The Pure Theory of Natural Selection: Fisher's Fundamental Theorem and Beyond by Arnold Faden Org

Lecture to the Iowa State University Statistics Department.

People realized soon after the publication of The Origin of Species (1859) that the principle of natural selection had applications far beyond its original scope, to competitive situations of all kinds: competition for wealth, power, office, beliefs among firms, nations, politicians, ideologies, theories, etc.

This suggests that it might be useful to identify the common core underlying these applications, stripping off the particular institutional trappings of each, and leaving the "pure" theory behind.

I take the key idea to be long-term differential growth rates. Prior to my paper of 1991, I take this subject to consist of just one theorem, by R. A. Fisher (1930, 1958), which may be stated as: the rate of change of mean fitness equals the variance of fitness. (For Fisher, "fitness" = growth rate). It turns out that this equation is just one of an infinite system of equations, and that the entire system is needed to answer some questions of interest such as: what distributions over growth rates perpetuate themselves (i.e., belong to the same location family at all different times)? Or, belong to the same scale family? Some results of relevance to "pure" probability theory will also be noted.

Afterwards I shall tentatively indicate how the theory may be modified and extended to make it more realistic by incorporating competition (which limits overall growth), variation, interaction and organization. And I shall try to assess the role of natural selection in a reasonable world view.