BIONJ: An Improved Version of the NJ Algorithm Based on a Simple Model of Sequence Data
01 Apr 1997-pp 1-35
TL;DR: An improved version of the neighbor-joining (NJ) algorithm of Saitou and Nei, BIONJ, follows the same agglomerative scheme as NJ, which consists of iteratively picking a pair of taxa, creating a new mode which represents the cluster of these taxa and reducing the distance matrix by replacing both taxa by this node.
Abstract: We propose an improved version of the neighbor-joining (NJ) algorithm of Saitou and Nei. This new algorithm, BIONJ, follows the same agglomerative scheme as NJ, which consists of iteratively picking a pair of taxa, creating a new mode which represents the cluster of these taxa, and reducing the distance matrix by replacing both taxa by this node. Moreover, BIONJ uses a simple first-order model of the variances and covariances of evolutionary distance estimates. This model is well adapted when these estimates are obtained from aligned sequences. At each step it permits the selection, from the class of admissible reductions, of the reduction which minimizes the variance of the new distance matrix. In this way, we obtain better estimates to choose the pair of taxa to be agglomerated during the next steps. Moreover, in comparison with NJ's estimates, these estimates become better and better as the algorithm proceeds. BIONJ retains the good properties of NJ--especially its low run time. Computer simulations have been performed with 12-taxon model trees to determine BIONJ's efficiency. When the substitution rates are low (maximum pairwise divergence approximately 0.1 substitutions per site) or when they are constant among lineages, BIONJ is only slightly better than NJ. When the substitution rates are higher and vary among lineages,BIONJ clearly has better topological accuracy. In the latter case, for the model trees and the conditions of evolution tested, the topological error reduction is on the average around 20%. With highly-varying-rate trees and with high substitution rates (maximum pairwise divergence approximately 1.0 substitutions per site), the error reduction may even rise above 50%, while the probability of finding the correct tree may be augmented by as much as 15%.
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TL;DR: The newest addition in MEGA5 is a collection of maximum likelihood (ML) analyses for inferring evolutionary trees, selecting best-fit substitution models, inferring ancestral states and sequences, and estimating evolutionary rates site-by-site.
Abstract: Comparative analysis of molecular sequence data is essential for reconstructing the evolutionary histories of species and inferring the nature and extent of selective forces shaping the evolution of genes and species. Here, we announce the release of Molecular Evolutionary Genetics Analysis version 5 (MEGA5), which is a user-friendly software for mining online databases, building sequence alignments and phylogenetic trees, and using methods of evolutionary bioinformatics in basic biology, biomedicine, and evolution. The newest addition in MEGA5 is a collection of maximum likelihood (ML) analyses for inferring evolutionary trees, selecting best-fit substitution models (nucleotide or amino acid), inferring ancestral states and sequences (along with probabilities), and estimating evolutionary rates site-by-site. In computer simulation analyses, ML tree inference algorithms in MEGA5 compared favorably with other software packages in terms of computational efficiency and the accuracy of the estimates of phylogenetic trees, substitution parameters, and rate variation among sites. The MEGA user interface has now been enhanced to be activity driven to make it easier for the use of both beginners and experienced scientists. This version of MEGA is intended for the Windows platform, and it has been configured for effective use on Mac OS X and Linux desktops. It is available free of charge from http://www.megasoftware.net.
39,110 citations
Cites methods from "BIONJ: An Improved Version of the N..."
...…or generated automatically by applying NJ and BIONJ algorithms to a matrix of pairwise distances estimated using a maximum composite likelihood approach for nucleotide sequences and a JTT model for amino acid sequences (Saitou and Nei 1987; Jones et al. 1992; Gascuel 1997; Tamura et al. 2004)....
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...The initial tree for the ML search can be supplied by the user (Newick format) or generated automatically by applying NJ and BIONJ algorithms to a matrix of pairwise distances estimated using a maximum composite likelihood approach for nucleotide sequences and a JTT model for amino acid sequences (Saitou and Nei 1987; Jones et al. 1992; Gascuel 1997; Tamura et al. 2004)....
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TL;DR: This work has used extensive and realistic computer simulations to show that the topological accuracy of this new method is at least as high as that of the existing maximum-likelihood programs and much higher than the performance of distance-based and parsimony approaches.
Abstract: The increase in the number of large data sets and the complexity of current probabilistic sequence evolution models necessitates fast and reliable phylogeny reconstruction methods. We describe a new approach, based on the maximum- likelihood principle, which clearly satisfies these requirements. The core of this method is a simple hill-climbing algorithm that adjusts tree topology and branch lengths simultaneously. This algorithm starts from an initial tree built by a fast distance-based method and modifies this tree to improve its likelihood at each iteration. Due to this simultaneous adjustment of the topology and branch lengths, only a few iterations are sufficient to reach an optimum. We used extensive and realistic computer simulations to show that the topological accuracy of this new method is at least as high as that of the existing maximum-likelihood programs and much higher than the performance of distance-based and parsimony approaches. The reduction of computing time is dramatic in comparison with other maximum-likelihood packages, while the likelihood maximization ability tends to be higher. For example, only 12 min were required on a standard personal computer to analyze a data set consisting of 500 rbcL sequences with 1,428 base pairs from plant plastids, thus reaching a speed of the same order as some popular distance-based and parsimony algorithms. This new method is implemented in the PHYML program, which is freely available on our web page: http://www.lirmm.fr/w3ifa/MAAS/. (Algorithm; computer simulations; maximum likelihood; phylogeny; rbcL; RDPII project.) The size of homologous sequence data sets has in- creased dramatically in recent years, and many of these data sets now involve several hundreds of taxa. More- over, current probabilistic sequence evolution models (Swofford et al., 1996 ; Page and Holmes, 1998 ), notably those including rate variation among sites (Uzzell and Corbin, 1971 ; Jin and Nei, 1990 ; Yang, 1996 ), require an increasing number of calculations. Therefore, the speed of phylogeny reconstruction methods is becoming a sig- nificant requirement and good compromises between speed and accuracy must be found. The maximum likelihood (ML) approach is especially accurate for building molecular phylogenies. Felsenstein (1981) brought this framework to nucleotide-based phy- logenetic inference, and it was later also applied to amino acid sequences (Kishino et al., 1990). Several vari- ants were proposed, most notably the Bayesian meth- ods (Rannala and Yang 1996; and see below), and the discrete Fourier analysis of Hendy et al. (1994), for ex- ample. Numerous computer studies (Huelsenbeck and Hillis, 1993; Kuhner and Felsenstein, 1994; Huelsenbeck, 1995; Rosenberg and Kumar, 2001; Ranwez and Gascuel, 2002) have shown that ML programs can recover the cor- rect tree from simulated data sets more frequently than other methods can. Another important advantage of the ML approach is the ability to compare different trees and evolutionary models within a statistical framework (see Whelan et al., 2001, for a review). However, like all optimality criterion-based phylogenetic reconstruction approaches, ML is hampered by computational difficul- ties, making it impossible to obtain the optimal tree with certainty from even moderate data sets (Swofford et al., 1996). Therefore, all practical methods rely on heuristics that obtain near-optimal trees in reasonable computing time. Moreover, the computation problem is especially difficult with ML, because the tree likelihood not only depends on the tree topology but also on numerical pa- rameters, including branch lengths. Even computing the optimal values of these parameters on a single tree is not an easy task, particularly because of possible local optima (Chor et al., 2000). The usual heuristic method, implemented in the pop- ular PHYLIP (Felsenstein, 1993 ) and PAUP ∗ (Swofford, 1999 ) packages, is based on hill climbing. It combines stepwise insertion of taxa in a growing tree and topolog- ical rearrangement. For each possible insertion position and rearrangement, the branch lengths of the resulting tree are optimized and the tree likelihood is computed. When the rearrangement improves the current tree or when the position insertion is the best among all pos- sible positions, the corresponding tree becomes the new current tree. Simple rearrangements are used during tree growing, namely "nearest neighbor interchanges" (see below), while more intense rearrangements can be used once all taxa have been inserted. The procedure stops when no rearrangement improves the current best tree. Despite significant decreases in computing times, no- tably in fastDNAml (Olsen et al., 1994 ), this heuristic becomes impracticable with several hundreds of taxa. This is mainly due to the two-level strategy, which sepa- rates branch lengths and tree topology optimization. In- deed, most calculations are done to optimize the branch lengths and evaluate the likelihood of trees that are finally rejected. New methods have thus been proposed. Strimmer and von Haeseler (1996) and others have assembled four- taxon (quartet) trees inferred by ML, in order to recon- struct a complete tree. However, the results of this ap- proach have not been very satisfactory to date (Ranwez and Gascuel, 2001 ). Ota and Li (2000, 2001) described
16,261 citations
Cites methods from "BIONJ: An Improved Version of the N..."
...BIONJ is just as fast as NJ but is slightly more accurate and requires O(n3) time....
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...This explains why our O(pns) ML optimization has computing time in the same range as distance methods such as NJ, BIONJ, and Weighbor, which requireO(n2s + n3) time, including distance estimation....
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...An initial tree is built from this matrix, using BIONJ (Gascuel, 1997)....
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TL;DR: A new algorithm to search the tree space with user-defined intensity using subtree pruning and regrafting topological moves and a new test to assess the support of the data for internal branches of a phylogeny are introduced.
Abstract: PhyML is a phylogeny software based on the maximum-likelihood principle. Early PhyML versions used a fast algorithm performing nearest neighbor interchanges to improve a reasonable starting tree topology. Since the original publication (Guindon S., Gascuel O. 2003. A simple, fast and accurate algorithm to estimate large phylogenies by maximum likelihood. Syst. Biol. 52:696-704), PhyML has been widely used (>2500 citations in ISI Web of Science) because of its simplicity and a fair compromise between accuracy and speed. In the meantime, research around PhyML has continued, and this article describes the new algorithms and methods implemented in the program. First, we introduce a new algorithm to search the tree space with user-defined intensity using subtree pruning and regrafting topological moves. The parsimony criterion is used here to filter out the least promising topology modifications with respect to the likelihood function. The analysis of a large collection of real nucleotide and amino acid data sets of various sizes demonstrates the good performance of this method. Second, we describe a new test to assess the support of the data for internal branches of a phylogeny. This approach extends the recently proposed approximate likelihood-ratio test and relies on a nonparametric, Shimodaira-Hasegawa-like procedure. A detailed analysis of real alignments sheds light on the links between this new approach and the more classical nonparametric bootstrap method. Overall, our tests show that the last version (3.0) of PhyML is fast, accurate, stable, and ready to use. A Web server and binary files are available from http://www.atgc-montpellier.fr/phyml/.
14,385 citations
Cites methods from "BIONJ: An Improved Version of the N..."
...Indeed, five SPR searches with a random starting tree plus one SPR search with a BioNJ starting tree are performed for each data set, which explains the multiplicative time factor compared with SPR (one NNI search is also performed, but the computing time is negligible compared with the six SPR searches)....
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...Our SPR algorithm comes in different flavors: 1) the “SPR” option relies on the algorithm described above, starting from a BioNJ (Gascuel 1997) or a maximum parsimony (MP) tree; 2) “BEST” runs both the SPR and the NNI algorithms and outputs the best of the two resulting trees (usually the SPR tree, but not always, see below); and 3) “RAND”: trees inferred by SPR starting from random trees (instead of BioNJ or MP) can also be added to the BEST option....
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...Our SPR algorithm comes in different flavors: 1) the “SPR” option relies on the algorithm described above, starting from a BioNJ (Gascuel 1997) or a maximum parsimony (MP) tree; 2) “BEST” runs both the SPR and the NNI algorithms and outputs the best of the two resulting trees (usually the SPR tree,…...
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...Pair agglomeration in BioNJ (used by PhyML to initiate the tree search) is an example of such choice, which should be random when some sequences are (nearly) identical....
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TL;DR: It is shown that a combination of hill-climbing approaches and a stochastic perturbation method can be time-efficiently implemented and found higher likelihoods between 62.2% and 87.1% of the studied alignments, thus efficiently exploring the tree-space.
Abstract: Large phylogenomics data sets require fast tree inference methods, especially for maximum-likelihood (ML) phylogenies. Fast programs exist, but due to inherent heuristics to find optimal trees, it is not clear whether the best tree is found. Thus, there is need for additional approaches that employ different search strategies to find ML trees and that are at the same time as fast as currently available ML programs. We show that a combination of hill-climbing approaches and a stochastic perturbation method can be time-efficiently implemented. If we allow the same CPU time as RAxML and PhyML, then our software IQ-TREE found higher likelihoods between 62.2% and 87.1% of the studied alignments, thus efficiently exploring the tree-space. If we use the IQ-TREE stopping rule, RAxML and PhyML are faster in 75.7% and 47.1% of the DNA alignments and 42.2% and 100% of the protein alignments, respectively. However, the range of obtaining higher likelihoods with IQ-TREE improves to 73.3-97.1%. IQ-TREE is freely available at http://www.cibiv.at/software/iqtree.
13,668 citations
Cites methods from "BIONJ: An Improved Version of the N..."
...starts with a BIONJ tree (Gascuel 1997) whereas RAxML...
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TL;DR: Improvements to FastTree are described that improve its accuracy without sacrificing scalability, and FastTree 2 allows the inference of maximum-likelihood phylogenies for huge alignments.
Abstract: Background
We recently described FastTree, a tool for inferring phylogenies for alignments with up to hundreds of thousands of sequences. Here, we describe improvements to FastTree that improve its accuracy without sacrificing scalability.
10,010 citations
Additional excerpts
...FastTree’s minimum-evolution SPR moves give it a better starting tree than PhyML’s starting tree, which is obtained with BIONJ (a weighted variant of neighbor joining [18])....
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References
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TL;DR: The neighbor-joining method and Sattath and Tversky's method are shown to be generally better than the other methods for reconstructing phylogenetic trees from evolutionary distance data.
Abstract: A new method called the neighbor-joining method is proposed for reconstructing phylogenetic trees from evolutionary distance data. The principle of this method is to find pairs of operational taxonomic units (OTUs [= neighbors]) that minimize the total branch length at each stage of clustering of OTUs starting with a starlike tree. The branch lengths as well as the topology of a parsimonious tree can quickly be obtained by using this method. Using computer simulation, we studied the efficiency of this method in obtaining the correct unrooted tree in comparison with that of five other tree-making methods: the unweighted pair group method of analysis, Farris's method, Sattath and Tversky's method, Li's method, and Tateno et al.'s modified Farris method. The new, neighbor-joining method and Sattath and Tversky's method are shown to be generally better than the other methods.
57,055 citations
Book•
01 Jun 1974
TL;DR: Since the lm function provides a lot of features it is rather complicated so it is going to instead use the function lsfit as a model, which computes only the coefficient estimates and the residuals.
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