In a diploid population, the initial allele frequencies are $p=0.70$ for allele A and $q=0.30$ for allele a. The population receives migrants equal to $m=0.10$ of its size from a neighboring population where $p_m=0.40$. After migration, selection acts against the homozygous recessive genotype $aa$ with fitness $w_{aa}=0.60$ 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. Apply migration: $p^{\prime }=(1-m)p+m{p}_m=0.9\times 0.70+0.1\times 0.40=0.63+0.04=0.67$.\nThus $q^{\prime }=1-p^{\prime }=0.33$.
2. After migration, genotype frequencies: $f_{AA}=p^{\prime 2}$, $f_{Aa}=2p^{\prime }{q}^{\prime }$, $f_{aa}=q^{\prime 2}$.
3. Compute mean fitness: $\bar{w}=f_{AA}{w}_{AA}+f_{Aa}{w}_{Aa}+f_{aa}{w}_{aa}=p^{\prime 2}+2p^{\prime }{q}^{\prime }+0.6q^{\prime 2}=1-0.4q^{\prime 2}=1-0.4(0.1089)=1-0.04356=0.95644$.
4. Allele frequency of A after selection: $p^{\prime \prime }=\frac{p^{\prime 2}{w}_{AA}+p^{\prime }{q}^{\prime }{w}_{Aa}}{\bar{w}}=\frac{p^{\prime 2}+p^{\prime }{q}^{\prime }}{\bar{w}}=\frac{0.67}{0.95644}\approx 0.7004$.
5. Rounded to three decimal places, $p^{\prime \prime }\approx 0.700$.

Concept tested: Migration and selection combined

Published 13 October 2026 · How this solution was prepared and checked