Mutation-selection balance

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 (e.g. balancing selection and genetic drift), 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 (i.e. balance between selective loss of variation and creation of variation by beneficial mutations).

As a simple example of mutation-selection balance, consider a single locus in a haploid population with two possible alleles: a normal allele A with frequency ${\displaystyle p}$, and a mutated deleterious allele B with frequency ${\displaystyle q}$, which has a small relative fitness disadvantage of ${\displaystyle s}$. Suppose that deleterious mutations from A to B occur at rate ${\displaystyle \mu }$, and the reverse beneficial mutation from B to A occurs rarely enough to be negligible (e.g. because the mutation rate is so low that ${\displaystyle q}$ is small). Then, each generation selection eliminates deleterious mutants reducing ${\displaystyle q}$ by an amount ${\displaystyle spq}$, while mutation creates more deleterious alleles increasing ${\displaystyle q}$ by an amount ${\displaystyle \mu p}$. Mutation–selection balance occurs when these forces cancel and ${\displaystyle q}$ is constant from generation to generation, implying ${\displaystyle q=\mu /s}$. Thus, provided that the mutant allele is not weakly deleterious (very small ${\displaystyle s}$) and the mutation rate is not very high, the equilibrium frequency of the deleterious allele will be small.

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