Using the tangle: a consistent construction of phylogenetic distance matrices for quartets

Distance based algorithms are a common technique in the construction of phylogenetic trees from taxonomic sequence data. The first step in the implementation of these algorithms is the calculation of a pairwise distance matrix to give a measure of the evolutionary change between any pair of the extant taxa. A standard technique is to use the log det formula to construct pairwise distances from aligned sequence data. We review a distance measure valid for the most general models, and show how the log det formula can be used as an estimator thereof. We then show that the foundation upon which the log det formula is constructed can be generalized to produce a previously unknown estimator which improves the consistency of the distance matrices constructed from the log det formula. This distance estimator provides a consistent technique for constructing quartets from phylogenetic sequence data under the assumption of the most general Markov model of sequence evolution.     

Fast calculation of the quartet distance between trees of arbitrary degrees

Background  

A number of algorithms have been developed for calculating the quartet distance between two evolutionary trees on the same set of species. The quartet distance is the number of quartets – sub-trees induced by four leaves – that differs between the trees. Mostly, these algorithms are restricted to work on binary trees, but recently we have developed algorithms that work on trees of arbitrary degree.     

Theoretical foundation of the balanced minimum evolution method of phylogenetic inference and its relationship to weighted least-squares tree fitting

Due to its speed, the distance approach remains the best hope for building phylogenies on very large sets of taxa. Recently (R. Desper and O. Gascuel, J. Comp. Biol. 9:687-705, 2002), we introduced a new "balanced" minimum evolution (BME) principle, based on a branch length estimation scheme of Y. Pauplin (J. Mol. Evol. 51:41-47, 2000). Initial simulations suggested that FASTME, our program implementing the BME principle, was more accurate than or equivalent to all other distance methods we tested, with running time significantly faster than Neighbor-Joining (NJ). This article further explores the properties of the BME principle, and it explains and illustrates its impressive topological accuracy. We prove that the BME principle is a special case of the weighted least-squares approach, with biologically meaningful variances of the distance estimates. We show that the BME principle is statistically consistent. We demonstrate that FASTME only produces trees with positive branch lengths, a feature that separates this approach from NJ (and related methods) that may produce trees with branches with biologically meaningless negative lengths. Finally, we consider a large simulated data set, with 5,000 100-taxon trees generated by the Aldous beta-splitting distribution encompassing a range of distributions from Yule-Harding to uniform, and using a covarion-like model of sequence evolution. FASTME produces trees faster than NJ, and much faster than WEIGHBOR and the weighted least-squares implementation of PAUP*. Moreover, FASTME trees are consistently more accurate at all settings, ranging from Yule-Harding to uniform distributions, and all ranges of maximum pairwise divergence and departure from molecular clock. Interestingly, the covarion parameter has little effect on the tree quality for any of the algorithms. FASTME is freely available on the web.     

Phylogenetic Inference with Weighted Codon Evolutionary Distances

We develop a new approach to estimate a matrix of pairwise evolutionary distances from a codon-based alignment based on a codon evolutionary model. The method first computes a standard distance matrix for each of the three codon positions. Then these three distance matrices are weighted according to an estimate of the global evolutionary rate of each codon position and averaged into a unique distance matrix. Using a large set of both real and simulated codon-based alignments of nucleotide sequences, we show that this approach leads to distance matrices that have a significantly better treelikeness compared to those obtained by standard nucleotide evolutionary distances. We also propose an alternative weighting to eliminate the part of the noise often associated with some codon positions, particularly the third position, which is known to induce a fast evolutionary rate. Simulation results show that fast distance-based tree reconstruction algorithms on distance matrices based on this codon position weighting can lead to phylogenetic trees that are at least as accurate as, if not better, than those inferred by maximum likelihood. Finally, a well-known multigene dataset composed of eight yeast species and 106 codon-based alignments is reanalyzed and shows that our codon evolutionary distances allow building a phylogenetic tree which is similar to those obtained by non-distance-based methods (e.g., maximum parsimony and maximum likelihood) and also significantly improved compared to standard nucleotide evolutionary distance estimates.     

A metric for phylogenetic trees based on matching

Comparing two or more phylogenetic trees is a fundamental task in computational biology. The simplest outcome of such a comparison is a pairwise measure of similarity, dissimilarity, or distance. A large number of such measures have been proposed, but so far all suffer from problems varying from computational cost to lack of robustness; many can be shown to behave unexpectedly under certain plausible inputs. For instance, the widely used Robinson-Foulds distance is poorly distributed and thus affords little discrimination, while also lacking robustness in the face of very small changes--reattaching a single leaf elsewhere in a tree of any size can instantly maximize the distance. In this paper, we introduce a new pairwise distance measure, based on matching, for phylogenetic trees. We prove that our measure induces a metric on the space of trees, show how to compute it in low polynomial time, verify through statistical testing that it is robust, and finally note that it does not exhibit unexpected behavior under the same inputs that cause problems with other measures. We also illustrate its usefulness in clustering trees, demonstrating significant improvements in the quality of hierarchical clustering as compared to the same collections of trees clustered using the Robinson-Foulds distance.     

Effectiveness of measures requiring and not requiring prior sequence alignment for estimating the dissimilarity of natural sequences

Summary Various measures of sequence dissimilarity have been evaluated by how well the additive least squares estimation of edges (branch lengths) of an unrooted evolutionary tree fit the observed pairwise dissimilarity measures and by how consistent the trees are for different data sets derived from the same set of sequences. This evaluation provided sensitive discrimination among dissimilarity measures and among possible trees. Dissimilarity measures not requiring prior sequence alignment did about as well as did the traditional mismatch counts requiring prior sequence alignment. Application of Jukes-Cantor correction to singlet mismatch counts worsened the results. Measures not requiring alignment had the advantage of being applicable to sequences too different to be critically alignable. Two different measures of pairwise dissimilarity not requiring alignment have been used: (1) multiplet distribution distance (MDD), the square of the Euclidean distance between vectors of the fractions of base singlets (or doublets, or triplets, or…) in the respective sequences, and (2) complements of long words (CLW), the count of bases not occurring in significantly long common words. MDD was applicable to sequences more different than was CLW (noncoding), but the latter often gave better results where both measures were available (coding). MDD results were improved by using longer multiplets and, if the sequences were coding, by using the larger amino acid and codon alphabets rather than the nucleotide alphabet. The additive least squares method could be used to provide a reasonable consensus of different trees for the same set of species (or related genes).     

Comparison of Tree-Child Phylogenetic Networks

Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of nontreelike evolutionary events, like recombination, hybridization, or lateral gene transfer. While much progress has been made to find practical algorithms for reconstructing a phylogenetic network from a set of sequences, all attempts to endorse a class of phylogenetic networks (strictly extending the class of phylogenetic trees) with a well-founded distance measure have, to the best of our knowledge and with the only exception of the bipartition distance on regular networks, failed so far. In this paper, we present and study a new meaningful class of phylogenetic networks, called tree-child phylogenetic networks, and we provide an injective representation of these networks as multisets of vectors of natural numbers, their path multiplicity vectors. We then use this representation to define a distance on this class that extends the well-known Robinson-Foulds distance for phylogenetic trees and to give an alignment method for pairs of networks in this class. Simple polynomial algorithms for reconstructing a tree-child phylogenetic network from its path multiplicity vectors, for computing the distance between two tree-child phylogenetic networks and for aligning a pair of tree-child phylogenetic networks, are provided. They have been implemented as a Perl package and a Java applet, which can be found at http://bioinfo.uib.es/~recerca/phylonetworks/mudistance/.     

SDT: A Virus Classification Tool Based on Pairwise Sequence Alignment and Identity Calculation

The perpetually increasing rate at which viral full-genome sequences are being determined is creating a pressing demand for computational tools that will aid the objective classification of these genome sequences. Taxonomic classification approaches that are based on pairwise genetic identity measures are potentially highly automatable and are progressively gaining favour with the International Committee on Taxonomy of Viruses (ICTV). There are, however, various issues with the calculation of such measures that could potentially undermine the accuracy and consistency with which they can be applied to virus classification. Firstly, pairwise sequence identities computed based on multiple sequence alignments rather than on multiple independent pairwise alignments can lead to the deflation of identity scores with increasing dataset sizes. Also, when gap-characters need to be introduced during sequence alignments to account for insertions and deletions, methodological variations in the way that these characters are introduced and handled during pairwise genetic identity calculations can cause high degrees of inconsistency in the way that different methods classify the same sets of sequences. Here we present Sequence Demarcation Tool (SDT), a free user-friendly computer program that aims to provide a robust and highly reproducible means of objectively using pairwise genetic identity calculations to classify any set of nucleotide or amino acid sequences. SDT can produce publication quality pairwise identity plots and colour-coded distance matrices to further aid the classification of sequences according to ICTV approved taxonomic demarcation criteria. Besides a graphical interface version of the program for Windows computers, command-line versions of the program are available for a variety of different operating systems (including a parallel version for cluster computing platforms).     

Semi-Supervised Fuzzy Clustering with Feature Discrimination

Semi-supervised clustering algorithms are increasingly employed for discovering hidden structure in data with partially labelled patterns. In order to make the clustering approach useful and acceptable to users, the information provided must be simple, natural and limited in number. To improve recognition capability, we apply an effective feature enhancement procedure to the entire data-set to obtain a single set of features or weights by weighting and discriminating the information provided by the user. By taking pairwise constraints into account, we propose a semi-supervised fuzzy clustering algorithm with feature discrimination (SFFD) incorporating a fully adaptive distance function. Experiments on several standard benchmark data sets demonstrate the effectiveness of the proposed method.     

On divide-and-conquer strategies for parsimony analysis of large data sets: Rec-I-DCM3 versus TNT

Roshan et al. recently described a "divide-and-conquer" technique for parsimony analysis of large data sets, Rec-I-DCM3, and stated that it compares very favorably to results using the program TNT. Their technique is based on selecting subsets of taxa to create reduced data sets or subproblems, finding most-parsimonious trees for each reduced data set, recombining all parts together, and then performing global TBR swapping on the combined tree. Here, we contrast this approach to sectorial searches, a divide-and-conquer algorithm implemented in TNT. This algorithm also uses a guide tree to create subproblems, with the first-pass state sets of the nodes that join the selected sectors with the rest of the topology; this allows exact length calculations for the entire topology (that is, any solution N steps shorter than the original, for the reduced subproblem, must also be N steps shorter for the entire topology). We show here that, for sectors of similar size analyzed with the same search algorithms, subdividing data sets with sectorial searches produces better results than subdividing with Rec-I-DCM3. Roshan et al.'s claim that Rec-I-DCM3 outperforms the techniques in TNT was caused by a poor experimental design and algorithmic settings used for the runs in TNT. In particular, for finding trees at or very close to the minimum known length of the analyzed data sets, TNT clearly outperforms Rec-I-DCM3. Finally, we show that the performance of Rec-I-DCM3 is bound by the efficiency of TBR implementation for the complete data set, as this method behaves (after some number of iterations) as a technique for cyclic perturbations and improvements more than as a divide-and-conquer strategy.     

Progressive sequence alignment as a prerequisitetto correct phylogenetic trees

A progressive alignment method is described that utilizes the Needleman and Wunsch pairwise alignment algorithm iteratively to achieve the multiple alignment of a set of protein sequences and to construct an evolutionary tree depicting their relationship. The sequences are assumed a priori to share a common ancestor, and the trees are constructed from difference matrices derived directly from the multiple alignment. The thrust of the method involves putting more trust in the comparison of recently diverged sequences than in those evolved in the distant past. In particular, this rule is followed: "once a gap, always a gap." The method has been applied to three sets of protein sequences: 7 superoxide dismutases, 11 globins, and 9 tyrosine kinase-like sequences. Multiple alignments and phylogenetic trees for these sets of sequences were determined and compared with trees derived by conventional pairwise treatments. In several instances, the progressive method led to trees that appeared to be more in line with biological expectations than were trees obtained by more commonly used methods.     

Is the composition of phytophagous insects and parasitic fungi among trees predictable?

We explore the relationship between the pairwise similarity of assemblages of exploiters (phytophagous insects and parasitic fungi) and pairwise genetic distance, range overlap, niche overlap as well as habitat overlap of host trees. Presence of exploiters was extracted from published literature for 23 tree genera occurring in central Europe (6164 host records of phytophagous insects and 860 host records of parasitic fungi). Across all pairs of tree genera, we found a strong negative correlation between the pairwise similarity of assemblages and genetic distances of hosts. This close correlation is due to deep differences in the composition of assemblages on coniferous and deciduous tree genera. Range, niche and habitat overlap were always of much less importance than genetic distance to explain the variation of pairwise similarity of assemblages of exploiters, although some correlations were significant. Therefore in general host switches of exploiters between related hosts are more important that host switches between hosts co-occurring in the same habitat. We found a robust relationship of the pairwise similarity of assemblages of insects and the pairwise similarity of assemblages of fungi which points to the possibility that insects are vectors for parasitic fungi which promotes correlated switches of insects and fungi.     

Improved parameterized complexity of the maximum agreement subtree and maximum compatible tree problems

Given a set of evolutionary trees on a same set of taxa, the maximum agreement subtree problem (MAST), respectively, maximum compatible tree problem (MCT), consists of finding a largest subset of taxa such that all input trees restricted to these taxa are isomorphic, respectively compatible. These problems have several applications in phylogenetics such as the computation of a consensus of phylogenies obtained from different data sets, the identification of species subjected to horizontal gene transfers and, more recently, the inference of supertrees, e.g., Trees Of Life. We provide two linear time algorithms to check the isomorphism, respectively, compatibility, of a set of trees or otherwise identify a conflict between the trees with respect to the relative location of a small subset of taxa. Then, we use these algorithms as subroutines to solve MAST and MCT on rooted or unrooted trees of unbounded degree. More precisely, we give exact fixed-parameter tractable algorithms, whose running time is uniformly polynomial when the number of taxa on which the trees disagree is bounded. The improves on a known result for MAST and proves fixed-parameter tractability for MCT.     

Neighbor joining algorithms for inferring phylogenies via LCA distances.

Reconstructing phylogenetic trees efficiently and accurately from distance estimates is an ongoing challenge in computational biology from both practical and theoretical considerations. We study algorithms which are based on a characterization of edge-weighted trees by distances to LCAs (Least Common Ancestors). This characterization enables a direct application of ultrametric reconstruction techniques to trees which are not necessarily ultrametric. A simple and natural neighbor joining criterion based on this observation is used to provide a family of efficient neighbor-joining algorithms. These algorithms are shown to reconstruct a refinement of the Buneman tree, which implies optimal robustness to noise under criteria defined by Atteson. In this sense, they outperform many popular algorithms such as Saitou and Nei's NJ. One member of this family is used to provide a new simple version of the 3-approximation algorithm for the closest additive metric under the iota (infinity) norm. A byproduct of our work is a novel technique which yields a time optimal O (n (2)) implementation of common clustering algorithms such as UPGMA.     

OrthologID: automation of genome-scale ortholog identification within a parsimony framework

MOTIVATION: The determination of gene orthology is a prerequisite for mining and utilizing the rapidly increasing amount of sequence data for genome-scale phylogenetics and comparative genomic studies. Until now, most researchers use pairwise distance comparisons algorithms, such as BLAST, COG, RBH, RSD and INPARANOID, to determine gene orthology. In contrast, orthology determination within a character-based phylogenetic framework has not been utilized on a genomic scale owing to the lack of efficiency and automation. RESULTS: We have developed OrthologID, a Web application that automates the labor-intensive procedures of gene orthology determination within a character-based phylogenetic framework, thus making character-based orthology determination on a genomic scale possible. In addition to generating gene family trees and determining orthologous gene sets for complete genomes, OrthologID can also identify diagnostic characters that define each orthologous gene set, as well as diagnostic characters that are responsible for classifying query sequences from other genomes into specific orthology groups. The OrthologID database currently includes several complete plant genomes, including Arabidopsis thaliana, Oryza sativa, Populus trichocarpa, as well as a unicellular outgroup, Chlamydomonas reinhardtii. To improve the general utility of OrthologID beyond plant species, we plan to expand our sequence database to include the fully sequenced genomes of prokaryotes and other non-plant eukaryotes. AVAILABILITY: http://nypg.bio.nyu.edu/orthologid/     

Normal-modes-based prediction of protein conformational changes guided by distance constraints

Based on the elastic network model, we develop a novel method that predicts the conformational change of a protein complex given its initial-state crystal structure together with a small set of pairwise distance constraints for the end state. The predicted conformational change, which is a linear combination of multiple low-frequency normal modes that are solved from the elastic network model, is computed as a response displacement induced by a perturbation to the system Hamiltonian that incorporates the given distance constraints. For a list of test cases, we find that the computed response displacement overlaps significantly with the measured conformational changes, when only a handful of pairwise constraints are used (相似文献   

A polynomial time solvable formulation of multiple sequence alignment.

Since traditional multiple alignment formulations are NP-hard, heuristics are commonly employed to find acceptable alignments with no guaranteed performance bound. This causes a substantial difficulty in understanding what the resulting alignment means and in assessing the quality of these alignments. We propose an alternative formulation of multiple alignment based on the idea of finding a multiple alignment of k sequences which preserves k - 1 pairwise alignments as specified by edges of a given tree. Although it is well known that such a preserving alignment always exists, it did not become a mainstream method for multiple alignment since it seems that a lot of information is lost from ignoring pairwise similarities outside the tree. In contrast, by using pairwise alignments that incorporate consistency information from other sequences, we show that it is possible to obtain very good accuracy with the preserving alignment formulation. We show that a reasonable objective function to use is to find the shortest preserving alignment, and, by a reduction to a graph-theoretic problem, that the problem of finding the shortest preserving multiple alignment can be solved in polynomial time. We demonstrate the success of this approach on three sets of benchmark multiple alignments by using consistency-based pairwise alignments from the first stage of two of the best performing progressive alignment algorithms TCoffee and ProbCons and replace the second heuristic progressive step of these algorithms by the exact preserving alignment step. We apply this strategy to TCoffee and show that our approach outperforms TCoffee on two of the three test sets. We apply the strategy to a variant of ProbCons with no iterative refinements and show that our approach achieves similar or better accuracy except on one test set. We also compare our performance to ProbCons with iterative refinements and show that our approach achieves similar or better accuracy on many subcategories even without further refinements. The most important advantage of the preserving alignment formulation is that we are certain that we can solve the problem in polynomial time without using a heuristic. A software program implementing this approach (PSAlign) is available at http://faculty.cs.tamu.edu/shsze/psalign.     

Reconstructing genome trees of prokaryotes using overlapping genes

Background  

Overlapping genes (OGs) are defined as adjacent genes whose coding sequences overlap partially or entirely. In fact, they are ubiquitous in microbial genomes and more conserved between species than non-overlapping genes. Based on this property, we have previously implemented a web server, named OGtree, that allows the user to reconstruct genome trees of some prokaryotes according to their pairwise OG distances. By analogy to the analyses of gene content and gene order, the OG distance between two genomes we defined was based on a measure of combining OG content (i.e., the normalized number of shared orthologous OG pairs) and OG order (i.e., the normalized OG breakpoint distance) in their whole genomes. A shortcoming of using the concept of breakpoints to define the OG distance is its inability to analyze the OG distance of multi-chromosomal genomes. In addition, the amount of overlapping coding sequences between some distantly related prokaryotic genomes may be limited so that it is hard to find enough OGs to properly evaluate their pairwise OG distances.