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 beta and by random mating with probability 1-beta. 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 beta = 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 1-1/2nN times as large as it is in generation t if N is large. This result will be generalized to populations with any beta > or = 0 and any offspring distribution. If n = 2 or 3, a result will be obtained that also holds for any probability of double reduction.
Pollak
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Department of Statistics, Iowa State University, Ames 50011, USA.
Sabran
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D007178:Inbreeding; D008433:Mathematics; D008957:Models, Genetic; D010944:Plants / Q000235:genetics; D011123:Polyploidy; D011156:Population Density; D011336:Probability