Aesthetics, mathematics, physics and biology

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art, biology, evolution, Jackson Pollock, mathematics, Natural selection, physics, Quantitative genetics, science, Stephen Jay Gould

One of Namuth’s many photos of Jackson Pollock painting with his “drip” method. (Photo credit: Wikipedia)

I’ve just started reading Paul J. Nahin’s book Doctor Euler’s Fabulous Formula about one of Leonhard Euler‘s famous equations. The preface establishes the author’s thesis that the great thing about Euler’s formula is that it is beautiful because it is the result of skill (or as the author says “disciplined reason”). He goes on to compare the beauty of a mathematical formula, and specifically mathematical formulae as expressions of concepts in physics, to the work of great artists. Beauty in art is something we can all relate to. What surprised me is that he based this comparison on the dichotomy between “disciplined artists,” such as Michelangelo and “undisciplined artists,” such as Jackson Pollock. To call what “two-year olds routinely do” on a daily basis art, he says, “is delusional or at least deeply confused…” (xix).

Nahin was wrong about Jackson Pollock. He knows he is wrong, i.e. I don’t think he really believes this, but this false dichotomy is highly illustrative. He happens to be wrong in a way that we can learn a lot from.  I would like to show that he’s illustrating the particular value of mathematics in evolutionary biology.  The value of mathematics in biology can only be seen if the level of application of models matches the proper place of the forces it models. If our application of broad theories is too narrow, then we will not find beautiful theories useful. On the other hand, if we view selection as a very broad force, as Stephen Jay Gould did in Wonderful Life, then we can see the “usefulness” of evolutionary theory.

NYC – MoMA: Jackson Pollock’s The She-Wolf (Photo credit: wallyg)

Jackson Pollock was disciplined and skilled. Consider several facts about his career, training and technique. Firstly, he was a trained artist. He worked hard to develop his techniques. If you look at his early work (e.g. “She-wolf”), it’s certainly not what he’s most remembered for, but it is distinctive. If he could have just splattered paint then why would he bother to develop all that technique? People took him seriously as an artist before he developed his splattering technique. Next consider the drip paintings that he’s remembered for. These paintings were the result of careful consideration and a disciplined technique. Just a few examples: he positioned his canvas on the floor; he carefully mixed the paint to a particular consistency to achieve the kind of “splatter” that he needed; he used carefully chosen brushes and other devices. Finally he chose colors that made sense in order to make a particular artistic statement.

Life, the subject of biology, is a Jackson Pollock painting. I enjoy a mathematical argument because it is logical, internally consistent, one thing builds on another. I can see what it is made out of. I know the goals the entire time the argument is building. Wouldn’t it be great to apply that kind of thinking to understanding living things and their origins? Yeah, that would be great, but it’s incredibly hard for two reasons. Since life is a Jackson Pollock painting, the constraints are incredibly broad; so broad that life has huge leeway to accomplish the same thing in different ways. “Higher fitness” is not very specific. The paint spatters in different ways every time, regardless of its consistency and color palette being the same. The other reason is a confusion about where the predictions of theory are supposed to lie. Because selection is very very broad, we need to make predictions that are similarly broad. We can use the theory we have now to predict that selection would favor earlier age of maturity. That doesn’t mean we can predict whether that age is six months or two years. There are also different developmental ways to accomplish that. The theory we have doesn’t predict whether faster cell growth or slackened mate preferences will produce earlier age of maturity.

Biological mathematical models, if they are to be beautiful in the same way that physical models are, need to be broad, in the same way that Jackson Pollock’s constraints were broad. Take the most beautiful equation in biology, the Price Equation, for example. The Price Equation is beautiful because it is simple, so easy to derive that it seems it must be true, and you can do all kinds of things with it. You can derive almost any model of evolution from the Price Equation (try it!). You can also deal with almost every kind of selection at any level, and genetic drift. Why? Because it is so broad that actually applying it to a population would be ridiculous. The Price Equation is exact, which means that the equation includes more information than we can ever hope to measure in a natural population. The only way to make the application of the equation exact is to dial down the constraints so much that the prediction the equation makes is almost worthless. In other words, to make the equation exact, you have to impose such strong selection that you can predict the result without the equation. Mike Wade might disagree with me about this, but I can bet he won’t disagree about the equation’s beauty. The Price Equation is so broad that Martin Nowak has gone so far as to call it a “mathematical tautology” (also available at arXiv).

Another example, slightly less contentious, but not quite as obvious, are the predictions of life-history theory. Russ Lande and Brian Charlesworth‘s equations (derived from Guess What) make definite, broad predictions about the evolution of age at first reproduction, reproductive output and other life-history traits. The breadth of these predictions matches the strength of selection to enact changes at the genotypic level. What I mean is that as long as evolution is proceeding in the particular direction predicted by Lande and Charlesworth, then the model is justified. The actual genotypic or even morphological changes, or the diversity of adaptations at a particular level, doesn’t matter to the predictions of the theory. It also doesn’t matter whether you’re talking about yeast, fruit flies, elephant birds or dinosaurs. That’s the level of prediction we have with the theory of selection. It’s not precise like Rembrandt or even early Picasso. It’s a lot more like Jackson Pollock. It’s a mess, but it’s a carefully constrained, disciplined mess that is beautiful itself.

Jackson Pollock; Mural Detail II (Photo credit: notanyron)

This morning I’ve realized yet again that the reason I love mathematics is largely aesthetic. I love math for the same reason that I love listening to a great piece of music. Beautiful models and theories are useful, Nahin and I contend, not because they are inherently “correct,” but because they inspire people to work hard at verifying and refining their logical consistency. Nahin points out that Newton and Einstein’s theories of graviation are “wrong” in the sense of making predictions that still hold true. But they are beautiful. We all say “yuck!” when we see someone try to fit a logistic curve to real data, but we don’t always know why we cringe. We cringe because we all know that the logistic wasn’t so well-studied because it was correct. It was so favored because it’s a beautiful equation. It’s as beautiful as the Mandelbrot set or Euler’s Formula, and it’s easy to teach to undergraduates. It makes sense. However, demographers and ecologists all know that it doesn’t really describe human populations. A.J. Lotka didn’t live to see that, but that doesn’t mean his time was wasted (see Lotka, Alfred J. 1998. Analytical theory of biological populations. New York: Plenum Press).

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Holidays 2013: Research Update

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evolution, figshare, open access, open access journal, PeerJ, PLoS Biology, research, science, sexual selection

Merry Christmas, it’s time for an update on my research. My first project on age-dependent sexual signals, long nicknamed Project Zero during the four years (!) I’ve been working on it has been published by PeerJ. Not only published, but featured on the homepage and the blog. There’s an interview there where you can read all about it, so I will skip the details here. This journal is open access, so you can read the article for free. You can also download the simulation code and all the data for the figures at figshare.

My next research project has been submitted to Ecology and Evolution, another open access journal, published by Wiley. I have already put the manuscript on ArXiv, so go read it!  I also presented this at the Evolution conference over the summer.  The scenario I describe in this paper is that when females have preferences for older males, as they would for an age-dependent trait, they will inevitably encounter deleterious mutations. Since mutations pile up in the male germ line with age, more attractive, older males may not necessarily yield more fit offspring.  If the female preference is directly costly, then natural selection may eliminate the preference.  What I found instead is that germ line mutation actually supplies the necessary genetic variation for selection to act, in other words, it reinforces sexual selection and further facilitates evolution of extravagance.

I’m still working through the math on a third paper.  The subject here is the evolution of female choosiness as a function of age.  Some studies show that females are more choosy when they are older, while others show that females are more choosy when they are young.  There are arguments on both sides suggesting how selection produces these patterns.  We just had a lab meeting where my colleagues helped me to clarify how to build the model.  My hope is to have this one ready for publication sometime in the early spring.

Another paper with my name on it was published in May, although it has been on the web and finished for so long that I didn’t notice its publication in PLoS Biology, the flagship open access biology journal. This article was a collaboration with people I mainly met on Twitter. We wrote an opinion piece on how biologists of all disciplines, but especially in ecology and evolution, could embrace putting their work online at preprint servers like ArXiv, Figshare, PeerJ Preprints, and F1000Research. This practice is common in mathematics and physics, and although it’s gaining popularity in biology, most biologists I know recoil in disgust at the thought of putting their work online before it’s peer-reviewed. Well, actually these days the younger scientists respond with interest rather than recoil in shock.

The funny thing about peer review is that it takes a really long time to get stuff published.  By “published” I mean “done with.”  I have been working on the first project above for over four years if you count the time I spent programming the multilocus genetics library.  I have submitted it to four journals, and it was outright rejected from the first three for various reasons, most of them not scientific.  What I don’t like is that I would like to spend time working on newer things.  I’m simply interested in new things now.  This reminds me of the situation in Pink Floyd’s 1980s and 1990s tours, where some fans wanted them to play their classics, and they wanted to play their new music (some of which they actually put a lot of effort into writing, and thought was better music, but what do they know?). However, I am grateful for all the chances I’ve had to revise that paper, since my understanding of science and how to do it are totally different four years later.  Even in the weeks since I submitted the paper to PeerJ and got the (very helpful!) reviews back, I have found better ways to express the ideas in the paper and improve the writing.  It’s a double-edged sword, and I’m not quite ready to do away with it.

The other drawback is not getting the research into a place where people can see it.  I’ve been showing that model to people for all but six months of the time I’ve been working on it, and it has taken another three years to get one step closer to publication.  That’s why we have arXiv and figshare.  People can see it pre-peer-review and get ideas from it.  They can even cite it.

Related articles

• Figshare for sharing academic papers with their datasets (jilltxt.net)
• A book chapter I can’t share with you but some figures that i can, thanks to Figshare (biogeopen.wordpress.com)
• New Preprint Server Aims to Be Biologists’ Answer to Physicists’ arXiv (news.sciencemag.org)

Evolution 2013 Greatest Hits

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biology, David Sloan Wilson, evolution, Fairfield University, Gene duplication, human evolution, Joan Roughgarden, publishing, Salt Lake City, science

This past week I attend the annual “Evolution conference,” which is a joint meeting of The Society for the Study of Evolution, the American Society of Naturalists and the Society of Systematic Biologists. Evolution 2013 was held in Snowbird, Utah, a ski resort and conference center that feels isolated despite being right up the road from Salt Lake City. I also attended a special workshop for undergraduate educators (there was also a workshop for K-12 educators). This workshop was so popular that they expanded the attendance from thirty participants to fifty. The focus on education was just one trend I noticed at this year’s meeting, where I saw many changes from when I first started attending meetings fifteen years ago.

View of Salt Lake valley from 11,000 foot summit of Hidden Peak, reached via Snowbird tram. (Photo credit: Wikipedia)

For those of you that haven’t attended one of these meetings, here’s a brief run-down of how it goes: during the day scientists present their research in twelve-minute talks. These are arranged in fifteen-minute blocks so that people have time to take questions and go from one room to another: there are up to ten of these sessions going on at the same time, hence they are called “concurrent sessions.” This is analogous to what people used to call “reading a paper” or “giving a paper,” but we call it “giving a talk” or “doing a talk.” In the evening there’s a long talk by a society president or someone getting a major award, and then people gather for a social event, usually a poster session. A poster session is when researchers present their data literally on a poster tacked to a wall, and stand beside it while people drinking wine and munching hors d’oeuvres walk by and receive five-minute mini-talks on the data in the poster. I presented a poster on my sexual selection research.

Interesting Talks and Posters

I found many of the talks and posters at the meeting very interesting. Going to scientific meetings is where we see the real communication in the scientific community. At a symposium entitled “Evolution out of bounds,” several speakers examined the promise and failings of evolution when applied to human problems.

David Sloan Wilson

David Sloan Wilson presented his collaborations with economists and the results of a project to help academically failing high-school students using the principles of evolution of cooperation. Joan Roughgarden presented an organismically based model of the evolution of physical intimacy. She had previously announced her talk as “Evolution of human sexuality,” but opened by apologizing and saying we can’t discuss the evolution of something we haven’t described completely. Roughgarden put forth the radical idea that we could consider immediate organismal causes for certain behaviors (i.e. something she called “fun”) before considering evolutionary consequences.

In regular paper sessions Michael Sheehan of Arizona University presented evidence that there is selection for diversity of human faces to aid in individual recognition. Corlett Wood of University of Virginia showed what might happen when the environment induces a correlation between response to selection and heritability. And one of many presentations on archaic hominins showed that the epigenetic changes between modern humans and Neanderthals lead to broadening of knees and other Neanderthal features. A packed room listened to Michael Turelli admit (in his own special way) that he had completely screwed up the statistical analyses in a talk that he had already been giving as an invited speaker — and submitted for publication! Opposite my own poster at the Sunday night poster session was one of a few studies of the development of feathers in pigeons and doves: the authors narrowed down the cause of curly feathers in certain dove breeds to a single biochemical factor, due to a single nucleotide change.

I missed a talk that had people talking by Adi Livnat of Virginia Tech. Based on one of my colleagues’ descriptions, Livnat is dissatisfied with adaptive explanations of the origin of new genes. Whenever anyone questions the gospel of adaptationism, people definitely start talking. Livnat was going further than questioning however, so a lot of people were talking. I actually overheard someone saying “Did you hear that? Wow…”

A new form of neofunctionalization

The talk that excited me most was the last talk of the meeting, about two hours before the banquet. I’ll admit that I was only there because I had dinner with the speaker after striking up a random conversation in the hotel lobby. Myself, Ashley Byun of Fairfield University and her former student and colleague Russ Meister of UConn were looking for a place to eat dinner the night before the education workshop. At the time of Ashley’s talk there were fewer than twelve people in the room, backing up our concensus from dinner that most people would be off showering for the banquet or hiking. Despite all this, for very important reasons I liked the last talk of the meeting the best.

Mutation by gene duplication (Photo credit: Ethan Hein)

Dr. Byun presented a new idea for the neofunctionalization of duplicated genes: protein subcellular relocalization. For many reasons in eukaryotic organisms (for example, animals, plants, fungi) genes can become duplicated so that for a while there are two copies of a gene doing the same thing. Theory suggests that while two copies is better than one for some genes, as long as they produce the same product, they are relatively redundant, and one of the copies may acquire mutations that cripple its function over evolutionary time. It may then degrade into junk (“die”). However, the theory goes, the duplicate gene may acquire a new function. The most common explanation (i.e. the one we tell students in basic science courses) is that the duplicate would mutate into a gene producing a new protein.

Duplicate genes acquiring new functions by producing new proteins is incredibly unlikely. If we assume that crippling mutations are more common than “beneficial” mutations (that enhance the function of a protein), then there’s probably no way getting a new function would happen before the duplicate gene turns into biochemical sewage. Despite this problem, we commonly teach undergrads that this exact process is what made the Cambrian Explosion possible.

A nifty function of eukaryotic cells is how they package proteins and tell them where to go in the cell (or out of the cell). When proteins leave the site of protein synthesis, they are tagged with a sequence of amino acids (the “signal peptide”) that tells them where to go in the cell, e.g. to mitochondria, endoplasmic reticulum or a chloroplast. Normally the signal peptide is just a signal and when the gene reaches its destination, it is cleaved off and does not do anything else. If this sequence mutates, the protein product could get sent to a new part of the cell, where Byun points out it could perform a new function.

Apoptosis Network (Photo credit: sjcockell)

Now I don’t want to get too excited, but this is the first positive hypothesis I’ve seen for neofunctionalization, which could explain two of the most puzzling (for me) features of eukaryotes: the complexity of body plans and the dazzling, bewildering, uber-complicatedness of eukaryotic epistatic gene networks. As I mentioned above, we commonly teach that gene duplication, especially in homeobox genes, was the key to the diversification of animal body plans, but we don’t point out the exceedingly unlikely events that would make gene duplication and neofunctionalization actually work. Over the past year I taught cellular and developmental biology, and then genetics and molecular biology. As one example of eukaryotic complexity I learned that between the already complicated steps of apoptosis in Caenorhabditis elegans and the same process in Homo sapiens there’s about a gazillion things making it more complicated. An answer for this based on adaptation is that humans are more complex than worms, and therefore need more complex signaling pathways. This hypothesis ignores the fact that humans didn’t exist before the pathway got more complex, or why such complex organisms exist in the first place. We often assume it’s adaptation. An answer that I find more likely is that these biochemical networks are built by patching together steps that are slight modifications of completely unrelated functions. Eukaryotic cells are like Rube Goldberg machines built by a team of six-year-olds all working on only one piece at the same time. At the end they all get together and link things up.

Dr. Byun’s talk showed compelling evidence that duplicated genes that acquire mutations in the signal peptide are more likely to stay alive over evolutionary time instead of degrading into junk. In other words, acquiring a new cellular destination appears to keep duplicate genes from acquiring mutations that would cripple their biochemical function. Let’s be clear: she did not show that these mutations actually do send duplicate gene products to new organelles. However, she looked over a huge diversity of taxa and a huge number of genes, and almost all the data was significantly in favor her hypothesis.

I found Byun’s talk compelling for another reason: her speaking style. First of all she went slowly and explained her hypothesis clearly enough that a guy with minimal experience with cell biology could understand it. Secondly, she prepared the audience in two ways: by explaining which numerical values would support her hypothesis, and by showing snippets of data before blowing away the audience with a huge array of results. She walked slowly through what a hazard ratio is, then explained “If this ratio is greater than 1…less than 1…equal to one…then…” Then she showed a slide that had results for about five genes (as I recall). On this she explained a color code that showed supportive, not supportive, and inconclusive results, and walked the audience through why each cell in the table was coded the way it was. Then she flipped the slide and showed a huge table with many species and it was clear from the predominance of green color that most of the results supported her hypothesis. She did all that without saying “This is really complicated so I’m going to walk you through it…” (For non-initiates, that is a phrase that some speakers use, but many have advised me not to, because it may sound condescending to the audience).

Trends

I noticed several trends developing at this meeting:

1. Focus on education: not only did I attend a workshop for educators, but the meeting was interspersed with papers and discussions of how to better teach evolution, not just of how to convince basic science students against creationism
2. Experimental evolution: Rich Lenski and his academic offspring have shown that experimental evolution directly tests the hypotheses of evolutionary theory. I saw many talks using artificial selection, and not just in microbes.
3. Applying evolution to non-biological systems: two symposia were devoted to applying evolutionary biology to problems outside the typical realm of discourse. This used to be unpopular, but is now gaining momentum.
4. Multilevel science: some people might derisively call it reductionism, but what I saw was a lot of researchers testing behavioral, anatomical and systematic hypotheses, and then going to the very lowest levels of biological organization to find data. Now that gene sequencing is becoming less expensive, technology is enabling scientists to find support for their predictions at all levels of biological organization, from genes up to global geographic data, quite often in the same study (e.g. Michael Sheehan’s work on faces).

The importance of scientific meetings

Attending the Evolution 2013 meeting reinforced to me that scientific meetings are where the most important scientific communication takes place. I find this quite important, especially considering all the discussion of publishing lately. If we consider that what you hear at meetings is mostly new, very little of it published, and that scientists at meetings are face-to-face where they can discuss ideas spontaneously, then publication appears in its proper place: as a public record, a way of preserving research for posterity, not as the end-all goal of scientific exploration. Much of what is presented at meetings is preliminary, some of it is just new ideas people have. Very little of it is so polished that it isn’t open to amendment or suggestion. And most scientists are open to new ideas at the stage where they are: once a paper is published, the work has been done for almost a year, sometimes five years. At that point, all that is left is to deposit something for archaeologists to dig up. In other words, going to meetings like this reminds me that publications are not science, nor are they even the best way of communicating science. The best way to communicate science, or anything, is face-to-face.

Related articles

• New research suggests complex animals evolved more than once (sciencenews.org)
• Two mutations triggered an evolutionary leap 500 million years ago (sciencedaily.com)
• Mutation-Driven Evolution (sandwalk.blogspot.com)

Attractiveness and sexually-selected traits

Tags

biology, evolution, insects, Mate choice, science, sexual selection

Suppose we want to test the hypothesis that females choose particular males so they will have more attractive offspring. Verifying that hypothesis would require mate choice trials showing that particular males get chosen more often, and then repeating those trials with the offspring.  Researchers often simplify the matter by choosing some proxy of attractiveness like a particular trait — the size of an ornament, for example — and look for correlations in that trait between sires and sons. If we don’t find that sons inherit their father’s trait then can we conclude that the trait does not signal male genetic quality? What if we could show that attractive fathers tend to have attractive sons regardless of their trait sizes? This way we’re letting female insects, rather than male or female primates, tell us who’s an attractive insect.

A recent study by Fiona Ingleby from University of Exeter used fruit flies (Drosophila simulans) to address whether a particular sexual signal was reliable as an indicator of heritable male attractiveness. Several studies have shown that cuticular hydrocarbons (CHCs) affect mate choice in fruit flies. CHCs are volatile chemicals given off by the “skin” of a fly that may act as pheromones.  Ingleby and her colleagues John Hunt and David Hosken were particularly interested to see how environmental variation would affect CHCs and mate choice. They also wanted to see if there was a genotype-by-environment interaction (abbreviated “GxE“): the genotype and the environment the flies grow up in could both affect their phenotpyes (CHC production). Would males be attractive in all environments, or would they be attractive in some environments, and unattractive in others?

Ingleby captured flies in Greece, then after a few generations of laboratory domestication raised their offspring in the lab on two different types of food (oats and soy) and at two different temperatures (23C versus 25C). Her paper stresses that these four environments were not that different from each other, and not extreme, and yet they found fairly dramatic variation in phenotypes depending on the environment. Cuticular hydrocarbon (CHC) signal varied across environments, but the researchers found very strong genetic effects on attractiveness across all the environments. Sons tended to resemble their fathers in attractiveness regardless of environment. However, Ingleby, Hunt and Hosken concluded that CHCs are not a reliable indicator of male attractiveness, since the CHC phenotype changed so much across the tested environments.

The researchers considered a few alternative hypotheses to explain this apparent discrepancy: multiple traits, direct benefits and the possibility that other traits account for variation in attractiveness. Perhaps females use not just CHCs but also many other males traits and behaviors when selecting a mate. Females might be able to tell which males’ semen will be less harmful, or more beneficial. This would benefit females directly, instead of just her offspring. Also, the researchers point out, some aspects of CHC profile were reliable indicators of male genotype, and so females are probably using just some CHCs along with other traits to assess males.

The aspect of this study I find most intriguing is showing the heritability of attractiveness, instead of focusing on an arbitrarily chosen trait. Whenever a researcher hypothesizes about a trait being under selection, he hast to make a huge set of assumptions that can only be verified after painstaking data collection that may take decades. Most Ph.D. dissertations are done in less than ten years. Even if a researcher could make a pretty good guess about what traits should correlate with fitness, she would have to have really good luck in finding or creating environmental conditions that would provide good control over that trait. By the time that laboratory-level control is attained, we may have lost touch with the reality of how species live in the wild. Then an experiment might provide a good case study, but it tells us little about the actual evolution of a species. I hope to see more empirical studies that use attractiveness rather than arbitrarily selected characters.

Related articles

• Sexual selection with age-dependent mutation (lxmx.wordpress.com)
• Are humans monogamous? (theratchet.ca)
• Males’ superior spatial ability likely is not an evolutionary adaptation (esciencenews.com)

Mutation rates and paternal age

Tags

biology, evolution, genetics, iceland, mutation, nature, science

I briefly want to talk about a newly minted shiny article published in one of the scientific ‘glossy’ journals, those high-profile journals that lead to the bulk of the science-news coverage. This one was published in Nature a week or so ago.

I wanted to wait a bit before writing about it, and now that we are nearing the end of the typical article news cycle (1-2 weeks) it is time. Here is the main conclusion from the article: older fathers pass-on more new mutations to their children than younger ones. The most important background fact is that mutation is the stuff of evolution. It is the raw change that allows all organisms on earth to adapt. Biologists generally hypothesize that mutation rates are constant, meaning that DNA changes accumulate at a certain rate as organisms age. In a recent work Augustine Kong potentially challenged that idea (see main article figure below).

Some mutations are linked to disease, a child with more mutations is at higher risk, just by laws of probability, of getting the ‘disease’ mutation. Importance of this data to the realm of human disease is obvious. The substantial media coverage following Kong’s publication almost entirely focused on the disease aspect. Here are some headlines from the usual suspects: “Older fathers linked to Kids’s Autism and Schizophrenia risk” says Time Magazine, “Older dads may raise risk for autism in kids” adds FOX, “Father’s age is linked to risk of autism and schizophrenia” finishes the New York Times while omitting the kids aspect in their title all together.

Here is what the headline, in my opinion, should of read “Mutation rates are not constant, new Iceland population study suggests.” It is not an especially catchy title and I see that. Disease is bad for people, good for biologists. Biologists sell their work and build careers by putting words like, disease, autism, dawns, and MS into the titles of their papers and grants. Augustine Kong is not first to insight  media frenzy with ‘disease’, and that’s OK because journalists got to do their job and no story sells better than a story that everyone is afraid to hear.

I read the journal article and swam the sea of biased media coverage waiting for the bile and rage to loosen its grip. Then I wrote this, and tried to mention the real interesting bit, the implications of this work on how biologists estimate divergence. Mutations are assumed to accumulate in a clocklike way, same rate over time for each type of organism. This allows comparisons between organisms, like humans and monkeys and squid and bacteria. Because of this constant ‘mutation clock’ biologists are able to say that genetically humans and monkeys are more similar that humans and tomatoes. Because of this ‘mutation clock’ biologists can estimate how long it takes for organisms to diverge and become different enough to be considered different species.

What Augustine Kong and friends showed is that the mutation rate is not constant, and they were as far as I know the first ones to actually calculate the rate of mutation increase with age.

With age fathers ‘give’ more new mutations to their children. Mechanistically, from the cell biology point of view, this implies that as males age they incorporate more genetic mistakes during sperm production. This is also extremely interesting. In males, the machinery that proofreads DNA replication during sperm formation may degrade with age. This last one is a crazy idea and there is very little substantial proof behind it, but it points to an interesting question of how these new mutations appear.

I want to end with this final point, it may be subtle and it is definitely intuitive. Demography matters. Kong’s work did move biology forward, and strengthened the link between the important ideas of genetics and demography. It is important when we mate and how many offspring we produce and how well we feed the first and the last ones.

Contributor Artur Romanchuk is a fifth-year graduate student at UNC Chapel Hill studying with Christina Burch and Corbin Jones. Artur primarily studies how bacteria pass genes to one another (“lateral transmission”) and how these new genes lead to the ability to infect new hosts. He is also an author and cartoonist: check out his other works at ingradients and WHandCats. His first daughter was born when he was in his mid-twenties, and should be relatively mutation-free.

Related articles

• More mutations in children of older fathers, and how it relates to human origins (dienekes.blogspot.com)
• Human Mutation Rate Is Gender Biased And Low (dispatchesfromturtleisland.blogspot.com)
• Father’s Age Affects Mutation Rate (the-scientist.com)
• Whole Genome Sequencing of Mutation Accumulation Lines Reveals a Low Mutation Rate in the Social Amoeba Dictyostelium discoideum (plosone.org)

The cost of reproduction in birds

Tags

biology, birds, evolution, Genetic drift, Natural selection, research, science

The concept of trade-off is paradigmatic in life-history theory. an organism can only acquire a finite amount of energy in its lifetime, so it must “choose” how to allocate that energy to growth and survival or reproduction. Reproduction is assumed to be costly so that individuals who spend more on reproduction, for example by laying more eggs, will not survive as well. We suppose that over evolutionary time, natural selection will act on genetic variation for these allocation decisions, so that the sequence of decisions over an individual’s lifetime will represent an optimal allocation of resources.

Unfortunately this intuitively appealing idea has been very hard to find in nature. In fact, many studies have come up with positive correlations: animals that reproduce more tend to survive better. A recent study by Eduardo Santos and S. Nakagawa found that this trade-off was almost impossible to detect in most studies, or non-existent altogether. In a meta-analysis of brood supplementation studies (researchers added eggs to the nests of breeding birds), they found little impact on survival. Their result held across all the major taxonomic groups of birds, the biggest division being between passerines (songbirds, crows, flycatchers, etc) and non-passerines (ducks, loons, parrots, woodpeckers). Regardless of overall “lifestyle” the birds tested in most studies were able to withstand the hypothesized survival cost of additional eggs dumped on them by researchers.

Why would this be the case? As always there is the possibility that the studies were poorly designed, or that brood supplementation is not a good way to test for a trade-off. Particularly, brood supplementation only taxes the parents of their ability to defend and feed offspring; it does nothing to the energy that females put into egg production. The other possibility is that adult birds just don’t put that much effort into reproduction in the first place. Perhaps survival is far more important. The trade-off is still there, but it’s just not important for most birds.

The hypothesis that life is just not as Malthusian as we have often supposed in evolutionary biology intrigues me greatly. If evolution acted in the “well-oiled machine” manner that many laypeople and professional scientists find appealing, then we’d expect selection to push annual reproduction right up to the level allowed by the trade-off. What studies have found is birds putting minimal effort into reproduction, parenting or anything that affects their survival. This means that selection is a lot weaker than we expect: this gives genetic drift a lot more room to account for polymorphism. It also makes sexual selection more plausible: if most species have fairly conservative lifestyles and selection for survival is not that strong, then males (or females) can afford costly ornaments.

An unrelated study also appeared this week that is getting a lot of press: researchers in Iceland found a strong relationship between the age of fathers and mutations passed to their offspring. This is the first study to quantify the per-year effect of paternal age on offspring mutations in humans, so it’s a pretty big deal. I will talk more about this in a future posting since it’s related to my dissertation research, but in the meantime, go read the article and enjoy the flurry of debate surrounding it.

E. S. A. Santos, S. Nakagawa (2012). The costs of parental care: a meta-analysis of the trade-off between parental effort and survival in birds Journal of Evolutionary Biology, 25, 1911-1917 DOI: 10.1111/j.1420-9101.2012.02569.x

Related articles

• Kiwis in ‘severe reproductive bottleneck’ (stuff.co.nz)
• Parent-offspring Conflict: Time to Listen to the Argument (psychologytoday.com)
• Better looking birds have more help at home with their chicks (esciencenews.com)
• Older fathers pass on more mutations (newscientist.com)

Drift and selection: the epic battle?

Tags

biology, evolution, Genetic drift, genetics, Natural selection, science

I learned a lot at last week’s Nescent Academy on Quantitative Genetics. I saw a lot of material that I wouldn’t have seen in other forums, like the Ornstein-Uhlenbeck models of genetic change under microevolution and macroevolution. During the last half of the week, which focused on macroevolution, I confirmed my impression that when talking about evolutionary history, genetic drift is really the name of the game. When population geneticists talk about the history of particular genes (for example, a gene implicated in a human disease), they rarely speak about selection. There was also a lot of good information on research findings from natural populations.

There were three points in particular that struck me:

1. When looking at natural populations, there is abundant genetic variation in almost any trait
2. Selection is generally weak and generally stabilizing selection
3. Stochastic processes, such as genetic drift, can account for a lot of diversification seen in nature

These findings were interesting to me because I study selection, usually using deterministic models and because I’ve seen the perspectives of other researchers about the relative roles of selection and drift. I have tended to assume, along with many other researchers, that most diversification is due to selection, and that for any “real” differences to matter over evolutionary time that selection must be involved. Why is this?

Selection and adaptation are appealing concepts and they are simple to understand. Darwin’s (three or four) postulates give us all we need to understand how adaptation comes about. Adaptation is a really nice idea: things become more efficient, better, over time. Not only is that aspect appealing, but it’s easy to understand how it could happen: selection eliminates the less efficient, and promotes the more efficient. All you need after that is inheritance. This is so easy that most people get it the first time. Leaving aside the appeal of this from the social perspective (read the first chapter of The Dialectical Biologist), it’s just easy. I teach evolution and ecology to undergraduates and most of them come in getting the basic idea of selection. It’s not hard.

Take genetic drift on the other hand. If you’re like most biologists who’ve tried to teach about genetic drift, you know that genetic drift is the opposite of selection from a teaching perspective. Genetic drift, like selection, removes variation from populations. Only mutation can bring it in. Under genetic drift alleles just disappear: by random chance they fail to make it into the next generation. This only happens in finite populations, that is every single real population. How? Think of it this way: you know that if you flip a coin a thousand times you will get close to 500 heads and the rest will be tails. Do this instead: flip a coin ten times ten times and record the number of heads you get for each ten coin flips. You could then make a graph depicting the number of times you get five heads, six heads and so on. You should get a nice looking histogram: close your eyes and put your finger on a spot on the graph. Your real population is that spot. It could be the one where you got zero heads.

There are two important things about genetic drift: one is how it leads to diversification, and the other is how it accounts for polymorphism. Drift leads to variation between populations because when populations are separated they randomly undergo drift, possibly with different end results: if there are two alleles A and B at a locus under drift, one population could lose allele B and the other could lose allele A. Repeat that over many loci and your get very different looking animals that don’t recognize each other when they get a chance to make babies. The second property is that when you observe polymorphism (genetic variation), it is probably due to drift. Drift over time removes genetic variation from a population, but before that happens the frequency of the allele in question bounces all over the place by random chance. The time window over which that happens is incredibly large, much longer than that for selection. Therefore the large amounts of genetic variation in natural populations are probably due to weak selection, strong drift and lots of mutation across the genome.

Here’s my explanation of the above findings: selection is always happening, but is generally weak. Selection is weak both because drift is happening at the same time, and because life is just not as hard as Darwin and Malthus had in mind. Selection in nature is usually stabilizing selection, meaning that there is some intermediate value that is favored most, and extreme values are selected against: the typical example is birth weight in industrialized societies. Small babies are prone to infection and pulmonary dysfunction and large babies are at greater risk for perinatal complications. However, in most cases, it appears that deviations from the optima that we can detect in nature are not heavily penalized. Especially in large-bodied, iteroparous organisms like birds, ungulates and primates, life just doesn’t seem that hard. This means drift has plenty to work with. Most of the organic diversity we see is probably due to drift randomly sending populations closer to new optima where stabilizing selection takes over again. This is basically Sewall Wright‘s shifting balance theory.

Wright in 1954 (Photo credit: Wikipedia)

This positively demonic process could account for most of the organic diversity we see out there, but it is not an appealing idea. I think most intellectuals go through a phase where they attribute everything to randomness — and I’m not suggesting we all get on that bus — but there’s also a Conspiracy to remove slack from the world. People generally don’t like the idea of random forces to explain things. Especially since a lot of biologists, including myself, don’t understand genetic drift (how could you?) it’s really hard to get behind the idea. However, especially when analyzing real populations, such as the evolutionary history of humans, and testing ideas about sexual selection, we have to consider the role of drift. Much of the persistent, between population variation we see that looks adaptive could be due to genetic drift.

Related articles

• Sexual selection in humans: some interesting recent work (lxmx.wordpress.com)
• Genetic variation within a population (ahschoolapbio2013.wordpress.com)
• Adaptation vs Drift at Evolution Ottawa 2012 (sandwalk.blogspot.com)
• A free online course in genetics and evolution by Mohamed Noor (whyevolutionistrue.wordpress.com)
• How do you do evolutionary theory? (lxmx.wordpress.com)

What is quantitative genetics?

Tags

biology, evolution, genetics, Quantitative genetics, science

Next week I’ll be attending a Nescent Academy “master class” on quantitative genetics, led by two teachers who have made major advances in this field. They will be assisted by other teachers who have done important work in the field. I’m really glad to have the opportunity so close to home: it’s always nice when the best students and teachers in a field come to my home town to lead a workshop like this 😉

This is a good opportunity to talk about quantitative genetics. What is it? As with many scientific topics, it means different things to different people, depending on your main research question. I do theory, but other researchers are primarily concerned with analyzing data, and conducting experiments. Quantitative genetics is a helpful set of ideas in all three of these areas, so I will try to explain my understanding of all of them.

First of all what is genetics? Genetics is the science of inheritance. The basic question of genetics is how do parents pass their traits to their offspring? We know the basics are that parents pass “particles of inheritance” to their offspring (genes) that the offspring express, thus creating likeness between offspring and parents. This theory works for traits like eye color and hair color, but what about for something like height? Height is a different kind of trait altogether, and people have known for a long time that offspring do not typically display the height of one parent or another, the way they do with eye color.

This disparity was actually the source of a vitriolic debate between “Mendelians” and “biometricians” at the turn of the twentieth century. The biometricians had been studying traits like human height in humans and animals for many decades, and then several botanists rediscovered the work of Mendel and started testing it out on plants and fruit flies. Mendelians caricaturishly believed that mutation was the only necessary evolutionary mechanism, and that Mendelian inheritance was the only mode of inheritance possible. They couldn’t explain the patterns of inheritance in traits like height, however.

The solution was a “fudge” or a “hack” by R.A. Fisher: what if height was controlled not by a single gene, but by many throughout the genome? Offspring will inherit some of these from mom, some from dad and the outcome should be a mix of contributions to the trait from each parent. Height, after all, or any trait, is a human construction, imposed by researchers onto an organism: why should there be just one gene that controls something arbitrarily decided by someone with a measuring tape? The outcome, Fisher showed, of Mendelian inheritance of a huge number of genes contributing small effects would be just the patterns observed by the biometricians. Keep in mind that in the first half of the twentieth century, people did not know what the actual genetic material was, or least of all how it worked.

Quantitative genetics then is a hack that ignores the genetic details of a particular trait and simply looks at the statistical patterns between parents and offspring. For experimenters, the crucial concerns are setting up breeding experiments that can explain how traits are inherited. For example, maternal half-sibs (offspring all born from the same mother) can eliminate the effects of the mother on the offspring. If the offspring all come from the same mother, then the mother’s genes will not explain the variation in the offspring. Only the population of fathers can supply the variation seen in the offspring.

Another approach to quantitative genetics comes straight from animal husbandry: if you want to breed animals that produce more of a certain product (the typical example is milk), then you can use equations to calculate how many cows to breed, and what their milk yields need to be, in order to produce a certain milk yield in the next generation. The difference in milk yield between offspring and parents is the “response to selection,” in this case artificial selection. This is the very idea of selective breeding that Darwin analogized to natural selection, so this same farming idea carries through to those of us studying the evolution of quantitative traits.

This last aspect is mainly my interest in quantitative genetics. We can use the equations I described in the last paragraph, and iterate them to simulate or describe the evolutionary process. The equilibrium solutions to these equations can tell us what traits are likely to evolve, all without going into the genetic details. Quantitative genetics involves a large number of approximations — skipping over the details — and that’s the nice thing about it mathematically. Despite using so many approximations, the equations are usually quite accurate.

The most recent development in quantitative genetics actually involves going beyond those approximations and mapping out actual genetic loci that are involved in the inheritance of quantitative traits. This is called Quantitative Trait Locus (QTL) analysis, and is also being called QTN analysis, for “quantitative trait nucleotide.” The meaning of the “N” should tell you just how specific some of these studies are getting. There is a controversy about this, however, since it appears that many studies from humans and animals show quite conclusively that the “hack” of quantitative genetics may not be so much a hack as a scientific reality. Genome-wide association studies and others that look at the whole genome are starting to show that indeed many loci of small effects are a better explanation than few genes of large effect in many cases, including human height and schizophrenia. This is especially weird, since Fisher’s “infinitesimal hypothesis” was only meant to solve a very specific problem, and probably was not meant as a real scientific hypothesis. What does this say about the operation of science?

I hope to meet some of you there next week. Thanks for reading.

Matthew V. Rockman (2012). THE QTN PROGRAM AND THE ALLELES THAT MATTER FOR EVOLUTION: ALL THAT’S GOLD DOES NOT GLITTER Evolution, 1-17 DOI: 10.1111/j.1558-5646.2011.01486.x

Related articles

• Population Genetics (plato.stanford.edu)
• Genetic variation and sexual selection: an introduction to my research (lxmx.wordpress.com)
• How Big Data Transformed the Dairy Industry (theatlantic.com)
• The Pea, the Cow, and the Giraffe (writescience.wordpress.com)
• Learning population and evolutionary genetics | Gene Expression (blogs.discovermagazine.com)
• How do you do evolutionary theory? (lxmx.wordpress.com)

The Handicap Principle

Tags

biology, birds, evolution, research, science, sexual selection, theory

Researchers use sexual selection theory to attempt to explain traits that are exaggerated, seemingly unrelated to survival and seemingly costly. I call these characters “ridiculous.” Almost every sexual selection talk starts with a collage of absolutely ridiculous-looking sexual ornaments and armaments. Most biologists have this “biological diversity slide” near the beginning, but other biologists have theirs filled with perfectly sensible looking animals. Animals that are clearly built for survival. Sexual selection, on the other hand, seeks to explain things like this:

Male Blue Peacock in Melbourne Zoo, Australia. (Photo credit: Wikipedia)

One way to explain these extravagances is not to use sexual selection at all, but to say that it is, indeed necessary for survival. In fact, the whole idea of sexual selection arises out of a Bob McGuire argument: “Come on, that can’t possibly be necessary for survival! Chuck, you’re crazy.” Bob McGuire was a timeshare salesman who tried to talk Dr. Adamson and I into buying by saying things like “Come on, you’re not gonna take a baby camping, come on!” These appeals to disbelief are rather common in science, not just in anti-science.

The alternative looks at how ridiculous-looking traits do impact survival: if they are really costly, perhaps that cost relates to their value as signals. Perhaps they tell females something. Perhaps the cost itself is really important, and females should pay attention to that cost. How would a signal convey all that?

These important things to consider are fitness components. We talk a lot about fitness, but there’s no one measurable quantity that actually is fitness. Survival forms one fitness component, attractiveness forms another. When females want to have attractive offspring, one way to get them is just to mate with an attractive male: “You mate with a good-lookin’ bird like me, you’ll have good-looking babies, and good-looking grandbabies and so on. It’s a win!” The trait doesn’t need to be particularly costly to tell females that their offspring will be attractive. But what if the offspring don’t survive to mate?

Handicap to the rescue!

A really costly signal, on the other hand, could tell females that a male not only is attractive, but he’s able to survive well. The signal tells females that males carrying them are able to survive well because their trait does not impact their health as much as it would someone who was less healthy. This is called the handicap principle: if a male shows a handicap, he must be well-adapted and healthy, or else he wouldn’t be able to handle the cost. This idea was first proposed independently by Bob Trivers and Amotz Zahavi, and roundly rejected as completely preposterous. The 1989 edition of The Selfish Gene contains the typical argument: if it’s costly, then it’s costly and it will be selected against.

However, in 1990 Alan Grafen showed that handicap signals are evolutionarily stable: if everyone in the population is using a costly signal, then someone using a non-costly signal to convey the same information can’t make a living. If a signal is truly costly, then you can’t fake it. Grafen showed with his characteristic style that this applied to communication across the board, not just in sexual signals. Some researchers go so far as to say that every signal is a handicap, although I think “the finger” is enough of a counterexample. Incidentally, “the finger” did originally have meaning: it meant you had never been captured in war and were still able to shoot an arrow. I think this meaning has been lost since the Battle of Agincourt.

Kinds of handicap

There are a few different ways to have a handicap. One is called “pure epistasis” or “Zahavi’s Handicap.” In this case, every male grows the same trait, but it kills less-healthy males more often than it kills more healthy males. This is the version that Zahavi came up with originally, and it was widely ridiculed. It turns out the ridicule was partially correct, and this sort of handicap doesn’t really work. Zahavi’s handicap doesn’t work because after selection for survival, all males will start to look pretty much the same, and then females have no incentive to choose among males (a female who mates randomly will get the same good genes as one who goes to the trouble of choosing). Then the trait is useless, and costly, and will be lost from the population.

The second way is the “revealing handicap.” In this case all males grow the trait, but the signal itself has much better quality in more healthy males. The caricature is of a peacock’s tail: all males grow similarly-sized tails, but less healthy males let theirs drag on the ground and get infested with mites. It doesn’t kill them, but it’s not as shiny and dazzling and sexy as it would be for a healthy male. In this case the signal itself tells females how healthy a male is. This kind of handicap can lead to an exaggerated male trait, as long as there is sufficient genetic or environmental variation for the tail dragging on the ground.

The third way is condition-dependent signaling: males who are of good health grow larger traits and are less impacted by the costs of carrying the trait. The nice thing about this theory is that everything seems to work as far as genetic variation. Females benefit by mating with showy males, from having more healthy male and female offspring. Also, if the trait is condition-dependent, there is plenty of mutation in “condition,” which is basically the sum of all the selective forces across the genome. There should always be plenty of genetic variation in condition, so females should always benefit from being choosy.

I study how condition-dependent signaling plays out over the lifespan. If a male is really healthy, he can expect to live a long time, and he could potentially conserve his resources until he gets older. By growing his trait over a long period of time, he would have more opportunities to mate, and be just as sexy in middle- or old-age when selection is less intense. This does present a few problems in how the traits would actually change over time. If selection is intense enough, a male might be killed even for having a small trait, and once he gets older, his sperm will be harboring more deleterious mutations. I’ll go into more detail about these in future posts.

Related articles

• Genetic variation and sexual selection: an introduction to my research (lxmx.wordpress.com)
• What human traits were evolved only for sexual attractiveness? (io9.com)
• Its All About the Mane! (pathpics.wordpress.com)
• Sexual selection in humans: some interesting recent work (lxmx.wordpress.com)

How do you do evolutionary theory?

Tags

biology, Darwin, evolution, genetics, mathematics, science, theory

Ronald Fisher in 1912 (Photo credit: Wikipedia)

My most frequently asked question has got to be: what organism do you work with? This is a funny question because I don’t work with any particular organism. The funny thing that happens is that after I tell people I don’t work with a particular organism and describe my work, they say “Oh, so in what kinds of animals?” This could be sending me several messages: one is that people have no idea that research into theory exists at all. I find this explanation unlikely since everybody knows about theoretical physics (which actually exists, it’s not just theoretical). There’s even a TV show in which everybody’s favorite character is a theoretical physicist. The message I get, instead, is that it’s quite strange to think about a “biologist” who doesn’t work in a lab, in a field, or a greenhouse. What would such a person do? How can you be a biologist and do all your work without touching real animals or plants? This is the point in the conversation when I tell people that I’m a mathematician getting a degree in biology. Basically what I tell people is “I do math” or “I solve math problems.”

The cool part is I get to decide what those problems are. I’d like to give everyone a better idea of what I actually do in my research. It’s one reason I started this blog and so I plan to explain things about my general way of working over a few posts.

Theoretical questions, mathematical answers

What scientists basically do is solve puzzles. These puzzles are usually posed as questions like “how does this plant grow?” or “When (in history) did this gene originate?” or something else highly empirical. When you want simply an accurate description of the world, when you want “How does this work?” you can go and get an organism and describe it. You can collect data, and you can formulate various hypotheses about the patterns in the data, then test those hypotheses by looking at other patterns in the data.

I do basically the same thing, except the questions that I handle are of a theoretical nature. That means that basically what I’m asking questions about are those hypotheses themselves, not the patterns in the data. I have a basic question about how sexual signals evolve. “How do they evolve?” means I want to know how a population of organisms, with some individuals carrying expensive organs or behaviors, would change over time. If a gene for such a signal arose, would most members of the population have it at some later time? Or would it go extinct? What does our existing theory tell us? How can I extend the theory we have so that we better understand this?

Sexual signals and behaviors appear to be costly, and so Darwin reasoned that they couldn’t come about by natural selection. He solved that puzzle by supposing a different form of selection that worked by mate competition, instead of simple competition to stay alive. Darwin was the first evolutionary theorist!

What Darwin didn’t have was a mathematical theory of how populations evolve. In evolutionary biology, we’re lucky to have such a theory, developed by the “Big Three” of Sewall Wright, Ronald Fisher and J.B.S. Haldane. Wright, Fisher and Haldane formulated the theory of population genetics as a mathematical description of how the frequencies of alleles change in populations over time. Just like Darwin, we don’t have to use math to answer these questions: we can take a guess or hypothesize, and go straight to testing that idea on real organisms. However, we can use mathematical tools to answer these questions, and mathematical answers are the most effective. There are several different ways to do this.

Some nuts and bolts

Everything I do can be called “mathematical modeling.” However, some of the time it is less mathematical, or more computational. If I am asking a question of how a gene frequency changes over time, then one way is the analytical approach: I write down a set of equations describing how the gene changes its frequency over time, and then I describe properties of those equations. The particular biological model I’m interested in will determine how the equations come out: all the information I need to say how the population will change should be in these dynamical equations.

The most important properties of dynamical equations are its equilibrium and the stability of that equilibrium. An equilibrium is a state (e.g. a gene frequency) that doesn’t change over time. So for example, in standard population genetics, if an allele’s frequency is zero, then it won’t change, unless there’s a mutation. Then zero is an equilibrium as long as I don’t allow mutation in the model. Stability means that when a population is close to equilibrium, it moves toward equilibrium. This is just like rolling a ball down a hill: when it gets to the bottom, it stops. That’s a stable equilibrium: if you throw the ball back up the hill, it rolls back down. This is important because we expect to find these equilibria in nature: we expect populations to get to a certain point and stay relatively close, and that’s what we should be able to see much of the time in nature. This is incredibly simplistic, but we have to start somewhere.

Another kind of dynamical model is a computational or simulation model. In this sort of modeling we input certain calculations as a computer program. Instead of writing out equations for how the variables change over time, we let the computer iterate a set of calculations to simulate how they would change. I could have a very good idea of the life cycle of a theoretical organism, and I program each piece (birth, growing up, mating and death) into a program, and then calculate how the gene or phenotype frequencies in the population(s) change over time. There’s two reasons to do things this way: the model of the life cycle might be extremely complicated, so that each piece might be a paper in itself before I solve my big question; or, we might explicitly mathematically know that there is no simple solution to the problem. In that case using a computer helps us come up with an approximation to the solution.

Both the analytical model I described and the computer model describe change over time: they are dynamical models. I like doing things this way. However, there’s another way, which is simply to mathematically describe how things are at a particular point in a population, or to describe the way an organism works. The solution to such a model is usually to say what the optimal phenotype of an organism is, given certain conditions. Evolutionary game theory and foraging theory are examples of this “phenotypic” approach. These approaches can be used to answer similar questions, but they do tell you fundamentally different things in most cases. A phenotypic model cannot tell you how something evolved, only the circumstances under which you could expect it to evolve. Phenotypic models are very popularly interpreted in behavioral ecology, where the researcher’s task is finding out how a particular strategy affects reproductive success of individuals. It’s not necessary to care, in that case, how something evolved: it’s just there and bears questioning.

The biological interpretation comes in when we consider the parameters of a particular model. Usually these special quantities determine if an equilibrium exists, and if it is stable or not, in a particular model. For example a particular model might have a mutation rate parameter, or a parameter describing the rates at which males and females meet, or a parameter describing the intensity of selection against a trait. Models of disease transmission have parameters describing how often a virus has a chance to move from one person to another. Parameters usually correspond to real biological quantities that could be measured, and that’s how hypotheses get formed and tested.

What is this all for?

The real point of doing all this is for somebody, a field or lab researcher, to be able to apply these ideas. If I can come up with a satisfactory solution to a theoretical puzzle, another researcher can take that theory to form a hypothesis and then test that hypothesis using fruit flies, or peacocks or some other real organism. My favorite kinds of applications look for patterns across large groups of organisms, many different species, and try to apply these ideas very broadly. Let’s say this species supports the conclusions of a model, and so does its closely-related species, since they correspond to different parameter values. Most of the time, however, theories get tested one organism at a time, and the research either supports the theory, or fails to support it in some way. This is the process of refinement, which is a lot of fun. For example, a theory could be supported in fruit flies, but not in cockroaches, but we find out that cockroaches are not a good species to use for testing the idea. This reveals a deficiency in the idea, since it doesn’t include cockroaches. Then I get to do some more work, and write another paper.

Related articles

• Research finds that maths-heavy evolutionary biology research papers are less often cited (aperiodical.com)
• The Good Fight (blogs.scientificamerican.com)
• BBC documentary: “What Darwin Didn’t Know” (whyevolutionistrue.wordpress.com)