A convergence theorem for Markov chains arising in population genetics and the coalescent with selfing

A simple convergence theorem for sequences of Markov chains is presented in order to derive new ‘convergence-to-the-coalescent’ results for diploid neutral population models. For the so-called diploid Wright-Fisher model with selfing probability s and mutation rate θ, it is shown that the ancestral structure of n sampled genes can be treated in the framework of an n-coalescent with mutation rate θ∼ :=θ(1 – s/2), if the population size N is large and if the time is measured in units of (2 – s)N generations.