We identified conserved expression
interactions using a probabilistic method.
For every pair of meta-genes, we computed the probability of observing
their gene-gene correlations by chance using the technique of order
statistics. We computed the *P*-value for every directed pair of
meta-genes *(m,m’)* based on their gene correlations in *n*
species. Let *g _{ms}* be a
gene belonging to meta-gene

See http://www.math.uah.edu/statold/sample/sample7.html
for a good description of the joint distribution of *n* order
statistics. We can efficiently compute
the above with the recursive formula:

where r_{0}=0 and the
recursive call to *P* supplies all of the original arguments except the (*n‑i+1*)^{th}
argument. Since we included 4 species
in the analysis we used *n*=4.

We then connected any two
meta-genes containing significantly low interaction *P*-values. To correct for the multiple tests performed,
we used an adjusted *P*-value cutoff. Specifically, for a significance level of α=0.05, we included
any meta-gene interactions with *P*-values less than α/*N* where
*N* was the total number of meta-genes containing data in at least two
organisms. In our case, *N=4725*,
giving a *P*-value cutoff of 1.05x10^{-5}. Using this cutoff, we expected *Nα *=
236 false positives.