Consider a diploid population with initial allele frequencies $p=0.3$ (A) and $q=0.7$ (a). Each generation the population receives migrants equal to $m=0.20$ of its size from a large neighboring population where $p_m=0.80$. After migration, selection acts against the homozygous recessive genotype $aa$ with fitness $w_{aa}=0.60$, while $w_{AA}=w_{Aa}=1$. Calculate the frequency of allele $A$ after one generation (migration followed by selection).

Step-by-step solution

1. After migration, the new allele frequency is $p^{\prime }=(1-m)p+m{p}_m=0.8\times 0.3+0.2\times 0.8=0.24+0.16=0.40$.
2. Compute $q^{\prime }=1-p^{\prime }=0.60$.
3. Calculate mean fitness after selection: $\overline{w}=p^{\prime 2}+2p^{\prime }{q}^{\prime }+q^{\prime 2}\times 0.60=0.16+0.48+0.36\times 0.60=0.856$.
4. Compute the numerator for $p^{\prime \prime }$: $p^{\prime 2}+p^{\prime }{q}^{\prime }=0.16+0.24=0.40$.
5. Divide by mean fitness: $p^{\prime \prime }=\frac{0.40}{0.856}\approx 0.467$.
6. Thus the allele frequency of $A$ after one generation is approximately 0.467.

Concept tested: Migration and selection effects

Published 1 October 2026 · How this solution was prepared and checked