The recently-developed statistical method known as the "bootstrap" can be used to place confidence intervals on phylogenies. It involves resampling points from one's own data, with replacement, to create a series of bootstrap samples of the same size as the original data. Each of these is analyzed, and the variation among the resulting estimates taken to indicate the size of the error involved in making estimates from the original data. In the case of phylogenies, it is argued that the proper method of resampling is to keep all of the original species while sampling characters with replacement, under the assumption that the characters have been independently drawn by the systematist and have evolved independently. Majority-rule consensus trees can be used to construct a phylogeny showing all of the inferred monophyletic groups that occurred in a majority of the bootstrap samples. If a group shows up 95% of the time or more, the evidence for it is taken to be statistically significant. Existing computer programs can be used to analyze different bootstrap samples by using weights on the characters, the weight of a character being how many times it was drawn in bootstrap sampling. When all characters are perfectly compatible, as envisioned by Hennig, bootstrap sampling becomes unnecessary; the bootstrap method would show significant evidence for a group if it is defined by three or more characters.

Confidence limits on phylogenies: an approach using the bootstrap.

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.

/pdf/mega5-molecular-evolutionary-genetics-analysis-using-maximum-2fhrdnt1zl.pdf

MEGA5: Molecular Evolutionary Genetics Analysis using Maximum Likelihood, Evolutionary Distance, and Maximum Parsimony Methods

Summary: The program MODELTEST uses log likelihood scores to establish the model of DNA evolution that best fits the data. Availability: The MODELTEST package, including the source code and some documentation is available at http://bioag.byu.edu/zoology/crandall―lab/modeltest.html. Contact: dp47@email.byu.edu.

/pdf/modeltest-testing-the-model-of-dna-substitution-2dmippvvyz.pdf

MODELTEST: testing the model of DNA substitution.

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

A simple, fast, and accurate algorithm to estimate large phylogenies by maximum likelihood.

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/.

https://www.zora.uzh.ch/id/eprint/155669/1/ZORA_NL_155669.pdf

New Algorithms and Methods to Estimate Maximum-Likelihood Phylogenies: Assessing the Performance of PhyML 3.0

The application of maximum likelihood techniques to the estimation of evolutionary trees from nucleic acid sequence data is discussed. A computationally feasible method for finding such maximum likelihood estimates is developed, and a computer program is available. This method has advantages over the traditional parsimony algorithms, which can give misleading results if rates of evolution differ in different lineages. It also allows the testing of hypotheses about the constancy of evolutionary rates by likelihood ratio tests, and gives rough indication of the error of the estimate of the tree.

Evolutionary trees from DNA sequences: A maximum likelihood approach

Recent years have seen a growth in numerical studies using the comparative method. The method usually involves a comparison of two phenotypes across a range of species or higher taxa, or a comparison of one phenotype with an environmental variable. Objectives of such studies vary, and include assessing whether one variable is correlated with another and assessing whether the regression of one variable on another differs significantly from some expected value. Notable recent studies using statistical methods of this type include Pilbeam and Gould's (1974) regressions of tooth area on several size measurements in mammals; Sherman's (1979) test of the relation between insect chromosome numbers and social behavior; Damuth's (1981) investigation of population density and body size in mammals; Martin's (1981) regression of brain weight in mammals on body weight; Givnish's (1982) examination of traits associated with dioecy across the families of angiosperms; and Armstrong's (1983) regressions of brain weight on body weight and basal metabolism rate in mammals. My intention is to point out a serious statistical problem with this approach, a problem that affects all of these studies. It arises from the fact that species are part of a hierarchically structured phylogeny, and thus cannot be regarded for statistical purposes as if drawn independently from the same distribution. This problem has been noticed before, and previous suggestions of ways of coping with it are briefly discussed. The nonindependence can be circumvented in principle if adequate information on the phylogeny is available. The information needed to do so and the limitations on its use will be discussed. The problem will be discussed and illustrated with reference to continuous variables, but the same statistical issues arise when one or both of the variables are discrete, in which case the statistical methods involve contingency tables rather than regressions and correlations.

/pdf/phylogenies-and-the-comparative-method-25unxl0l1q.pdf

Phylogenies and the Comparative Method

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The Genetic Basis of Evolutionary Change

Felsenstein, J. (Department of Genetics, University of Washington, Seattle, WA 98195) 1978. Cases in which parsimony or compatibility methods will be positively misleading. Syst. Zool. 27:401-410.-For some simple threeand four-species cases involving a character with two states, it is determined under what conditions several methods of phylogenetic inference will fail to converge to the true phylogeny as mo,re and more data are accumulated. The methods are the Camin-Sokal parsimony method, the compatibility method, and Farris's unrooted Wagner tree parsimony method. In all cases the conditions for this failure (which is the failure to be statistically consistent) are essentially that parallel changes exceed informative, nonparallel changes. It is possible for these methods to be inconsistent even when change is improbable a priori, provided that evolutionary rates in different lineages are sufficiently unequal. It is by extension of this approach that we may provide a sound methodology for evaluating methods of phylogenetic inference. [Numerical cladistics; phylogenetic inference; maximum likelihood estimation; parsimony; compatibility.] Parsimony or minimum evolution methods were first introduced into phylogenetic inference by Camin and Sokal (1965). This class of methods for inferring an evolutionary tree from discrete-character data involves making a reconstruction of the changes in a given set of characters on a given tree, counting the smallest number of times that a given kind of event need have happened, and using this as the measure of the adequacy of the evolutionary tree. (Alternatively, one can compute the weighted sum of the numbers of times several different kinds of events have occurred.) One attempts to find that evolutionary tree which requires the fewest of these evolutionary events to explain the observed data. Camin and Sokal treated the case of irreversible changes along a character state tree, minimizing the number of changes I This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Department of Energy, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privatelyowned rights. of character states required. A number of other parsimony methods have since appeared in the systematic literature (Kluge and Farris, 1969; Farris, 1969, 1970, 1972, 1977; Farris, Kluge, and Eckhardt, 1970) and parsimony methods have also found widespread use in studies of molecular evolution (Fitch and Margoliash, 1967, 1970; Dayhoff and Eck, 1968; see also Fitch, 1973). Cavalli-Sforza and Edwards (1967; Edwards and Cavalli-Sforza, 1964) earlier formulated a minimum evolution method for continuous-character data. An alternative methodology for phylogenetic inference is the compatibility method, introduced by Le Quesne (1969, 1972). He suggested that phylogenetic inference be based on finding the largest possible set of characters -which could simultaneously have all states be uniquely derived -on the same ftree. The estimate of the phylogeny is then takento be that tree.-While Le Quesne's specific suggestions as to how this might be done have been criticized by Farris (1969), his general approach, which is based on Camin and Sokal's (1965) concept of the compatibility of two characters, has been made rigorous and extended in a series of papers by G. F. Estabrook, C. S. Johnson, Jr., and F. R. McMorris (Estabrook,

https://www.jstor.org/stable/pdfplus/2412923.pdf

Joseph Felsenstein

Papers

Confidence limits on phylogenies: an approach using the bootstrap.

Evolutionary trees from DNA sequences: A maximum likelihood approach

Phylogenies and the Comparative Method

The Genetic Basis of Evolutionary Change

Cases in which Parsimony or Compatibility Methods will be Positively Misleading