How Dobzhansky-Muller Incompatibilities accumulate in presence of gene flow?

Interest in speciation research has experienced a recent shift from the classical problem of “When does it happen?” to more process-oriented questions: “How does it happen?” This is of relevance, in particular, for parapatric speciation, where the build-up of pre- or postzygotic barriers to gene-flow is a gradual process. The standard mechanism for the evolution of postzygotic isolation is the accumulation of Dobzhansky-Muller incompatibilities (DMI). While this process is reasonably well understood for allopatric speciation, one can ask how it unfolds in the face of gene flow. In a recent paper, Bank et al. (2012) have studied the very first step of this process and described the conditions for a first two-locus DMI to appear and be maintained. Here, we extend this model to study more than one DMI. In particular, we are interested in the influence of the presence of a first DMI on the fate of a second one and in predictions about the genetic architecture of the growing barrier. Using a combination of analytical and numerical methods, we analyze a migration-selection model with unidirectional gene flow from a continent to an island. As expected, we generally find that the presence of a first DMI makes it easier for further DMI's to be stably maintained – once it is established. However, the picture is much more complex for the establishment process of the second DMI itself. Depending on linkage patterns and the strength of the incompatibilities, the presence of the first DMI may either facilitate the origination of a second one or impede it. We interpret our results in the light of recent ideas of “islands of speciation” or “genome hitch-hiking.”