The evolution of genomic islands by increased establishment probability of linked alleles

Genomic islands are clusters of loci with elevated divergence that are commonly found in population genomic studies of local adaptation and speciation. One explanation for their evolution is that linkage between selected alleles confers a benefit, which increases the establishment probability of new mutations that are linked to existing locally adapted polymorphisms. Previous theory suggested there is only limited potential for the evolution of islands via this mechanism, but involved some simplifying assumptions that may limit the accuracy of this inference. Here, we extend previous analytical approaches to study the effect of linkage on the establishment probability of new mutations and identify parameter regimes that are most likely to lead to evolution of islands via this mechanism. We show how the interplay between migration and selection affects the establishment probability of linked vs. unlinked alleles, the expected maximum size of genomic islands, and the expected time required for their evolution. Our results agree with previous studies, suggesting that this mechanism alone is unlikely to be a general explanation for the evolution of genomic islands. However, this mechanism could occur more readily if there were other pre-adaptations to reduce local rates of recombination or increase the local density of mutational targets within the region of the island. We also show that island formation via erosion following secondary contact is much more rapid than island formation from de novo mutations, suggesting that this mechanism may be more likely.