Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec H3C 3J7, Canada.
Genetics. 2012 Feb;190(2):691-707. doi: 10.1534/genetics.111.136309. Epub 2011 Nov 17.
We use the ancestral influence graph (AIG) for a two-locus, two-allele selection model in the limit of a large population size to obtain an analytic approximation for the probability of ultimate fixation of a single mutant allele A. We assume that this new mutant is introduced at a given locus into a finite population in which a previous mutant allele B is already segregating with a wild type at another linked locus. We deduce that the fixation probability increases as the recombination rate increases if allele A is either in positive epistatic interaction with B and allele B is beneficial or in no epistatic interaction with B and then allele A itself is beneficial. This holds at least as long as the recombination fraction and the selection intensity are small enough and the population size is large enough. In particular this confirms the Hill-Robertson effect, which predicts that recombination renders more likely the ultimate fixation of beneficial mutants at different loci in a population in the presence of random genetic drift even in the absence of epistasis. More importantly, we show that this is true from weak negative epistasis to positive epistasis, at least under weak selection. In the case of deleterious mutants, the fixation probability decreases as the recombination rate increases. This supports Muller's ratchet mechanism to explain the accumulation of deleterious mutants in a population lacking recombination.
我们使用祖先影响图（AIG）来研究两基因座、两等位基因的选择模型，在大种群数量的极限下，我们得到了一个单一突变等位基因 A 最终固定的概率的解析近似值。我们假设，在一个有限的种群中，一个新的突变体 A 被引入到一个特定的基因座中，而另一个基因座上已经存在着一个与野生型分离的先前的突变体 B。我们推断，如果等位基因 A 与 B 存在正的上位性相互作用且 B 有利，或者 A 与 B 没有上位性相互作用且 A 自身有利，那么随着重组率的增加，固定的概率会增加。只要重组分数和选择强度足够小，种群数量足够大，这种情况就会成立。特别是，这证实了 Hill-Robertson 效应，该效应预测，即使不存在上位性，在随机遗传漂变的情况下，重组也会使不同基因座上有利突变体最终固定的可能性增加。更重要的是，我们表明，至少在弱选择下，从弱负上位性到正上位性都是如此。对于有害突变体，随着重组率的增加，固定的概率会降低。这支持了 Muller 的棘轮机制，该机制可以解释在缺乏重组的情况下，有害突变体在种群中积累的现象。
