Tuesday, May 22, 2007

Adaptive radiation in biology and academia: Why math matters   posted by agnostic @ 5/22/2007 10:42:00 AM

The idea that a species will undergo diversifying selection as it begins to colonize an environment made up of many niches never seen before -- adaptive radiation -- is pretty intuitive. It's obvious enough qualitatively that you'd figure it out on your own if thinking about biology were your day job: the forms of life around us seem so different mostly because they are adapted to different habitats. That idea should probably scale down to sub-populations of a single species. What biologists get paid to do is flesh out the finer-grained quantitative details of how that happens, how much diversity will be maintained by what conditions, and so on. We talk a lot here about recent human evolution (that is, after the invention of agriculture), and so it's worth knowing some of the key points that emerge from quantitative studies of adaptive radiation.

Toward that end, here is a free journal article from PNAS by Gavrilets & Vose which has pointers to the lit and is brief / very readable (although if you want, you can skip their "model" and "methods" sections and focus on "results and interpretations" and "discussion"). Since it's pretty short, I'll let readers peruse it themselves rather than report its contents, but one thing's worth noting: speciation in their model occurred in huge initial bursts. This is yet more evidence that it's foolish to argue that natural selection "hasn't had enough time" to differentiate human populations within 10,000 years, since adaptation doesn't creep steadily. See also the review and simulation articles by H.A. Orr to this effect. Clearly, to the extent that we've moved from one form of society to another more quickly over this time period, these bursts are probably occurring more frequently than in pre-agricultural times. If anything, the only thing that there "hasn't been enough time for" is the settling down of the adaptive process toward a steady state.

Now, the non-math-phobes will have noticed a few phrases lifted from math lingo in the previous paragraph -- the rate of change is increasing (acceleration), are we in a steady vs transient state, etc. But how many here -- not least of which is me -- would know what to do with the jargon of knots, braids, links, or anything else from the field of topology? The only incorporation of these kinds of ideas that I've seen is the chapter on evolutionary graph theory in Martin Nowak's Evolutionary Dynamics. Maybe there are similar articles or book chapters out there, but the point is that there is a mostly unsettled niche begging to be exploited by biologists whose math toolkit contains more than "engineering math" (i.e., non-expert levels of calculus & differential equations, linear algebra, and statistics & probability).

That's no slight to knowing this much math -- but since these tools have been applied for so many decades, it makes it harder to create something original using them. If you were the first to learn, say, knot theory and apply it to biology, you'd blaze a new trail. Even if you personally didn't perform optimally in this area, your intellectual descendants would become increasingly adapted to it and really exploit it (you'd still get credit as the progenitor). Hell, you wouldn't even need to invent new math -- you could absorb what's already understood in math, and maybe roughly how it's used in applications (which would probably be in physics). All you'd have to do is use a bit of analogical reasoning to figure out what pattern in biology it looks like -- or perhaps predict a biological phenomenon that's currently not known, and investigate that.

Edison didn't give much of a role to inspiration, but we could go farther and say that sometimes inspiration is 99% canny opportunism: taking already invented tools to excavate a virgin mine in your own neck of the woods. Most "big ideas" in evolutionary biology are like this: the diffusion equation to model the spread of alleles through a population, game theory to study altruism, extreme value theory to deal with a mutation more beneficial than all extant alleles, and so on. I'm just harping on topology because of a neat little pop-math book I just read called Knots (review by Derbyshire; review by knot theorist). You'd better start settling now, since the corresponding niche in physics appears very crowded, and many of them must feel pressure to migrate to biology where they'd find it much easier to make a name for themselves.

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