Feller's Contributions to Mathematical Biology

TL;DR

This paper reviews William Feller's influential work in mathematical biology, highlighting his pioneering contributions to stochastic processes in genetics and evolutionary biology, including foundational ideas and critical analyses of genetic concepts.

Contribution

It summarizes Feller's novel development of stochastic models in genetics and his critical insights into natural selection and genetic load, shaping modern mathematical biology.

Findings

Feller introduced key stochastic models like diffusion processes in genetics.

He provided foundational characterizations such as Feller's branching diffusion.

Feller critically analyzed the concept of genetic load in evolutionary theory.

Abstract

This is a review of William Feller's important contributions to mathematical biology. The seminal paper [Feller1951] "Diffusion processes in genetics" was particularly influential on the development of stochastic processes at the interface to evolutionary biology, and interesting ideas in this direction (including a first characterization of what is nowadays known as "Feller's branching diffusion") already shaped up in the paper [Feller 1939] (written in German) "The foundations of a probabistic treatment of Volterra's theory of the struggle for life". Feller's article "On fitness and the cost of natural selection" [Feller 1967] contains a critical analysis of the concept of "genetic load".