Improved Heuristics for Minimum-Flip Supertree Construction

The utility of the matrix representation with flipping (MRF) supertree method has been limited by the speed of its heuristic algorithms. We describe a new heuristic algorithm for MRF supertree construction that improves upon the speed of the previous heuristic by a factor of n (the number of taxa in the supertree). This new heuristic makes MRF tractable for large-scale supertree analyses and allows the first comparisons of MRF with other supertree methods using large empirical data sets. Analyses of three published supertree data sets with between 267 to 571 taxa indicate that MRF supertrees are equally or more similar to the input trees on average than matrix representation with parsimony (MRP) and modified mincut supertrees. The results also show that large differences may exist between MRF and MRP supertrees and demonstrate that the MRF supertree method is a practical and potentially more accurate alternative to the nearly ubiquitous MRP super-tree method.

Implementing and testing Bayesian and maximum-likelihood supertree methods in phylogenetics

Since their advent, supertrees have been increasingly used in large-scale evolutionary studies requiring a phylogenetic framework and substantial efforts have been devoted to developing a wide variety of supertree methods (SMs). Recent advances in supertree theory have allowed the implementation of maximum likelihood (ML) and Bayesian SMs, based on using an exponential distribution to model incongruence between input trees and the supertree. Such approaches are expected to have advantages over commonly used non-parametric SMs, e.g. matrix representation with parsimony (MRP). We investigated new implementations of ML and Bayesian SMs and compared these with some currently available alternative approaches. Comparisons include hypothetical examples previously used to investigate biases of SMs with respect to input tree shape and size, and empirical studies based either on trees harvested from the literature or on trees inferred from phylogenomic scale data. Our results provide no evidence of size or shape biases and demonstrate that the Bayesian method is a viable alternative to MRP and other non-parametric methods. Computation of input tree likelihoods allows the adoption of standard tests of tree topologies (e.g. the approximately unbiased test). The Bayesian approach is particularly useful in providing support values for supertree clades in the form of posterior probabilities.

An experimental study of Quartets MaxCut and other supertree methods

BACKGROUND

Supertree methods represent one of the major ways by which the Tree of Life can be estimated, but despite many recent algorithmic innovations, matrix representation with parsimony (MRP) remains the main algorithmic supertree method.

RESULTS

We evaluated the performance of several supertree methods based upon the Quartets MaxCut (QMC) method of Snir and Rao and showed that two of these methods usually outperform MRP and five other supertree methods that we studied, under many realistic model conditions. However, the QMC-based methods have scalability issues that may limit their utility on large datasets. We also observed that taxon sampling impacted supertree accuracy, with poor results obtained when all of the source trees were only sparsely sampled. Finally, we showed that the popular optimality criterion of minimizing the total topological distance of the supertree to the source trees is only weakly correlated with supertree topological accuracy. Therefore evaluating supertree methods on biological datasets is problematic.

CONCLUSIONS

Our results show that supertree methods that improve upon MRP are possible, and that an effort should be made to produce scalable and robust implementations of the most accurate supertree methods. Also, because topological accuracy depends upon taxon sampling strategies, attempts to construct very large phylogenetic trees using supertree methods should consider the selection of source tree datasets, as well as supertree methods. Finally, since supertree topological error is only weakly correlated with the supertree's topological distance to its source trees, development and testing of supertree methods presents methodological challenges.

A simulation study comparing supertree and combined analysis methods using SMIDGen

Background

Supertree methods comprise one approach to reconstructing large molecular phylogenies given multi-marker datasets: trees are estimated on each marker and then combined into a tree (the "supertree") on the entire set of taxa. Supertrees can be constructed using various algorithmic techniques, with the most common being matrix representation with parsimony (MRP). When the data allow, the competing approach is a combined analysis (also known as a "supermatrix" or "total evidence" approach) whereby the different sequence data matrices for each of the different subsets of taxa are concatenated into a single supermatrix, and a tree is estimated on that supermatrix.

Results

In this paper, we describe an extensive simulation study we performed comparing two supertree methods, MRP and weighted MRP, to combined analysis methods on large model trees. A key contribution of this study is our novel simulation methodology (Super-Method Input Data Generator, or SMIDGen) that better reflects biological processes and the practices of systematists than earlier simulations. We show that combined analysis based upon maximum likelihood outperforms MRP and weighted MRP, giving especially big improvements when the largest subtree does not contain most of the taxa.

Conclusions

This study demonstrates that MRP and weighted MRP produce distinctly less accurate trees than combined analyses for a given base method (maximum parsimony or maximum likelihood). Since there are situations in which combined analyses are not feasible, there is a clear need for better supertree methods. The source tree and combined datasets used in this study can be used to test other supertree and combined analysis methods.

Fast and consistent estimation of species trees using supermatrix rooted triples

Concatenated sequence alignments are often used to infer species-level relationships. Previous studies have shown that analysis of concatenated data using maximum likelihood (ML) can produce misleading results when loci have differing gene tree topologies due to incomplete lineage sorting. Here, we develop a polynomial time method that utilizes the modified mincut supertree algorithm to construct an estimated species tree from inferred rooted triples of concatenated alignments. We term this method SuperMatrix Rooted Triple (SMRT) and use the notation SMRT-ML when rooted triples are inferred by ML. We use simulations to investigate the performance of SMRT-ML under Jukes-Cantor and general time-reversible substitution models for four- and five-taxon species trees and also apply the method to an empirical data set of yeast genes. We find that SMRT-ML converges to the correct species tree in many cases in which ML on the full concatenated data set fails to do so. SMRT-ML can be conservative in that its output tree is often partially unresolved for problematic clades. We show analytically that when the species tree is clocklike and mutations occur under the Cavender-Farris-Neyman substitution model, as the number of genes increases, SMRT-ML is increasingly likely to infer the correct species tree even when the most likely gene tree does not match the species tree. SMRT-ML is therefore a computationally efficient and statistically consistent estimator of the species tree when gene trees are distributed according to the multispecies coalescent model.

Increasing data transparency and estimating phylogenetic uncertainty in supertrees: Approaches using nonparametric bootstrapping

The estimation of ever larger phylogenies requires consideration of alternative inference strategies, including divide-and-conquer approaches that decompose the global inference problem to a set of smaller, more manageable component problems. A prominent locus of research in this area is the development of supertree methods, which estimate a composite tree by combining a set of partially overlapping component topologies. Although promising, the use of component tree topologies as the primary data dissociates supertrees from complexities within the underling character data and complicates the evaluation of phylogenetic uncertainty. We address these issues by exploring three approaches that variously incorporate nonparametric bootstrapping into a common supertree estimation algorithm (matrix representation with parsimony, although any algorithm might be used), including bootstrap-weighting, source-tree bootstrapping, and hierarchical bootstrapping. We illustrate these procedures by means of hypothetical and empirical examples. Our preliminary experiments suggest that these methods have the potential to improve the correspondence of supertree estimates to those derived from simultaneous analysis of the combined data and to allow uncertainty in supertree topologies to be quantified. The ability to increase the transparency of supertrees to the underlying character data has several practical implications and sheds new light on an old debate. These methods have been implemented in the freely available program, tREeBOOT.

Minimum-flip supertrees: complexity and algorithms

The input to a supertree problem is a collection of phylogenetic trees that intersect pairwise in their leaf sets; the goal is to construct a single tree that retains as much as possible of the information in the input. This task is complicated by inconsistencies due to errors. We consider the case where the input trees are rooted and are represented by the clusters they exhibit. The problem is to find the minimum number of flips needed to resolve all inconsistencies, where each flip moves a taxon into or out of a cluster. We prove that the minimum-flip problem is NP-complete, but show that it is fixed-parameter tractable and give approximation algorithms for special cases.

The Shape of Supertrees to Come: Tree Shape Related Properties of Fourteen Supertree Methods

Using a simple example and simulations, we explore the impact of input tree shape upon a broad range of supertree methods. We find that input tree shape can affect how conflict is resolved by several supertree methods and that input tree shape effects may be substantial. Standard and irreversible matrix representation with parsimony (MRP), MinFlip, duplication-only Gene Tree Parsimony (GTP), and an implementation of the average consensus method have a tendency to resolve conflict in favor of relationships in unbalanced trees. Purvis MRP and the average dendrogram method appear to have an opposite tendency. Biases with respect to tree shape are correlated with objective functions that are based upon unusual asymmetric tree-to-tree distance or fit measures. Split, quartet, and triplet fit, most similar supertree, and MinCut methods (provided the latter are interpreted as Adams consensus-like supertrees) are not revealed to have any bias with respect to tree shape by our example, but whether this holds more generally is an open problem. Future development and evaluation of supertree methods should consider explicitly the undesirable biases and other properties that we highlight. In the meantime, use of a single, arbitrarily chosen supertree method is discouraged. Use of multiple methods and/or weighting schemes may allow practical assessment of the extent to which inferences from real data depend upon methodological biases with respect to input tree shape or size.

Identifying optimal incomplete phylogenetic data sets from sequence databases

We introduce a new method for identifying optimal incomplete data sets from large sequence databases based on the graph theoretic concept of alpha-quasi-bicliques. The quasi-biclique method searches large sequence databases to identify useful phylogenetic data sets with a specified amount of missing data while maintaining the necessary amount of overlap among genes and taxa. The utility of the quasi-biclique method is demonstrated on large simulated sequence databases and on a data set of green plant sequences from GenBank. The quasi-biclique method greatly increases the taxon and gene sampling in the data sets while adding only a limited amount of missing data. Furthermore, under the conditions of the simulation, data sets with a limited amount of missing data often produce topologies nearly as accurate as those built from complete data sets. The quasi-biclique method will be an effective tool for exploiting sequence databases for phylogenetic information and also may help identify critical sequences needed to build large phylogenetic data sets.

The evolution of supertrees

Supertrees result from combining many smaller, overlapping phylogenetic trees into a single, more comprehensive tree. As such, supertree construction is probably as old as the field of systematics itself, and remains our only way of visualizing the Tree of Life as a whole. Over the past decade, supertree construction has gained a more formal, objective footing, and has become an area of active theoretical and practical research. Here, I review the history of the supertree approach, focusing mainly on its current implementation. The supertrees of today represent some of the largest, complete phylogenies available for many groups, but are not without their critics. I conclude by arguing that the ever-growing molecular revolution will result in supertree construction taking on a new role and implementation in the future for analyzing large DNA sequence matrices as part of a divide-and-conquer phylogenetic approach.