During a range expansion, deleterious mutations can “surf” on the colonization front. The resultant decrease in fitness is known as expansion load. An Allee effect is known to reduce the loss of genetic diversity of expanding populations, by changing the nature of the expansion from “pulled” to “pushed”. We study the impact of an Allee effect on the formation of an expansion load with a new model, in which individuals have the genetic structure of a Muller’s ratchet. A key feature of Muller’s ratchet is that the population fatally accumulates deleterious mutations due to the stochastic loss of the fittest individuals, an event called a click of the ratchet. We observe fast clicks of the ratchet at the colonization front owing to small population size, followed by a slow fitness recovery due to migration of fit individuals from the bulk of the population, leading to a transient expansion load. For large population size, we are able to derive quantitative features of the expansion wave, such as the wave speed and the frequency of individuals carrying a given number of mutations. Using simulations, we show that the presence of an Allee effect reduces the rate at which clicks occur at the front, and thus reduces the expansion load.

在范围扩大期间，有害突变会在定居前沿“冲浪”。导致的适应性下降称为膨胀负荷。众所周知，通过将扩展的性质从“拉动”变为“推动”，Allee效应可以减少扩展种群遗传多样性的丧失。我们使用新模型研究了Allee效应对扩展负荷形成的影响，在该模型中，个体具有穆勒棘轮的遗传结构。穆勒棘轮的一个关键特征是，由于适者个体的随机丧失，该种群致命地积累了有害的突变，这一事件被称为棘轮喀哒声。由于人口规模小，我们观察到棘齿在殖民地的快速咔嗒声，随后由于适应个体从大多数人口中迁移而导致健身恢复缓慢，从而导致短暂的扩张负荷。对于较大的人口规模，我们能够得出扩展波的定量特征，例如波速和携带给定数量突变的个体的频率。通过仿真，我们发现Allee效应的存在降低了前端喀哒声的发生率，从而降低了扩展负荷。