# Fixation index (FST)

Subpopulation 1 Subpopulation 2 Subpopulation 3 Total
Genotype AA 125 50 100
Aa 250 30 500
aa 125 20 400
Number of individual 500 100 1000 1600
Number of alleles 1000 200 2000 3200
Step 1. Calculate the gene (allele) frequencies
Observed allele frequency A (p) (125*2+250)/1000=0.5 (50*2+30)/200=0.65 (2*100+500)/2000=0.35
a (q) 0.5 0.35 0.65
Step 2. Calculate the expected genotypic counts under Hardy-Weinberg Equilibrium, and then calculate the excess or deficiency of homozygotes in each subpopulation. Summary of homozygote deficiency or excess relative to HWE: Pop. 1. Observed = Expected: perfect fit Pop. 2. Excess of 15.5 homozygotes: some inbreeding Pop. 3. Deficiency of 45 homozygotes: outbred or experiencing a Wahlund effect (isolate breaking).
Expected allele frequency AA 500*0.5^2 = 125 (= observed) 100*0.65^2 = 42.25 (observed has excess of 7.75) 1,000*0.35^2 = 122.5 (observed has deficiency of 22.5)
Aa 50020.5*0.5 = 250 (= observed) 10020.65*0.35 = 45.5 (observed has deficit of 15.5) 1,00020.65*0.35 = 455 (observed has excess of 45)
aa 500*0.5^2 = 125 (= observed) 100*0.35^2 = 12.25 (observed has excess of 7.75) 1,000*0.35^2 = 422.5 (observed has deficiency of 22.5)
Step 3. Calculate the local observed heterozygosities of each subpopulation (we will call them Hobs s, where the s subscript refers to the sth of n populations – 3 in this example).
Local observed heterozygosities 250/500 = 0.5 (Hobs 1) 30/100 = 0.3 (Hobs 2) 500/1000 = 0.5(Hobs 3)
Step 4. Calculate the local expected heterozygosity, or gene diversity, of each subpopulation Hexp = 2pq
Local expected heterozygosity 20.50.5=0.5 (Hexp 1) 20.653.5=0.455 (Hexp 2) 20.350.65=0.455 (Hexp 2)
Step 5. Calculate the local inbreeding coefficient of each subpopulation F = (Hexps -Hobs)/Hexp [positive F means fewer heterozygotes than expected indicates inbreeding] [negative F means more heterozygotes than expected means excess outbreeding]
F1=(0.5—0.5)/0.5=0 F2=(0.455—0.3)/0.455=0.341 F3=(0.455—0.5)/0.455=-0.099
Step 6. and 7. Calculate p-bar (p-bar, the frequency of allele A) over the total population. Calculate q-bar (q-bar, the frequency of allele a) over the total population. Check: p-bar + q-bar = 1.0
the frequency of allele over the total population p-bar (0.51000+0.65200+0.35*2000)/3200=0.4156
q-bar (0.51000+0.35200+0.65*2000)/3200=0.5844
Step 8. Calculate the global heterozygosity indices (over Individuals, Subpopulations and Total population) HI based on observed heterozygosities in individuals in subpopulations HS based on expected heterozygosities in subpopulations HT based on expected heterozygosities for overall total population
HI (observed) (0.5500+0.3100+0.5*1000)/1600=0.4875
HS (expected) (0.5500+0.455100+0.455*1000)/1600=0.4691
HT (in overall total population) 2*p-bar *q-bar = 2 * 0.4156 * 0.5844 = 0.4858
Step 9. Calculate the global F-statistics Compare and contrast the global FISbelow with the “local inbreeding coefficient” Fs of Step 5. Here we are using a weighted average of the individual heterozygosities over all the subpopulations. Both FIS and Fs are, however, based on the observed heterozygosities, whereas FST and FIT are based on expected heterozygosities.
FIS (Hs-Hi)/Hs=(0.4691-0.4875)/0.4691=-0.0393
FST (Ht-Hs)/Ht=(0.4858-0.4691)/0.4858=-0.0344
FIT (Ht-Hi)/Ht=(0.4858-0.4875)/0.4858=-0.0036
Step 10 conclusions

Finally, draw some conclusions about the genetic structure of the population and its subpopulations. 1) One of the possible HWE conclusions we could make: Pop. 1 is consistent with HWE (results of Step

1. Two of the possible “local inbreeding” conclusions we could make from Step 5:

Pop. 2 is inbred (results of Step 5), and

Pop. 3 may have disassortative mating or be experiencing a Wahlund effect (more heterozygotes than expected).

1. Conclusion concerning overall degree of genetic differentiation (FST)

Subdivision of populations, possibly due to genetic drift, accounts for approx. 3.4% of the total genetic variation (result of Eqn FST.8 FST calculation in Step 9),

1. No excess or deficiency of heterozygotes over the total population (FIT is nearly zero).