Pfaffelhuber P, Studeny A
Ludwig-Maximilian University Munich, Munich, Germany.
J Math Biol. 2007 Sep;55(3):299-330. doi: 10.1007/s00285-007-0085-7. Epub 2007 Mar 30.
Consider a genetic locus carrying a strongly beneficial allele which has recently fixed in a large population. As strongly beneficial alleles fix quickly, sequence diversity at partially linked neutral loci is reduced. This phenomenon is known as a selective sweep. The fixation of the beneficial allele not only affects sequence diversity at single neutral loci but also the joint allele distribution of several partially linked neutral loci. This distribution can be studied using the ancestral recombination graph for samples of partially linked neutral loci during the selective sweep. To approximate this graph, we extend recent work by Etheridge et al. (Ann Appl Probab 16:685-729, 2006) and Schweinsberg and Durrett (Ann Appl Probab 15:1591-1651, 2005) using a marked Yule tree for the genealogy at a single neutral locus linked to a strongly beneficial one. We focus on joint genealogies at two partially linked neutral loci in the case of large selection coefficients alpha and recombination rates rho = theta(alpha/log alpha) between loci. Our approach leads to a full description of the genealogy with accuracy of theta((log alpha)(-2)) in probability. As an application, we derive the expectation of Lewontin's D as a measure for non-random association of alleles.
考虑一个携带近期在一个大群体中固定下来的强有益等位基因的遗传位点。由于强有益等位基因快速固定，部分连锁中性位点处的序列多样性会降低。这种现象被称为选择性清除。有益等位基因的固定不仅影响单个中性位点处的序列多样性，还影响几个部分连锁中性位点的联合等位基因分布。可以使用选择性清除期间部分连锁中性位点样本的祖先重组图来研究这种分布。为了近似这个图，我们扩展了埃瑟里奇等人（《应用概率年鉴》16:685 - 729，2006）以及施温斯贝格和杜雷特（《应用概率年鉴》15:1591 - 1651，2005）近期的工作，使用一个标记的尤尔树来表示与一个强有益位点连锁的单个中性位点的谱系。我们关注在选择系数α较大且位点间重组率ρ = θ(α / log α)的情况下，两个部分连锁中性位点的联合谱系。我们的方法以概率θ((log α)(-2))的精度对谱系进行了完整描述。作为一个应用，我们推导出作为等位基因非随机关联度量的莱温廷D的期望值。
