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.
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 <math> p </math>, and a mutated deleterious allele B with frequency <math> q </math>, which has a small relative fitness disadvantage of <math>s</math>. Suppose that deleterious mutations from A to B occur at rate <math> \mu </math>, 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 <math>q</math> is small). Then, each generation selection eliminates deleterious mutants reducing <math> q </math> by an amount <math>spq</math>, while mutation creates more deleterious alleles increasing <math> q </math> by an amount <math> \mu p </math>. Mutation–selection balance occurs when these forces cancel and <math> q </math> is constant from generation to generation, implying <math> q = \mu/s </math>.
Multilocus mutation-selection balance
Several studies have extended mutation-selection balance to whole-genome models.
For asexual organisms, let all mutations have the same multiplicative effect on fitness, that is the relative fitness of an individual with <math>k</math> segregating mutations is <math>w_i = (1-s)^k</math>. At mutation-selection balance, the probability that an individual has <math>k</math> segregating mutations follows a Poisson distribution with mean <math>\frac{U_d}{s_d}</math> where <math>U_d</math> is the whole genome deleterious mutation rate.
The prevalence of hemophilia among males is <math>p \in [4, 17] \times 10^{-5}</math>. The fertility ratio of males with hemophilia to males without hemophilia is <math>f \in [0.1, 0.25]</math>, where <math>f = \frac{\#(\text{offsprings of abnormal allele){\#(\text{offsprings of normal allele)
</math>.
Assuming hemophilia is purely due to mutations on the X chromosome, the mutation rate can be estimated as follows.
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 <math>\mu</math>. On the other hand, the relative fitness of hemophilia patients is <math>f</math>, so <math>(1-f)</math> times the existing hemophilia cases are lost every generation due to selection. The mutation-selection balance thus gives
<math display="block">
\mu = (1-f) p.
</math>
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). Thus, the equation
<math display="block">
\mu \approx (1-f)p/3 \in [1, 5] \times 10^{-5},
</math>
is obtained, where the numerical range was obtained by plugging in the ranges for <math>p</math> and <math>f</math>. Subsequent research using different methods showed that the mutation rate in many genes is indeed on the order of <math>10^{-5}</math> per generation.
See also
- Negative selection
- Dysgenics
- Viral quasispecies