Minimum Contradiction Matrices in Whole Genome Phylogenies

Minimum contradiction matrices are a useful complement to distance-based phylogenies. A minimum contradiction matrix represents phylogenetic information under the form of an ordered distance matrix Y(i)(,) (j)(n). A matrix element corresponds to the distance from a reference vertex n to the path (i, j). For an X-tree or a split network, the minimum contradiction matrix is a Robinson matrix. It therefore fulfills all the inequalities defining perfect order: Y(i)(,) (j)(n) ≥ Y(i)(,)(k)(n)(,) Y(k j)(n) ≥ Y(k)(,) (I)(n), i ≤ j ≤ k < n. In real phylogenetic data, some taxa may contradict the inequalities for perfect order. Contradictions to perfect order correspond to deviations from a tree or from a split network topology. Efficient algorithms that search for the best order are presented and tested on whole genome phylogenies with 184 taxa including many Bacteria, Archaea and Eukaryota. After optimization, taxa are classified in their correct domain and phyla. Several significant deviations from perfect order correspond to well-documented evolutionary events.