Dispersal history of SARS-CoV-2 in Galicia, Spain.

The dynamics of SARS-CoV-2 transmission are influenced by a variety of factors, including social restrictions and the emergence of distinct variants. In this study, we delve into the origins and dissemination of the Alpha, Delta, and Omicron variants of concern in Galicia, northwest Spain. For this, we leveraged genomic data collected by the EPICOVIGAL Consortium and from the GISAID database, along with mobility information from other Spanish regions and foreign countries. Our analysis indicates that initial introductions during the Alpha phase were predominantly from other Spanish regions and France. However, as the pandemic progressed, introductions from Portugal and the USA became increasingly significant. Notably, Galicia's major coastal cities emerged as critical hubs for viral transmission, highlighting their role in sustaining and spreading the virus. This research emphasizes the critical role of regional connectivity in the spread of SARS-CoV-2 and offers essential insights for enhancing public health strategies and surveillance measures.

Contemporary and historical human migration patterns shape hepatitis B virus diversity.

Infection by hepatitis B virus (HBV) is responsible for approximately 296 million chronic cases of hepatitis B, and roughly 880,000 deaths annually. The global burden of HBV is distributed unevenly, largely owing to the heterogeneous geographic distribution of its subtypes, each of which demonstrates different severity and responsiveness to antiviral therapy. It is therefore crucial to the global public health response to HBV that the spatiotemporal spread of each genotype is well characterized. In this study, we describe a collection of 133 newly sequenced HBV strains from recent African immigrants upon their arrival in Belgium. We incorporate these sequences-all of which we determine to come from genotypes A, D, and E-into a large-scale phylogeographic study with genomes sampled across the globe. We focus on investigating the spatio-temporal processes shaping the evolutionary history of the three genotypes we observe. We incorporate several recently published ancient HBV genomes for genotypes A and D to aid our analysis. We show that different spatio-temporal processes underlie the A, D, and E genotypes with the former two having originated in southeastern Asia, after which they spread across the world. The HBV E genotype is estimated to have originated in Africa, after which it spread to Europe and the Americas. Our results highlight the use of phylogeographic reconstruction as a tool to understand the recent spatiotemporal dynamics of HBV, and highlight the importance of supporting vulnerable populations in accordance with the needs presented by specific HBV genotypes.

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

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

Risk assessment of SARS-CoV-2 replicating and evolving in animals.

The retransmissions of SARS-CoV-2 from several mammals - primarily mink and white-tailed deer - to humans have raised concerns for the emergence of a new animal-derived SARS-CoV-2 variant to worsen the pandemic. Here, we discuss animal species that are susceptible to natural or experimental infection with SARS-CoV-2 and can transmit the virus to mates or humans. We describe cutting-edge techniques to assess the impact of a mutation in the viral spike (S) protein on its receptor and on antibody binding. Our review of spike sequences of animal-derived viruses identified nine unique amino acid exchanges in the receptor-binding domain (RBD) that are not present in any variant of concern (VOC). These mutations are present in SARS-CoV-2 found in companion animals such as dogs and cats, and they exhibit a higher frequency in SARS-CoV-2 found in mink and white-tailed deer, suggesting that sustained transmissions may contribute to maintaining novel mutations. Four of these exchanges, such as Leu452Met, could undermine acquired immune protection in humans while maintaining high affinity for the human angiotensin-converting enzyme 2 (ACE2) receptor. Finally, we discuss important avenues of future research into animal-derived viruses with public health risks.

Optimizing ancestral trait reconstruction of large HIV Subtype C datasets through multiple-trait subsampling.

Large datasets along with sampling bias represent a challenge for phylodynamic reconstructions, particularly when the study data are obtained from various heterogeneous sources and/or through convenience sampling. In this study, we evaluate the presence of unbalanced sampled distribution by collection date, location, and risk group of human immunodeficiency virus Type 1 Subtype C using a comprehensive subsampling strategy and assess their impact on the reconstruction of the viral spatial and risk group dynamics using phylogenetic comparative methods. Our study shows that a most suitable dataset for ancestral trait reconstruction can be obtained through subsampling by all available traits, particularly using multigene datasets. We also demonstrate that sampling bias is inflated when considerable information for a given trait is unavailable or of poor quality, as we observed for the trait risk group. In conclusion, we suggest that, even if traits are not well recorded, including them deliberately optimizes the representativeness of the original dataset rather than completely excluding them. Therefore, we advise the inclusion of as many traits as possible with the aid of subsampling approaches in order to optimize the dataset for phylodynamic analysis while reducing the computational burden. This will benefit research communities investigating the evolutionary and spatio-temporal patterns of infectious diseases.

Investigation of an international water polo tournament in Czechia as a potential source for early introduction of the SARS-CoV-2 Omicron variant into Belgium, Switzerland and Germany, November 2021.

BackgroundThe earliest recognised infections by the SARS-CoV-2 Omicron variant (Pango lineage B.1.1.529) in Belgium and Switzerland suggested a connection to an international water polo tournament, held 12-14 November 2021 in Brno, Czechia.AimTo study the arrival and subsequent spread of the Omicron variant in Belgium and Switzerland, and understand the overall importance of this international sporting event on the number of infections in the two countries.MethodsWe performed intensive forward and backward contact tracing in both countries, supplemented by phylogenetic investigations using virus sequences of the suspected infection chain archived in public databases.ResultsThrough contact tracing, we identified two and one infected athletes of the Belgian and Swiss water polo teams, respectively, and subsequently also three athletes from Germany. In Belgium and Switzerland, four and three secondary infections, and three and one confirmed tertiary infections were identified. Phylogenetic investigation demonstrated that this sporting event played a role as the source of infection, but without a direct link with infections from South Africa and not as a superspreading event; the virus was found to already be circulating at that time in the countries involved.ConclusionThe SARS-CoV-2 Omicron variant started to circulate in Europe several weeks before its identification in South Africa on 24 November 2021. Accordingly, it can be assumed that travel restrictions are usually implemented too late to prevent the spread of newly detected SARS-CoV-2 variants to other regions. Phylogenetic analysis may modify the perception of an apparently clear result of intensive contact tracing.

Shrinkage-based Random Local Clocks with Scalable Inference.

Molecular clock models undergird modern methods of divergence-time estimation. Local clock models propose that the rate of molecular evolution is constant within phylogenetic subtrees. Current local clock inference procedures exhibit one or more weaknesses, namely they achieve limited scalability to trees with large numbers of taxa, impose model misspecification, or require a priori knowledge of the existence and location of clocks. To overcome these challenges, we present an autocorrelated, Bayesian model of heritable clock rate evolution that leverages heavy-tailed priors with mean zero to shrink increments of change between branch-specific clocks. We further develop an efficient Hamiltonian Monte Carlo sampler that exploits closed form gradient computations to scale our model to large trees. Inference under our shrinkage clock exhibits a speed-up compared to the popular random local clock when estimating branch-specific clock rates on a variety of simulated datasets. This speed-up increases with the size of the problem. We further show our shrinkage clock recovers known local clocks within a rodent and mammalian phylogeny. Finally, in a problem that once appeared computationally impractical, we investigate the heritable clock structure of various surface glycoproteins of influenza A virus in the absence of prior knowledge about clock placement. We implement our shrinkage clock and make it publicly available in the BEAST software package.

Genomic monitoring of SARS-CoV-2 variants using sentinel SARI hospital surveillance.

Background: To support the COVID-19 pandemic response, many countries, including Belgium, implemented baseline genomic surveillance (BGS) programs aiming to early detect and characterize new SARS-CoV-2 variants. In parallel, Belgium maintained a sentinel network of six hospitals that samples patients with severe acute respiratory infections (SARI) and integrated SARS-CoV-2 detection within a broader range of respiratory pathogens. We evaluate the ability of the SARI surveillance to monitor general trends and early signals of viral genetic evolution of SARS-CoV-2 and compare it with the BGS as a reference model. Methods: Nine-hundred twenty-five SARS-CoV-2 positive samples from patients fulfilling the Belgian SARI definition between January 2020 and December 2022 were sequenced using the ARTIC Network amplicon tiling approach on a MinION platform. Weekly variant of concern (VOC) proportions and types were compared to those that were circulating between 2021 and 2022, using 96,251 sequences of the BGS. Results: SARI surveillance allowed timely detection of the Omicron (BA.1, BA.2, BA.4, and BA.5) and Delta (B.1.617.2) VOCs, with no to 2 weeks delay according to the start of their epidemic growth in the Belgian population. First detection of VOCs B.1.351 and P.1 took longer, but these remained minor in Belgium. Omicron BA.3 was never detected in SARI surveillance. Timeliness could not be evaluated for B.1.1.7, being already major at the start of the study period. Conclusions: Genomic surveillance of SARS-CoV-2 using SARI sentinel surveillance has proven to accurately reflect VOCs detected in the population and provides a cost-effective solution for long-term genomic monitoring of circulating respiratory viruses.

Newly identified lineages of porcine hemagglutinating encephalomyelitis virus exhibit respiratory phenotype.

Swine pathogens have a long history of zoonotic transmission to humans, occasionally leading to sustained outbreaks or pandemics. Through a retrospective epidemiological study of swine populations in China, we describe novel lineages of porcine hemagglutinating encephalomyelitis virus (PHEV) complex coronaviruses (CoVs) that cause exclusively respiratory symptoms with no signs of the neurological symptoms typically associated with classical PHEV infection. Through large-scale epidemiological surveillance, we show that these novel lineages have circulated in at least eight provinces in southeastern China. Phylogenetic and recombination analyses of twenty-four genomes identified two major viral lineages causing respiratory symptoms with extensive recombination within them, between them, and between classical PHEV and the novel respiratory variant PHEV (rvPHEV) lineages. Divergence times among the sampled lineages in the PHEV virus complex date back to 1886-1958 (mean estimate 1928), with the two major rvPHEV lineages separating approximately 20 years later. Many rvPHEV viruses show amino acid substitutions at the carbohydrate-binding site of hemagglutinin esterase (HE) and/or have lost the cysteine required for HE dimerization. This resembles the early adaptation of human CoVs, where HE lost its hemagglutination ability to adapt to growth in the human respiratory tract. Our study represents the first report of the evolutionary history of rvPHEV circulating in swine and highlights the importance of characterizing CoV diversity and recombination in swine to identify pathogens with outbreak potential that could threaten swine farming.

Detecting Episodic Evolution through Bayesian Inference of Molecular Clock Models.

Molecular evolutionary rate variation is a key aspect of the evolution of many organisms that can be modeled using molecular clock models. For example, fixed local clocks revealed the role of episodic evolution in the emergence of SARS-CoV-2 variants of concern. Like all statistical models, however, the reliability of such inferences is contingent on an assessment of statistical evidence. We present a novel Bayesian phylogenetic approach for detecting episodic evolution. It consists of computing Bayes factors, as the ratio of posterior and prior odds of evolutionary rate increases, effectively quantifying support for the effect size. We conducted an extensive simulation study to illustrate the power of this method and benchmarked it to formal model comparison of a range of molecular clock models using (log) marginal likelihood estimation, and to inference under a random local clock model. Quantifying support for the effect size has higher sensitivity than formal model testing and is straight-forward to compute, because it only needs samples from the posterior and prior distribution. However, formal model testing has the advantage of accommodating a wide range molecular clock models. We also assessed the ability of an automated approach, known as the random local clock, where branches under episodic evolution may be detected without their a priori definition. In an empirical analysis of a data set of SARS-CoV-2 genomes, we find "very strong" evidence for episodic evolution. Our results provide guidelines and practical methods for Bayesian detection of episodic evolution, as well as avenues for further research into this phenomenon.

Integrating full and partial genome sequences to decipher the global spread of canine rabies virus.

Despite the rapid growth in viral genome sequencing, statistical methods face challenges in handling historical viral endemic diseases with large amounts of underutilized partial sequence data. We propose a phylogenetic pipeline that harnesses both full and partial viral genome sequences to investigate historical pathogen spread between countries. Its application to rabies virus (RABV) yields precise dating and confident estimates of its geographic dispersal. By using full genomes and partial sequences, we reduce both geographic and genetic biases that often hinder studies that focus on specific genes. Our pipeline reveals an emergence of the present canine-mediated RABV between years 1301 and 1403 and reveals regional introductions over a 700-year period. This geographic reconstruction enables us to locate episodes of human-mediated introductions of RABV and examine the role that European colonization played in its spread. Our approach enables phylogeographic analysis of large and genetically diverse data sets for many viral pathogens.

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.

Dynamics of eastern equine encephalitis virus during the 2019 outbreak in the Northeast United States.

Eastern equine encephalitis virus (EEEV) causes a rare but severe disease in horses and humans and is maintained in an enzootic transmission cycle between songbirds and Culiseta melanura mosquitoes. In 2019, the largest EEEV outbreak in the United States for more than 50 years occurred, centered in the Northeast. To explore the dynamics of the outbreak, we sequenced 80 isolates of EEEV and combined them with existing genomic data. We found that, similar to previous years, cases were driven by multiple independent but short-lived virus introductions into the Northeast from Florida. Once in the Northeast, we found that Massachusetts was important for regional spread. We found no evidence of any changes in viral, human, or bird factors which would explain the increase in cases in 2019, although the ecology of EEEV is complex and further data is required to explore these in more detail. By using detailed mosquito surveillance data collected by Massachusetts and Connecticut, however, we found that the abundance of Cs. melanura was exceptionally high in 2019, as was the EEEV infection rate. We employed these mosquito data to build a negative binomial regression model and applied it to estimate early season risks of human or horse cases. We found that the month of first detection of EEEV in mosquito surveillance data and vector index (abundance multiplied by infection rate) were predictive of cases later in the season. We therefore highlight the importance of mosquito surveillance programs as an integral part of public health and disease control.

The Principles of SARS-CoV-2 Intervariant Competition Are Exemplified in the Pre-Omicron Era of the Colombian Epidemic.

The first 18 months of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections in Colombia were characterized by three epidemic waves. During the third wave, from March through August 2021, intervariant competition resulted in Mu replacing Alpha and Gamma. We employed Bayesian phylodynamic inference and epidemiological modeling to characterize the variants in the country during this period of competition. Phylogeographic analysis indicated that Mu did not emerge in Colombia but acquired increased fitness there through local transmission and diversification, contributing to its export to North America and Europe. Despite not having the highest transmissibility, Mu's genetic composition and ability to evade preexisting immunity facilitated its domination of the Colombian epidemic landscape. Our results support previous modeling studies demonstrating that both intrinsic factors (transmissibility and genetic diversity) and extrinsic factors (time of introduction and acquired immunity) influence the outcome of intervariant competition. This analysis will help set practical expectations about the inevitable emergences of new variants and their trajectories. IMPORTANCE Before the appearance of the Omicron variant in late 2021, numerous SARS-CoV-2 variants emerged, were established, and declined, often with different outcomes in different geographic areas. In this study, we considered the trajectory of the Mu variant, which only successfully dominated the epidemic landscape of a single country: Colombia. We demonstrate that Mu competed successfully there due to its early and opportune introduction time in late 2020, combined with its ability to evade immunity granted by prior infection or the first generation of vaccines. Mu likely did not effectively spread outside of Colombia because other immune-evading variants, such as Delta, had arrived in those locales and established themselves first. On the other hand, Mu's early spread within Colombia may have prevented the successful establishment of Delta there. Our analysis highlights the geographic heterogeneity of early SARS-CoV-2 variant spread and helps to reframe the expectations for the competition behaviors of future variants.

Immunovirological and environmental screening reveals actionable risk factors for fatal COVID-19 during post-vaccination nursing home outbreaks.

Coronavirus Disease 2019 (COVID-19) vaccination has resulted in excellent protection against fatal disease, including in older adults. However, risk factors for post-vaccination fatal COVID-19 are largely unknown. We comprehensively studied three large nursing home outbreaks (20-35% fatal cases among residents) by combining severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) aerosol monitoring, whole-genome phylogenetic analysis and immunovirological profiling of nasal mucosa by digital nCounter transcriptomics. Phylogenetic investigations indicated that each outbreak stemmed from a single introduction event, although with different variants (Delta, Gamma and Mu). SARS-CoV-2 was detected in aerosol samples up to 52 d after the initial infection. Combining demographic, immune and viral parameters, the best predictive models for mortality comprised IFNB1 or age, viral ORF7a and ACE2 receptor transcripts. Comparison with published pre-vaccine fatal COVID-19 transcriptomic and genomic signatures uncovered a unique IRF3 low/IRF7 high immune signature in post-vaccine fatal COVID-19 outbreaks. A multi-layered strategy, including environmental sampling, immunomonitoring and early antiviral therapy, should be considered to prevent post-vaccination COVID-19 mortality in nursing homes.

Phylogeographic reconstruction of the emergence and spread of Powassan virus in the northeastern United States.

Powassan virus is an emerging tick-borne virus of concern for public health, but very little is known about its transmission patterns and ecology. Here, we expanded the genomic dataset by sequencing 279 Powassan viruses isolated from Ixodes scapularis ticks from the northeastern United States. Our phylogeographic reconstructions revealed that Powassan virus lineage II was likely introduced or emerged from a relict population in the Northeast between 1940 and 1975. Sequences strongly clustered by sampling location, suggesting a highly focal geographical distribution. Our analyses further indicated that Powassan virus lineage II emerged in the northeastern United States mostly following a south-to-north pattern, with a weighted lineage dispersal velocity of ~3 km/y. Since the emergence in the Northeast, we found an overall increase in the effective population size of Powassan virus lineage II, but with growth stagnating during recent years. The cascading effect of population expansion of white-tailed deer and I. scapularis populations likely facilitated the emergence of Powassan virus in the northeastern United States.

Zoonotic risk assessment among farmed mammals.

Farmed mammals may act as hosts for zoonotic viruses that can cause disease outbreaks in humans. This SnapShot shows which farmed mammals, and to what extent, are of particular risk of harboring and spreading viruses from viral families that are commonly associated with zoonotic disease. It also discusses genome surveillance methods and biosafety measures. To view this SnapShot, open or download the PDF.

Variant-specific introduction and dispersal dynamics of SARS-CoV-2 in New York City - from Alpha to Omicron.

Since the latter part of 2020, SARS-CoV-2 evolution has been characterised by the emergence of viral variants associated with distinct biological characteristics. While the main research focus has centred on the ability of new variants to increase in frequency and impact the effective reproductive number of the virus, less attention has been placed on their relative ability to establish transmission chains and to spread through a geographic area. Here, we describe a phylogeographic approach to estimate and compare the introduction and dispersal dynamics of the main SARS-CoV-2 variants - Alpha, Iota, Delta, and Omicron - that circulated in the New York City area between 2020 and 2022. Notably, our results indicate that Delta had a lower ability to establish sustained transmission chains in the NYC area and that Omicron (BA.1) was the variant fastest to disseminate across the study area. The analytical approach presented here complements non-spatially-explicit analytical approaches that seek a better understanding of the epidemiological differences that exist among successive SARS-CoV-2 variants of concern.

Dynamics of Eastern equine encephalitis virus during the 2019 outbreak in the Northeast United States.

Eastern equine encephalitis virus (EEEV) causes a rare but severe disease in horses and humans, and is maintained in an enzootic transmission cycle between songbirds and Culiseta melanura mosquitoes. In 2019, the largest EEEV outbreak in the United States for more than 50 years occurred, centered in the Northeast. To explore the dynamics of the outbreak, we sequenced 80 isolates of EEEV and combined them with existing genomic data. We found that, like previous years, cases were driven by frequent short-lived virus introductions into the Northeast from Florida. Once in the Northeast, we found that Massachusetts was important for regional spread. We found no evidence of any changes in viral, human, or bird factors which would explain the increase in cases in 2019. By using detailed mosquito surveillance data collected by Massachusetts and Connecticut, however, we found that the abundance of Cs. melanura was exceptionally high in 2019, as was the EEEV infection rate. We employed these mosquito data to build a negative binomial regression model and applied it to estimate early season risks of human or horse cases. We found that the month of first detection of EEEV in mosquito surveillance data and vector index (abundance multiplied by infection rate) were predictive of cases later in the season. We therefore highlight the importance of mosquito surveillance programs as an integral part of public health and disease control.

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

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