King's formula for the mutation load with epistasis.
A formula by J. L. King gives the equilibrium mutation load as L = 2 sigma ui(1 - qi)/z - x) in which ui is the mutation rate to deleterious alleles at the ith locus, qi is the frequency of mutant alleles at this locus, x is the mean number of such mutant genes per individual before selection, z is the mean number in individuals eliminated by selection, and the summation is over all relevant loci. We show that this rule is inaccurate for intense selection and that a correct formula is L = 2 sigma ui(1 - qi) w/(z - x) = 2U w/(z - x) = 2U/(z - x + 2U) in which U is the mean number of new mutations per haploid genome in the population and w is the mean relative fitness before selection. If w/(z - x) less than 1/2, the mutation load is less than the Haldane value (U less than or equal to L less than or equal to 2U) and can be considerably less. In a diploid asexual population, however, with independent occurrence of mutations, L = 1 - e-2U regardless of the mode of selection.
Kondrashov
A S
AS
Research Computer Center, Academy of Sciences, Pushchino, Moscow Region, USSR.
Crow
J F
JF
D004843:Epistasis, Genetic; D008433:Mathematics; D008957:Models, Genetic; D009154:Mutation; D012100:Reproduction, Asexual