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 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.
[3] 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,[5][4] 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).
[6] 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
, which has a small relative fitness disadvantage of
Suppose that deleterious mutations from A to B occur at rate
Then, each generation selection eliminates deleterious mutants reducing
, while mutation creates more deleterious alleles increasing
Mutation–selection balance occurs when these forces cancel and
[3] Thus, provided that the mutant allele is not weakly deleterious (very small
) 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 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
For simplicity, suppose that mating is random.
The degree of dominance affects the relative importance of selection on heterozygotes versus homozygotes.
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
This case is approximately equivalent to the preceding haploid case, where mutation converts normal homozygotes to heterozygotes at rate
), deleterious alleles are only removed by selection on BB homozygotes.
due to the selective elimination of recessive homozygotes, while mutation causes
[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.
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] The first paper on the subject was (Haldane, 1935), which used the prevalence and fertility ratio of haemophilia in males to estimate mutation rate in human genes.
At mutation-selection balance, the rate of new hemophilia cases due to mutations should be equal to the rate of hemophilia cases lost due to the lower fitness of hemophilia patients.
Since every male has one X chromosome, the rate of new hemophilia cases due to mutations is
On the other hand, the relative fitness of hemophilia patients is
times the existing hemophilia cases are lost every generation due to selection.
However, since females have two X chromosomes, only about 1/3 of the new mutations would appear in males (assuming an equal sex ratio at birth).
Subsequent research using different methods showed that the mutation rate in many genes is indeed on the order of