Question

Evolution question: consider the following population genetic model in which the absolute fitness we are:

AA 5

Aa 4

aa 3

And the frequency of the A allele is 0.8. Calculate the frequency of the A allele in the next generation.

Answer 1

As per the question, for the current generation we have frequency of A allele as: 0.8

Allelic frequency of A ( p) = 0.8

As per hardy weinberg equilibrium,p+q =1

Therefore allelic frequency of a (q )= (1-p) = (1- 0.8) = 0.2

Genotypic frequency of AA (p² )= (0.8)² = 0.64

Genotypic frequency of Aa( 2pq )= 2(0.8)*(0.2) = 0.32

Genotypic frequency of aa (q² )= (0.2)² = 0.04

We find out the relative fitness by dividing absolute fitness of each genotype with highest absolute fitness.

In this case, highest absolute fitness = AA =5

So, accordingly we get relative fitness as below:

Relative fitness of AA ( w_AA )= 5/5 = 1

Relative fitness of Aa ( w_Aa )= 4/5 = 0.8

Relative fitness of aa ( w_aa )= 3/5 = 0.6

Next calculate mean fitness as below:

W= { p² (w_AA) } + { 2pq (w_Aa) } + { q² (w_aa) }

= { (0.64)*(1) } + { (0.32)*(0.8) } + { (0.04)*(0.6) }

= { 0.64 + 0.256 + 0.024 }

= 0.92

For next generation, we can calculate the new genotypic frequencies and this can be done by dividing the current genotypic frequencies with the mean fitness.

So,accordingly, we get new genotypic frequency of AA = p² / W

= 0.64 / 0.92

= 0.7

New allelic frequency of A = 0.7

= 0.8366

=0.84 (ans)