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

Abstract

Abstract The 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; for example consensus methods, supertree methods, species-tree methods, distance metrics and even phylogenetic reconstruction. However, three-taxon statement methods are subject to important flaws related to information redundancy. Here we aim to study the behaviour of three-taxon statements and the interactions among them in order to enhance their performance in evolutionary studies. We show how specific interactions between three-taxon statements are responsible for the emergence of redundancy and dependency within trees, and how they can be used for the improvement of weighting procedures. Our proposal is subsequently tested empirically in the supertree framework using simulations. We show that three-taxon statements using fractional weights perform much better than classical methods such as MRP (matrix representation with parsimony) 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 them, such as in consensus, supertrees, distance metrics, and phylogenetic or biogeographical analyses.