Frequency-Dependent Selection in Randomly Mating Populations

Abstract

A general model which accommodates different fitness values of an individual in association with each other type of individual is studied. The model in conjunction with population composition, in which individuals are assumed to be dispersed at random, determines the relative fitness values of individuals. Expressions for the change in gene frequency and for the mean are derived for one locus with two alleles in a random mating population. Equilibrium and max/min mean compositions generally require solving third-degree equations, but explicit expressions are found for models with general levels of dominance and some of their variants. Protected polymorphisms, genetic loads, inbreeding depressions, and the cost of a gene substitution are also considered. Many additional features of the statics and dynamics of populations are introduced with the effects of population composition on fitnesses. A single globally stable equilibrium can exist without any dominance. There may be multiple equilibria, up to three, with various stability characteristics, some of which are protected polymorphisms. There need not be any correspondence between compositions for max/min means and those for equilibria. Inbreeding depressions may be curvilinear, and even stable equilibrium populations may show negative inbreeding depressions. Very different models may give the same genetic load. The number of genetic deaths required for a gene substitution may be as few as twice the population size. One appeal of the model is that it encompasses several classes of models, including those with constant fitness values, and thus provides a basis for determining the appropriate model. After considering alternative experiments and measures of discrimination, we conclude that only survival values of the genotypes for several population compositions would be sufficient to discriminate between certain models.