← Evolutionary Mathematics

Mutation and selection

Mutation creates new genetic variants or converts one allele into another, while selection changes frequencies according to fitness differences.

Mutation alone

If \(A\) mutates to \(a\) at rate \(\mu\) and \(a\) mutates to \(A\) at rate \(\nu\), a continuous approximation for allele frequency \(p\) is

\[\frac{dp}{dt}=\nu(1-p)-\mu p.\]

Mutation–selection balance

Selection can remove a deleterious allele while recurrent mutation continually reintroduces it. Their opposing effects can produce a non-zero equilibrium frequency.

Key idea. Evolutionary change can reflect a balance between mechanisms that generate variation and mechanisms that differentially preserve it.