Consider rare disorders in a population caused by an autosomal recessive mutation. From the frequencies of the disorder in the population given, calculate the percentage of heterozygous carriers:
0.09

Verified step by step guidance

1. Identify the given information: the frequency of individuals affected by the autosomal recessive disorder is 0.09. This frequency corresponds to the homozygous recessive genotype (q\^2) in the population.
2. Calculate the allele frequency of the recessive allele (q) by taking the square root of the affected frequency: \(q = \sqrt{0.09}\).
3. Determine the frequency of the dominant allele (p) using the relationship \(p + q = 1\), so \(p = 1 - q\).
4. Calculate the frequency of heterozygous carriers (the individuals with genotype Aa) using the Hardy-Weinberg formula for heterozygotes: \$2pq$.
5. Convert the frequency of heterozygous carriers to a percentage by multiplying the result by 100.

Key Concepts

Autosomal Recessive Inheritance

Autosomal recessive disorders require two copies of a mutant allele for the phenotype to be expressed. Individuals with only one mutant allele are carriers and typically do not show symptoms. Understanding this inheritance pattern is essential to relate genotype frequencies to disease prevalence.

Hardy-Weinberg Equilibrium

The Hardy-Weinberg principle provides a mathematical framework to relate allele and genotype frequencies in a population under random mating and no evolutionary forces. It allows calculation of carrier frequencies from disease prevalence using p² + 2pq + q² = 1, where q² represents affected individuals.

Calculating Carrier Frequency from Disease Prevalence

For autosomal recessive disorders, the frequency of affected individuals (q²) is known, allowing calculation of q (mutant allele frequency). The carrier frequency is 2pq, where p ≈ 1 for rare disorders. This calculation estimates the percentage of heterozygous carriers in the population.