Pollak E
Department of Statistics, Iowa State University, Ames 50011, USA.
Math Biosci. 1998 Aug 1;151(2):123-34. doi: 10.1016/s0025-5564(98)10009-3.
Consider a large population, with the same age distribution at times 0, 1, 2, ..., in which there is reproduction by selfing with probability beta and by random mating with probability 1-beta. An individual between i and i + 1 units of age at time t is said to be in age group i at that time. Let L be the mean, among copies of an allele A in genotypes of offspring in age group 0, of ages of parents when the inbreeding coefficient has attained an equilibrium value. Then if there is no selection and allele A is originally present in one heterozygote, the probability that it is ultimately fixed is 1/(2N0L), where N0 is the number of individuals in age group 0 at any time. The effective population size can then be derived. It turns out to be the same as for a population with discrete generations having the same mean and variance of the number of successful gametes produced during a lifetime and the same number of individuals entering the population per generation.
考虑一个大群体，在时刻0、1、2……具有相同的年龄分布，其中自交繁殖的概率为β，随机交配的概率为1 - β。在时刻t年龄介于i和i + 1单位之间的个体在该时刻被称为处于年龄组i。令L为年龄组0的后代基因型中等位基因A的拷贝中，当近交系数达到平衡值时亲本年龄的均值。那么，如果没有选择且等位基因A最初存在于一个杂合子中，它最终固定的概率为1/(2N0L)，其中N0是任何时刻年龄组0中的个体数量。然后可以推导出有效种群大小。结果表明，它与具有离散世代的群体相同，该群体在一生中产生的成功配子数量具有相同的均值和方差，并且每代进入群体的个体数量相同。
