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 dominant allele at the locus

Verified step by step guidance

1. Understand the problem: Albinism is an autosomal recessive trait, meaning individuals with the condition are homozygous recessive (aa). Brachydactyly is an autosomal dominant trait, meaning individuals with the condition have at least one dominant allele (Bb or BB). We are tasked with calculating the frequency of the dominant allele for each trait using the Hardy-Weinberg equilibrium principle.
2. Recall the Hardy-Weinberg equation: The equation is p² + 2pq + q² = 1, where p is the frequency of the dominant allele, q is the frequency of the recessive allele, p² represents the frequency of homozygous dominant individuals, 2pq represents the frequency of heterozygous individuals, and q² represents the frequency of homozygous recessive individuals.
3. For albinism, identify the given data: The frequency of individuals with albinism (homozygous recessive, q²) is 1/4000. Use this value to calculate q, the frequency of the recessive allele, by taking the square root of q². Then, calculate p, the frequency of the dominant allele, using the relationship p + q = 1.
4. For brachydactyly, identify the given data: The frequency of individuals with brachydactyly (those with at least one dominant allele, Bb or BB) is 1/6000. This value represents the combined frequency of p² (homozygous dominant) and 2pq (heterozygous). To calculate p, the frequency of the dominant allele, use the Hardy-Weinberg equation and solve for p iteratively or algebraically.
5. Summarize the results: After calculating p for both traits, you will have the frequency of the dominant allele for albinism and brachydactyly. These frequencies represent the proportion of the dominant allele in the population for each trait.

Key Concepts

Autosomal Recessive and Dominant Traits

Autosomal recessive traits require two copies of the recessive allele for expression, while dominant traits only need one copy of the dominant allele. In the case of albinism, individuals must inherit two recessive alleles (aa) to exhibit the trait, whereas for brachydactyly, inheriting just one dominant allele (B_) is sufficient for expression.

Hardy-Weinberg Equilibrium

Hardy-Weinberg equilibrium describes a population that is not evolving, where allele and genotype frequencies remain constant from generation to generation. This principle allows for the calculation of allele frequencies based on observed genotype frequencies, assuming no selection, mutation, migration, or genetic drift.

Allele Frequency Calculation

To calculate the frequency of alleles in a population, the Hardy-Weinberg equation (p^2 + 2pq + q^2 = 1) is used, where p is the frequency of the dominant allele and q is the frequency of the recessive allele. For albinism, the frequency of the recessive phenotype (q^2) can be used to find q, and subsequently p, while for brachydactyly, the frequency of the dominant phenotype helps determine p directly.