A-WRIGHT-FISHER PROCESSES WITH GENERAL SELECTION AND OPPOSING ENVIRONMENTAL EFFECTS: FIXATION AND COEXISTENCE

• 成果类型: Article
• 署名作者: Cordero, Fernando; Hummel, Sebastian; Vechambre, Gregoire
• 署名单位: University of Bielefeld; University of California System; University of California Berkeley; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2117
• 发表日期: 2025
• 页码: 393-457
• 关键词: coalescent processes; stochastic-equations; FLOWS; Duality; MODEL

摘要

Our results characterize the long-term behavior for a broad class of ronmental selection. In particular, we reveal a rich variety of parameterdependent behaviors and provide explicit criteria to discriminate between them. That includes the situation in which both boundary points, 0 and 1, are repelling-a new phenomenon in this context. This has significant biological implications, because it means that selection alone can maintain genetic variation, that is, coexistence. If a boundary point is attractive, we derive polynomial/exponential decay rates for the probability of not being polynomially/exponentially close to that boundary, depending on some weak/strong integrability conditions. Moreover, we provide a handy representation of the fixation probability. In our proofs we make use of Siegmund duality. The dual process can be sandwiched near the boundaries in-between transformed L & eacute;vy processes. In this way we relate the boundary behavior of the dual process to fluctuation properties of these L & eacute;vy processes and shed new light on previously established conditions for attractive/repelling boundary points. Our method allows us to treat models that so far could not be analyzed by means of moment or Bernstein duality. This closes an existing gap in the literature.