Genomic epidemiology uncovers the timing and origin of the emergence of mpox in humans.

Five years before the 2022-2023 global mpox outbreak Nigeria reported its first cases in nearly 40 years, with the ongoing epidemic since driven by sustained human-to-human transmission. However, limited genomic data has left questions about the timing and origin of the mpox virus' (MPXV) emergence. Here we generated 112 MPXV genomes from Nigeria from 2021-2023. We identify the closest zoonotic outgroup to the human epidemic in southern Nigeria, and estimate that the lineage transmitting from human-to-human emerged around July 2014, circulating cryptically until detected in September 2017. The epidemic originated in Southern Nigeria, particularly Rivers State, which also acted as a persistent and dominant source of viral dissemination to other states. We show that APOBEC3 activity increased MPXV's evolutionary rate twenty-fold during human-to-human transmission. We also show how Delphy, a tool for near-real-time Bayesian phylogenetics, can aid rapid outbreak analytics. Our study sheds light on MPXV's establishment in West Africa before the 2022-2023 global outbreak and highlights the need for improved pathogen surveillance and response.

Modeling the velocity of evolving lineages and predicting dispersal patterns.

Accurate estimation of the dispersal velocity or speed of evolving organisms is no mean feat. In fact, existing probabilistic models in phylogeography or spatial population genetics generally do not provide an adequate framework to define velocity in a relevant manner. For instance, the very concept of instantaneous speed simply does not exist under one of the most popular approaches that models the evolution of spatial coordinates as Brownian trajectories running along a phylogeny [30]. Here, we introduce a new family of models - the so-called "Phylogenetic Integrated Velocity" (PIV) models - that use Gaussian processes to explicitly model the velocity of evolving lineages instead of focusing on the fluctuation of spatial coordinates over time. We describe the properties of these models and show an increased accuracy of velocity estimates compared to previous approaches. Analyses of West Nile virus data in the U.S.A. indicate that PIV models provide sensible predictions of the dispersal of evolving pathogens at a one-year time horizon. These results demonstrate the feasibility and relevance of predictive phylogeography in monitoring epidemics in time and space.

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

The dynamics of severe acute respiratory syndrome coronavirus 2 (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-BA.1 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 United States became increasingly significant. The number of detected introductions varied from 96 and 101 for Alpha and Delta to 39 for Omicron-BA.1. Most of these introductions left a low number of descendants (<10), suggesting a limited impact on the evolution of the pandemic in Galicia. 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.

spread.gl: visualising pathogen dispersal in a high-performance browser application.

Phylogeographic analyses are able to exploit the location data associated with sampled molecular sequences to reconstruct the spatio-temporal dispersal history of a pathogen. Visualisation software is commonly used to facilitate the interpretation of the accompanying estimation results, as these are not always easily interpretable. spread.gl is a powerful, open-source and feature-rich browser application that enables smooth, intuitive and user-friendly visualisation of both discrete and continuous phylogeographic inference results, enabling the animation of pathogen geographic dispersal through time. spread.gl can render and combine the visualisation of several data layers, including a geographic layer (e.g., a world map), multiple layers that contain information extracted from the input phylogeny, and different types of layers that represent environmental data. As such, users can explore which environmental data may have shaped pathogen dispersal patterns, that can subsequently be formally tested through more principled statistical analyses. We showcase the visualisation features of spread.gl on several representative pathogen dispersal examples, including the smooth animation of a phylogeny encompassing over 17,000 genomic sequences resulting from a large-scale SARS-CoV-2 analysis.

Zoonotic infections by avian influenza virus: changing global epidemiology, investigation, and control.

Avian influenza virus continues to pose zoonotic, epizootic, and pandemic threats worldwide, as exemplified by the 2020-23 epizootics of re-emerging H5 genotype avian influenza viruses among birds and mammals and the fatal jump to humans of emerging A(H3N8) in early 2023. Future influenza pandemic threats are driven by extensive mutations and reassortments of avian influenza viruses rooted in frequent interspecies transmission and genetic mixing and underscore the urgent need for more effective actions. We examine the changing global epidemiology of human infections caused by avian influenza viruses over the past decade, including dramatic increases in both the number of reported infections in humans and the spectrum of avian influenza virus subtypes that have jumped to humans. We also discuss the use of advanced surveillance, diagnostic technologies, and state-of-the-art analysis methods for tracking emerging avian influenza viruses. We outline an avian influenza virus-specific application of the One Health approach, integrating enhanced surveillance, tightened biosecurity, targeted vaccination, timely precautions, and timely clinical management, and fostering global collaboration to control the threats of avian influenza viruses.

Computational Phenomapping of Randomized Clinical Trials to Enable Assessment of their Real-world Representativeness and Personalized Inference.

Importance: Randomized clinical trials (RCTs) are the standard for defining an evidence-based approach to managing disease, but their generalizability to real-world patients remains challenging to quantify. Objective: To develop a multidimensional patient variable mapping algorithm to quantify the similarity and representation of electronic health record (EHR) patients corresponding to an RCT and estimate the putative treatment effects in real-world settings based on individual treatment effects observed in an RCT. Design: A retrospective analysis of the Treatment of Preserved Cardiac Function Heart Failure with an Aldosterone Antagonist Trial (TOPCAT; 2006-2012) and a multi-hospital patient cohort from the electronic health record (EHR) in the Yale New Haven Hospital System (YNHHS; 2015-2023). Setting: A multicenter international RCT (TOPCAT) and multi-hospital patient cohort (YNHHS). Participants: All TOPCAT participants and patients with heart failure with preserved ejection fraction (HFpEF) and ≥1 hospitalization within YNHHS. Exposures: 63 pre-randomization characteristics measured across the TOPCAT and YNNHS cohorts. Main Outcomes and Measures: Real-world generalizability of the RCT TOPCAT using a multidimensional phenotypic distance metric between TOPCAT and YNHHS cohorts. Estimation of the individualized treatment effect of spironolactone use on all-cause mortality within the YNHHS cohort based on phenotypic distance from the TOPCAT cohort. Results: There were 3,445 patients in TOPCAT and 11,712 HFpEF patients across five hospital sites. Across the 63 TOPCAT variables mapped by clinicians to the EHR, there were larger differences between TOPCAT and each of the 5 EHR sites (median SMD 0.200, IQR 0.037-0.410) than between the 5 EHR sites (median SMD 0.062, IQR 0.010-0.130). The synthesis of these differences across covariates using our multidimensional similarity score also suggested substantial phenotypic dissimilarity between the TOPCAT and EHR cohorts. By phenotypic distance, a majority (55%) of TOPCAT participants were closer to each other than any individual EHR patient. Using a TOPCAT-derived model of individualized treatment benefit from spironolactone, those predicted to derive benefit and receiving spironolactone in the EHR cohorts had substantially better outcomes compared with predicted benefit and not receiving the medication (HR 0.74, 95% CI 0.62-0.89). Conclusions and Relevance: We propose a novel approach to evaluating the real-world representativeness of RCT participants against corresponding patients in the EHR across the full multidimensional spectrum of the represented phenotypes. This enables the evaluation of the implications of RCTs for real-world patients. KEY POINTS: Question: How can we examine the multi-dimensional generalizability of randomized clinical trials (RCT) to real-world patient populations?Findings: We demonstrate a novel phenotypic distance metric comparing an RCT to real-world populations in a large multicenter RCT of heart failure patients and the corresponding patients in multisite electronic health records (EHRs). Across 63 pre-randomization characteristics, pairwise assessments of members of the RCT and EHR cohorts were more discordant from each other than between members of the EHR cohort (median standardized mean difference 0.200 [0.037-0.410] vs 0.062 [0.010-0.130]), with a majority (55%) of RCT participants closer to each other than any individual EHR patient. The approach also enabled the quantification of expected real world outcomes based on effects observed in the RCT.Meaning: A multidimensional phenotypic distance metric quantifies the generalizability of RCTs to a given population while also offering an avenue to examine expected real-world patient outcomes based on treatment effects observed in the RCT.

Comparing penalization methods for linear models on large observational health data.

OBJECTIVE: This study evaluates regularization variants in logistic regression (L1, L2, ElasticNet, Adaptive L1, Adaptive ElasticNet, Broken adaptive ridge [BAR], and Iterative hard thresholding [IHT]) for discrimination and calibration performance, focusing on both internal and external validation. MATERIALS AND METHODS: We use data from 5 US claims and electronic health record databases and develop models for various outcomes in a major depressive disorder patient population. We externally validate all models in the other databases. We use a train-test split of 75%/25% and evaluate performance with discrimination and calibration. Statistical analysis for difference in performance uses Friedman's test and critical difference diagrams. RESULTS: Of the 840 models we develop, L1 and ElasticNet emerge as superior in both internal and external discrimination, with a notable AUC difference. BAR and IHT show the best internal calibration, without a clear external calibration leader. ElasticNet typically has larger model sizes than L1. Methods like IHT and BAR, while slightly less discriminative, significantly reduce model complexity. CONCLUSION: L1 and ElasticNet offer the best discriminative performance in logistic regression for healthcare predictions, maintaining robustness across validations. For simpler, more interpretable models, L0-based methods (IHT and BAR) are advantageous, providing greater parsimony and calibration with fewer features. This study aids in selecting suitable regularization techniques for healthcare prediction models, balancing performance, complexity, and interpretability.

Random-effects substitution models for phylogenetics via scalable gradient approximations.

Phylogenetic and discrete-trait evolutionary inference depend heavily on an appropriate characterization of the underlying character substitution process. In this paper, we present random-effects substitution models that extend common continuous-time Markov chain models into a richer class of processes capable of capturing a wider variety of substitution dynamics. As these random-effects substitution models often require many more parameters than their usual counterparts, inference can be both statistically and computationally challenging. Thus, we also propose an efficient approach to compute an approximation to the gradient of the data likelihood with respect to all unknown substitution model parameters. We demonstrate that this approximate gradient enables scaling of sampling-based inference, namely Bayesian inference via Hamiltonian Monte Carlo, under random-effects substitution models across large trees and state-spaces. Applied to a dataset of 583 SARS-CoV-2 sequences, an HKY model with random-effects shows strong signals of nonreversibility in the substitution process, and posterior predictive model checks clearly show that it is a more adequate model than a reversible model. When analyzing the pattern of phylogeographic spread of 1441 influenza A virus (H3N2) sequences between 14 regions, a random-effects phylogeographic substitution model infers that air travel volume adequately predicts almost all dispersal rates. A random-effects state-dependent substitution model reveals no evidence for an effect of arboreality on the swimming mode in the tree frog subfamily Hylinae. Simulations reveal that random-effects substitution models can accommodate both negligible and radical departures from the underlying base substitution model. We show that our gradient-based inference approach is over an order of magnitude more time efficient than conventional approaches.

Massive Parallelization of Massive Sample-size Survival Analysis.

Large-scale observational health databases are increasingly popular for conducting comparative effectiveness and safety studies of medical products. However, increasing number of patients poses computational challenges when fitting survival regression models in such studies. In this paper, we use graphics processing units (GPUs) to parallelize the computational bottlenecks of massive sample-size survival analyses. Specifically, we develop and apply time- and memory-efficient single-pass parallel scan algorithms for Cox proportional hazards models and forward-backward parallel scan algorithms for Fine-Gray models for analysis with and without a competing risk using a cyclic coordinate descent optimization approach. We demonstrate that GPUs accelerate the computation of fitting these complex models in large databases by orders of magnitude as compared to traditional multi-core CPU parallelism. Our implementation enables efficient large-scale observational studies involving millions of patients and thousands of patient characteristics. The above implementation is available in the open-source R package Cyclops (Suchard et al., 2013).

Assessing Covariate Balance with Small Sample Sizes.

Propensity score adjustment addresses confounding by balancing covariates in subject treatment groups through matching, stratification, inverse probability weighting, etc. Diagnostics ensure that the adjustment has been effective. A common technique is to check whether the standardized mean difference for each relevant covariate is less than a threshold like 0.1. For small sample sizes, the probability of falsely rejecting the validity of a study because of chance imbalance when no underlying balance exists approaches 1. We propose an alternative diagnostic that checks whether the standardized mean difference statistically significantly exceeds the threshold. Through simulation and real-world data, we find that this diagnostic achieves a better trade-off of type 1 error rate and power than standard nominal threshold tests and not testing for sample sizes from 250 to 4000 and for 20 to 100,000 covariates. In network studies, meta-analysis of effect estimates must be accompanied by meta-analysis of the diagnostics or else systematic confounding may overwhelm the estimated effect. Our procedure for statistically testing balance at both the database level and the meta-analysis level achieves the best balance of type-1 error rate and power. Our procedure supports the review of large numbers of covariates, enabling more rigorous diagnostics.

Integrating dynamical modeling and phylogeographic inference to characterize global influenza circulation.

Global seasonal influenza circulation involves a complex interplay between local (seasonality, demography, host immunity) and global factors (international mobility) shaping recurrent epidemic patterns. No studies so far have reconciled the two spatial levels, evaluating the coupling between national epidemics, considering heterogeneous coverage of epidemiological and virological data, integrating different data sources. We propose a novel combined approach based on a dynamical model of global influenza spread (GLEAM), integrating high-resolution demographic and mobility data, and a generalized linear model of phylogeographic diffusion that accounts for time-varying migration rates. Seasonal migration fluxes across global macro-regions simulated with GLEAM are tested as phylogeographic predictors to provide model validation and calibration based on genetic data. Seasonal fluxes obtained with a specific transmissibility peak time and recurrent travel outperformed the raw air-transportation predictor, previously considered as optimal indicator of global influenza migration. Influenza A subtypes supported autumn-winter reproductive number as high as 2.25 and an average immunity duration of 2 years. Similar dynamics were preferred by influenza B lineages, with a lower autumn-winter reproductive number. Comparing simulated epidemic profiles against FluNet data offered comparatively limited resolution power. The multiscale approach enables model selection yielding a novel computational framework for describing global influenza dynamics at different scales - local transmission and national epidemics vs. international coupling through mobility and imported cases. Our findings have important implications to improve preparedness against seasonal influenza epidemics. The approach can be generalized to other epidemic contexts, such as emerging disease outbreaks to improve the flexibility and predictive power of modeling.

How fast are viruses spreading in the wild?

Genomic data collected from viral outbreaks can be exploited to reconstruct the dispersal history of viral lineages in a two-dimensional space using continuous phylogeographic inference. These spatially explicit reconstructions can subsequently be used to estimate dispersal metrics allowing to unveil the dispersal dynamics and evaluate the capacity to spread among hosts. Heterogeneous sampling intensity of genomic sequences can however impact the accuracy of dispersal insights gained through phylogeographic inference. In our study, we implement a simulation framework to evaluate the robustness of three dispersal metrics - a lineage dispersal velocity, a diffusion coefficient, and an isolation-by-distance signal metric - to the sampling effort. Our results reveal that both the diffusion coefficient and isolation-by-distance signal metrics appear to be robust to the number of samples considered for the phylogeographic reconstruction. We then use these two dispersal metrics to compare the dispersal pattern and capacity of various viruses spreading in animal populations. Our comparative analysis reveals a broad range of isolation-by-distance patterns and diffusion coefficients mostly reflecting the dispersal capacity of the main infected host species but also, in some cases, the likely signature of rapid and/or long-distance dispersal events driven by human-mediated movements through animal trade. Overall, our study provides key recommendations for the lineage dispersal metrics to consider in future studies and illustrates their application to compare the spread of viruses in various settings.

The genomic evolutionary dynamics and global circulation patterns of respiratory syncytial virus.

Respiratory syncytial virus (RSV) is a leading cause of acute lower respiratory tract infection in young children and the second leading cause of infant death worldwide. While global circulation has been extensively studied for respiratory viruses such as seasonal influenza, and more recently also in great detail for SARS-CoV-2, a lack of global multi-annual sampling of complete RSV genomes limits our understanding of RSV molecular epidemiology. Here, we capitalise on the genomic surveillance by the INFORM-RSV study and apply phylodynamic approaches to uncover how selection and neutral epidemiological processes shape RSV diversity. Using complete viral genome sequences, we show similar patterns of site-specific diversifying selection among RSVA and RSVB and recover the imprint of non-neutral epidemic processes on their genealogies. Using a phylogeographic approach, we provide evidence for air travel governing the global patterns of RSVA and RSVB spread, which results in a considerable degree of phylogenetic mixing across countries. Our findings highlight the potential of systematic global RSV genomic surveillance for transforming our understanding of global RSV spread.

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.

Similar Risk of Kidney Failure among Patients with Blinding Diseases Who Receive Ranibizumab, Aflibercept, and Bevacizumab: An Observational Health Data Sciences and Informatics Network Study.

PURPOSE: To characterize the incidence of kidney failure associated with intravitreal anti-VEGF exposure; and compare the risk of kidney failure in patients treated with ranibizumab, aflibercept, or bevacizumab. DESIGN: Retrospective cohort study across 12 databases in the Observational Health Data Sciences and Informatics (OHDSI) network. SUBJECTS: Subjects aged ≥ 18 years with ≥ 3 monthly intravitreal anti-VEGF medications for a blinding disease (diabetic retinopathy, diabetic macular edema, exudative age-related macular degeneration, or retinal vein occlusion). METHODS: The standardized incidence proportions and rates of kidney failure while on treatment with anti-VEGF were calculated. For each comparison (e.g., aflibercept versus ranibizumab), patients from each group were matched 1:1 using propensity scores. Cox proportional hazards models were used to estimate the risk of kidney failure while on treatment. A random effects meta-analysis was performed to combine each database's hazard ratio (HR) estimate into a single network-wide estimate. MAIN OUTCOME MEASURES: Incidence of kidney failure while on anti-VEGF treatment, and time from cohort entry to kidney failure. RESULTS: Of the 6.1 million patients with blinding diseases, 37 189 who received ranibizumab, 39 447 aflibercept, and 163 611 bevacizumab were included; the total treatment exposure time was 161 724 person-years. The average standardized incidence proportion of kidney failure was 678 per 100 000 persons (range, 0-2389), and incidence rate 742 per 100 000 person-years (range, 0-2661). The meta-analysis HR of kidney failure comparing aflibercept with ranibizumab was 1.01 (95% confidence interval [CI], 0.70-1.47; P = 0.45), ranibizumab with bevacizumab 0.95 (95% CI, 0.68-1.32; P = 0.62), and aflibercept with bevacizumab 0.95 (95% CI, 0.65-1.39; P = 0.60). CONCLUSIONS: There was no substantially different relative risk of kidney failure between those who received ranibizumab, bevacizumab, or aflibercept. Practicing ophthalmologists and nephrologists should be aware of the risk of kidney failure among patients receiving intravitreal anti-VEGF medications and that there is little empirical evidence to preferentially choose among the specific intravitreal anti-VEGF agents. FINANCIAL DISCLOSURES: Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Scalable gradients enable Hamiltonian Monte Carlo sampling for phylodynamic inference under episodic birth-death-sampling models.

Birth-death models play a key role in phylodynamic analysis for their interpretation in terms of key epidemiological parameters. In particular, models with piecewise-constant rates varying at different epochs in time, to which we refer as episodic birth-death-sampling (EBDS) models, are valuable for their reflection of changing transmission dynamics over time. A challenge, however, that persists with current time-varying model inference procedures is their lack of computational efficiency. This limitation hinders the full utilization of these models in large-scale phylodynamic analyses, especially when dealing with high-dimensional parameter vectors that exhibit strong correlations. We present here a linear-time algorithm to compute the gradient of the birth-death model sampling density with respect to all time-varying parameters, and we implement this algorithm within a gradient-based Hamiltonian Monte Carlo (HMC) sampler to alleviate the computational burden of conducting inference under a wide variety of structures of, as well as priors for, EBDS processes. We assess this approach using three different real world data examples, including the HIV epidemic in Odesa, Ukraine, seasonal influenza A/H3N2 virus dynamics in New York state, America, and Ebola outbreak in West Africa. HMC sampling exhibits a substantial efficiency boost, delivering a 10- to 200-fold increase in minimum effective sample size per unit-time, in comparison to a Metropolis-Hastings-based approach. Additionally, we show the robustness of our implementation in both allowing for flexible prior choices and in modeling the transmission dynamics of various pathogens by accurately capturing the changing trend of viral effective reproductive number.

Comparative safety and effectiveness of angiotensin converting enzyme inhibitors and thiazides and thiazide-like diuretics under strict monotherapy.

Previous work comparing safety and effectiveness outcomes for new initiators of angiotensin converting-enzyme inhibitors (ACEi) and thiazides demonstrated more favorable outcomes for thiazides, although cohort definitions allowed for addition of a second antihypertensive medication after a week of monotherapy. Here, we modify the monotherapy definition, imposing exit from cohorts upon addition of another antihypertensive medication. We determine hazard ratios (HR) for 55 safety and effectiveness outcomes over six databases and compare results to earlier findings. We find, for all primary outcomes, statistically significant differences in effectiveness between ACEi and thiazides were not replicated (HRs: 1.11, 1.06, 1.12 for acute myocardial infarction, hospitalization with heart failure and stroke, respectively). While statistical significance is similarly lost for several safety outcomes, the safety profile of thiazides remains more favorable. Our results indicate a less striking difference in effectiveness of thiazides compared to ACEi and reflect some sensitivity to the monotherapy cohort definition modification.

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).

On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2.

The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC's infinitesimal generator (rate) matrix. Motivated by the derivative's extreme computational complexity as a function of state space cardinality, recent work demonstrates the surprising effectiveness of a naive, first-order approximation for a host of problems in computational biology. In response to this empirical success, we obtain rigorous deterministic and probabilistic bounds for the error accrued by the naive approximation and establish a "blessing of dimensionality" result that is universal for a large class of rate matrices with random entries. Finally, we apply the first-order approximation within surrogate-trajectory Hamiltonian Monte Carlo for the analysis of the early spread of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology.