Mutation–selection balance is an equilibrium in the number of deleterious alleles in a population that occurs when the rate at which deleterious alleles are created by mutation equals the rate at which deleterious alleles are eliminated by selection. The majority of genetic mutations are neutral or deleterious; beneficial mutations are relatively rare. The resulting influx of deleterious mutations into a population over time is counteracted by negative selection, which acts to purge deleterious mutations. Setting aside other factors, the equilibrium number of deleterious alleles is then determined by a balance between the deleterious mutation rate and the rate at which selection purges those mutations. Mutation–selection balance was originally proposed to explain how genetic variation is maintained in populations, although several other ways for deleterious mutations to persist are now recognized, notably balancing selection. Nevertheless, the concept is still widely used in evolutionary genetics, e.g. to explain the persistence of deleterious alleles as in the case of spinal muscular atrophy, or, in theoretical models, mutation-selection balance can appear in a variety of ways and has even been applied to beneficial mutations.
Haploid population
As a simple example of mutation-selection balance, consider a single locus in a haploid population with two possible alleles: a normal alleleA with frequency, and a mutated deleterious allele B with frequency, which has a small relative fitness disadvantage of. Suppose that deleterious mutations from A to B occur at rate, and the reverse beneficial mutation from B to A occurs rarely enough to be negligible. Then, each generation selection eliminates deleterious mutants reducing by an amount, while mutation creates more deleterious alleles increasing by an amount. Mutation–selection balance occurs when these forces cancel and is constant from generation to generation, implying. Thus, provided that the mutant allele is not weakly deleterious and the mutation rate is not very high, the equilibrium frequency of the deleterious allele will be small.
In a diploid population, a deleterious allele B may have different effects on individual fitness in heterozygotesAB and homozygotesBB depending on the degree of dominance of the normal allele A. To represent this mathematically, let the relative fitness of deleterious homozygotes and heterozygotes be smaller than that of normal homozygotes AA by factors of and respectively, where is a number between and measuring the degree of dominance. For simplicity, suppose that mating is random. The degree of dominance affects the relative importance of selection on heterozygotes versus homozygotes. If A is not completely dominant, then deleterious mutations are primarily removed by selection on heterozygotes because heterozygotes contain the vast majority of deleterious B alleles. This case is approximately equivalent to the preceding haploid case, where mutation converts normal homozygotes to heterozygotes at rate and selection acts on heterozygotes with selection coefficient ; thus. In the case of complete dominance, deleterious alleles are only removed by selection on BB homozygotes. Let, and be the frequencies of the corresponding genotypes. The frequency of normal alleles A increases at rate due to the selective elimination of recessive homozygotes, while mutation causes to decrease at rate . Mutation–selection balance then gives, and so the frequency of deleterious alleles is. This equilibrium frequency is potentially substantially larger than for the case of partial dominance, because a large number of mutant alleles are carried in heterozygotes and are shielded from selection.
