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unweighted average of single-locus ratio estimators, \( \tilde{\theta }_{U}\protect \):


\begin{displaymath}
\tilde{\theta }_{U}=\frac{1}{m}\sum ^{m}_{l=1}\tilde{\theta }_{l}\end{displaymath}

, with \( \tilde{\theta }_{l}=\frac{a_{l}}{a_{l}+b_{l}} \). The estimates of the components of variance of interest for the lth locus are within populations, r is the number of populations examined:

\begin{displaymath}
b_{l}=2\sum ^{r}_{i=1}\frac{n_{i}\tilde{\alpha }_{il}}{r(2\bar{n}-1)}\end{displaymath}

and between populations:


\begin{displaymath}
a_{l}=\frac{\left[ 2\sum ^{r}_{i=1}n_{i}\sum ^{v_{l}}_{u=1}\...
...^{2}-\left( r-1\right) b_{l}\right] }{2\left( r-1\right) n_{c}}\end{displaymath}

When there are just two populations, r = 2, the usual genetic distance situation obtains, and the most convenient computing formulas for the variance components are (used in Populations)


\begin{displaymath}
a_{l}=\frac{1}{2}\sum _{u}\left( \tilde{p}_{1lu}-\tilde{p}_{...
...\alpha }_{2l}\right) }{4n_{1}n_{2}\left( n_{1}+n_{2}-1\right) }\end{displaymath}


\begin{displaymath}
a_{l}+b_{l}=\frac{1}{2}\sum _{u}\left( \tilde{p}_{1lu}-\tild...
...\alpha }_{2l}\right) }{4n_{1}n_{2}\left( n_{1}+n_{2}-1\right) }\end{displaymath}



Olivier Langella 2002-03-20