Question

Show all work/formulas used:

1) Based on the following data:

Genotype: AA Aa aa

Relative fitness:   WAA= 1 WAa= 1 Waa= 0.5

Number of young: 100 100 800

1a) Estimate the frequency of 'aa' young individuals after 5 and 10 generations

2b) Show (graph) how the frequency of the alleles 'A' and 'a' change for 20 generations

2) If the initial Frequency of a lethal recessive allele is 10%, how many generations are needed to reduce it to 5%? (assume random mating, no new mutations and no drift)

Answer 1

Answer 1a:)

Frequency of aa genotype (q²) in the first generation = Total aa individuals/ Total population

Frequency of aa genotype (q²) in the first generation = 800/1000

Frequency of aa genotype (q²) in the first generation = 0.8

Allele frequency q = √(q²)

Allele frequency q = √0.8

Allele frequency q = 0.89

Allele frequency of A allele (p) = 1 – 0.89

Allele frequency of A allele (p) = 0.11

To calculate the frequency of aa genotype in the 5^th generation, first use the following formula to calculate allele frequency p:

In this equation, t is the generation, (0) is the initial frequency, and W is the fitness.

By putting all values in the formula

q(5) = 1 - 0.79

q(5) = 0.21

After the 10th generation:

q(10) = 1 - 0.99

q(10) = 0.01

Answer 1b:)

To make the graph, put generations on X-axis and Allele frequencies on Y-axis.

Generations	Allele A (p)	Allele a (q)
1	0.2	0.89
5	0.79	0.21
10	0.99	0.01
20	0.99	0.01

After the 10th generation, the frequencies will be constant in which allele q is nearly lost. The graph is below: