Robustness of Topological Supertree Methods for Reconciling Dense Incompatible Data

Abstract

Abstract-Given a collection of rooted phylogenetic trees with overlapping sets of leaves, a compatible supertree S is a single tree whose set of leaves is the union of the input sets of leaves and such that S agrees with each input tree when restricted to the leaves of the input tree. Typically with trees from real data, no compatible supertree exists, and various methods may be utilized to reconcile the incompatibilities in the input trees. This paper focuses on a measure of robustness of a supertree method called its "radius" R. The larger the value of R is, the further the data set can be from a natural correct tree T and yet the method will still output T .It is shown that the maximal possible radius for a method is R = 1/2. Many familiar methods, both for supertrees and consensus trees, are shown to have R = 0, indicating that they need not output a tree T that would seem to be the natural correct answer. A polynomial-time method Normalized Triplet Supertree (NTS) with the maximal possible R = 1/2 is defined. A geometric interpretion is given, and NTS is shown to solve an optimization problem. Additional properties of NTS are described.

Performance of Matrix Representation with Parsimony for Inferring Species from Gene Trees

“…The fact that triplet supertree methods are expected to be consistent under the multispecies coalescent suggests that a comparative study of the performance of triplet-based supertree and consensus methods for inferring species trees would be valuable for future study, including triplet MRP, rooted triple consensus (Ewing et al, 2008), normalized triplet supertrees (Willson, 2009), supertriplets (Ranwez et al, 2010), and some recent model-based methods such as maximum pseudolikelihood estimated species tree (Liu et al, 2010a) and a quartet version (for unrooted trees) of Bayesian Concordance Analysis (Larget et al, 2010). In addition to the theoretical results that rooted triple methods are typically robust, the simulations in this paper show that t-MRP can outperform MRP consensus for some species trees even with finite numbers of loci and using estimated gene trees (Figures 8 and 9), suggesting that a more thorough simulation study of t-MRP for estimating species trees would be warranted.…”

Fast and Consistent Estimation of Species Trees Using Supermatrix Rooted Triples

“…If there are n species and i individuals sampled per species, this procedure would result in i 3 n 3 inferred rooted triples from which the species tree could be constructed using a supertree method such as MMC. With multiple rooted triples estimated on the same choice of three taxa, a supertree algorithm designed for high levels of conflict in the input triples might be useful, for example, normalized triplet supertree (Willson 2009).…”

“…Hence, if all rooted triples are inferred correctly, then the tree that displays those rooted triples is the species tree topology. A broad class of supertree algorithms can be used to prove this result including BUILD (Aho et al 1981), matrix representation using parsimony (Baum 1992;Ragan 1992), mincut (Semple and Steel 2000), MMC (Page 2002), matrix representation using flipping (Chen et al 2003), and normalized triplet supertrees (Willson 2009).…”

“…The absence of AGTs for rooted three-taxon trees motivates the development of methods for inferring species trees using rooted triples, or three taxa at a time (Degnan and Rosenberg, 2006), as has been described for rooted triple consensus methods (Ewing et al 2008;) and supertree methods (Steel and Rodrigo 2008;Willson 2009). Supertree methods generalize consensus methods to the setting in which input gene trees have overlapping subsets of taxa that need not be identical (Bininda-Emonds 2004).…”