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FST is the average inbreeding coefficient of a total population. The equation is:

$F_{ST} = \frac{Var(S)}{Var(T)} $

$Var(S)$ = variance in the frequency of the allele between different subpopulations, weighted by the sizes of subpopulations

$Var(T)$ = variance of the allelic state in the total population

If $F_{ST}$ equals 0 that means there is no population differentiation and there is no heterozygosity in the population. The ceiling for $F_{ST}$ is one so there is population differentiation and the population is all heterozygotes.

If the population is asexual, meaning they are parthenogenetic, would $F_{ST}$ be at or close to 0? Can this not be assumed?

In the context of this question I am considering the whole genome or just one allele.

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It depends on whether mutation exists. Generally mutation is happening in biology, but in its absence, yes it will be at or near zero:

Note that in the absence of any mutation, $F_{ST}$ would be defined but equal to 0, as all the genetic variance is within individuals and none between individuals and subpopulations.

From that paper, see this figure:

Fst across different rates of clonality

So, basically, the exact level of $F_{ST}$ in such cases will be controlled by the mutation rate. That figure shows a value above zero at 100% clonal reproduction because it does have a nonzero mutation rate. There is also nonzero migration between populations, so that will have the effect of reducing $F_{ST}$ somewhat. So here the value is controlled by those 2 factors. Another thing worth noting is that, if there is no initial variation between populations before the split, that will tend to increase $F_{ST}$. So it does matter how much variation exists overall.

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