New perspectives in phylogenetic support assessment: using the new Relative Contradiction Index to investigate the phylogenetic controversies in Crocodylia.

Numerous tools have been developed since the advent of phylogenetic methods to assess tree robustness. Identifying the degree of contradiction in a phylogenetic matrix, as well as the specific contribution of each taxon and character, is essential for estimating its reliability. In parsimony-based phylogenetic inferences, classically used by paleontologists, a phylogeny results from the interaction of all the characters used in the analysis. Consequently, the support initially provided by the characters in the matrix may differ from that after after optimization in the final tree, severing the link between the phylogenetic content of the matrix and that of the final tree. Thus, all methods aimed at measuring support only do so indirectly and the impact of individual characters or taxa can only be assessed after the analysis. Three-taxon analysis (3ta) is a phylogenetic method that can circumvent these issues by precisely measuring the support of targeted characters and/or taxa directly from the phylogenetic matrix. In 3ta, characters are coded as trees and decomposed into three-taxon statements (3ts). The analysis searches for the largest set of non-contradicting 3ts to compute the optimal phylogeny. Because the analysis is a compatibility procedure, not an optimization procedure, character supports on the tree are independent from one another. This enables direct assessment of support from the matrix, providing meaningful insights into the topology of the optimal trees. Moreover, the decomposition of characters into 3ts allows for precise quantification of the impact of the characters/taxa in the results. In this study, focusing on Crocodylia (a subject of ongoing debate over recent decades), we use 3ta to measure the support of specific characters and/or taxa in the recently published matrix of Rio and Mannion (2021). This conflict revolves around two competing hypotheses - Longirostres and Brevirostres - supporting a different placement of the Gavialoidea clade. We also introduce here the Relative Contradiction Index (RCI) to evaluate node support, a metric that reflects the degree of contradiction in a matrix between competing cladistic hypotheses, ranging from 0.5 (maximum contradiction) to 1 (no contradiction). We show that although the Longirostres hypothesis is the best-supported, it is strongly challenged by the Brevirostres hypothesis (RCI = 0.62). Furthermore, we find that Tomistominae provides 61% of the supporting evidence for the Longirostres hypothesis, such that, when removed, the matrix supports the Brevirostres hypothesis. Individual tomistomines' contributions vary only from 2% to 7% of the total support to the Longirostres hypothesis. Finally, we show that characters correlated to longirostry only provide a fraction (22%) of the total support to the Longirostres hypothesis. Thus, our method can quantify the impact of specific characters or taxa on a phylogenetic result. This should prove very useful to phylogeneticists, especially when dealing with incomplete material such as fossils.