A stochastic model for reproductive isolation under asymmetrical mating preferences

More and more evidence shows that mating preference is a mechanism that can lead to a reproductive isolation event. In this paper, we consider a haploid population living on two patches linked by migration. Individuals are ecologically and demographically neutral on the space and differ only on a trait, a or A, determining both mating success and migration rate. The special feature of this paper is to assume that the strength of the mating preference and the migration depend on the trait carried. Indeed patterns of mating preferences are generally asymmetrical between the subspecies of a population. We prove that mating preference alone can lead to a reproductive isolation and we explicit the time before reproductive isolation occurs. To reach this result we use an original method to study the limiting dynamical system, analyzing first the system without migration and adding migration with a perturbation method. Then using simulations, we study the time before reproductive isolation with respect to the strength of migration and the strength of both mating preferences, highlighting that large migration rates tend to favor the most permissive types.