THE ADVANCE OF MULLER RATCHET IN A HAPLOID ASEXUAL POPULATION - APPROXIMATE SOLUTIONS BASED ON DIFFUSION-THEORY

Asexual populations experiencing random genetic drift can accumulate a n increasing number of deleterious mutations, a process called Muller' s ratchet. We present here diffusion approximations for the rate at wh ich Muller's ratchet advances in asexual haploid populations. The most important parameter of this process is n0 = N e(-U/s), where N is pop ulation size, U the genomic mutation rate and s the selection coeffici ent. In a very large population, n0 is the equilibrium size of the mut ation-free class. We examined the case n0 > 1 and developed one approx imation for intermediate values of N and s and one for large values of N and s. For intermediate values, the expected time at which the ratc het advances increases linearly with n0. For large values, the time in creases in a more or less exponential fashion with n0. In addition to n0, s is also an important determinant of the speed of the ratchet. If N and s are intermediate and n0 is fixed, we find that increasing s a ccelerates the ratchet. In contrast, for a given n0, but large N and s , increasing s slows the ratchet. Except when s is small, results base d on our approximations fit well those from computer simulations.