Final answer:
Calculating allele frequencies in a given population with a known number of individuals expressing a recessive trait, we use the Hardy-Weinberg principle.
Step-by-step explanation:
In a population of Biology instructors where 250 out of 1000 have a receding hairline, and assuming receding hairline is a recessive trait expressed by the homozygous recessive genotype 'aa', we can calculate the allele frequencies, genotype frequencies, and heterozygous individuals.
To determine the allele frequencies of each allele (A for non-receding and a for receding), we can use the Hardy-Weinberg principle, which states that the frequency of the recessive allele 'q' is the square root of the frequency of the homozygous recessive genotype (the population with a receding hairline). Here, q² = 250/1000 = 0.25, so q = sqrt(0.25) = 0.5. The frequency of the dominant allele 'p' would be 1 - q, so p = 1 - 0.5 = 0.5.
The expected genotype frequencies can be calculated as p² for homozygous dominant (AA), 2pq for heterozygous (Aa), and q² for homozygous recessive (aa). These are p² = 0.5² = 0.25 (AA), 2pq = 2(0.5)(0.5) = 0.50 (Aa), and q² = 0.5² = 0.25 (aa).
To find the number of heterozygous individuals, we use the frequency of heterozygotes (2pq) and multiply it by the total population size: 0.50 x 1000 = 500. This means 500 individuals are expected to be heterozygous for the hairline trait.