In a diploid population the initial allele frequencies are $p = 0.7$ (allele $A$ ) and $q = 0.3$ (allele $a$ ). Fitness values are $w_{AA} = 1$ , $w_{A a} = 0.9$ , $w_{aa} = 0.5$ . Find the frequency of allele $A$ after one generation of selection.

medium 2 marks Class 12 · Biology · Organisms and Populations

Answer

p^{'} \approx 0.744

The correct answer is $p^{'} \approx 0.744$ — Round to three decimal places: $p^{'} \approx 0.744$ .

Step-by-step solution

Calculate the genotype frequencies before selection using $p$ and $q$ : $AA = p^{2} = 0.49$ , $A a = 2 pq = 0.42$ , $aa = q^{2} = 0.09$ .
Multiply each genotype frequency by its fitness to obtain the post‑selection contributions: $A A^{'} = 0.49 \times 1 = 0.49$ , $A a^{'} = 0.42 \times 0.9 = 0.378$ , $a a^{'} = 0.09 \times 0.5 = 0.045$ .
Find the mean fitness $\overset{w}{ˉ}$ by summing the post‑selection contributions: $\overset{w}{ˉ} = 0.49 + 0.378 + 0.045 = 0.913$ .
Normalize the post‑selection contributions by $\overset{w}{ˉ}$ to get the genotype frequencies after selection: $A A^{''} = 0.49/0.913 = 0.5366$ , $A a^{''} = 0.378/0.913 = 0.414$ , $a a^{''} = 0.045/0.913 = 0.0493$ .
Compute the new allele $A$ frequency using $p^{'} = freq (A A^{''}) + \frac{1}{2} freq (A a^{''})$ : $p^{'} = 0.5366 + 0.5 \times 0.414 = 0.5366 + 0.207 = 0.7436$ .
Round to three decimal places: $p^{'} \approx 0.744$ .

Common mistake: Forgetting to divide by the mean fitness

\overset{w}{ˉ}

before calculating the new allele frequency.

Concept tested: Allele frequency change by selection