# Mutation-Selection-Drift Equilibrium

mutation-selection-drift equilibrium is one of the most important concept of population genetics. I could easily find the calculations for mutation-secltion equilibrium and for mutation-drift equilibrium but not for mutation-selection-drift equilibrium.

mutation-selection equilibrium

At mutation-selection equilibrium the expected frequency $p$ of a given allele is

$$p ≈ \frac{\mu}{s\cdot h}$$

, where $\mu$ is the mutation rate, $s$ is the selection coefficient and $h$ is the coefficient of dominance.

mutation-drift equilibrium

At mutation-drift equilibrium the expected frequency $p$ of a given allele is

$$p ≈ \frac{1}{4N\mu+1}$$

, where $N$ is the population size.

What is the allelic frequency at mutation-selection-drift equilibrium?

• I think this paper might be relevant. From what I can see they derive an analytical approx for deleterious allele frequency in MSD equilibrium.ncbi.nlm.nih.gov/pmc/articles/PMC1894624 – A. Kennard Oct 18 '14 at 16:00
• Drift doesn't change the expected frequency of alleles. In your equation for the mutation-drift equilibrium, I don't think that $f$ is an allele frequency -- it's the homozygosity. – Daniel Weissman Nov 17 '14 at 5:45
• "expected frequency f of a given locus is" are you sure this is correct? do you mean frequency of an allele rather than locus? According to Charlesworth & Charlesworth it should be $q^*$ which is the equilibrium frequency of $A_2$ the mutant allele – rg255 Dec 12 '14 at 8:10
• (I'm concerned with the definition not the notation - I've seen $f$ used elsewhere) – rg255 Dec 12 '14 at 8:26
• Oh I missed your comment for some reason. You are right "frequency of a locus" makes no sense. I corrected it. Also I replaced $f$ by $p$ as $p$ (or $x$) are more often used to represent allele frequency. Thanks – Remi.b Dec 30 '14 at 7:20