Calculating the Number of Individuals Affected by a Recessive Disease Using Hardy-Weinberg Law

Understanding how genetic diseases are distributed in a population is a crucial aspect of population genetics and public health. The Hardy-Weinberg equilibrium provides a powerful tool for estimating the number of individuals affected by a recessive disease when the allele frequency is known. Here’s how you can use this principle to make accurate predictions.

Problem Statement

In a population of 10,000, the frequency of the recessive allele (q) causing a disease in the homozygous recessive condition is 0.04. How many people in this population are expected to be affected by the disease?

Step 1: Applying the Hardy-Weinberg Equation

The Hardy-Weinberg equation is:

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

Where:

• $p$ = frequency of the dominant allele

• $q$ = frequency of the recessive allele

• q2q2 = frequency of homozygous recessive individuals (those affected by the disease)

Step 2: Calculate the Frequency of Affected Individuals

Given:

• $q=0.04$

So,

q2=(0.04)2=0.0016q2=(0.04)2=0.0016

Step 3: Calculate the Number of Affected Individuals

Multiply the frequency of affected individuals by the total population:

Number of affected individuals=q2×Total populationNumber of affected individuals=q2×Total population$$=0.0016\times 10,000=16$$

Step 4: Choose the Correct Option

From the options:

• (1) 16

• (2) 400

• (3) 3600

• (4) 496

The correct answer is 16.

Why This Calculation Matters

• Public Health: Estimating the number of affected individuals helps in planning healthcare resources and genetic counseling.

• Population Genetics: Understanding genotype frequencies aids in tracking the inheritance and prevalence of genetic diseases.

• Evolutionary Insights: Hardy-Weinberg equilibrium provides a baseline for detecting evolutionary changes in populations.

Conclusion

If the frequency of a recessive allele causing a disease is 0.04 in a population of 10,000, then 16 people are expected to be affected by the disease under Hardy-Weinberg equilibrium.

Correct answer: (1) 16