Mutation–selection balance

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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.^[1][2][3][4] 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

Haploid population

As a simple example of mutation-selection balance, consider a single

${\displaystyle p}$, 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 ${\displaystyle q=\mu /s}$.^[3] 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.

Diploid population

In a

be smaller than that of normal homozygotes AA by factors of ${\displaystyle 1-hs}$ and ${\displaystyle 1-s}$ respectively, where ${\displaystyle h}$ is a number between ${\displaystyle 0}$ and ${\displaystyle 1}$ measuring the degree of dominance (${\displaystyle h=0}$ indicates that A is completely dominant while ${\displaystyle h=1/2}$ 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. ${\displaystyle h}$ 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 ${\displaystyle \mu }$ is not very large). This case is approximately equivalent to the preceding haploid case, where mutation converts normal homozygotes to heterozygotes at rate ${\displaystyle \mu }$ and selection acts on heterozygotes with selection coefficient ${\displaystyle hs}$; thus ${\displaystyle q\approx \mu /hs}$.^[1]

In the case of complete dominance (${\displaystyle h=0}$), deleterious alleles are only removed by selection on BB homozygotes. Let ${\displaystyle p_{AA}}$, ${\displaystyle 2p_{AB}}$ and ${\displaystyle p_{BB}}$ be the frequencies of the corresponding genotypes. The frequency ${\displaystyle p=p_{AA}+p_{AB}}$ of normal alleles A increases at rate ${\displaystyle 1/(1-sp_{BB})}$ due to the selective elimination of recessive homozygotes, while mutation causes ${\displaystyle p}$ to decrease at rate ${\displaystyle 1-\mu }$ (ignoring

). Mutation–selection balance then gives ${\displaystyle p_{BB}=\mu /s}$, and so the frequency of deleterious alleles is ${\displaystyle q={\sqrt {\mu /s}}}$.^[1] 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.^[7][8]

See also

• Negative selection
• Dysgenics
• Viral quasispecies

References