Kermode bears (Ursus americanus kermodeii) are white bears that can be found in

Question

Kermode bears (Ursus americanus kermodeii) are white bears that can be found
in the rainforest on Princess Royal and Gribbell islands along the coast of British
Columbia. This subspecies of black bears is known as the Spirit Bear. Its white fur is
the result of a single nucleotide replacement in the melanocortin-1 (Mc1r) receptor
portion of that gene that leads to the production of adenine instead of guanine. The
white fur allele is a recessive allele unique to this subspecies. Dr. Kermit Ritland and
his colleagues found that approximately 20 percent of the bears on Princess Royal
and Gribbell islands are white; the rest are black. The percentage of white bears on
the mainland drops off drastically with distance from those islands.

Assuming complete dominance, calculate the expected genotype frequencies:

q2 equals

0.31
0.50
0.67
0.49
0.25
0.20

p2 equals

0.31
0.50
0.67
0.49
0.25
0.20

2pq equals

0.31
0.50
0.67
0.49
0.25
0.20

Explanation / Answer

And. Allele denotation: Let the dominant allele be B and recessive allele be b.

Let the total population size be 100 bears.

Number of white bears (bb) = 20% of 100 = 20

Number of Black bears (BB + Bb) = Total population – Number of white bears

                                    = 100 – 20 = 80

Now, Hardy- Weinberg Equation for 2 allele system (for a population at HW equilibrium) is given by-

p + q = 1                                 - equation 1

(p + q)2 = p2 + q2 + 2pq = 1               - equation 2

Where,

p = allelic frequency of allele dominant allele

q = allelic frequency of allele recessive allele

p2 = genotypic frequency of homozygous dominant

q2 = genotypic frequency of homozygous recessive

2pq = genotypic frequency of heterozygote

Given,

            Genotype frequency of bb, q2 = 20% = 0.20

                        Or, q = (0.2)1/2 = 0.4472                              ; (0.2)1/2 = (under root 0.20)

So, we get: q2 = 0.20                       ; q = 0.4472

Now,

            Putting the value of q in equation 1-

            p = 1.0 – 0.4472 = 0.5528

            So, p2 = (0.5528)2 = 0.3056

So, we get: p = 0.5528                   ; p2 = 0.3056 (= 0.31, approx.)

Ans,

            2pq = 2 x 0.5528 x 0.4472 = 0.4944

            Thus, 2pq = 0.49

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