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Abstract Background Gene tree - species tree reconciliation problems infer the patterns and processes of gene evolution within a species tree. Gene tree parsimony approaches seek the evolutionary scenario that implies the fewest gene duplications, duplications and losses, or deep coalescence (incomplete lineage sorting) events needed to reconcile a gene tree and a species tree. While a gene tree parsimony approach can be informative about genome evolution and phylogenetics, error in gene trees can profoundly bias the results. Results We introduce efficient algorithms that rapidly search local Subtree Prune and Regraft (SPR) or Tree Bisection and Reconnection (TBR) neighborhoods of a given gene tree to identify a topology that implies the fewest duplications, duplication and losses, or deep coalescence events. These algorithms improve on the current solutions by a factor of n for searching SPR neighborhoods and n2 for searching TBR neighborhoods, where n is the number of taxa in the given gene tree. They provide a fast error correction protocol for ameliorating the effects of gene tree error by allowing small rearrangements in the topology to improve the reconciliation cost. We also demonstrate a simple protocol to use the gene rearrangement algorithm to improve gene tree parsimony phylogenetic analyses. Conclusions The new gene tree rearrangement algorithms provide a fast method to address gene tree error. They do not make assumptions about the underlying processes of genome evolution, and they are amenable to analyses of large-scale genomic data sets. These algorithms are also easily incorporated into gene tree parsimony phylogenetic analyses, potentially producing more credible estimates of reconciliation cost.

Abstract Background Genomic data provide a wealth of new information for phylogenetic analysis. Yet making use of this data requires phylogenetic methods that can efficiently analyze extremely large data sets and account for processes of gene evolution, such as gene duplication and loss, incomplete lineage sorting (deep coalescence), or horizontal gene transfer, that cause incongruence among gene trees. One such approach is gene tree parsimony, which, given a set of gene trees, seeks a species tree that requires the smallest number of evolutionary events to explain the incongruence of the gene trees. However, the only existing algorithms for gene tree parsimony under the duplication-loss or deep coalescence reconciliation cost are prohibitively slow for large datasets. Results We describe novel algorithms for SPR and TBR based local search heuristics under the duplication-loss cost, and we show how they can be adapted for the deep coalescence cost. These algorithms improve upon the best existing algorithms for these problems by a factor of n, where n is the number of species in the collection of gene trees. We implemented our new SPR based local search algorithm for the duplication-loss cost and demonstrate the tremendous improvement in runtime and scalability it provides compared to existing implementations. We also evaluate the performance of our algorithm on three large-scale genomic data sets. Conclusion Our new algorithms enable, for the first time, gene tree parsimony analyses of thousands of genes from hundreds of taxa using the duplication-loss and deep coalescence reconciliation costs. Thus, this work expands both the size of data sets and the range of evolutionary models that can be incorporated into genome-scale phylogenetic analyses.

Abstract Background There is much interest in developing fast and accurate supertree methods to infer the tree of life. Supertree methods combine smaller input trees with overlapping sets of taxa to make a comprehensive phylogenetic tree that contains all of the taxa in the input trees. The intrinsically hard triplet supertree problem takes a collection of input species trees and seeks a species tree (supertree) that maximizes the number of triplet subtrees that it shares with the input trees. However, the utility of this supertree problem has been limited by a lack of efficient and effective heuristics. Results We introduce fast hill-climbing heuristics for the triplet supertree problem that perform a step-wise search of the tree space, where each step is guided by an exact solution to an instance of a local search problem. To realize time efficient heuristics we designed the first nontrivial algorithms for two standard search problems, which greatly improve on the time complexity to the best known (naïve) solutions by a factor of n and n2 (the number of taxa in the supertree). These algorithms enable large-scale supertree analyses based on the triplet supertree problem that were previously not possible. We implemented hill-climbing heuristics that are based on our new algorithms, and in analyses of two published supertree data sets, we demonstrate that our new heuristics outperform other standard supertree methods in maximizing the number of triplets shared with the input trees. Conclusion With our new heuristics, the triplet supertree problem is now computationally more tractable for large-scale supertree analyses, and it provides a potentially more accurate alternative to existing supertree methods.

Abstract Background We consider the problem of finding the maximum frequent agreement subtrees (MFASTs) in a collection of phylogenetic trees. Existing methods for this problem often do not scale beyond datasets with around 100 taxa. Our goal is to address this problem for datasets with over a thousand taxa and hundreds of trees. Results We develop a heuristic solution that aims to find MFASTs in sets of many, large phylogenetic trees. Our method works in multiple phases. In the first phase, it identifies small candidate subtrees from the set of input trees which serve as the seeds of larger subtrees. In the second phase, it combines these small seeds to build larger candidate MFASTs. In the final phase, it performs a post-processing step that ensures that we find a frequent agreement subtree that is not contained in a larger frequent agreement subtree. We demonstrate that this heuristic can easily handle data sets with 1000 taxa, greatly extending the estimation of MFASTs beyond current methods. Conclusions Although this heuristic does not guarantee to find all MFASTs or the largest MFAST, it found the MFAST in all of our synthetic datasets where we could verify the correctness of the result. It also performed well on large empirical data sets. Its performance is robust to the number and size of the input trees. Overall, this method provides a simple and fast way to identify strongly supported subtrees within large phylogenetic hypotheses.

Abstract Background Supertree 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. Results We 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. Conclusions Our 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.

Abstract Background Phylogenetic analyses of angiosperm relationships have used only a small percentage of available sequence data, but phylogenetic data matrices often can be augmented with existing data, especially if one allows missing characters. We explore the effects on phylogenetic analyses of adding 378 matK sequences and 240 26S rDNA sequences to the complete 3-gene, 567-taxon angiosperm phylogenetic matrix of Soltis et al. Results We performed maximum likelihood bootstrap analyses of the complete, 3-gene 567-taxon data matrix and the incomplete, 5-gene 567-taxon data matrix. Although the 5-gene matrix has more missing data (27.5%) than the 3-gene data matrix (2.9%), the 5-gene analysis resulted in higher levels of bootstrap support. Within the 567-taxon tree, the increase in support is most evident for relationships among the 170 taxa for which both matK and 26S rDNA sequences were added, and there is little gain in support for relationships among the 119 taxa having neither matK nor 26S rDNA sequences. The 5-gene analysis also places the enigmatic Hydrostachys in Lamiales (BS = 97%) rather than in Cornales (BS = 100% in 3-gene analysis). The placement of Hydrostachys in Lamiales is unprecedented in molecular analyses, but it is consistent with embryological and morphological data. Conclusion Adding available, and often incomplete, sets of sequences to existing data sets can be a fast and inexpensive way to increase support for phylogenetic relationships and produce novel and credible new phylogenetic hypotheses.

Abstract Background Bioinformatic tools are needed to store and access the rapidly growing phylogenetic data. These tools should enable users to identify existing phylogenetic trees containing a specified taxon or set of taxa and to compare a specified phylogenetic hypothesis to existing phylogenetic trees. Results PhyloFinder is an intelligent search engine for phylogenetic databases that we have implemented using trees from TreeBASE. It enables taxonomic queries, in which it identifies trees in the database containing the exact name of the query taxon and/or any synonymous taxon names, and it provides spelling suggestions for the query when there is no match. Additionally, PhyloFinder can identify trees containing descendants or direct ancestors of the query taxon. PhyloFinder also performs phylogenetic queries, in which it identifies trees that contain the query tree or topologies that are similar to the query tree. Conclusion PhyloFinder can enhance the utility of any tree database by providing tools for both taxonomic and phylogenetic queries as well as visualization tools that highlight the query results and provide links to NCBI and TBMap. An implementation of PhyloFinder using trees from TreeBASE is available from the web client application found in the availability and requirements section.