Crow James F, Denniston Carter
Genetics Department, University of Wisconsin, Madison, WI, 53706.
Evolution. 1988 May;42(3):482-495. doi: 10.1111/j.1558-5646.1988.tb04154.x.
In this paper, a correction and extension of earlier work, we derive expressions for the inbreeding effective number, N , and the variance effective number, N , with various models. Diploidy, random mating, and discrete generations are assumed and formulas for N 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 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 is the covariance of the number of male (m) and female (f) progeny of a parent of sex s (s = m or f), μ and μ are the mean numbers of sons and daughters of a parent of sex s, and N 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.
在本文中，作为对早期工作的修正与扩展，我们推导了不同模型下近交有效数(N_i)和方差有效数(N_v)的表达式。假定为二倍体、随机交配及离散世代，并给出了六种情况下(N_i)的公式：允许或排除自交的同配雌雄同体种群；区分雄配子和雌配子、允许或排除自交的雌雄同体种群；以及区分或不区分雌雄后代的两性种群。给出了雌雄同体和两性种群的(N_v)。大多数高等动物为两性，且区分雌雄后代。令下标(t)表示近交效应显现的世代，近交有效数为([公式：见原文])，其中(\sigma)是性别为(s)（(s = m)或(f)）的亲本所产生的雄性（(m)）和雌性（(f)）后代数量的协方差，(\mu_m)和(\mu_f)是性别为(s)的亲本所生儿子和女儿的平均数量，(N)是祖代的个体数量。对于方差有效数([公式：见原文])，其中([公式：见原文])，(\sigma_{sm}^2)和(\sigma_{sf}^2)是性别为(s)的亲本所生儿子和女儿数量的方差。在每一代中均在相同年龄进行观测。
