Question

Sicle cell disease (SCD) is found in numerous populations whose ancestral homes are in the malaria belt of Africa and Asia. SCD is an autosomal recessive disorder that results from homozygosity for a mutant β-globin gene allele. Data on one affected population indicates that approximately 8 in 100 newborn infants have SCD.Epidemiologic data on this population reveal that before the application of modern medical treatment, natural selection played a major role in shaping the frequencies of alleles. Heterozygous individuals have the highest relative fitness, and in comparison to heterozygotes, those who are βAβA have a relative fitness of 89 percent, but only about 43 percent of those with SCD survived to reproduce. What is the frequency of the wild-type (beta A) allele in this population? Express your answer using two decimal places. What is the frequency of the mutant (beta 8) allele in this population? Express your answer using two decimal places. What is the frequency of carriers of SCD in the population? Express your answer using two decimal places.

Answer 1

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Step-by-step explanation:

Answer 2

The frequency of the wild-type (βA) allele in the population is approximately 0.72 (72%), the frequency of the mutant (βS) allele is approximately 0.28 (28%), and the frequency of carriers (heterozygotes) for sickle cell disease (SCD) is about 0.41 (41%).

Step-by-step explanation:

To find the frequency of the wild-type allele (βA) and the mutant allele (βS) in the population, we will use the Hardy-Weinberg equation:

p² + 2pq + q² = 1

p is the frequency of the dominant allele (βA)

q is the frequency of the recessive allele (βS)

pq represents the frequency of the heterozygous genotype.

Given that 8 in 100 newborn infants have SCD (q²), we find q by taking the square root of 0.08, which gives us q ≈ 0.2828.

Using p + q = 1, we can calculate p ≈ 1 - 0.2828 ≈ 0.7172.

Therefore, the frequency of the wild-type (βA) allele is approximately 0.72 (72%), and the frequency of the mutant (βS) allele is approximately 0.28 (28%).

To determine the frequency of carriers of SCD (heterozygotes, 2pq), we multiply 2 by the frequency of each allele,

2 × 0.7172 × 0.2828 ≈ 0.4065 or 40.65%.