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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.