Ornstein-Uhlenbeck fluctuations for the line counting process of the ancestral selection graph

Florin Boenkost, Anna-Lena Weinel
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Abstract

For the Moran model with strong or moderately strong selection we prove that the fluctuations around the deterministic limit of the line counting process of the ancestral selection graph converges to an Ornstein-Uhlenbeck process. To this purpose we provide an extension of a functional limit theorem by Ethier and Kurtz 1986. This result and a small adaptation of our arguments can also be used to obtain the scaling limit for the fluctuations of certain logistic branching processes.
祖先选择图的线计数过程的奥恩斯坦-乌伦贝克波动
对于具有强选择或中度强选择的莫兰模型,我们证明了祖先选择图的线计数过程的确定性极限附近的波动收敛于奥恩斯坦-乌伦贝克过程。为此,我们对 1986 年 Ethier 和 Kurtz 的函数极限定理进行了扩展。这一结果和我们的论证稍作调整,也可用于获得某些逻辑分支过程波动的缩放极限。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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