Fitting stochastic epidemic models to gene genealogies using linear noise approximation.

Phylodynamics is a set of population genetics tools that aim at reconstructing demographic history of a population based on molecular sequences of individuals sampled from the population of interest. One important task in phylodynamics is to estimate changes in (effective) population size. When applied to infectious disease sequences such estimation of population size trajectories can provide information about changes in the number of infections. To model changes in the number of infected individuals, current phylodynamic methods use non-parametric approaches (e.g., Bayesian curve-fitting based on change-point models or Gaussian process priors), parametric approaches (e.g., based on differential equations), and stochastic modeling in conjunction with likelihood-free Bayesian methods. The first class of methods yields results that are hard to interpret epidemiologically. The second class of methods provides estimates of important epidemiological parameters, such as infection and removal/recovery rates, but ignores variation in the dynamics of infectious disease spread. The third class of methods is the most advantageous statistically, but relies on computationally intensive particle filtering techniques that limits its applications. We propose a Bayesian model that combines phylodynamic inference and stochastic epidemic models, and achieves computational tractability by using a linear noise approximation (LNA) - a technique that allows us to approximate probability densities of stochastic epidemic model trajectories. LNA opens the door for using modern Markov chain Monte Carlo tools to approximate the joint posterior distribution of the disease transmission parameters and of high dimensional vectors describing unobserved changes in the stochastic epidemic model compartment sizes (e.g., numbers of infectious and susceptible individuals). In a simulation study, we show that our method can successfully recover parameters of stochastic epidemic models. We apply our estimation technique to Ebola genealogies estimated using viral genetic data from the 2014 epidemic in Sierra Leone and Liberia.

Use of High-Resolution Geospatial and Genomic Data to Characterize Recent Tuberculosis Transmission, Botswana.

Combining genomic and geospatial data can be useful for understanding Mycobacterium tuberculosis transmission in high-burden tuberculosis (TB) settings. We performed whole-genome sequencing on M. tuberculosis DNA extracted from sputum cultures from a population-based TB study conducted in Gaborone, Botswana, during 2012-2016. We determined spatial distribution of cases on the basis of shared genotypes among isolates. We considered clusters of isolates with ≤5 single-nucleotide polymorphisms identified by whole-genome sequencing to indicate recent transmission and clusters of ≥10 persons to be outbreaks. We obtained both molecular and geospatial data for 946/1,449 (65%) participants with culture-confirmed TB; 62 persons belonged to 5 outbreaks of 10-19 persons each. We detected geospatial clustering in just 2 of those 5 outbreaks, suggesting heterogeneous spatial patterns. Our findings indicate that targeted interventions applied in smaller geographic areas of high-burden TB identified using integrated genomic and geospatial data might help interrupt TB transmission during outbreaks.

A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts.

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS-CoV-2 dynamics, and apply our method to national surveillance counts from the 2013-2015 West Africa Ebola outbreak.

Predictors of Test Positivity, Mortality, and Seropositivity during the Early Coronavirus Disease Epidemic, Orange County, California, USA.

We conducted a detailed analysis of coronavirus disease in a large population center in southern California, USA (Orange County, population 3.2 million), to determine heterogeneity in risks for infection, test positivity, and death. We used a combination of datasets, including a population-representative seroprevalence survey, to assess the actual burden of disease and testing intensity, test positivity, and mortality. In the first month of the local epidemic (March 2020), case incidence clustered in high-income areas. This pattern quickly shifted, and cases next clustered in much higher rates in the north-central area of the county, which has a lower socioeconomic status. Beginning in April 2020, a concentration of reported cases, test positivity, testing intensity, and seropositivity in a north-central area persisted. At the individual level, several factors (e.g., age, race or ethnicity, and ZIP codes with low educational attainment) strongly affected risk for seropositivity and death.

A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts.

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS-CoV-2 dynamics, and apply our method to national surveillance counts from the 2013--2015 West Africa Ebola outbreak.

Optimal experimental design for mathematical models of haematopoiesis.

The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters.

Locally adaptive Bayesian birth-death model successfully detects slow and rapid rate shifts.

Birth-death processes have given biologists a model-based framework to answer questions about changes in the birth and death rates of lineages in a phylogenetic tree. Therefore birth-death models are central to macroevolutionary as well as phylodynamic analyses. Early approaches to studying temporal variation in birth and death rates using birth-death models faced difficulties due to the restrictive choices of birth and death rate curves through time. Sufficiently flexible time-varying birth-death models are still lacking. We use a piecewise-constant birth-death model, combined with both Gaussian Markov random field (GMRF) and horseshoe Markov random field (HSMRF) prior distributions, to approximate arbitrary changes in birth rate through time. We implement these models in the widely used statistical phylogenetic software platform RevBayes, allowing us to jointly estimate birth-death process parameters, phylogeny, and nuisance parameters in a Bayesian framework. We test both GMRF-based and HSMRF-based models on a variety of simulated diversification scenarios, and then apply them to both a macroevolutionary and an epidemiological dataset. We find that both models are capable of inferring variable birth rates and correctly rejecting variable models in favor of effectively constant models. In general the HSMRF-based model has higher precision than its GMRF counterpart, with little to no loss of accuracy. Applied to a macroevolutionary dataset of the Australian gecko family Pygopodidae (where birth rates are interpretable as speciation rates), the GMRF-based model detects a slow decrease whereas the HSMRF-based model detects a rapid speciation-rate decrease in the last 12 million years. Applied to an infectious disease phylodynamic dataset of sequences from HIV subtype A in Russia and Ukraine (where birth rates are interpretable as the rate of accumulation of new infections), our models detect a strongly elevated rate of infection in the 1990s.

Estimating effective population size changes from preferentially sampled genetic sequences.

Coalescent theory combined with statistical modeling allows us to estimate effective population size fluctuations from molecular sequences of individuals sampled from a population of interest. When sequences are sampled serially through time and the distribution of the sampling times depends on the effective population size, explicit statistical modeling of sampling times improves population size estimation. Previous work assumed that the genealogy relating sampled sequences is known and modeled sampling times as an inhomogeneous Poisson process with log-intensity equal to a linear function of the log-transformed effective population size. We improve this approach in two ways. First, we extend the method to allow for joint Bayesian estimation of the genealogy, effective population size trajectory, and other model parameters. Next, we improve the sampling time model by incorporating additional sources of information in the form of time-varying covariates. We validate our new modeling framework using a simulation study and apply our new methodology to analyses of population dynamics of seasonal influenza and to the recent Ebola virus outbreak in West Africa.

A Bayesian phylogenetic hidden Markov model for B cell receptor sequence analysis.

The human body generates a diverse set of high affinity antibodies, the soluble form of B cell receptors (BCRs), that bind to and neutralize invading pathogens. The natural development of BCRs must be understood in order to design vaccines for highly mutable pathogens such as influenza and HIV. BCR diversity is induced by naturally occurring combinatorial "V(D)J" rearrangement, mutation, and selection processes. Most current methods for BCR sequence analysis focus on separately modeling the above processes. Statistical phylogenetic methods are often used to model the mutational dynamics of BCR sequence data, but these techniques do not consider all the complexities associated with B cell diversification such as the V(D)J rearrangement process. In particular, standard phylogenetic approaches assume the DNA bases of the progenitor (or "naive") sequence arise independently and according to the same distribution, ignoring the complexities of V(D)J rearrangement. In this paper, we introduce a novel approach to Bayesian phylogenetic inference for BCR sequences that is based on a phylogenetic hidden Markov model (phylo-HMM). This technique not only integrates a naive rearrangement model with a phylogenetic model for BCR sequence evolution but also naturally accounts for uncertainty in all unobserved variables, including the phylogenetic tree, via posterior distribution sampling.

Horseshoe-based Bayesian nonparametric estimation of effective population size trajectories.

Phylodynamics is an area of population genetics that uses genetic sequence data to estimate past population dynamics. Modern state-of-the-art Bayesian nonparametric methods for recovering population size trajectories of unknown form use either change-point models or Gaussian process priors. Change-point models suffer from computational issues when the number of change-points is unknown and needs to be estimated. Gaussian process-based methods lack local adaptivity and cannot accurately recover trajectories that exhibit features such as abrupt changes in trend or varying levels of smoothness. We propose a novel, locally adaptive approach to Bayesian nonparametric phylodynamic inference that has the flexibility to accommodate a large class of functional behaviors. Local adaptivity results from modeling the log-transformed effective population size a priori as a horseshoe Markov random field, a recently proposed statistical model that blends together the best properties of the change-point and Gaussian process modeling paradigms. We use simulated data to assess model performance, and find that our proposed method results in reduced bias and increased precision when compared to contemporary methods. We also use our models to reconstruct past changes in genetic diversity of human hepatitis C virus in Egypt and to estimate population size changes of ancient and modern steppe bison. These analyses show that our new method captures features of the population size trajectories that were missed by the state-of-the-art methods.

19 Dubious Ways to Compute the Marginal Likelihood of a Phylogenetic Tree Topology.

The marginal likelihood of a model is a key quantity for assessing the evidence provided by the data in support of a model. The marginal likelihood is the normalizing constant for the posterior density, obtained by integrating the product of the likelihood and the prior with respect to model parameters. Thus, the computational burden of computing the marginal likelihood scales with the dimension of the parameter space. In phylogenetics, where we work with tree topologies that are high-dimensional models, standard approaches to computing marginal likelihoods are very slow. Here, we study methods to quickly compute the marginal likelihood of a single fixed tree topology. We benchmark the speed and accuracy of 19 different methods to compute the marginal likelihood of phylogenetic topologies on a suite of real data sets under the JC69 model. These methods include several new ones that we develop explicitly to solve this problem, as well as existing algorithms that we apply to phylogenetic models for the first time. Altogether, our results show that the accuracy of these methods varies widely, and that accuracy does not necessarily correlate with computational burden. Our newly developed methods are orders of magnitude faster than standard approaches, and in some cases, their accuracy rivals the best established estimators.

Survival analysis of DNA mutation motifs with penalized proportional hazards.

Antibodies, an essential part of our immune system, develop through an intricate process to bind a wide array of pathogens. This process involves randomly mutating DNA sequences encoding these antibodies to find variants with improved binding, though mutations are not distributed uniformly across sequence sites. Immunologists observe this nonuniformity to be consistent with "mutation motifs", which are short DNA subsequences that affect how likely a given site is to experience a mutation. Quantifying the effect of motifs on mutation rates is challenging: a large number of possible motifs makes this statistical problem high dimensional, while the unobserved history of the mutation process leads to a nontrivial missing data problem. We introduce an ℓ 1-penalized proportional hazards model to infer mutation motifs and their effects. In order to estimate model parameters, our method uses a Monte Carlo EM algorithm to marginalize over the unknown ordering of mutations. We show that our method performs better on simulated data compared to current methods and leads to more parsimonious models. The application of proportional hazards to mutation processes is, to our knowledge, novel and formalizes the current methods in a statistical framework that can be easily extended to analyze the effect of other biological features on mutation rates.

Recombination-independent rapid convergent evolution of the gastric pathogen Helicobacter pylori.

BACKGROUND: Helicobacter pylori is a human stomach pathogen, naturally-competent for DNA uptake, and prone to homologous recombination. Extensive homoplasy (i.e., phylogenetically-unlinked identical variations) observed in H. pylori genes is considered a hallmark of such recombination. However, H. pylori also exhibits a high mutation rate. The relative adaptive role of homologous recombination and mutation in species diversity is a highly-debated issue in biology. Recombination results in homoplasy. While convergent mutation can also account for homoplasy, its contribution is thought to be minor. We demonstrate here that, contrary to dogma, convergent mutation is a key contributor to Helicobacter pylori homoplasy, potentially driven by adaptive evolution of proteins. RESULTS: Our present genome-wide analysis shows that homoplastic nonsynonymous (amino acid replacement) changes are not typically accompanied by homoplastic synonymous (silent) variations. Moreover, the majority of the codon positions with homoplastic nonsynonymous changes also contain different (i.e. non-homoplastic) nonsynonymous changes arising from mutation only. This indicates that, to a considerable extent, nonsynonymous homoplasy is due to convergent mutations. High mutation rate or limited availability of evolvable sites cannot explain this excessive convergence, as suggested by our simulation studies. Rather, the genes with convergent mutations are overrepresented in distinct functional categories, suggesting possible selective responses to conditions such as distinct micro-niches in single hosts, and to differences in host genotype, physiology, habitat and diet. CONCLUSIONS: We propose that mutational convergence is a key player in H. pylori's adaptation and extraordinary persistence in human hosts. High frequency of mutational convergence could be due to saturation of evolvable sites capable of responding to selection pressures, while the number of mutable residues is far from saturation. We anticipate a similar scenario of mutational vs. recombinational genome dynamics or plasticity for other naturally competent microbes where strong positive selection could favor frequent convergent mutations in adaptive protein evolution.

Predicting B cell receptor substitution profiles using public repertoire data.

B cells develop high affinity receptors during the course of affinity maturation, a cyclic process of mutation and selection. At the end of affinity maturation, a number of cells sharing the same ancestor (i.e. in the same "clonal family") are released from the germinal center; their amino acid frequency profile reflects the allowed and disallowed substitutions at each position. These clonal-family-specific frequency profiles, called "substitution profiles", are useful for studying the course of affinity maturation as well as for antibody engineering purposes. However, most often only a single sequence is recovered from each clonal family in a sequencing experiment, making it impossible to construct a clonal-family-specific substitution profile. Given the public release of many high-quality large B cell receptor datasets, one may ask whether it is possible to use such data in a prediction model for clonal-family-specific substitution profiles. In this paper, we present the method "Substitution Profiles Using Related Families" (SPURF), a penalized tensor regression framework that integrates information from a rich assemblage of datasets to predict the clonal-family-specific substitution profile for any single input sequence. Using this framework, we show that substitution profiles from similar clonal families can be leveraged together with simulated substitution profiles and germline gene sequence information to improve prediction. We fit this model on a large public dataset and validate the robustness of our approach on two external datasets. Furthermore, we provide a command-line tool in an open-source software package (https://github.com/krdav/SPURF) implementing these ideas and providing easy prediction using our pre-fit models.

Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors.

We present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework. This method uses shrinkage priors to induce sparsity in order-k differences in the latent trend function, providing a combination of local adaptation and global control. Using a scale mixture of normals representation of shrinkage priors, we make explicit connections between our method and kth order Gaussian Markov random field smoothing. We call the resulting processes shrinkage prior Markov random fields (SPMRFs). We use Hamiltonian Monte Carlo to approximate the posterior distribution of model parameters because this method provides superior performance in the presence of the high dimensionality and strong parameter correlations exhibited by our models. We compare the performance of three prior formulations using simulated data and find the horseshoe prior provides the best compromise between bias and precision. We apply SPMRF models to two benchmark data examples frequently used to test nonparametric methods. We find that this method is flexible enough to accommodate a variety of data generating models and offers the adaptive properties and computational tractability to make it a useful addition to the Bayesian nonparametric toolbox.

Using Genotype Abundance to Improve Phylogenetic Inference.

Modern biological techniques enable very dense genetic sampling of unfolding evolutionary histories, and thus frequently sample some genotypes multiple times. This motivates strategies to incorporate genotype abundance information in phylogenetic inference. In this article, we synthesize a stochastic process model with standard sequence-based phylogenetic optimality, and show that tree estimation is substantially improved by doing so. Our method is validated with extensive simulations and an experimental single-cell lineage tracing study of germinal center B cell receptor affinity maturation.

Birth/birth-death processes and their computable transition probabilities with biological applications.

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth/birth-death process, a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution.

Myosin-independent cytokinesis in Giardia utilizes flagella to coordinate force generation and direct membrane trafficking.

Devoid of all known canonical actin-binding proteins, the prevalent parasite Giardia lamblia uses an alternative mechanism for cytokinesis. Unique aspects of this mechanism can potentially be leveraged for therapeutic development. Here, live-cell imaging methods were developed for Giardia to establish division kinetics and the core division machinery. Surprisingly, Giardia cytokinesis occurred with a median time that is ∼60 times faster than mammalian cells. In contrast to cells that use a contractile ring, actin was not concentrated in the furrow and was not directly required for furrow progression. Live-cell imaging and morpholino depletion of axonemal Paralyzed Flagella 16 indicated that flagella-based forces initiated daughter cell separation and provided a source for membrane tension. Inhibition of membrane partitioning blocked furrow progression, indicating a requirement for membrane trafficking to support furrow advancement. Rab11 was found to load onto the intracytoplasmic axonemes late in mitosis and to accumulate near the ends of nascent axonemes. These developing axonemes were positioned to coordinate trafficking into the furrow and mark the center of the cell in lieu of a midbody/phragmoplast. We show that flagella motility, Rab11, and actin coordination are necessary for proper abscission. Organisms representing three of the five eukaryotic supergroups lack myosin II of the actomyosin contractile ring. These results support an emerging view that flagella play a central role in cell division among protists that lack myosin II and additionally implicate the broad use of membrane tension as a mechanism to drive abscission.

Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time.

Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences.