evolution of lost digits and long-term persistence of intermediate body forms. Evolution. Wiley Online Library.
Felsenstein, J. 2004. Inferring phylogenies. Sinauer Associates, Inc., Sunderland, MA.
Hedges, S. B., J. Dudley, and S. Kumar. 2006. TimeTree: A public knowledge-base of divergence times among organisms. Bioinformatics 22:2971–2972.
Lewis, P. O. 2001. A likelihood approach to estimating phylogeny from discrete morphological character data. Syst. Biol. 50:913–925.
Moch, J. G., and P. Senter. 2011. Vestigial structures in the appendicular skeletons of eight African skink species (squamata, scincidae). J. Zool. 285:274–280. Blackwell Publishing Ltd.
Pagel, M. 1994. Detecting correlated evolution on phylogenies: A general method for the comparative analysis of discrete characters. Proc. R. Soc. Lond. B Biol. Sci. 255:37–45. The Royal Society.
Paradis, E., J. Claude, and K. Strimmer. 2004. APE: Analyses of phylogenetics and evolution in R language. Bioinformatics 20:289–290. academic.oup.com.
Pianka, E. R., L. J. Vitt, N. Pelegrin, D. B. Fitzgerald, and K. O. Winemiller. 2017. Toward a periodic table of niches, or exploring the lizard niche hypervolume. Am. Nat. 190:601–616. journals.uchicago.edu.
Posada, D. 2008. jModelTest: Phylogenetic model averaging. Mol. Biol. Evol. 25:1253–1256. academic.oup.com.
Streicher, J. W., and J. J. Wiens. 2017. Phylogenomic analyses of more than 4000 nuclear loci resolve the origin of snakes among lizard families. Biol. Lett. 13. rsbl.royalsocietypublishing.org.
Vitt, L. J., E. R. Pianka, W. E. Cooper Jr, and K. Schwenk. 2003. History and the global ecology of squamate reptiles. Am. Nat. 162:44–60. journals.uchicago.edu.
Yang, Z. 2006. Computational molecular evolution. Oxford University Press. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/07%3A_Models_of_Discrete_Character_Evolution/7.0S%3A_7.S%3A_Models_of_Discrete_Character_Evolution_%28Summary%29.txt |
In this chapter, the Felsenstein’s pruning algorithm was presented and show to be used to calculate the likelihoods of Mk and extended-Mk models on phylogenetic trees. I have also described both ML and Bayesian frameworks that can be used to test hypotheses about character evolution. This chapter also includes a description of the “total garbage” test, which will tell you if your data has information about evolutionary rates of a given character.
08: Fitting Models of Discrete Character Evolution
In the introduction to Chapter 7, I mentioned that squamates had lost their limbs repeatedly over their evolutionary history. This is a pattern that has been known for decades, but analyses have been limited by the lack of a large, well-supported species-level phylogenetic tree of squamates (but see Brandley et al. 2008). Only in the past few years have phylogenetic trees been produced at a scale broad enough to take a comprehensive look at this question [e.g. Bergmann and Irschick (2012); Pyron et al. (2013); see Figure 8.1]. Such efforts to reconstruct this section of the tree of life provide exciting potential to revisit old questions with new data.
Plotting the pattern of limbed and limbless species on the tree leads to interesting questions about the tempo and mode of this trait in squamates. For example, are there multiple gains as well as losses of limbs? Do gains and losses happen at the same rate, or (as we might expect) are gains more rare than losses? We can test hypothesis such as these using the the Mk and extended-Mk models (see chapter 7). In this chapter we will fit these models to phylogenetic comparative data.
8.02: Fitting Mk models to Comparative Data
The equations in Chapter 7 give us enough information to calculate the likelihood for comparative data on a tree. To understand how this is done, we can first consider the simplest case, where we know the beginning state of a character, the branch length, and the end state. We can then apply the method across an entire tree using a pruning algorithm, which will allow calculation of the likelihood of the data given the model and phylogenetic tree.
Imagine that a two-state character changes from a state of 0 to a state of 1 sometime over a time interval of t = 3. What is the likelihood of these data under the Mk model? As we did in equation 7.17, we can set a rate parameter q = 0.5 to calculate a probability matrix:
$\mathbf{P}(t) = e^{\mathbf{Q} t} = exp( \begin{bmatrix} -0.5 & 0.5 \ 0.5 & -0.5 \ \end{bmatrix} \cdot 3) = \begin{bmatrix} 0.525 & 0.475 \ 0.475 & 0.525 \ \end{bmatrix} \label{8.1}$
For this simple example, we started with state 0, so we look at the first row. Along this branch, we ended at state 1, so we should look specifically at p12(t): the probability of starting with state 0 and ending with state 1 over time t. This value is the probability of obtaining the data given the model (i.e. the likelihood): L = 0.475.
This likelihood applies to the evolutionary process along this single branch.
When we have comparative data the situation is more complex. If we knew the ancestral character states and states at every node in the tree, then calculation of the overall likelihood would be straightforward – we could just apply the approach above many times, once for each branch of the tree. However, there are two problems. First, we don’t know the starting state of the character at the root of the tree, and must treat that as an unknown. Second, we are modeling a process that is happening independently on many branches in a phylogenetic tree, and only observe the states at the end of these branches. All of the character states at internal nodes of the tree are unknown. The likelihood that we want to calculate has to be summed across all of these unknown character state possibilities on the internal branches of the tree.
Thankfully, Felsenstein (1973) provides an elegant algorithm for calculating the likelihoods for discrete characters on a tree. This algorithm, called Felsenstein’s pruning algorithm, is described with an example in the appendix to this chapter. Felsenstein’s pruning algorithm was important in the history of phylogenetics because it allowed scientists to efficiently calculate the likelihoods of comparative data given a tree and a model. One can then maximize that likelihood by changing model parameters (and perhaps also the topology and branch lengths of the tree; see Felsenstein 2004).
Pruning also gives some insight into how we can calculate probabilities on trees; many other problems in comparative methods can be approached using different pruning algorithms.
Felsenstein’s pruning algorithm proceeds backwards in time from the tips to the root of the tree (see appendix, section 8.8). At the root, we must specify the probabilities of each character state in the common ancestor of the species in the clade. As mentioned in Chapter 7, there are at least three possible methods for doing this. First, one can assume that each state can occur at the root with equal probability. Second, one can assume that the states are drawn from their stationary distribution, as given by the model. The stationary distribution is a stable probability distribution of states that is reached by the model after a long amount of time. Third, one might have some information about the root state – perhaps from fossils, or information about character states in a set of outgroup taxa – that can be used to assign probabilities to the states. In practice, the first two of these methods are more common. In the case discussed above – an Mk model with all transition rates equal – the stationary distribution is one where all states are equally probable, so the first two methods are identical. In general, though, these three methods can give different results. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/08%3A_Fitting_Models_of_Discrete_Character_Evolution/8.01:_The_Evolution_of_Limbs_and_Limblessness.txt |
The algorithm in the appendix below gives the likelihood for any particular discrete-state Markov model on a tree, but requires us to specify a value of the rate parameter q. In the example given, this rate parameter q = 1.0 corresponds to a lnL of -6.5. But is this the best value of q to use for our Mk model? Probably not. We can use maximum likelihood to find a better estimate of this parameter.
If we apply the pruning algorithm across a range of different values of q, the likelihood changes. To find the ML estimate of q, we can again use numerical optimization methods, calculating the likelihood by pruning for many values of q and finding the maximum.
Applying this method to the lizard data, we obtain a maximum liklihood estimate of q = 0.001850204 corresponding to lnL = −80.487176.
The example above considers maximization of a single parameter, which is a relatively simple problem. When we extend this to a multi-parameter model – for example, the extended Mk model will all rates different (ARD) – maximizing the likelihood becomes much more difficult. R packages solve this problem by using sophisticated algorithms and applying them multiple times to make sure that the value found is actually a maximum.
8.04: Using Bayesian MCMC to estimate parameters of the Mk model
We can also analyze this model using a Bayesian MCMC framework. We can modify the standard approach to Bayesian MCMC (see chapter 2):
1. Sample a starting parameter value, q, from its prior distributions. For this example, we can set our prior distribution as uniform between 0 and 1. (Note that one could also treat probabilities of states at the root as a parameter to be estimated from the data; in this case we will assign equal probabilities to each state).
2. Given the current parameter value, select new proposed parameter values using the proposal density Q(q′|q). For example, we might use a uniform proposal density with width 0.2, so that Q(q′|q) U(q − 0.1, q + 0.1).
3. Calculate three ratios:
• a. The prior odds ratio, Rprior. In this case, since our prior is uniform, Rprior = 1.
• b. The proposal density ratio, Rproposal. In this case our proposal density is symmetrical, so Rproposal = 1.
• c. The likelihood ratio, Rlikelihood. We can calculate the likelihoods using Felsenstein’s pruning algorithm (Box 8.1); then calculate this value based on equation 2.26.
4. Find Raccept as the product of the prior odds, proposal density ratio, and the likelihood ratio. In this case, both the prior odds and proposal density ratios are 1, so Raccept = Rlikelihood
5. Draw a random number u from a uniform distribution between 0 and 1. If u < Raccept, accept the proposed value of both parameters; otherwise reject, and retain the current value of the two parameters.
6. Repeat steps 2-5 a large number of times.
We can run this analysis on our squamate data, obtaining a posterior with a mean estimate of q = 0.001980785 and a 95% credible interval of 0.001174813 − 0.003012715. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/08%3A_Fitting_Models_of_Discrete_Character_Evolution/8.03:_Using_Maximum_likelihood_to_Estimate_Parameters_of_the_Mk_model.txt |
One problem that arises sometimes in maximum likelihood optimization happens when instead of a peak, the likelihood surface has a long flat “ridge” of equally likely parameter values. In the case of the Mk model, it is common to find that all values of q greater than a certain value have the same likelihood. This is because above a certain rate, evolution has been so rapid that all traces of the history of evolution of that character have been obliterated. After this point, character states of each lineage are random, and have no relationship to the shape of the phylogenetic tree. Our optimization techniques will not work in this case because there is no value of q that has a higher likelihood than other values. Once we get onto the ridge, all values of q have the same likelihood.
For Mk models, there is a simple test that allows us to recognize when the likelihood surface has a long ridge, and q values cannot be estimated. I like to call this test the “total garbage” test because it can tell you if your data are “garbage” with respect to historical inference – that is, your data have no information about historical patterns of trait change. One can predict states just as well by choosing each species at random.
To carry out the total garbage test, imagine that you are just drawing trait values at random. That is, each species has some probability p of having character state 0, and some probability ( 1 − p) of having state 1 (one can also generalize this test to multi-state models). This likelihood is easy to write down. For a tree of size $n$, the probability of drawing n0 species with state 0 is:
$L_{garbage} = p^{n_0}(1 − p)^{n − n_0} \label{8.2}$
This equation gives the likelihood of the “total garbage” model for any value of p. Equation 8.1 is related to a binomial distribution (lacking only the factorial term). We also know from probability theory that the ML estimate of p is n0/n, with likelihood given by the above formula.
Now consider the likelihood surface of the Mk model. When Mk likelihood surfaces have long ridges, they are nearly always for high values of q – and when the transition rate of character changes is high, this model converges to our “drawing from a hat” (or “garbage”) model. The likelihood ridge lies at the value that is exactly taken from equation 8.10 above.
Thus, one can compare the likelihood of our Mk model to the total garbage model. If the maximum likelihood value of q has the same likelihood as our garbage model, then we know that we are on a ridge of the likelihood surface and q cannot be estimated. We also have no ability to make any statements about the past evolution of our character – in particular, we cannot estimate ancestral character state with any precision. By contrast, if the likelihood of the Mk model is greater than the total garbage model, then our data contains some historical information. We can also make this comparison using AIC, considering the total garbage model as having a single parameter p.
For the squamates, we have n = 258 and n0 = 207. We calculate p = n0/n = 207/258 = 0.8023256. So the likelihood of our garbage model is
Lgarbage = pn0(1 − p)n − n0 = 0.8023256207(1 − 0.8023256)51 = 1.968142e − 56.
This calculation is both easier and more useful, though, on a natural-log scale:
lnLgarbage = n0 ⋅ ln(p)+(n − n0)⋅ln(1 − p)=207 ⋅ ln(0.8023256)+51 ⋅ ln(1 − 0.8023256)= − 128.2677.
Compare this to the log-likelihood of our Mk model, lnL = −80.487176, and you will see that the garbage model is a terrible fit to these data. There is, in fact, some historical information about species' traits in our data. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/08%3A_Fitting_Models_of_Discrete_Character_Evolution/8.05%3A_Exploring_Mk_-_the_%22total_garbage%22_test.txt |
I have been referring to an example of lizard limb evolution throughout this chapter, but we have not yet tested the hypothesis that I stated in the introduction: that transition rates for losing limbs are higher than rates of gaining limbs.
To do this, we can compare our one-rate Mk model with a two-rate model with differences in the rate of forwards and backwards transitions. The character states are 1 (no limbs) and 2 (limbs), and the forward transition represents gaining limbs. This is a special case of the “all-rates different” model discussed in chapter two. Q matrices for these two models will be, for model 1 (equal rates):
$\mathbf{Q_{ER}} = \begin{bmatrix} -q & q \ q & -q \ \end{bmatrix} \label{8.3A}$
$\mathbf{\pi_{ER}} = \begin{bmatrix} 1/2 & 1/2 \ \end{bmatrix} \label{8.3B}$
And for model 2, asymmetric:
$\mathbf{Q_{ASY}} = \begin{bmatrix} -q_1 & q_1 \ q_2 & -q_2 \ \end{bmatrix} \label{8.4A}$
$\mathbf{\pi_{ASY}} = \begin{bmatrix} 1/2 & 1/2 \ \end{bmatrix} \label{8.4B}$
Notice that the ER model has one parameter, while the ASY model has two. Also we have specified equal probabilities of each character at the root of the tree, which may not be justified. But this comparison is still useful as a simple example.
One can compare the two nested models using standard methods discussed in previous chapters – that is, a likelihood-ratio test, AIC, BIC, or other similar methods.
We can apply all of the above methods to analyze the evolution of limblessness in squamates. We can use the tree and character state data from Brandley et al. (2008), which is plotted with ancestral state reconstructions under an ER model in Figure 8.2.
If we fit an Mk model to these data assuming equal state frequencies at the root of the tree, we obtain a lnL of -80.5 and an estimate of the QER matrix as:
$\mathbf{Q_{ER}} = \begin{bmatrix} -0.0019 & 0.0019 \ 0.0019 & -0.0019 \ \end{bmatrix} \label{8.5}$
The ASY model with different forward and backward rates gives a lnL of -79.4 and:
$\mathbf{Q_{ASY}} = \begin{bmatrix} -0.0016 & 0.0016 \ 0.0038 & -0.0038 \ \end{bmatrix} \label{8.6}$
Note that the ASY model has a higher backwards than forwards rate; as expected, we estimate a rate of losing limbs that is higher than the rate of gaining them (although the difference is surprisingly low). Is this statistically supported? We can compare the AIC scores of the two models. For the ER model, AICc = 163.0, while for the ASY model AICc = 162.8. The AICc score is higher for the unequal rates model, but only by about 0.2 – which is not definitive either way. So based on this analysis, we cannot rule out the possibility that forward and backward rates are equal.
A Bayesian analysis of the ASY model gives similar conclusions (Figure 8.3). We can see that the posterior distribution for the backwards rate (q21) is higher than the forwards rate (q12), but that the two distributions are broadly overlapping.
You might wonder about how we can reconcile these results, which suggest that squamates gain limbs at least as frequently as they lose them, with our biological intuition that limbs should be much more difficult to gain than they are to lose. But keep in mind that our comparative analysis is not using any information other than the states of extant species to reconstruct these rates. In particular, identifying irreversible evolution using comparative methods is a problem that is known to be quite difficult, and might require outside information in order to resolve conclusively. For example, if we had some information about the relative number of mutational steps required to gain and lose limbs, we could use an informative prior – which would, I suspect, suggest that limbs are more difficult to gain than they are to lose. Such a prior could dramatically alter the results presented in Figure 8.3. We will return to the problem of irreversible evolution later in the book (Chapter 13). | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/08%3A_Fitting_Models_of_Discrete_Character_Evolution/8.06:_Testing_for_Differences_in_the_Forwards_and_Backwards_Rate_of_Character_Change.txt |
Felsenstein’s pruning algorithm (1973) is an example of dynamic programming, a type of algorithm that has many applications in comparative biology. In dynamic programming, we break down a complex problem into a series of simpler steps that have a nested structure. This allows us to reuse computations in an efficient way and speeds up the time required to make calculations.
The best way to illustrate Felsenstein’s algorithm is through an example, which is presented in the panels below. We are trying to calculate the likelihood for a three-state character on a phylogenetic tree that includes six species.
Figure 8.4A. Each tip and internal node in the tree has three boxes, which will contain the probabilities for the three character states at that point in the tree. The first box represents a state of 0, the second state 1, and the third state 2. Image by the author, can be reused under a CC-BY-4.0 license.
1. The first step in the algorithm is to fill in the probabilities for the tips. In this case, we know the states at the tips of the tree. Mathematically, we state that we know precisely the character states at the tips; the probability that that species has the state that we observe is 1, and all other states have probability zero:
1. Next, we identify a node where all of its immediate descendants are tips. There will always be at least one such node; often, there will be more than one, in which case we will arbitrarily choose one. For this example, we will choose the node that is the most recent common ancestor of species A and B, labeled as node 1 in Figure 8.2B.
2. We then use equation 7.6 to calculate the conditional likelihood for each character state for the subtree that includes the node we chose in step 2 and its tip descendants. For each character state, the conditional likelihood is the probability, given the data and the model, of obtaining the tip character states if you start with that character state at the root. In other words, we keep track of the likelihood for the tipward parts of the tree, including our data, if the node we are considering had each of the possible character states. This calculation is:
$L_P(i) = (\sum\limits_{x \in k}Pr(x|i,t_L)L_L(x)) \cdot (\sum\limits_{x \in k}Pr(x|i,t_R)L_R(x)) \label{8.7}$
where i and x are both indices for the k character states, with sums taken across all possible states at the branch tips (x), and terms calculated for each possible state at the node (i). The two pieces of the equation are the left and right descendant of the node of interest. Branches can be assigned as left or right arbitrarily without affecting the final outcome, and the approach also works for polytomies (but the equation is slightly different). Furthermore, each of these two pieces itself has two parts: the probability of starting and ending with each state along the two branches being considered, and the current conditional likelihoods that enter the equation at the tips of the subtree (LL(x) and LR(x)). Branch lengths are denoted as tL and tR for the left and right, respectively.
One can think of the likelihood "flowing" down the branches of the tree, and conditional likelihoods for the left and right branches get combined via multiplication at each node, generating the conditional likelihood for the parent node for each character state (LP(i)).
Consider the subtree leading to species A and B in the example given. The two tip character states are 0 (for species A) and 1 (for species B). We can calculate the conditional likelihood for character state 0 at node 1 as:
$L_P(0) = \left(\sum\limits_{x \in k}Pr(x|0,t_L=1.0)L_L(x)\right) \cdot \left(\sum\limits_{x \in k}Pr(x|0,t_R=1.0)L_R(x)\right) \label{8.8}$
Next, we can calculate the probability terms from the probability matrix P. In this case tL = tR = 1.0, so for both the left and right branch:
$\mathbf{Q}t = \begin{bmatrix} -2 & 1 & 1 \ 1 & -2 & 1 \ 1 & 1 & -2 \ \end{bmatrix} \cdot 1.0 = \begin{bmatrix} -2 & 1 & 1 \ 1 & -2 & 1 \ 1 & 1 & -2 \ \end{bmatrix} \label{8.9}$
So that:
$\mathbf{P} = e^{Qt} = \begin{bmatrix} 0.37 & 0.32 & 0.32 \ 0.32 & 0.37 & 0.32 \ 0.32 & 0.32 & 0.37 \ \end{bmatrix} \label{8.10}$
Now notice that, since the left character state is known to be zero, LL(0)=1 and LL(1)=LL(2)=0. Similarly, the right state is one, so LR(1)=1 and LR(0)=LR(2)=0.
We can now fill in the two parts of equation 8.2:
$\sum\limits_{x \in k}Pr(x|0,t_L=1.0)L_L(x) = 0.37 \cdot 1 + 0.32 \cdot 0 + 0.32 \cdot 0 = 0.37 \label{8.11}$
and:
$\sum\limits_{x \in k}Pr(x|0,t_R=1.0)L_R(x) = 0.37 \cdot 0 + 0.32 \cdot 1 + 0.32 \cdot 0 = 0.32 \label{8.11B}$
So:
LP(0)=0.37 ⋅ 0.32 = 0.12.
This means that under the model, if the state at node 1 were 0, we would have a likelihood of 0.12 for this small section of the tree. We can use a similar approach to find that:
(eq. 8.13)
LP(1)=0.32 ⋅ 0.37 = 0.12.
LP(2)=0.32 ⋅ 0.32 = 0.10.
Now we have the likelihood for all three possible ancestral states. These numbers can be entered into the appropriate boxes:
1. We then repeat the above calculation for every node in the tree. For nodes 3-5, not all of the LL(x) and LR(x) terms are zero; their values can be read out of the boxes on the tree. The result of all of these calculations:
1. We can now calculate the likelihood across the whole tree using the conditional likelihoods for the three states at the root of the tree.
$L = \sum\limits_{x \in k} \pi_x L_{root} (x) \label{8.14}$
Where πx is the prior probability of that character state at the root of the tree. For this example, we will take these prior probabilities to be uniform, equal for each state (πx = 1/k = 1/3). The likelihood for our example, then, is:
$L = 1/3 ⋅ 0.00150 + 1/3 ⋅ 0.00151 + 1/3 ⋅ 0.00150 = 0.00150 \label{8.15}$
Note that if you try this example in another software package, like GEIGER or PAUP*, the software will calculate a ln-likelihood of -6.5, which is exactly the natural log of the value calculated here.
8.0S: 8.S: Fitting models of discrete character evolution (Summary)
In this chapter I describe how Felsenstein’s pruning algorithm can be used to calculate the likelihoods of Mk and extended-Mk models on phylogenetic trees. I have also described both ML and Bayesian frameworks that can be used to test hypotheses about character evolution. This chapter also includes a description of the “total garbage” test, which will tell you if your data has information about evolutionary rates of a given character.
Analyzing our example of lizard limbs shows the power of this approach; we can estimate transition rates for this character over macroevolutionary time, and we can say with some certainty that transitions between limbed and limbless have been asymmetric. In the next chapter, we will build on the Mk model and further develop our comparative toolkit for understanding the evolution of discrete characters.
References
Bergmann, P. J., and D. J. Irschick. 2012. Vertebral evolution and the diversification of squamate reptiles. Evolution 66:1044–1058. Wiley Online Library.
Brandley, M. C., J. P. Huelsenbeck, and J. J. Wiens. 2008. Rates and patterns in the evolution of snake-like body form in squamate reptiles: Evidence for repeated re-evolution of lost digits and long-term persistence of intermediate body forms. Evolution. Wiley Online Library.
Felsenstein, J. 2004. Inferring phylogenies. Sinauer Associates, Inc., Sunderland, MA.
Felsenstein, J. 1973. Maximum likelihood and minimum steps methods for estimating evolutionary trees from data on discrete characters. Syst. Biol. 22:240–249. Oxford University Press.
Pyron, R. A., F. T. Burbrink, and J. J. Wiens. 2013. A phylogeny and revised classification of squamata, including 4161 species of lizards and snakes. BMC Evol. Biol. 13:93. bmcevolbiol.biomedcentral.com.
Rosindell, J., and L. J. Harmon. 2012. OneZoom: A fractal explorer for the tree of life. PLoS Biol. 10:e1001406. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/08%3A_Fitting_Models_of_Discrete_Character_Evolution/8.07%3A_Appendix_-_Felsenstein's_Pruning_Algorithm.txt |
The simple Mk model provides a useful foundation for a number of innovative methods. These methods capture evolutionary processes that are more complicated than the original model, including models that vary through time or across clades. Modeling more than one discrete character at a time allows us to test for the correlated evolution of discrete characters.
09: Beyond the Mk Model
Frog reproduction is one of the most bizarrely interesting topics in all of biology. Across the nearly 6,000 species of living frogs, one can observe a bewildering variety of reproductive strategies and modes (Zamudio et al. 2016). As children, we learn of the “classic” frog life history strategy: the female lays jellied eggs in water, which hatch into tadpoles, then later metamorphose into their adult form [e.g. Rey (2007); Figure 9.1A]. But this is really just the tip of the frog reproduction iceberg. Many species have direct development, where the tadpole stage is skipped and tiny froglets hatch from eggs. There are foam-nesting frogs, which hang their eggs from leaves in foamy sacs over streams; when the eggs hatch, they drop into the water [e.g. Fukuyama (1991); Figure 9.1B]. Male midwife toads carry fertilized eggs on their backs until they are ready to hatch, at which point they wade into water and their tadpoles wriggle free [Marquez and Verrell (1991); Figure 9.1C]. Perhaps most bizarre of all are the gastric-brooding frogs, now thought to be extinct. In this species, female frogs swallow their fertilized eggs, which hatch and undergo early development in their mother’s stomach (Tyler and Carter 1981). The young were then regurgitated to start their independent lives.
The great diversity of frog reproductive modes brings up several key questions that can potentially be addressed via comparative methods. How rapidly do these different types of reproductive modes evolve? Do they evolve more than once on the tree? Were “ancient” frogs more flexible in their reproductive mode than more recent species? Do some clades of frog show more flexibility in reproductive mode than others?
Many of the key questions stated above do not fall neatly into the Mk or extended-Mk framework presented in the previous characters. In this chapter, I will review approaches that elaborate on this framework and allow scientists to address a broader range of questions about the evolution of discrete traits.
To explore these questions, I will refer to a dataset of frog reproductive modes from Gomez-Mestre et al. (2012), specifically data classifying species as those that lay eggs in water, lay eggs on land without direct development (terrestrial), and species with direct development (Figure 9.2).
Figure 9.2. Ancestral state reconstruction of frog reproductive modes. Data from Gomez-Mestre et al. (2012). Image by the author, can be reused under a CC-BY-4.0 license.
9.02: Beyond the Mk model
In Chapter 8, we considered the evolution of discrete characters on phylogenetic trees. These models fall under the general category of continuous-time Markov models, which consider a process that can occupy two or more states. Transitions occur between those states in continuous time. The Markov property means that, at some time t, what happens next in the model depends only on the current state of the process and not on anything that came before.
In evolutionary biology, the most detailed work on continuous time Markov models has focused on DNA or protein sequence data. As mentioned earlier, an extremely large set of models are available for modeling and analyzing these molecular sequences. One can also elaborate on these models by adding rate heterogeneity across sites (e.g. the gamma parameter, as in GTR + Γ), or other complications related to mechanisms of sequence evolution (for a review, see Liò and Goldman 1998).
However, there are two important differences between models of sequence evolution and models of character change on trees that make our task distinct from the task of modeling DNA or amino acid sequences. First, when analyzing molecular sequences, one typically has data for many thousands (or millions) of characters. Data sets for other characters – like the phenotypic characters of species – are typically much smaller (and harder to collect). Second, sequence analysis very often assumes that each character evolves independently from all other characters, but that all characters (or at least certain large subsets of those characters) evolve under a shared model (Liò and Goldman 1998; Yang 2006). This means that, for example, the frequency of transitions between A and C at one location in a gene sequence contribute information about the same transition in a different location in the sequence.
Unfortunately, when analyzing morphological character evolution, we are often interested in single characters, and the use of shared models across characters seems impossible to justify. There is usually no equivalence between different character states for different characters: an A is an A for sequences, but a “1” in a character matrix usually corresponds to the presence of two completely different characters. The consequence of this difference is reflected in the statistical property of multivariate data. For gene sequence problems, adding more data in the form of additional characters (sites) makes model-fitting easier, as each site adds information about the overall (shared) model across sites. With character data, additional characters do not make the problem any easier, because each character comes with its own model parameters. In fact, we will see that when considering character correlations using a generalized Mk model, adding characters actually makes the problem more and more difficult. Perhaps these issues partially explain the slow pace of model development for fitting discrete characters to trees. There are a few potential solutions, such as threshold models [Felsenstein (2005); Felsenstein (2012); discussed below]. More work is desperately needed in this area.
In this chapter, we will first discuss extensions of Mk models that allow us to add complexity to this simple model. We also discuss threshold models, a relatively new approach in comparative methods that is distinct from Mk models and has some potential for future development. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/09%3A_Beyond_the_Mk_Model/9.01%3A_The_Evolution_of_Frog_Life_History_Strategies.txt |
The three Pagel models discussed in Chapter 6 (Pagel 1999a,b) can also be applied to discrete characters. We do not create a phylogenetic variance-covariance matrix for species under an Mk model, so these three models can, in this case, only be interpreted in terms of transformations of the tree’s branch lengths. However, the meaning of each parameter is the same as in the continuous case:
• λ scales the tree from its original form to a “star” phylogeny, and thus quantifies whether the data fits a tree-based model or one where all species are independent;
• δ captures changes in the rate of trait evolution through time; and
• κ scales branch lengths between their original values and one, and mimics a speciational model of evolution (but only if all species are sampled and there has been no extinction).
Just as with discrete characters, the three Pagel models can be evaluated in either an ML / AICc framework or using Bayesian analysis. One might expect these models to behave differently when applied to discrete rather than continuous characters, though. The main reason for this is that discrete characters, when they evolve rapidly, lose historical information surprisingly quickly. That means that models with high rates of character transitions will be quite similar to both models with low “phylogenetic signal” (i.e. λ = 0) and with rates that accelerate through time (i.e. δ > 0). This indicates potential problems with model identifiability, and warns us that we might not have good power to differentiate one model from another.
We can apply these three models to data on frog reproductive modes. But first, we should try the Mk and extended-Mk models. Doing so, we find the following results:
Model lnL AICc ΔAICc AIC Weight
ER -316.0 633.9 38.0 0.00
SYM -296.6 599.2 3.2 0.17
ARD -291.9 596.0 0.0 0.83
We can interpret this as strong evidence against the ER model, with ARD as the best, and weak support in favor of ARD over SYM. We can then try the three Pagel parameters. Since the support for SYM and ARD were similar, we will add the extra parameters to each of them. Doing so, we obtain:
Model Extra parameter lnL AICc ΔAICc AIC weight
ER -316.0 633.9 38.0 0.00
SYM -296.6 599.2 5.2 0.02
ARD -291.9 596.0 0 0.37
SYM λ -296.6 601.2 5.2 0.02
SYM κ -296.6 601.2 5.2 0.02
SYM δ -295.6 599.2 3.2 0.07
ARD λ -292.1 598.3 2.3 0.11
ARD κ -291.3 596.9 0.9 0.24
ARD δ -292.4 599.0 3.0 0.08
Notice that our results are somewhat ambiguous, with AIC weights spread fairly evenly across the three Pagel models. Interestingly, the overall lowest AIC score (and the most AIC weight, though only just more than 1/3 of the total) is on the ARD model with no additional Pagel parameters. I interpret this to mean that, for these data, the standard ARD model with no alterations is probably a reasonable fit to the data compared to the Pagel-style alternatives considered above, especially given the additional complexity of interpreting tree transformations in terms of evolutionary processes. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/09%3A_Beyond_the_Mk_Model/9.03%3A_Pagel%E2%80%99s_%CE%BB%2C_%CE%B4%2C_and_%CE%BA.txt |
Another generalization of the Mk model we might imagine is a Mk model where rate parameters vary, either across clades or through time. There is some recent work along these lines, with two approaches that consider the possibility that rates of evolution for an Mk model vary on different branches of a phylogenetic tree (Marazzi et al. 2012; Beaulieu et al. 2013).
We can understand how these methods work in general terms by considering a simple case where the rate of character evolution is faster in one clade than in the rest of the tree. This is the discrete-character version of the approaches for continuous characters that I discussed in Chapter 6 (O’Meara et al. 2006; Thomas et al. 2006). The simplest way to implement a multi-rate discrete model is to directly incorporate variation across models into the pruning algorithm that is used to calculate the Mk model on a phylogenetic tree (see FitzJohn 2012 for implementation).
One can, for example, consider a model where the overall rate of evolution varies between clades in a phylogenetic tree. To do this, we can specify the background rate of evolution using some transition matrix Q, and then assume that within our focal clade evolution can be modeled with some scalar value r, such that the new rate matrix is rQ. Given Q and r, one can calculate the likelihood for this model using the pruning algorithm, modified in such a way that the appropriate transition matrix is used along each branch in the tree; one can then maximize the likelihood of the model for all parameters (those describing Q, as well as r, which describes the relative rate of evolution in the focal clade compared to the background).
In even more general terms, we will consider the situation where we can describe the model of evolution using a set of Q matrices: Q1, Q2, …, Qn, each of which can be assigned to a particular branch in a phylogenetic tree (or be assigned to branches depending on some other character that influences the rate of the focal character; Marazzi et al. 2012). The only limit here is that each Q matrix adds a new set of model parameters that must be estimated from the data, and it is easy to imagine this model becoming overparametized. If we imagine a model where every branch has its own Q-matrix, then we are actually describing the “no common mechanism” model (Tuffley and Steel 1997; Steel and Penny 2000), which is statistically identical to parsimony. It should also be possible to create a method that explores all models connecting simple Mk and the no common mechanism model using the machinery of reversible-jump MCMC, although I do not think such an approach has ever been implemented (but see Huelsenbeck et al. 2004).
One can also describe a situation where rate parameters in the Q matrix change through time. This might follow a constant pattern of increase or decrease through time, or might be related to some external driver like temperature. One can mimic models where rates change through time by changing the branch lengths of phylogenetic trees. If deep branches are lengthened relative to shallow branches, as is done by Pagel's δ, then we can fit a model where rates of evolution slow through time; conversely, lengthening shallow branches relative to deep ones creates a model where the overall rate of evolution accelerates through time (see FitzJohn 2012).
More work could certainly be done in the area of time-varying rates of change. The most general approach is to write a set of differential equations that describe the changes in character state along single branches in the tree. Parameters in those equations can be made to vary, either through time or even in a way that is correlated with some external variable hypothesized to influence rates of change, like temperature or rainfall. Given such a model, the reverse-time approach of Maddison et al. (2007) can then be used to fit general time-varying (or even clade-varying) Mk models to data (see Uyeda et al. 2016). | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/09%3A_Beyond_the_Mk_Model/9.04%3A_Mk_models_where_parameters_vary_across_clades_and/or_through_time.txt |
Recently, Joe Felsenstein (2005, 2012) introduced a model from quantitative genetics, the threshold model, to comparative methods. Threshold models work by modeling a discrete character as underlain by some other, unobserved, continuous trait (called the liability). If the liability crosses a certain threshold value, then the discrete state changes. More specifically, we can consider a single trait, y, with two states, 0 and 1, which is in turn determined by some underlying continuous variable, x, called the liability. If x is greater than the threshold, t, then y is 1; otherwise, y is 0. Felsenstein (2005) assumes that x evolves under a Brownian motion model, although other models like OU are, in principle, possible.
We can find the likelihood to this model by considering the observations of character states at the tips of the tree. We observe the state of each species, yi. We do not know the liability values for these species. However, we treat these liabilities as unobserved and consider their distributions. Under a Brownian motion model, we know that the liabilities will follow a multivariate normal distribution (see chapter 3). We can calculate the probability of observing the data (yi) by finding the integral of the distributions of liabilities on the side of the threshold that matches the data. So if the distribution of the liability for species i is pi(x), then:
$p(y_i = 0) = {\int\limits_{-\infty}^{t} p_i (x) dx} \label{9.1}$
and
$p(y_i = 1) = {\int\limits_{t}^{\infty} p_i (x) dx}$
(see Figure 9.3 for an illustration of this calculation, which is easier than it looks since there are standard formulas for finding the area under a normal distribution).
Figure 9.3. Illustration of the integral in Equation \ref{9.1}. For a trait with observed state zero we calculate the area under the curve from negative infinity to the threshold t. Image by the author, can be reused under a CC-BY-4.0 license.
One can fit this model using standard ML or Bayesian methods. Current implementations include an expectation-maximization (EM) algorithm (Felsenstein 2005, 2012) and a Bayesian MCMC (Revell 2014).
The threshold model differs in some key ways from standard Mk-type models. First of all, threshold characters evolve differently than non-threshold characters because of their underlying liability. In particular, the effective rate of change of the discrete character depends on the amount of time that a lineage has been in that character state. Characters that have just changed (say, from 0 to 1) are likely to change back (from 1 to 0), since the liability is likely to be near the threshold. By contrast, characters that have been in one state or the other for a long time tend to be more unlikely to change (since the liability is likely very far from the threshold). This difference matches biological intuition for some characters, where millions of years in one state means that change to a different state might be unlikely. This behavior of the threshold model can potentially account for variation in transition rates across clades without adding additional model parameters. Second, the threshold model scales to cover more than one character more readily than Mk models. Finally, in a threshold framework, it is straightforward to extend the model to include a mixture of both discrete and continuous characters – basically, one assumes that the continuous characters are like “observed liabilities,” and can be modeled together with the discrete characters.
9.06: Modeling more than one Discrete Character at a Time
It is extremely common to have datasets with more than one discrete character – in fact, one could argue that multivariate discrete datasets are the cornerstone of systematics. Nowadays, the most common multivariate discrete datasets are composed of genetic/genomic data. However, the foundations of modern phylogenetic comparative biology were laid out by Hennig (1966) and the other early cladists, who worked out methods for using discrete character data to obtain phylogenetic trees that show the evolutionary history of clades.
Almost all phylogenetic reconstruction methods that use discrete characters as data make a key assumption: that each of these characters evolves independently from one another. Mathematically, one calculates the likelihood for each single character, then multiplies this likelihood (or, equivalently, adds the log-likelihood) across all characters to obtain the likelihood of the data.
The assumption of character independence is clearly not true in general. In the case of morphological characters, structures often interact with one another to determine the fitness of an individual, and it seems very likely that those structures are not independent. In fact, some times we are specifically interested in whether or not particular sets of characters evolve independently or not. Methods that assume character independence a priori are not useful for that sort of framework.
Felsenstein (1985) made a huge impact on the field of evolutionary biology with a statistical argument about species: species can not be considered independent data points because they share an evolutionary history. Species that are most closely related to one another will covary, simply due to that shared history. Nowadays, one cannot publish a paper in comparative biology without accounting directly for the non-independence of species that evolve on a tree. However, it is still very common to ignore the non-independence of characters, even when they occur together in the same organism! Surely the shared developmental history of two characters within one body commonly leads to correlations across these characters. | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/09%3A_Beyond_the_Mk_Model/9.05%3A_Threshold_Models.txt |
Hypotheses in evolutionary biology often relate to whether two (or more) traits affect the evolution of one another (Chapter 5). One can have a standard correlation between two discrete traits if knowing the state of one trait allows you to predict the state of the other. However, in evolution, these correlations will arise due to the shared patterns of relatedness across species. We are typically more interested in evolutionary correlations (Chapter 5). With discrete traits, we can define evolutionary correlations in a specific way: two discrete traits share an evolutionary correlation if the state of one character affects the relative transition rates of a second.
Imagine that we are considering the evolution of two traits, trait 1 and trait 2, on a phylogenetic tree. Both traits have two possible character states, one and zero. We can show these two traits visually as Figure 9.4.
In the figure, each trait has two possible transition rates, from 0 to 1 and from 1 to 0. For now, let’s assume that backwards and forward rates are equal. Any species can have one of four possible combinations of the two traits (00, 01, 10, or 11). We can draw the transitions among these four combinations as Figure 9.5.
Figure 9.5. Transitions among states for two traits with two character states each where characters evolve independently of one another. Image by the author, can be reused under a CC-BY-4.0 license.
In Figure 9.6, I have marked the distinct rates with different rectangles – black represents changes in trait 1, while checkered is changes in trait 2. Notice that, in this figure, we are assuming that the two traits are independent. That is, in this model the transition rates of trait one do not depend on the state of trait 2, and vice-versa. What would happen to our model if we allow the traits to evolve in a dependent manner?
Figure 9.6. Transitions among states for two traits with two character states each where characters evolve at rates that depend on the character state of the other trait. Image by the author, can be reused under a CC-BY-4.0 license.
Notice that in Figure 9.6, we have four different transition rates. Consider first the solid rectangles. The grey rectangle represents the transition rate for trait 1 when trait 2 has state 0, while the black rectangle represents the transition rate for trait 1 when trait 2 has state 1. If these two rates are different, then the traits are dependent on each other – that is, the rate of evolution of trait 1 depends on the character state of trait 2.
These two models have different numbers of parameters, but are relatively easy to fit using the maximum-likelihood approach outlined in this chapter. The key is to write down the transition matrix (Q) for each model. For example, a transition matrix for model in figure 9.4 is:
$\mathbf{Q} = \begin{bmatrix} -q_1 - q_2 & q_1 & q_2 & 0\ q_1 & -q_1 - q_2 & 0 & q_2\ q_2 & 0 & -q_1 - q_2 & q_1\ 0 & q_2 & q_1 & -q_1 - q_2\ \end{bmatrix} \label{9.2}$
In the matrix above, each row and column corresponds to a particular combination of states for character 1 and 2: (0,0), (0,1), (1,0), and (1,1). Note that some possible transitions in this model have rate 0, meaning they do not occur. These are transitions that would require both characters to change exactly simultaneously (e.g. (0,0) to (1,1) – a possibility that is excluded from this model.
Similarly, we can write a transition matrix for the model in figure 9.5:
$\mathbf{Q} = \begin{bmatrix} -q_1 - q_2 & q_1 & q_2 & 0\ q_1 & -q_1 - q_3 & 0 & q_3\ q_2 & 0 & -q_2 - q_4 & q_4\ 0 & q_3 & q_4 & -q_3 - q_4\ \end{bmatrix} \label{9.3}$
Notice that the simple, 2-parameter independent evolution model is a special case of the more complex, 4-parameter dependent model. Because of this, we can compare the two with a likelihood ratio test. Alternatively, AIC or Bayes factors can be used. If we find support for the 4-parameter model, we can conclude that the evolution of at least one of the two characters depends on the state of the other.
It is worth noting that there are other models that one can fit for the evolution of two binary traits that I did not discuss above. For example, one can model the situation where the two traits each have different forwards and backwards rates, but are evolving independently. This is a four-parameter model. Additionally, one can allow both forward and backward rates to differ and to depend on the character state of the other trait: an eight-parameter model. This is the model one needs to truly see a correlation between the two characters, one where certain combinations tend to accumulate in the tree. All of these models – and others not described here – can be compared using AIC, BIC, or Bayes Factors. Pagel and Meade (2006) describe a particularly innovative and synthetic method to test hypotheses about correlated evolution of discrete characters in a Bayesian framework using reversible-jump MCMC.
One can also test for correlations among discrete characters using threshold models. Here, one tests whether or not the liabilities for the two characters evolve in a correlated fashion. More specifically, we can model liabilities for the two threshold characters using a bivariate Brownian motion model, with some evolutionary covariance σ122 between the two liabilities. We can then use either ML or Bayesian methods to determine if the evolutionary covariance between the two characters is non-zero (following the methods described in chapter 5, but using likelihoods based on discrete characters as described above). | textbooks/bio/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/09%3A_Beyond_the_Mk_Model/9.07%3A_Testing_for_non-independent_evolution_of_different_characters.txt |
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