Biologists collect genetic and breeding data for small popul

Biologists collect genetic and breeding data for small population of wombats on a tiny island next to Tasmania. 9a. Calculate the relative fitness values for the genotypes below. 9b. If the population has the allelic frequencies A1 = 0.7 and A2 = 0.3, what is the mean fitness for the population? 9c.What are the population’s genotypic frequencies before and after selection?

Please explain this problem to me.

Genotype

A₁A₁

A₁A₂

A₂A₂

Breeding wombats

30

48

62

Offspring

120

128

186

Solution

First we calculate reproductive rates:

Genotype

A1A1

A1A2

A2A2

Breeding wombats

30

48

62

Offspring

120

128

186

Reproductive rate

120/30 = 4

128/48 = 2.667

186/62 = 3

Relative Fitness (w) is the reproductive rate of a genotype relative to the maximum reproductive rate. The maximum reproductive rate in the population is 4 (for the genotype A1A1). Therefore, relative fitness can be calculated as:

Relative fitness (w)

4/4 = 1.0

2.667/4 = 0.667

3/4 = 0.75

Mean fitness is the sum of the products of relative fitness and genotypic frequency. Given that allelic frequencies are A1= 0.7 and A2 = 0.3. Therefore, genotypic frequencies and mean fitness are:

Genotypic frequency

0.7×0.7 = 0.49

2×0.7×0.3 = 0.42

0.3×0.3 = 0.09

w×(genotypic freq.)

1.0×0.49 = 0.490

0.667×0.42 = 0.280

0.75×0.09 = 0.067

Mean fitness = 0.490 + 0.280 + 0.067 = 0.837