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.

Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

The Theory of Island Biogeography

Evolution of Protein Molecules

Methods for analysing fish stomach contents are listed and critically assessed with a view to their suitability for determining dietary importance—this term is defined. Difficulties in the application of these methods are discussed and, where appropriate, alternative approaches proposed. Modifications which have practical value are also considered. The necessity of linking measurements of dietary importance to stomach capacity is emphasized and the effects of differential digestion upon interpretation of stomach contents outlined. The best measure of dietary importance is proposed as one where both the amount and bulk of a food category are recorded.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1095-8649.1980.tb02775.x

Stomach contents analysis—a review of methods and their application

Phylogenetic trees have a multitude of applications in biology, epidemiology, conservation and even forensics. However, the inference of phylogenetic trees can be extremely computationally intensive. The computational burden of such analyses becomes even greater when model-based methods are used. Model-based methods have been repeatedly shown to be the most accurate choice for the reconstruction of phylogenetic trees, and thus are an attractive choice despite their high computational demands. Using the Maximum Likelihood (ML) criterion to choose among phylogenetic trees is one commonly used model-based technique. Until recently, software for performing ML analyses of biological sequence data was largely intractable for more vi than about one hundred sequences. Because advances in sequencing technology now make the assembly of datasets consisting of thousands of sequences common, ML search algorithms that are able to quickly and accurately analyze such data must be developed if ML techniques are to remain a viable option in the future. I have developed a fast and accurate algorithm that allows ML phylogenetic searches to be performed on datasets consisting of thousands of sequences. My software uses a genetic algorithm approach, and is named GARLI (Genetic Algorithm for Rapid Likelihood Inference). The speed of this new algorithm results primarily from its novel technique for partial optimization of branch-length parameters following topological rearrangements. Experiments performed with GARLI show that it is able to analyze large datasets in a small fraction of the time required by the previous generation of search algorithms. The program also performs well relative to two other recently introduced fast ML search programs. Large parallel computer clusters have become common at academic institutions in recent years, presenting a new resource to be used for phylogenetic analyses. The P-GARLI algorithm extends the approach of GARLI to allow simultaneous use of many computer processors. The processors may be instructed to work together on a phylogenetic search in either a highly coordinated or largely independent fashion.

Genetic algorithm approaches for the phylogenetic analysis of large biological sequence datasets under the maximum likelihood criterion

DAVID L. SWOFFORD,1,6 PETER J. WADDELL,2 JOHN P. HUELSENBECK,3 PETER G. FOSTER,1,7 PAUL O. LEWIS,4 AND JAMES S. ROGERS5 Laboratory of Molecular Systematics, National Museum of Natural History, Smithsonian Institution Museum Support Center, 4210 Silver Hill Road, Suitland, Maryland 20746, USA; E-mail: swofford@lms.si.edu Institute of Molecular BioSciences, Massey University, Palmerston North, New Zealand; E-mail: waddell@onyx.si.edu Department of Biology, University of Rochester, Rochester, New York 14627, USA; E-mail: johnh@brahms.biology.rochester.edu Department of Ecology and Evolutionary Biology, The University of Connecticut, U-43, 75 N. Eagleville Road, Storrs, Connecticut 06269-30437 , USA; E-mail: plewis@uconnvm.uconn.edu Department of Biological Sciences, University of New Orleans, New Orleans, Louisiana 70148, USA; E-mail: jsrogers@uno.edu

/pdf/bias-in-phylogenetic-estimation-and-its-relevance-to-the-46xxm8lw2e.pdf

Bias in phylogenetic estimation and its relevance to the choice between parsimony and likelihood methods.

We have developed a rapid parsimony method for reconstructing ancestral nucleotide states that allows calculation of initial branch lengths that are good approximations to optimal maximum-likelihood estimates under several commonly used substitution models. Use of these approximate branch lengths (rather than fixed arbitrary values) as starting points significantly reduces the time required for iteration to a solution that maximizes the likelihood of a tree. These branch lengths are close enough to the optimal values that they can be used without further iteration to calculate approximate maximum-likelihood scores that are very close to the "exact" scores found by iteration. Several strategies are described for using these approximate scores to substantially reduce times needed for maximum-likelihood tree searches.

A fast method for approximating maximum likelihoods of phylogenetic trees from nucleotide sequences.

Exemples pris sur des populations de poissons des genres Hypentelium et Notropis et de dipteres Tephritidae des genres Rhagoletis, Epochara, Zonosemata et Oedicarena

Deriving Phylogenetic Trees from Allele Frequencies

Maximum likelihood estimation of phylogenetic trees from nucleotide sequences is completely consistent when nucleotide substitution is governed by the general time reversible (GTR) model with rates that vary over sites according to the invariable sites plus gamma (I + gamma) distribution.

/pdf/maximum-likelihood-estimation-of-phylogenetic-trees-is-2iqgvihat2.pdf

Maximum likelihood estimation of phylogenetic trees is consistent when substitution rates vary according to the invariable sites plus gamma distribution.

Felsenstein (1973, 1978, 1981) and other workers have advocated the method of maximum likelihood (ML) for estimating phylogenetic trees from discrete character data, particularly nucleotide sequences, in part because it is thought to be consistent, i.e., it will converge on the true tree as more and more data are accumulated. In contrast, the method of maximum parsimony is known to converge, under certain conditions, on the wrong tree as more data are added (Felsenstein, 1978). Felsenstein's (1973) argument for the consistency of the ML method was based on earlier work (Wald, 1949) that demonstrated that maximum likelihood estimation of statistical parameters, such as means, variances, etc., is consistent under a wide variety of conditions. This work also guarantees the consistency of the ML estimate of the branch lengths of a phylogenetic tree, given the correct tree topology and nucleotide substitution model. However, as pointed out by several workers (e.g., Nei, 1987:325; Saitou, 1988; Yang, 1994, 1996; Yang et al, 1995; Russo et al., 1996), these attributes do not guarantee the consistency of the ML method for estimating the tree topology. The usual ML method for estimating a tree involves finding the ML branch lengths for a given tree topology and substitution model, repeating the process for several to many other topologies, and then selecting the topology with the highest ML value as the best estimate of the true tree (Felsenstein, 1981). Yang (1994:329-330) wrote that

James S. Rogers

Papers

Bias in phylogenetic estimation and its relevance to the choice between parsimony and likelihood methods.

A fast method for approximating maximum likelihoods of phylogenetic trees from nucleotide sequences.

Deriving Phylogenetic Trees from Allele Frequencies

Maximum likelihood estimation of phylogenetic trees is consistent when substitution rates vary according to the invariable sites plus gamma distribution.

On the consistency of maximum likelihood estimation of phylogenetic trees from nucleotide sequences.