Blath Jochen, Cronjäger Mathias Christensen, Eldon Bjarki, Hammer Matthias
TU Berlin, Institut für Mathematik, 10623 Berlin, Germany.
University of Oxford, Department of Statistics, OX1 3LB Oxford, UK.
Theor Popul Biol. 2016 Aug;110:36-50. doi: 10.1016/j.tpb.2016.04.002. Epub 2016 Apr 22.
We give recursions for the expected site-frequency spectrum associated with so-called Xi-coalescents, that is exchangeable coalescents which admit simultaneous multiple mergers of ancestral lineages. Xi-coalescents arise, for example, in association with population models of skewed offspring distributions with diploidy, recurrent advantageous mutations, or strong bottlenecks. In contrast, the simpler Lambda-coalescents admit multiple mergers of lineages, but at most one such merger each time. Xi-coalescents, as well as Lambda-coalescents, can predict an excess of singletons, compared to the Kingman coalescent. We compare estimates of coalescent parameters when Xi-coalescents are applied to data generated by Lambda-coalescents, and vice versa. In general, Xi-coalescents predict fewer singletons than corresponding Lambda-coalescents, but a higher count of mutations of size larger than singletons. We fit examples of Xi-coalescents to unfolded site-frequency spectra obtained for autosomal loci of the diploid Atlantic cod, and obtain different coalescent parameter estimates than obtained with corresponding Lambda-coalescents. Our results provide new inference tools, and suggest that for autosomal population genetic data from diploid or polyploid highly fecund populations who may have skewed offspring distributions, one should not apply Lambda-coalescents, but Xi-coalescents.
我们给出了与所谓的Xi-合并相关的期望位点频率谱的递推关系，即允许祖先谱系同时进行多次合并的可交换合并。例如，Xi-合并与具有二倍体、反复出现的有利突变或强烈瓶颈效应的偏态后代分布的种群模型相关。相比之下，更简单的Lambda-合并允许谱系进行多次合并，但每次最多只有一次这样的合并。与金曼合并相比，Xi-合并以及Lambda-合并都可以预测单倍体的过量。我们比较了将Xi-合并应用于由Lambda-合并生成的数据时以及反之亦然时合并参数的估计值。一般来说，Xi-合并预测的单倍体比相应的Lambda-合并少，但大于单倍体大小的突变计数更高。我们将Xi-合并的例子拟合到从二倍体大西洋鳕鱼的常染色体位点获得的展开位点频率谱上，并获得了与相应的Lambda-合并不同的合并参数估计值。我们的结果提供了新的推断工具，并表明对于来自可能具有偏态后代分布的二倍体或多倍体高繁殖力种群的常染色体群体遗传数据，不应应用Lambda-合并，而应应用Xi-合并。
