  The evolutionary force of recombination is lacking in asexually reproducing
populations. As a consequence, the population can suffer an irreversible
accumulation of deleterious mutations, a phenomenon known as Muller's ratchet.
We formulate discrete and continuous time versions of Muller's ratchet.
Inspired by Haigh's (1978) analysis of a dynamical system which arises in the
limit of large populations, we identify the parameter gamma =
N*lambda/(Ns*log(N*lambda)) as most important for the speed of accumulation of
deleterious mutations. Here N is population size, s is the selection
coefficient and lambda is the deleterious mutation rate. For large parts of the
parameter range, measuring time in units of size N, deleterious mutations
accumulate according to a power law in N*lambda with exponent gamma if
gamma>0.5. For gamma<0.5 mutations cannot accumulate. We obtain diffusion
approximations for three different parameter regimes, depending on the speed of
the ratchet. Our approximations shed new light on analyses of Stephan et al.
(1993) and Gordo & Charlesworth (2000). The heuristics leading to the
approximations are supported by simulations.
