Abstract
Collections of phylogenetic trees are usually summarized using consensus methods. These methods build a single tree, supposed to be representative of the collection. However, in the case of heterogeneous collections of trees, the resulting consensus may be poorly resolved (strict consensus, majority-rule consensus...), or may perform arbitrary choices among mutually incompatible clades, or splits (greedy consensus). Here, we propose an alternative method, which we call the Multi-Polar Consensus (MPC). Its aim is to display all the splits having a support above a pre-defined threshold, in a minimum number of consensus trees, or poles. We show that the problem is equivalent to a graph coloring problem, and propose an implementation of the method. Finally, we apply the MPC to real datasets. Our results indicate that, typically, all the splits down to a weight of 10% can be displayed in no more than 4 trees. In addition, in some cases, biologically relevant secondary signals, that would not have been present in any of the classical consensus trees, are indeed captured by our method, indicating that the MPC provides a convenient exploratory method for phylogenetic analysis. The method was implemented in a package freely available at http://www.lirmm.fr/~cbonnard/MPC.html.