Calculating Homozygotes in a Hardy-Weinberg Population: Step-by-Step Guide

The Hardy-Weinberg equilibrium is a cornerstone of population genetics, providing a mathematical framework to predict genotype frequencies from allele frequencies in a non-evolving population. If you know the frequencies of two alleles in a population, you can easily calculate the expected number of homozygotes and heterozygotes. Let’s walk through a practical example using a population of 250 individuals with two alleles at frequencies 0.2 and 0.8.

Step 1: Understanding the Hardy-Weinberg Equation

The Hardy-Weinberg equation for a gene with two alleles (let’s call them A and a) is:

p2+2pq+q2=1p2+2pq+q2=1

Where:

• $p$ = frequency of allele A

• $q$ = frequency of allele a

• p2p2 = frequency of homozygous AA

• q2q2 = frequency of homozygous aa

• $2pq$ = frequency of heterozygous Aa

Step 2: Assigning Allele Frequencies

Given:

• Frequency of one allele ($p$) = 0.2

• Frequency of the other allele ($q$) = 0.8

Check: $p+q=0.2+0.8=1$

Step 3: Calculating Genotype Frequencies

• Homozygous for allele 1 (AA): p2=(0.2)2=0.04p2=(0.2)2=0.04

• Homozygous for allele 2 (aa): q2=(0.8)2=0.64q2=(0.8)2=0.64

• Heterozygotes (Aa): $2pq=2\times 0.2\times 0.8=0.32$

Step 4: Calculating Number of Homozygotes in the Population

Total population = 250

• Number of AA homozygotes: $0.04\times 250=10$

• Number of aa homozygotes: $0.64\times 250=160$

• Total number of homozygotes: $10+160=170$

Step 5: Identifying the Correct Answer

From the options provided:

• (1) 32

• (2) 10

• (3) 40

• (4) 170

The correct answer is (4) 170.

Why This Matters

Knowing how to calculate genotype frequencies using the Hardy-Weinberg principle is essential for:

• Predicting genetic disease risk in populations

• Understanding population structure and evolution

• Detecting deviations from equilibrium, which may indicate evolutionary forces at work

Conclusion

If the frequency of one allele is 0.2 and the other is 0.8 in a population of 250 individuals at Hardy-Weinberg equilibrium, the number of homozygotes in the population is 170. This includes both types of homozygotes (AA and aa).

Correct answer: (4) 170