Huss Elisabeth, Pfaffelhuber Peter
Abteilung für Mathematische Stochastik, Albert-Ludwigs University of Freiburg, Ernst-Zermelo-Straße 1, D - 79104 Freiburg, Germany.
Abteilung für Mathematische Stochastik, Albert-Ludwigs University of Freiburg, Ernst-Zermelo-Straße 1, D - 79104 Freiburg, Germany.
Theor Popul Biol. 2020 Feb;131:2-11. doi: 10.1016/j.tpb.2019.10.002. Epub 2019 Nov 21.
For a panmictic population of constant size evolving under neutrality, Kingman's coalescent describes the genealogy of a population sample in equilibrium. However, for genealogical trees under selection, not even expectations for most basic quantities like height and length of the resulting random tree are known. Here, we give an analytic expression for the distribution of the total tree length of a sample of size n under low levels of selection in a two-alleles model. We can prove that trees are shorter than under neutrality under genic selection and if the beneficial mutant has dominance h<1∕2, but longer for h>1∕2. The difference from neutrality is O(α) for genic selection with selection intensity α and O(α) for other modes of dominance.
对于在中性条件下进化的恒定大小的随机交配群体，金曼合并理论描述了处于平衡状态的群体样本的谱系。然而，对于在选择作用下的谱系树，即使是关于所得随机树的高度和长度等最基本数量的期望值也尚不明确。在此，我们给出了在双等位基因模型中低选择水平下大小为(n)的样本的总树长分布的解析表达式。我们可以证明，在基因选择下，树比在中性条件下更短，并且如果有益突变具有显性(h < 1/2)，但当(h > 1/2)时则更长。对于选择强度为(\alpha)的基因选择，与中性的差异为(O(\alpha))，对于其他显性模式则为(O(\alpha))。
