Olusanya, O.; Barton, N. H.; Polechova, J.

This study extends existing soft selection models of local adaptation in metapopulations from two habitats to a multi-habitat scenario, where each habitat exerts unique selection pressures. Specifically, we examine a three-habitat multilocus model in which each allele is favored in habitat 1, disfavored in habitat 3, and the selection pressure in the intermediate habitat may be different across loci. Employing the diffusion and fixed state approximations under the assumption of linkage equilibrium, we investigate conditions for the persistence of a polymorphism. We derive analytical thresholds for such persistence, which reveal scaling for the model parameters, local deme size (N), migration rate (m), selection pressure (si) and the proportion, (i) of each habitat. We show that under the assumption of infinitely many islands and selective neutrality in the intermediate habitat, the size of the intermediate habitat does not affect the maintenance of polymorphism. With symmetric selection pressure (s1=s3=s) in habitats 1 and 3, the system can be fully characterized by the product Ns, the product Nm, and a parameter {beta}, defined as the ratio of the size of habitat 1 (favoring the allele) to habitat 3 (where the allele is disfavored). We find that the range of polymorphism widens as gene flow between demes decreases and the symmetry of habitats increases ({beta} approaches 1). In the final section, we explore the effect of drift on the critical migration threshold as well as the effect of symmetry between selection. We demonstrate that genetic drift considerably lowers the critical migration threshold required for the maintenance of polymorphism. Furthermore, when each island is small but there are (infinitely) many of them, relatively low levels of gene flow can have a large impact in preventing genetic differentiation in a fragmented population.