标题： 母系依赖的中性突变模型的等位基因树及其在稀有突变情形下的尺度极限 显示英文标题

标题： Allele trees for the mother-dependent neutral mutations model and their scaling limits in the rare mutations regime

摘要： 母系依赖的中性突变模型描述了在一个离散世代的种群中进化的过程，在该模型中，中性突变发生在有限可能等位基因集合之中。 在此模型中，每个突变后代都会获得与其母亲不同的类型，并以均匀随机的方式选择。 在这项工作中，我们定义了与该模型相关的多类型等位树，并通过追踪等位亚家族及其突变后代规模的马尔可夫链来分析其缩放极限。 我们证明了这个马尔可夫链收敛到一个连续状态的马尔可夫过程，其转移概率取决于初始等位群体及其第一代突变后代的规模。 因此，等位树收敛到一个多维极限对象，可以由Bertoin（2010）提出的通用等位树来描述。 显示英文摘要

摘要： The mother-dependent neutral mutations model describes the evolution of a population across discrete generations, where neutral mutations occur among a finite set of possible alleles. In this model, each mutant child acquires a type different from that of its mother, chosen uniformly at random. In this work, we define a multitype allele tree associated with this model and analyze its scaling limit through a Markov chain that tracks the sizes of allelic subfamilies and their mutant descendants. We show that this Markov chain converges to a continuous-state Markov process, whose transition probabilities depend on the sizes of the initial allelic populations and those of their mutant offspring in the first allelic generation. As a result, the allele tree converges to a multidimensional limiting object, which can be described in terms of the universal allele tree introduced by Bertoin (2010).