Mutation–Selection Balance, explained.
Mutation–selection balance is a state where new copies introduced by mutation offset copies removed by selection.
Why it happens
Recessive aa fitness is 1−s while AA and Aa fitness is one. Selection changes q to q(1−sq)/(1−sq²), then forward mutation gives q′=qSelected+μ(1−qSelected). Start q=0.5 and compare the recurrence with the rare-allele approximation √(μ/s).
Mutation–selection balance is a state where new copies introduced by mutation offset copies removed by selection.
Read the result
Compare current q with the approximate reference over many generations. The persistent allele is not evidence that selection stopped operating.
A worked example
A recessive allele replenished by mutation
Leave mutation at 0.005 and the recessive fitness loss at 0.5, giving an approximate balance of ten percent.
Run successive hundred-generation blocks from q equal to one half and observe how selection and mutation approach a balance.
Increase mutation and restart. More replenishment raises the reference balance while the selection rule remains unchanged.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Recessive aa fitness is 1−s while AA and Aa fitness is one. Selection changes q to q(1−sq)/(1−sq²), then forward mutation gives q′=qSelected+μ(1−qSelected). Start q=0.5 and compare the recurrence with the rare-allele approximation √(μ/s).
Where this idea is useful
A practical use
An allele can remain present because heterozygotes carry it and recurrent mutation supplies new copies.
A common misconception
“Selection must eventually remove every harmful allele.”
New mutation can replenish an allele, and recessive copies can persist in heterozygotes. A balance need not mean the allele is beneficial.
What this explanation leaves out
- The model assumes random mating, an infinite population, no back mutation, no migration and complete recessivity. The square-root approximation is not exact at all parameter values or after a finite run; no clinical inference is intended.
Is the square-root line the exact equilibrium?
It is a rare-allele approximation under restrictive assumptions. The recurrence is the actual model being iterated, and a finite run may not reach equilibrium.
What replenishes the quantity being removed in the system you are studying?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.