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Syst Biol. 2016 Nov;65(6):1041-1056. Epub 2016 Jul 1.

Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates.

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Department of Statistics, Columbia University, New York, NY 10027, USA.
Department of Microbiology and Immunology, Rega Institute, KU Leuven, Minderbroederstaat 10, 3000 Leuven, Belgium.
Department of Microbiology, California Academy of Sciences, San Francisco, CA 94118, USA.
Boyd Orr Centre for Population and Ecosystem Health, Institute of Biodiversity, Animal Health and Comparative Medicine, College of Medical, Veterinary and Life Sciences, University of Glasgow, Glasgow G12 8QQ, UK.
Department of Biomathematics, David Geffen School of Medicine at UCLA, University of California, Los Angeles, CA 90095, USA.
Department of Human Genetics, David Geffen School of Medicine at UCLA, Universtiy of California, Los Angeles, CA 90095, USA.
Department of Biostatistics, Jonathan and Karin Fielding School of Public Health, University of California, Los Angeles, CA 90095, USA.


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.

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