The accumulation of deleterious mutations is driven by rare fluctuations
which lead to the loss of all mutation free individuals, a process known as
Muller's ratchet. Even though Muller's ratchet is a paradigmatic process in
population genetics, a quantitative understanding of its rate is still lacking.
The difficulty lies in the nontrivial nature of fluctuations in the fitness
distribution which control the rate of extinction of the fittest genotype. We
address this problem using the simple but classic model of mutation selection
balance with deleterious mutations all having the same effect on fitness. We
show analytically how fluctuations among the fittest individuals propagate to
individuals of lower fitness and have a dramatically amplified effects on the
bulk of the population at a later time. If a reduction in the size of the
fittest class reduces the mean fitness only after a delay, selection opposing
this reduction is also delayed. This delayed restoring force speeds up Muller's
ratchet. We show how the delayed response can be accounted for using a path
integral formulation of the stochastic dynamics and provide an expression for
the rate of the ratchet that is accurate across a broad range of parameters.Comment: Genetics 201
