The evolution of dispersal in random environment

In this paper we introduce a stochastic model for a population living and migrating between s sites without distinction in the states between residents and immigrants. The evolutionary stable strategies (ESS) is characterized by the maximization of a stochastic growth rate. We obtain that the expectation of reproductive values, normalized by some random quantity, are constant on all sites and that the expectation of the normalized vector population structure is proportional to eigenvector of the dispersion matrix associated to eigenvalue one, which are, in some way, analogous to the results obtained in the deterministic case.