A stochastic model for reproductive isolation under asymmetrical mating preferences

TL;DR

This paper models how asymmetrical mating preferences and migration influence reproductive isolation in a haploid population, revealing conditions under which isolation occurs and how parameters affect the timing.

Contribution

It introduces a stochastic model incorporating trait-dependent asymmetrical mating preferences and migration, analyzing their combined effect on reproductive isolation timing.

Findings

Mating preferences interacting with migration can lead to reproductive isolation.

Large migration rates tend to favor types with weaker mating preferences.

The model describes the time scale for reproductive isolation to occur.

Abstract

More and more evidence shows that mating preference is a mechanism that may lead to a reproductive isolation event. In this paper, a haploid population living on two patches linked by migration is considered. Individuals are ecologically and demographically neutral on the space and differ only on a trait, $a$ or $A$, affecting both mating success and migration rate. The special feature of this paper is to assume that the strengths 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. I prove that mating preference interacting with frequency-dependent migration behavior can lead to a reproductive isolation. Then, I describe the time before reproductive isolation occurs. To reach this result, I use an original method to study the limiting dynamical system, analyzing first the system without migration and adding migration with a perturbation method. Finally, I study how the time before reproductive isolation is influenced by the parameters of migration and of mating preferences, highlighting that large migration rates tend to favor types with weak mating preferences.