Sickle 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.What is the frequency of carriers of SCD in the population?

Verified step by step guidance

1. Step 1: Recognize that this problem involves Hardy-Weinberg equilibrium, which is used to calculate allele and genotype frequencies in a population. The equation is p² + 2pq + q² = 1, where p and q are the frequencies of the dominant and recessive alleles, respectively.
2. Step 2: Identify the given information. The problem states that 8 in 100 newborns have SCD, which corresponds to the homozygous recessive genotype (q²). Thus, q² = 0.08.
3. Step 3: Calculate the frequency of the recessive allele (q) by taking the square root of q². Use the formula q = √q².
4. Step 4: Determine the frequency of the dominant allele (p) using the relationship p + q = 1. Rearrange the equation to solve for p: p = 1 - q.
5. Step 5: Calculate the frequency of carriers (heterozygotes) using the Hardy-Weinberg formula for heterozygotes: 2pq. Multiply 2 by the frequency of p and the frequency of q to find the carrier frequency.

Key Concepts

Autosomal Recessive Inheritance

Autosomal recessive inheritance refers to a pattern where two copies of a mutated gene (one from each parent) are necessary for an individual to express a genetic disorder. In the case of sickle cell disease (SCD), individuals who are homozygous for the mutant β-globin gene allele exhibit the disease, while heterozygous individuals (carriers) do not show symptoms but can pass the allele to their offspring.

Hardy-Weinberg Principle

The Hardy-Weinberg principle provides a mathematical framework for understanding genetic variation in a population at equilibrium. It states that allele and genotype frequencies will remain constant from generation to generation in the absence of evolutionary influences. This principle can be used to estimate carrier frequencies in populations by applying the equations p² + 2pq + q² = 1, where p and q represent the frequencies of the dominant and recessive alleles, respectively.

Carrier Frequency Calculation

Carrier frequency refers to the proportion of individuals in a population who carry one copy of a recessive allele for a genetic disorder. To calculate the carrier frequency for SCD, one can use the prevalence of the disease (homozygous individuals) to determine the frequency of the recessive allele (q) and then apply the formula 2pq to find the frequency of carriers (heterozygous individuals), where p is the frequency of the dominant allele.