We study a mutation-selection model with a fluctuating environment. More precisely, individuals in a large population are assumed to have a modifier locus determining the mutation rate $u \in [0,\vartheta]$ at a second locus with types $v \in [0,1]$. In addition, the environment fluctuates, meaning that individual types change their fitness at some high rate. Fitness only depends on the type of the second locus. We obtain general limit results for the evolution of the allele frequency distribution for rapidly fluctuating environments. As an application, we make use of the resulting Fleming-Viot process and compute the fixation probabilities for higher mutation rates in the special case of two bi-allelic loci in the limit of small fitness differences at the second locus.

中文翻译：

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选择性波动环境中突变率的修正

我们研究了具有波动环境的突变选择模型。更准确地说，假设大群体中的个体在具有类型 $v \in [0,1]$ 的第二个基因座上具有决定突变率 $u \in [0,\vartheta]$ 的修饰基因座。此外，环境会波动，这意味着个体类型会以较高的速度改变其适应度。适应度仅取决于第二个轨迹的类型。我们获得了快速波动环境中等位基因频率分布演化的一般极限结果。作为一个应用，我们利用得到的 Fleming-Viot 过程并计算在两个双等位基因位点的特殊情况下更高突变率的固定概率，在第二个位点的适应度差异很小。