Frequency-Dependent Selection, Disruptive Selection, and the Evolution of Reproductive Isolation

Mathematical models have been developed and analyzed to determine the conditions required for the evolution of premating reproductive isolation via disruptive selection in a potentially panmictic population. The models describe changes in genotypic frequencies through time for a population which is polymorphic at two loci. Disruptive selection due to reduced viability of the heterozygote at a polymorphic equilibrium is assumed to operate at the first locus. Mating is assumed to be occurring assortatively within the population, based on phenotypic characters determined by the second locus. Reproductive isolation results from epistatic interaction of these two loci which reduces the number of intergenotypic crosses at the disruptive selection locus. Analysis of the models involves searching for conditions which yield stable polymorphic equilibria with the two loci epistatically associated, and determining the relationship between the degree of association at equilibrium (and hence the degree of reproductive isolation) and the conditions of the models. Results indicate that the equilibrium degree of reproductive isolation depends on the following factors: (1) the intensity of disruptive selection; (2) the proportion of individuals in the population which mate assortatively (i.e., the penetrance of the genes for assortative mating behavior); (3) the amount of recombination between the disruptive selection locus and the assortative mating locus; and (4) the extent to which fitness values of genotypes at the disruptive selection locus depend on gene frequency. Premating reproductive isolation will not evolve at all unless the following two criteria are satisfied: (1) As a result of recombinational inertia, the intensity of disruptive selection must be greater than a threshold value which is an increasing function of the amount of recombination between the two loci and a decreasing function of the degree of assortative mating, and (2) the destabilizing effect of disruptive selection on polymorphic equilibria must be compensated for by the stabilizing effect of frequency-dependent selection. Assuming these criteria are satisfied, the degree of reproductive isolation at equilibrium is an increasing function of the intensity of disruptive selection, an increasing function of the degree of assortative mating, a decreasing function of the amount of recombination, and independent of the degree of frequency-dependent selection. Once partial premating isolation has been achieved, it may be enhanced by evolution of some of the parameters of the model. For example, natural selection should favor genetically based mechanisms for increasing the penetrance of the assortative mating genes and for decreasing the amount of recombination between the disruptive selection locus and the assortative mating locus. To the extent that these results can be generalized, they suggest that frequency-dependent processes (resulting from niche heterogeneity or from a number of other potential mechanisms) can play an important role in the evolution of reproductive isolation. Hence obtaining an understanding of the causes and relative significance of frequency-dependent processes in natural systems is an important task for the development of evolutionary theory.