ONE CAN still find, on occasion, scientists that suffer from a disease that is not all that easy to cure: physics-envy. It has even been called the biologist's curse; though it is also found among psychologists. Would it not be wonderful, a devilish small voice whispers, if you too could bring your subject under mathematical control?
I have something of a vested interest in this issue, as an editor of the Journal of Theoretical Biology. Theoretical biology? Surely biology is essentially an observational and experimental science? This seems like a clear case of physics-envy, with biologists attempting to ape theoretical physics, a most highly-regarded field. It is astonishing how even apparently exotic branches of mathematics have provided physicists with invaluable tools. No wonder that physicists can suffer from mathematics-envy. Just why mathematics should be so successful in describing the universe, is not obvious; at the least it shows the world is as logical and consistent as mathematics itself. Also it is free of cultural or ethical baggage.
But it is possible to do theoretical biology without mathematics - Darwin's wonderful theory of evolution contained none. However, since then it has acquired numbers and equations which have both filled in, and underpinned the theory. Evolutionary genetics is largely mathematical. One major advance was made by Bill Hamilton, whose mathematical analysis is an extension of J B S Haldane's remark that he would lay down his life for eight of his cousins, since they possessed more of his genes than he did. It provided key insights into altruism. Another is John Maynard Smith's use of algebra to analyse interactions between members of a population with respect, for example, to hawk-like and dove-like behaviour. He showed that only certain strategies would survive; too many hawk-like attacks would be, in the long run, a disadvantage to the individuals. I am pleased to say that both published their early ideas in our journal. …