Many-core algorithms for high-dimensional gradients on phylogenetic trees.

MOTIVATION: Advancements in high-throughput genomic sequencing are delivering genomic pathogen data at an unprecedented rate, positioning statistical phylogenetics as a critical tool to monitor infectious diseases globally. This rapid growth spurs the need for efficient inference techniques, such as Hamiltonian Monte Carlo (HMC) in a Bayesian framework, to estimate parameters of these phylogenetic models where the dimensions of the parameters increase with the number of sequences N. HMC requires repeated calculation of the gradient of the data log-likelihood with respect to (wrt) all branch-length-specific (BLS) parameters that traditionally takes O(N2) operations using the standard pruning algorithm. A recent study proposes an approach to calculate this gradient in O(N), enabling researchers to take advantage of gradient-based samplers such as HMC. The CPU implementation of this approach makes the calculation of the gradient computationally tractable for nucleotide-based models but falls short in performance for larger state-space size models, such as Markov-modulated and codon models. Here, we describe novel massively parallel algorithms to calculate the gradient of the log-likelihood wrt all BLS parameters that take advantage of graphics processing units (GPUs) and result in many fold higher speedups over previous CPU implementations. RESULTS: We benchmark these GPU algorithms on three computing systems using three evolutionary inference examples exploring complete genomes from 997 dengue viruses, 62 carnivore mitochondria and 49 yeasts, and observe a >128-fold speedup over the CPU implementation for codon-based models and >8-fold speedup for nucleotide-based models. As a practical demonstration, we also estimate the timing of the first introduction of West Nile virus into the continental Unites States under a codon model with a relaxed molecular clock from 104 full viral genomes, an inference task previously intractable. AVAILABILITY AND IMPLEMENTATION: We provide an implementation of our GPU algorithms in BEAGLE v4.0.0 (https://github.com/beagle-dev/beagle-lib), an open-source library for statistical phylogenetics that enables parallel calculations on multi-core CPUs and GPUs. We employ a BEAGLE-implementation using the Bayesian phylogenetics framework BEAST (https://github.com/beast-dev/beast-mcmc).

A topology-marginal composite likelihood via a generalized phylogenetic pruning algorithm.

Bayesian phylogenetics is a computationally challenging inferential problem. Classical methods are based on random-walk Markov chain Monte Carlo (MCMC), where random proposals are made on the tree parameter and the continuous parameters simultaneously. Variational phylogenetics is a promising alternative to MCMC, in which one fits an approximating distribution to the unnormalized phylogenetic posterior. Previous work fit this variational approximation using stochastic gradient descent, which is the canonical way of fitting general variational approximations. However, phylogenetic trees are special structures, giving opportunities for efficient computation. In this paper we describe a new algorithm that directly generalizes the Felsenstein pruning algorithm (a.k.a. sum-product algorithm) to compute a composite-like likelihood by marginalizing out ancestral states and subtrees simultaneously. We show the utility of this algorithm by rapidly making point estimates for branch lengths of a multi-tree phylogenetic model. These estimates accord with a long MCMC run and with estimates obtained using a variational method, but are much faster to obtain. Thus, although generalized pruning does not lead to a variational algorithm as such, we believe that it will form a useful starting point for variational inference.

Automatic Differentiation is no Panacea for Phylogenetic Gradient Computation.

Gradients of probabilistic model likelihoods with respect to their parameters are essential for modern computational statistics and machine learning. These calculations are readily available for arbitrary models via "automatic differentiation" implemented in general-purpose machine-learning libraries such as TensorFlow and PyTorch. Although these libraries are highly optimized, it is not clear if their general-purpose nature will limit their algorithmic complexity or implementation speed for the phylogenetic case compared to phylogenetics-specific code. In this paper, we compare six gradient implementations of the phylogenetic likelihood functions, in isolation and also as part of a variational inference procedure. We find that although automatic differentiation can scale approximately linearly in tree size, it is much slower than the carefully implemented gradient calculation for tree likelihood and ratio transformation operations. We conclude that a mixed approach combining phylogenetic libraries with machine learning libraries will provide the optimal combination of speed and model flexibility moving forward.

Fidelity of hyperbolic space for Bayesian phylogenetic inference.

Bayesian inference for phylogenetics is a gold standard for computing distributions of phylogenies. However, Bayesian phylogenetics faces the challenging computational problem of moving throughout the high-dimensional space of trees. Fortunately, hyperbolic space offers a low dimensional representation of tree-like data. In this paper, we embed genomic sequences as points in hyperbolic space and perform hyperbolic Markov Chain Monte Carlo for Bayesian inference in this space. The posterior probability of an embedding is computed by decoding a neighbour-joining tree from the embedding locations of the sequences. We empirically demonstrate the fidelity of this method on eight data sets. We systematically investigated the effect of embedding dimension and hyperbolic curvature on the performance in these data sets. The sampled posterior distribution recovers the splits and branch lengths to a high degree over a range of curvatures and dimensions. We systematically investigated the effects of the embedding space's curvature and dimension on the Markov Chain's performance, demonstrating the suitability of hyperbolic space for phylogenetic inference.

Many-core algorithms for high-dimensional gradients on phylogenetic trees.

The rapid growth in genomic pathogen data spurs the need for efficient inference techniques, such as Hamiltonian Monte Carlo (HMC) in a Bayesian framework, to estimate parameters of these phylogenetic models where the dimensions of the parameters increase with the number of sequences $N$. HMC requires repeated calculation of the gradient of the data log-likelihood with respect to (wrt) all branch-length-specific (BLS) parameters that traditionally takes $\mathcal{O}(N^2)$ operations using the standard pruning algorithm. A recent study proposes an approach to calculate this gradient in $\mathcal{O}(N)$, enabling researchers to take advantage of gradient-based samplers such as HMC. The CPU implementation of this approach makes the calculation of the gradient computationally tractable for nucleotide-based models but falls short in performance for larger state-space size models, such as codon models. Here, we describe novel massively parallel algorithms to calculate the gradient of the log-likelihood wrt all BLS parameters that take advantage of graphics processing units (GPUs) and result in many fold higher speedups over previous CPU implementations. We benchmark these GPU algorithms on three computing systems using three evolutionary inference examples: carnivores, dengue and yeast, and observe a greater than 128-fold speedup over the CPU implementation for codon-based models and greater than 8-fold speedup for nucleotide-based models. As a practical demonstration, we also estimate the timing of the first introduction of West Nile virus into the continental Unites States under a codon model with a relaxed molecular clock from 104 full viral genomes, an inference task previously intractable. We provide an implementation of our GPU algorithms in BEAGLE v4.0.0, an open source library for statistical phylogenetics that enables parallel calculations on multi-core CPUs and GPUs.

Escherichia coli ST8196 is a novel, locally evolved, and extensively drug resistant pathogenic lineage within the ST131 clonal complex.

The H30Rx subclade of Escherichia coli ST131 is a clinically important, globally dispersed pathogenic lineage that typically displays resistance to fluoroquinolones and extended spectrum ß-lactams. Isolates EC233 and EC234, variants of ST131-H30Rx with a novel sequence type (ST) 8196, isolated from unrelated patients presenting with bacteraemia at a Sydney Hospital in 2014 are characterised here. EC233 and EC234 are phylogroup B2, serotype O25:H4A, and resistant to ampicillin, amoxicillin, cefoxitin, ceftazidime, ceftriaxone, ciprofloxacin, norfloxacin and gentamicin and are likely clonal. Both harbour an IncFII_2 plasmid (pSPRC_Ec234-FII) that carries most of the resistance genes on an IS26 associated translocatable unit, two small plasmids and a novel IncI1 plasmid (pSPRC_Ec234-I). SNP-based phylogenetic analysis of the core genome of representatives within the ST131 clonal complex places both isolates in a subclade with three clinical Australian ST131-H30Rx clade-C isolates. A MrBayes phylogeny analysis of EC233 and EC234 indicates ST8196 share a most recent common ancestor with ST131-H30Rx strain EC70 isolated from the same hospital in 2013. Our study identified genomic hallmarks that define the ST131-H30Rx subclade in the ST8196 isolates and highlights a need for unbiased genomic surveillance approaches to identify novel high-risk MDR E. coli pathogens that impact healthcare facilities.

Systematic Exploration of the High Likelihood Set of Phylogenetic Tree Topologies.

Bayesian Markov chain Monte Carlo explores tree space slowly, in part because it frequently returns to the same tree topology. An alternative strategy would be to explore tree space systematically, and never return to the same topology. In this article, we present an efficient parallelized method to map out the high likelihood set of phylogenetic tree topologies via systematic search, which we show to be a good approximation of the high posterior set of tree topologies on the data sets analyzed. Here, "likelihood" of a topology refers to the tree likelihood for the corresponding tree with optimized branch lengths. We call this method "phylogenetic topographer" (PT). The PT strategy is very simple: starting in a number of local topology maxima (obtained by hill-climbing from random starting points), explore out using local topology rearrangements, only continuing through topologies that are better than some likelihood threshold below the best observed topology. We show that the normalized topology likelihoods are a useful proxy for the Bayesian posterior probability of those topologies. By using a nonblocking hash table keyed on unique representations of tree topologies, we avoid visiting topologies more than once across all concurrent threads exploring tree space. We demonstrate that PT can be used directly to approximate a Bayesian consensus tree topology. When combined with an accurate means of evaluating per-topology marginal likelihoods, PT gives an alternative procedure for obtaining Bayesian posterior distributions on phylogenetic tree topologies.

19 Dubious Ways to Compute the Marginal Likelihood of a Phylogenetic Tree Topology.

The marginal likelihood of a model is a key quantity for assessing the evidence provided by the data in support of a model. The marginal likelihood is the normalizing constant for the posterior density, obtained by integrating the product of the likelihood and the prior with respect to model parameters. Thus, the computational burden of computing the marginal likelihood scales with the dimension of the parameter space. In phylogenetics, where we work with tree topologies that are high-dimensional models, standard approaches to computing marginal likelihoods are very slow. Here, we study methods to quickly compute the marginal likelihood of a single fixed tree topology. We benchmark the speed and accuracy of 19 different methods to compute the marginal likelihood of phylogenetic topologies on a suite of real data sets under the JC69 model. These methods include several new ones that we develop explicitly to solve this problem, as well as existing algorithms that we apply to phylogenetic models for the first time. Altogether, our results show that the accuracy of these methods varies widely, and that accuracy does not necessarily correlate with computational burden. Our newly developed methods are orders of magnitude faster than standard approaches, and in some cases, their accuracy rivals the best established estimators.

BEAST 2.5: An advanced software platform for Bayesian evolutionary analysis.

Elaboration of Bayesian phylogenetic inference methods has continued at pace in recent years with major new advances in nearly all aspects of the joint modelling of evolutionary data. It is increasingly appreciated that some evolutionary questions can only be adequately answered by combining evidence from multiple independent sources of data, including genome sequences, sampling dates, phenotypic data, radiocarbon dates, fossil occurrences, and biogeographic range information among others. Including all relevant data into a single joint model is very challenging both conceptually and computationally. Advanced computational software packages that allow robust development of compatible (sub-)models which can be composed into a full model hierarchy have played a key role in these developments. Developing such software frameworks is increasingly a major scientific activity in its own right, and comes with specific challenges, from practical software design, development and engineering challenges to statistical and conceptual modelling challenges. BEAST 2 is one such computational software platform, and was first announced over 4 years ago. Here we describe a series of major new developments in the BEAST 2 core platform and model hierarchy that have occurred since the first release of the software, culminating in the recent 2.5 release.

Identification of a novel lineage of plasmids within phylogenetically diverse subclades of IncHI2-ST1 plasmids.

IncHI2-ST1 plasmids play an important role in co-mobilizing genes conferring resistance to critically important antibiotics and heavy metals. Here we present the identification and analysis of IncHI2-ST1 plasmid pSPRC-Echo1, isolated from an Enterobacter hormaechei strain from a Sydney hospital, which predates other multi-drug resistant IncHI2-ST1 plasmids reported from Australia. Our time-resolved phylogeny analysis indicates pSPRC-Echo1 represents a new lineage of IncHI2-ST1 plasmids and show how their diversification relates to the era of antibiotics.

Evaluating probabilistic programming and fast variational Bayesian inference in phylogenetics.

Recent advances in statistical machine learning techniques have led to the creation of probabilistic programming frameworks. These frameworks enable probabilistic models to be rapidly prototyped and fit to data using scalable approximation methods such as variational inference. In this work, we explore the use of the Stan language for probabilistic programming in application to phylogenetic models. We show that many commonly used phylogenetic models including the general time reversible substitution model, rate heterogeneity among sites, and a range of coalescent models can be implemented using a probabilistic programming language. The posterior probability distributions obtained via the black box variational inference engine in Stan were compared to those obtained with reference implementations of Markov chain Monte Carlo (MCMC) for phylogenetic inference. We find that black box variational inference in Stan is less accurate than MCMC methods for phylogenetic models, but requires far less compute time. Finally, we evaluate a custom implementation of mean-field variational inference on the Jukes-Cantor substitution model and show that a specialized implementation of variational inference can be two orders of magnitude faster and more accurate than a general purpose probabilistic implementation.

Local and relaxed clocks: the best of both worlds.

Time-resolved phylogenetic methods use information about the time of sample collection to estimate the rate of evolution. Originally, the models used to estimate evolutionary rates were quite simple, assuming that all lineages evolve at the same rate, an assumption commonly known as the molecular clock. Richer and more complex models have since been introduced to capture the phenomenon of substitution rate variation among lineages. Two well known model extensions are the local clock, wherein all lineages in a clade share a common substitution rate, and the uncorrelated relaxed clock, wherein the substitution rate on each lineage is independent from other lineages while being constrained to fit some parametric distribution. We introduce a further model extension, called the flexible local clock (FLC), which provides a flexible framework to combine relaxed clock models with local clock models. We evaluate the flexible local clock on simulated and real datasets and show that it provides substantially improved fit to an influenza dataset. An implementation of the model is available for download from https://www.github.com/4ment/flc.

The Biological Object Notation (BON): a structured file format for biological data.

The large size and high complexity of biological data can represent a major methodological challenge for the analysis and exchange of data sets between computers and applications. There has also been a substantial increase in the amount of metadata associated with biological data sets, which is being increasingly incorporated into existing data formats. Despite the existence of structured formats based on XML, biological data sets are mainly formatted using unstructured file formats, and the incorporation of metadata results in increasingly complex parsing routines such that they become more error prone. To overcome these problems, we present the "biological object notation" (BON) format, a new way to exchange and parse nearly all biological data sets more efficiently and with less error than other currently available formats. Based on JavaScript Object Notation (JSON), BON simplifies parsing by clearly separating the biological data from its metadata and reduces complexity compared to XML based formats. The ability to selectively compress data up to 87% compared to other file formats and the reduced complexity results in improved transfer times and less error prone applications.

Effective Online Bayesian Phylogenetics via Sequential Monte Carlo with Guided Proposals.

Modern infectious disease outbreak surveillance produces continuous streams of sequence data which require phylogenetic analysis as data arrives. Current software packages for Bayesian phylogenetic inference are unable to quickly incorporate new sequences as they become available, making them less useful for dynamically unfolding evolutionary stories. This limitation can be addressed by applying a class of Bayesian statistical inference algorithms called sequential Monte Carlo (SMC) to conduct online inference, wherein new data can be continuously incorporated to update the estimate of the posterior probability distribution. In this article, we describe and evaluate several different online phylogenetic sequential Monte Carlo (OPSMC) algorithms. We show that proposing new phylogenies with a density similar to the Bayesian prior suffers from poor performance, and we develop "guided" proposals that better match the proposal density to the posterior. Furthermore, we show that the simplest guided proposals can exhibit pathological behavior in some situations, leading to poor results, and that the situation can be resolved by heating the proposal density. The results demonstrate that relative to the widely used MCMC-based algorithm implemented in MrBayes, the total time required to compute a series of phylogenetic posteriors as sequences arrive can be significantly reduced by the use of OPSMC, without incurring a significant loss in accuracy.

A Surrogate Function for One-Dimensional Phylogenetic Likelihoods.

Phylogenetics has seen a steady increase in data set size and substitution model complexity, which require increasing amounts of computational power to compute likelihoods. This motivates strategies to approximate the likelihood functions for branch length optimization and Bayesian sampling. In this article, we develop an approximation to the 1D likelihood function as parametrized by a single branch length. Our method uses a four-parameter surrogate function abstracted from the simplest phylogenetic likelihood function, the binary symmetric model. We show that it offers a surrogate that can be fit over a variety of branch lengths, that it is applicable to a wide variety of models and trees, and that it can be used effectively as a proposal mechanism for Bayesian sampling. The method is implemented as a stand-alone open-source C library for calling from phylogenetics algorithms; it has proven essential for good performance of our online phylogenetic algorithm sts.

The impact of migratory flyways on the spread of avian influenza virus in North America.

BACKGROUND: Wild birds are the major reservoir hosts for influenza A viruses (AIVs) and have been implicated in the emergence of pandemic events in livestock and human populations. Understanding how AIVs spread within and across continents is therefore critical to the development of successful strategies to manage and reduce the impact of influenza outbreaks. In North America many bird species undergo seasonal migratory movements along a North-South axis, thereby providing opportunities for viruses to spread over long distances. However, the role played by such avian flyways in shaping the genetic structure of AIV populations remains uncertain. RESULTS: To assess the relative contribution of bird migration along flyways to the genetic structure of AIV we performed a large-scale phylogeographic study of viruses sampled in the USA and Canada, involving the analysis of 3805 to 4505 sequences from 36 to 38 geographic localities depending on the gene segment data set. To assist in this we developed a maximum likelihood-based genetic algorithm to explore a wide range of complex spatial models, depicting a more complete picture of the migration network than determined previously. CONCLUSIONS: Based on phylogenies estimated from nucleotide sequence data sets, our results show that AIV migration rates are significantly higher within than between flyways, indicating that the migratory patterns of birds play a key role in viral dispersal. These findings provide valuable insights into the evolution, maintenance and transmission of AIVs, in turn allowing the development of improved programs for surveillance and risk assessment.

Seqotron: a user-friendly sequence editor for Mac OS X.

BACKGROUND: Accurate multiple sequence alignment is central to bioinformatics and molecular evolutionary analyses. Although sophisticated sequence alignment programs are available, manual adjustments are often required to improve alignment quality. Unfortunately, few programs offer a simple and intuitive way to edit sequence alignments. RESULTS: We present Seqotron, a sequence editor that reads and writes files in a wide variety of sequence formats. Sequences can be easily aligned and manually edited using the mouse and keyboard. The program also allows the user to estimate both phylogenetic trees and distance matrices. CONCLUSIONS: Seqotron will benefit researchers who need to manipulate and align complex sequence data. Seqotron is a Mac OS X compatible open source project and is available from Github https://github.com/4ment/seqotron/.

Eighteenth century Yersinia pestis genomes reveal the long-term persistence of an historical plague focus.

The 14th-18th century pandemic of Yersinia pestis caused devastating disease outbreaks in Europe for almost 400 years. The reasons for plague's persistence and abrupt disappearance in Europe are poorly understood, but could have been due to either the presence of now-extinct plague foci in Europe itself, or successive disease introductions from other locations. Here we present five Y. pestis genomes from one of the last European outbreaks of plague, from 1722 in Marseille, France. The lineage identified has not been found in any extant Y. pestis foci sampled to date, and has its ancestry in strains obtained from victims of the 14th century Black Death. These data suggest the existence of a previously uncharacterized historical plague focus that persisted for at least three centuries. We propose that this disease source may have been responsible for the many resurgences of plague in Europe following the Black Death.

Genome-scale rates of evolutionary change in bacteria.

Estimating the rates at which bacterial genomes evolve is critical to understanding major evolutionary and ecological processes such as disease emergence, long-term host-pathogen associations and short-term transmission patterns. The surge in bacterial genomic data sets provides a new opportunity to estimate these rates and reveal the factors that shape bacterial evolutionary dynamics. For many organisms estimates of evolutionary rate display an inverse association with the time-scale over which the data are sampled. However, this relationship remains unexplored in bacteria due to the difficulty in estimating genome-wide evolutionary rates, which are impacted by the extent of temporal structure in the data and the prevalence of recombination. We collected 36 whole genome sequence data sets from 16 species of bacterial pathogens to systematically estimate and compare their evolutionary rates and assess the extent of temporal structure in the absence of recombination. The majority (28/36) of data sets possessed sufficient clock-like structure to robustly estimate evolutionary rates. However, in some species reliable estimates were not possible even with 'ancient DNA' data sampled over many centuries, suggesting that they evolve very slowly or that they display extensive rate variation among lineages. The robustly estimated evolutionary rates spanned several orders of magnitude, from approximately 10-5 to 10-8 nucleotide substitutions per site year-1. This variation was negatively associated with sampling time, with this relationship best described by an exponential decay curve. To avoid potential estimation biases, such time-dependency should be considered when inferring evolutionary time-scales in bacteria.

Evolution of Influenza B Virus in Kuala Lumpur, Malaysia, between 1995 and 2008.

Influenza B virus causes significant disease but remains understudied in tropical regions. We sequenced 72 influenza B viruses collected in Kuala Lumpur, Malaysia, from 1995 to 2008. The predominant circulating lineage (Victoria or Yamagata) changed every 1 to 3 years, and these shifts were associated with increased incidence of influenza B. We also found poor lineage matches with recommended influenza virus vaccine strains. While most influenza B virus lineages in Malaysia were short-lived, one circulated for 3 to 4 years.