The Evolutionary Dynamics of a Genetic Barrier to Gene Flow: From the Establishment to the Emergence of a Peak of Divergence.

Divergent selection works when an allele establishes in the subpopulations in which it is adaptive, but not in the ones in which it is deleterious. While such a locally adaptive allele is maintained, the target locus of selection works as a genetic barrier to gene flow or a barrier locus. The genetic divergence (or FST) around the barrier locus can be maintained, while in other regions of the genome, genetic variation can be mixed by gene flow or migration. In this work, we consider theoretically the evolutionary process of a barrier locus, from its birth to stable preservation. Under a simple two-population model, we use a diffusion approach to obtain analytical expressions for the probability of initial establishment of a locally adaptive allele, the reduction of genetic variation due to the spread of the adaptive allele, and the process to the development of a sharp peak of divergence (genomic island of divergence). Our results will be useful to understanding how genomes evolve through local adaptation and divergent selection.