INBREEDING AND VARIANCE EFFECTIVE POPULATION NUMBERS

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 is1 N eI=σ mm , mf + μ mmμ mf4 N m , t ‐ 2μ mmμ mf+σ fm , ff + μ fmμ ff4 N f , t ‐ 2μ fmμ ffin which σ s m, s f is the covariance of the number of male (m) and female (f) progeny of a parent of sex s ( s = m or f), μ s m and μ s f 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 number1 N eV≈ 1 4 N eVm+ 1 4 N eVfin which1 N eV s= 1 2 ( 2 N s , t ‐ 1 ‐ 1 )[ 1 μ s m+ 1 μ s f+σ s m 2μ s m 2+ 2 σ s m , s fμ s mμ s f+σ s f 2μ s f 2]andσ s m 2andσ s f 2are 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.