GRAPHON-VALUED STOCHASTIC PROCESSES FROM POPULATION GENETICS

• 成果类型: Article
• 署名作者: Athreya, Siva; den Hollander, Frank; Rollin, Adrian
• 署名单位: Indian Statistical Institute; Indian Statistical Institute Bangalore; Leiden University; Leiden University - Excl LUMC; National University of Singapore
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1631
• 发表日期: 2021
• 页码: 1724-1745
• 关键词: limits

摘要

The goal of this paper is to construct a natural class of graphon-valued processes arising from population genetics. We consider finite populations where individuals carry one of finitely many genetic types and change type according to Fisher-Wright resampling. At any time, each pair of individuals is linked by an edge with a probability that is given by a type-connection matrix, whose entries depend on the current types of the two individuals and on the current empirical type distribution of the entire population via a fitness function. We show that, in the large-population-size limit and with an appropriate scaling of time, the evolution of the associated adjacency matrix converges to a random process in the space of graphons, driven by the type-connection matrix and the underlying Fisher-Wright diffusion on the multi-type simplex. In the limit as the number of types tends to infinity, the limiting process is driven by the type-connection kernel and the underlying Fleming-Viot diffusion.