论文标题
在选择和父依赖突变下合并模型中采样和过渡概率的渐近行为
Asymptotic behaviour of sampling and transition probabilities in coalescent models under selection and parent dependent mutations
论文作者
论文摘要
本文的结果提供了有关经典模型的渐近特性的新信息：在一般有限的甲壳虫下中性的金曼合并，父母依赖的突变机制及其概括，即祖先选择图。当突变取决于父母时，与这些基本模型相关的几个相关数量尚不清楚。示例包括从人群中采集的样本具有一定类型的配置的概率，以及其块计数跳链的过渡概率。在本文中，由于样本量为无穷大，因此为这些数量得出了渐近结果。结果表明，取样概率在样本量中多项式衰减，取决于赖特 - 法派扩散的固定密度，并且过渡概率将过渡概率收敛到样本中类型频率的极限。
The results in this paper provide new information on asymptotic properties of classical models: the neutral Kingman coalescent under a general finite-alleles, parent-dependent mutation mechanism, and its generalisation, the ancestral selection graph. Several relevant quantities related to these fundamental models are not explicitly known when mutations are parent dependent. Examples include the probability that a sample taken from a population has a certain type configuration, and the transition probabilities of their block counting jump chains. In this paper, asymptotic results are derived for these quantities, as the sample size goes to infinity. It is shown that the sampling probabilities decay polynomially in the sample size with multiplying constant depending on the stationary density of the Wright-Fisher diffusion and that the transition probabilities converge to the limit of frequencies of types in the sample.
