Bayesian coestimation of phylogeny and sequence alignment

Background  

Two central problems in computational biology are the determination of the alignment and phylogeny of a set of biological sequences. The traditional approach to this problem is to first build a multiple alignment of these sequences, followed by a phylogenetic reconstruction step based on this multiple alignment. However, alignment and phylogenetic inference are fundamentally interdependent, and ignoring this fact leads to biased and overconfident estimations. Whether the main interest be in sequence alignment or phylogeny, a major goal of computational biology is the co-estimation of both.     

BAli-Phy: simultaneous Bayesian inference of alignment and phylogeny

SUMMARY: BAli-Phy is a Bayesian posterior sampler that employs Markov chain Monte Carlo to explore the joint space of alignment and phylogeny given molecular sequence data. Simultaneous estimation eliminates bias toward inaccurate alignment guide-trees, employs more sophisticated substitution models during alignment and automatically utilizes information in shared insertion/deletions to help infer phylogenies. AVAILABILITY: Software is available for download at http://www.biomath.ucla.edu/msuchard/bali-phy.     

Mitochondrial phylogeny of the Chrysisignita (Hymenoptera: Chrysididae) species group based on simultaneous Bayesian alignment and phylogeny reconstruction

The ignita species group within the genus Chrysis includes over 100 cuckoo wasp species, which all lead a parasitic lifestyle and exhibit very similar morphology. The lack of robust, diagnostic morphological characters has hindered phylogenetic reconstructions and contributed to frequent misidentification and inconsistent interpretations of species in this group. Therefore, molecular phylogenetic analysis is the most suitable approach for resolving the phylogeny and taxonomy of this group. We present a well-resolved phylogeny of the Chrysis ignita species group based on mitochondrial sequence data from 41 ingroup and six outgroup taxa. Although our emphasis was on European taxa, we included samples from most of the distribution range of the C. ignita species group to test for monophyly. We used a continuous mitochondrial DNA sequence consisting of 16S rRNA, tRNA(Val), 12S rRNA and ND4. The location of the ND4 gene at the 3' end of this continuous sequence, following 12S rRNA, represents a novel mitochondrial gene arrangement for insects. Due to difficulties in aligning rRNA genes, two different Bayesian approaches were employed to reconstruct phylogeny: (1) using a reduced data matrix including only those positions that could be aligned with confidence; or (2) using the full sequence dataset while estimating alignment and phylogeny simultaneously. In addition maximum-parsimony and maximum-likelihood analyses were performed to test the robustness of the Bayesian approaches. Although all approaches yielded trees with similar topology, considerably more nodes were resolved with analyses using the full data matrix. Phylogenetic analysis supported the monophyly of the C. ignita species group and divided its species into well-supported clades. The resultant phylogeny was only partly in accordance with published subgroupings based on morphology. Our results suggest that several taxa currently treated as subspecies or names treated as synonyms may in fact constitute separate species. Our study provides a solid basis for further systematic investigations of this enigmatic insect group.     

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.     

Simultaneous statistical multiple alignment and phylogeny reconstruction

Although the reconstruction of phylogenetic trees and the computation of multiple sequence alignments are highly interdependent, these two areas of research lead quite separate lives, the former often making use of stochastic modeling, whereas the latter normally does not. Despite the fact that reasonable insertion and deletion models for sequence pairs were already introduced more than 10 years ago, they have only recently been applied to multiple alignment and only in their simplest version. In this paper we present and discuss a strategy based on simulated annealing, which makes use of these models to infer a phylogenetic tree for a set of DNA or protein sequences together with the sequences'indel history, i.e., their multiple alignment augmented with information about the positioning of insertion and deletion events in the tree. Our method is also the first application of the TKF2 model in the context of multiple sequence alignment. We validate the method via simulations and illustrate it using a data set of primate mtDNA.     

Bayesian adaptive sequence alignment algorithms

The selection of a scoring matrix and gap penalty parameters continues to be an important problem in sequence alignment. We describe here an algorithm, the 'Bayes block aligner, which bypasses this requirement. Instead of requiring a fixed set of parameter settings, this algorithm returns the Bayesian posterior probability for the number of gaps and for the scoring matrices in any series of interest. Furthermore, instead of returning the single best alignment for the chosen parameter settings, this algorithm returns the posterior distribution of all alignments considering the full range of gapping and scoring matrices selected, weighing each in proportion to its probability based on the data. We compared the Bayes aligner with the popular Smith-Waterman algorithm with parameter settings from the literature which had been optimized for the identification of structural neighbors, and found that the Bayes aligner correctly identified more structural neighbors. In a detailed examination of the alignment of a pair of kinase and a pair of GTPase sequences, we illustrate the algorithm's potential to identify subsequences that are conserved to different degrees. In addition, this example shows that the Bayes aligner returns an alignment-free assessment of the distance between a pair of sequences.      

Cytochrome b and Bayesian inference of whale phylogeny

In the mid 1990s cytochrome b and other mitochondrial DNA data reinvigorated cetacean phylogenetics by proposing many novel and provocative hypotheses of cetacean relationships. These results sparked a revision and reanalysis of morphological datasets, and the collection of new nuclear DNA data from numerous loci. Some of the most controversial mitochondrial hypotheses have now become benchmark clades, corroborated with nuclear DNA and morphological data; others have been resolved in favor of more traditional views. That major conflicts in cetacean phylogeny are disappearing is encouraging. However, most recent papers aim specifically to resolve higher-level conflicts by adding characters, at the cost of densely sampling taxa to resolve lower-level relationships. No molecular study to date has included more than 33 cetaceans. More detailed molecular phylogenies will provide better tools for evolutionary studies. Until more genes are available for a high number of taxa, can we rely on readily available single gene mitochondrial data? Here, we estimate the phylogeny of 66 cetacean taxa and 24 outgroups based on Cytb sequences. We judge the reliability of our phylogeny based on the recovery of several deep-level benchmark clades. A Bayesian phylogenetic analysis recovered all benchmark clades and for the first time supported Odontoceti monophyly based exclusively on analysis of a single mitochondrial gene. The results recover the monophyly of all but one family level taxa within Cetacea, and most recently proposed super- and subfamilies. In contrast, parsimony never recovered all benchmark clades and was sensitive to a priori weighting decisions. These results provide the most detailed phylogeny of Cetacea to date and highlight the utility of both Bayesian methodology in general, and of Cytb in cetacean phylogenetics. They furthermore suggest that dense taxon sampling, like dense character sampling, can overcome problems in phylogenetic reconstruction.     

Effects of nucleotide sequence alignment on phylogeny estimation: a case study of 18S rDNAs of apicomplexa

The reconstruction of phylogenetic history is predicated on being able to accurately establish hypotheses of character homology, which involves sequence alignment for studies based on molecular sequence data. In an empirical study investigating nucleotide sequence alignment, we inferred phylogenetic trees for 43 species of the Apicomplexa and 3 of Dinozoa based on complete small-subunit rDNA sequences, using six different multiple-alignment procedures: manual alignment based on the secondary structure of the 18S rRNA molecule, and automated similarity-based alignment algorithms using the PileUp, ClustalW, TreeAlign, MALIGN, and SAM computer programs. Trees were constructed using neighboring-joining, weighted-parsimony, and maximum- likelihood methods. All of the multiple sequence alignment procedures yielded the same basic structure for the estimate of the phylogenetic relationship among the taxa, which presumably represents the underlying phylogenetic signal. However, the placement of many of the taxa was sensitive to the alignment procedure used; and the different alignments produced trees that were on average more dissimilar from each other than did the different tree-building methods used. The multiple alignments from the different procedures varied greatly in length, but aligned sequence length was not a good predictor of the similarity of the resulting phylogenetic trees. We also systematically varied the gap weights (the relative cost of inserting a new gap into a sequence or extending an already-existing gap) for the ClustalW program, and this produced alignments that were at least as different from each other as those produced by the different alignment algorithms. Furthermore, there was no combination of gap weights that produced the same tree as that from the structure alignment, in spite of the fact that many of the alignments were similar in length to the structure alignment. We also investigated the phylogenetic information content of the helical and nonhelical regions of the rDNA, and conclude that the helical regions are the most informative. We therefore conclude that many of the literature disagreements concerning the phylogeny of the Apicomplexa are probably based on differences in sequence alignment strategies rather than differences in data or tree-building methods.      

Nucleotide substitution models and estimation of phylogeny

The nucleotide substitution matrix inferred from avian data sets using cytochrome b differs considerably from the models commonly used in phylogenetic analyses. To analyze the possible effects of this particular pattern of change in phylogeny estimation we performed a computer simulation in which we started with a real sequence and used the inferred model of change to produce a tree of 10 species. Maximum parsimony (MP), maximum likelihood (ML), and various distance methods were then used to recover the topology and the branch lengths. We used two kinds of data with varying levels of variation. In addition, we tested with the removal of third positions and different weighting schemes. At low levels of variation, MP was outstanding in recovering the topology (90% correct), while unweighted pair-group method, arithmetic average (UPGMA), regardless of distances used, was poor (40%). At the higher level, most methods had a chance of around 40%-58% of finding the true tree. However, in most cases, the trees found were only slightly wrong, with only one or a few branches misplaced. On the other hand, the use of a "wrong" model had serious effects on the estimation of branch lengths (distances). Although precision was high, accuracy was poor with most methods, giving branch lengths that were biased downward. When seeded with the true distance matrix, Fitch and NJ always found the true tree, while UPGMA frequently failed to do so. The effect of removing third positions was dramatic at low levels of variation, because only one MP program was able to find a true tree at all, albeit rarely, while none of the others ever did so. At higher levels, the situation was better, but still much worse than with the whole data set.     

Treelength optimization for phylogeny estimation

The standard approach to phylogeny estimation uses two phases, in which the first phase produces an alignment on a set of homologous sequences, and the second phase estimates a tree on the multiple sequence alignment. POY, a method which seeks a tree/alignment pair minimizing the total treelength, is the most widely used alternative to this two-phase approach. The topological accuracy of trees computed under treelength optimization is, however, controversial. In particular, one study showed that treelength optimization using simple gap penalties produced poor trees and alignments, and suggested the possibility that if POY were used with an affine gap penalty, it might be able to be competitive with the best two-phase methods. In this paper we report on a study addressing this possibility. We present a new heuristic for treelength, called BeeTLe (Better Treelength), that is guaranteed to produce trees at least as short as POY. We then use this heuristic to analyze a large number of simulated and biological datasets, and compare the resultant trees and alignments to those produced using POY and also maximum likelihood (ML) and maximum parsimony (MP) trees computed on a number of alignments. In general, we find that trees produced by BeeTLe are shorter and more topologically accurate than POY trees, but that neither POY nor BeeTLe produces trees as topologically accurate as ML trees produced on standard alignments. These findings, taken as a whole, suggest that treelength optimization is not as good an approach to phylogenetic tree estimation as maximum likelihood based upon good alignment methods.     

Nematode small subunit phylogeny correlates with alignment parameters

The number of nuclear small subunit (SSU) ribosomal RNA (rRNA) sequences for Nematoda has increased dramatically in recent years, and although their use in constructing phylogenies has also increased, relatively little attention has been given to their alignment. Here we examined the sensitivity of the nematode SSU data set to different alignment parameters and to the removal of alignment ambiguous regions. Ten alignments were created with CLUSTAL W using different sets of alignment parameters (10 full alignments), and each alignment was examined by eye and alignment ambiguous regions were removed (creating 10 reduced alignments). These alignment ambiguous regions were analyzed as a third type of data set, culled alignments. Maximum parsimony, neighbor-joining, and parsimony bootstrap analyses were performed. The resulting phylogenies were compared to each other by the symmetric difference distance tree comparison metric (SymD). The correlation of the phylogenies with the alignment parameters was tested by comparing matrices from SymD with corresponding matrices of Manhattan distances representing the alignment parameters. Differences among individual parsimony trees from the full alignments were frequently correlated with the differences among alignment parameters (580/1000 tests), as were trees from the culled alignments (403/1000 tests). Differences among individual parsimony trees from the reduced alignments were less frequently correlated with the differences among alignment parameters (230/1000 tests). Differences among majority-rule consensus trees (50%) from the parsimony analysis of the full alignments were significantly correlated with the differences among alignment parameters, whereas consensus trees from the reduced and culled analyses were not correlated with the alignment parameters. These patterns of correlation confirm that choice of alignment parameters has the potential to bias the resultant phylogenies for the nematode SSU data set, and suggest that the removal of alignment ambiguous regions reduces this effect. Finally, we discuss the implications of conservative phylogenetic hypotheses for Nematoda produced by exploring alignment space and removing alignment ambiguous regions for SSU rDNA.     

Potential applications and pitfalls of Bayesian inference of phylogeny

Only recently has Bayesian inference of phylogeny been proposed. The method is now a practical alternative to the other methods; indeed, the method appears to possess advantages over the other methods in terms of ability to use complex models of evolution, ease of interpretation of the results, and computational efficiency. However, the method should be used cautiously. The results of a Bayesian analysis should be examined with respect to the sensitivity of the results to the priors used and the reliability of the Markov chain Monte Carlo approximation of the probabilities of trees.     

Effects of sequence alignment procedures on estimates of phylogeny

Previous debate about statistical variation in inferred phylogenies has focused on procedures for the estimation of evolutionary relationships from aligned sequences. Morrison and Ellis¹ have recently drawn attention to additional variation attributable to the alignment procedure used and have suggested that this may be highly significant. This raises doubts about our ability to infer reliable phylogenies. Although concerns may not be as serious as their analyses at first imply, Morrison and Ellis¹ have performed a useful service in reminding us that accurate sequence alignment is a crucial part of molecular phylogenetics. BioEssays 20 :287-290, 1998.© 1998 John Wiley & Sons, Inc.     

Bayesian logistic regression using a perfect phylogeny

Haplotype data capture the genetic variation among individuals in a population and among populations. An understanding of this variation and the ancestral history of haplotypes is important in genetic association studies of complex disease. We introduce a method for detecting associations between disease and haplotypes in a candidate gene region or candidate block with little or no recombination. A perfect phylogeny demonstrates the evolutionary relationship between single-nucleotide polymorphisms (SNPs) in the haplotype blocks. Our approach extends the logic regression technique of Ruczinski and others (2003) to a Bayesian framework, and constrains the model space to that of a perfect phylogeny. Environmental factors, as well as their interactions with SNPs, may be incorporated into the regression framework. We demonstrate our method on simulated data from a coalescent model, as well as data from a candidate gene study of sarcoidosis.     

Branch-length prior influences Bayesian posterior probability of phylogeny

The Bayesian method for estimating species phylogenies from molecular sequence data provides an attractive alternative to maximum likelihood with nonparametric bootstrap due to the easy interpretation of posterior probabilities for trees and to availability of efficient computational algorithms. However, for many data sets it produces extremely high posterior probabilities, sometimes for apparently incorrect clades. Here we use both computer simulation and empirical data analysis to examine the effect of the prior model for internal branch lengths. We found that posterior probabilities for trees and clades are sensitive to the prior for internal branch lengths, and priors assuming long internal branches cause high posterior probabilities for trees. In particular, uniform priors with high upper bounds bias Bayesian clade probabilities in favor of extreme values. We discuss possible remedies to the problem, including empirical and full Bayesian methods and subjective procedures suggested in Bayesian hypothesis testing. Our results also suggest that the bootstrap proportion and Bayesian posterior probability are different measures of accuracy, and that the bootstrap proportion, if interpreted as the probability that the clade is true, can be either too liberal or too conservative.     

Bayesian estimation of genomic distance

We present a Bayesian approach to the problem of inferring the number of inversions and translocations separating two species. The main reason for developing this method is that it will allow us to test hypotheses about the underlying mechanisms, such as the distribution of inversion track lengths or rate constancy among lineages. Here, we apply these methods to comparative maps of eggplant and tomato, human and cat, and human and cattle with 170, 269, and 422 markers, respectively. In the first case the most likely number of events is larger than the parsimony value. In the last two cases the parsimony solutions have very small probability.     

BigFoot: Bayesian alignment and phylogenetic footprinting with MCMC

Background  

We have previously combined statistical alignment and phylogenetic footprinting to detect conserved functional elements without assuming a fixed alignment. Considering a probability-weighted distribution of alignments removes sensitivity to alignment errors, properly accommodates regions of alignment uncertainty, and increases the accuracy of functional element prediction. Our method utilized standard dynamic programming hidden markov model algorithms to analyze up to four sequences.