A general analysis of genetic models with frequency-dependent mating

Abstract

A particular phenotype is assumed to mate with a frequency that is any general function, g(w), of its population frequency, w. Genetic models are analysed in which two phenotypes, one dominant to the other, mate with relative frequencies g(w) and 1 —g(w). If the selection that determines the function g(w) acts either on one sex alone or on both sexes equally, then it is shown that the equilibrium frequency, the conditions for the stability of the equilibrium and the eigenvalue that determines the rate of approach to the equilibrium can all be found in terms of simple formulae containing the function g(w) and its derivative. These formulae are applied to some specific models of frequency-dependent sexual and natural selection. © 1980 The Genetical Society of Great Britain.