INBREEDING AND VARIANCE EFFECTIVE POPULATION NUMBERS

Abstract

In this paper, a correction and extension of earlier work, we derive expressions for the inbreeding effective number, Neb and the variance effective number, N ev , with various models. Diploidy, random mating, and discrete generations are assumed and formulas for N e ! are given for six situations: isogamous monoecious populations with self-fertilization permitted or excluded; monoecious populations, male and female gametes distinguished, with self-fertilization permitted or excluded; and separate sexes with or without male and female progeny distinguished. N ev is given for monoecious and separate-sexed populations. Most higher animals have separate sexes, and male and female progeny are distinguished. Letting the subscript t represent the generation in which the inbreeding effect is manifest, the inbreeding effective number is (fmm,mr + J.LmmJ.tmf + (fern,IT + J.LfmlJ-cr No! 4Nm ,t-2 llm m ll m f 4Nf,t-2llfm llff in which Usm,sf is the covariance of the number of male (m) and female (f) progeny of a parent of sex s (s = m or f), Ilsm and Ilsf are the mean numbers of sons and daughters of a parent of sex s, and N s ,t-2 is the number in the grandparental generation. For the variance effective number I I I-~-+-­ N ev 4N ev m 4N ev f in which and u sm 2 and us'> are the variances in the number of sons and daughters of a parent of sex s. Observations are made at the same age in each generation.