棘轮多久发出一次咔嗒声？事实，逻辑，渐近
How often does the ratchet click? Facts, heuristics, asymptotics
摘要：
在无性繁殖的种群中，重组的进化力量是缺乏的。因此，种群可能遭受有害突变的不可逆转的积累，这种现象被称为穆勒棘轮。我们制定离散和连续时间版本的穆勒棘轮。受Haigh（1978）对大种群极限下出现的动力系统的分析的启发，我们确定参数γ = N*lambda/（Ns*log（N*lambda））对于有害突变的积累速度是最重要的。这里N是总体规模，s是选择系数，λ是有害突变率。对于参数范围的大部分，以大小N为单位测量时间，如果γ>0.5，则有害突变根据N* λ中的幂律累积，其中指数为γ。对于γ <0.5，突变不能累积。我们得到三个不同的参数制度的扩散近似，根据棘轮的速度。我们的近似值为Stephan et al.（1993）和Gordo & Charlesworth（2000）的分析提供了新的思路。模拟结果支持了导致近似的数学模型。
英文摘要：
The evolutionary force of recombination is lacking in asexually reproducing populations. As a consequence, the population can suffer an irreversible accumulation of deleterious mutations, a phenomenon known as Muller's ratchet. We formulate discrete and continuous time versions of Muller's ratchet. Inspired by Haigh's (1978) analysis of a dynamical system which arises in the limit of large populations, we identify the parameter gamma = N*lambda/(Ns*log(N*lambda)) as most important for the speed of accumulation of deleterious mutations. Here N is population size, s is the selection coefficient and lambda is the deleterious mutation rate. For large parts of the parameter range, measuring time in units of size N, deleterious mutations accumulate according to a power law in N*lambda with exponent gamma if gamma>0.5. For gamma<0.5 mutations cannot accumulate. We obtain diffusion approximations for three different parameter regimes, depending on the speed of the ratchet. Our approximations shed new light on analyses of Stephan et al. (1993) and Gordo & Charlesworth (2000). The heuristics leading to the approximations are supported by simulations.
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