Question

Consider a population of 100 individuals and the frequency of the A allele is 0.6 and the frequency of the a allele is 0.4. If the following fitness values for each genotype are applied to the next generation, what will be the frequency of the A allele in the next generation?

wAA = 1

wAa = 0.25

waa = 0.25

Answer Choices:

a. .81

b. .64

c. .92

d. .73

e. .54

Answer 1

The answer will be 0.81 (Option a).

Explanation: Given, frequency of A = 0.6, frequency of a = 0.4, wAA = 1, wAa = 0.25, waa = 0.25

So, frequency of AA = (frequency of A)² = (0.6)² = 0.36

So, frequency of aa = (frequency of a)² = (0.4)² = 0.16

So, frequency of Aa = 2 x frequency of A x frequency of a = 2 x 0.6 x 0.4 = 0.48

Now, mean relative fitness = (Frequency of AA x Fitness of AA) + (Frequency of Aa x Fitness of Aa) + (Frequency of aa x Fitness of aa) = (0.36 x 1) + (0.48 x 0.25) + (0.16 x 0.25) = 0.36 + 0.12 + 0.04 = 0.52

Now, after selection frequency of AA = (Frequency of AA x Fitness of AA) / mean relative fitness = (0.36 x 1) / 0.52 = 0.692 (Up to 3 decimal)

Now, after selection frequency of Aa = (Frequency of Aa x Fitness of Aa) / mean fitness = (0.48 x 0.25) / 0.52 = 0.231 (Up to 3 decimal)

So, frequency of A allele in the next generation = Frequency of AA + 1/2 of Frequency of Aa = 0.692 + (0.5 x 0.231) = 0.80755 = 0.81 (Up to 2 decimal)