BackgroundSupertree methods synthesize collections of small phylogenetic trees with incomplete taxon overlap into comprehensive trees, or supertrees, that include all taxa found in the input trees. Supertree methods based on the well established Robinson-Foulds (RF) distance have the potential to build supertrees that retain much information from the input trees. Specifically, the RF supertree problem seeks a binary supertree that minimizes the sum of the RF distances from the supertree to the input trees. Thus, an RF supertree is a supertree that is consistent with the largest number of clusters (or clades) from the input trees.ResultsWe introduce efficient, local search based, hill-climbing heuristics for the intrinsically hard RF supertree problem on rooted trees. These heuristics use novel non-trivial algorithms for the SPR and TBR local search problems which improve on the time complexity of the best known (naïve) solutions by a factor of Θ(n) and Θ(n2) respectively (where n is the number of taxa, or leaves, in the supertree). We use an implementation of our new algorithms to examine the performance of the RF supertree method and compare it to matrix representation with parsimony (MRP) and the triplet supertree method using four supertree data sets. Not only did our RF heuristic provide fast estimates of RF supertrees in all data sets, but the RF supertrees also retained more of the information from the input trees (based on the RF distance) than the other supertree methods.ConclusionsOur heuristics for the RF supertree problem, based on our new local search algorithms, make it possible for the first time to estimate large supertrees by directly optimizing the RF distance from rooted input trees to the supertrees. This provides a new and fast method to build accurate supertrees. RF supertrees may also be useful for estimating majority-rule(-) supertrees, which are a generalization of majority-rule consensus trees.

DupTree for Mac OS X, Windows, and Linux along with a sample dataset and an on-line manual are available at http://genome.cs.iastate.edu/CBL/DupTree

Phylogenetic analyses using genome-scale data sets must confront incongruence among gene trees, which in plants is exacerbated by frequent gene duplications and losses. Gene tree parsimony (GTP) is a phylogenetic optimization criterion in which a species tree that minimizes the number of gene duplications induced among a set of gene trees is selected. The run time performance of previous implementations has limited its use on large-scale data sets. We used new software that incorporates recent algorithmic advances to examine the performance of GTP on a plant data set consisting of 18,896 gene trees containing 510,922 protein sequences from 136 plant taxa (giving a combined alignment length of >2.9 million characters). The relationships inferred from the GTP analysis were largely consistent with previous large-scale studies of backbone plant phylogeny and resolved some controversial nodes. The placement of taxa that were present in few gene trees generally varied the most among GTP bootstrap replicates. Excluding these taxa either before or after the GTP analysis revealed high levels of phylogenetic support across plants. The analyses supported magnoliids sister to a eudicot + monocot clade and did not support the eurosid I and II clades. This study presents a nuclear genomic perspective on the broad-scale phylogenic relationships among plants, and it demonstrates that nuclear genes with a history of duplication and loss can be phylogenetically informative for resolving the plant tree of life.

Supertree methods are used to assemble separate phylogenetic trees with shared taxa into larger trees (supertrees) in an effort to construct more comprehensive phylogenetic hypotheses. In spite of much recent interest in supertrees, there are still few methods for supertree construction. The flip supertree problem is an error correction approach that seeks to find a minimum number of changes (flips) to the matrix representation of the set of input trees to resolve their incompatibilities. A previous flip supertree algorithm was limited to finding exact solutions and was only feasible for small input trees. We developed a heuristic algorithm for the flip supertree problem suitable for much larger input trees. We used a series of 48- and 96-taxon simulations to compare supertrees constructed with the flip supertree heuristic algorithm with supertrees constructed using other approaches, including MinCut (MC), modified MC (MMC), and matrix representation with parsimony (MRP). Flip supertrees are generally far more accurate than supertrees constructed using MC or MMC algorithms and are at least as accurate as supertrees built with MRP. The flip supertree method is therefore a viable alternative to other supertree methods when the number of taxa is large.

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