In a diploid population, the initial allele frequencies are $p=0.35$ for allele $A$ and $q=0.65$ for allele $a$. Each generation the population receives migrants equal to $m=0.15$ of its size from a large neighboring population where allele $A$ frequency is $p_m=0.50$. After migration, selection acts against the homozygous recessive genotype $aa$ with fitness $w_{aa}=0.70$ while $w_{AA}=w_{Aa}=1$. What is the frequency of allele $A$ after one generation (migration followed by selection)?

Step-by-step solution

1. After migration, the allele frequency of $A$ is $p_{\text{mig}}=(1-m)p+m{p}_m=0.85\times 0.35+0.15\times 0.50=0.3725$.
2. Hence $q_{\text{mig}}=1-0.3725=0.6275$.
3. Genotype frequencies after migration: $AA:p_{\text{mig}}^2=0.1389$, $Aa:2p_{\text{mig}}{q}_{\text{mig}}=0.4675$, $aa:q_{\text{mig}}^2=0.3936$.
4. Mean fitness after selection: $\bar{w}=0.1389\times 1+0.4675\times 1+0.3936\times 0.70=0.8819$.
5. Allele $A$ frequency after selection: $p^{\prime }=\frac{p_{\text{mig}}^2\times 1+p_{\text{mig}}{q}_{\text{mig}}\times 1}{\bar{w}}=\frac{0.1389+0.2338}{0.8819}\approx 0.423$.

Concept tested: Migration and selection on allele frequencies

Published 10 October 2026 · How this solution was prepared and checked