# Why is $H_{S}$ divided by $H_{T}$ in Wright's $F_{st}$ equation?

$$F_{st} = H_{t}-\frac{H_{s}}{H_{T}}$$, where $$H_{T}$$ stands for expected average heterozygosity in the meta population and $$H_{S}$$ stands for expected average heterozygosity in the sub-population.

As I understand it, $$H_{T}$$ is the heterozygosity assuming that all of the sub-populations are from the same population and if it's true, there would be no gap with $$H_{S}$$ (if it's in Hardy-Weinberg equilibrium).

Than why is it divided again with $$H_{T}$$? Is it some kind of standardisation? I don't think it's necessary.

Why can't it be used like heterozygosity of population of meta population (variation of meta population)/heterozygosity of sub populations (variation of sub-populations) somewhat like F-value of F-test.

Also why is it done with expected heterozygosity, not with observed heterozygosity

I'm talking about fixation index and as I know, there are some other formulas for fixation index but this one is commonly used

uwyo.edu/dbmcd/popecol/maylects/fst.html

• There are multiple distinct statistics called "Fst". What are you referring to specifically? May 12, 2022 at 17:49
• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
May 12, 2022 at 20:52
• I'm talking about fixation index and as I know, there are some other formulas for fixation index but this one is commonly used uwyo.edu/dbmcd/popecol/maylects/fst.html May 13, 2022 at 5:26
• $F_{ST}$, as defined by Nei 1973, is $F_{ST} = \frac{H_T-H_S}{H_T}$ and not $F_{ST} = H_T - \frac{H_S}{H_T}$. It is, to my knowledge, equivalent to to original Wright's definition $F_{ST} = \frac{var(p)}{\bar p}$, where $var(p)$ is the mean (over all loci) variance (over all subpopulations) in allele frequency and $\bar p$ is the mean (over all loci) mean (over all subpopulations) allele frequency. Other formulations exist, either considering population weights or considering specific bias in estimate (e.g. Weir-Cockerham) May 13, 2022 at 9:09