Metastability between the clicks of Muller's ratchet

• 成果类型: Article
• 署名作者: Mariani, Mauro; Pardoux, Etienne; Velleret, Aurelien
• 署名单位: HSE University (National Research University Higher School of Economics); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01377-6
• 发表日期: 2025
• 页码: 721-802
• 关键词: conditional distributions; UNIFORM-CONVERGENCE; gene-transfer; population

摘要

We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual reproduction mode in preventing the accumulation of deleterious mutations through natural selection alone. The main considered model is non-classical, as it is a stochastic diffusion evolving on an irregular set of infinite dimension with hard killing on a hyperplane. We are nonetheless able to prove exponential convergence in total variation to the quasi-stationary distribution even in this case. The parameters in this last convergence result are directly related to the core parameters of Muller's ratchet. The speed of convergence to the quasi-stationary distribution is deduced both for the infinite dimensional model and for approximations with a large yet finite number of potential mutations. Likewise, we give uniform moment estimates of the empirical distribution of mutations in the population under quasi-stationarity.