Your little sister has become inordinately fond of guinea pi

Your little sister has become inordinately fond of guinea pigs and really, really, really wants one for her birthday. You visit a breeder that has three possible color combinations for you to choose from: black (BB), brindle (Bb) and cinnamon (bb). If the breeder has 108 black (BB), 84 brindle (Bb), and 8 cinnamon (bb) guinea pigs: What are the observed frequencies of each genotype in the population? What is the observed frequency of the b allele in the population? How many individuals of each genotype would you expect to see in a population of 200 if the population of guinea pigs is in HWE?

Solution

Part-a:

BB (p²) = 108/200 = 0.54

Bb(2pq) = 84/200 = 0.42

bb (q²) = 8/200 = 0.04

Part-b:

Observed \"b allele\" frequency

Freq of \"B\" = p = p² + 1/2 (2pq) = 0.54 + 1/2 (0.42) = 0.54 + 0.21 = 0.75

Freq of \"b\" = q = 1-p = 1 - 0.75 = 0.25

Part-c:

EXPECTED GENOTYPE FREQUENCIES (assuming Hardy-Weinberg):

BB (p²) = (0.75)² = 0.56

Bb(2pq) = 2 (0.75)(0.25) = 0.37

bb (q²) = (0.25)² = 0.063

EXPECTED NUMBER OF INDIVIDUALS of EACH GENOTYPE:

# BB = 0.56 X 200 = 112

# M₁₃ M₁₇= 0.37 X 200 = 74

# M₁₇ M₁₇ = 0.06 X 200 = 12