Gaussian Process-Based Bayesian Nonparametric Inference of Population Trajectories from Gene Genealogies

Details Gaussian Process-Based Bayesian Nonparametric Inference of Population Trajectories from Gene Genealogies Gaussian Process-Based Bayesian Nonparametric Inference of Population Trajectories from Gene Genealogies

2011-12-18

arxiv.org/abs/1112.4138v1

Statistics

Methodology

23 pages with 6 figures

Scientific paper

Changes in population size influence genetic diversity of the population and, as a result, leave imprints in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that the times where genealogical lineages coalesce contain all information about population size dynamics. Viewing these coalescent times as a point process, estimation of population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state of the art Gaussian Markov random field (GMRF) methods for estimating population size dynamics. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C virus in Egypt and human Influenza A virus sampled in New York. In both cases, we recover more known aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method.

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