文章基本信息

标题：Beneficial mutation-selection dynamics in finite asexual populations: a free boundary approach
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作者：Lionel Roques ; Jimmy Garnier ; Guillaume Martin 等
期刊名称：Scientific Reports
电子版ISSN：2045-2322
出版年度：2017
卷号：7
期号：1
页码：17838
DOI：10.1038/s41598-017-17212-5
语种：English
出版社：Springer Nature
摘要：Using a free boundary approach based on an analogy with ice melting models, we propose a deterministic PDE framework to describe the dynamics of fitness distributions in the presence of beneficial mutations with non-epistatic effects on fitness. Contrarily to most approaches based on deterministic models, our framework does not rely on an infinite population size assumption, and successfully captures the transient as well as the long time dynamics of fitness distributions. In particular, consistently with stochastic individual-based approaches or stochastic PDE approaches, it leads to a constant asymptotic rate of adaptation at large times, that most deterministic approaches failed to describe. We derive analytic formulas for the asymptotic rate of adaptation and the full asymptotic distribution of fitness. These formulas depend explicitly on the population size, and are shown to be accurate for a wide range of population sizes and mutation rates, compared to individual-based simulations. Although we were not able to derive an analytic description for the transient dynamics, numerical computations lead to accurate predictions and are computationally efficient compared to stochastic simulations. These computations show that the fitness distribution converges towards a travelling wave with constant speed, and whose profile can be computed analytically.