Quartet Supertrees

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.

Anchoring quartet-based phylogenetic distances and applications to species tree reconstruction

Background

Inferring species trees from gene trees using the coalescent-based summary methods has been the subject of much attention, yet new scalable and accurate methods are needed.

Results

We introduce DISTIQUE, a new statistically consistent summary method for inferring species trees from gene trees under the coalescent model. We generalize our results to arbitrary phylogenetic inference problems; we show that two arbitrarily chosen leaves, called anchors, can be used to estimate relative distances between all other pairs of leaves by inferring relevant quartet trees. This results in a family of distance-based tree inference methods, with running times ranging between quadratic to quartic in the number of leaves.

Conclusions

We show in simulated studies that DISTIQUE has comparable accuracy to leading coalescent-based summary methods and reduced running times.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-016-3098-z) contains supplementary material, which is available to authorized users.

Consensus and confusion in molluscan trees: evaluating morphological and molecular phylogenies

Mollusks are the most morphologically disparate living animal phylum, they have diversified into all habitats, and have a deep fossil record. Monophyly and identity of their eight living classes is undisputed, but relationships between these groups and patterns of their early radiation have remained elusive. Arguments about traditional morphological phylogeny focus on a small number of topological concepts but often without regard to proximity of the individual classes. In contrast, molecular studies have proposed a number of radically different, inherently contradictory, and controversial sister relationships. Here, we assembled a data set of 42 unique published trees describing molluscan interrelationships. We used these data to ask several questions about the state of resolution of molluscan phylogeny compared with a null model of the variation possible in random trees constructed from a monophyletic assemblage of eight terminals. Although 27 different unique trees have been proposed from morphological inference, the majority of these are not statistically different from each other. Within the available molecular topologies, only four studies to date have included the deep sea class Monoplacophora; but 36.4% of all trees are not significantly different. We also present supertrees derived from two data partitions and three methods, including all available molecular molluscan phylogenies, which will form the basis for future hypothesis testing. The supertrees presented here were not constructed to provide yet another hypothesis of molluscan relationships, but rather to algorithmically evaluate the relationships present in the disparate published topologies. Based on the totality of available evidence, certain patterns of relatedness among constituent taxa become clear. The internodal distance is consistently short between a few taxon pairs, particularly supporting the relatedness of Monoplacophora and the chitons, Polyplacophora. Other taxon pairs are rarely or never found in close proximity, such as the vermiform Caudofoveata and Bivalvia. Our results have specific utility for guiding constructive research planning to better test relationships in Mollusca as well as other problematic groups. Taxa with consistently proximate relationships should be the focus of a combined approach in a concerted assessment of potential genetic and anatomical homology, whereas unequivocally distant taxa will make the most constructive choices for exemplar selection in higher level phylogenomic analyses.

Supertrees Based on the Subtree Prune-and-Regraft Distance

Supertree methods reconcile a set of phylogenetic trees into a single structure that is often interpreted as a branching history of species. A key challenge is combining conflicting evolutionary histories that are due to artifacts of phylogenetic reconstruction and phenomena such as lateral gene transfer (LGT). Many supertree approaches use optimality criteria that do not reflect underlying processes, have known biases, and may be unduly influenced by LGT. We present the first method to construct supertrees by using the subtree prune-and-regraft (SPR) distance as an optimality criterion. Although calculating the rooted SPR distance between a pair of trees is NP-hard, our new maximum agreement forest-based methods can reconcile trees with hundreds of taxa and>50 transfers in fractions of a second, which enables repeated calculations during the course of an iterative search. Our approach can accommodate trees in which uncertain relationships have been collapsed to multifurcating nodes. Using a series of benchmark datasets simulated under plausible rates of LGT, we show that SPR supertrees are more similar to correct species histories than supertrees based on parsimony or Robinson-Foulds distance criteria. We successfully constructed an SPR supertree from a phylogenomic dataset of 40,631 gene trees that covered 244 genomes representing several major bacterial phyla. Our SPR-based approach also allowed direct inference of highways of gene transfer between bacterial classes and genera. A Small number of these highways connect genera in different phyla and can highlight specific genes implicated in long-distance LGT. [Lateral gene transfer; matrix representation with parsimony; phylogenomics; prokaryotic phylogeny; Robinson-Foulds; subtree prune-and-regraft; supertrees.].

DendroBLAST: approximate phylogenetic trees in the absence of multiple sequence alignments

The rapidly growing availability of genome information has created considerable demand for both fast and accurate phylogenetic inference algorithms. We present a novel method called DendroBLAST for reconstructing phylogenetic dendrograms/trees from protein sequences using BLAST. This method differs from other methods by incorporating a simple model of sequence evolution to test the effect of introducing sequence changes on the reliability of the bipartitions in the inferred tree. Using realistic simulated sequence data we demonstrate that this method produces phylogenetic trees that are more accurate than other commonly-used distance based methods though not as accurate as maximum likelihood methods from good quality multiple sequence alignments. In addition to tests on simulated data, we use DendroBLAST to generate input trees for a supertree reconstruction of the phylogeny of the Archaea. This independent analysis produces an approximate phylogeny of the Archaea that has both high precision and recall when compared to previously published analysis of the same dataset using conventional methods. Taken together these results demonstrate that approximate phylogenetic trees can be produced in the absence of multiple sequence alignments, and we propose that these trees will provide a platform for improving and informing downstream bioinformatic analysis. A web implementation of the DendroBLAST method is freely available for use at http://www.dendroblast.com/.

Quartet decomposition server: a platform for analyzing phylogenetic trees

Background

The frequent exchange of genetic material among prokaryotes means that extracting a majority or plurality phylogenetic signal from many gene families, and the identification of gene families that are in significant conflict with the plurality signal is a frequent task in comparative genomics, and especially in phylogenomic analyses. Decomposition of gene trees into embedded quartets (unrooted trees each with four taxa) is a convenient and statistically powerful technique to address this challenging problem. This approach was shown to be useful in several studies of completely sequenced microbial genomes.

Results

We present here a web server that takes a collection of gene phylogenies, decomposes them into quartets, generates a Quartet Spectrum, and draws a split network. Users are also provided with various data download options for further analyses. Each gene phylogeny is to be represented by an assessment of phylogenetic information content, such as sets of trees reconstructed from bootstrap replicates or sampled from a posterior distribution. The Quartet Decomposition server is accessible at http://quartets.uga.edu.

Conclusions

The Quartet Decomposition server presented here provides a convenient means to perform Quartet Decomposition analyses and will empower users to find statistically supported phylogenetic conflicts.

Detecting highways of horizontal gene transfer

In a horizontal gene transfer (HGT) event, a gene is transferred between two species that do not have an ancestor-descendant relationship. Typically, no more than a few genes are horizontally transferred between any two species. However, several studies identified pairs of species between which many different genes were horizontally transferred. Such a pair is said to be linked by a highway of gene sharing. We present a method for inferring such highways. Our method is based on the fact that the evolutionary histories of horizontally transferred genes disagree with the corresponding species phylogeny. Specifically, given a set of gene trees and a trusted rooted species tree, each gene tree is first decomposed into its constituent quartet trees and the quartets that are inconsistent with the species tree are identified. Our method finds a pair of species such that a highway between them explains the largest (normalized) fraction of inconsistent quartets. For a problem on n species and m input quartet trees, we give an efficient O(m + n(2))-time algorithm for detecting highways, which is optimal with respect to the quartets input size. An application of our method to a dataset of 1128 genes from 11 cyanobacterial species, as well as to simulated datasets, illustrates the efficacy of our method.

Phylogenetic analysis based on spectral methods

Whole-genome or multiple gene phylogenetic analysis is of interest since single gene analysis often results in poorly resolved trees. Here, the use of spectral techniques for analyzing multigene data sets is explored. The protein sequences are treated as categorical time series, and a measure of similarity between a pair of sequences, the spectral covariance, is based on the common periodicity between these two sequences. Unlike the other methods, the spectral covariance method focuses on the relationship between the sites of genetic sequences. By properly scaling the dissimilarity measures derived from different genes between a pair of species, we can use the mean of these scaled dissimilarity measures as a summary statistic to measure the taxonomic distances across multiple genes. The methods are applied to three different data sets, one noncontroversial and two with some dispute over the correct placement of the taxa in the tree. Trees are constructed using two distance-based methods, BIONJ and FITCH. A variation of block bootstrap sampling method is used for inference. The methods are able to recover all major clades in the corresponding reference trees with moderate to high bootstrap support. Through simulations, we show that the covariance-based methods effectively capture phylogenetic signal even when structural information is not fully retained. Comparisons of simulation results with the bootstrap permutation results indicate that the covariance-based methods are fairly robust under perturbations in sequence similarity but more sensitive to perturbations in structural similarity.

Accuracy of phylogeny reconstruction methods combining overlapping gene data sets

Background

The availability of many gene alignments with overlapping taxon sets raises the question of which strategy is the best to infer species phylogenies from multiple gene information. Methods and programs abound that use the gene alignment in different ways to reconstruct the species tree. In particular, different methods combine the original data at different points along the way from the underlying sequences to the final tree. Accordingly, they are classified into superalignment, supertree and medium-level approaches. Here, we present a simulation study to compare different methods from each of these three approaches.

Results

We observe that superalignment methods usually outperform the other approaches over a wide range of parameters including sparse data and gene-specific evolutionary parameters. In the presence of high incongruency among gene trees, however, other combination methods show better performance than the superalignment approach. Surprisingly, some supertree and medium-level methods exhibit, on average, worse results than a single gene phylogeny with complete taxon information.

Conclusions

For some methods, using the reconstructed gene tree as an estimation of the species tree is superior to the combination of incomplete information. Superalignment usually performs best since it is less susceptible to stochastic error. Supertree methods can outperform superalignment in the presence of gene-tree conflict.

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.

Conditioned genome reconstruction: how to avoid choosing the conditioning genome

Genome phylogenies can be inferred from data on the presence and absence of genes across taxa. Logdet distances may be a good method, because they allow expected genome size to vary across the tree. Recently, Lake and Rivera proposed conditioned genome reconstruction (calculation of logdet distances using only those genes present in a conditioning genome) to deal with unobservable genes that are absent from every taxon of interest. We prove that their method can consistently estimate the topology for almost any choice of conditioning genome. Nevertheless, the choice of conditioning genome is important for small samples. For real bacterial genome data, different choices of conditioning genome can result in strong bootstrap support for different tree topologies. To overcome this problem, we developed supertree methods that combine information from all choices of conditioning genome. One of these methods, based on the BIONJ algorithm, performs well on simulated data and may have applications to other supertree problems. However, an analysis of 40 bacterial genomes using this method supports an incorrect clade of parasites. This is a common feature of model-based gene content methods and is due to parallel gene loss.

SDM: a fast distance-based approach for (super) tree building in phylogenomics

Phylogenomic studies aim to build phylogenies from large sets of homologous genes. Such "genome-sized" data require fast methods, because of the typically large numbers of taxa examined. In this framework, distance-based methods are useful for exploratory studies and building a starting tree to be refined by a more powerful maximum likelihood (ML) approach. However, estimating evolutionary distances directly from concatenated genes gives poor topological signal as genes evolve at different rates. We propose a novel method, named super distance matrix (SDM), which follows the same line as average consensus supertree (ACS; Lapointe and Cucumel, 1997) and combines the evolutionary distances obtained from each gene into a single distance supermatrix to be analyzed using a standard distance-based algorithm. SDM deforms the source matrices, without modifying their topological message, to bring them as close as possible to each other; these deformed matrices are then averaged to obtain the distance supermatrix. We show that this problem is equivalent to the minimization of a least-squares criterion subject to linear constraints. This problem has a unique solution which is obtained by resolving a linear system. As this system is sparse, its practical resolution requires O(naka) time, where n is the number of taxa, k the number of matrices, and a < 2, which allows the distance supermatrix to be quickly obtained. Several uses of SDM are proposed, from fast exploratory studies to more accurate approaches requiring heavier computing time. Using simulations, we show that SDM is a relevant alternative to the standard matrix representation with parsimony (MRP) method, notably when the taxa sets of the different genes have low overlap. We also show that SDM can be used to build an excellent starting tree for an ML approach, which both reduces the computing time and increases the topogical accuracy. We use SDM to analyze the data set of Gatesy et al. (2002, Syst. Biol. 51: 652-664) that involves 48 genes of 75 placental mammals. The results indicate that these genes have strong rate heterogeneity and confirm the simulation conclusions.

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.