Qu Jiayi, Kachman Stephen D, Garrick Dorian, Fernando Rohan L, Cheng Hao
Department of Animal Science, University of California, Davis, Davis, CA, United States.
Department of Statistics, University of Nebraska Lincoln, Lincoln, NE, United States.
Front Genet. 2020 Apr 21;11:362. doi: 10.3389/fgene.2020.00362. eCollection 2020.
Linkage disequilibrium (LD), often expressed in terms of the squared correlation ( ) between allelic values at two loci, is an important concept in many branches of genetics and genomics. Genetic drift and recombination have opposite effects on LD, and thus will keep changing until the effects of these two forces are counterbalanced. Several approximations have been used to determine the expected value of at equilibrium in the presence or absence of mutation. In this paper, we propose a probability-based approach to compute the exact distribution of allele frequencies at two loci in a finite population at any generation conditional on the distribution at generation - 1. As is a function of this distribution of allele frequencies, this approach can be used to examine the distribution of over generations as it approaches equilibrium. The exact distribution of LD from our method is used to describe, quantify, and compare LD at different equilibria, including equilibrium in the absence or presence of mutation, selection, and filtering by minor allele frequency. We also propose a deterministic formula for expected LD in the presence of mutation at equilibrium based on the exact distribution of LD.
连锁不平衡（LD）通常用两个位点等位基因值之间的平方相关性（ ）来表示，是遗传学和基因组学许多分支中的一个重要概念。遗传漂变和重组对LD有相反的影响，因此 会不断变化，直到这两种力量的影响达到平衡。在有或没有突变的情况下，已经使用了几种近似方法来确定平衡时 的期望值。在本文中，我们提出了一种基于概率的方法，以计算有限群体中任意一代两个位点等位基因频率的精确分布，条件是基于第 - 1代的分布。由于 是这种等位基因频率分布的函数，当 接近平衡时，这种方法可用于检验其在几代中的分布。我们方法中LD的精确分布用于描述、量化和比较不同平衡状态下的LD，包括在没有或存在突变、选择以及按次要等位基因频率进行筛选时的平衡状态。我们还基于LD的精确分布提出了一个在平衡时有突变情况下预期LD的确定性公式。
