Lineage dynamics and mutation–selection balance in non-adapting asexual populations

In classical population genetics, mutation–selection balance refers to the equilibrium frequency of a deleterious allele established and maintained under two opposing forces: recurrent mutation, which tends to increase the frequency of the allele; and selection, which tends to decrease its frequency. In a haploid population, if μ denotes the per capita rate of production of the deleterious allele by mutation and s denotes the selective disadvantage of carrying the allele, then the classical mutation–selection balance frequency of the allele is approximated by μ/s. This calculation assumes that lineages carrying the mutant allele in question—the 'focal allele'—do not accumulate deleterious mutations linked to the focal allele. In principle, indirect selection against the focal allele caused by such additional mutations can decrease the frequency of the focal allele below the classical mutation–selection balance. This effect of indirect selection will be strongest in an asexual population, in which the entire genome is in linkage. Here, we use an approach based on a multitype branching process to investigate this effect, analyzing lineage dynamics under mutation, direct selection, and indirect selection in a non-adapting asexual population. We find that the equilibrium balance between recurrent mutation to the focal allele and the forces of direct and indirect selection against the focal allele is closely approximated by γμ/(s + U) (s = 0 if the focal allele is neutral), where γ ≈ eθθ−(ω+θ)(ω + θ)(Γ(ω + θ) − Γ(ω + θ,θ)), θ=U/ s-tilde , and ω=s/ s-tilde ; U denotes the genomic deleterious mutation rate and s-tilde denotes the geometric mean selective disadvantage of deleterious mutations elsewhere on the genome. This mutation–selection balance for asexual populations can remain surprisingly invariant over wide ranges of the mutation rate. (paper)