STOCHASTIC ANALYSIS OF EMERGENCE OF EVOLUTIONARY CYCLIC BEHAVIOR IN POPULATION DYNAMICS WITH TRANSFER

• 成果类型: Article
• 署名作者: Champagnat, Nicolas; Meleard, Sylvie; Viet Chi Tran
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1635
• 发表日期: 2021
• 页码: 1820-1867
• 关键词: gene-transfer

摘要

Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilateral conjugation with frequency dependent rate. Our goal is to analyze the trade-off between natural evolution to higher birth rates on one side, and transfer which drives the population towards lower birth rates on the other side. Simulations show that evolutionary outcomes include evolutionary suicide or cyclic re-emergence of small populations with well-adapted traits. We focus on a parameter scaling where individual mutations are rare but the global mutation rate tends to infinity. This implies that negligible subpopulations may have a strong contribution to evolution. Our main result quantifies the asymptotic dynamics of subpopulation sizes on a logarithmic scale. We characterize the possible evolutionary outcomes with explicit criteria on the model parameters. An important ingredient for the proofs lies in comparisons of the stochastic population process with linear or logistic birth-death processes with immigration. For the latter processes, we derive several results of independent interest.