Probabilistic phylogenetic inference with insertions and deletions

A fundamental task in sequence analysis is to calculate the probability of a multiple alignment given a phylogenetic tree relating the sequences and an evolutionary model describing how sequences change over time. However, the most widely used phylogenetic models only account for residue substitution events. We describe a probabilistic model of a multiple sequence alignment that accounts for insertion and deletion events in addition to substitutions, given a phylogenetic tree, using a rate matrix augmented by the gap character. Starting from a continuous Markov process, we construct a non-reversible generative (birth-death) evolutionary model for insertions and deletions. The model assumes that insertion and deletion events occur one residue at a time. We apply this model to phylogenetic tree inference by extending the program dnaml in phylip. Using standard benchmarking methods on simulated data and a new "concordance test" benchmark on real ribosomal RNA alignments, we show that the extended program dnamlepsilon improves accuracy relative to the usual approach of ignoring gaps, while retaining the computational efficiency of the Felsenstein peeling algorithm.     

OPTIMIZATION ALIGNMENT: THE END OF MULTIPLE SEQUENCE ALIGNMENT IN PHYLOGENETICS?

Abstract— A method is described to assess directly the number of DNA sequence transformations, evolutionary events, required by a phylogenetic topology without the use of multiple sequence alignment. This is accomplished through a generalization of existing character optimization procedures to include insertion and deletion events (indels) in addition to base substitutions. The crux of the model is the treatment of indels as processes as opposed to the patterns implied by multiple sequence alignment. The results of this procedure are directly compatible with parsimony-based tree lengths. In addition to the simplicity of the method, it appears to generate more efficient (simpler) explanations of sequence variation than does multiple alignment.     

Phylogenetic inference from conserved sites alignments.

Molecular sequences provide a rich source of data for inferring the phylogenetic relationships among species. However, recent work indicates that even an accurate multiple alignment of a large sequence set may yield an incorrect phylogeny and that the quality of the phylogenetic tree improves when the input consists only of the highly conserved, motif regions of the alignment. This work introduces two methods of producing multiple alignments that include only the conserved regions of the initial alignment. The first method retains conserved motifs, whereas the second retains individual conserved sites in the initial alignment. Using parsimony analysis on a mitochondrial data set containing 19 species among which the phylogenetic relationships are widely accepted, both conserved alignment methods produce better phylogenetic trees than the complete alignment. Unlike any of the 19 inference methods used before to analyze this data, both methods produce trees that are completely consistent with the known phylogeny. The motif-based method employs far fewer alignment sites for comparable error rates. For a larger data set containing mitochondrial sequences from 39 species, the site-based method produces a phylogenetic tree that is largely consistent with known phylogenetic relationships and suggests several novel placements. J. Exp. Zool. ( Mol. Dev. Evol.) 285:128-139, 1999.     

A framework for phylogenetic sequence alignment

A phylogenetic alignment differs from other forms of multiple sequence alignment because it must align homologous features. Therefore, the goal of the alignment procedure should be to identify the events associated with the homologies, so that the aligned sequences accurately reflect those events. That is, an alignment is a set of hypotheses about historical events rather than about residues, and any alignment algorithm must be designed to identify and align such events. Some events (e.g., substitution) involve single residues, and our current algorithms can successfully align those events when sequence similarity is great enough. However, the other common events (such as duplication, translocation, deletion, insertion and inversion) can create complex sequence patterns that defeat such algorithms. There is therefore currently no computerized algorithm that can successfully align molecular sequences for phylogenetic analysis, except under restricted circumstances. Manual re-alignment of a preliminary alignment is thus the only feasible contemporary methodology, although it should be possible to automate such a procedure.     

indel-Seq-Gen: a new protein family simulator incorporating domains, motifs, and indels

Reconstructing the evolutionary history of protein sequences will provide a better understanding of divergence mechanisms of protein superfamilies and their functions. Long-term protein evolution often includes dynamic changes such as insertion, deletion, and domain shuffling. Such dynamic changes make reconstructing protein sequence evolution difficult and affect the accuracy of molecular evolutionary methods, such as multiple alignments and phylogenetic methods. Unfortunately, currently available simulation methods are not sufficiently flexible and do not allow biologically realistic dynamic protein sequence evolution. We introduce a new method, indel-Seq-Gen (iSG), that can simulate realistic evolutionary processes of protein sequences with insertions and deletions (indels). Unlike other simulation methods, iSG allows the user to simulate multiple subsequences according to different evolutionary parameters, which is necessary for generating realistic protein families with multiple domains. iSG tracks all evolutionary events including indels and outputs the "true" multiple alignment of the simulated sequences. iSG can also generate a larger sequence space by allowing the use of multiple related root sequences. With all these functions, iSG can be used to test the accuracy of, for example, multiple alignment methods, phylogenetic methods, evolutionary hypotheses, ancestral protein reconstruction methods, and protein family classification methods. We empirically evaluated the performance of iSG against currently available methods by simulating the evolution of the G protein-coupled receptor and lipocalin protein families. We examined their true multiple alignments, reconstruction of the transmembrane regions and beta-strands, and the results of similarity search against a protein database using the simulated sequences. We also presented an example of using iSG for examining how phylogenetic reconstruction is affected by high indel rates.     

Joint Bayesian estimation of alignment and phylogeny

We describe a novel model and algorithm for simultaneously estimating multiple molecular sequence alignments and the phylogenetic trees that relate the sequences. Unlike current techniques that base phylogeny estimates on a single estimate of the alignment, we take alignment uncertainty into account by considering all possible alignments. Furthermore, because the alignment and phylogeny are constructed simultaneously, a guide tree is not needed. This sidesteps the problem in which alignments created by progressive alignment are biased toward the guide tree used to generate them. Joint estimation also allows us to model rate variation between sites when estimating the alignment and to use the evidence in shared insertion/deletions (indels) to group sister taxa in the phylogeny. Our indel model makes use of affine gap penalties and considers indels of multiple letters. We make the simplifying assumption that the indel process is identical on all branches. As a result, the probability of a gap is independent of branch length. We use a Markov chain Monte Carlo (MCMC) method to sample from the posterior of the joint model, estimating the most probable alignment and tree and their support simultaneously. We describe a new MCMC transition kernel that improves our algorithm's mixing efficiency, allowing the MCMC chains to converge even when started from arbitrary alignments. Our software implementation can estimate alignment uncertainty and we describe a method for summarizing this uncertainty in a single plot.     

On comparing two structured RNA multiple alignments

We present a method, called BlockMatch, for aligning two blocks, where a block is an RNA multiple sequence alignment with the consensus secondary structure of the alignment in Stockholm format. The method employs a quadratic-time dynamic programming algorithm for aligning columns and column pairs of the multiple alignments in the blocks. Unlike many other tools that can perform pairwise alignment of either single sequences or structures only, BlockMatch takes into account the characteristics of all the sequences in the blocks along with their consensus structures during the alignment process, thus being able to achieve a high-quality alignment result. We apply BlockMatch to phylogeny reconstruction on a set of 5S rRNA sequences taken from fifteen bacteria species. Experimental results showed that the phylogenetic tree generated by our method is more accurate than the tree constructed based on the widely used ClustalW tool. The BlockMatch algorithm is implemented into a web server, accessible at http://bioinformatics.njit.edu/blockmatch. A jar file of the program is also available for download from the web server.     

A Bayesian model for detecting past recombination events in DNA multiple alignments.

Most phylogenetic tree estimation methods assume that there is a single set of hierarchical relationships among sequences in a data set for all sites along an alignment. Mosaic sequences produced by past recombination events will violate this assumption and may lead to misleading results from a phylogenetic analysis due to the imposition of a single tree along the entire alignment. Therefore, the detection of past recombination is an important first step in an analysis. A Bayesian model for the changes in topology caused by recombination events is described here. This model relaxes the assumption of one topology for all sites in an alignment and uses the theory of Hidden Markov models to facilitate calculations, the hidden states being the underlying topologies at each site in the data set. Changes in topology along the multiple sequence alignment are estimated by means of the maximum a posteriori (MAP) estimate. The performance of the MAP estimate is assessed by application of the model to data sets of four sequences, both simulated and real.     

Inferring horizontal transfers in the presence of rearrangements by the minimum evolution criterion

MOTIVATION: The evolution of viruses is very rapid and in addition to local point mutations (insertion, deletion, substitution) it also includes frequent recombinations, genome rearrangements and horizontal transfer of genetic materials (HGTS). Evolutionary analysis of viral sequences is therefore a complicated matter for two main reasons: First, due to HGTs and recombinations, the right model of evolution is a network and not a tree. Second, due to genome rearrangements, an alignment of the input sequences is not guaranteed. These facts encourage developing methods for inferring phylogenetic networks that do not require aligned sequences as input. RESULTS: In this work, we present the first computational approach which deals with both genome rearrangements and horizontal gene transfers and does not require a multiple alignment as input. We formalize a new set of computational problems which involve analyzing such complex models of evolution. We investigate their computational complexity, and devise algorithms for solving them. Moreover, we demonstrate the viability of our methods on several synthetic datasets as well as four biological datasets. AVAILABILITY: The code is available from the authors upon request.     

SATe-II: very fast and accurate simultaneous estimation of multiple sequence alignments and phylogenetic trees

Highly accurate estimation of phylogenetic trees for large data sets is difficult, in part because multiple sequence alignments must be accurate for phylogeny estimation methods to be accurate. Coestimation of alignments and trees has been attempted but currently only SATé estimates reasonably accurate trees and alignments for large data sets in practical time frames (Liu K., Raghavan S., Nelesen S., Linder C.R., Warnow T. 2009b. Rapid and accurate large-scale coestimation of sequence alignments and phylogenetic trees. Science. 324:1561-1564). Here, we present a modification to the original SATé algorithm that improves upon SATé (which we now call SATé-I) in terms of speed and of phylogenetic and alignment accuracy. SATé-II uses a different divide-and-conquer strategy than SATé-I and so produces smaller more closely related subsets than SATé-I; as a result, SATé-II produces more accurate alignments and trees, can analyze larger data sets, and runs more efficiently than SATé-I. Generally, SATé is a metamethod that takes an existing multiple sequence alignment method as an input parameter and boosts the quality of that alignment method. SATé-II-boosted alignment methods are significantly more accurate than their unboosted versions, and trees based upon these improved alignments are more accurate than trees based upon the original alignments. Because SATé-I used maximum likelihood (ML) methods that treat gaps as missing data to estimate trees and because we found a correlation between the quality of tree/alignment pairs and ML scores, we explored the degree to which SATé's performance depends on using ML with gaps treated as missing data to determine the best tree/alignment pair. We present two lines of evidence that using ML with gaps treated as missing data to optimize the alignment and tree produces very poor results. First, we show that the optimization problem where a set of unaligned DNA sequences is given and the output is the tree and alignment of those sequences that maximize likelihood under the Jukes-Cantor model is uninformative in the worst possible sense. For all inputs, all trees optimize the likelihood score. Second, we show that a greedy heuristic that uses GTR+Gamma ML to optimize the alignment and the tree can produce very poor alignments and trees. Therefore, the excellent performance of SATé-II and SATé-I is not because ML is used as an optimization criterion for choosing the best tree/alignment pair but rather due to the particular divide-and-conquer realignment techniques employed.     

Detecting recombination with MCMC

MOTIVATION: We present a statistical method for detecting recombination, whose objective is to accurately locate the recombinant breakpoints in DNA sequence alignments of small numbers of taxa (4 or 5). Our approach explicitly models the sequence of phylogenetic tree topologies along a multiple sequence alignment. Inference under this model is done in a Bayesian way, using Markov chain Monte Carlo (MCMC). The algorithm returns the site-dependent posterior probability of each tree topology, which is used for detecting recombinant regions and locating their breakpoints. RESULTS: The method was tested on a synthetic and three real DNA sequence alignments, where it was found to outperform the established detection methods PLATO, RECPARS, and TOPAL.     

Pandit: a database of protein and associated nucleotide domains with inferred trees

MOTIVATION: A large, high-quality database of homologous sequence alignments with good estimates of their corresponding phylogenetic trees will be a valuable resource to those studying phylogenetics. It will allow researchers to compare current and new models of sequence evolution across a large variety of sequences. The large quantity of data may provide inspiration for new models and methodology to study sequence evolution and may allow general statements about the relative effect of different molecular processes on evolution. RESULTS: The Pandit 7.6 database contains 4341 families of sequences derived from the seed alignments of the Pfam database of amino acid alignments of families of homologous protein domains (Bateman et al., 2002). Each family in Pandit includes an alignment of amino acid sequences that matches the corresponding Pfam family seed alignment, an alignment of DNA sequences that contain the coding sequence of the Pfam alignment when they can be recovered (overall, 82.9% of sequences taken from Pfam) and the alignment of amino acid sequences restricted to only those sequences for which a DNA sequence could be recovered. Each of the alignments has an estimate of the phylogenetic tree associated with it. The tree topologies were obtained using the neighbor joining method based on maximum likelihood estimates of the evolutionary distances, with branch lengths then calculated using a standard maximum likelihood approach.     

Multiple sequence alignment accuracy and phylogenetic inference

Phylogenies are often thought to be more dependent upon the specifics of the sequence alignment rather than on the method of reconstruction. Simulation of sequences containing insertion and deletion events was performed in order to determine the role that alignment accuracy plays during phylogenetic inference. Data sets were simulated for pectinate, balanced, and random tree shapes under different conditions (ultrametric equal branch length, ultrametric random branch length, nonultrametric random branch length). Comparisons between hypothesized alignments and true alignments enabled determination of two measures of alignment accuracy, that of the total data set and that of individual branches. In general, our results indicate that as alignment error increases, topological accuracy decreases. This trend was much more pronounced for data sets derived from more pectinate topologies. In contrast, for balanced, ultrametric, equal branch length tree shapes, alignment inaccuracy had little average effect on tree reconstruction. These conclusions are based on average trends of many analyses under different conditions, and any one specific analysis, independent of the alignment accuracy, may recover very accurate or inaccurate topologies. Maximum likelihood and Bayesian, in general, outperformed neighbor joining and maximum parsimony in terms of tree reconstruction accuracy. Results also indicated that as the length of the branch and of the neighboring branches increase, alignment accuracy decreases, and the length of the neighboring branches is the major factor in topological accuracy. Thus, multiple-sequence alignment can be an important factor in downstream effects on topological reconstruction.     

The deterministic effects of alignment bias in phylogenetic inference

Alignment of nucleotide and/or amino acid sequences is a fundamental component of sequence‐based molecular phylogenetic studies. Here we examined how different alignment methods affect the phylogenetic trees that are inferred from the alignments. We used simulations to determine how alignment errors can lead to systematic biases that affect phylogenetic inference from those sequences. We compared four approaches to sequence alignment: progressive pairwise alignment, simultaneous multiple alignment of sequence fragments, local pairwise alignment and direct optimization. When taking into account branch support, implied alignments produced by direct optimization were found to show the most extreme behaviour (based on the alignment programs for which nearly equivalent alignment parameters could be set) in that they provided the strongest support for the correct tree in the simulations in which it was easy to resolve the correct tree and the strongest support for the incorrect tree in our long‐branch‐attraction simulations. When applied to alignment‐sensitive process partitions with different histories, direct optimization showed the strongest mutual influence between the process partitions when they were aligned and phylogenetically analysed together, which makes detecting recombination more difficult. Simultaneous alignment performed well relative to direct optimization and progressive pairwise alignment across all simulations. Rather than relying upon methods that integrate alignment and tree search into a single step without accounting for alignment uncertainty, as with implied alignments, we suggest that simultaneous alignment using the similarity criterion, within the context of information available on biological processes and function, be applied whenever possible for sequence‐based phylogenetic analyses.     

Phylogenetic information improves homology detection.

We present a database search method that is based on phylogenetic trees (treesearch). The method is used to search a protein sequence database for homologs to a protein family. In preparation for the search, a phylogenetic tree is constructed from a given multiple alignment of the family. During the search, each database sequence is temporarily inserted into the tree, thus adding a new edge to the tree. Homology between family and sequence is then judged from the length of this edge. In a comparison of our method to profiles (ISREC pfsearch), two implementations of hidden Markov models (HMMER hmmsearch and SAM hmmscore), and to the family pairwise search (FPS) method on 43 families from the SCOP database based on minimum false-positive counts (min-FPCs), we found a considerable gain in sensitivity. In 69% of the test cases, treesearch showed a min-FPC of at most 50, whereas the two second best methods (hmmsearch and FPS) showed this performance only in 53% cases. A similar impression holds for a large range of min-FPC thresholds. The results demonstrate that phylogenetic information can significantly improve the detection of distant homologies and justify our method as a useful alternative to existing methods.     

BEAST: Bayesian evolutionary analysis by sampling trees

Background  

The evolutionary analysis of molecular sequence variation is a statistical enterprise. This is reflected in the increased use of probabilistic models for phylogenetic inference, multiple sequence alignment, and molecular population genetics. Here we present BEAST: a fast, flexible software architecture for Bayesian analysis of molecular sequences related by an evolutionary tree. A large number of popular stochastic models of sequence evolution are provided and tree-based models suitable for both within- and between-species sequence data are implemented.     

Tree-based maximal likelihood substitution matrices and hidden Markov models

There has been considerable interest in the problem of making maximum likelihood (ML) evolutionary trees which allow insertions and deletions. This problem is partly one of formulation: how does one define a probabilistic model for such trees which treats insertion and deletion in a biologically plausible manner? A possible answer to this question is proposed here by extending the concept of a hidden Markov model (HMM) to evolutionary trees. The model, called a tree-HMM, allows what may be loosely regarded as learnable affine-type gap penalties for alignments. These penalties are expressed in HMMs as probabilities of transitions between states. In the tree-HMM, this idea is given an evolutionary embodiment by defining trees of transitions. Just as the probability of a tree composed of ungapped sequences is computed, by Felsenstein's method, using matrices representing the probabilities of substitutions of residues along the edges of the tree, so the probabilities in a tree-HMM are computed by substitution matrices for both residues and transitions. How to define these matrices by a ML procedure using an algorithm that learns from a database of protein sequences is shown here. Given these matrices, one can define a tree-HMM likelihood for a set of sequences, assuming a particular tree topology and an alignment of the sequences to the model. If one could efficiently find the alignment which maximizes (or comes close to maximizing) this likelihood, then one could search for the optimal tree topology for the sequences. An alignment algorithm is defined here which, given a particular tree topology, is guaranteed to increase the likelihood of the model. Unfortunately, it fails to find global optima for realistic sequence sets. Thus further research is needed to turn the tree-HMM into a practical phylogenetic tool.     

AliGROOVE – visualization of heterogeneous sequence divergence within multiple sequence alignments and detection of inflated branch support

Background

Masking of multiple sequence alignment blocks has become a powerful method to enhance the tree-likeness of the underlying data. However, existing masking approaches are insensitive to heterogeneous sequence divergence which can mislead tree reconstructions. We present AliGROOVE, a new method based on a sliding window and a Monte Carlo resampling approach, that visualizes heterogeneous sequence divergence or alignment ambiguity related to single taxa or subsets of taxa within a multiple sequence alignment and tags suspicious branches on a given tree.

Results

We used simulated multiple sequence alignments to show that the extent of alignment ambiguity in pairwise sequence comparison is correlated with the frequency of misplaced taxa in tree reconstructions. The approach implemented in AliGROOVE allows to detect nodes within a tree that are supported despite the absence of phylogenetic signal in the underlying multiple sequence alignment. We show that AliGROOVE equally well detects heterogeneous sequence divergence in a case study based on an empirical data set of mitochondrial DNA sequences of chelicerates.

Conclusions

The AliGROOVE approach has the potential to identify single taxa or subsets of taxa which show predominantly randomized sequence similarity in comparison with other taxa in a multiple sequence alignment. It further allows to evaluate the reliability of node support in a novel way.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-294) contains supplementary material, which is available to authorized users.     

Cirripede phylogeny using a novel approach: molecular morphometrics

We present a new method using nucleic acid secondary structure to assess phylogenetic relationships among species. In this method, which we term "molecular morphometrics," the measurable structural parameters of the molecules (geometrical features, bond energies, base composition, etc.) are used as specific characters to construct a phylogenetic tree. This method relies both on traditional morphological comparison and on molecular sequence comparison. Applied to the phylogenetic analysis of Cirripedia, molecular morphometrics supports the most recent morphological analyses arguing for the monophyly of Cirripedia sensu stricto (Thoracica + Rhizocephala + Acrothoracica). As a proof, a classical multiple alignment was also performed, either using or not using the structural information to realign the sequence segments considered in the molecular morphometrics analysis. These methods yielded the same tree topology as the direct use of structural characters as a phylogenetic signal. By taking into account the secondary structure of nucleic acids, the new method allows investigators to use the regions in which multiple alignments are barely reliable because of a large number of insertions and deletions. It thus appears to be complementary to classical primary sequence analysis in phylogenetic studies.     

Improving the performance of protein threading using insertion/deletion frequency arrays

As a protein evolves, not every part of the amino acid sequence has an equal probability of being deleted or for allowing insertions, because not every amino acid plays an equally important role in maintaining the protein structure. However, the most prevalent models in fold recognition methods treat every amino acid deletion and insertion as equally probable events. We have analyzed the alignment patterns for homologous and analogous sequences to determine patterns of insertion and deletion, and used that information to determine the statistics of insertions and deletions for different amino acids of a target sequence. We define these patterns as insertion/deletion (indel) frequency arrays (IFAs). By applying IFAs to the protein threading problem, we have been able to improve the alignment accuracy, especially for proteins with low sequence identity. We have also demonstrated that the application of this information can lead to an improvement in fold recognition.