The genetic balance between varying population size and selective neutrality

This note extends to an arbitrary offspring distribution the generalized model for random fluctuation of allele frequency, where population size is permitted to fluctuate randomly from generation to generation. Martingale methods analogous to those of Seneta (1974) and Heyde and Seneta (1975) are applied to discuss conditions for Pr(Y(1–Y)>0)>0, where Y is the (almost sure) limiting frequency of one allele. An overlapping generation study of the same phenomenon has recently been made by Heyde (1981).