Robert Skipper
Institute of Advanced Study, University of Durham, and Dept. of Philosophy, University of Cincinnati

"What's Fundamental about Fisher's Fundamental Theorem of Natural Selection?"
14 May Monday
5pm in room G3, 22 Gordon Square

Abstract

The locus classicus on the origins of theoretical population genetics is R. A. Fisher's 1930, The Genetical Theory of Natural Selection. The center piece of Fisher's natural selection theory developed there is his Fundamental Theorem of Natural Selection. Fisher's 1930 statement of the theorem is that "the rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time." Fisher's theorem is notoriously abstruse as stated. And so the immediate questions to ask are "What does the theorem say?" and "What's fundamental about it?"

Warren Ewens' 1989 rediscovery of George Price's 1972 derivation and interpretation of the theorem resolved to the satisfaction of most everyone the first question. The theorem states, "the rate of increase in the mean fitness of any population at any time ascribable to natural selection acting through changes in gene frequencies is exactly equal to its genic variance in fitness at that time" (following A. W. F. Edwards).

There are a number of alternative assessments of the "fundamentality" of Fisher's theorem. Probably, the Price-Ewens assessment of theorem is the most well known: According to Price and Ewens, Fisher's theorem is broad in scope, but it's otherwise not so fundamental because it is, as they say, incomplete, capturing only a partial change in mean fitness. This is an assessment of what one might call the "biological depth" of the theorem. But others have argued that Fisher's theorem is fundamental in its influences (Edwards) and its role in Fisher's argument for neo-Darwinism (Anya Plutynski). The aim of this talk is to sort out the alternative assessments of the theorem with the aim of arriving at the correct one. My view is that the right assessment is to be made on the basis of the theorem's biological depth. I argue, in the company of Edwards and Alan Grafen and contra Price and Ewens that Fisher's statement about the partial change is indeed the biologically deep statement Fisher thought it was.