Swapping Birth and Death: Symmetries and Transformations in Phylodynamic Models.
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ABSTRACT:
SUBMITTER: Stadler T
PROVIDER: S-EPMC6701459 | biostudies-literature | 2019 Sep
REPOSITORIES: biostudies-literature
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Project description:Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the birth–death-sampling model (BDM), in the context of estimating population size and birth rates in a population growing exponentially according to the birth–death branching process. For sequences sampled at a single time, we found the coalescent and the BDM gave virtually indistinguishable results in terms of the growth rates and fraction of the population sampled, even when sampling from a small population. For sequences sampled at multiple time points, we find that the birth–death model estimators are subject to large bias if the sampling process is misspecified. Since BDMs incorporate a model of the sampling process, we show how much of the statistical power of BDMs arises from the sequence of sample times and not from the genealogical tree. This motivates the development of a new coalescent estimator, which is augmented with a model of the known sampling process and is potentially more precise than the coalescent that does not use sample time information.
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Project description: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.
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Project description: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.
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Project description:Coalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates.
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Project description:Population genetic modeling can enhance Bayesian phylogenetic inference by providing a realistic prior on the distribution of branch lengths and times of common ancestry. The parameters of a population genetic model may also have intrinsic importance, and simultaneous estimation of a phylogeny and model parameters has enabled phylodynamic inference of population growth rates, reproduction numbers, and effective population size through time. Phylodynamic inference based on pathogen genetic sequence data has emerged as useful supplement to epidemic surveillance, however commonly-used mechanistic models that are typically fitted to non-genetic surveillance data are rarely fitted to pathogen genetic data due to a dearth of software tools, and the theory required to conduct such inference has been developed only recently. We present a framework for coalescent-based phylogenetic and phylodynamic inference which enables highly-flexible modeling of demographic and epidemiological processes. This approach builds upon previous structured coalescent approaches and includes enhancements for computational speed, accuracy, and stability. A flexible markup language is described for translating parametric demographic or epidemiological models into a structured coalescent model enabling simultaneous estimation of demographic or epidemiological parameters and time-scaled phylogenies. We demonstrate the utility of these approaches by fitting compartmental epidemiological models to Ebola virus and Influenza A virus sequence data, demonstrating how important features of these epidemics, such as the reproduction number and epidemic curves, can be gleaned from genetic data. These approaches are provided as an open-source package PhyDyn for the BEAST2 phylogenetics platform.
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Project description:Phylodynamic modelling, which studies the joint dynamics of epidemiological and evolutionary processes, has made significant progress in recent years due to increasingly available genomic data and advances in statistical modelling. These advances have greatly improved our understanding of transmission dynamics of many important pathogens. Nevertheless, there remains a lack of effective, targetted diagnostic tools for systematically detecting model mis-specification. Development of such tools is essential for model criticism, refinement, and calibration. The idea of utilising latent residuals for model assessment has already been exploited in general spatio-temporal epidemiological settings. Specifically, by proposing appropriately designed non-centered, re-parameterizations of a given epidemiological process, one can construct latent residuals with known sampling distributions which can be used to quantify evidence of model mis-specification. In this paper, we extend this idea to formulate a novel model-diagnostic framework for phylodynamic models. Using simulated examples, we show that our framework may effectively detect a particular form of mis-specification in a phylodynamic model, particularly in the event of superspreading. We also exemplify our approach by applying the framework to a dataset describing a local foot-and-mouth (FMD) outbreak in the UK, eliciting strong evidence against the assumption of no within-host-diversity in the outbreak. We further demonstrate that our framework can facilitate model calibration in real-life scenarios, by proposing a within-host-diversity model which appears to offer a better fit to data than one that assumes no within-host-diversity of FMD virus.
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Project description:BackgroundPhylogenetic birth-death models are opening a new window on the processes of genome evolution in studies of the evolution of gene and protein families, protein-protein interaction networks, microRNAs, and copy number variation. Given a species tree and a set of genomic characters in present-day species, the birth-death approach estimates the most likely rates required to explain the observed data and returns the expected ancestral character states and the history of character state changes. Achieving a balance between model complexity and generalizability is a fundamental challenge in the application of birth-death models. While more parameters promise greater accuracy and more biologically realistic models, increasing model complexity can lead to overfitting and a heavy computational cost.ResultsHere we present a systematic, empirical investigation of these tradeoffs, using protein domain families in six metazoan genomes as a case study. We compared models of increasing complexity, implemented in the Count program, with respect to model fit, robustness, and stability. In addition, we used a bootstrapping procedure to assess estimator variability. The results show that the most complex model, which allows for both branch-specific and family-specific rate variation, achieves the best fit, without overfitting. Variance remains low with increasing complexity, except for family-specific loss rates. This variance is reduced when the number of discrete rate categories is increased.ConclusionsThe work presented here evaluates model choice for genomic birth-death models in a systematic way and presents the first use of bootstrapping to assess estimator variance in birth-death models. We find that a model incorporating both lineage and family rate variation yields more accurate estimators without sacrificing generality. Our results indicate that model choice can lead to fundamentally different evolutionary conclusions, emphasizing the importance of more biologically realistic and complex models.
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Project description:Quantifying epidemiological dynamics is crucial for understanding and forecasting the spread of an epidemic. The coalescent and the birth-death model are used interchangeably to infer epidemiological parameters from the genealogical relationships of the pathogen population under study, which in turn are inferred from the pathogen genetic sequencing data. To compare the performance of these widely applied models, we performed a simulation study. We simulated phylogenetic trees under the constant rate birth-death model and the coalescent model with a deterministic exponentially growing infected population. For each tree, we re-estimated the epidemiological parameters using both a birth-death and a coalescent based method, implemented as an MCMC procedure in BEAST v2.0. In our analyses that estimate the growth rate of an epidemic based on simulated birth-death trees, the point estimates such as the maximum a posteriori/maximum likelihood estimates are not very different. However, the estimates of uncertainty are very different. The birth-death model had a higher coverage than the coalescent model, i.e. contained the true value in the highest posterior density (HPD) interval more often (2-13% vs. 31-75% error). The coverage of the coalescent decreases with decreasing basic reproductive ratio and increasing sampling probability of infecteds. We hypothesize that the biases in the coalescent are due to the assumption of deterministic rather than stochastic population size changes. Both methods performed reasonably well when analyzing trees simulated under the coalescent. The methods can also identify other key epidemiological parameters as long as one of the parameters is fixed to its true value. In summary, when using genetic data to estimate epidemic dynamics, our results suggest that the birth-death method will be less sensitive to population fluctuations of early outbreaks than the coalescent method that assumes a deterministic exponentially growing infected population.
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Project description:Phylodynamics requires an interdisciplinary understanding of phylogenetics, epidemiology, and statistical inference. It has also experienced more intense application than ever before amid the SARS-CoV-2 pandemic. In light of this, we present a review of phylodynamic models beginning with foundational models and assumptions. Our target audience is public health researchers, epidemiologists, and biologists seeking a working knowledge of the links between epidemiology, evolutionary models, and resulting epidemiological inference. We discuss the assumptions linking evolutionary models of pathogen population size to epidemiological models of the infected population size. We then describe statistical inference for phylodynamic models and list how output parameters can be rearranged for epidemiological interpretation. We go on to cover more sophisticated models and finish by highlighting future directions.
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