ON THE THEORY OF PARTIALLY INBREEDING FINITE POPULATIONS .4. THE EFFECTIVE POPULATION-SIZE FOR POLYPLOIDS REPRODUCING BY PARTIAL SELFING

Consider a population of size N in which there is reproduction by self ing with probability beta and by random mating with probability 1 - be ta. In each cell of any individual, homologous chromosomes appear 2n t imes, with n among them having been contributed by each parent. Wright [Proc. Natl. Acad. Sci. 24:372 (1938)] showed that if beta = 0, there is no double reduction in gamete formation, and a Poisson offspring d istribution, the probability of nonidentity by descent of two random c opies of a gene in an individual of generation t + 1 is approximately 1-1/2nN times as large as it is in generation 1 if N is large. This re sult will be generalized to populations with any beta greater than or equal to 0 and any offspring distribution. If n = 2 or 3, a result wil l be obtained that also holds for any probability of double reduction.