Question

A population of beetles was scored for color. The frequencies of the genotypes and their relative fitness values are given in the table below.

Genotype	BB	Bb	bb
Phenotype	Black	Brown	White
Frequency	0.16	0.48	0.36
Fitness	0.57	0.83	1

1. What is the average fitness for color in this population of beetles? Please round your answer correctly to 4 decimal digits.

2. What is the frequency of black beetles after selection? Please round your answer correctly to 4 decimal digits.

3. What is the frequency of brown beetles after selection? Please round your answer correctly to 4 decimal digits.

4.

What is the frequency of white beetles after selection? Please round your answer correctly to 4 decimal digits.

Answer 1

Solution:

Frequency of genotype BB or p² = 0.16

Fitness for BB (W_BB) = 0.57

Frequency of genotype Bb or 2pq = 0.48

Fitness for Bb (W_Bb) = 0.83

Frequency of genotype bb or q² = 0.36

Fitness for bb (W_bb) = 1

1. In order to calculate mean fitness or w-bar, we put our known values in the equation below:

p² (W_BB) + 2pq (W_Bb) + q² (W_bb) = w-bar

(0.16 0.57) + (0.48 0.83) + (0.36 1) = w-bar

0.0912 + 0.3984 + 0.36 = w-bar

0.8496 = w - bar

, the average fitness for color in this population = 0.8496

Now,we divide all terms by w-bar to get the frequencies after one round of selection

2.  New frequency (BB) =p² (W_BB) w - bar = 0.0912 0.8496 = 0.1073

,  the frequency of black beetles after selection = 0.1073

3. New frequency (Bb) = 2pq (W_Bb) w- bar = 0.3984 0.8496 = 0.4689

, the frequency of brown beetles after selection = 0.4689

4. New frequency (bb) = q² (W_bb) w - bar = 0.36 0.8496 =0.4237

, the frequency of white beetles after selection = 0.4237