The advance of Muller's ratchet in a haploid asexual population: approximate solutions based on diffusion theory

Abstract

SummaryAsexual populations experiencing random genetic drift can accumulate an increasing number of deleterious mutations, a process called Muller's ratchet. We present here diffusion approximations for the rate at which Muller's ratchet advances in asexual haploid populations. The most important parameter of this process isn0=N e−U/s, whereNis population size,Uthe genomic mutation rate andsthe selection coefficient. In a very large population,n0is the equilibrium size of the mutation-free class. We examined the casen0> 1 and developed one approximation for intermediate values ofNandsand one for large values ofNands. For intermediate values, the expected time at which the ratchet advances increases linearly withn0. For large values, the time increases in a more or less exponential fashion withn0. In addition ton0,sis also an important determinant of the speed of the ratchet. IfNandsare intermediate andn0is fixed, we find that increasingsaccelerates the ratchet. In contrast, for a givenn0, but largeNands, increasingsslows the ratchet. Except whensis small, results based on our approximations fit well those from computer simulations.