Question

In a population of birds, there are 16 animals with red tail feathers (which is a recessive trait) and 34 animals with blue tail feathers (dominant trait). What is the frequency of the red allele?

A) 0.32
B) 0.68
C) 0.16
D) 0.84

Answer 1

The frequency of the red allele in the given bird population is 0.57, calculated using the Hardy-Weinberg principle and the known quantity of red-tailed birds, which are homozygous recessive. This factor accounts for the total pool of alleles in the population, both from red- and blue-tailed birds.

Step-by-step explanation:

To find the frequency of the red allele in the population of birds described, we can use the Hardy-Weinberg principle for a population in genetic equilibrium. Since red tail feathers are a recessive trait represented by a, and blue tail feathers are dominant, represented by A, we know that the 16 birds with red tail feathers are homozygous recessive (aa). The frequency of the homozygous recessive genotype (aa) is the square of the frequency of allele a (q2).

If there are a total of 50 birds (16 red + 34 blue), we can calculate the frequency of the homozygous recessive trait in the population as 16/50, which is 0.32. This is q2. To find q (the frequency of the red allele), we take the square root of q2, which is √0.32. This equals approximately 0.57. However, it's important to note that we need the frequency of only the red allele, not the frequency of homozygous individuals.

To calculate the frequency of the red allele (a), we must also consider the blue-tailed birds. Since blue is dominant, we cannot know just from the phenotype how many of the blue-tailed birds are heterozygous (Aa) or homozygous dominant (AA). But we can use the frequency of the recessive allele to infer the frequencies of the other genotypes. First, we find the frequency of the dominant allele A (p), as p + q = 1. Therefore, p = 1 - q, which is 1 - 0.57 = 0.43. Then, because allele frequencies are calculated per allele rather than per individual, we double the population number to get the total number of alleles, which is 100 alleles (50 birds x 2 alleles per bird).

The frequency of the red allele (a), which is q, is therefore 57% or 0.57. This is not the square of the red phenotype but the frequency of the red allele itself among all alleles in the population.