NOTE: This post was originally published on November 21, 2006, on an old version of this site.
Dr. Warren J. Ewens is an internationally recognized mathematician whose contributions to population genetics earned him membership in the Australian Academy of Science in 1981 and membership in the Royal Society in 2000. He has been a professor of biology at the University of Pennsylvania since 1972, and has motivated unquantifiable numbers of students and colleagues with his warmth and extraordinary ability to explain things you thought you didn’t understand.
I spoke to him in his office in Philadelphia.
How has math been important in advancing the field of evolutionary biology?
Mathematics quantifies a subject. If you don’t have some kind of quantification, you are relying on purely verbal arguments. So mathematics would come into it if you asked, Has there been enough time for the observed evolution that we see to have occurred? How does the observed amount of genetic variation relate to mutation rate? Is it consistent with the population sizes that we observe? What is the effect of natural selection? In my view, all of these questions can only be answered by a mathematical approach.
Some people reject the idea of evolution because they argue that the world as we know it can’t be due to just “random chance.” Can you explain the role of stochasticity in biology, particularly in evolution?
I think it’s a good idea here to make an analogy. Let’s imagine a casino. Clearly there is random chance with respect to which slot the ball lands in on a roulette wheel, and so on. Thus the amount of money which the casino owners make on any one day or in any one year is random. But you can be pretty sure that they’ll make money in the long run. In other words, even though there’s randomness, there’s something like a deterministic process at work, in that the casino is quite sure to be making a profit overall. Now in the genetical context, the analogy might be something like this: certainly there is randomness in the sense that the mutations which arise are assumed to be random with respect to their fitnesses; they just arise spontaneously. Perhaps 99.9% of them are unfit mutations, they are bad mutations that are then lost from the population. But a small fraction, perhaps 0.1%, happen to be good mutations and they are the ones that will eventually spread through a population and make that population in some sense better. So even though mutations arise from a random process, just as a casino has a random process, you can be certain that in the long run, enough good mutations will accumulate for evolution to occur.
Population genetics is an important component of evolutionary biology, because of the theoretical framework it provides. How would you characterize the important contributions to population genetics?
Quite a few of the formulas in population genetics have found applications in other areas of science, like physics and mathematics. But I would say, perhaps unfortunately, almost nothing of mathematical population genetics has made its way into the outside world, because so very few people understand it, want to understand it… perhaps some want not to understand it! Overall the greatest contributions to population genetics have stayed inside the theory. But within the field, it has led to a substantial quantification of the procedure, and to the extent that quantification is important in any scientific activity, it’s been important in that regard.
Do you have a philosophy on teaching?
Well, that is a very hard question to answer. I don’t think I have a philosophy that is at all unusual. I would say the main thing is you have to let the students see, especially in biology, the amazing things we are discussing: the structure of the body, the evolutionary process, things like this; and try to transfer that amazement and wonder to them so that they will be enthused themselves to become interested in those areas.