Weak convergence of non-neutral genealogies to Kingman's coalescent
Weak convergence of non-neutral genealogies to Kingman's coalescent
复制标题
非中立谱系与金曼合并的弱收敛
DOI：
10.1016/j.spa.2023.04.016
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发表时间：
2023
影响因子：
1.4
通讯作者：
Brown S
中科院分区：
文献类型：
--
作者：
Brown S
经历重复突变和选择步骤的相互作用粒子系统模拟了遗传进化，并且还描述了一大类连续蒙特卡罗方法。嵌入系统中的谱系树在这两种应用中都很重要。在中立性下，当粒子的适应性与其父母的适应性无关时，已知重新调整的谱系会收敛到金曼的合并。最近的工作已经建立了非中性下的收敛性，但仅限于有限维分布。我们证明了标准假设下非中性谱系在 càdlàg 路径空间上的弱收敛性，从而能够对整个谱系树进行分析。
Interacting particle systems undergoing repeated mutation and selection steps model genetic evolution, and also describe a broad class of sequential Monte Carlo methods. The genealogical tree embedded into the system is important in both applications. Under neutrality, when fitnesses of particles are independent from those of their parents, rescaled genealogies are known to converge to Kingman’s coalescent. Recent work has established convergence under non-neutrality, but only for finite-dimensional distributions. We prove weak convergence of non-neutral genealogies on the space of càdlàg paths under standard assumptions, enabling analysis of the whole genealogical tree.