论文标题
与突变和选择的合并过程小时的扩散限制
Diffusion Limits at Small Times for Coalescent Processes with Mutation and Selection
论文作者
论文摘要
祖先选择图（ASG）是一个重要的家谱过程，它扩展了著名的金曼合并以结合自然选择。我们表明，与Kingman Colescent的限制行为一致，ASG带有和没有突变的ASG谱系渐近为$ 2/t $。我们使用Poisson随机测量构建将这些过程逐渐在相同的概率空间上进行，这使我们能够精确比较其打击时间。这些比较使我们能够表征从ASG的无穷大及其在功能性中心极限定理中的波动的速度。这扩展了金曼合并的类似结果。
The Ancestral Selection Graph (ASG) is an important genealogical process which extends the well-known Kingman coalescent to incorporate natural selection. We show that the number of lineages of the ASG with and without mutation is asymptotic to $2/t$ as $t\to 0$, in agreement with the limiting behaviour of the Kingman coalescent. We couple these processes on the same probability space using a Poisson random measure construction that allows us to precisely compare their hitting times. These comparisons enable us to characterise the speed of coming down from infinity of the ASG as well as its fluctuations in a functional central limit theorem. This extends similar results for the Kingman coalescent.
