发表机构
Rutgers, The State University of New Jersey; The Hebrew University of Jerusalem（新泽西州立罗格斯大学; 耶路撒冷希伯来大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用涨落定理重新推导木村固定概率公式，并提出多等位基因固定概率的递归解析解，用于精确描述克隆干扰下有益突变的命运，显著优于平均场近似。
AI 中文摘要
出现在有限群体中的突变基因，从长远来看，要么从群体中消失，要么被固定，使得群体中的所有成员都携带该突变基因的副本。因此，确定突变基因的固定概率是对有限群体中的进化动态进行建模的先决条件。在扩散理论框架内，突变体与野生型基因的竞争由木村资生（Motoo Kimura）于1962年推导的突变固定概率的一维后向柯尔莫哥洛夫方程的闭式解来描述。然而，在无性生殖群体中，适应速率和替代进化途径的相对重要性受到克隆干扰的影响——即由不同的有益或有害突变产生的多个谱系之间的竞争。克隆干扰的定量描述需要计算同时存在多个等位基因的群体中的固定概率——这是一个艰巨的数学问题，相当于求解多维后向柯尔莫哥洛夫方程。在此，我们利用涨落定理（非平衡统计力学中的一组精确等式）来重新推导木村的固定概率公式。当扩展到多等位基因系统时，涨落定理提供了一个任何有效的固定概率集合都必须满足的约束条件。此外，我们提出了多等位基因固定概率问题的递归解析解。我们使用我们的形式体系来研究克隆干扰情景中新型有益突变的命运，发现我们的精确处理与平均场近似（其中目标突变与单个有效基因型竞争）之间存在显著偏差。我们的形式体系可用于替代无性进化模型中的显式模拟和近似解析结果。
英文摘要
A mutant gene that appears in a finite population will, in the long run, either disappear from it or become fixed, so that all members of the population will carry a copy of the mutant gene. Determining the fixation probability of a mutant gene is thus a prerequisite for modeling evolutionary dynamics in finite populations. Within the diffusion theory framework, the mutant's competition with the wild-type genes is described by the closed-form solution of a one-dimensional backward Kolmogorov equation for the mutant fixation probability, derived by Motoo Kimura in 1962. However, in asexual populations the rate of adaptation and the relative importance of alternative evolutionary pathways are shaped by clonal interference - the competition between several lineages arising from distinct beneficial or deleterious mutations. Quantitative descriptions of clonal interference require computing fixation probabilities in populations where multiple alleles are present simultaneously - a formidable mathematical problem which amounts to solving a multi-dimensional backward Kolmogorov equation. Here, we employ fluctuation theorems (a set of exact equalities in non-equilibrium statistical mechanics) in order to re-derive Kimura's fixation probability formula. When extended to multi-allele systems, fluctuation theorems provide a constraint which must be satisfied by any valid set of fixation probabilities. Moreover, we present a recursive analytical solution of the multi-allele fixation probability problem. We use our formalism to study the fate of a novel beneficial mutation in a clonal interference scenario, discovering substantial deviations between our exact treatment and the mean-field approximation in which the target mutation competes with a single effective genotype. Our formalism can be used to replace both explicit simulations and approximate analytical results in models of asexual evolution.
Comments17 pages, 4 figures in the main text, 6 figures in the supplement
