Pollak E
Department of Statistics, Iowa State University, Ames 50011.
Genetics. 1988 Sep;120(1):303-11. doi: 10.1093/genetics/120.1.303.
It is assumed that a population has M males in every generation, each of which is permanently mated with c-1 females, and that a proportion beta of matings are between males and their full sisters or half-sisters. Recurrence equations are derived for the inbreeding coefficient of one random individual, coefficients of kinship of random pairs of mates and probabilities of allelic identity when the infinite alleles model holds. If Ft is the inbreeding coefficient at time t and M is large, (1-Ft)/(1-Ft-1)----1-1/(2Ne) as t increases. The effective population number Ne = aM/[1 + (2a-1)FIS], where FIS is the inbreeding coefficient at equilibrium when M is infinite and the constant a depends upon the conditional probabilities of matings between full sibs and the two possible types of half-sibs. When there are M permanent couples, an approximation to the probability that an allele A survives if it is originally present in one AA heterozygote is proportional to FISs1 + (1-FIS)s2, where s1 and s2 are the selective advantages of AA and AA in comparison with AA. The paper concludes with a comparison between the results when there is partial selfing, partial full sib mating (c = 2) and partial sib mating when c is large.
假设每一代种群中有M个雄性个体，每个雄性个体都与c - 1个雌性个体永久交配，并且有比例为β的交配发生在雄性与其全姐妹或半姐妹之间。当无限等位基因模型成立时，推导出了一个随机个体的近交系数、随机配偶对的亲缘系数以及等位基因同一性概率的递归方程。如果Ft是时间t时的近交系数且M很大，随着t增加，(1 - Ft)/(1 - Ft - 1) ---- 1 - 1/(2Ne)。有效种群数量Ne = aM/[1 + (2a - 1)FIS]，其中FIS是当M为无穷大时平衡状态下的近交系数，常数a取决于全同胞之间以及两种可能类型半同胞之间交配的条件概率。当存在M个永久配偶对时，如果等位基因A最初存在于一个AA杂合子中，其存活概率的近似值与FISs1 + (1 - FIS)s2成比例，其中s1和s2分别是AA与AA相比AA的选择优势。本文最后比较了存在部分自交、部分全同胞交配（c = 2）以及c很大时部分半同胞交配情况下的结果。
