The accumulation of deleterious mutations is driven by rare fluctuations which lead to the loss of all mutation free individuals, a process known as Muller's ratchet. Even though Muller's ratchet is a paradigmatic process in population genetics, a quantitative understanding of its rate is still lacking. The difficulty lies in the nontrivial nature of fluctuations in the fitness distribution which control the rate of extinction of the fittest genotype. We address this problem using the simple but classic model of mutation selection balance with deleterious mutations all having the same effect on fitness. We show analytically how fluctuations among the fittest individuals propagate to individuals of lower fitness and have a dramatically amplified effects on the bulk of the population at a later time. If a reduction in the size of the fittest class reduces the mean fitness only after a delay, selection opposing this reduction is also delayed. This delayed restoring force speeds up Muller's ratchet. We show how the delayed response can be accounted for using a path integral formulation of the stochastic dynamics and provide an expression for the rate of the ratchet that is accurate across a broad range of parameters.
Analytical results on the Muller's ratchet effect in growing populations
Fontanari等人介绍了[Phys. Rev. Lett. 91，218101（2003）]的一个模型，用于研究穆勒的棘轮现象在不断增长的无性种群。他们研究了两种情况，包括或不包括每个新生儿的死亡概率，但只能在无衰变的情况下找到解析（递归）表达式。在本文中，一个分支过程的形式主义是用来找到recorrence方程，除了确认有趣的效果，他们的模拟显示，推广的分析结果的原始文件。
