How to Calculate Carrier Frequency for an Autosomal Recessive Condition: A Hardy-Weinberg Approach

Autosomal recessive conditions are genetic disorders that only manifest when an individual inherits two copies of the mutated gene—one from each parent. Many people who carry just one copy of the gene (carriers) are healthy but can pass the gene to their offspring. Understanding the frequency of carriers in a population is crucial for genetic counseling, disease prediction, and public health planning.

Problem Overview

• Incidence of disease: 1 in 10,000 newborns affected

• Inheritance: Autosomal recessive

• Population: Random mating, Hardy-Weinberg equilibrium

• Question: What is the approximate expected frequency of carriers in this population?

Step 1: Assign Hardy-Weinberg Variables

Let:

• q² = frequency of affected individuals (homozygous recessive, aa)

• q = frequency of the recessive allele (a)

• p = frequency of the normal allele (A), so p + q = 1

• 2pq = frequency of carriers (heterozygotes, Aa)

Step 2: Find the Frequency of the Recessive Allele

Given:

q2=110,000=0.0001q2=10,0001=0.0001q=0.0001=0.01q=0.0001=0.01

Step 3: Find the Frequency of the Normal Allele

$$p=1-q=1-0.01=0.99$$

Step 4: Calculate Carrier Frequency (2pq)

$$2pq=2\times 0.99\times 0.01=0.0198$$

This means approximately 1.98% of the population are carriers.

Step 5: Convert to “1 in X” Format

10.0198≈50.50.01981≈50.5

So, about 1 in 50 newborns is expected to be a carrier for the condition.

Step 6: Match with the Provided Options

• (1) 1 in 1000 newborns

• (2) 1 in 500 newborns

• (3) 1 in 100 newborns

• (4) 1 in 50 newborns

The correct answer is (4) 1 in 50 newborns.

Conclusion

For an autosomal recessive condition affecting 1 in 10,000 newborns, the expected carrier frequency in a Hardy-Weinberg population is about 1 in 50 newborns. This highlights how carriers can be relatively common even when the disease itself is rare.