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, N_eI , and the variance effective number, N_eV , with various models. Diploidy, random mating, and discrete generations are assumed and formulas for N_eI 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 [Formula: see text] in which σ_sm,sf is the covariance of the number of male (m) and female (f) progeny of a parent of sex s (s = m or f), μ_sm and μ_sf 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 [Formula: see text] in which [Formula: see text] and σsm2 and σsf2 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.