In a diploid population, allele $A$ has initial frequency $p=0.6$ and allele $a$ has $q=0.4$. Each generation the population receives migrants equal to $m=0.10$ of its size from a large neighboring population where $p_m=0.2$. After migration, selection acts against the homozygous recessive genotype $aa$ with fitness $w_{aa}=0.7$, while $w_{AA}=w_{Aa}=1$. Calculate the frequency of allele $A$ after one generation (migration followed by selection).

Step-by-step solution

1. Apply migration first: $p^{\ast }=(1-m)p+m{p}_m=0.9\times 0.6+0.1\times 0.2=0.54+0.02=0.56$.
2. Thus after migration $p^{\ast }=0.56$, $q^{\ast }=1-p^{\ast }=0.44$.
3. Assume Hardy–Weinberg proportions before selection:
4. Genotype frequencies: $AA=(p^{\ast }{)}^2=0.3136$, $Aa=2p^{\ast }{q}^{\ast }=0.4928$, $aa=(q^{\ast }{)}^2=0.1936$.
5. Apply selection: fitnesses $w_{AA}=1$, $w_{Aa}=1$, $w_{aa}=0.7$.
6. Mean fitness $\bar{w}=0.3136\times 1+0.4928\times 1+0.1936\times 0.7=0.3136+0.4928+0.13552=0.94192$.
7. Allele $A$ after selection:
8. $p^{\prime }=\frac{[AA]\times w_{AA}+\frac{1}{2}[Aa]\times w_{Aa}}{\bar{w}}=\frac{0.3136+0.5\times 0.4928}{0.94192}=\frac{0.5600}{0.94192}\approx 0.5948$.
9. Round to three decimal places: $p^{\prime }\approx 0.595$.

Concept tested: Combined migration and selection on allele frequency

Published 26 September 2026 · How this solution was prepared and checked