Estimates of early outbreak-specific SARS-CoV-2 epidemiological parameters from genomic data

We estimate the basic reproductive number and case counts for 15 distinct Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) outbreaks, distributed across 11 populations (10 countries and one cruise ship), based solely on phylodynamic analyses of genomic data. Our results indicate that, prior to significant public health interventions, the reproductive numbers for 10 (out of 15) of these outbreaks are similar, with median posterior estimates ranging between 1.4 and 2.8. These estimates provide a view which is complementary to that provided by those based on traditional line listing data. The genomic-based view is arguably less susceptible to biases resulting from differences in testing protocols, testing intensity, and import of cases into the community of interest. In the analyses reported here, the genomic data primarily provide information regarding which samples belong to a particular outbreak. We observe that once these outbreaks are identified, the sampling dates carry the majority of the information regarding the reproductive number. Finally, we provide genome-based estimates of the cumulative number of infections for each outbreak. For 7 out of 11 of the populations studied, the number of confirmed cases is much bigger than the cumulative number of infections estimated from the sequence data, a possible explanation being the presence of unsequenced outbreaks in these populations.

ReMASTER: improved phylodynamic simulation for BEAST 2.7

SUMMARY

Phylodynamic models link phylogenetic trees to biologically-relevant parameters such as speciation and extinction rates (macroevolution), effective population sizes and migration rates (ecology and phylogeography), and transmission and removal/recovery rates (epidemiology) to name a few. Being able to simulate phylogenetic trees and population dynamics under these models is the basis for (i) developing and testing of phylodynamic inference algorithms, (ii) performing simulation studies which quantify the biases stemming from model-misspecification, and (iii) performing so-called model adequacy assessments by simulating samples from the posterior predictive distribution. Here I introduce ReMASTER, a package for the phylogenetic inference platform BEAST 2 that provides a simple and efficient approach to specifying and simulating the phylogenetic trees and population dynamics arising from phylodynamic models. Being a component of BEAST 2 allows ReMASTER to also form the basis of joint simulation and inference analyses. ReMASTER is a complete rewrite of an earlier package, MASTER, and boasts improved efficiency, ease of use, flexibility of model specification, and deeper integration with BEAST 2.

AVAILABILITY AND IMPLEMENTATION

ReMASTER can be installed directly from the BEAST 2 package manager, and its documentation is available online at https://tgvaughan.github.io/remaster. ReMASTER is free software, and is distributed under version 3 of the GNU General Public License. The Java source code for ReMASTER is available from https://github.com/tgvaughan/remaster.

Decoding the fundamental drivers of phylodynamic inference

Despite its increasing role in the understanding of infectious disease transmission at the applied and theoretical levels, phylodynamics lacks a well-defined notion of ideal data and optimal sampling. We introduce a method to visualise and quantify the relative impact of pathogen genome sequence and sampling times-two fundamental sources of data for phylodynamics under birth-death-sampling models-to understand how each drive phylodynamic inference. Applying our method to simulated data and real-world SARS-CoV-2 and H1N1 Influenza data, we use this insight to elucidate fundamental trade-offs and guidelines for phylodynamic analyses to draw the most from sequence data. Phylodynamics promises to be a staple of future responses to infectious disease threats globally. Continuing research into the inherent requirements and trade-offs of phylodynamic data and inference will help ensure phylodynamic tools are wielded in ever more targeted and efficient ways.

Bayesian phylodynamics reveals the transmission dynamics of avian influenza A(H7N9) virus at the human-live bird market interface in China

In 2013 to 2017, avian influenza A(H7N9) virus has caused five severe epidemic waves of human infections in China. The role of live bird markets (LBMs) in the transmission dynamics of H7N9 remains unclear. Using a Bayesian phylodynamic approach, we shed light on past H7N9 transmission events at the human-LBM interface that were not directly observed using case surveillance data-based approaches. Our results reveal concurrent circulation of H7N9 lineages in Yangtze and Pearl River Delta regions, with evidence of local transmission during each wave. Our results indicate that H7N9 circulated in humans and LBMs for weeks to months before being first detected. Our findings support the seasonality of H7N9 transmission and suggest a high number of underreported infections, particularly in LBMs. We provide evidence for differences in virus transmissibility between low and highly pathogenic H7N9. We demonstrate a regional spatial structure for the spread of H7N9 among LBMs, highlighting the importance of further investigating the role of local live poultry trade in virus transmission. Our results provide estimates of avian influenza virus (AIV) transmission at the LBM level, providing a unique opportunity to better prepare surveillance plans at LBMs for response to future AIV epidemics.

Swiss public health measures associated with reduced SARS-CoV-2 transmission using genome data

Genome sequences from evolving infectious pathogens allow quantification of case introductions and local transmission dynamics. We sequenced 11,357 severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) genomes from Switzerland in 2020-the sixth largest effort globally. Using a representative subset of these data, we estimated viral introductions to Switzerland and their persistence over the course of 2020. We contrasted these estimates with simple null models representing the absence of certain public health measures. We show that Switzerland's border closures decoupled case introductions from incidence in neighboring countries. Under a simple model, we estimate an 86 to 98% reduction in introductions during Switzerland's strictest border closures. Furthermore, the Swiss 2020 partial lockdown roughly halved the time for sampled introductions to die out. Last, we quantified local transmission dynamics once introductions into Switzerland occurred using a phylodynamic model. We found that transmission slowed 35 to 63% upon outbreak detection in summer 2020 but not in fall. This finding may indicate successful contact tracing over summer before overburdening in fall. The study highlights the added value of genome sequencing data for understanding transmission dynamics.

Comparative Epidemiology of Rabbit Haemorrhagic Disease Virus Strains from Viral Sequence Data

Since their introduction in 1859, European rabbits (Oryctolagus cuniculus) have had a devastating impact on agricultural production and biodiversity in Australia, with competition and land degradation by rabbits being one of the key threats to agricultural and biodiversity values in Australia. Biocontrol agents, with the most important being the rabbit haemorrhagic disease virus 1 (RHDV1), constitute the most important landscape-scale control strategies for rabbits in Australia. Monitoring field strain dynamics is complex and labour-intensive. Here, using phylodynamic models to analyse the available RHDV molecular data, we aimed to: investigate the epidemiology of various strains, use molecular data to date the emergence of new variants and evaluate whether different strains are outcompeting one another. We determined that the two main pathogenic lagoviruses variants in Australia (RHDV1 and RHDV2) have had similar dynamics since their release, although over different timeframes (substantially shorter for RHDV2). We also found a strong geographic difference in their activities and evidence of overall competition between the two viruses.

The effect of sequencing and assembly on the inference of horizontal gene transfer on chromosomal and plasmid phylogenies

The spread of antibiotic resistance genes on plasmids is a threat to human and animal health. Phylogenies of bacteria and their plasmids contain clues regarding the frequency of plasmid transfer events, as well as the co-evolution of plasmids and their hosts. However, whole genome sequencing data from diverse ecological or clinical bacterial samples are rarely used to study plasmid phylogenies and resistance gene transfer. This is partially due to the difficulty of extracting plasmids from short-read sequencing data. Here, we use both short- and long-read sequencing data of 24 clinical extended-spectrum β-lactamase (ESBL)-producing Escherichia coli to estimate chromosomal and plasmid phylogenies. We compare the impact of different sequencing and assembly methodologies on these phylogenies and on the inference of horizontal gene transfer. We find that chromosomal phylogenies can be estimated robustly with all methods, whereas plasmid phylogenies have more variable topology and branch lengths across the methods used. Specifically, hybrid methods that use long reads to resolve short-read assemblies (HybridSPAdes and Unicycler) perform better than those that started from long reads during assembly graph generation (Canu). By contrast, the inference of plasmid and antibiotic resistance gene transfer using a parsimony-based criterion is mostly robust to the choice of sequencing and assembly method.

This article is part of a discussion meeting issue ‘Genomic population structures of microbial pathogens’.

TreeKnit: Inferring ancestral reassortment graphs of influenza viruses

When two influenza viruses co-infect the same cell, they can exchange genome segments in a process known as reassortment. Reassortment is an important source of genetic diversity and is known to have been involved in the emergence of most pandemic influenza strains. However, because of the difficulty in identifying reassortment events from viral sequence data, little is known about their role in the evolution of the seasonal influenza viruses. Here we introduce TreeKnit, a method that infers ancestral reassortment graphs (ARG) from two segment trees. It is based on topological differences between trees, and proceeds in a greedy fashion by finding regions that are compatible in the two trees. Using simulated genealogies with reassortments, we show that TreeKnit performs well in a wide range of settings and that it is as accurate as a more principled bayesian method, while being orders of magnitude faster. Finally, we show that it is possible to use the inferred ARG to better resolve segment trees and to construct more informative visualizations of reassortments.

Influenza viruses evolve quickly and escape immune defenses which requires frequent update of vaccines. Understanding this evolution is key to an effective public health response. The genome of influenza viruses is made up of 8 pieces called segments, each coding for different viral proteins. Within each segment, evolution is an asexual process in which genetic diversity is generated by mutations. But influenza also diversifies through reassortment which can occur when two different viruses infect the same cell: offsprings can then contain a combination of segments from both viruses. Reassortment is akin to sexual reproduction and can generate viruses that combine segments from diverged viral lineages. Reassortment is a crucial component of viral evolution, but it is challenging to reconstruct where reassortments happened and which segments share history. Here, we develop a method called TreeKnit to detect reassortment events. TreeKnit is based on genealogical trees of single segments that can be reconstructed using standard bioinformatics tools. Inconsistencies between these trees are then used as signs of reassortment. We show that TreeKnit is as accurate as other recent methods, but runs much faster. Our method will facilitate the study of reassortment and its consequences for influenza evolution.

Disentangling the role of poultry farms and wild birds in the spread of highly pathogenic avian influenza virus in Europe

In winter 2016-7, Europe was severely hit by an unprecedented epidemic of highly pathogenic avian influenza viruses (HPAIVs), causing a significant impact on animal health, wildlife conservation, and livestock economic sustainability. By applying phylodynamic tools to virus sequences collected during the epidemic, we investigated when the first infections occurred, how many infections were unreported, which factors influenced virus spread, and how many spillover events occurred. HPAIV was likely introduced into poultry farms during the autumn, in line with the timing of wild birds' migration. In Germany, Hungary, and Poland, the epidemic was dominated by farm-to-farm transmission, showing that understanding of how farms are connected would greatly help control efforts. In the Czech Republic, the epidemic was dominated by wild bird-to-farm transmission, implying that more sustainable prevention strategies should be developed to reduce HPAIV exposure from wild birds. Inferred transmission parameters will be useful to parameterize predictive models of HPAIV spread. None of the predictors related to live poultry trade, poultry census, and geographic proximity were identified as supportive predictors of HPAIV spread between farms across borders. These results are crucial to better understand HPAIV transmission dynamics at the domestic-wildlife interface with the view to reduce the impact of future epidemics.

Epidemiological Inference From Pathogen Genomes: A Review of Phylodynamic Models and Applications

Phylodynamics requires an interdisciplinary understanding of phylogenetics, epidemiology, and statistical inference. It has also experienced more intense application than ever before amid the SARS-CoV-2 pandemic. In light of this, we present a review of phylodynamic models beginning with foundational models and assumptions. Our target audience is public health researchers, epidemiologists, and biologists seeking a working knowledge of the links between epidemiology, evolutionary models, and resulting epidemiological inference. We discuss the assumptions linking evolutionary models of pathogen population size to epidemiological models of the infected population size. We then describe statistical inference for phylodynamic models and list how output parameters can be rearranged for epidemiological interpretation. We go on to cover more sophisticated models and finish by highlighting future directions.

Joint Inference of Migration and Reassortment Patterns for Viruses with Segmented Genomes

The structured coalescent allows inferring migration patterns between viral subpopulations from genetic sequence data. However, these analyses typically assume that no genetic recombination process impacted the sequence evolution of pathogens. For segmented viruses, such as influenza, that can undergo reassortment this assumption is broken. Reassortment reshuffles the segments of different parent lineages upon a coinfection event, which means that the shared history of viruses has to be represented by a network instead of a tree. Therefore, full genome analyses of such viruses are complex or even impossible. Although this problem has been addressed for unstructured populations, it is still impossible to account for population structure, such as induced by different host populations, whereas also accounting for reassortment. We address this by extending the structured coalescent to account for reassortment and present a framework for investigating possible ties between reassortment and migration (host jump) events. This method can accurately estimate subpopulation dependent effective populations sizes, reassortment, and migration rates from simulated data. Additionally, we apply the new model to avian influenza A/H5N1 sequences, sampled from two avian host types, Anseriformes and Galliformes. We contrast our results with a structured coalescent without reassortment inference, which assumes independently evolving segments. This reveals that taking into account segment reassortment and using sequencing data from several viral segments for joint phylodynamic inference leads to different estimates for effective population sizes, migration, and clock rates. This new model is implemented as the Structured Coalescent with Reassortment package for BEAST 2.5 and is available at https://github.com/jugne/SCORE.

Novel Integrative Modeling of Molecules and Morphology across Evolutionary Timescales

Evolutionary models account for either population- or species-level processes but usually not both. We introduce a new model, the FBD-MSC, which makes it possible for the first time to integrate both the genealogical and fossilization phenomena, by means of the multispecies coalescent (MSC) and the fossilized birth–death (FBD) processes. Using this model, we reconstruct the phylogeny representing all extant and many fossil Caninae, recovering both the relative and absolute time of speciation events. We quantify known inaccuracy issues with divergence time estimates using the popular strategy of concatenating molecular alignments and show that the FBD-MSC solves them. Our new integrative method and empirical results advance the paradigm and practice of probabilistic total evidence analyses in evolutionary biology.[Caninae; fossilized birth–death; molecular clock; multispecies coalescent; phylogenetics; species trees.]

Spread of a SARS-CoV-2 variant through Europe in the summer of 2020

Following its emergence in late 2019, the spread of SARS-CoV-2^1,2 has been tracked by phylogenetic analysis of viral genome sequences in unprecedented detail^3-5. Although the virus spread globally in early 2020 before borders closed, intercontinental travel has since been greatly reduced. However, travel within Europe resumed in the summer of 2020. Here we report on a SARS-CoV-2 variant, 20E (EU1), that was identified in Spain in early summer 2020 and subsequently spread across Europe. We find no evidence that this variant has increased transmissibility, but instead demonstrate how rising incidence in Spain, resumption of travel, and lack of effective screening and containment may explain the variant's success. Despite travel restrictions, we estimate that 20E (EU1) was introduced hundreds of times to European countries by summertime travellers, which is likely to have undermined local efforts to minimize infection with SARS-CoV-2. Our results illustrate how a variant can rapidly become dominant even in the absence of a substantial transmission advantage in favourable epidemiological settings. Genomic surveillance is critical for understanding how travel can affect transmission of SARS-CoV-2, and thus for informing future containment strategies as travel resumes.

Emergence and spread of a SARS-CoV-2 variant through Europe in the summer of 2020

Following its emergence in late 2019, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused a global pandemic resulting in unprecedented efforts to reduce transmission and develop therapies and vaccines (WHO Emergency Committee, 2020; Zhu et al., 2020). Rapidly generated viral genome sequences have allowed the spread of the virus to be tracked via phylogenetic analysis (Worobey et al., 2020; Hadfield et al., 2018; Pybus et al., 2020). While the virus spread globally in early 2020 before borders closed, intercontinental travel has since been greatly reduced, allowing continent-specific variants to emerge. However, within Europe travel resumed in the summer of 2020, and the impact of this travel on the epidemic is not well understood. Here we report on a novel SARS-CoV-2 variant, 20E (EU1), that emerged in Spain in early summer, and subsequently spread to multiple locations in Europe. We find no evidence of increased transmissibility of this variant, but instead demonstrate how rising incidence in Spain, resumption of travel across Europe, and lack of effective screening and containment may explain the variant's success. Despite travel restrictions and quarantine requirements, we estimate 20E (EU1) was introduced hundreds of times to countries across Europe by summertime travellers, likely undermining local efforts to keep SARS-CoV-2 cases low. Our results demonstrate how a variant can rapidly become dominant even in absence of a substantial transmission advantage in favorable epidemiological settings. Genomic surveillance is critical to understanding how travel can impact SARS-CoV-2 transmission, and thus for informing future containment strategies as travel resumes.

Field validation of phylodynamic analytical methods for inference on epidemiological processes in wildlife

Amongst newly developed approaches to analyse molecular data, phylodynamic models are receiving much attention because of their potential to reveal changes to viral populations over short periods. This knowledge can be very important for understanding disease impacts. However, their accuracy needs to be fully understood, especially in relation to wildlife disease epidemiology, where sampling and prior knowledge may be limited. The release of the rabbit haemorrhagic disease virus (RHDV) as biological control in naïve rabbit populations in Australia in 1996 provides a unique data set with which to validate phylodynamic models. By comparing results obtained from RHDV sequence data with our current understanding of RHDV epidemiology in Australia, we evaluated the performances of these recently developed models. In line with our expectations, coalescent analyses detected a sharp increase in the virus population size in the first few months after release, followed by a more gradual increase. Phylodynamic analyses using a birth-death model generated effective reproductive number estimates (the average number of secondary infections per each infectious case, R_e ) larger than one for most of the epochs considered. However, the possible range of the initial R_e included estimates lower than one despite the known rapid spread of RHDV in Australia. Furthermore, the analyses that accounted for geographical structuring failed to converge. We argue that the difficulties that we encountered most likely stem from the fact that the samples available from 1996 to 2014 were too sparse with respect to both geographic and within outbreak coverage to adequately infer some of the model parameters. In general, while these phylodynamic analyses proved to be greatly informative in some regards, we caution that their interpretation may not be straightforward. We recommend further research to evaluate the robustness of these models to assumption violations and sensitivity to sampling regimes.

The origin and early spread of SARS-CoV-2 in Europe

The investigation of migratory patterns during the SARS-CoV-2 pandemic before spring 2020 border closures in Europe is a crucial first step toward an in-depth evaluation of border closure policies. Here we analyze viral genome sequences using a phylodynamic model with geographic structure to estimate the origin and spread of SARS-CoV-2 in Europe prior to border closures. Based on SARS-CoV-2 genomes, we reconstruct a partial transmission tree of the early pandemic and coinfer the geographic location of ancestral lineages as well as the number of migration events into and between European regions. We find that the predominant lineage spreading in Europe during this time has a most recent common ancestor in Italy and was probably seeded by a transmission event in either Hubei, China or Germany. We do not find evidence for preferential migration paths from Hubei into different European regions or from each European region to the others. Sustained local transmission is first evident in Italy and then shortly thereafter in the other European regions considered. Before the first border closures in Europe, we estimate that the rate of occurrence of new cases from within-country transmission was within the bounds of the estimated rate of new cases from migration. In summary, our analysis offers a view on the early state of the epidemic in Europe and on migration patterns of the virus before border closures. This information will enable further study of the necessity and timeliness of border closures.

A Multitype Birth-Death Model for Bayesian Inference of Lineage-Specific Birth and Death Rates

Heterogeneous populations can lead to important differences in birth and death rates across a phylogeny. Taking this heterogeneity into account is necessary to obtain accurate estimates of the underlying population dynamics. We present a new multitype birth–death model (MTBD) that can estimate lineage-specific birth and death rates. This corresponds to estimating lineage-dependent speciation and extinction rates for species phylogenies, and lineage-dependent transmission and recovery rates for pathogen transmission trees. In contrast with previous models, we do not presume to know the trait driving the rate differences, nor do we prohibit the same rates from appearing in different parts of the phylogeny. Using simulated data sets, we show that the MTBD model can reliably infer the presence of multiple evolutionary regimes, their positions in the tree, and the birth and death rates associated with each. We also present a reanalysis of two empirical data sets and compare the results obtained by MTBD and by the existing software BAMM. We compare two implementations of the model, one exact and one approximate (assuming that no rate changes occur in the extinct parts of the tree), and show that the approximation only slightly affects results. The MTBD model is implemented as a package in the Bayesian inference software BEAST 2 and allows joint inference of the phylogeny and the model parameters.[Birth–death; lineage specific rates, multi-type model.]

Estimating Epidemic Incidence and Prevalence from Genomic Data

Modern phylodynamic methods interpret an inferred phylogenetic tree as a partial transmission chain providing information about the dynamic process of transmission and removal (where removal may be due to recovery, death, or behavior change). Birth–death and coalescent processes have been introduced to model the stochastic dynamics of epidemic spread under common epidemiological models such as the SIS and SIR models and are successfully used to infer phylogenetic trees together with transmission (birth) and removal (death) rates. These methods either integrate analytically over past incidence and prevalence to infer rate parameters, and thus cannot explicitly infer past incidence or prevalence, or allow such inference only in the coalescent limit of large population size. Here, we introduce a particle filtering framework to explicitly infer prevalence and incidence trajectories along with phylogenies and epidemiological model parameters from genomic sequences and case count data in a manner consistent with the underlying birth–death model. After demonstrating the accuracy of this method on simulated data, we use it to assess the prevalence through time of the early 2014 Ebola outbreak in Sierra Leone.

Detection of HIV transmission clusters from phylogenetic trees using a multi-state birth-death model

HIV patients form clusters in HIV transmission networks. Accurate identification of these transmission clusters is essential to effectively target public health interventions. One reason for clustering is that the underlying contact network contains many local communities. We present a new maximum-likelihood method for identifying transmission clusters caused by community structure, based on phylogenetic trees. The method employs a multi-state birth–death (MSBD) model which detects changes in transmission rate, which are interpreted as the introduction of the epidemic into a new susceptible community, i.e. the formation of a new cluster. We show that the MSBD method is able to reliably infer the clusters and the transmission parameters from a pathogen phylogeny based on our simulations. In contrast to existing cutpoint-based methods for cluster identification, our method does not require that clusters be monophyletic nor is it dependent on the selection of a difficult-to-interpret cutpoint parameter. We present an application of our method to data from the Swiss HIV Cohort Study. The method is available as an easy-to-use R package.

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.

IcyTree: rapid browser-based visualization for phylogenetic trees and networks

Summary

IcyTree is an easy-to-use application which can be used to visualize a wide variety of phylogenetic trees and networks. While numerous phylogenetic tree viewers exist already, IcyTree distinguishes itself by being a purely online tool, having a responsive user interface, supporting phylogenetic networks (ancestral recombination graphs in particular), and efficiently drawing trees that include information such as ancestral locations or trait values. IcyTree also provides intuitive panning and zooming utilities that make exploring large phylogenetic trees of many thousands of taxa feasible.

Availability and Implementation

IcyTree is a web application and can be accessed directly at http://tgvaughan.github.com/icytree . Currently supported web browsers include Mozilla Firefox and Google Chrome. IcyTree is written entirely in client-side JavaScript (no plugin required) and, once loaded, does not require network access to run. IcyTree is free software, and the source code is made available at http://github.com/tgvaughan/icytree under version 3 of the GNU General Public License.

Contact

tgvaughan@gmail.com.

Taming the BEAST-A Community Teaching Material Resource for BEAST 2

Phylogenetics and phylodynamics are central topics in modern evolutionary biology. Phylogenetic methods reconstruct the evolutionary relationships among organisms, whereas phylodynamic approaches reveal the underlying diversification processes that lead to the observed relationships. These two fields have many practical applications in disciplines as diverse as epidemiology, developmental biology, palaeontology, ecology, and linguistics. The combination of increasingly large genetic data sets and increases in computing power is facilitating the development of more sophisticated phylogenetic and phylodynamic methods. Big data sets allow us to answer complex questions. However, since the required analyses are highly specific to the particular data set and question, a black-box method is not sufficient anymore. Instead, biologists are required to be actively involved with modeling decisions during data analysis. The modular design of the Bayesian phylogenetic software package BEAST 2 enables, and in fact enforces, this involvement. At the same time, the modular design enables computational biology groups to develop new methods at a rapid rate. A thorough understanding of the models and algorithms used by inference software is a critical prerequisite for successful hypothesis formulation and assessment. In particular, there is a need for more readily available resources aimed at helping interested scientists equip themselves with the skills to confidently use cutting-edge phylogenetic analysis software. These resources will also benefit researchers who do not have access to similar courses or training at their home institutions. Here, we introduce the “Taming the Beast” (https://taming-the-beast.github.io/) resource, which was developed as part of a workshop series bearing the same name, to facilitate the usage of the Bayesian phylogenetic software package BEAST 2.

Inferring Ancestral Recombination Graphs from Bacterial Genomic Data

Homologous recombination is a central feature of bacterial evolution, yet it confounds traditional phylogenetic methods. While a number of methods specific to bacterial evolution have been developed, none of these permit joint inference of a bacterial recombination graph and associated parameters. In this article, we present a new method which addresses this shortcoming. Our method uses a novel Markov chain Monte Carlo algorithm to perform phylogenetic inference under the ClonalOrigin model. We demonstrate the utility of our method by applying it to ribosomal multilocus sequence typing data sequenced from pathogenic and nonpathogenic Escherichia coli serotype O157 and O26 isolates collected in rural New Zealand. The method is implemented as an open source BEAST 2 package, Bacter, which is available via the project web page at http://tgvaughan.github.io/bacter.

Molecular Approaches to Understanding Transmission and Source Attribution in Nontyphoidal Salmonella and Their Application in Africa

Nontyphoidal Salmonella (NTS) is a frequent cause of diarrhea around the world, yet in many African countries it is more commonly associated with invasive bacterial disease. Various source attribution models have been developed that utilize microbial subtyping data to assign cases of human NTS infection to different animal populations and foods of animal origin. Advances in molecular microbial subtyping approaches, in particular whole-genome sequencing, provide higher resolution data with which to investigate these sources. In this review, we provide updates on the source attribution models developed for Salmonella, and examine the application of whole-genome sequencing data combined with evolutionary modeling to investigate the putative sources and transmission pathways of NTS, with a focus on the epidemiology of NTS in Africa. This is essential information to decide where, what, and how control strategies might be applied most effectively.

Phylodynamics with Migration: A Computational Framework to Quantify Population Structure from Genomic Data

When viruses spread, outbreaks can be spawned in previously unaffected regions. Depending on the time and mode of introduction, each regional outbreak can have its own epidemic dynamics. The migration and phylodynamic processes are often intertwined and need to be taken into account when analyzing temporally and spatially structured virus data. In this article, we present a fully probabilistic approach for the joint reconstruction of phylodynamic history in structured populations (such as geographic structure) based on a multitype birth-death process. This approach can be used to quantify the spread of a pathogen in a structured population. Changes in epidemic dynamics through time within subpopulations are incorporated through piecewise constant changes in transmission parameters.We analyze a global human influenza H3N2 virus data set from a geographically structured host population to demonstrate how seasonal dynamics can be inferred simultaneously with the phylogeny and migration process. Our results suggest that the main migration path among the northern, tropical, and southern region represented in the sample analyzed here is the one leading from the tropics to the northern region. Furthermore, the time-dependent transmission dynamics between and within two HIV risk groups, heterosexuals and injecting drug users, in the Latvian HIV epidemic are investigated. Our analyses confirm that the Latvian HIV epidemic peaking around 2001 was mainly driven by the injecting drug user risk group.

How well can the exponential-growth coalescent approximate constant-rate birth-death population dynamics?

One of the central objectives in the field of phylodynamics is the quantification of population dynamic processes using genetic sequence data or in some cases phenotypic data. Phylodynamics has been successfully applied to many different processes, such as the spread of infectious diseases, within-host evolution of a pathogen, macroevolution and even language evolution. Phylodynamic analysis requires a probability distribution on phylogenetic trees spanned by the genetic data. Because such a probability distribution is not available for many common stochastic population dynamic processes, coalescent-based approximations assuming deterministic population size changes are widely employed. Key to many population dynamic models, in particular epidemiological models, is a period of exponential population growth during the initial phase. Here, we show that the coalescent does not well approximate stochastic exponential population growth, which is typically modelled by a birth–death process. We demonstrate that introducing demographic stochasticity into the population size function of the coalescent improves the approximation for values of R₀ close to 1, but substantial differences remain for large R₀. In addition, the computational advantage of using an approximation over exact models vanishes when introducing such demographic stochasticity. These results highlight that we need to increase efforts to develop phylodynamic tools that correctly account for the stochasticity of population dynamic models for inference.

Efficient Bayesian inference under the structured coalescent

Motivation: Population structure significantly affects evolutionary dynamics. Such structure may be due to spatial segregation, but may also reflect any other gene-flow-limiting aspect of a model. In combination with the structured coalescent, this fact can be used to inform phylogenetic tree reconstruction, as well as to infer parameters such as migration rates and subpopulation sizes from annotated sequence data. However, conducting Bayesian inference under the structured coalescent is impeded by the difficulty of constructing Markov Chain Monte Carlo (MCMC) sampling algorithms (samplers) capable of efficiently exploring the state space.

Results: In this article, we present a new MCMC sampler capable of sampling from posterior distributions over structured trees: timed phylogenetic trees in which lineages are associated with the distinct subpopulation in which they lie. The sampler includes a set of MCMC proposal functions that offer significant mixing improvements over a previously published method. Furthermore, its implementation as a BEAST 2 package ensures maximum flexibility with respect to model and prior specification. We demonstrate the usefulness of this new sampler by using it to infer migration rates and effective population sizes of H3N2 influenza between New Zealand, New York and Hong Kong from publicly available hemagglutinin (HA) gene sequences under the structured coalescent.

Availability and implementation: The sampler has been implemented as a publicly available BEAST 2 package that is distributed under version 3 of the GNU General Public License at http://compevol.github.io/MultiTypeTree.

Contact:tgvaughan@gmail.com

Supplementary information:Supplementary data are available at Bioinformatics online.

Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth-death SIR model

The evolution of RNA viruses, such as human immunodeficiency virus (HIV), hepatitis C virus and influenza virus, occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible–infected–removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our birth–death SIR method to two viral datasets. First, five HIV type 1 clusters sampled in the UK between 1999 and 2003 are analysed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 1990s. The analysis of a hepatitis C virus genotype 2c dataset shows that the local epidemic in the Córdoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880 to 1920. The estimated time of epidemic peak is around 1970.

A stochastic simulator of birth-death master equations with application to phylodynamics

In this article, we present a versatile new software tool for the simulation and analysis of stochastic models of population phylodynamics and chemical kinetics. Models are specified via an expressive and human-readable XML format and can be used as the basis for generating either single population histories or large ensembles of such histories. Importantly, phylogenetic trees or networks can be generated alongside the histories they correspond to, enabling investigations into the interplay between genealogies and population dynamics. Summary statistics such as means and variances can be recorded in place of the full ensemble, allowing for a reduction in the amount of memory used--an important consideration for models including large numbers of individual subpopulations or demes. In the case of population size histories, the resulting simulation output is written to disk in the flexible JSON format, which is easily read into numerical analysis environments such as R for visualization or further processing. Simulated phylogenetic trees can be recorded using the standard Newick or NEXUS formats, with extensions to these formats used for non-tree-like inheritance relationships.

Within-host demographic fluctuations and correlations in early retroviral infection

In this paper we analyze the demographic fluctuations and correlations present in within-host populations of viruses and their target cells during the early stages of infection. In particular, we present an exact treatment of a discrete-population, stochastic, continuous-time master equation description of HIV or similar retroviral infection dynamics, employing Monte Carlo simulations. The results of calculations employing Gillespie's direct method clearly demonstrate the importance of considering the microscopic details of the interactions which constitute the macroscopic dynamics. We then employ the τ-leaping approach to study the statistical characteristics of infections involving realistic absolute numbers of within-host viral and cellular populations, before going on to investigate the effect that initial viral population size plays on these characteristics. Our main conclusion is that cross-correlations between infected cell and virion populations alter dramatically over the course of the infection. We suggest that these statistical correlations offer a novel and robust signature for the acute phase of retroviral infection.

Einstein-Podolsky-Rosen entanglement strategies in two-well Bose-Einstein condensates

Criteria suitable for measuring entanglement between two different potential wells in a Bose-Einstein condensation are evaluated. We show how to generate the required entanglement, utilizing either an adiabatic two-mode or a dynamic four-mode interaction strategy, with techniques that take advantage of s-wave scattering interactions to provide the nonlinear coupling. The dynamic entanglement method results in an entanglement signature with spatially separated detectors, as in the Einstein-Podolsky-Rosen paradox.

Extinction times in autocatalytic systems

Systems evolving under the influence of autocatalytic processes have been the subject of much study due to their appearance in a wide variety of contexts. Well known examples range from the simplest autocatalytic chemical reactions, biochemical models of ribozyme or prion replication, right up to the duplication of entire organisms in models of population dynamics. While the deterministic approach frequently taken to model such systems is adequate in the limit of large reactant numbers, the intrinsic fluctuations exert an important influence on the dynamics when the supply of reactants is limited. In particular, when combined with spontaneous degradation of the autocatalytic reactant population, such fluctuations can lead to the extinction of that population. In this paper, we study reversible autocatalytic processes of the form X + Y ⇌ 2X in the limit that there exists a surplus of Y and in the presence of a spontaneous degradation process X → Z. Through the use of the Poisson representation, we identify an exact analytical expression for the mean extinction time of the X population. We show that the exact result can be neatly approximated by an Arrhenius-like expression involving an effective activation energy separating a quasi-stationary state from the extinct state.