Question

In a given population, 1 out of 400 individuals has cancer caused by a recessive allele ‘p’. Assuming the population is in Hardy-Weinberg equilibrium, what is the expected proportion of individuals who carry the ‘p’ allele but do not develop cancer?

1. 1/400

2. 19/400

3. 20/200

4. 38/400

Detailed Explanation

In this problem, we are dealing with a genetic disease caused by a recessive allele (p) that results in cancer. According to Hardy-Weinberg equilibrium, allele and genotype frequencies in a population remain constant from generation to generation unless disturbed by specific evolutionary forces.

We know that in Hardy-Weinberg equilibrium:

• p represents the frequency of the dominant allele.

• q represents the frequency of the recessive allele.

• The genotype frequencies are given by:

  • p² for the homozygous dominant genotype (PP)

  • 2pq for the heterozygous genotype (Pp)

  • q² for the homozygous recessive genotype (pp)

In this case:

• Individuals with pp (homozygous recessive) have cancer.

Given that 1 out of 400 individuals has cancer, this corresponds to the frequency of pp in the population, which is q²:

• q² = 1/400

Step 1: Calculate the frequency of the recessive allele (q)

• q = √(1/400)

• q = 1/20

Step 2: Calculate the carrier frequency

Carriers of the recessive allele are individuals with the heterozygous genotype Pp. The frequency of Pp is given by 2pq.

• Since p + q = 1, we can calculate p:

  • p = 1 – q = 1 – 1/20 = 19/20

Now, calculate the carrier frequency 2pq:

• 2pq = 2 * (19/20) * (1/20) = 38/400

Thus, the expected proportion of individuals who carry the ‘p’ allele but do not develop cancer (heterozygous individuals) is 38/400.

Answer

The correct answer is:

4. 38/400

Conclusion

This calculation shows how Hardy-Weinberg equilibrium can be used to determine the frequency of carriers for a genetic trait, even when dealing with a recessive genetic disorder. In this case, the expected proportion of individuals who are carriers for cancer-causing allele p but do not develop cancer is 38/400. Understanding the Hardy-Weinberg principles can help in understanding the distribution of genetic traits and the impact of recessive alleles in populations.