On the theory of partially inbreeding finite populations. V. The effective size of a partially selfing age-structured population

Consider a large population, with the same age distribution at times 0,1,2,…, in which there is reproduction by selfing with probability β and by random mating with probability 1 − β. An individual between i and i + 1 units of age at time t is said to be in age group i at that time. Let L be the mean, among copies of an allele A in genotypes of offspring in age group 0, of ages of parents when the inbreeding coefficient has attained an equilibrium value. Then if there is no selection and allele A is originally present in one heterozygote, the probability that it is ultimately fixed is 1/(2N0L), where N0 is the number of individuals in age group 0 at any time. The effective population size can then be derived. It turns out to be the same as for a population with discrete generations having the same mean and variance of the number of successful gametes produced during a lifetime and the same number of individuals entering the population per generation.