Risk of population extinction from fixation of deleterious and reverse mutations

A model is developed for alternate fixations of mildly deleterious and wild-type alleles arising by forward and reverse mutation in a finite population. For almost all parameter values, this gives an equilibrium load that agrees closely with the general expression derived from diffusion theory. Nearly neutral mutations with selection coefficient a few times larger than 1/(2N(e)) do the most damage by increasing the equilibrium load. The model of alternate fixations facilitates dynamical analysis of the expected load and the mean time to extinction in a population that has been suddenly reduced from a very large size to a small size. Reverse mutation can substantially improve population viability, increasing the mean time to extinction by an order of magnitude or more, but because many mutations are irreversible the effects may not be large. Populations with initially high mean fitness and small effective size, N(e) below a few hundred individuals, may be at serious risk of extinction from fixation of deleterious mutations within 10(3) to 10(4) generations.