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      Inference of Epidemiological Dynamics Based on Simulated Phylogenies Using Birth-Death and Coalescent Models

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          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.

          Author Summary

          The control or prediction of an epidemic outbreak requires the quantification of the parameters of transmission and recovery. These parameters can be inferred from phylogenetic relationships among the pathogen strains isolated from infected individuals. The coalescent and the birth-death process are two mathematical models commonly used in such inferences. No benchmark on the performance of these models currently exists. We aimed to objectively compare two specific models, namely the constant rate birth-death model and the coalescent with a deterministic exponentially growing infected population. We compare coverage, accuracy, and precision with which they can capture the true epidemic growth rate parameter using simulated datasets. We find that the constant rate birth-death process can account for early stochasticity and is thus capable of recovering the epidemic growth rates more successfully. Provided one of the parameters is known, e.g. the sampling proportion of infected individuals, then the basic reproductive ratio can also be estimated reliably. We conclude that a birth-death-based method is generally a more reliable method than a deterministic coalescent-based method for epidemiological parameter inference from phylogenies representing epidemic outbreaks. Care should be taken if sampling is not constant through time or across individuals, such scenarios require so-called birth-death skyline models or multi-type birth-death models.

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          Most cited references 22

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          BEAST: Bayesian evolutionary analysis by sampling trees

          Background The evolutionary analysis of molecular sequence variation is a statistical enterprise. This is reflected in the increased use of probabilistic models for phylogenetic inference, multiple sequence alignment, and molecular population genetics. Here we present BEAST: a fast, flexible software architecture for Bayesian analysis of molecular sequences related by an evolutionary tree. A large number of popular stochastic models of sequence evolution are provided and tree-based models suitable for both within- and between-species sequence data are implemented. Results BEAST version 1.4.6 consists of 81000 lines of Java source code, 779 classes and 81 packages. It provides models for DNA and protein sequence evolution, highly parametric coalescent analysis, relaxed clock phylogenetics, non-contemporaneous sequence data, statistical alignment and a wide range of options for prior distributions. BEAST source code is object-oriented, modular in design and freely available at under the GNU LGPL license. Conclusion BEAST is a powerful and flexible evolutionary analysis package for molecular sequence variation. It also provides a resource for the further development of new models and statistical methods of evolutionary analysis.
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            BEAST 2: A Software Platform for Bayesian Evolutionary Analysis

            We present a new open source, extensible and flexible software platform for Bayesian evolutionary analysis called BEAST 2. This software platform is a re-design of the popular BEAST 1 platform to correct structural deficiencies that became evident as the BEAST 1 software evolved. Key among those deficiencies was the lack of post-deployment extensibility. BEAST 2 now has a fully developed package management system that allows third party developers to write additional functionality that can be directly installed to the BEAST 2 analysis platform via a package manager without requiring a new software release of the platform. This package architecture is showcased with a number of recently published new models encompassing birth-death-sampling tree priors, phylodynamics and model averaging for substitution models and site partitioning. A second major improvement is the ability to read/write the entire state of the MCMC chain to/from disk allowing it to be easily shared between multiple instances of the BEAST software. This facilitates checkpointing and better support for multi-processor and high-end computing extensions. Finally, the functionality in new packages can be easily added to the user interface (BEAUti 2) by a simple XML template-based mechanism because BEAST 2 has been re-designed to provide greater integration between the analysis engine and the user interface so that, for example BEAST and BEAUti use exactly the same XML file format.
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              Bayesian coalescent inference of past population dynamics from molecular sequences.

              We introduce the Bayesian skyline plot, a new method for estimating past population dynamics through time from a sample of molecular sequences without dependence on a prespecified parametric model of demographic history. We describe a Markov chain Monte Carlo sampling procedure that efficiently samples a variant of the generalized skyline plot, given sequence data, and combines these plots to generate a posterior distribution of effective population size through time. We apply the Bayesian skyline plot to simulated data sets and show that it correctly reconstructs demographic history under canonical scenarios. Finally, we compare the Bayesian skyline plot model to previous coalescent approaches by analyzing two real data sets (hepatitis C virus in Egypt and mitochondrial DNA of Beringian bison) that have been previously investigated using alternative coalescent methods. In the bison analysis, we detect a severe but previously unrecognized bottleneck, estimated to have occurred 10,000 radiocarbon years ago, which coincides with both the earliest undisputed record of large numbers of humans in Alaska and the megafaunal extinctions in North America at the beginning of the Holocene.

                Author and article information

                Role: Editor
                PLoS Comput Biol
                PLoS Comput. Biol
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                November 2014
                6 November 2014
                : 10
                : 11
                [1 ]Department of Biosystems Science & Engineering (D-BSSE), Eidgenössische Technische Hochschule (ETH) Zürich, Basel, Switzerland
                [2 ]Institute of Integrative Biology, Eidgenössische Technische Hochschule (ETH) Zürich, Zürich, Switzerland
                Duke University, United States of America
                Author notes

                The authors have declared that no competing interests exist.

                Conceived and designed the experiments: VB SB TS. Performed the experiments: VB TS. Contributed reagents/materials/analysis tools: VB TS. Wrote the paper: VB SB TS.


                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                Pages: 18
                TS and SB thank ETH Zürich and the Swiss National Science foundation for funding. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Research Article
                Biology and Life Sciences
                Evolutionary Biology
                Evolutionary Systematics
                Plant Science
                Plant Pathology
                Infectious Disease Epidemiology
                Population Biology
                Medicine and Health Sciences

                Quantitative & Systems biology


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