Sex-specific incompatibility generates locus-specific rates of introgression between species.

Disruption of interactions among ensembles of epistatic loci has been shown to contribute to reproductive isolation among various animal and plant species. Under the Bateson-Dobzhansky-Muller model, such interspecific incompatibility arises as a by-product of genetic divergence in each species, and the Orr-Turelli model indicates that the number of loci involved in incompatible interactions may "snowball" over time. We address the combined effect of multiple incompatibility loci on the rate of introgression at neutral marker loci across the genome. Our analysis extends previous work by accommodating sex specificity: differences between the sexes in the expression of incompatibility, in rates of crossing over between neutral markers and incompatibility loci, and in transmission of markers or incompatibility factors. We show that the evolutionary process at neutral markers in a genome subject to incompatibility selection is well approximated by a purely neutral process with migration rates appropriately scaled to reflect the influence of selection targeted to incompatibility factors. We confirm that in the absence of sex specificity and functional epistasis among incompatibility factors, the barrier to introgression induced by multiple incompatibility factors corresponds to the product of the barriers induced by the factors individually. A new finding is that barriers to introgression due to sex-specific incompatibility depart in general from multiplicativity. Our partitioning of variation in relative reproductive rate suggests that such departures derive from associations between sex and incompatibility and between sex and neutral markers. Concordant sex-specific incompatibility (for example, greater impairment of male hybrids or longer map lengths in females) induces lower barriers (higher rates of introgression) than expected under multiplicativity, and discordant sex-specific incompatibility induces higher barriers.