Nei's $G_{st}$

Nei and Chesser [3] described one approach to accounting for sampling error. So far as I've been able to determine, there aren't any currently supported programs that calculate the bias-corrected versions of $G_{st}$.⁸ I calculated the results in Table 2

The calculations are tedious, which is why you'll want to find some way of automating the caluclations if you want to do them.⁹

$$\begin{eqnarray*} H_{i} &=& 1 - {1 \over N} \sum_{k=1}^{N} \sum_{i=1}^{m} {X_{ki... ...{2}} + {H_{S} \over {\tilde n}} - {H_{I} \over {2 \tilde n N}} \end{eqnarray*}$$

where we have $N$ subpopulations, ${\bar {\hat x_{i}^{2}}} = \sum_{k=1}^{N} {x_{ki}^{2}}/N$, ${\bar x_{i}} = \sum_{k=1}^{N} x_{ki}/N$, $\tilde n$ is the harmonic mean of the population sample sizes, i.e., $\tilde n = \frac{1}{\frac{1}{N} \sum_{k=1}^{N} \frac{1}{n_k}}$, $X_{kii}$ is the frequency of genotype $A_{i}A_{i}$ in population $k$, $x_{ki}$ is the frequency of allele $A_{i}$ in population $k$, and $n_k$ is the sample size from population $k$. Recall that

$$\begin{eqnarray*} F_{is} &=& 1 - {H_{i} \over H_{s}} \\ F_{st} &=& 1 - {H_{s} \over H_{t}} \\ F_{it} &=& 1 - {H_{i} \over H_{t}} \quad . \end{eqnarray*}$$