世代重叠的穆勒棘轮
Muller's ratchet with overlapping generations
摘要：
米勒棘轮是一个在有限规模的人口中有害突变积累的典范模型。当所有具有最少数量有害突变的个体由于随机波动而不可逆转地丢失时，棘轮的点击就会发生。尽管该模型简单，但对该过程的定量理解仍然是一个公开的挑战。与以往的工作相比，我们在这里研究的莫兰模型的棘轮与重叠的世代。采用近似描述最适合的个人作为一个类，其余的作为第二类，我们得到封闭的分析表达式的棘轮率在罕见的点击制度。由于点击在这个制度是由一个罕见的大波动从亚稳态，我们不诉诸于扩散近似，但适用于近似方案，这是特别适合于描述灭绝事件从亚稳态。该方法还允许导出最适合类的准平稳分布的表达式。此外，我们证实了数值计算与重叠世代的配方导致相同的结果，扩散近似和相应的Wright-Fisher模型与非重叠世代。
英文摘要：
Muller's ratchet is a paradigmatic model for the accumulation of deleterious mutations in a population of finite size. A click of the ratchet occurs when all individuals with the least number of deleterious mutations are lost irreversibly due to a stochastic fluctuation. In spite of the simplicity of the model, a quantitative understanding of the process remains an open challenge. In contrast to previous works, we here study a Moran model of the ratchet with overlapping generations. Employing an approximation which describes the fittest individuals as one class and the rest as a second class, we obtain closed analytical expressions of the ratchet rate in the rare clicking regime. As a click in this regime is caused by a rare large fluctuation from a metastable state, we do not resort to a diffusion approximation but apply an approximation scheme which is especially well suited to describe extinction events from metastable states. This method also allows for a derivation of expressions for the quasi-stationary distribution of the fittest class. Additionally, we confirm numerically that the formulation with overlapping generations leads to the same results as the diffusion approximation and the corresponding Wright-Fisher model with non-overlapping generations.
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