RAxML-III: a fast program for maximum likelihood-based inference of large phylogenetic trees

MOTIVATION: The computation of large phylogenetic trees with statistical models such as maximum likelihood or bayesian inference is computationally extremely intensive. It has repeatedly been demonstrated that these models are able to recover the true tree or a tree which is topologically closer to the true tree more frequently than less elaborate methods such as parsimony or neighbor joining. Due to the combinatorial and computational complexity the size of trees which can be computed on a Biologist's PC workstation within reasonable time is limited to trees containing approximately 100 taxa. RESULTS: In this paper we present the latest release of our program RAxML-III for rapid maximum likelihood-based inference of large evolutionary trees which allows for computation of 1.000-taxon trees in less than 24 hours on a single PC processor. We compare RAxML-III to the currently fastest implementations for maximum likelihood and bayesian inference: PHYML and MrBayes. Whereas RAxML-III performs worse than PHYML and MrBayes on synthetic data it clearly outperforms both programs on all real data alignments used in terms of speed and final likelihood values. Availability SUPPLEMENTARY INFORMATION: RAxML-III including all alignments and final trees mentioned in this paper is freely available as open source code at http://wwwbode.cs.tum/~stamatak CONTACT: stamatak@cs.tum.edu.     

Accurate reconstruction of insertion-deletion histories by statistical phylogenetics

The Multiple Sequence Alignment (MSA) is a computational abstraction that represents a partial summary either of indel history, or of structural similarity. Taking the former view (indel history), it is possible to use formal automata theory to generalize the phylogenetic likelihood framework for finite substitution models (Dayhoff's probability matrices and Felsenstein's pruning algorithm) to arbitrary-length sequences. In this paper, we report results of a simulation-based benchmark of several methods for reconstruction of indel history. The methods tested include a relatively new algorithm for statistical marginalization of MSAs that sums over a stochastically-sampled ensemble of the most probable evolutionary histories. For mammalian evolutionary parameters on several different trees, the single most likely history sampled by our algorithm appears less biased than histories reconstructed by other MSA methods. The algorithm can also be used for alignment-free inference, where the MSA is explicitly summed out of the analysis. As an illustration of our method, we discuss reconstruction of the evolutionary histories of human protein-coding genes.     

Phylogeny reconstruction: increasing the accuracy of pairwise distance estimation using Bayesian inference of evolutionary rates

Distance-based methods for phylogeny reconstruction are the fastest and easiest to use, and their popularity is accordingly high. They are also the only known methods that can cope with huge datasets of thousands of sequences. These methods rely on evolutionary distance estimation and are sensitive to errors in such estimations. In this study, a novel Bayesian method for estimation of evolutionary distances is developed. The proposed method enables the use of a sophisticated evolutionary model that better accounts for among-site rate variation (ASRV), thereby improving the accuracy of distance estimation. Rate variations are estimated within a Bayesian framework by extracting information from the entire dataset of sequences, unlike standard methods that can only use one pair of sequences at a time. We compare the accuracy of a cascade of distance estimation methods, starting from commonly used methods and moving towards the more sophisticated novel method. Simulation studies show significant improvements in the accuracy of distance estimation by the novel method over the commonly used ones. We demonstrate the effect of the improved accuracy on tree reconstruction using both real and simulated protein sequence alignments. An implementation of this method is available as part of the SEMPHY package.     

Reconstructing evolution of sequences subject to recombination using parsimony

The parsimony principle states that a history of a set of sequences that minimizes the amount of evolution is a good approximation to the real evolutionary history of the sequences. This principle is applied to the reconstruction of the evolution of homologous sequences where recombinations or horizontal transfer can occur. First it is demonstrated that the appropriate structure to represent the evolution of sequences with recombinations is a family of trees each describing the evolution of a segment of the sequence. Two trees for neighboring segments will differ by exactly the transfer of a subtree within the whole tree. This leads to a metric between trees based on the smallest number of such operations needed to convert one tree into the other. An algorithm is presented that calculates this metric. This metric is used to formulate a dynamic programming algorithm that finds the most parsimonious history that fits a given set of sequences. The algorithm is potentially very practical, since many groups of sequences defy analysis by methods that ignore recombinations. These methods give ambiguous or contradictory results because the sequence history cannot be described by one phylogeny, but only a family of phylogenies that each describe the history of a segment of the sequences. The generalization of the algorithm to reconstruct gene conversions and the possibility for heuristic versions of the algorithm for larger data sets are discussed.     

Evolution of RNA-dependent RNA-polymerases from positive RNA viruses: comparison of phylogenetic trees constructed by different methods

Presumptive phylogenetic trees of evolutionary conserved fragments of RNA-dependent RNA polymerases of 26 positive strand RNA viruses were generated using a simple clustering procedure or a novel approach based on the so-called maximal topologic similarity principle. The latter methodology involves a quantitative measure of the degree of correspondence between the topology of generated trees and structure of the initial distance matrix. The algorithm for tree construction based on the maximal topologic similarity principle does not include the assumption of evolutionary rate constancy, as opposed to the clustering procedure. Nevertheless, it is demonstrated that the trees generated by the two methods are topologically similar, indicating that no drastic change of evolutionary rate had occurred in evolution of the positive strand RNA virus RNA polymerases. This in turn suggests that RNA-dependent RNA polymerases (or at least their evolutionary conserved core domains used for construction of the phylogenetic trees) are principally functionally equivalent in all positive strand RNA viruses.     

Fast recovery of evolutionary trees with thousands of nodes.

We present a novel distance-based algorithm for evolutionary tree reconstruction. Our algorithm reconstructs the topology of a tree with n leaves in O(n(2)) time using O(n) working space. In the general Markov model of evolution, the algorithm recovers the topology successfully with (1 - o(1)) probability from sequences with polynomial length in n. Moreover, for almost all trees, our algorithm achieves the same success probability on polylogarithmic sample sizes. The theoretical results are supported by simulation experiments involving trees with 500, 1,895, and 3,135 leaves. The topologies of the trees are recovered with high success from 2,000 bp DNA sequences.     

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

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/.     

Identifiability and inference of non-parametric rates-across-sites models on large-scale phylogenies

Mutation rate variation across loci is well known to cause difficulties, notably identifiability issues, in the reconstruction of evolutionary trees from molecular sequences. Here we introduce a new approach for estimating general rates-across-sites models. Our results imply, in particular, that large phylogenies are typically identifiable under rate variation. We also derive sequence-length requirements for high-probability reconstruction. Our main contribution is a novel algorithm that clusters sites according to their mutation rate. Following this site clustering step, standard reconstruction techniques can be used to recover the phylogeny. Our results rely on a basic insight: that, for large trees, certain site statistics experience concentration-of-measure phenomena.     

A principle of maximum topological similarity in molecular systematics

The paper deals with the problem of phylogenetic reconstruction on the basis of comparative analysis of features. Main attention is paid to comparison and classification of the biopolymer sequences. Different approaches to this task are critically reviewed. The novel principle of construction of tree-like classification schemes permitting subsequent evolutionary analysis is proposed. It concentrates on reconstruction of the tree with a topologic structure that is most close to topologic features, imprinted in the source distance matrix. Realization of this approach was made possible by development of the special formalism, enabling evaluation and comparison of topologic features of distance matrices and trees.     

Scelestial: Fast and accurate single-cell lineage tree inference based on a Steiner tree approximation algorithm

Single-cell genome sequencing provides a highly granular view of biological systems but is affected by high error rates, allelic amplification bias, and uneven genome coverage. This creates a need for data-specific computational methods, for purposes such as for cell lineage tree inference. The objective of cell lineage tree reconstruction is to infer the evolutionary process that generated a set of observed cell genomes. Lineage trees may enable a better understanding of tumor formation and growth, as well as of organ development for healthy body cells. We describe a method, Scelestial, for lineage tree reconstruction from single-cell data, which is based on an approximation algorithm for the Steiner tree problem and is a generalization of the neighbor-joining method. We adapt the algorithm to efficiently select a limited subset of potential sequences as internal nodes, in the presence of missing values, and to minimize cost by lineage tree-based missing value imputation. In a comparison against seven state-of-the-art single-cell lineage tree reconstruction algorithms—BitPhylogeny, OncoNEM, SCITE, SiFit, SASC, SCIPhI, and SiCloneFit—on simulated and real single-cell tumor samples, Scelestial performed best at reconstructing trees in terms of accuracy and run time. Scelestial has been implemented in C++. It is also available as an R package named RScelestial.     

GeneTRACE-reconstruction of gene content of ancestral species

While current computational methods allow the reconstruction of individual ancestral protein sequences, reconstruction of complete gene content of ancestral species is not yet an established task. In this paper, we describe GENETRACE, an efficient linear-time algorithm that allows the reconstruction of evolutionary history of individual protein families as well as the complete gene content of ancestral species. The performance of the method was validated with a simulated evolution program called SimulEv. Our results indicate that given a set of correct phylogenetic profiles and a correct species tree, ancestral gene content can be reconstructed with sensitivity and selectivity of more than 90%. SimulEv simulations were also used to evaluate performance of the reconstruction of gene content-based phylogenetic trees, suggesting that these trees may be accurate at the terminal branches but suffer from long branch attraction near the root of the tree.     

A signal-to-noise analysis of phylogeny estimation by neighbor-joining: Insufficiency of polynomial length sequences

Phylogeny reconstruction is the process of inferring evolutionary relationships from molecular sequences, and methods that are expected to accurately reconstruct trees from sequences of reasonable length are highly desirable. To formalize this concept, the property of fast-convergence has been introduced to describe phylogeny reconstruction methods that, with high probability, recover the true tree from sequences that grow polynomially in the number of taxa n. While provably fast-converging methods have been developed, the neighbor-joining (NJ) algorithm of Saitou and Nei remains one of the most popular methods used in practice. This algorithm is known to converge for sequences that are exponential in n, but no lower bound for its convergence rate has been established. To address this theoretical question, we analyze the performance of the NJ algorithm on a type of phylogeny known as a 'caterpillar tree'. We find that, for sequences of polynomial length in the number of taxa n, the variability of the NJ criterion is sufficiently high that the algorithm is likely to fail even in the first step of the phylogeny reconstruction process, regardless of the degree of polynomial considered. This result demonstrates that, for general n-taxa trees, the exponential bound cannot be improved.     

RAxML-VI-HPC: maximum likelihood-based phylogenetic analyses with thousands of taxa and mixed models

RAxML-VI-HPC (randomized axelerated maximum likelihood for high performance computing) is a sequential and parallel program for inference of large phylogenies with maximum likelihood (ML). Low-level technical optimizations, a modification of the search algorithm, and the use of the GTR+CAT approximation as replacement for GTR+Gamma yield a program that is between 2.7 and 52 times faster than the previous version of RAxML. A large-scale performance comparison with GARLI, PHYML, IQPNNI and MrBayes on real data containing 1000 up to 6722 taxa shows that RAxML requires at least 5.6 times less main memory and yields better trees in similar times than the best competing program (GARLI) on datasets up to 2500 taxa. On datasets > or =4000 taxa it also runs 2-3 times faster than GARLI. RAxML has been parallelized with MPI to conduct parallel multiple bootstraps and inferences on distinct starting trees. The program has been used to compute ML trees on two of the largest alignments to date containing 25,057 (1463 bp) and 2182 (51,089 bp) taxa, respectively. AVAILABILITY: icwww.epfl.ch/~stamatak     

Approximate likelihood-ratio test for branches: A fast, accurate, and powerful alternative

We revisit statistical tests for branches of evolutionary trees reconstructed upon molecular data. A new, fast, approximate likelihood-ratio test (aLRT) for branches is presented here as a competitive alternative to nonparametric bootstrap and Bayesian estimation of branch support. The aLRT is based on the idea of the conventional LRT, with the null hypothesis corresponding to the assumption that the inferred branch has length 0. We show that the LRT statistic is asymptotically distributed as a maximum of three random variables drawn from the chi(0)2 + chi(1)2 distribution. The new aLRT of interior branch uses this distribution for significance testing, but the test statistic is approximated in a slightly conservative but practical way as 2(l1- l2), i.e., double the difference between the maximum log-likelihood values corresponding to the best tree and the second best topological arrangement around the branch of interest. Such a test is fast because the log-likelihood value l2 is computed by optimizing only over the branch of interest and the four adjacent branches, whereas other parameters are fixed at their optimal values corresponding to the best ML tree. The performance of the new test was studied on simulated 4-, 12-, and 100-taxon data sets with sequences of different lengths. The aLRT is shown to be accurate, powerful, and robust to certain violations of model assumptions. The aLRT is implemented within the algorithm used by the recent fast maximum likelihood tree estimation program PHYML (Guindon and Gascuel, 2003).     

Phylogenomic networks

Phylogenomics is aimed at studying functional and evolutionary aspects of genome biology using phylogenetic analysis of whole genomes. Current approaches to genome phylogenies are commonly founded in terms of phylogenetic trees. However, several evolutionary processes are non tree-like in nature, including recombination and lateral gene transfer (LGT). Phylogenomic networks are a special type of phylogenetic network reconstructed from fully sequenced genomes. The network model, comprising genomes connected by pairwise evolutionary relations, enables the reconstruction of both vertical and LGT events. Modeling genome evolution in the form of a network enables the use of an extensive toolbox developed for network research. The structural properties of phylogenomic networks open up fundamentally new insights into genome evolution.     

The morphofunctional approach in paleontology

The principle of actualism is regarded as the major principle in morphofunctional studies of fossil organisms, which is based on comparisons of evolutionary series of both extinct and extant taxa. The objects and specificity of morphofunctional studies in paleontology are discussed. The revelation of relationships between morphological and functional archetypes are considered to be the major task of these studies. The ecosystem approach, constrains on actualistic reconstruction imposed by various morphofunctional modi, hierarchy of functions at different levels of structural organization and at different phylogenetic stages are considered. It is shown that parallel development and the mosaic pattern of characters are accounted for by general morphogenetic mechanisms and heterochronies.     

Calculating the evolutionary rates of different genes: a fast, accurate estimator with applications to maximum likelihood phylogenetic analysis

In phylogenetic analyses with combined multigene or multiprotein data sets, accounting for differing evolutionary dynamics at different loci is essential for accurate tree prediction. Existing maximum likelihood (ML) and Bayesian approaches are computationally intensive. We present an alternative approach that is orders of magnitude faster. The method, Distance Rates (DistR), estimates rates based upon distances derived from gene/protein sequence data. Simulation studies indicate that this technique is accurate compared with other methods and robust to missing sequence data. The DistR method was applied to a fungal mitochondrial data set, and the rate estimates compared well to those obtained using existing ML and Bayesian approaches. Inclusion of the protein rates estimated from the DistR method into the ML calculation of trees as a branch length multiplier resulted in a significantly improved fit as measured by the Akaike Information Criterion (AIC). Furthermore, bootstrap support for the ML topology was significantly greater when protein rates were used, and some evident errors in the concatenated ML tree topology (i.e., without protein rates) were corrected. [Bayesian credible intervals; DistR method; multigene phylogeny; PHYML; rate heterogeneity.].     

The roots of phylogeny: how did Haeckel build his trees?

Haeckel created much of our current vocabulary in evolutionary biology, such as the term phylogeny, which is currently used to designate trees. Assuming that Haeckel gave the same meaning to this term, one often reproduces Haeckel's trees as the first illustrations of phylogenetic trees. A detailed analysis of Haeckel's own evolutionary vocabulary and theory revealed that Haeckel's trees were genealogical trees and that Haeckel's phylogeny was a morphological concept. However, phylogeny was actually the core of Haeckel's tree reconstruction, and understanding the exact meaning Haeckel gave to phylogeny is crucial to understanding the information Haeckel wanted to convey in his famous trees. Haeckel's phylogeny was a linear series of main morphological stages along the line of descent of a given species. The phylogeny of a single species would provide a trunk around which lateral branches were added as mere ornament; the phylogeny selected for drawing a tree of a given group was considered the most complete line of progress from lower to higher forms of this group, such as the phylogeny of Man for the genealogical tree of Vertebrates. Haeckel's phylogeny was mainly inspired by the idea of the scala naturae, or scale of being. Therefore, Haeckel's genealogical trees, which were only branched on the surface, mainly represented the old idea of scale of being. Even though Haeckel decided to draw genealogical trees after reading On the Origin of Species and was called the German Darwin, he did not draw Darwinian branching diagrams. Although Haeckel always saw Lamarck, Goethe, and Darwin as the three fathers of the theory of evolution, he was mainly influenced by Lamarck and Goethe in his approach to tree reconstruction.     

Quartet-based phylogenetic inference: improvements and limits

We analyze the performance of quartet methods in phylogenetic reconstruction. These methods first compute four-taxon trees (4-trees) and then use a combinatorial algorithm to infer a phylogeny that respects the inferred 4-trees as much as possible. Quartet puzzling (QP) is one of the few methods able to take weighting of the 4-trees, which is inferred by maximum likelihood, into account. QP seems to be widely used. We present weight optimization (WO), a new algorithm which is also based on weighted 4-trees. WO is faster and offers better theoretical guarantees than QP. Moreover, computer simulations indicate that the topological accuracy of WO is less dependent on the shape of the correct tree. However, although the performance of WO is better overall than that of QP, it is still less efficient than traditional phylogenetic reconstruction approaches based on pairwise evolutionary distances or maximum likelihood. This is likely related to long-branch attraction, a phenomenon to which quartet methods are very sensitive, and to inappropriate use of the initial results (weights) obtained by maximum likelihood for every quartet.     

An approach of orthology detection from homologous sequences under minimum evolution

In the field of phylogenetics and comparative genomics, it is important to establish orthologous relationships when comparing homologous sequences. Due to the slight sequence dissimilarity between orthologs and paralogs, it is prone to regarding paralogs as orthologs. For this reason, several methods based on evolutionary distance, phylogeny and BLAST have tried to detect orthologs with more precision. Depending on their algorithmic implementations, each of these methods sometimes has increased false negative or false positive rates. Here, we developed a novel algorithm for orthology detection that uses a distance method based on the phylogenetic criterion of minimum evolution. Our algorithm assumes that sets of sequences exhibiting orthologous relationships are evolutionarily less costly than sets that include one or more paralogous relationships. Calculation of evolutionary cost requires the reconstruction of a neighbor-joining (NJ) tree, but calculations are unaffected by the topology of any given NJ tree. Unlike tree reconciliation, our algorithm appears free from the problem of incorrect topologies of species and gene trees. The reliability of the algorithm was tested in a comparative analysis with two other orthology detection methods using 95 manually curated KOG datasets and 21 experimentally verified EXProt datasets. Sensitivity and specificity estimates indicate that the concept of minimum evolution could be valuable for the detection of orthologs.