GENEALOGICAL CONSTRUCTIONS OF POPULATION MODELS

• 成果类型: Article
• 署名作者: Etheridge, Alison M.; Kurtz, Thomas G.
• 署名单位: University of Oxford; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1266
• 发表日期: 2019
• 页码: 1827-1910
• 关键词: representation; EQUATIONS; Markov

摘要

Representations of population models in terms of countable systems of particles are constructed, in which each particle has a type, typically recording both spatial position and genetic type, and a level. For finite intensity models, the levels are distributed on [0, lambda], whereas in the infinite intensity limit lambda -> infinity, at each time t, the joint distribution of types and levels is conditionally Poisson, with mean measure Xi(t) x l where l denotes Lebesgue measure and Xi(t) is a measure-valued population process. The time-evolution of the levels captures the genealogies of the particles in the population. Key forces of ecology and genetics can be captured within this common framework. Models covered incorporate both individual and event based births and deaths, one-for-one replacement, immigration, independent thinning and independent or exchangeable spatial motion and mutation of individuals. Since birth and death probabilities can depend on type, they also include natural selection. The primary goal of the paper is to present particle-with-level or lookdown constructions for each of these elements of a population model. Then the elements can be combined to specify the desired model. In particular, a nontrivial extension of the spatial Lambda-Fleming-Viot process is constructed.