Density-Regulated Selection with Genotypic Interactions

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Abstract
A deterministic model of density-regulated selection with genotypic interactions is developed for a diploid population with discrete, nonoverlapping generations. The population is polymorphic for two alleles at an autosomal locus. Before selection in each generation, the three genotypes are in Hardy-Weinberg frequencies, but genotypes differ in their selective values because of genotypic differences in their intrinsic rates of increase, carrying capacities, and genotypic interactions. The genotypic interactions specify the effect of an individual of one genotype on the fitness of another genotype. By analogy to the Lotka-Volterra model for interspecific competition, our model for intraspecific competition assumes that the selective value of a genotype strictly decreases with numbers of each genotype; therefore, selective values depend on both density and gene frequency. Sufficient conditions for a protected polymorphism are surprisingly simple: the heterozygote must have a carrying capacity greater than that of either homozygote multiplied by the interaction coefficient which expresses the effect of that homozygote on the heterozygote; or, alternatively each homozygous individual must inhibit the fitness of its own genotype, and hence its contribution to population growth, more than it inhibits the fitness of the heterozygote.