Question

1. Calculate Fst for the random-mating subpopulations below based on the specified allele frequencies. Be sure to show your work (including work to obtain Hs and HT). Hint: These 3 subpopulations belong to the same total population. There should only be one Fst value. Subpopulation 1 Subpopulation 2 Subpopulation 3 Allele 1 0.1 0.2 0.3 Allele 2 0.3 0.3 0.3 Allele 3 0.6 0.5 0.4

This is the only information provided, and I am unsure how to solve for FST. Allelic Frequencies for each Subpopulation are listed in the graph.

Answer 1

N (number of individuals genotyped. The sum of each of the rows in the table)

population 1: 1

population 2: 1

population 3: 1

Remember that the number of alleles is TWICE the number of genotypes

1. Calculate the gene (allele) frequencies

Each homozygote will have two alleles, each heterozygote will have one allele.

Note that the denominator will be twice N_i (twice as many alleles as individuals)

p1 = 2 X 0.1 + 0.3 / 2 = 0.25

q1 = 1 - P1 = 1 - 0.25 = 0.75

p2 = 2 X 0.2 + 0.3 / 2 = 0.35

q2 = 1 - P2 = 1 - 0.35 = 0. 65

p3 = 2 X 0.3 + 0.3/ 2 = 0.45

q3 = 1 - P3 = 1 - 0.45 = 0.55

2. Calculate the local observed heterozygosity of each subpopulation. Here we count genotypes:

H_obs 1 = 0.3 / 1 = 0.3

H_obs 2 = 0.3 / 1 = 0.3

H_obs 3 = 0.3/ 1 = 0.3

3. Calculate the local expected heterozygosity, or gene diversity, of each subpopulation

H_exp1 = 1 - $\sum$ (p1² + q1²) = 1 - (0.0625 + 0.5625) = 0.375

H_exp2 = 1 - $\sum$ (p2² + q2²) = 1 - (0.1225 + 0.4225) = 0.455

H_exp3 = 1 - $\sum$ (p3² + q3²) = 1 - (0.2025 + 0.3025) = 0.495

Fs = H_exp - H_obs / H_exp

F1 = 0.375 - 0.3 / 0.375 = 0.2

F2 = 0.455 - 0.3 / 0.455 = 0.34

F3 = 0.495 - 0.3 / 0.495 = 0.39

4. Calculate P- (p-bar, the frequency of allele 1) over the total population

2 X 0.1 + 0.3 + 2 X 0.2 + 0.3 + 2 X 0.3 + 0.3 / 2 + 2 + 2 = 0.35

5. Calculate q- (q-bar, the frequency of allele 3) over the total population

2 x 0.6 + 0.3 + 2 x 0.5 + 0.3 + 2 x 0.4 + 0.3 / 2 + 2 + 2 = 0.65

6. H_S based on expected heterozygosity in subpopulations

H_exp1 x N₁ + H_exp2 X N₂ + H_exp3 X N₃ / N_total = 0.375 x 1 + 0.455 x 1 + 0.495 x 1 / 3 = 0.411

7. H_T based on expected heterozygosity for overall total population

1 - $\sum$ (p-² + q-²) = 1 - (0.1225 + 0.4225) = 0.455

8. FST = H_T - H_S / H_{T =} 0.455 - 0.411 / 0.455 = 0.0967