Adaptive MCMC in Bayesian phylogenetics: an application to analyzing partitioned data in BEAST

Evolution is coupled with branching across many granularities of life

Across many scales of life, the rate of evolutionary change is often accelerated at the time when one lineage splits into two. The emergence of novel protein function can be facilitated by gene duplication (neofunctionalization); rapid morphological change is often accompanied by speciation (punctuated equilibrium); and the establishment of cultural identity is frequently driven by sociopolitical division (schismogenesis). In each case, the changes resist re-homogenization; promoting assortment into distinct lineages that are susceptible to different selective pressures, leading to rapid divergence. The traditional gradualistic view of evolution struggles to detect this phenomenon. We propose a probabilistic framework that constructs phylogenies, tests for saltative branching and improves divergence time estimation by estimating the independent contributions of gradual and abrupt change on each lineage. We provide evidence of saltative branching for proteins (aminoacyl transfer RNA (tRNA) synthetases), animal morphologies (cephalopods) and human languages (Indo-European). These three cases provide unique insights: for aminoacyl-tRNA synthetases, the trees are substantially different from those obtained under gradualist models; we estimate that 99% of cephalopod morphological changes coincided with speciation events; and Indo-European dispersal is estimated to have started around 6000 BCE, corroborating the recently proposed hybrid explanation. Our open-source code is available under a General Public License.

Viral introductions and return to baseline sexual behaviors maintain low-level mpox incidence in Los Angeles County, USA, 2023-2024

In 2022, mpox clade llb disseminated around the world, causing outbreaks in more than 117 countries. Despite the decay of the 2022 epidemic and the expected accumulation of immunity within queer sexual networks, mpox continues to persist at low incidence in North America without extinction, raising concerns of future outbreaks. We combined phylodynamic inference and microsimulation modeling to understand the heterogeneous dynamics governing local mpox persistence in Los Angeles County (LAC) from 2023-2024. Our Bayesian phylodynamic analysis revealed a time-varying pattern of viral importations into the county that seeded a heavy-tailed distribution of mpox outbreak clusters that display a "stuttering chains" dynamic. Our phylodynamics-informed microsimulation model demonstrated that the persistent number of mpox cases in LAC can be explained by a combination of waves of viral introductions and a return to near-baseline sexual behaviors that were altered during the 2022 epidemic. Finally, our counterfactual scenario modeling showed that public health interventions that either promote increased isolation of symptomatic, infectious individuals or enact behavior-modifying campaigns during the periods with the highest viral importation intensity are both actionable and effective at curbing mpox cases. Our work highlights the heterogeneous factors that maintain present-day mpox dynamics in a large, urban US county and describes how to leverage these results to design timely and community-centered public health interventions.

Mediating role of systemic inflammation in the association between volatile organic compounds exposure and periodontitis: NHANES 2011-2014

BACKGROUND

Volatile organic compounds (VOCs) are ubiquitous environmental pollutants which have been suggested to have adverse effects on human health. While the influence of environmental pollutant exposures on periodontitis has attracted elevating attention in recent years, the epidemiological evidence on the association between VOCs exposure and periodontitis was scarce. This study aimed to investigate the potential mediating role of systemic inflammation factors in the complex association between VOCs exposure and periodontitis.

METHODS

Utilizing data from the National Health and Nutrition Examination Survey (NHANES) 2011-2014, we examined the impacts of VOCs exposure on periodontitis. Concentrations of urinary metabolites of VOCs (mVOCs) were measured using electrospray tandem mass spectrometry to evaluate internal VOCs exposure. Multivariable logistic regression, restricted cubic spline regression (RCS), Bayesian kernel machine regression (BKMR) and Quantile g-computation (QGC) models were performed to investigate the impacts of VOCs exposure on periodontitis. Mediation models were applied to assess the mediated effects of systemic inflammation on the association between mixed VOCs exposure and periodontitis. Besides, we analyzed the association between mixed VOCs exposure and periodontitis in stratified age, gender, and smoking status subgroups.

RESULTS

1,551 participants were ultimately included for further analyses, of whom 45.20% suffering from periodontitis. Multivariable logistic regression and RCS identified positive associations between single urinary mVOCs and periodontitis (P < 0.05). Notably, BKMR and QGC models suggested that mixed VOCs exposure was significantly associated with periodontitis, with 2-Aminothiazoline-4-carboxylic acid (ATCA) contributing the most (conditional posterior inclusion probability = 0.997). Moreover, systemic inflammation markers (leukocyte and lymphocyte counts) were found to partly mediate the association between VOCs exposure and periodontitis (P < 0.05). No interaction effect was identified between mixed VOCs exposure and periodontitis in age, gender and smoking status subgroups (P > 0.05).

CONCLUSION

This study demonstrated a positive association between VOCs exposure and periodontitis, which was potentially mediated by systemic inflammation factors. Further longitudinal researches are demanded to clarify the underlying mechanisms.

Spatiotemporal and Species-Crossing Transmission Dynamics of Subclade 2.3.4.4b H5Nx HPAIVs

Subclade 2.3.4.4b H5Nx highly pathogenic avian influenza (HPAI) viruses, emerged in 2013 with multiple subtypes of H5N8, H5N1, and H5N6, had unprecedently caused a global epizootic by H5N1 since 2021, which had devasted multiple species of wild birds, poultry, and wild mammals (terrestrial and marine) with a high mortality, causing severe ecological damage. The infected wild mammals may become new "mixers" for influenza viruses, posing the potential transmission to human. Frequent outbreaks of subclade 2.3.4.4b H5Nx viruses among wild birds and poultry had exposed major gaps in our knowledge on their evolution, spatiotemporal diffusion, and species-crossing transmission. Here, we integrated the phylogenetic and epidemiological data of subclade 2.3.4.4b H5Nx viruses in public database and used Bayesian phylodynamic analysis to reveal the pattern of the global large-scale transmission. Phylogenic analysis demonstrated that the HA gene of these viruses diverged into two dominant clusters around 2015 and 2016. The Bayesian phylodynamic analysis illustrated that the viruses presented spatiotemporally complex transmission network with geographical and host relative expansion and recombination with different subtypes of NA segment. Spatially, the Russian Federation (Siberia) was identified as the primary hub for virus transmission, which was further facilitated by the establishment of strong epidemiological linkages between West Europe and broader regions, such as North America. As for hosts, wild Anseriformes were the primary species for the virus spillover, contributing to the spatial expansion and rapid diffusion globally of subclade 2.3.4.4b viruses. We investigated the phylogeny of subclade 2.3.4.4b H5Nx viruses and the spatiotemporal pattern of transmission with initial location and the primary host, which could provide comprehensive insights for subclade 2.3.4.4b H5Nx viruses. Due to the wild birds involved the widespread of subclade 2.3.4.4b H5Nx viruses, the epizootics in poultry are inevitable, so we highly recommend to apply the policy of culling plus with vaccination to protect the poultry industry and potentially protect the public health.

Underdetected dispersal and extensive local transmission drove the 2022 mpox epidemic

The World Health Organization declared mpox a public health emergency of international concern in July 2022. To investigate global mpox transmission and population-level changes associated with controlling spread, we built phylogeographic and phylodynamic models to analyze MPXV genomes from five global regions together with air traffic and epidemiological data. Our models reveal community transmission prior to detection, changes in case reporting throughout the epidemic, and a large degree of transmission heterogeneity. We find that viral introductions played a limited role in prolonging spread after initial dissemination, suggesting that travel bans would have had only a minor impact. We find that mpox transmission in North America began declining before more than 10% of high-risk individuals in the USA had vaccine-induced immunity. Our findings highlight the importance of broader routine specimen screening surveillance for emerging infectious diseases and of joint integration of genomic and epidemiological information for early outbreak control.

MASCOT-Skyline integrates population and migration dynamics to enhance phylogeographic reconstructions

The spread of infectious diseases is shaped by spatial and temporal aspects, such as host population structure or changes in the transmission rate or number of infected individuals over time. These spatiotemporal dynamics are imprinted in the genome of pathogens and can be recovered from those genomes using phylodynamics methods. However, phylodynamic methods typically quantify either the temporal or spatial transmission dynamics, which leads to unclear biases, as one can potentially not be inferred without the other. Here, we address this challenge by introducing a structured coalescent skyline approach, MASCOT-Skyline that allows us to jointly infer spatial and temporal transmission dynamics of infectious diseases using Markov chain Monte Carlo inference. To do so, we model the effective population size dynamics in different locations using a non-parametric function, allowing us to approximate a range of population size dynamics. We show, using a range of different viral outbreak datasets, potential issues with phylogeographic methods. We then use these viral datasets to motivate simulations of outbreaks that illuminate the nature of biases present in the different phylogeographic methods. We show that spatial and temporal dynamics should be modeled jointly even if one seeks to recover just one of the two. Further, we showcase conditions under which we can expect phylogeographic analyses to be biased, particularly different subsampling approaches, as well as provide recommendations of when we can expect them to perform well. We implemented MASCOT-Skyline as part of the open-source software package MASCOT for the Bayesian phylodynamics platform BEAST2.

HetMM: A Michaelis-Menten model for non-homogeneous enzyme mixtures

The Michaelis-Menten model requires its reaction velocities to come from a preparation of homogeneous enzymes, with identical or near-identical catalytic activities. However, this condition is not always met. We introduce a kinetic model that relaxes this requirement, by assuming there are an unknown number of enzyme species drawn from a probability distribution whose standard deviation is estimated. Through simulation studies, we demonstrate the method accurately discriminates between homogeneous and heterogeneous data, even with moderate levels of experimental error. We applied this model to three homogeneous and three heterogeneous biological systems, showing that the standard and heterogeneous models outperform respectively. Lastly, we show that heterogeneity is not readily distinguished from negatively cooperative binding under the Hill model. These two distinct attributes-inequality in catalytic ability and interference between binding sites-yield similar Michaelis-Menten curves that are not readily resolved without further experimentation. Our user-friendly software package allows homogeneity testing and parameter estimation.

Genotype F of Echovirus 25 with multiple recombination pattern have been persistently and extensively circulating in Chinese mainland

Echovirus 25 (E25), a member of the Enterovirus B (EV-B) species, can cause aseptic meningitis (AM), viral meningitis (VM), and acute flaccid paralysis (AFP). However, systematic studies on the molecular epidemiology of E25, especially those concerning its evolution and recombination, are lacking. In this study, 18 strains of E25, isolated from seven provinces of China between 2009 and 2018, were collected based on the Chinese hand, foot, and mouth disease (HFMD) surveillance network, and 95 sequences downloaded from GenBank were also screened. Based on the phylogenetic analysis of 113 full-length VP1 sequences worldwide, globally occurring E25 strains were classified into 9 genotypes (A-I), and genotype F was the dominant genotype in the Chinese mainland. The average nucleotide substitution rate of E25 was 6.08 × 10-3 substitutions/site/year, and six important transmission routes were identified worldwide. Seventeen recombination patterns were determined, of which genotype F can be divided into 9 recombination patterns. A positive selector site was found in the capsid protein region of genotype F. Recombination analysis and pressure selection analysis for genotype F showed multiple recombination patterns and evolution characteristics, which may be responsible for it being the dominant genotype in the Chinese mainland. This study provides a theoretical basis for the subsequent prevention and control of E25.

Scalable Bayesian Divergence Time Estimation With Ratio Transformations

Divergence time estimation is crucial to provide temporal signals for dating biologically important events from species divergence to viral transmissions in space and time. With the advent of high-throughput sequencing, recent Bayesian phylogenetic studies have analyzed hundreds to thousands of sequences. Such large-scale analyses challenge divergence time reconstruction by requiring inference on highly correlated internal node heights that often become computationally infeasible. To overcome this limitation, we explore a ratio transformation that maps the original $N-1$ internal node heights into a space of one height parameter and $N-2$ ratio parameters. To make the analyses scalable, we develop a collection of linear-time algorithms to compute the gradient and Jacobian-associated terms of the log-likelihood with respect to these ratios. We then apply Hamiltonian Monte Carlo sampling with the ratio transform in a Bayesian framework to learn the divergence times in 4 pathogenic viruses (West Nile virus, rabies virus, Lassa virus, and Ebola virus) and the coralline red algae. Our method both resolves a mixing issue in the West Nile virus example and improves inference efficiency by at least 5-fold for the Lassa and rabies virus examples as well as for the algae example. Our method now also makes it computationally feasible to incorporate mixed-effects molecular clock models for the Ebola virus example, confirms the findings from the original study, and reveals clearer multimodal distributions of the divergence times of some clades of interest.

Local-Scale phylodynamics reveal differential community impact of SARS-CoV-2 in metropolitan US county

SARS-CoV-2 transmission is largely driven by heterogeneous dynamics at a local scale, leaving local health departments to design interventions with limited information. We analyzed SARS-CoV-2 genomes sampled between February 2020 and March 2022 jointly with epidemiological and cell phone mobility data to investigate fine scale spatiotemporal SARS-CoV-2 transmission dynamics in King County, Washington, a diverse, metropolitan US county. We applied an approximate structured coalescent approach to model transmission within and between North King County and South King County alongside the rate of outside introductions into the county. Our phylodynamic analyses reveal that following stay-at-home orders, the epidemic trajectories of North and South King County began to diverge. We find that South King County consistently had more reported and estimated cases, COVID-19 hospitalizations, and longer persistence of local viral transmission when compared to North King County, where viral importations from outside drove a larger proportion of new cases. Using mobility and demographic data, we also find that South King County experienced a more modest and less sustained reduction in mobility following stay-at-home orders than North King County, while also bearing more socioeconomic inequities that might contribute to a disproportionate burden of SARS-CoV-2 transmission. Overall, our findings suggest a role for local-scale phylodynamics in understanding the heterogeneous transmission landscape.

Molecular Characteristics and Genetic Evolution of Echovirus 33 in Mainland of China

Echovirus, a member of the Enterovirus B (EV-B) family, has led to numerous outbreaks and pandemics, causing a broad spectrum of diseases. Based on the national hand, foot, and mouth disease (HFMD) surveillance system, seven strains of echovirus 33 (E33) were isolated from Mainland of China between 2010 and 2018. The whole genomes of these strains were isolated and sequenced, and phylogenetic trees were constructed based on the gene sequences in different regions of the EV-B prototype strains. It was found that E33 may be recombined in the P2 and P3 regions. Five genotypes (A–E) were defined based on the entire VP1 region of E33, of which the C gene subtype was the dominant gene subtype at present. Recombinant analysis showed that genotype C strains likely recombined with EV-B80, EV-B85, E13, and CVA9 in the P2 and P3 regions, while genotype E had the possibility of recombination with CVB3, E3, E6, and E4. Results of Bayesian analysis indicated that E33 may have appeared around 1955 (95% confidence interval: 1945–1959), with a high evolutionary rate of 1.11 × 10⁻² substitution/site/year (95% highest posterior density (HPD): 8.17 × 10⁻³ to 1.4 × 10⁻² substitution/site/year). According to spatial transmission route analysis, two significant transmission routes were identified: from Australia to India and from Oman to Thailand, which the E33 strain in Mainland of China likely introduced from Mexico and India. In conclusion, our study fills the gaps in the evolutionary analysis of E33 and can provide important data for enterovirus surveillance.

Tracing the international arrivals of SARS-CoV-2 Omicron variants after Aotearoa New Zealand reopened its border

In the second quarter of 2022, there was a global surge of emergent SARS-CoV-2 lineages that had a distinct growth advantage over then-dominant Omicron BA.1 and BA.2 lineages. By generating 10,403 Omicron genomes, we show that Aotearoa New Zealand observed an influx of these immune-evasive variants (BA.2.12.1, BA.4, and BA.5) through the border. This is explained by the return to significant levels of international travel following the border's reopening in March 2022. We estimate one Omicron transmission event from the border to the community for every ~5,000 passenger arrivals at the current levels of travel and restriction. Although most of these introductions did not instigate any detected onward transmission, a small minority triggered large outbreaks. Genomic surveillance at the border provides a lens on the rate at which new variants might gain a foothold and trigger new waves of infection.

Scalable Bayesian phylogenetics

Recent advances in Bayesian phylogenetics offer substantial computational savings to accommodate increased genomic sampling that challenges traditional inference methods. In this review, we begin with a brief summary of the Bayesian phylogenetic framework, and then conceptualize a variety of methods to improve posterior approximations via Markov chain Monte Carlo (MCMC) sampling. Specifically, we discuss methods to improve the speed of likelihood calculations, reduce MCMC burn-in, and generate better MCMC proposals. We apply several of these techniques to study the evolution of HIV virulence along a 1536-tip phylogeny and estimate the internal node heights of a 1000-tip SARS-CoV-2 phylogenetic tree in order to illustrate the speed-up of such analyses using current state-of-the-art approaches. We conclude our review with a discussion of promising alternatives to MCMC that approximate the phylogenetic posterior. This article is part of a discussion meeting issue 'Genomic population structures of microbial pathogens'.

Data integration in Bayesian phylogenetics

Researchers studying the evolution of viral pathogens and other organisms increasingly encounter and use large and complex data sets from multiple different sources. Statistical research in Bayesian phylogenetics has risen to this challenge. Researchers use phylogenetics not only to reconstruct the evolutionary history of a group of organisms, but also to understand the processes that guide its evolution and spread through space and time. To this end, it is now the norm to integrate numerous sources of data. For example, epidemiologists studying the spread of a virus through a region incorporate data including genetic sequences (e.g. DNA), time, location (both continuous and discrete) and environmental covariates (e.g. social connectivity between regions) into a coherent statistical model. Evolutionary biologists routinely do the same with genetic sequences, location, time, fossil and modern phenotypes, and ecological covariates. These complex, hierarchical models readily accommodate both discrete and continuous data and have enormous combined discrete/continuous parameter spaces including, at a minimum, phylogenetic tree topologies and branch lengths. The increased size and complexity of these statistical models have spurred advances in computational methods to make them tractable. We discuss both the modeling and computational advances below, as well as unsolved problems and areas of active research.

OUP accepted manuscript

As genomic sequence data become increasingly available, inferring the phylogeny of the species as that of concatenated genomic data can be enticing. However, this approach makes for a biased estimator of branch lengths and substitution rates and an inconsistent estimator of tree topology. Bayesian multispecies coalescent (MSC) methods address these issues. This is achieved by constraining a set of gene trees within a species tree and jointly inferring both under a Bayesian framework. However, this approach comes at the cost of increased computational demand. Here, we introduce StarBeast3—a software package for efficient Bayesian inference under the MSC model via Markov chain Monte Carlo. We gain efficiency by introducing cutting-edge proposal kernels and adaptive operators, and StarBeast3 is particularly efficient when a relaxed clock model is applied. Furthermore, gene-tree inference is parallelized, allowing the software to scale with the size of the problem. We validated our software and benchmarked its performance using three real and two synthetic data sets. Our results indicate that StarBeast3 is up to one-and-a-half orders of magnitude faster than StarBeast2, and therefore more than two orders faster than *BEAST, depending on the data set and on the parameter, and can achieve convergence on large data sets with hundreds of genes. StarBeast3 is open-source and is easy to set up with a friendly graphical user interface. [Adaptive; Bayesian inference; BEAST 2; effective population sizes; high performance; multispecies coalescent; parallelization; phylogenetics.]

Mimicry can drive convergence in structural and light transmission features of transparent wings in Lepidoptera

Müllerian mimicry is a positive interspecific interaction, whereby co-occurring defended prey species share a common aposematic signal. In Lepidoptera, aposematic species typically harbour conspicuous opaque wing colour patterns with convergent optical properties among co-mimetic species. Surprisingly, some aposematic mimetic species have partially transparent wings, raising the questions of whether optical properties of transparent patches are also convergent, and of how transparency is achieved. Here, we conducted a comparative study of wing optics, micro and nanostructures in neotropical mimetic clearwing Lepidoptera, using spectrophotometry and microscopy imaging. We show that transparency, as perceived by predators, is convergent among co-mimics in some mimicry rings. Underlying micro- and nanostructures are also sometimes convergent despite a large structural diversity. We reveal that while transparency is primarily produced by microstructure modifications, nanostructures largely influence light transmission, potentially enabling additional fine-tuning in transmission properties. This study shows that transparency might not only enable camouflage but can also be part of aposematic signals.

Viral genomes reveal patterns of the SARS-CoV-2 outbreak in Washington State

The rapid spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has gravely affected societies around the world. Outbreaks in different parts of the globe have been shaped by repeated introductions of new viral lineages and subsequent local transmission of those lineages. Here, we sequenced 3940 SARS-CoV-2 viral genomes from Washington State (USA) to characterize how the spread of SARS-CoV-2 in Washington State in early 2020 was shaped by differences in timing of mitigation strategies across counties and by repeated introductions of viral lineages into the state. In addition, we show that the increase in frequency of a potentially more transmissible viral variant (614G) over time can potentially be explained by regional mobility differences and multiple introductions of 614G but not the other variant (614D) into the state. At an individual level, we observed evidence of higher viral loads in patients infected with the 614G variant. However, using clinical records data, we did not find any evidence that the 614G variant affects clinical severity or patient outcomes. Overall, this suggests that with regard to D614G, the behavior of individuals has been more important in shaping the course of the pandemic in Washington State than this variant of the virus.

Adaptive dating and fast proposals: Revisiting the phylogenetic relaxed clock model

Relaxed clock models enable estimation of molecular substitution rates across lineages and are widely used in phylogenetics for dating evolutionary divergence times. Under the (uncorrelated) relaxed clock model, tree branches are associated with molecular substitution rates which are independently and identically distributed. In this article we delved into the internal complexities of the relaxed clock model in order to develop efficient MCMC operators for Bayesian phylogenetic inference. We compared three substitution rate parameterisations, introduced an adaptive operator which learns the weights of other operators during MCMC, and we explored how relaxed clock model estimation can benefit from two cutting-edge proposal kernels: the AVMVN and Bactrian kernels. This work has produced an operator scheme that is up to 65 times more efficient at exploring continuous relaxed clock parameters compared with previous setups, depending on the dataset. Finally, we explored variants of the standard narrow exchange operator which are specifically designed for the relaxed clock model. In the most extreme case, this new operator traversed tree space 40% more efficiently than narrow exchange. The methodologies introduced are adaptive and highly effective on short as well as long alignments. The results are available via the open source optimised relaxed clock (ORC) package for BEAST 2 under a GNU licence (https://github.com/jordandouglas/ORC).

Adaptive Tree Proposals for Bayesian Phylogenetic Inference

Bayesian inference of phylogeny with MCMC plays a key role in the study of evolution. Yet, this method still suffers from a practical challenge identified more than two decades ago: designing tree topology proposals that efficiently sample tree spaces. In this article, I introduce the concept of adaptive tree proposals for unrooted topologies, that is tree proposals adapting to the posterior distribution as it is estimated. I use this concept to elaborate two adaptive variants of existing proposals and an adaptive proposal based on a novel design philosophy in which the structure of the proposal is informed by the posterior distribution of trees. I investigate the performance of these proposals by first presenting a metric that captures the performance of each proposal within a mixture of proposals. Using this metric, I compare the performance of the adaptive proposals to the performance of standard and parsimony-guided proposals on 11 empirical datasets. Using adaptive proposals led to consistent performance gains and resulted in up to 18-fold increases in mixing efficiency and 6-fold increases in convergence rate without increasing the computational cost of these analyses.

Viral genomes reveal patterns of the SARS-CoV-2 outbreak in Washington State

The rapid spread of SARS-CoV-2 has gravely impacted societies around the world. Outbreaks in different parts of the globe are shaped by repeated introductions of new lineages and subsequent local transmission of those lineages. Here, we sequenced 3940 SARS-CoV-2 viral genomes from Washington State to characterize how the spread of SARS-CoV-2 in Washington State (USA) was shaped by differences in timing of mitigation strategies across counties, as well as by repeated introductions of viral lineages into the state. Additionally, we show that the increase in frequency of a potentially more transmissible viral variant (614G) over time can potentially be explained by regional mobility differences and multiple introductions of 614G, but not the other variant (614D) into the state. At an individual level, we see evidence of higher viral loads in patients infected with the 614G variant. However, using clinical records data, we do not find any evidence that the 614G variant impacts clinical severity or patient outcomes. Overall, this suggests that at least to date, the behavior of individuals has been more important in shaping the course of the pandemic than changes in the virus.

OBAMA: OBAMA for Bayesian amino-acid model averaging

Background

Bayesian analyses offer many benefits for phylogenetic, and have been popular for analysis of amino acid alignments. It is necessary to specify a substitution and site model for such analyses, and often an ad hoc, or likelihood based method is employed for choosing these models that are typically of no interest to the analysis overall.

Methods

We present a method called OBAMA that averages over substitution models and site models, thus letting the data inform model choices and taking model uncertainty into account. It uses trans-dimensional Markov Chain Monte Carlo (MCMC) proposals to switch between various empirical substitution models for amino acids such as Dayhoff, WAG, and JTT. Furthermore, it switches base frequencies from these substitution models or use base frequencies estimated based on the alignment. Finally, it switches between using gamma rate heterogeneity or not, and between using a proportion of invariable sites or not.

Results

We show that the model performs well in a simulation study. By using appropriate priors, we demonstrate both proportion of invariable sites and the shape parameter for gamma rate heterogeneity can be estimated. The OBAMA method allows taking in account model uncertainty, thus reducing bias in phylogenetic estimates. The method is implemented in the OBAMA package in BEAST 2, which is open source licensed under LGPL and allows joint tree inference under a wide range of models.

Online Bayesian Phylodynamic Inference in BEAST with Application to Epidemic Reconstruction

Reconstructing pathogen dynamics from genetic data as they become available during an outbreak or epidemic represents an important statistical scenario in which observations arrive sequentially in time and one is interested in performing inference in an "online" fashion. Widely used Bayesian phylogenetic inference packages are not set up for this purpose, generally requiring one to recompute trees and evolutionary model parameters de novo when new data arrive. To accommodate increasing data flow in a Bayesian phylogenetic framework, we introduce a methodology to efficiently update the posterior distribution with newly available genetic data. Our procedure is implemented in the BEAST 1.10 software package, and relies on a distance-based measure to insert new taxa into the current estimate of the phylogeny and imputes plausible values for new model parameters to accommodate growing dimensionality. This augmentation creates informed starting values and re-uses optimally tuned transition kernels for posterior exploration of growing data sets, reducing the time necessary to converge to target posterior distributions. We apply our framework to data from the recent West African Ebola virus epidemic and demonstrate a considerable reduction in time required to obtain posterior estimates at different time points of the outbreak. Beyond epidemic monitoring, this framework easily finds other applications within the phylogenetics community, where changes in the data-in terms of alignment changes, sequence addition or removal-present common scenarios that can benefit from online inference.

Phylogenetic tree building in the genomic age

Knowing phylogenetic relationships among species is fundamental for many studies in biology. An accurate phylogenetic tree underpins our understanding of the major transitions in evolution, such as the emergence of new body plans or metabolism, and is key to inferring the origin of new genes, detecting molecular adaptation, understanding morphological character evolution and reconstructing demographic changes in recently diverged species. Although data are ever more plentiful and powerful analysis methods are available, there remain many challenges to reliable tree building. Here, we discuss the major steps of phylogenetic analysis, including identification of orthologous genes or proteins, multiple sequence alignment, and choice of substitution models and inference methodologies. Understanding the different sources of errors and the strategies to mitigate them is essential for assembling an accurate tree of life.

In Search of Covariates of HIV-1 Subtype B Spread in the United States-A Cautionary Tale of Large-Scale Bayesian Phylogeography

Infections with HIV-1 group M subtype B viruses account for the majority of the HIV epidemic in the Western world. Phylogeographic studies have placed the introduction of subtype B in the United States in New York around 1970, where it grew into a major source of spread. Currently, it is estimated that over one million people are living with HIV in the US and that most are infected with subtype B variants. Here, we aim to identify the drivers of HIV-1 subtype B dispersal in the United States by analyzing a collection of 23,588 pol sequences, collected for drug resistance testing from 45 states during 2004-2011. To this end, we introduce a workflow to reduce this large collection of data to more computationally-manageable sample sizes and apply the BEAST framework to test which covariates associate with the spread of HIV-1 across state borders. Our results show that we are able to consistently identify certain predictors of spread under reasonable run times across datasets of up to 10,000 sequences. However, the general lack of phylogenetic structure and the high uncertainty associated with HIV trees make it difficult to interpret the epidemiological relevance of the drivers of spread we are able to identify. While the workflow we present here could be applied to other virus datasets of a similar scale, the characteristic star-like shape of HIV-1 phylogenies poses a serious obstacle to reconstructing a detailed evolutionary and spatial history for HIV-1 subtype B in the US.

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.

BEAGLE 3: Improved Performance, Scaling, and Usability for a High-Performance Computing Library for Statistical Phylogenetics

BEAGLE is a high-performance likelihood-calculation library for phylogenetic inference. The BEAGLE library defines a simple, but flexible, application programming interface (API), and includes a collection of efficient implementations for calculation under a variety of evolutionary models on different hardware devices. The library has been integrated into recent versions of popular phylogenetics software packages including BEAST and MrBayes and has been widely used across a diverse range of evolutionary studies. Here, we present BEAGLE 3 with new parallel implementations, increased performance for challenging data sets, improved scalability, and better usability. We have added new OpenCL and central processing unit-threaded implementations to the library, allowing the effective utilization of a wider range of modern hardware. Further, we have extended the API and library to support concurrent computation of independent partial likelihood arrays, for increased performance of nucleotide-model analyses with greater flexibility of data partitioning. For better scalability and usability, we have improved how phylogenetic software packages use BEAGLE in multi-GPU (graphics processing unit) and cluster environments, and introduced an automated method to select the fastest device given the data set, evolutionary model, and hardware. For application developers who wish to integrate the library, we also have developed an online tutorial. To evaluate the effect of the improvements, we ran a variety of benchmarks on state-of-the-art hardware. For a partitioned exemplar analysis, we observe run-time performance improvements as high as 5.9-fold over our previous GPU implementation. BEAGLE 3 is free, open-source software licensed under the Lesser GPL and available at https://beagle-dev.github.io.

Advances in Visualization Tools for Phylogenomic and Phylodynamic Studies of Viral Diseases

Genomic and epidemiological monitoring have become an integral part of our response to emerging and ongoing epidemics of viral infectious diseases. Advances in high-throughput sequencing, including portable genomic sequencing at reduced costs and turnaround time, are paralleled by continuing developments in methodology to infer evolutionary histories (dynamics/patterns) and to identify factors driving viral spread in space and time. The traditionally static nature of visualizing phylogenetic trees that represent these evolutionary relationships/processes has also evolved, albeit perhaps at a slower rate. Advanced visualization tools with increased resolution assist in drawing conclusions from phylogenetic estimates and may even have potential to better inform public health and treatment decisions, but the design (and choice of what analyses are shown) is hindered by the complexity of information embedded within current phylogenetic models and the integration of available meta-data. In this review, we discuss visualization challenges for the interpretation and exploration of reconstructed histories of viral epidemics that arose from increasing volumes of sequence data and the wealth of additional data layers that can be integrated. We focus on solutions that address joint temporal and spatial visualization but also consider what the future may bring in terms of visualization and how this may become of value for the coming era of real-time digital pathogen surveillance, where actionable results and adequate intervention strategies need to be obtained within days.

Metagenomic sequencing at the epicenter of the Nigeria 2018 Lassa fever outbreak

The 2018 Nigerian Lassa fever season saw the largest ever recorded upsurge of cases, raising concerns over the emergence of a strain with increased transmission rate. To understand the molecular epidemiology of this upsurge, we performed, for the first time at the epicenter of an unfolding outbreak, metagenomic nanopore sequencing directly from patient samples, an approach dictated by the highly variable genome of the target pathogen. Genomic data and phylogenetic reconstructions were communicated immediately to Nigerian authorities and the World Health Organization to inform the public health response. Real-time analysis of 36 genomes and subsequent confirmation using all 120 samples sequenced in the country of origin revealed extensive diversity and phylogenetic intermingling with strains from previous years, suggesting independent zoonotic transmission events and thus allaying concerns of an emergent strain or extensive human-to-human transmission.

High-Performance Computing in Bayesian Phylogenetics and Phylodynamics Using BEAGLE

In this chapter, we focus on the computational challenges associated with statistical phylogenomics and how use of the broad-platform evolutionary analysis general likelihood evaluator (BEAGLE), a high-performance library for likelihood computation, can help to substantially reduce computation time in phylogenomic and phylodynamic analyses. We discuss computational improvements brought about by the BEAGLE library on a variety of state-of-the-art multicore hardware, and for a range of commonly used evolutionary models. For data sets of varying dimensions, we specifically focus on comparing performance in the Bayesian evolutionary analysis by sampling trees (BEAST) software between multicore central processing units (CPUs) and a wide range of graphics processing cards (GPUs). We put special emphasis on computational benchmarks from the field of phylodynamics, which combines the challenges of phylogenomics with those of modelling trait data associated with the observed sequence data. In conclusion, we show that for increasingly large molecular sequence data sets, GPUs can offer tremendous computational advancements through the use of the BEAGLE library, which is available for software packages for both Bayesian inference and maximum-likelihood frameworks.

Evolutionary and genotypic analyses of global porcine epidemic diarrhea virus strains

Porcine epidemic diarrhea virus (PEDV), which re-emerged in China in October 2010, has spread rapidly worldwide. Detailed analyses of the complete genomes of different PEDV strains are essential to understand the relationships among re-emerging and historic strains worldwide. Here, we analysed the complete genomes of 409 strains from different countries, which were classified into five subgroup strains (i.e., GI-a, GI-b, GII-a, GII-b, and GII-c). Phylogenetic study of different genes in the PEDV strains revealed that the newly discovered subgroup GII-c exhibited inconsistent topologies between the spike gene and other genes. Furthermore, recombination analysis indicated that GII-c viruses evolved from a recombinant virus that acquired the 5' part of the spike gene from the GI-a subgroup and the remaining genomic regions from the GII-a subgroup. Molecular clock analysis showed that divergence of the GII-c subgroup spike gene occurred in April 2010, suggesting that the subgroup originated from recombination events before the PEDV re-emergence outbreaks. Interestingly, Ascaris suum, a large roundworm occurring in pigs, was found to be an unusual PEDV host, providing potential support for cross-host transmission. This study has significant implications for understanding ongoing global PEDV outbreaks and will guide future efforts to develop effective preventative measures against PEDV.

Bayesian phylogenetic and phylodynamic data integration using BEAST 1.10

The Bayesian Evolutionary Analysis by Sampling Trees (BEAST) software package has become a primary tool for Bayesian phylogenetic and phylodynamic inference from genetic sequence data. BEAST unifies molecular phylogenetic reconstruction with complex discrete and continuous trait evolution, divergence-time dating, and coalescent demographic models in an efficient statistical inference engine using Markov chain Monte Carlo integration. A convenient, cross-platform, graphical user interface allows the flexible construction of complex evolutionary analyses.