PAML 4: phylogenetic analysis by maximum likelihood

PAML, currently in version 4, is a package of programs for phylogeneticanalyses of DNA and protein sequences using maximum likelihood(ML). The programs may be used to compare and test phylogenetictrees, but their main strengths lie in the rich repertoire ofevolutionary models implemented, which can be used to estimateparameters in models of sequence evolution and to test interestingbiological hypotheses. Uses of the programs include estimationof synonymous and nonsynonymous rates (d_N and d_S) between twoprotein-coding DNA sequences, inference of positive Darwinianselection through phylogenetic comparison of protein-codinggenes, reconstruction of ancestral genes and proteins for molecularrestoration studies of extinct life forms, combined analysisof heterogeneous data sets from multiple gene loci, and estimationof species divergence times incorporating uncertainties in fossilcalibrations. This note discusses some of the major applicationsof the package, which includes example data sets to demonstratetheir use. The package is written in ANSI C, and runs underWindows, Mac OSX, and UNIX systems. It is available at http://abacus.gene.ucl.ac.uk/software/paml.html.     

An approximate maximum likelihood approach, applied to phylogenetic trees.

A novel type of approximation scheme to the maximum likelihood (ML) approach is presented and discussed in the context of phylogenetic tree reconstruction from aligned DNA sequences. It is based on a parameterized approximation to the conditional distribution of hidden variables (related, e.g., to the sequences of unobserved branch point ancestors) given the observed data. A modified likelihood, based on the extended data, is then maximized with respect to the parameters of the model as well as to those involved in the approximation. With a suitable form of the approximation, the proposed method allows for simpler updating of the parameters, at the cost of an increased parameter count and a slight decrease in performance. The method is tested on phylogenetic tree reconstruction from artificially generated sequences, and its performance is compared to that of ML, showing that the approach is competitive for reasonably similar sequences. The method is also applied to real DNA sequences from primates, yielding a result consistent with those obtained by other standard algorithms.     

TREE-PUZZLE: maximum likelihood phylogenetic analysis using quartets and parallel computing

SUMMARY: TREE-PUZZLE is a program package for quartet-based maximum-likelihood phylogenetic analysis (formerly PUZZLE, Strimmer and von Haeseler, Mol. Biol. Evol., 13, 964-969, 1996) that provides methods for reconstruction, comparison, and testing of trees and models on DNA as well as protein sequences. To reduce waiting time for larger datasets the tree reconstruction part of the software has been parallelized using message passing that runs on clusters of workstations as well as parallel computers. AVAILABILITY: http://www.tree-puzzle.de. The program is written in ANSI C. TREE-PUZZLE can be run on UNIX, Windows and Mac systems, including Mac OS X. To run the parallel version of PUZZLE, a Message Passing Interface (MPI) library has to be installed on the system. Free MPI implementations are available on the Web (cf. http://www.lam-mpi.org/mpi/implementations/).     

Efficiencies of maximum likelihood methods of phylogenetic inferences when different substitution models are used

Choice of a substitution model is a crucial step in the maximum likelihood (ML) method of phylogenetic inference, and investigators tend to prefer complex mathematical models to simple ones. However, when complex models with many parameters are used, the extent of noise in statistical inferences increases, and thus complex models may not produce the true topology with a higher probability than simple ones. This problem was studied using computer simulation. When the number of nucleotides used was relatively large (1000 bp), the HKY+Gamma model showed smaller d(T) topological distance between the inferred and the true trees) than the JC and Kimura models. In the cases of shorter sequences (300 bp) simpler model and search algorithm such as JC model and SA+NNI search were found to be as efficient as more complicated searches and models in terms of topological distances, although the topologies obtained under HKY+Gamma model had the highest likelihood values. The performance of relatively simple search algorithm SA+NNI was found to be essentially the same as that of more extensive SA+TBR search under all models studied. Similarly to the conclusions reached by Takahashi and Nei [Mol. Biol. Evol. 17 (2000) 1251], our results indicate that simple models can be as efficient as complex models, and that use of complex models does not necessarily give more reliable trees compared with simple models.     

fastDNAml: a tool for construction of phylogenetic trees of DNA sequences using maximum likelihood

We have developed a new tool, called fastDNAml, for constructingphylogenetic trees from DNA sequences. The program can be runon a wide variety of computers ranging from Unix workstationsto massively parallel systems, and is available from the RibosomalDatabase Project (RDP) by anonymous FTP. Our program uses amaximum likelihood approach and is based on version 3.3 of Felsenstein'sdnaml program. Several enhancements, including algorithmic changes,significantly improve performance and reduce memory usage, makingit feasible to construct even very large trees. Trees containing40–100 taxa have been easily generated, and phylogeneticestimates are possible even when hundreds of sequences exist.We are currently using the tool to construct a phylogenetictree based on 473 small subunit rRNA sequences from prokaryotes.     

Upper bounds on maximum likelihood for phylogenetic trees

We introduce a mechanism for analytically deriving upper bounds on the maximum likelihood for genetic sequence data on sets of phylogenies. A simple 'partition' bound is introduced for general models. Tighter bounds are developed for the simplest model of evolution, the two state symmetric model of nucleotide substitution under the molecular clock. This follows earlier theoretical work which has been restricted to this model by analytic complexity. A weakness of current numerical computation is that reported 'maximum likelihood' results cannot be guaranteed, both for a specified tree (because of the possibility of multiple maxima) or over the full tree space (as the computation is intractable for large sets of trees). The bounds we develop here can be used to conclusively eliminate large proportions of tree space in the search for the maximum likelihood tree. This is vital in the development of a branch and bound search strategy for identifying the maximum likelihood tree. We report the results from a simulation study of approximately 10(6) data sets generated on clock-like trees of five leaves. In each trial a likelihood value of one specific instance of a parameterised tree is compared to the bound determined for each of the 105 possible rooted binary trees. The proportion of trees that are eliminated from the search for the maximum likelihood tree ranged from 92% to almost 98%, indicating a computational speed-up factor of between 12 and 44.     

Improving the efficiency of SPR moves in phylogenetic tree search methods based on maximum likelihood

MOTIVATION: Maximum likelihood (ML) methods have become very popular for constructing phylogenetic trees from sequence data. However, despite noticeable recent progress, with large and difficult datasets (e.g. multiple genes with conflicting signals) current ML programs still require huge computing time and can become trapped in bad local optima of the likelihood function. When this occurs, the resulting trees may still show some of the defects (e.g. long branch attraction) of starting trees obtained using fast distance or parsimony programs. METHODS: Subtree pruning and regrafting (SPR) topological rearrangements are usually sufficient to intensively search the tree space. Here, we propose two new methods to make SPR moves more efficient. The first method uses a fast distance-based approach to detect the least promising candidate SPR moves, which are then simply discarded. The second method locally estimates the change in likelihood for any remaining potential SPRs, as opposed to globally evaluating the entire tree for each possible move. These two methods are implemented in a new algorithm with a sophisticated filtering strategy, which efficiently selects potential SPRs and concentrates most of the likelihood computation on the promising moves. RESULTS: Experiments with real datasets comprising 35-250 taxa show that, while indeed greatly reducing the amount of computation, our approach provides likelihood values at least as good as those of the best-known ML methods so far and is very robust to poor starting trees. Furthermore, combining our new SPR algorithm with local moves such as PHYML's nearest neighbor interchanges, the time needed to find good solutions can sometimes be reduced even more.     

A short proof that phylogenetic tree reconstruction by maximum likelihood is hard

Maximum likelihood is one of the most widely used techniques to infer evolutionary histories. Although it is thought to be intractable, a proof of its hardness has been lacking. Here, we give a short proof that computing the maximum likelihood tree is NP-hard by exploiting a connection between likelihood and parsimony observed by Tuffley and Steel.     

The robustness of two phylogenetic methods: four-taxon simulations reveal a slight superiority of maximum likelihood over neighbor joining

The robustness (sensitivity to violation of assumptions) of the maximum- likelihood and neighbor-joining methods was examined using simulation. Maximum likelihood and neighbor joining were implemented with Jukes- Cantor, Kimura, and gamma models of DNA substitution. Simulations were performed in which the assumptions of the methods were violated to varying degrees on three model four-taxon trees. The performance of the methods was evaluated with respect to ability to correctly estimate the unrooted four-taxon tree. Maximum likelihood outperformed neighbor joining in 29 of the 36 cases in which the assumptions of both methods were satisfied. In 133 of 180 of the simulations in which the assumptions of the maximum-likelihood and neighbor-joining methods were violated, maximum likelihood outperformed neighbor joining. These results are consistent with a general superiority of maximum likelihood over neighbor joining under comparable conditions. They extend and clarify an earlier study that found an advantage for neighbor joining over maximum likelihood for gamma-distributed mutation rates.      

Stochastic search strategy for estimation of maximum likelihood phylogenetic trees

The maximum likelihood (ML) method of phylogenetic tree construction is not as widely used as other tree construction methods (e.g., parsimony, neighbor-joining) because of the prohibitive amount of time required to find the ML tree when the number of sequences under consideration is large. To overcome this difficulty, we propose a stochastic search strategy for estimation of the ML tree that is based on a simulated annealing algorithm. The algorithm works by moving through tree space by way of a "local rearrangement" strategy so that topologies that improve the likelihood are always accepted, whereas those that decrease the likelihood are accepted with a probability that is related to the proportionate decrease in likelihood. Besides greatly reducing the time required to estimate the ML tree, the stochastic search strategy is less likely to become trapped in local optima than are existing algorithms for ML tree estimation. We demonstrate the success of the modified simulated annealing algorithm by comparing it with two existing algorithms (Swofford's PAUP* and Felsenstein's DNAMLK) for several theoretical and real data examples.     

Improving estimates of genetic maps: a maximum likelihood approach

As a result of previous large, multipoint linkage studies there is a substantial amount of existing marker data. Due to the increased sample size, genetic maps estimated from these data could be more accurate than publicly available maps. However, current methods for map estimation are restricted to data sets containing pedigrees with a small number of individuals, or cannot make full use of marker data that are observed at several loci on members of large, extended pedigrees. In this article, a maximum likelihood (ML) method for map estimation that can make full use of the marker data in a large, multipoint linkage study is described. The method is applied to replicate sets of simulated marker data involving seven linked loci, and pedigree structures based on the real multipoint linkage study of Abkevich et al. (2003, American Journal of Human Genetics 73, 1271-1281). The variance of the ML estimate is accurately estimated, and tests of both simple and composite null hypotheses are performed. An efficient procedure for combining map estimates over data sets is also suggested.     

Comparison of Bayesian and maximum likelihood bootstrap measures of phylogenetic reliability

Owing to the exponential growth of genome databases, phylogenetic trees are now widely used to test a variety of evolutionary hypotheses. Nevertheless, computation time burden limits the application of methods such as maximum likelihood nonparametric bootstrap to assess reliability of evolutionary trees. As an alternative, the much faster Bayesian inference of phylogeny, which expresses branch support as posterior probabilities, has been introduced. However, marked discrepancies exist between nonparametric bootstrap proportions and Bayesian posterior probabilities, leading to difficulties in the interpretation of sometimes strongly conflicting results. As an attempt to reconcile these two indices of node reliability, we apply the nonparametric bootstrap resampling procedure to the Bayesian approach. The correlation between posterior probabilities, bootstrap maximum likelihood percentages, and bootstrapped posterior probabilities was studied for eight highly diverse empirical data sets and were also investigated using experimental simulation. Our results show that the relation between posterior probabilities and bootstrapped maximum likelihood percentages is highly variable but that very strong correlations always exist when Bayesian node support is estimated on bootstrapped character matrices. Moreover, simulations corroborate empirical observations in suggesting that, being more conservative, the bootstrap approach might be less prone to strongly supporting a false phylogenetic hypothesis. Thus, apparent conflicts in topology recovered by the Bayesian approach were reduced after bootstrapping. Both posterior probabilities and bootstrap supports are of great interest to phylogeny as potential upper and lower bounds of node reliability, but they are surely not interchangeable and cannot be directly compared.     

A maximum likelihood approach to two-dimensional crystals

Maximum likelihood (ML) processing of transmission electron microscopy images of protein particles can produce reconstructions of superior resolution due to a reduced reference bias. We have investigated a ML processing approach to images centered on the unit cells of two-dimensional (2D) crystal images. The implemented software makes use of the predictive lattice node tracking in the MRC software, which is used to window particle stacks. These are then noise-whitened and subjected to ML processing. Resulting ML maps are translated into amplitudes and phases for further processing within the 2dx software package. Compared with ML processing for randomly oriented single particles, the required computational costs are greatly reduced as the 2D crystals restrict the parameter search space. The software was applied to images of negatively stained or frozen hydrated 2D crystals of different crystal order. We find that the ML algorithm is not free from reference bias, even though its sensitivity to noise correlation is lower than for pure cross-correlation alignment. Compared with crystallographic processing, the newly developed software yields better resolution for 2D crystal images of lower crystal quality, and it performs equally well for well-ordered crystal images.     

A maximum likelihood approach to non-linear ordination

Summary A non-linear method of ordinating vegetation samples based on the fitting of bell-shaped response curves is lescribed. For each species two Gaussian curves were itted, one to quantitative values, where the species was present, the other to probabilities of absence. A maximum likelihood approach was then used to obtain a best approximation of the positions of the samples along a one-dimensional gradient. By an iterative process successively better approximations were obtained.The method was successful in recovering gradients based on hypothetical data. With two sets of real data the gradient produced was more ecologically satisfying and far less distorted than that revealed by principal component analysis.     

Indel information eliminates trivial sequence alignment in maximum likelihood phylogenetic analysis

Although there has been a recent proliferation in maximum‐likelihood (ML)‐based tree estimation methods based on a fixed sequence alignment (MSA), little research has been done on incorporating indel information in this traditional framework. We show, using a simple model on a single character example, that a trivial alignment of a different form than that previously identified for parsimony is optimal in ML under standard assumptions treating indels as “missing” data, but that it is not optimal when indels are incorporated into the character alphabet. We show that the optimality of the trivial alignment is not an artefact of simplified theory assumptions by demonstrating that trivial alignment likelihoods of five different multiple sequence alignment datasets exhibit this phenomenon. These results demonstrate the need for use of indel information in likelihood analysis on fixed MSAs, and suggest that caution must be exercised when drawing conclusions from software implementations claiming improvements in likelihood scores under an indels‐as‐missing assumption. © The Willi Hennig Society 2012.     

Spatially explicit maximum likelihood methods for capture-recapture studies

Live-trapping capture-recapture studies of animal populations with fixed trap locations inevitably have a spatial component: animals close to traps are more likely to be caught than those far away. This is not addressed in conventional closed-population estimates of abundance and without the spatial component, rigorous estimates of density cannot be obtained. We propose new, flexible capture-recapture models that use the capture locations to estimate animal locations and spatially referenced capture probability. The models are likelihood-based and hence allow use of Akaike's information criterion or other likelihood-based methods of model selection. Density is an explicit parameter, and the evaluation of its dependence on spatial or temporal covariates is therefore straightforward. Additional (nonspatial) variation in capture probability may be modeled as in conventional capture-recapture. The method is tested by simulation, using a model in which capture probability depends only on location relative to traps. Point estimators are found to be unbiased and standard error estimators almost unbiased. The method is used to estimate the density of Red-eyed Vireos (Vireo olivaceus) from mist-netting data from the Patuxent Research Refuge, Maryland, U.S.A. Estimates agree well with those from an existing spatially explicit method based on inverse prediction. A variety of additional spatially explicit models are fitted; these include models with temporal stratification, behavioral response, and heterogeneous animal home ranges.     

MEGA5: molecular evolutionary genetics analysis using maximum likelihood, evolutionary distance, and maximum parsimony methods

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.     

A maximum likelihood approach to the detection of selection from a phylogeny

Summary A large amount of information is contained within the phylogentic relationships between species. In addition to their branching patterns it is also possible to examine other aspects of the biology of the species. The influence that deleterious selection might have is determined here. The likelihood of different phylogenies in the presence of selection is explored to determine the properties of such a likelihood surface. The calculation of likelihoods for a phylogeny in the presence and absence of selection, permits the application of a likelihood ratio test to search for selection. It is shown that even a single selected site can have a strong effect on the likelihood. The method is illustrated with an example fromDrosophila melanogaster and suggests that delerious selection may be acting on transposable elements.     

Flexible maximum likelihood methods for bivariate proportional hazards models

This article presents methodology for multivariate proportional hazards (PH) regression models. The methods employ flexible piecewise constant or spline specifications for baseline hazard functions in either marginal or conditional PH models, along with assumptions about the association among lifetimes. Because the models are parametric, ordinary maximum likelihood can be applied; it is able to deal easily with such data features as interval censoring or sequentially observed lifetimes, unlike existing semiparametric methods. A bivariate Clayton model (1978, Biometrika 65, 141-151) is used to illustrate the approach taken. Because a parametric assumption about association is made, efficiency and robustness comparisons are made between estimation based on the bivariate Clayton model and "working independence" methods that specify only marginal distributions for each lifetime variable.