Calculating the Number of Carriers in a Population Using Hardy-Weinberg Equilibrium

The Hardy-Weinberg principle is a fundamental tool in population genetics that allows us to predict genotype frequencies, including carriers of recessive alleles, in populations under certain assumptions. When allele frequencies are known, it becomes straightforward to estimate how many individuals carry a particular allele without expressing the recessive trait.

Given Data

• Total population size = 200

• Frequency of dominant allele (A) = $p=0.7$

• Frequency of recessive allele (a) = $q=0.3$

Step 1: Understanding Carrier Frequency

Carriers are heterozygous individuals (genotype Aa) who carry one copy of the recessive allele but do not express the recessive phenotype. The frequency of heterozygotes in the population is given by:

$$2pq$$

Step 2: Calculate Heterozygote Frequency

$$2pq=2\times 0.7\times 0.3=2\times 0.21=0.42$$

So, 42% of the population are carriers.

Step 3: Calculate Number of Carriers

Multiply the heterozygote frequency by the total population:

$$0.42\times 200=84$$

Step 4: Select the Correct Answer

From the options:

• (1) 18

• (2) 42

• (3) 84

• (4) 98

The correct answer is 84.

Why This Matters

• Genetic Counseling: Knowing carrier frequencies helps in assessing the risk of recessive genetic diseases.

• Population Health: Estimating carriers can guide screening programs.

• Evolutionary Studies: Helps understand genetic variation and potential for disease expression.

Conclusion

In a population of 200 individuals with allele frequencies $p=0.7$ and $q=0.3$, the number of carriers (heterozygotes) is expected to be 84 according to Hardy-Weinberg equilibrium.

Correct answer: (3) 84