Tree congruence: quantifying similarity between dendrogram topologies

Tree congruence metrics are typically global indices that describe the similarity or dissimilarity between dendrograms. This study principally focuses on topological congruence metrics that quantify similarity between two dendrograms and can give a normalised score between 0 and 1. Specifically, this article describes and tests two metrics the Clade Retention Index (CRI) and the MASTxCF which is derived from the combined information available from a maximum agreement subtree and a strict consensus. The two metrics were developed to study differences between evolutionary trees, but their applications are multidisciplinary and can be used on hierarchical cluster diagrams derived from analyses in science, technology, maths or social sciences disciplines. A comprehensive, but non-exhaustive review of other tree congruence metrics is provided and nine metrics are further analysed. 1,620 pairwise analyses of simulated dendrograms (which could be derived from any type of analysis) were conducted and are compared in Pac-man piechart matrices. Kendalls tau-b is used to demonstrate the concordance of the different metrics and Spearmans rho ranked correlations are used to support these findings. The results support the use of the CRI and MASTxCF as part of a suite of metrics, but it is recommended that permutation metrics such as SPR distances and weighted metrics are disregarded for the specific purpose of measuring similarity.