The inbreeding effective population number and the expected homozygosity for an X-linked locus

Assuming random mating and discrete nonoverlapping generations, the inbreeding effective population number, N(i)e, is calculated for an X-linked locus. For large populations, the result agrees with the variance effective population number. As an application, the maintenance of genetic variability by the joint action of mutation and random drift is investigated. It is shown that, if every allele mutates at rate u to new types, then the probabilities of identify in state (and hence the expected homozygosity of females) converge to the approximate value (1 + 4N(i)eu)-1 at the approximate asymptotic rate exp(-[2u + (2N(i)e)-1]t).