Tables 4 and 5 present the rejection rates for two matrices that have been simulated on identical trees (i.e., complete congruence), and nearly all cases tested rejected the null hypothesis of complete incongruence, regardless of the evolutionary parameters used.
In Table 2, CM correspond to distance matrices obtained from nucleotide sequences simulated on identical trees (CMI), whereas in Table 3, CM correspond to distance matrices obtained from nucleotide sequences simulated on partly similar trees with 40% of permuted taxa (CMP).
Power was also calculated for distance matrices obtained from nucleotide sequences simulated on identical trees under a GTR model, with identical or different evolutionary parameters.
Given that H0 postulates complete incongruence resulting from independent phylogenetic processes, we considered H0 to be true by construct when distance matrices calculated on nucleotide sequences simulated on independently-generated phylogenetic trees were compared.
Specifically, the type I error rate and power of the global and a posteriori CADM tests were assessed using distance matrices obtained from nucleotide sequences simulated on additive trees under various phylogenetic conditions.
When the proportion of permuted taxa is equal to 0, the distance matrices were obtained from nucleotide sequences simulated on identical trees (CMI).
When the proportion of permuted taxa is greater than 0, the distance matrices were obtained from nucleotide sequences simulated on partly similar trees (CMP), and thus, it corresponds to different levels of partial congruence (depending on the number of permuted taxa).
Given that the sequences were simulated on randomly-generated phylogenetic trees, the distance matrices obtained are incongruent matrices (IM).
It was applied to additive distance matrices representing phylogenies and to genetic distance matrices obtained from nucleotide sequences of different lengths that were simulated on randomly generated trees of varying sizes, and under different evolutionary conditions.
The values of matrix π i,n were built up from sampling over the ensemble of trajectories simulated on P. We used Bayesian MCMC to sample networks based on their associated likelihood values (Wasserman, 2004).
