The Limits to Parapatric Speciation II: Strengthening a Preexisting Genetic Barrier to Gene Flow in Parapatry

Parapatric speciation has recently received a lot of attention. By encompassing the whole continuum between allopatric and sympatric scenarios, it includes many potential scenarios for the evolution of new species. Building upon previous work, we investigate how a genetic barrier to gene flow, that relies on a single postzygotic genetic incompatibility, may further evolve. We consider a continent island model with three loci involved in pairwise Dobzhansky-Muller incompatibilities (DMIs). Using a deterministic and analytic approach, we derive the conditions for invasion of a new mutation and its consequences on an already existing genetic barrier to gene flow. We focus on quantifying the impact of the epistasis generated by the new mutation on the genetic barrier. We show that the accumulation of genetic incompatibilities in the presence of gene flow is a complex process, where new mutations can either strengthen or destroy a preexisting barrier. In particular, preexisting polymorphism and incompatibilities do not always facilitate the growth of the genetic barrier by accumulation of further barrier genes. Migration may disrupt the snowball effect (the accelerating rate of DMI accumulation in allopatry) because incompatibilities are directly tested by selection. Our results also show an ambiguous role of gene flow, which can either impede or facilitate the strengthening of the genetic barrier. Overall, our results illustrate how the inclusion of gene flow renders the building of a genetic barrier difficult to analyze.