Soluble model for the accumulation of mutations in asexual populations

Finite asexual populations can accumulate an increasing number of deleterious mutations by a process known as Muller's ratchet, which consists of successive losses of the fittest or least-loaded classes of individuals in the population. We present here a simplified theoretical framework to describe the serial bottleneck passages setup used in experiments to demonstrate the decrease of the population mean fitness due to the operation of ratchet. In particular, we calculate the expected time between consecutive clicks of the ratchet and derive expressions relating the moments of the mean fitness distribution to the mutation and selection parameters.