Santiago E, Caballero A
Institute of Cell, Animal and Population Biology, University of Edinburgh, Scotland.
Genetics. 1995 Feb;139(2):1013-30. doi: 10.1093/genetics/139.2.1013.
Equations to approximate the effective size (Ne) of populations under continued selection are obtained that include the possibility of partial full-sib mating and other systems such as assortative mating. The general equation for the case of equal number of sexes and constant number of breeding individuals (N) is Ne = 4N/[2(1 - alpha I) + (Sk2 + 4Q2C2) (1 + alpha I + 2 alpha O)], where Sk2 is the variance of family size due to sampling without selection, C2 is the variance of selective advantages among families (the squared coefficient of variation of the expected number of offspring per family), alpha I is the deviation from Hardy-Weinberg proportions, alpha O is the correlation between genes of male and female parents, and Q2 is the term accounting for the cumulative effect of selection on an inherited trait. This is obtained as Q = 2/[2 - G(1 + r)], where G is the remaining proportion of genetic variance in selected individuals and r is the correlation of the expected selective values of male and female parents. The method is also extended to the general case of different numbers of male and female parents. The predictive value of the formulae is tested under a model of truncation selection with the infinitesimal model of gene effects, where C2 and G are a function of the selection intensity, the heritability and the intraclass correlation of sibs. Under random mating r = alpha I = -1/(N - 1) and alpha O = 0. Under partial full-sib mating with an average proportion beta of full-sib matings per generation, r approximately beta and alpha O approximately alpha I approximately beta/(4 - 3 beta). The prediction equation is compared to other approximations based on the long-term contributions of ancestors to descendants. Finally, based on the approach followed, a system of mating (compensatory mating) is proposed to reduce rates of inbreeding without loss of response in selection programs in which selected individuals from the largest families are mated to those from the smallest families.
得出了用于估算持续选择下种群有效大小（Ne）的方程，其中考虑了部分全同胞交配的可能性以及其他交配系统，如选型交配。在性别数量相等且繁殖个体数量恒定（N）的情况下，通用方程为Ne = 4N/[2(1 - αI) + (Sk2 + 4Q2C2) (1 + αI + 2αO)]，其中Sk2是无选择抽样时家庭大小的方差，C2是家庭间选择优势的方差（每个家庭预期后代数量的变异系数平方），αI是偏离哈迪-温伯格比例的偏差，αO是雄性和雌性亲本基因之间的相关性，Q2是考虑选择对遗传性状累积效应的项。其计算方式为Q = 2/[2 - G(1 + r)]，其中G是所选个体中遗传方差的剩余比例，r是雄性和雌性亲本预期选择值的相关性。该方法还扩展到了雄性和雌性亲本数量不同的一般情况。在基因效应的无穷小模型下的截断选择模型中，对公式的预测值进行了检验，其中C2和G是选择强度、遗传力和同胞组内相关性的函数。在随机交配情况下，r = αI = -1/(N - 1)且αO = 0。在每代全同胞交配平均比例为β的部分全同胞交配情况下，r约为β，αO约为αI约为β/(4 - 3β)。将预测方程与基于祖先对后代长期贡献的其他近似方法进行了比较。最后，基于所采用的方法，提出了一种交配系统（补偿性交配），以降低近亲繁殖率，同时在选择计划中不损失选择响应，即在该计划中，将来自最大家庭的所选个体与来自最小家庭的个体进行交配。
