Establishment and maintenance of adaptive genetic divergence under migration, selection, and drift

There is a long tradition in population genetics of exploring the maintenance of variation under migration-selection balance using deterministic models that assume infinite population size. With finite population size, stochastic dynamics can greatly reduce the potential for the maintenance of polymorphism, but this has yet to be explored in detail. Here, classical two-patch models are extended to predict: (1) the probability of a locally beneficial mutation rising in frequency in the patch where it is favored and (2) the critical threshold migration rate above which the maintenance of polymorphism is much less likely. Individual-based simulations show that these approximations provide accurate predictions across a wide range of parameter space.