How to Calculate the Frequency of a Dominant Allele from Homozygous Recessive Disease Prevalence

Understanding how genetic traits are distributed in a population is a cornerstone of population genetics. The Hardy-Weinberg equilibrium provides a mathematical framework to relate genotype frequencies to allele frequencies. If you know the frequency of a homozygous recessive disease in a population, you can easily calculate the frequency of the dominant allele. Let’s walk through the process step by step.

Step 1: Identify the Given Data

The question states:

• The frequency of a homozygous recessive disease (genotype aa) in the population is 16%.

This means:

• q2=0.16q2=0.16

  • Here, $q$ is the frequency of the recessive allele (a), and $p$ is the frequency of the dominant allele (A).

Step 2: Calculate the Frequency of the Recessive Allele

To find $q$:

q=q2=0.16=0.4q=q2=0.16=0.4

Step 3: Calculate the Frequency of the Dominant Allele

The Hardy-Weinberg principle states:

$$p+q=1$$

So,

$$p=1-q=1-0.4=0.6$$

Step 4: Select the Correct Answer

From the given options:

• (1) 0.84

• (2) 0.6

• (3) 0.16

• (4) 0.4

The frequency of the dominant allele is 0.6.

Why This Matters

Calculating allele frequencies is essential for:

• Predicting genetic disease risk in populations

• Assessing genetic diversity

• Understanding evolutionary dynamics

Conclusion

If the frequency of a homozygous recessive disease in a population is 16%, the frequency of the dominant allele is 0.6.

Correct answer: (2) 0.6