Abstract
Gene flow tends to impede the accumulation of genetic divergence. Here, we determine the limits for the evolution of postzygotic reproductive isolation in a model of two populations that are connected by gene flow. We consider two selective mechanisms for the creation and maintenance of a genetic barrier: local adaptation leads to divergence among incipient species due to selection against migrants, and Dobzhansky-Muller incompatibilities (DMIs) reinforce the genetic barrier through selection against hybrids. In particular, we are interested in the maximum strength of the barrier under a limited amount of local adaptation, a challenge that may initially face many incipient species. We first confirm that with classical two-locus DMIs, the maximum amount of local adaptation is indeed a limit to the strength of a genetic barrier. However, with three or more loci and cryptic epistasis, this limit holds no longer. In particular, we identify a minimal configuration of three epistatically interacting mutations that is sufficient to confer strong reproductive isolation.