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A limit theorem for two-locus diffusion models in population genetics

A limit theorem of Kurtz for perturbed operator semigroups is applied to show that the two-locus diffusion model in population genetics (allowing for selection, mutation, and migration) converges to a linkage-equilibrium diffusion model as Nc →∞, where N is the population size and c is the recombination fraction; in fact, with an appropriate change of variables, the limiting diffusion is what has been called the independent-loci diffusion model. This generalizes a result of Littler.