Additive Genetic Variation under Intraspecific Competition and Stabilizing Selection: A Two-Locus Study

A diallelic two-locus model is investigated in which the loci determine the genotypic value of a quantitative trait additively. Fitness has two components: stabilizing selection on the trait and a frequency-dependent component, as induced, for instance, if the ability to utilize different food resources depends on this trait. Since intraspecific competition induces disruptive selection, this model leads to a conflict of selective forces. We study how the underlying genetics (recombination rate and allelic effects) interacts with the selective forces, and explore the resulting equilibrium structure. For the special case of equal effects, global stability results are proved. Unless the locus effects are sufficiently different, the genetic variance maintained at equilibrium displays a threshold-like dependence on the strength of competition. For loci with equal effects, the equilibrium fitnesses of genotypic values exhibit disruptive selection if and only if competition is strong enough to maintain a stable two-locus polymorphism. For unequal effects, disruptive selection can be observed for weaker competition and in the absence of a stable polymorphism.