Rarely clicking Muller's ratchets

In populations of finite size, weakly deleterious mutations can fix by chance. This phenomenon has been termed Muller's ratchet and one click of the ratchet refers to the loss of the fittest class of individuals with the fewest mutations. Despite the simplicity of the classical mathematical model of Muller's ratchet, surprisingly little is known in the biologically relevant regime where a click of the ratchet is a rare event. Here we show numerically that in this regime the rate of the ratchet strongly depends on the applied microscopic formulation (Wiright-Fisher/Moran) of the model, thus challenging the widely used diffusion approximation. Furthermore by employing a WKB-approximation in a simplified model, we obtain analytical results for the click rate, which agree well with the click rate of the full ratchet of the corresponding microscopical model.