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:
0.000081

Verified step by step guidance

1. Identify the given value as the frequency of individuals affected by the autosomal recessive disorder, which corresponds to the homozygous recessive genotype frequency \(q^2 = 0.000081\).
2. Calculate the allele frequency of the recessive allele \(q\) by taking the square root of the affected frequency: \(q = \sqrt{q^2}\).
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 carriers) using the Hardy-Weinberg formula for heterozygotes: \$2pq$.
5. Convert the heterozygous carrier frequency \$2pq$ into a percentage by multiplying by 100 to express the final answer as a percentage of the population.

Key Concepts

Autosomal Recessive Inheritance

Autosomal recessive disorders require two copies of a mutated gene for the phenotype to appear. Individuals with only one mutated 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 an autosomal recessive disorder, the disease frequency equals q² (homozygous recessive). The carrier frequency is 2pq, where p ≈ 1 for rare alleles. By taking the square root of disease frequency to find q, one can estimate the percentage of heterozygous carriers in the population.