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 are the frequencies of the wild-type (βᴬ) and mutant (βˢ) alleles in this population?

Verified step by step guidance

1. Understand the problem: Sickle cell disease (SCD) is an autosomal recessive disorder, meaning individuals with the disease are homozygous for the mutant allele (βˢβˢ). The problem provides the frequency of affected individuals in the population (q² = 8/100 = 0.08) and asks for the allele frequencies of the wild-type (βᴬ) and mutant (βˢ) alleles.
2. Recall the Hardy-Weinberg principle: The Hardy-Weinberg equation is p² + 2pq + q² = 1, where p is the frequency of the wild-type allele (βᴬ), q is the frequency of the mutant allele (βˢ), p² represents the frequency of homozygous wild-type individuals, 2pq represents the frequency of heterozygous carriers, and q² represents the frequency of homozygous mutant individuals.
3. Determine the frequency of the mutant allele (q): Since q² = 0.08, take the square root of q² to find q. Mathematically, q = √(0.08).
4. Calculate the frequency of the wild-type allele (p): Using the relationship p + q = 1, solve for p by subtracting q from 1. Mathematically, p = 1 - q.
5. Summarize the allele frequencies: The frequency of the wild-type allele (βᴬ) is p, and the frequency of the mutant allele (βˢ) is q. These values represent the proportion of each allele in the population.

Key Concepts

Autosomal Recessive Inheritance

Autosomal recessive inheritance means that a trait or disorder is expressed only when an individual has two copies of the recessive allele, one from each parent. In the case of sickle cell disease (SCD), individuals must be homozygous for the mutant β-globin gene allele (βˢ) to exhibit the disease. Carriers, who have one wild-type allele (βᴬ) and one mutant allele (βˢ), do not show symptoms but can pass the mutant allele to their offspring.

Hardy-Weinberg Principle

The Hardy-Weinberg principle provides a mathematical framework for understanding allele frequencies in a population at equilibrium. It states that the frequencies of alleles and genotypes will remain constant from generation to generation in the absence of evolutionary influences. This principle can be used to calculate the frequencies of the wild-type (βᴬ) and mutant (βˢ) alleles in the population based on the prevalence of the disease.

Allele Frequency Calculation

Allele frequency refers to how often a particular allele appears in a population. For a recessive disorder like SCD, if the prevalence of the disease is known, the frequency of the mutant allele can be calculated using the formula p² + 2pq + q² = 1, where q² represents the frequency of the homozygous recessive genotype. From this, the frequencies of both the mutant (q) and wild-type (p) alleles can be derived, allowing for a better understanding of genetic diversity in the population.