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How well can the exponential-growth coalescent approximate constant-rate birth-death population dynamics?

ABSTRACT: One of the central objectives in the field of phylodynamics is the quantification of population dynamic processes using genetic sequence data or in some cases phenotypic data. Phylodynamics has been successfully applied to many different processes, such as the spread of infectious diseases, within-host evolution of a pathogen, macroevolution and even language evolution. Phylodynamic analysis requires a probability distribution on phylogenetic trees spanned by the genetic data. Because such a probability distribution is not available for many common stochastic population dynamic processes, coalescent-based approximations assuming deterministic population size changes are widely employed. Key to many population dynamic models, in particular epidemiological models, is a period of exponential population growth during the initial phase. Here, we show that the coalescent does not well approximate stochastic exponential population growth, which is typically modelled by a birth-death process. We demonstrate that introducing demographic stochasticity into the population size function of the coalescent improves the approximation for values of R0 close to 1, but substantial differences remain for large R0. In addition, the computational advantage of using an approximation over exact models vanishes when introducing such demographic stochasticity. These results highlight that we need to increase efforts to develop phylodynamic tools that correctly account for the stochasticity of population dynamic models for inference.

SUBMITTER: Stadler T

PROVIDER: S-EPMC4426635 | biostudies-literature | 2015 May

REPOSITORIES: biostudies-literature

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How well can the exponential-growth coalescent approximate constant-rate birth-death population dynamics?

Stadler Tanja T Vaughan Timothy G TG Gavryushkin Alex A Guindon Stephane S Kühnert Denise D Leventhal Gabriel E GE Drummond Alexei J AJ

Proceedings. Biological sciences 20150501 1806

One of the central objectives in the field of phylodynamics is the quantification of population dynamic processes using genetic sequence data or in some cases phenotypic data. Phylodynamics has been successfully applied to many different processes, such as the spread of infectious diseases, within-host evolution of a pathogen, macroevolution and even language evolution. Phylodynamic analysis requires a probability distribution on phylogenetic trees spanned by the genetic data. Because such a pro ...[more]

PMID: 25876846

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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.

Project description: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.

Project description:The stress-induced mutagenesis hypothesis postulates that in response to stress, bacteria increase their genome-wide mutation rate, in turn increasing the chances that a descendant is able to better withstand the stress. This has implications for antibiotic treatment: exposure to subinhibitory doses of antibiotics has been reported to increase bacterial mutation rates and thus probably the rate at which resistance mutations appear and lead to treatment failure. More generally, the hypothesis posits that stress increases evolvability (the ability of a population to generate adaptive genetic diversity) and thus accelerates evolution. Measuring mutation rates under stress, however, is problematic, because existing methods assume there is no death. Yet subinhibitory stress levels may induce a substantial death rate. Death events need to be compensated by extra replication to reach a given population size, thus providing more opportunities to acquire mutations. We show that ignoring death leads to a systematic overestimation of mutation rates under stress. We developed a system based on plasmid segregation that allows us to measure death and division rates simultaneously in bacterial populations. Using this system, we found that a substantial death rate occurs at the tested subinhibitory concentrations previously reported to increase mutation rate. Taking this death rate into account lowers and sometimes removes the signal for stress-induced mutagenesis. Moreover, even when antibiotics increase mutation rate, we show that subinhibitory treatments do not increase genetic diversity and evolvability, again because of effects of the antibiotics on population dynamics. We conclude that antibiotic-induced mutagenesis is overestimated because of death and that understanding evolvability under stress requires accounting for the effects of stress on population dynamics as much as on mutation rate. Our goal here is dual: we show that population dynamics and, in particular, the numbers of cell divisions are crucial but neglected parameters in the evolvability of a population, and we provide experimental and computational tools and methods to study evolvability under stress, leading to a reassessment of the magnitude and significance of the stress-induced mutagenesis paradigm.

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How well can the exponential-growth coalescent approximate constant-rate birth-death population dynamics?

Publications

How well can the exponential-growth coalescent approximate constant-rate birth-death population dynamics?

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