Mutation-selection balance


A genetic variant caused by mutation that is deleterious may not immediately be removed from the population. The frequency of the variant upon appearing in the population is 1/N (or 1/2N in a diploid population) and this value may drift up or down before returning to zero. In an infinitely sized population, the frequency would never return to zero; the forces of mutation and selection counteract each other until the frequency reaches some equilibrium. This is called the mutation-selection balance.

The equilibrium frequency, f, of a mutant allele for a haploid population or the dominant allele of a diploid population is f = µ/s where µ is the rate of mutation and s is the deleterious selection coefficient (the decrease in relative fitness). For recessive alleles in a diploid population, f = √ µ/s. A useful approximation for alleles of intermediate dominance is f ~ μ / (sh) where h is the coefficient of dominance. All of these formulae are approximations because they ignore back-mutations, typically a trivial effect.