Key role of recombination in evolutionary processes with migration between two habitats

Recombination is one of the leading forces of evolutionary dynamics. Although the importance of both recombination and migration in evolution is well recognized, there is currently no exact theory of evolutionary dynamics for large genome models that incorporates recombination, mutation, selection (quasispecies model with recombination), and spatial dynamics. To address this problem, we analyze the simplest spatial evolutionary process, namely, evolution of haploid populations with mutation, selection, recombination, and unidirectional migration, in its exact analytical form. This model is based on the quasispecies theory with recombination, but with replicators migrating from one habitat to another. In standard evolutionary models involving one habitat, the evolutionary processes depend on the ratios of fitness for different sequences. In the case of migration, we consider the absolute fitness values because there is no competition for resources between the population of different habitats. In the standard model without epistasis, recombination does not affect the mean fitness of the population. When migration is introduced, the situation changes drastically such that recombination can affect the mean fitness as strongly as mutation, as has been observed by Li and Nei for a few loci model without mutations. We have solved our model in the limit of large genome size for the fitness landscapes having different peaks in the first and second habitats and obtained the total population sizes for both habitats as well as the proportion of the population around two peak sequences in the second habitat. We identify four phases in the model and present the exact solutions for three of them.