Effective population numbers and mean times to extinction in dioecious populations with overlapping generations

Abstract

We consider a finite dioecious random mating population that is observed at times 0,1,… Let there be age groups 0,1,…,K1 among males and age groups 0,1,…,K2 among females, so that the population consists of K1+K2+2 parts, called age-sex classes. It is assumed that the numbers of individuals in the various age-sex classes do not change with time and that there is no mutation, selection, or migration. One locus, with an allele A1 that is initially rare, is studied. A general result obtained by Pollak (1979) is then used to obtain expressions for the effective population number, whether the locus under consideration is autosomal or sex-linked. Another result in the same paper is used to derive expressions for the mean time to extinction of a line of individuals with A1, which are descended from a single ancestor in age-sex class (ai), where i=1,2 and a=1,…,Ki.