The reinforcement of mating preferences on an island

We develop a haploid model for the reinforcement of female mating preferences on an island that receives migrants from a continent. We find that preferences will evolve to favor island males under a broad range of conditions: when the average male display trait on the island and continent differ, when the preference acts on that difference, and when there is standing genetic variance for the preference. A difference between the mean display trait on the continent and on the island is sufficient to drive reinforcement of preferences. Additional postzygotic isolation, caused, for example, by either epistatic incompatibility or ecological selection against hybrids, will amplify reinforcement but is not necessary. Under some conditions, the degree of preference reinforcement is a simple function of quantities that can be estimated entirely from phenotypic data. We go on to study how postzygotic isolation caused by epistatic incompatibilities affects reinforcement of the preference. With only one pair of epistatic loci, reinforcement is enhanced by tighter linkage between the preference genes and the genes causing hybrid incompatibility. Reinforcement of the preference is also affected by the number of epistatically interacting genes involved in incompatibility, independent of the overall intensity of selection against hybrids.