Rates of Approach to Homozygosity for Finite Stochastic Models with Variable Population Size

A model based on the classical Wright-Fisher random sampling formulation, but allowing general offspring number distribution and fluctuations in population size, is discussed. With the general theory of Markoff chains, the rate of approach to homozygosity is obtained as the largest eigenvalue of a certain matrix. A number of examples are considered to take account of completely random, cyclic, and some other kinds of fluctuations in the population size. In the multiallelic case, the rate of loss of an allele is obtained.