Information Content of Trees: Three-taxon Statements Inference Rules and Dependency

Abstract

AbstractThe three-taxon statement is the fundamental unit of rooted trees in Cladistics, stating that for three terminal taxa, two are more related to each other than to a third. 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, and even phylogenetic reconstruction. However, three-taxon statements methods are subject to important flaws related to information redundancy. We aim to study the behavior of three-taxon statements and the interactions among them in order to enhance their performance in evolutionary studies. We show here how specific interactions between three-taxon statements are responsible of the emergence of redundancy and dependency within trees, and how they can be used for the improvement of weighting procedures. Our proposal is subsequently empirically tested in the supertree framework using simulations. We show that three-taxon statements using fractional weights perform drastically better than classical methods such as MRP or methods using unweighted statements. Our study shows that appropriate fractional weighting of three taxon statements 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.