Abstract
Adaptation in spatially heterogeneous environments results from the balance between local selection, mutation and migration. We study the interplay among these di↵erent evolutionary forces and demography in a classical two-habitat scenario with asexual reproduction. We develop a new theoretical approach that goes beyond the Adaptive Dynamics framework and allows us to explore the e↵ect of high mutation rates on the stationary phenotypic distribution. We show that this approach improves the classical Gaussian approximation and captures accurately the shape of this equilibrium phenotypic distribution in one and two-population scenarios. 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 di↵erentiation 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.