Nonparametric coalescent-based models are often employed to infer past population dynamics over time. Several of these models, such as the skyride and skygrid models, are equipped with a block-updating Markov chain Monte Carlo sampling scheme to efficiently estimate model parameters. The advent of powerful computational hardware along with the use of high-performance libraries for statistical phylogenetics has, however, made the development of alternative estimation methods feasible. We here present the implementation and performance assessment of a Hamiltonian Monte Carlo gradient-based sampler to infer the parameters of the skygrid model. The skygrid is a popular and flexible coalescent-based model for estimating population dynamics over time and is available in BEAST 1.10.5, a widely-used software package for Bayesian pylogenetic and phylodynamic analysis. Taking into account the increased computational cost of gradient evaluation, we report substantial increases in effective sample size per time unit compared to the established block-updating sampler. We expect gradient-based samplers to assume an increasingly important role for different classes of parameters typically estimated in Bayesian phylogenetic and phylodynamic analyses.

Markov models of character substitution on phylogenies form the foundation of phylogenetic inference frameworks. Early models made the simplifying assumption that the substitution process is homogeneous over time and across sites in the molecular sequence alignment. While standard practice adopts extensions that accommodate heterogeneity of substitution rates across sites, heterogeneity in the process over time in a site-specific manner remains frequently overlooked. This is problematic, as evolutionary processes that act at the molecular level are highly variable, subjecting different sites to different selective constraints over time, impacting their substitution behavior. We propose incorporating time variability through Markov-modulated models (MMMs), which extend covarion-like models and allow the substitution process (including relative character exchange rates as well as the overall substitution rate) at individual sites to vary across lineages. We implement a general MMM framework in BEAST, a popular Bayesian phylogenetic inference software package, allowing researchers to compose a wide range of MMMs through flexible XML specification. Using examples from bacterial, viral, and plastid genome evolution, we show that MMMs impact phylogenetic tree estimation and can substantially improve model fit compared to standard substitution models. Through simulations, we show that marginal likelihood estimation accurately identifies the generative model and does not systematically prefer the more parameter-rich MMMs. To mitigate the increased computational demands associated with MMMs, our implementation exploits recent developments in BEAGLE, a high-performance computational library for phylogenetic inference. [Bayesian inference; BEAGLE; BEAST; covarion, heterotachy; Markov-modulated models; phylogenetics.].

Understanding the processes that give rise to quantitative measurements associated with molecular sequence data remains an important issue in statistical phylogenetics. Examples of such measurements include geographic coordinates in the context of phylogeography and phenotypic traits in the context of comparative studies. A popular approach is to model the evolution of continuously varying traits as a Brownian diffusion process acting on a phylogenetic tree. However, standard Brownian diffusion is quite restrictive and may not accurately characterize certain trait evolutionary processes. Here, we relax one of the major restrictions of standard Brownian diffusion by incorporating a nontrivial estimable mean into the process. We introduce a relaxed directional random walk (RDRW) model for the evolution of multivariate continuously varying traits along a phylogenetic tree. Notably, the RDRW model accommodates branch-specific variation of directional trends while preserving model identifiability. Furthermore, our development of a computationally efficient dynamic programming approach to compute the data likelihood enables scaling of our method to large data sets frequently encountered in phylogenetic comparative studies and viral evolution. We implement the RDRW model in a Bayesian inference framework to simultaneously reconstruct the evolutionary histories of molecular sequence data and associated multivariate continuous trait data, and provide tools to visualize evolutionary reconstructions. We demonstrate the performance of our model on synthetic data, and we illustrate its utility in two viral examples. First, we examine the spatiotemporal spread of HIV-1 in central Africa and show that the RDRW model uncovers a clearer, more detailed picture of the dynamics of viral dispersal than standard Brownian diffusion. Second, we study antigenic evolution in the context of HIV-1 resistance to three broadly neutralizing antibodies. Our analysis reveals evidence of a continuous drift at the HIV-1 population level towards enhanced resistance to neutralization by the VRC01 monoclonal antibody over the course of the epidemic. [Brownian Motion; Diffusion Processes; Phylodynamics; Phylogenetics; Phylogeography; Trait Evolution.].

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

Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics and evolutionary biology. Kingman's coalescent process enables inference of past population dynamics directly from molecular sequence data, and researchers have developed a number of flexible coalescent-based models for Bayesian nonparametric estimation of the effective population size as a function of time. Major goals of demographic reconstruction include identifying driving factors of effective population size, and understanding the association between the effective population size and such factors. Building upon Bayesian nonparametric coalescent-based approaches, we introduce a flexible framework that incorporates time-varying covariates that exploit Gaussian Markov random fields to achieve temporal smoothing of effective population size trajectories. To approximate the posterior distribution, we adapt efficient Markov chain Monte Carlo algorithms designed for highly structured Gaussian models. Incorporating covariates into the demographic inference framework enables the modeling of associations between the effective population size and covariates while accounting for uncertainty in population histories. Furthermore, it can lead to more precise estimates of population dynamics. We apply our model to four examples. We reconstruct the demographic history of raccoon rabies in North America and find a significant association with the spatiotemporal spread of the outbreak. Next, we examine the effective population size trajectory of the DENV-4 virus in Puerto Rico along with viral isolate count data and find similar cyclic patterns. We compare the population history of the HIV-1 CRF02_AG clade in Cameroon with HIV incidence and prevalence data and find that the effective population size is more reflective of incidence rate. Finally, we explore the hypothesis that the population dynamics of musk ox during the Late Quaternary period were related to climate change. [Coalescent; effective population size; Gaussian Markov random fields; phylodynamics; phylogenetics; population genetics.

Spatially explicit phylogeographic analyses can be performed with an inference framework that employs relaxed random walks to reconstruct phylogenetic dispersal histories in continuous space. This core model was first implemented 10 years ago and has opened up new opportunities in the field of phylodynamics, allowing researchers to map and analyze the spatial dissemination of rapidly evolving pathogens. We here provide a detailed and step-by-step guide on how to set up, run, and interpret continuous phylogeographic analyses using the programs BEAUti, BEAST, Tracer, and TreeAnnotator.

During the first phase of the COVID-19 epidemic, New York City rapidly became the epicenter of the pandemic in the United States. While molecular phylogenetic analyses have previously highlighted multiple introductions and a period of cryptic community transmission within New York City, little is known about the circulation of SARS-CoV-2 within and among its boroughs. We here perform phylogeographic investigations to gain insights into the circulation of viral lineages during the first months of the New York City outbreak. Our analyses describe the dispersal dynamics of viral lineages at the state and city levels, illustrating that peripheral samples likely correspond to distinct dispersal events originating from the main metropolitan city areas. In line with the high prevalence recorded in this area, our results highlight the relatively important role of the borough of Queens as a transmission hub associated with higher local circulation and dispersal of viral lineages toward the surrounding boroughs.

Computational analyses of pathogen genomes are increasingly used to unravel the dispersal history and transmission dynamics of epidemics. Here, we show how to go beyond historical reconstructions and use spatially-explicit phylogeographic and phylodynamic approaches to formally test epidemiological hypotheses. We illustrate our approach by focusing on the West Nile virus (WNV) spread in North America that has substantially impacted public, veterinary, and wildlife health. We apply an analytical workflow to a comprehensive WNV genome collection to test the impact of environmental factors on the dispersal of viral lineages and on viral population genetic diversity through time. We find that WNV lineages tend to disperse faster in areas with higher temperatures and we identify temporal variation in temperature as a main predictor of viral genetic diversity through time. By contrasting inference with simulation, we find no evidence for viral lineages to preferentially circulate within the same migratory bird flyway, suggesting a substantial role for non-migratory birds or mosquito dispersal along the longitudinal gradient.

After the first wave of SARS-CoV-2 infections in spring 2020, Europe experienced a resurgence of the virus starting in late summer 2020 that was deadlier and more difficult to contain¹. Relaxed intervention measures and summer travel have been implicated as drivers of the second wave². Here we build a phylogeographical model to evaluate how newly introduced lineages, as opposed to the rekindling of persistent lineages, contributed to the resurgence of COVID-19 in Europe. We inform this model using genomic, mobility and epidemiological data from 10 European countries and estimate that in many countries more than half of the lineages circulating in late summer resulted from new introductions since 15 June 2020. The success in onward transmission of newly introduced lineages was negatively associated with the local incidence of COVID-19 during this period. The pervasive spread of variants in summer 2020 highlights the threat of viral dissemination when restrictions are lifted, and this needs to be carefully considered in strategies to control the current spread of variants that are more transmissible and/or evade immunity. Our findings indicate that more effective and coordinated measures are required to contain the spread through cross-border travel even as vaccination is reducing disease burden.