High School

Given the frequencies of genotypes:

- Aa: 0.30
- AA: 0.60
- aa: 0.10

If the selection coefficients associated with AA, Aa, and aa are 1.00, 1.00, and 0.50, respectively, determine:

(i) The allelic frequencies in the current generation.

(ii) The expected allelic frequencies in the next generation.

Answer :

The A allele is expected to increase in frequency to 0.96, while the a allele is expected to decrease to 0.04 in the next generation.

To determine the allelic frequencies, we need to first calculate the genotype frequencies using the Hardy-Weinberg equation:

p^2 + 2pq + q^2 = 1

where p and q are the frequencies of the two alleles, A and a, respectively.

Given the frequencies of Aa (0.30), AA (0.60), and aa (0.10), we can calculate p and q as follows:

p + q = 1 (since there are only two alleles)

2pq = 0.30 (since Aa has both A and a alleles)

Solving these equations simultaneously, we get:

p = 0.6

q = 0.4

These are the allelic frequencies in the current generation.

To calculate the expected allelic frequencies in the next generation, we need to use the selection coefficients:

s(AA) = 1.00

s(Aa) = 1.00

s(aa) = 0.50

The change in frequency of the A allele (Δp) can be calculated using the following equation:

Δp = p(s(AA)q^2 + s(Aa)2pq) / W

where W is the mean fitness of the population. Since we don't have information on the mean fitness, we assume that it is equal to 1. In that case, we get:

Δp = p(s(AA)q^2 + s(Aa)2pq)

= 0.6(1.00)(0.16) + 0.6(1.00)(0.48)

= 0.36

Therefore, the expected allelic frequencies in the next generation are:

p' = p + Δp

= 0.6 + 0.36

= 0.96

q' = 1 - p'

= 1 - 0.96

= 0.04

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