On some multilocus migration-selection models
Seminar Room 1, Newton Institute
The dynamics and equilibrium structure of a general deterministic population-genetic model of migration and selection acting on multiple multiallelic loci is studied. A large population of diploid individuals is distributed over finitely many demes connected by migration. Generations are discrete and nonoverlapping, migration is ergodic, all pairwise recombination rates are positive, and selection may vary across demes. It is proved that, in the absence of selection, all trajectories converge at a geometric rate to a manifold on which global linkage equilibrium holds and allele frequencies are identical across demes. For two are particularly interesting limiting cases, weak or strong migration, global (regular or singular) perturbation results establish generic convergence of trajectories and allow for a detailed study of the equilibrium structure. Applications to the problem of the maintenance of genetic variation in structured populations are briefly outlined.