Which characters support which clades? Exploring the distribution of phylogenetic signal using mutual information

Understanding which individual characters provide evidence for specific edges in a phylogeny is crucial when evaluating datasets of discrete phylogenetic characters, yet most support measures summarize evidence across all sites. I introduce clustering concordance, an information theoretic approach that quantifies the normalized mutual information shared between each character and each edge, without assuming an underpinning evolutionary model; and an analogue based on non-redundant quartet statements. Aggregating these values across edges summarizes how much of each character's information is reflected across a set of splits, whilst aggregating across characters quantifies the concordance between an edge and a combined dataset. Across 999 simulated datasets, these measures track rate-driven homoplasy, and discriminate edges that occur in the generative tree. An empirical analysis of total-group brachiopods shows how concordance measures pinpoint morphological characters that underpin specific clades, and reveal where information is concentrated within the dataset. Concordance complements existing measures of statistical branch support, and provides an objective, per-character map to inform dataset design-for example, by highlighting problematic characters or sites whose scoring, formulation, alignment or inclusion merits closer scrutiny. The methods are implemented in the TreeSearch R package.