FST - Fixation Index - What is it? Interpretation and Examples

FST (fixation index) measures how much of the total genetic variation is due to differences between populations. It is a measure of genetic differentiation between populations.

Its mathematical value varies between 0 (genetically identical populations) and 1 (totally genetically differentiated populations).

The classic formula to define FST is:

where:

HT is the expected heterozygosity (if all populations were one)

HS is the mean heterozygosity within populations

Relation with migration:

In simple model in equilibrium between migration and drift, FST has the following value:

where Nm is the number of migrants per generation. So, if the number of migrants is high (high gene flow), FST tends to zero. The opposite occurs for isolation.

Relation with genetic variance:

A third way of defining FST is the most straightforward, using Wright's formula (as we'll see next):

where:

Var(p) is the variance of allele frequencies among populations

p is the mean allele frequency across all populations

p(1-p) is the expected variance in allele frequency if the populations were panmictic (no structure).

Examples:

Let's use the following loci from two populations as example:

Pop1 - p1 = 0.3

Pop2 - p2 = 0.7

Step 1 - Calculate mean allele frequency (p):

p = 0.5

Two methods:

Step 2.1 - Calculate Var(p):

Step 2.2 - Calculate FST:

Step 3.1 - Calculate expected heterozygosity:

HT = 2p(1-p) = 0.5

Step 3.2 - Calculate mean heterozygosity within populations:

Each H = 2px(1-px):

Pop1 - 2p1(1-p1) = 2 x 0.3 x 0.7 = 0.42
Pop2 - 2p2(1-p2) = 2 x 0.7 x 0.3 = 0.42

HT = (0.42 + 0.42) / 2 = 0.42

Step3.3 - Calculate FST:

FST = (0.5 − 0.42) / 0.5 = 0.16

Step 4 - On Wright model for migration:

    a total 1.3 migrations were enough to generate a genetic differentiation of 0.16.

Biological interpretation:

1. Migration:

Migration is the dominant factor when it comes to the influence on FST. When migration occurs, alleles tend to "mix" and FST decreases. When populations differentiate (no migration), FST increases.

E.g. Plants with local polinization have high FST while insects with long range flights have low FST.

2. Genetic drift:

When populations are small, alleles are altered or deleted due to randomness. So, in this case, variance is higher, so FST is also higher, while on larger populations, with greater stability, FST is lower.

3. Time since separation:

Populations separated at a longer time tend to have local adaptation and diversification by selection and genetic drift. So, a longer time means a higher FST.

4. Genomic regions under selection:

When comparing specific loci:

- an outlier locus with higher FST than the mean tend to be on positive selection by fixation of beneficiary alleles on the population;

- an outlier locus with lower FST than the mean tend to be on balancing selection, where alleles are mantained on the population.

Some FST values:

- In humans: ~ 0.1 between continents and < 0.01 within european populations

- Fishes or plants with limited dispersion: 0.3-0.5

- Species with extreme isolation (islands): > 0.7