Question

If the incidence of cystic fibrosis is 1/2,500 among a population of Europeans, what is the predicted incidence of heterozygous carriers of a cystic fibrosis mutation in this population?

A. 1/25
B. 1/50
C. 2/2,500
D. 1/2,500
E. (1/2,500)²

Answer 1

Using the principles of autosomal recessive inheritance and the Hardy-Weinberg principle, the predicted incidence of heterozygous carriers of the cystic fibrosis mutation is 1/25.

Step-by-step explanation:

If the incidence of cystic fibrosis is 1/2,500 among a population of Europeans, the predicted incidence of heterozygous carriers of a cystic fibrosis mutation can be calculated using the principles of autosomal recessive inheritance. Since cystic fibrosis (CF) is an autosomal recessive disorder, a person with the disease has two copies of the mutant gene (ff). To find the carrier frequency (Ff), we can apply the Hardy-Weinberg principle, which states that the square root of the frequency of the homozygous recessive genotype (q²) gives us the frequency of the recessive allele (q). The other allele's frequency (p) can be calculated by assuming p + q = 1. We are given the frequency of the disease (q²) as 1/2,500. Taking the square root of 1/2,500 gives us q = 1/50, and hence p = 1 - 1/50. The frequency of the heterozygous genotype (2pq) would be 2(1/50)(49/50), which simplifies to approximately 1/25. Therefore, the incidence of heterozygous carriers is predicted to be 1/25.