Two linked loci under mutation-selection balance and Muller's ratchet

We report complete analysis of a deterministic model of deleterious mutations and negative selection against them at two haploid loci without recombination. As long as mutation is a weaker force than selection, mutant alleles remain rare at the only stable equilibrium, and otherwise, a variety of dynamics are possible. If the mutation-free genotype is absent, generally the only stable equilibrium is the one that corresponds to fixation of the mutant allele at the locus where it is less deleterious. This suggests that fixation of a deleterious allele that follows a click of the Muller's ratchet is governed by natural selection, instead of random drift.