A dwindling population of 250 American Badgers occupies a small grassland prairi

Question

A dwindling population of 250 American Badgers occupies a small grassland prairie habitat along the north shore of Lake Erie. To help preserve the species, scientists caught 50 American Badgers and started two breeding programs with 25 individuals each. This species has a gene that affects coat color. The wild population has two alleles for this gene: A and a, with frequencies 0.6 and 0.4, respectively.

Will be the allele frequencies of A and a be the same in both captive populations? Why or why not?

Explanation / Answer

The allele frequencies of A and a will be same in both the captive poplulation according to the Hardy weinberg law:

p2 + 2pq + q2 = 1 and p + q = 1

p = frequency of the dominant allele in the population
q = frequency of the recessive allele in the population
p2 = percentage of homozygous dominant individuals
q2 = percentage of homozygous recessive individuals
2pq = percentage of heterozygous individuals

The frequency of the "aa" genotype. The frequency of the "a" allele. The frequency of aa is 36%, which means that q2 = 0.36,. If q2 = 0.36, then q = 0.6, Since q equals the frequency of the a allele, then the frequency is 60%.

The frequency of the "A" allele. q = 0.6, and p + q = 1, then p = 0.4; the frequency of A is equal to p, so it is 40%.

The frequencies of the genotypes "AA" and "Aa." The frequency of AA is equal to p2, and the frequency of Aa is equal to 2pq. So, using the formula p2 + 2pq + q2 = 1 and p + q = 1 , the frequency of AA is 16% (i.e. p2 is 0.4 x 0.4 = 0.16) and Aa is 48% (2pq = 2 x 0.4 x 0.6 = 0.48).

The frequencies of the two possible phenotypes if "A" is completely dominant over "a." As"A" is totally dominate over "a", the dominant phenotype will show if either the homozygous "AA" or heterozygous "Aa" genotypes occur. The recessive phenotype is controlled by the homozygous aa genotype. Therefore, the frequency of the dominant phenotype equals the sum of the frequencies of AA and Aa, and the recessive phenotype is simply the frequency of aa. Therefore, the dominant frequency is 64% and the recessive frequency is 36%.

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