MRBAYES: Bayesian inference of phylogenetic trees

SUMMARY: The program MRBAYES performs Bayesian inference of phylogeny using a variant of Markov chain Monte Carlo. AVAILABILITY: MRBAYES, including the source code, documentation, sample data files, and an executable, is available at http://brahms.biology.rochester.edu/software.html.     

Guided tree topology proposals for Bayesian phylogenetic inference

Increasingly, large data sets pose a challenge for computationally intensive phylogenetic methods such as Bayesian Markov chain Monte Carlo (MCMC). Here, we investigate the performance of common MCMC proposal distributions in terms of median and variance of run time to convergence on 11 data sets. We introduce two new Metropolized Gibbs Samplers for moving through "tree space." MCMC simulation using these new proposals shows faster average run time and dramatically improved predictability in performance, with a 20-fold reduction in the variance of the time to estimate the posterior distribution to a given accuracy. We also introduce conditional clade probabilities and demonstrate that they provide a superior means of approximating tree topology posterior probabilities from samples recorded during MCMC.     

Empirical evaluation of a prior for Bayesian phylogenetic inference

The Bayesian method of phylogenetic inference often produces high posterior probabilities (PPs) for trees or clades, even when the trees are clearly incorrect. The problem appears to be mainly due to large sizes of molecular datasets and to the large-sample properties of Bayesian model selection and its sensitivity to the prior when several of the models under comparison are nearly equally correct (or nearly equally wrong) and are of the same dimension. A previous suggestion to alleviate the problem is to let the internal branch lengths in the tree become increasingly small in the prior with the increase in the data size so that the bifurcating trees are increasingly star-like. In particular, if the internal branch lengths are assigned the exponential prior, the prior mean mu0 should approach zero faster than 1/square root n but more slowly than 1/n, where n is the sequence length. This paper examines the usefulness of this data size-dependent prior using a dataset of the mitochondrial protein-coding genes from the baleen whales, with the prior mean fixed at mu0=0.1n(-2/3). In this dataset, phylogeny reconstruction is sensitive to the assumed evolutionary model, species sampling and the type of data (DNA or protein sequences), but Bayesian inference using the default prior attaches high PPs for conflicting phylogenetic relationships. The data size-dependent prior alleviates the problem to some extent, giving weaker support for unstable relationships. This prior may be useful in reducing apparent conflicts in the results of Bayesian analysis or in making the method less sensitive to model violations.     

MrBayes 3: Bayesian phylogenetic inference under mixed models

MrBayes 3 performs Bayesian phylogenetic analysis combining information from different data partitions or subsets evolving under different stochastic evolutionary models. This allows the user to analyze heterogeneous data sets consisting of different data types-e.g. morphological, nucleotide, and protein-and to explore a wide variety of structured models mixing partition-unique and shared parameters. The program employs MPI to parallelize Metropolis coupling on Macintosh or UNIX clusters.     

Parallel Metropolis coupled Markov chain Monte Carlo for Bayesian phylogenetic inference

MOTIVATION: Bayesian estimation of phylogeny is based on the posterior probability distribution of trees. Currently, the only numerical method that can effectively approximate posterior probabilities of trees is Markov chain Monte Carlo (MCMC). Standard implementations of MCMC can be prone to entrapment in local optima. Metropolis coupled MCMC [(MC)(3)], a variant of MCMC, allows multiple peaks in the landscape of trees to be more readily explored, but at the cost of increased execution time. RESULTS: This paper presents a parallel algorithm for (MC)(3). The proposed parallel algorithm retains the ability to explore multiple peaks in the posterior distribution of trees while maintaining a fast execution time. The algorithm has been implemented using two popular parallel programming models: message passing and shared memory. Performance results indicate nearly linear speed improvement in both programming models for small and large data sets.     

FPGA acceleration of the phylogenetic likelihood function for Bayesian MCMC inference methods

Background  

Likelihood (ML)-based phylogenetic inference has become a popular method for estimating the evolutionary relationships among species based on genomic sequence data. This method is used in applications such as RAxML, GARLI, MrBayes, PAML, and PAUP. The Phylogenetic Likelihood Function (PLF) is an important kernel computation for this method. The PLF consists of a loop with no conditional behavior or dependencies between iterations. As such it contains a high potential for exploiting parallelism using micro-architectural techniques. In this paper, we describe a technique for mapping the PLF and supporting logic onto a Field Programmable Gate Array (FPGA)-based co-processor. By leveraging the FPGA's on-chip DSP modules and the high-bandwidth local memory attached to the FPGA, the resultant co-processor can accelerate ML-based methods and outperform state-of-the-art multi-core processors.     

A reversible jump method for Bayesian phylogenetic inference with a nonhomogeneous substitution model

Nonhomogeneous substitution models have been introduced for phylogenetic inference when the substitution process is nonstationary, for example, when sequence composition differs between lineages. Existing models can have many parameters, and it is then difficult and computationally expensive to learn the parameters and to select the optimal model complexity. We extend an existing nonhomogeneous substitution model by introducing a reversible jump Markov chain Monte Carlo method for efficient Bayesian inference of the model order along with other phylogenetic parameters of interest. We also introduce a new hierarchical prior which leads to more reasonable results when only a small number of lineages share a particular substitution process. The method is implemented in the PHASE software, which includes specialized substitution models for RNA genes with conserved secondary structure. We apply an RNA-specific nonhomogeneous model to a structure-based alignment of rRNA sequences spanning the entire tree of life. A previous study of the same genes from a similar set of species found robust evidence for a mesophilic last universal common ancestor (LUCA) by inference of the G+C composition at the root of the tree. In the present study, we find that the helical GC composition at the root is strongly dependent on the root position. With a bacterial rooting, we find that there is no longer strong support for either a mesophile or a thermophile LUCA, although a hyperthermophile LUCA remains unlikely. We discuss reasons why results using only RNA helices may differ from results using all aligned sites when applying nonhomogeneous models to RNA genes.     

MAC5: Bayesian inference of phylogenetic trees from DNA sequences incorporating gaps

SUMMARY: MAC5 implements MCMC sampling of the posterior distribution of tree topologies from DNA sequences containing gaps by using a five state model of evolution (the four nucleotides and the gap character).     

An examination of the monophyly of morning glory taxa using Bayesian phylogenetic inference

The objective of this study was to obtain a quantitative assessment of the monophyly of morning glory taxa, specifically the genus Ipomoea and the tribe Argyreieae. Previous systematic studies of morning glories intimated the paraphyly of Ipomoea by suggesting that the genera within the tribe Argyreieae are derived from within Ipomoea; however, no quantitative estimates of statistical support were developed to address these questions. We applied a Bayesian analysis to provide quantitative estimates of monophyly in an investigation of morning glory relationships using DNA sequence data. We also explored various approaches for examining convergence of the Markov chain Monte Carlo (MCMC) simulation of the Bayesian analysis by running 18 separate analyses varying in length. We found convergence of the important components of the phylogenetic model (the tree with the maximum posterior probability, branch lengths, the parameter values from the DNA substitution model, and the posterior probabilities for clade support) for these data after one million generations of the MCMC simulations. In the process, we identified a run where the parameter values obtained were often outside the range of values obtained from the other runs, suggesting an aberrant result. In addition, we compared the Bayesian method of phylogenetic analysis to maximum likelihood and maximum parsimony. The results from the Bayesian analysis and the maximum likelihood analysis were similar for topology, branch lengths, and parameters of the DNA substitution model. Topologies also were similar in the comparison between the Bayesian analysis and maximum parsimony, although the posterior probabilities and the bootstrap proportions exhibited some striking differences. In a Bayesian analysis of three data sets (ITS sequences, waxy sequences, and ITS + waxy sequences) no supoort for the monophyly of the genus Ipomoea, or for the tribe Argyreieae, was observed, with the estimate of the probability of the monophyly of these taxa being less than 3.4 x 10(-7).     

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method

An improved Bayesian method is presented for estimating phylogenetic treesusing DNA sequence data. The birth-death process with species sampling isused to specify the prior distribution of phylogenies and ancestralspeciation times, and the posterior probabilities of phylogenies are usedto estimate the maximum posterior probability (MAP) tree. Monte Carlointegration is used to integrate over the ancestral speciation times forparticular trees. A Markov Chain Monte Carlo method is used to generate theset of trees with the highest posterior probabilities. Methods aredescribed for an empirical Bayesian analysis, in which estimates of thespeciation and extinction rates are used in calculating the posteriorprobabilities, and a hierarchical Bayesian analysis, in which theseparameters are removed from the model by an additional integration. TheMarkov Chain Monte Carlo method avoids the requirement of our earliermethod for calculating MAP trees to sum over all possible topologies (whichlimited the number of taxa in an analysis to about five). The methods areapplied to analyze DNA sequences for nine species of primates, and the MAPtree, which is identical to a maximum-likelihood estimate of topology, hasa probability of approximately 95%.     

MrBayes 3.2: efficient Bayesian phylogenetic inference and model choice across a large model space

Since its introduction in 2001, MrBayes has grown in popularity as a software package for Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC) methods. With this note, we announce the release of version 3.2, a major upgrade to the latest official release presented in 2003. The new version provides convergence diagnostics and allows multiple analyses to be run in parallel with convergence progress monitored on the fly. The introduction of new proposals and automatic optimization of tuning parameters has improved convergence for many problems. The new version also sports significantly faster likelihood calculations through streaming single-instruction-multiple-data extensions (SSE) and support of the BEAGLE library, allowing likelihood calculations to be delegated to graphics processing units (GPUs) on compatible hardware. Speedup factors range from around 2 with SSE code to more than 50 with BEAGLE for codon problems. Checkpointing across all models allows long runs to be completed even when an analysis is prematurely terminated. New models include relaxed clocks, dating, model averaging across time-reversible substitution models, and support for hard, negative, and partial (backbone) tree constraints. Inference of species trees from gene trees is supported by full incorporation of the Bayesian estimation of species trees (BEST) algorithms. Marginal model likelihoods for Bayes factor tests can be estimated accurately across the entire model space using the stepping stone method. The new version provides more output options than previously, including samples of ancestral states, site rates, site d(N)/d(S) rations, branch rates, and node dates. A wide range of statistics on tree parameters can also be output for visualization in FigTree and compatible software.     

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.     

Ribosomal ITS sequences and plant phylogenetic inference

One of the most popular sequences for phylogenetic inference at the generic and infrageneric levels in plants is the internal transcribed spacer (ITS) region of the 18S-5.8S-26S nuclear ribosomal cistron. The prominence of this source of nuclear DNA sequence data is underscored by a survey of phylogenetic publications involving comparisons at the genus level or below, which reveals that of 244 papers published over the last five years, 66% included ITS sequence data. Perhaps even more striking is the fact that 34% of all published phylogenetic hypothesis have been based exclusively on ITS sequences. Notwithstanding the many important contributions of ITS sequence data to phylogenetic understanding and knowledge of genome relationships, a number of molecular genetic processes impact ITS sequences in ways that may mislead phylogenetic inference. These molecular genetic processes are reviewed here, drawing attention to both underlying mechanism and phylogenetic implications. Among the most prevalent complications for phylogenetic inference is the existence in many plant genomes of extensive sequence variation, arising from ancient or recent array duplication events, genomic harboring of pseudogenes in various states of decay, and/or incomplete intra- or inter-array homogenization. These phenomena separately and collectively create a network of paralogous sequence relationships potentially confounding accurate phylogenetic reconstruction. Homoplasy is shown to be higher in ITS than in other DNA sequence data sets, most likely because of orthology/paralogy conflation, compensatory base changes, problems in alignment due to indel accumulation, sequencing errors, or some combination of these phenomena. Despite the near-universal usage of ITS sequence data in plant phylogenetic studies, its complex and unpredictable evolutionary behavior reduce its utility for phylogenetic analysis. It is suggested that more robust insights are likely to emerge from the use of single-copy or low-copy nuclear genes.     

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.     

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.     

Bayesian inference of character evolution

Much recent progress in evolutionary biology is based on the inference of ancestral states and past transformations in important traits on phylogenetic trees. These exercises often assume that the tree is known without error and that ancestral states and character change can be mapped onto it exactly. In reality, there is often considerable uncertainty about both the tree and the character mapping. Recently introduced Bayesian statistical methods enable the study of character evolution while simultaneously accounting for both phylogenetic and mapping uncertainty, adding much needed credibility to the reconstruction of evolutionary history.     

Spiking networks for Bayesian inference and choice

Systems neuroscience traditionally conceptualizes a population of spiking neurons as merely encoding the value of a stimulus. Yet, psychophysics has revealed that people take into account stimulus uncertainty when performing sensory or motor computations and do so in a nearly Bayes-optimal way. This suggests that neural populations do not encode just a single value but an entire probability distribution over the stimulus. Several such probabilistic codes have been proposed, including one that utilizes the structure of neural variability to enable simple neural implementations of probabilistic computations such as optimal cue integration. This approach provides a quantitative link between Bayes-optimal behaviors and specific neural operations. It allows for novel ways to evaluate probabilistic codes and for predictions for physiological population recordings.     

The evolution of base composition and phylogenetic inference

Base composition varies at all levels of the phylogenetic hierarchy and throughout the genome, and can be caused by active selection or passive mutation pressure. This variation can make reconstructing trees difficult. However, recent tree-based analyses have shed light on the forces responsible for the evolution of base composition, forces that might be very general. More explicit tree-based work is encouraged.