In a diploid population with initial allele frequencies $p=0.6$ (allele A) and $q=0.4$ (allele a), a selection coefficient $s=0.2$ acts against the homozygous recessive genotype $aa$ (fitness $w_{aa}=0.8$). There is no migration or mutation and random mating occurs. Find the allele frequency of $A$ after one generation of selection.

Step-by-step solution

1. Compute pre‑selection genotype frequencies: $AA=p^2=0.36$, $Aa=2pq=0.48$, $aa=q^2=0.16$.
2. Apply fitness: $w_{AA}=1$, $w_{Aa}=1$, $w_{aa}=0.8$ to get weighted frequencies: $AA=0.36$, $Aa=0.48$, $aa=0.128$.
3. Calculate mean fitness $\bar{w}=0.36+0.48+0.128=1.056$.
4. Normalize: $A{A}^{\prime }=0.36/1.056=0.341$, $A{a}^{\prime }=0.48/1.056=0.455$, $a{a}^{\prime }=0.128/1.056=0.121$.
5. New allele frequency $p^{\prime }=A{A}^{\prime }+\frac{1}{2}A{a}^{\prime }=0.341+0.2275=0.5685\approx 0.569$.

Concept tested: Selection in population genetics

Published 28 September 2026 · How this solution was prepared and checked