Consider a diploid population with 4 alleles 1 A2 A3 A4 at a

Consider a diploid population with 4 alleles ?_1, A_2, A_3, A_4 at a locus. An experiment on 100 individuals revealed the following counts of heterozygous individuals. Design and implement a tool that estimates the most likely allele frequencies in the population, assuming HWE is satisfied.

Solution

The cross is related to four allele frequencies A1, A2, A3 and A4. According the HWE law, all frequencies f1, f2, f3, f4 respectively should be accountable for 1. So

(f1 +f2+f3+f4)² = f₁² +f₂²+f₃²+f₄²+ 2f₁f₂+2f₁f₃+2f₁f₄ + 2f₂f₃ +2f₂f₄ + 2f₃f₄

A1A2 progenies are = 18 in 100 so frequency = 18/100 = .18

2f₁f₂ = 0.18, so on; 2f₁f₃ =0.21, 2f₁f₄ = 0.12, 2f₂f₃ =0.07, 2f₂f₄ =0.03, 2f₃f₄ = 0.05

f₁f₂ = 0.09, so on; f₁f₃ =0.105, f₁f₄ = 0.06, f₂f₃ = 0.035, f₂f₄ =0.015, f₃f₄ = 0.025

in f2f3 = 0.035 and f1f3 = 0.105; f1<f3 and f3<= 0.35 so if we take f3= 0.35

Then f2 = 0.1

Then f1 x 0.35 = 0.105; f1 =0.3

So f2 = f1f2= 0.3 x f2 =0.09 = f2 = 0.3

Now the values of f2 is contradictory so f2 and f3 values are sure 0.45 and 0.75

F1= 0.2,

The values are most likely