论文标题
同时具有强大和弱选择的Moran模型：融合$λ$ -Wright-Fisher SDE
Moran model with simultaneous strong and weak selections: convergence towards a $Λ$-Wright-Fisher SDE
论文作者
论文摘要
我们研究一个固定尺寸的人群模型，经历了强大的选择，其中个体积累了有益的突变，即带有选择的Moran模型。在具有强烈选择的特定环境中，Schweinsberg表明人口的家谱由所谓的Bolthausen-Sznitman的合并描述。在本文中，我们通过将种群分成两个对抗亚组来复选该模型，这些亚组可以解释为两个不同的等位基因，其中一个比其他等位基因具有较弱的选择性优势。我们表明，处于弱势个人的比例会收敛于随机微分方程（SDE）的解决方案，因为人口的大小输入了无穷大，称为$λ$ -Wright-wright-wright-fisher SDE，并带有选择。这个随机微分方程已经出现在$λ$ - 求的模型中，其中BAH和PARDOUX研究的选择是在Bolthausen-Sznitman的合并中描述了人口家谱的情况下。
We study a population model of fixed size undergoing strong selection where individuals accumulate beneficial mutations, namely the Moran model with selection. In a specific setting with strong selection, Schweinsberg showed that the genealogy of the population is described by the so-called Bolthausen-Sznitman's coalescent. In this paper we sophisticate the model by splitting the population into two adversarial subgroups, that can be interpreted as two different alleles, one of which has a weak selective advantage over the other. We show that the proportion of disadvantaged individuals converges to the solution of a stochastic differential equation (SDE) as the population's size goes to infinity, named the $Λ$-Wright-Fisher SDE with selection. This stochastic differential equation already appeared in the $Λ$-lookdown model with selection studied by Bah and Pardoux, in the case where the population's genealogy is described by Bolthausen-Sznitman's coalescent.
