Information content of trees: three-taxon statements, inference rules and dependency

Abstract

The three-taxon statement (also called triplet) is the fundamental unit of rooted trees in phylogenetic systematics. Various supertree and phylogenetic methods use three-taxon statements that are minimal rooted statements of degree of kinship relationships. Because of their fundamental role in phylogenetics, three-taxon statements are present in methodological research of various disciplines in evolutionary biology, as in consensus methods, supertree methods, species-tree methods, distance metrics, phylogenetics, and cladistic biogeography. Three-taxon statements are thus widely used. However, their theoretical properties have been poorly investigated. As a result, three-taxon statements methods are subject to important flaws related to information redundancy. Correcting these biases is essential to improve the efficiency of methods using three-taxon statements. Our aim is to study the behavior of three-taxon statements and the interactions among them in order to enhance their performance in phylogenetic studies. We have identified new types of very specific interactions between three-taxon statements responsible of the emergence of redundancy and dependency in trees. We propose for the first time a classification of three-taxon statements interactions and trace the link between those and the emergence of dependency and redundancy. A new fractional weighting procedure for suppressing redundancy of three-taxon statements is proposed. Our method is subsequently empirically tested in the supertree framework using simulations. We show that three-taxon statements using fractional weights perform drastically better than classical supertree methods such as MRP or methods using unweighted three-taxon statements. Our study shows that appropriate fractional weighting of three taxon statements is an efficient measure of phylogenetic information content for rooted trees. Fractional weighting is of critical importance for removing redundancy in any method using three-taxon statements, as in consensus, supertrees, distance metrics, and phylogenetic or biogeographic analyses.