论文标题
缩放跳跃链的融合弱和金曼聚集的突变数量
Weak convergence of the scaled jump chain and number of mutations of the Kingman coalescent
论文作者
论文摘要
Kingman合并是人群遗传学的一个基本过程，该过程对及时倒退的个体样本的血统进行了建模。在本文中，在大型制度中，我们研究了在中立和一般有限的 - 链球突变方案下合并的渐近特性，即包括父母独立和父母依赖性突变。特别是，我们考虑了一系列与融合有关的马尔可夫链，由块计数和突变计数组成组成。我们表明，适当缩放的这些组件分别弱化为确定性组件和泊松过程，分别具有不同的强度。一路走来，我们基于度量的变化开发了一种新颖的方法，以将父母独立于父母依赖的突变设置概括，其中几个关键量不明确。
The Kingman coalescent is a fundamental process in population genetics modelling the ancestry of a sample of individuals backwards in time. In this paper, in a large-sample-size regime, we study asymptotic properties of the coalescent under neutrality and a general finite-alleles mutation scheme, i.e. including both parent independent and parent dependent mutation. In particular, we consider a sequence of Markov chains that is related to the coalescent and consists of block-counting and mutation-counting components. We show that these components, suitably scaled, converge weakly to deterministic components and Poisson processes with varying intensities, respectively. Along the way, we develop a novel approach, based on a change of measure, to generalise the convergence result from the parent independent to the parent dependent mutation setting, in which several crucial quantities are not known explicitly.
