Albinism, an autosomal recessive trait characterized by an absence of skin pigmentation, is found in 1 in 4000 people in populations at equilibrium. Brachydactyly, an autosomal dominant trait producing shortened fingers and toes, is found in 1 in 6000 people in populations at equilibrium. For each of these traits, calculate the frequency of the recessive allele at the locus

Verified step by step guidance

1. Understand the problem: Albinism is an autosomal recessive trait, meaning individuals with the condition must have two copies of the recessive allele (aa). The frequency of individuals with albinism in the population is given as 1 in 4000. This corresponds to the genotype frequency of homozygous recessive individuals (q²). Similarly, for brachydactyly, an autosomal dominant trait, the frequency of affected individuals is 1 in 6000, which includes both heterozygous (Aa) and homozygous dominant (AA) genotypes.
2. For albinism, use the Hardy-Weinberg equation to calculate the frequency of the recessive allele (q). The Hardy-Weinberg equation is p² + 2pq + q² = 1, where p is the frequency of the dominant allele, q is the frequency of the recessive allele, p² is the frequency of homozygous dominant individuals, 2pq is the frequency of heterozygous individuals, and q² is the frequency of homozygous recessive individuals. Since q² = 1/4000, calculate q by taking the square root of q²: q = √(1/4000).
3. For brachydactyly, note that the frequency of affected individuals (1/6000) includes both heterozygous (2pq) and homozygous dominant (p²) genotypes. To calculate the frequency of the recessive allele (q), first determine the frequency of unaffected individuals (q²), which is the complement of the affected frequency: q² = 1 - (frequency of affected individuals). Then calculate q by taking the square root of q²: q = √q².
4. Once you have calculated q for both traits, you can also calculate the frequency of the dominant allele (p) using the relationship p + q = 1. Rearrange this equation to solve for p: p = 1 - q.
5. Summarize the results: The frequency of the recessive allele (q) for albinism and brachydactyly can be determined using the Hardy-Weinberg principle. Ensure that all calculations are consistent with the assumptions of Hardy-Weinberg equilibrium, such as random mating, no mutation, no migration, no selection, and a large population size.

Key Concepts

Hardy-Weinberg Principle

The Hardy-Weinberg Principle provides a mathematical framework for understanding allele frequencies in a population at genetic equilibrium. It states that allele and genotype frequencies will remain constant from generation to generation in the absence of evolutionary influences. This principle is essential for calculating allele frequencies, particularly in traits governed by simple Mendelian inheritance.

Autosomal Recessive Inheritance

Autosomal recessive inheritance occurs when a trait is expressed only when an individual has two copies of the recessive allele. In the case of albinism, the absence of skin pigmentation results from inheriting two recessive alleles. Understanding this inheritance pattern is crucial for calculating the frequency of the recessive allele in a population.

Allele Frequency Calculation

Allele frequency calculation involves determining the proportion of a specific allele within a population. For recessive traits, the frequency of the recessive allele can be derived from the proportion of individuals expressing the trait, using the formula q^2 = frequency of recessive phenotype. This calculation is vital for understanding genetic variation and predicting the likelihood of traits in future generations.