What is the frequency of the recessive allele in the bear’s gene pool?
The “Spirit Bear” or Kermode bear is a pure white mutant of the American black bear that is found on Princess Royal Island off the central BC coast. First Nations all along the coast believe in the special powers of the bear and hold it in high regard. The following problems study the frequency of the normal dark allele and the recessive white allele. For the purposes of these problems assume A is the allele for black fur and a is the allele for white fur and 45 of 75 bears in a local Princess Royal Island population have the recessive phenotype of white fur.
To calculate the frequency of an allele by using the Hardy-Weinberg principle, we first must identify the frequencies of the dominant and recessive traits in the current generation. The frequency of A is designated as the variable p, and the frequency of a as the variable q. Because there are only two alleles in this example, their frequencies must add to 100%, so p+q = 1.
` ` Some of the black bears have an a allele that we cannot observe directly, so we must account for them mathematically when we calculate the frequencies of the alleles in the population. Thus
`q=aa + 1/2 Aa`
` ` and `p = A A + 1/2 Aa`
Also, according to Hardy-Weinberg:
`p^2 + 2pq + q^2 = 1`
In your example, 45 out of 75 bears are white. This means that the frequency of the genotype aa = 45/75 = 0.6, which is equal to q2.
Taking the square root of 0.6 gets us 0.775, which is the frequency of the a allele within the population.
Since the sum of p and q is 1, subtracting 0.775 from 1 gives us 0.225, which is the frequency of the A allele in the population.