Group selection on the boundary of a stable population

A model of group selection is constructed for the case of differential extinction acting on small boundary populations of a large, fixed population and the conditions under which differential extinction is most likely to produce a significant effect are discussed.

Abstract

This article presents a model of group selection via differential extinction acting on small boundary populations of a large, fixed population. We restrict consideration to extinction of populations at or near habitat carrying capacity, thus modeling the kind of situation envisioned by Wynne-Edwards (1962). Under the assumption that the extinction rate is large relative to individual genetic parameters, we discuss the effect of differential extinction on the distribution of gene frequencies within boundary micropopulations. In these circumstances, it is shown that differential extinction is most likely to produce a bimodal distribution of the gene frequencies if the form of the extinction operator approximates a step function, with a critical allele frequency at which the extinction rate shifts from high to low. The need for a rather close approximation to such discontinuous behavior limits the possible conditions under which differential extinction might be important. We conclude with a comparison of our model with that of Levins (1970a) and suggest some technically feasible generalizations of our approach.