Abstract
We consider the model of asexual evolution with migration, which was proposed by Waclaw etal. [Phys. Rev. Lett. 105, 268101 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.268101]. This model setting is based on the standard mutation scheme from the quasispecies theory but with replicators moving from one habitat to another. The primary goal is to solve exactly the infinite population-genome length version of the model for the independent random distribution of fitnesses considered in the original paper. Moreover, we propose the analytical solution for the single peak and the symmetric fitness landscape. Our analytical solution is exact at the limit of large N. We found two phases-the correlated phase with the identical distributions of mutations in both habitats and the uncorrelated phase where the second habitat is choosing another peak of distribution in sequence space compared to the peak in the first habitat.
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