CROSSING A FITNESS VALLEY AS A METASTABLE TRANSITION IN A STOCHASTIC POPULATION MODEL

• 成果类型: Article
• 署名作者: Bovier, Anton; Coquille, Loren; Smadi, Charline
• 署名单位: University of Bonn; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); INRAE; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1487
• 发表日期: 2019
• 页码: 3541-3589
• 关键词: antibiotic-resistance; Adaptive dynamics; moment equations; EVOLUTION; adaptation; escape; time

摘要

We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0, 1, . . . , L} and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation towards neighbouring traits at each reproduction event. We choose parameters such that the induced fitness landscape exhibits a valley: mutant individuals with negative fitness have to be created in order for the population to reach a trait with positive fitness. We focus on the limit of large population and rare mutations at several speeds. In particular, when the mutation rate is low enough, metastability occurs: the exit time of the valley is an exponentially distributed random variable.