How to Calculate the Frequency of Heterozygotes for Red Hair Using Hardy-Weinberg Equilibrium

Red hair in humans is a classic example of a recessive genetic trait. In population genetics, the Hardy-Weinberg equilibrium provides a powerful tool for calculating the expected frequencies of various genotypes—including heterozygotes—when given the frequency of a recessive phenotype in a randomly mating population.

Step 1: Understanding the Problem

• Red hair is recessive.

• 9% of individuals are red-haired.

• The population is in Hardy-Weinberg equilibrium.

Step 2: Define the Alleles and Frequencies

Let:

• p = frequency of the dominant allele (non-red hair)

• q = frequency of the recessive allele (red hair)

According to Hardy-Weinberg:

• The frequency of homozygous recessive individuals (red-haired) = q2q2

• The frequency of heterozygotes (carriers, not red-haired) = $2pq$

Given:

• q2=0.09q2=0.09 (since 9% are red-haired)

Step 3: Calculate q and p

• q=0.09=0.3q=0.09=0.3

• $p=1-q=1-0.3=0.7$

Step 4: Calculate the Frequency of Heterozygotes

• Frequency of heterozygotes = $2pq=2\times 0.7\times 0.3=0.42$

• As a percentage: $0.42\times 100=42\%$

Step 5: Match with the Options

• (1) 81%

• (2) 49%

• (3) 42%

• (4) 18%

The correct answer is (3) 42%.

Why This Calculation Matters

• Carrier Frequency: Many individuals carry the red hair allele without expressing the trait.

• Genetic Counseling: Helps estimate the likelihood of red-haired offspring.

• Population Genetics: Demonstrates how recessive traits can persist in populations.

Conclusion

When approximately 9% of a randomly mating population has red hair, the frequency of heterozygotes (carriers of the red hair allele) is 42%.

Correct answer: (3) 42%