Uecker Hildegard, Setter Derek, Hermisson Joachim
Mathematics and Biosciences Group, Faculty of Mathematics and Max F. Perutz Laboratories, University of Vienna, 1090 , Vienna, Austria,
J Math Biol. 2015 Jun;70(7):1523-80. doi: 10.1007/s00285-014-0802-y. Epub 2014 Jul 4.
By hybridization and backcrossing, alleles can surmount species boundaries and be incorporated into the genome of a related species. This introgression of genes is of particular evolutionary relevance if it involves the transfer of adaptations between populations. However, any beneficial allele will typically be associated with other alien alleles that are often deleterious and hamper the introgression process. In order to describe the introgression of an adaptive allele, we set up a stochastic model with an explicit genetic makeup of linked and unlinked deleterious alleles. Based on the theory of reducible multitype branching processes, we derive a recursive expression for the establishment probability of the beneficial allele after a single hybridization event. We furthermore study the probability that slightly deleterious alleles hitchhike to fixation. The key to the analysis is a split of the process into a stochastic phase in which the advantageous alleles establishes and a deterministic phase in which it sweeps to fixation. We thereafter apply the theory to a set of biologically relevant scenarios such as introgression in the presence of many unlinked or few closely linked deleterious alleles. A comparison to computer simulations shows that the approximations work well over a large parameter range.
通过杂交和回交，等位基因可以跨越物种界限，并被整合到相关物种的基因组中。如果基因渗入涉及种群间适应性的转移，那么这种基因渗入在进化上具有特殊的相关性。然而，任何有益的等位基因通常会与其他外来等位基因相关联，这些外来等位基因往往是有害的，并会阻碍基因渗入过程。为了描述适应性等位基因的渗入，我们建立了一个具有连锁和非连锁有害等位基因明确遗传组成的随机模型。基于可约多类型分支过程的理论，我们推导出了单个杂交事件后有益等位基因建立概率的递归表达式。我们还研究了轻微有害等位基因搭便车固定的概率。分析的关键在于将该过程分为一个有利等位基因建立的随机阶段和一个它席卷至固定的确定性阶段。此后，我们将该理论应用于一组生物学相关的情景，如存在许多非连锁或少数紧密连锁有害等位基因时的基因渗入。与计算机模拟的比较表明，这些近似在很大的参数范围内都能很好地发挥作用。
