Coalescent theory combined with statistical modeling allows us to estimate effective population size fluctuations from molecular sequences of individuals sampled from a population of interest. When sequences are sampled serially through time and the distribution of the sampling times depends on the effective population size, explicit statistical modeling of sampling times improves population size estimation. Previous work assumed that the genealogy relating sampled sequences is known and modeled sampling times as an inhomogeneous Poisson process with log-intensity equal to a linear function of the log-transformed effective population size. We improve this approach in two ways. First, we extend the method to allow for joint Bayesian estimation of the genealogy, effective population size trajectory, and other model parameters. Next, we improve the sampling time model by incorporating additional sources of information in the form of time-varying covariates. We validate our new modeling framework using a simulation study and apply our new methodology to analyses of population dynamics of seasonal influenza and to the recent Ebola virus outbreak in West Africa.
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