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).

Haploid population

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 Mutation–Selection Balance , and a mutated deleterious allele B with frequency Mutation–Selection Balance , which has a small relative fitness disadvantage of Mutation–Selection Balance . Suppose that deleterious mutations from A to B occur at rate Mutation–Selection Balance , 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 Mutation–Selection Balance  is small). Then, each generation selection eliminates deleterious mutants reducing Mutation–Selection Balance  by an amount Mutation–Selection Balance , while mutation creates more deleterious alleles increasing Mutation–Selection Balance  by an amount Mutation–Selection Balance . Mutation–selection balance occurs when these forces cancel and Mutation–Selection Balance  is constant from generation to generation, implying Mutation–Selection Balance . Thus, provided that the mutant allele is not weakly deleterious (very small Mutation–Selection Balance ) and the mutation rate is not very high, the equilibrium frequency of the deleterious allele will be small.

Diploid population

In a diploid population, a deleterious allele B may have different effects on individual fitness in heterozygotes AB and homozygotes BB 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 Mutation–Selection Balance  and Mutation–Selection Balance  respectively, where Mutation–Selection Balance  is a number between Mutation–Selection Balance  and Mutation–Selection Balance  measuring the degree of dominance (Mutation–Selection Balance  indicates that A is completely dominant while Mutation–Selection Balance  indicates no 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 (i.e. Mutation–Selection Balance  is not close to zero), then deleterious mutations are primarily removed by selection on heterozygotes because heterozygotes contain the vast majority of deleterious B alleles (assuming that the deleterious mutation rate Mutation–Selection Balance  is not very large). This case is approximately equivalent to the preceding haploid case, where mutation converts normal homozygotes to heterozygotes at rate Mutation–Selection Balance  and selection acts on heterozygotes with selection coefficient Mutation–Selection Balance ; thus Mutation–Selection Balance .

In the case of complete dominance (Mutation–Selection Balance ), deleterious alleles are only removed by selection on BB homozygotes. Let Mutation–Selection Balance , Mutation–Selection Balance  and Mutation–Selection Balance  be the frequencies of the corresponding genotypes. The frequency Mutation–Selection Balance  of normal alleles A increases at rate Mutation–Selection Balance  due to the selective elimination of recessive homozygotes, while mutation causes Mutation–Selection Balance  to decrease at rate Mutation–Selection Balance  (ignoring back mutations). Mutation–selection balance then gives Mutation–Selection Balance , and so the frequency of deleterious alleles is Mutation–Selection Balance . 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.

Many properties of a non random mating population can be explained by a random mating population whose effective population size is adjusted. However, in non-steady state population dynamics there can be a lower prevalence for recessive disorders in a random mating population during and after a growth phase.

See also

References

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Mutation–Selection Balance Haploid populationMutation–Selection Balance Diploid populationMutation–Selection BalanceAlleleBalancing selectionGenetic driftMutationNatural selectionNegative selection (natural selection)

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