Consensus networks: A method for visualising incompatibilities in collections of trees Barbara Holland 1 and Vincent Moulton 2 1 Allan Wilson Centre for Molecular Ecology and Evolution, Massey University, New Zealand. B.R.Holland@massey.ac.nz 2 The Linnaeus Centre for Bioinformatics, Uppsala University, Box 598, 751 24 Uppsala, Sweden. vincent.moulton@lcb.uu.se Abstract. We present a method for summarising collections of phylogenetic trees that ex- tends the notion of consensus trees. Each branch in a phylogenetic tree corresponds to a bipartition or split of the set of taxa labelling its leaves. Given a collection of phylogenetic trees, each labelled by the same set of taxa, all those splits that appear in more than a prede- fined threshold proportion of the trees are displayed using a median network. The complexity of this network is bounded as a function of the threshold proportion. We demonstrate the method for a collection of 5000 trees resulting from a Monte Carlo Markov Chain analysis of 37 mammal mitochondrial genomes, and also for a collection of 80 equally parsimonious trees resulting from a heuristic search on 53 human mitochondrial sequences. Keywords: Evolutionary trees, consensus trees, phylogenetic networks, median networks, k- compatibility 1 Introduction A central task in evolutionary biology is the construction of phylogenetic trees and, accordingly, many methods have been developed for performing this task. Quite often these methods produce a collection of trees rather than a point estimate of an optimal tree, since such a tree with no measure of reliability may not be particularly helpful. Examples of methods producing collections of trees include Monte Carlo Markov Chain (MCMC) methods [14], [12], and bootstrapping [8]. Heuristic or exact searches [21] can also produce collections of trees if the optimal solution is not unique. Large collections of trees can be difficult to interpret and draw conclusions from. Thus, when faced with such a collection, it is common practice to construct a consensus tree, i.e., a tree that attempts to reconcile the information contained within all of the trees. Many ways have been devised for constructing consensus trees (see [5] for a comprehensive, recent overview). However, they all suffer from a common limitation: By summarizing all of the given trees by a single output tree, information about conflicting hypotheses is necessarily lost in the final representation. Motivated by this problem we have developed a new approach to visualizing collections of trees that naturally generalizes consensus trees. This approach is based on the construction of phylogenetic networks, networks that are regularly used by biologists to visualize and analyze complex phylogenetic data sets. In particular, we will focus on the use of median networks [2] to visualize collections of trees as we now describe. 2 Methods First we summarize some necessary concepts.