The performance of the Congruence Among Distance Matrices (CADM) test in phylogenetic analysis

Abstract

Background: CADM is a statistical test used to estimate the level of Congruence Among Distance Matrices. It has been shown in previous studies to have a correct rate of type I error and good power when applied to dissimilarity matrices and to ultrametric distance matrices. Contrary to most other tests of incongruence used in phylogenetic analysis, the null hypothesis of the CADM test assumes complete incongruence of the phylogenetic trees instead of congruence. In this study, we performed computer simulations to assess the type I error rate and power of the test. 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.

Results: Our results showed that the test has an accurate type I error rate and good power. As expected, power increased with the number of objects (i.e., taxa), the number of partially or completely congruent matrices and the level of congruence among distance matrices.

Conclusions: Based on our results, we suggest that CADM is an excellent candidate to test for congruence and, when present, to estimate its level in phylogenomic studies where numerous genes are analysed simultaneously.

Figure 1

Rejection rates of H₀ for the global CADM test, comparing data sets simulated on partly similar trees, with identical evolutionary parameters (GTR+ Γ+ I). Three partially congruent matrices (CM_P) and two incongruent matrices (IM) were included in each test, for a total of five distance matrices (M = 5). CM_P were generated by permuting an increasing number of taxa from a total of 10 taxa (dashed line) and 50 taxa (solid line), which corresponds to different level of congruence, and for L = 10 000 bp. Rejection rates are given at a significance level of 0.05, with 95% confidence intervals represented by vertical lines, calculated from 1000 replicates.

Figure 2

Rejection rates of H₀ for a posteriori CADM tests, comparing data sets simulated on partly similar trees, with identical evolutionary parameters (GTR+ Γ+ I). Three partially congruent matrices (CM_P) and two incongruent matrices (IM) were included in each test, for a total of five distance matrices (M = 5). CM_P were generated by permuting an increasing number of taxa from a total of 10 taxa (dashed line) and 50 taxa (solid line), which corresponds to different level of congruence, and for L = 10 000 bp. Rejection rates for the five distance matrices compared are given in Figure 1 for the global CADM test. For a posteriori tests, the power curves are given for each of the five matrices permuted separately, and numbered from 1 to 5. Rejection rates are given at a significance level of 0.05, with 95% confidence intervals represented by vertical lines, calculated from 1000 replicates.

Figure 3

Performing tests of incongruence. Three different incongruence tests are possible: directly on the pairwise genetic distance matrices (Test 1), on the path-length distance matrices corresponding to the phylogenetic trees (Test 2), and on the topological distance matrices obtained by setting all branch length to 1 in the phylogenies (Test 3).

Figure 4

Application of the CADM test. Graphical and numerical example showing a particular case for which two phylogenetic trees are incongruent in their path-length distances (Test 2, Figure 3) but topologically congruent (Test 3, Figure 3).

Figure 5

Simulation protocol to generate distance matrices. The simulation protocol involves three steps: 1) additive distance matrices (A to X) are generated, 2) phylogenetic trees are inferred, and 3) DNA sequences are simulated on the trees.