Chesser R K, Rhodes O E, Sugg D W, Schnabel A
Savannah River Ecology Laboratory, Aiken, South Carolina 29802.
Genetics. 1993 Dec;135(4):1221-32. doi: 10.1093/genetics/135.4.1221.
Many derivations of effective population sizes have been suggested in the literature; however, few account for the breeding structure and none can readily be expanded to subdivided populations. Breeding structures influence gene correlations through their effects on the number of breeding individuals of each sex, the mean number of progeny per female, and the variance in the number of progeny produced by males and females. Additionally, hierarchical structuring in a population is determined by the number of breeding groups and the migration rates of males and females among such groups. This study derives analytical solutions for effective sizes that can be applied to subdivided populations. Parameters that encapsulate breeding structure and subdivision are utilized to derive the traditional inbreeding and variance effective sizes. Also, it is shown that effective sizes can be determined for any hierarchical level of population structure for which gene correlations can accrue. Derivations of effective sizes for the accumulation of gene correlations within breeding groups (coancestral effective size) and among breeding groups (intergroup effective size) are given. The results converge to traditional, single population measures when similar assumptions are applied. In particular, inbreeding and intergroup effective sizes are shown to be special cases of the coancestral effective size, and intergroup and variance effective sizes will be equal if the population census remains constant. Instantaneous solutions for effective sizes, at any time after gene correlation begins to accrue, are given in terms of traditional F statistics or transition equations. All effective sizes are shown to converge upon a common asymptotic value when breeding tactics and migration rates are constant. The asymptotic effective size can be expressed in terms of the fixation indices and the number of breeding groups; however, the rate of approach to the asymptote is dependent upon dispersal rates. For accurate assessment of effective sizes, initial, instantaneous or asymptotic, the expressions must be applied at the lowest levels at which migration among breeding groups is nonrandom. Thus, the expressions may be applicable to lineages within socially structured populations, fragmented populations (if random exchange of genes prevails within each population), or combinations of intra- and interpopulation discontinuities of gene flow. Failure to recognize internal structures of populations may lead to considerable overestimates of inbreeding effective size, while usually underestimating variance effective size.
文献中已经提出了许多有效种群大小的推导方法；然而，很少有方法考虑繁殖结构，并且没有一种方法能够轻易扩展到细分种群。繁殖结构通过影响每种性别的繁殖个体数量、每个雌性的平均后代数量以及雄性和雌性产生的后代数量的方差来影响基因相关性。此外，种群中的层次结构由繁殖群体的数量以及雄性和雌性在这些群体之间的迁移率决定。本研究推导了可应用于细分种群的有效大小的解析解。利用封装繁殖结构和细分的参数来推导传统的近交有效大小和方差有效大小。此外，研究表明，对于任何能够积累基因相关性的种群结构层次水平，都可以确定有效大小。给出了繁殖群体内基因相关性积累的有效大小（共同祖先有效大小）和繁殖群体间基因相关性积累的有效大小（群体间有效大小）的推导。当应用类似假设时，结果收敛于传统的单一种群度量。特别是，近交有效大小和群体间有效大小被证明是共同祖先有效大小的特殊情况，如果种群普查保持不变，群体间有效大小和方差有效大小将相等。根据传统的F统计量或转移方程，给出了基因相关性开始积累后任何时间的有效大小的瞬时解。当繁殖策略和迁移率恒定时，所有有效大小都收敛于一个共同的渐近值。渐近有效大小可以用固定指数和繁殖群体数量来表示；然而，接近渐近线的速率取决于扩散率。为了准确评估初始、瞬时或渐近的有效大小，这些表达式必须应用于繁殖群体间迁移非随机的最低层次。因此，这些表达式可能适用于社会结构种群中的谱系、碎片化种群（如果每个种群内基因随机交换）或基因流的种群内和种群间不连续性的组合。未能认识到种群的内部结构可能导致近交有效大小的显著高估，而通常会低估方差有效大小。
