Sickle-cell disease is caused by a recessive allele. Roughly one out of every 400 African Americans (0.25%) is afflicted with sickle-cell disease. Use the Hardy-Weinberg equation to calculate the percentage of African Americans who are carriers of the sickle-cell allele. (Hint: q² = 0.0025.)

Verified step by step guidance

1. Start by recalling the Hardy-Weinberg equation: \( p^2 + 2pq + q^2 = 1 \), where \( p \) represents the frequency of the dominant allele, \( q \) represents the frequency of the recessive allele, \( p^2 \) represents the frequency of homozygous dominant individuals, \( 2pq \) represents the frequency of heterozygous carriers, and \( q^2 \) represents the frequency of homozygous recessive individuals.
2. From the problem, we are given that \( q^2 = 0.0025 \), which represents the frequency of individuals afflicted with sickle-cell disease. To find \( q \), take the square root of \( q^2 \): \( q = \sqrt{0.0025} \).
3. Once you have \( q \), calculate \( p \) using the relationship \( p + q = 1 \). Rearrange the equation to solve for \( p \): \( p = 1 - q \).
4. Now, use the Hardy-Weinberg equation to calculate the frequency of heterozygous carriers (\( 2pq \)). Substitute the values of \( p \) and \( q \) into the term \( 2pq \): \( 2pq = 2 \cdot p \cdot q \).
5. The result of \( 2pq \) represents the percentage of African Americans who are carriers of the sickle-cell allele. Convert this frequency into a percentage by multiplying by 100.

Key Concepts

Sickle-Cell Disease

Sickle-cell disease is a genetic disorder caused by a mutation in the hemoglobin gene, leading to the production of abnormal hemoglobin known as hemoglobin S. This results in red blood cells becoming rigid and sickle-shaped, which can cause various health complications. The disease is inherited in an autosomal recessive manner, meaning that an individual must inherit two copies of the mutated allele to exhibit symptoms.

Hardy-Weinberg Principle

The Hardy-Weinberg principle is a fundamental concept in population genetics that describes how allele and genotype frequencies remain constant from generation to generation in a large, randomly mating population, provided that certain conditions are met. The principle is often expressed using the equation p² + 2pq + q² = 1, where p and q represent the frequencies of the dominant and recessive alleles, respectively. This principle allows for the calculation of carrier frequencies in a population.

Carrier Frequency

Carrier frequency refers to the proportion of individuals in a population who carry one copy of a recessive allele but do not exhibit the associated phenotype. In the context of sickle-cell disease, carriers have one normal allele and one sickle-cell allele, which means they can pass the allele to their offspring. The carrier frequency can be calculated using the Hardy-Weinberg equation, specifically the term 2pq, where q represents the frequency of the recessive allele.