Evolution of specialization in heterogeneous environments: equilibrium between selection, mutation and migration

Adaptation in spatially heterogeneous environments results from the balance between local selection, mutation and migration. We study the interplay among these different evolutionary forces and demography in a classical two habitat scenario with asexual reproduction. We develop a new theoretical approach that fills a gap between the restrictive assumptions of Adaptive Dynamics and Quantitative Genetics. This analysis yields more accurate predictions of the equilibrium phenotypic distribution in different habitats. We examine the evolutionary equilibrium under general conditions where demography and selection may be non-symmetric between the two habitats. In particular we show how migration may increase differentiation in a source-sink scenario. We discuss the implications of these analytic results for the adaptation of organisms with large mutation rates such as RNA viruses.