共祖系数为概率f_AB，表示一个来自个体A，另一个来自个体B的两个同源基因（或等位基因）在系谱上是一致或相同的概率，也就是说来自同一祖先基因的概率。而其互补的概率1-f_AB，表示两个同源基因（或等位基因）来自没有亲缘关系的祖先的概率。（The probability f_AB that two homologous genes , one from individual A and the other from individual B, are identical by descent, i.e., are descended from the same ancestral gene. The complementary probability, 1- f_AB, is the probability that these two genes come from unrelated ancestors.）

 

    共祖系数（coancestry coefficient）、θ或FST，是用来描述从一个亚群中不同个体上采集样本，样本中两个基因（严格而言是等位基因）之间的相关关系。（An essential population genetics parameter is the ‘coancestry coefficient’, or θ, or FST, which is the correlation between two genes sampled from distinct individuals within a subpopulation.）

 

    附件中有Reynolds J, Weir BS, Cockerham CC发表在Genetics上的原始论文《共祖系数估算：短期遗传距离的基础》（Estimation of the coancestry coefficient: Basis for a short-term genetic distance）。

        A distance measure for populations diverging by drift only is based on the coancestry coefficient θ, and three estimators of the distance D = -ln(1 -θ) are constructed for multiallelic, multilocus data. Simulations of a monoecious population mating at random showed that a weighted ratio of single-locus estimators performed better than an unweighted average or a least squares estimator. Jackknifing over loci provided satisfactory variance estimates of distance values. In the drift situation, in which mutation is excluded, the weighted estimator of D appears to be a better measure of distance than others that have appeared in the literature.

 

    另见网站“司法科学中的共祖系数”（The Coancestry Coefficient in Forensic Science）链接：

http://www.promega.com/geneticidproc/ussymp8proc/25.html

        There are several ways of describing the meaning of theta, but they all refer to the relationship of pairs of alleles within subpopulations.

Identity by descent

        Alleles that descend from a single ancestral allele are said to be identical by descent, ibd, and theta can be defined as the probability that two alleles, one taken at random from each of two individuals, are ibd. The probability that an individual carries allele Ai, given that another individual in the same subpopulation has been found to carry that allele, is Pr(Ai/Ai) = θ+(1-θ)Pi.

        This result follows from the definition of theta as an ibd probability, or it could be used to define theta. It is, however, a result that holds as an average over all replicates of a subpopulation with this value of theta.

        The concept of identity by descent is a probabilistic one - even if two alleles are known to have come from the same individual, there is only a 50% chance that they are copies of the same allele carried by that individual. This random choice of alleles for transmission from parent to offspring is one of the reasons why evolution is a stochastic process. The evolutionary outcome of a particular history for a population cannot be specified exactly, but the expected outcome(s) can be described. The conditional probability statement in Equation 2 is a statement about random pairs of individuals, averaged over subpopulations.

Estimation of the coancestry coefficient

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