Aesthetics, mathematics, physics and biology


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One of Namuth's many photos of Jackson Pollock...

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

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.

Mural Detail II

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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The Latest Update

Dear Readers,

I am still in graduate school.  I could have saved myself repeating the same conversation about 10^ℵ times by posting this last month.  About three days before my proposed defense, my committee members raised some serious concerns about  the mathematics in my thesis (aka dissertation).  After my parents got on their plane to North Carolina I decided to postpone my defense until I could take a more disciplined, rigorous approach to deriving the dynamical equations.  I have just not been careful over the past couple of years.  In my haste to create something I have failed to create something beautiful, at the very least verifiable.  So I am taking another shot at it and hope to be done by the end of the summer.  More about mathematical aesthetics coming soon!

Another Update


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Hello Dear Readers!  Time to give you another update.  I have had my mutation manuscript accepted with minor revisions at Ecology and Evolution.  I will update the arXiv version once I incorporate the reviewer comments and submit it back to the journal.  That will happen by the end of April.

However, I’m much more busy getting ready to defend my thesis.  My third chapter is about the evolution of female choosiness under extended lifespans.  I’ve included the same age-dependent mutation factor as my second paper, and some of the results crucially depend on that.   As soon as that’s done, I plan to do a lot more writing and reading.

If you’d like to be there, the defense date is April 11, at 11:00 AM in Coker 215.


Holidays 2013: Research Update


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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.

Evolution 2013 Greatest Hits


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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 summ...

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.

This is an image of the American anthropologis...

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

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

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).


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.

Attractiveness and sexually-selected traits


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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.

Sexual selection with age-dependent mutation


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I recently got the opportunity to give a talk at both UNC and Eastern Carolina University on my current research project. The talk is available over at figshare if you’d like to scrutinize the details. I’ll give you some of the background here since the talks have no narration.

For starters I’m interested in males that provide only potential genetic benefits to their offspring; I’m also looking at the model where females are assessing male genetic quality based on a male morphological trait (such as an ornament, weapon or body size). This means that females expect to have offspring that are both more sexy and who survive better when she mates with a highly ornamented male, rather than a less well-ornamented male. The problem in this setting is the “lek paradox,” where eventually a female will do just as good to mate randomly as she would to be choosy, since there will be no genetic variation in ornamentation or condition. Usually in models we use mutation to maintain genetic variation for condition; I think I’ve found that being more specific about the type of mutation gives us a good theory that will resolve the lek paradox (yet again!).

The bighorn sheep is Alberta's provincial animal

The bighorn sheep is Alberta’s provincial animal (Photo credit: Wikipedia)

My question specifically deals with the scenario where males all start out with the same trait value and then grow that trait throughout their lives (I call this an age-dependent trait). Females can’t tell who is in good condition when looking just at young males. Several models have shown that age-dependent traits are a good strategy for males with relatively good health. They will have more matings over their lifetimes if they ramp up their signaling over their lifetimes. One particular model showed that if males are in good health, they should delay as long as possible, so as not to incur the wrath of natural selection, until they have had lots of opportunities to mate. Lower condition males should adopt a “hope I die before I get old” strategy and be as sexy as possible, as soon as possible.

The problem with these models is that they assume the full range of strategic variation is present in a particular population. They don’t represent changes over time; they just say what the best strategies are. I showed in a previous model that in a population-genetic simulation an age-dependent trait that starts out small will lead to the evolution of preferences and age-dependent traits. This makes sense from a dynamical point of view because selection is weaker at older ages: since older-aged males are only a small fraction of the population, any genetic variation in those males will not contribute much to the whole pot of variation. Selection can’t do much with genetic variation in older males, hence they are relatively free to be as extravagant as they want.

But what if old, sexy males are carrying mutations in their sperm that females cannot detect? I assumed that males will contribute harmful (deleterious) mutations to their offspring at a rate that is basically their age times a per-age mutation rate. I also assumed that the trait increases linearly. This is not realistic, as a lot of traits grow up to a point and then stop or even decline in old age. However, it gets the point across that young males are similarly sized and old males vary in their traits depending on their condition.

The results I have as of yet show that this process actually ensures continued genetic variation in the overall condition trait. The equilibrium female preference hovers above the equilibrium trait size, ensuring that females will always be going for the older, sexier males that carry mutations in their sperm. Mate choice therefore reinforces the process that keeps genetic variation in the population. I hope this result holds up under further mathematical scrutiny, because it’s a nice surprise.

I have a few snags to work out before I write this up; the feedback I got from the talks was invaluable. A few people had really great ideas, like a female strategy to screen sperm for deleterious mutations, and a research strategy to scan sperm samples for such mutations. Although my first reaction was “that’s going to be a lot of work!” my host chimed in that someone actually is doing this already. Wow!

Student-Centered Teaching


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I recently prepared an essay on my philosophy of teaching. Part of my rationale for starting this blog was to explain to friends and family members how I do my research. Teaching is really the core of what I do, however, so I should also spend some time talking about teaching. I prepared the essay for two reasons: firstly, I think it’s important for students and other teachers to know where I’m coming from, and what they can learn about concepts in education. The other main reason was to have some kind of a record for myself of all the research I’ve done on the topic, and also construct a set of working hypotheses to guide my teaching work.

The philosophy has three main hypotheses: (1) children are born motivated, i.e. motivation is not something that teachers have to put into them; (2) students can, and should be encouraged to self-assess, i.e. to find their own answers; and (3) research and teaching are essentially the same activity, not things to divide up a scientist’s schedule. The corollary to all these is that the teacher’s main jobs are (a) to set up the right environment for learning and (b) remove obstacles for learning.

Motivation is probably the most important aspect. Motivation is a matter that I often find troubling to talk about with my fellow educators: I’m simply surprised how often I find that scientists think that their own topics are so boring that they need to get students interested. The students are interested already! For one reason or another, they want to learn. Many of them just love learning.

Self-assessment is easy to implement, encourages students by making assessment part of the discovery process, and offers genuine, highly informational feedback. The main way I do this is by never answering a question directly: I tell students to test their own logic, do their own research and figure out if their particular guess is “right.” This gives them more information, is more fun, and incorporates more learning than simply checking “right” or “wrong” and giving them a grade.

Research and teaching are bound together like painting and seeing. I find this to be a necessity: I just can’t teach something unless I apply the same learning attitude as I do when I’m doing research. All I have to do to teach students is demonstrate the approach (show them!). Last semester when I was teaching a topic I had never studied myself (cell and developmental biology) I showed them the approach that I was currently taking to learn the topic. There is no good reason we can’t have the same attitude about our large-scale research projects.

Starting in the 1950s Carl Rogers brought Pers...

Carl Rogers who developed student-centered teaching along with his client-centered therapy (Photo credit: Wikipedia)

I want to emphasize that this is my philosophy of teaching. I am not suggesting that anyone wholeheartedly take on my own philosophy. There are lots of teaching philosophies out there in science education, and I’m glad to see people experimenting. The lecturer I’m working with this semester is one of several who has a reputation for experimentation, and it’s fun being in that setting. If you wanted to pick a teaching philosophy out of a hat, you could. You would be better off to work closely with someone who has a definite philosophy, and then adapt that philosophy based on your own experience.

Much of the research I’ve read falls under the heading of “motivational psychology,” which is largely concerned with (depending on perspective) how to motivate people, or what motivates people. I would suggest reading Alfie Kohn‘s classic book Punished by Rewards for a start on that topic. Much of our theory of education and governmental policy is based on operant conditioning, an adaptation of animal training that was elevated to the status of an all-encompassing scientific theory. Kohn’s book challenges the logic of that in education, parenting and the workplace.

Here’s an excerpt from my teaching philosophy:

Observing children, students and my own learning history has shown me that the energy to learn comes from within students themselves. Spending time at the playground and with my own children, I see that children don’t need to be taught: do children need to learn from a book how a family works before they play house? Children set up organizations, create dramas and negotiate conflicts by figuring it out as they go. They also conduct controlled experiments, especially when playing alone: “If I roll the ball this way, how fast does it go? What if I roll a bigger ball down the same track?” This is exactly what Galileo actually did, and kids do it all the time. Richard Feynman first discovered inertia while playing with a ball and a toy wagon before he was five years old. Note that I’m not saying children would do these things without being told about them; they are not born with the concepts needed to play house or form a club on the playground. But they do figure out how to do it without instruction.

High School Students Visit the Lab


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Recently I got the chance to host some high-school students in the lab and show them what I do as a graduate student.  My motivation was mainly that I enjoy teaching, and I know that when I was a high-school student I would have enjoyed seeing what a theorist actually does.  This project was part of UNC’s Academic Day: according to the organizer, biology was the most popular major to explore during this event that hosts high school students from around the state to show them what universities are all about.

I told them what I do day-to-day, what the track is for someone getting a Ph.D. and the nature of my research.  I then explained some basics of population genetics, like the Hardy-Weinberg trinomial and a few other things. Then we conducted an activity where the goal was to show the action of natural selection and genetic drift. This was the fun part.

The Activity

I had eight students, all female, and all but one with brown eyes. This in itself could have provided data for an activity, but I had brought “populations” of Skittles. The students started each with a population of twenty Skittles and measured the frequencies of each color (the “phenotype”). Having a population of twenty makes calculating frequencies easy: just multiply by five and you’ve got a frequency out of 100. Most of the students had a predominance of one color. I provided them with paper and pencil, since they were visiting.

First I asked the students to come up with a way of coding (and hence measuring) the phenotype. I had already come up with a method that the students found acceptable, which was to score the colors from 1 to 5 starting with green, so that green = 1, yellow = 2, orange = 3, red = 4 and purple = 5. Then the students measured the average phenotype by multiplying the frequencies and color scores. Then came the eating: students on the left side of the table ate 10 Skittles randomly; the students on the right of the table at according to some rule that they were free to concoct. The left side represented genetic drift, and the right side selection. The goal of the experiment was to see how much the average trait value would change between the parent population (before eating) and the offspring population (after eating).

The results were interesting: I really didn’t know if this would work, or if the students would care enough to actually try it. The mean phenotypes on the genetic drift side of the table changed very little, but several of the students lost a color in the process, which represents the loss of alleles that can happen with drift. The means on the selection side of the table did change, but what was more interesting was that the students all chose different rules. Some started by eating green and progressed to yellow when they ran out of green. This represents directional selection, or selection against one extreme phenotype. Some started at the other end with purple, which is also directional selection. Others ate from both ends of the spectrum (green and purple, progressing to yellow and red). This corresponds to stabilizing selection, or favoring intermediate phenotypes. Others started with orange; this results in disruptive selection, that penalizes intermediate phenotypes. I did not plan on telling them about these modes of selection at the outset. This was a very pleasant accident.

Thoughts and conclusions

The biggest obstacle was time: I only had about forty minutes with these young ladies, and so telling them about graduate school and doing the experiment was kinda tight. Another interesting way to do things might have been to use their own physical characteristics (e.g. hair and eye color) as the data, but I didn’t think of that until I saw the Founder Effect that had landed in our lab: they all had brown eyes, except for one student. I explained that if they were to form a parthenogenetic colony on an island somewhere, that after a few years either all their offspring would have blue eyes or brown eyes. This joke might have been a little more uncomfortable to hear had there been any dudes in the room other than me.

Wright in 1954

Sewall Wright, who couldn’t make it on a Thursday (Photo credit: Wikipedia)

I was really glad to have the chance to show these students that theory is a part of science. Without showing them any high-tech gear I was able to show them what I do as a scientist. People, especially young people, often confuse measurement for science, and the techniques of science with the actual intellectual exercise of science. Honestly I was surprised to be surrounded by eight eager teenagers as soon as I held up my hand and said “evolutionary theory.” I expected everyone would want to hear about more sexy things like developmental biology.

Mutation rates and paternal age


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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).

English: DNA replication or DNA synthesis is t...

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.

English: zebrafish histology atlas; testis; sp...

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.


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