The inbreeding effective number and the effective number of alleles in a population that varies in size

Consider a population that does not change in size. If it is assumed that there are an infinite number of possible neutral alleles at a locus and u is the probability that a particular gene mutates to some other gene in one generation, the effective number of alleles n_e is computed to be 4N_eu + 1, where N_e is the inbreeding effective population number. It is assumed in this paper that the number of individuals in a monoecious population, or the numbers of males and females in a dioecious population, are states in a finite irreducible Markov chain. In general it is impossible to obtain a single value of n_e. In some cases where the computation of n_e is possible, the results are as follows. When the population is monoecious, N_e is the reciprocal of the asymptotic average, over population sizes, of the probabilities that two gametes uniting to form an individual came from the same individual one generation earlier. In dioecious populations, N_e is the reciprocal of the long-run average of the probabilities that two homologous genes in separate individuals of one generation came from the same individual one generation earlier. Special cases are discussed.