On the theory of partially inbreeding finite populations. IV. The effective population size for polyploids reproducing by partial selfing

Consider a population of size N in which there is reproduction by selfing with probability β and by random mating with probability 1 − β. In each cell of any individual, homologous chromosomes appear 2n times, with n among them having been contributed by each parent. Wright [Proc. Natl. Acad. Sci. 24:372 (1938)] showed that if β = 0, there is no double reduction in gamete formation, and a Poisson offspring distribution, the probability of nonidentity by descent of two random copies of a gene in an individual of generation t + 1 is approximately 1 − 12nN times as large as it is in generation t if N is large. This result will be generalized to populations with any β ≥ 0 and any offspring distribution. If n = 2 or 3, a result will be obtained that also holds for any probability of double reduction.