Bayesian Modeling of Viral Phylodynamics

Viral phylodynamics is the study of how immunodynamics, epidemiology, and evolutionary processes act and interact to shape viral phylogenies. We build upon the foundation of Bayesian phylogenetic inference to develop statistical tools to address phylodynamic problems. First, we present a flexible nonparametric Bayesian framework to infer the effective population size as a function of time directly from molecular sequence data. The effective population size is an abstract quantity that characterizes a population's genetic diversity, and it is of fundamental interest in population genetics, conservation biology, and infectious disease epidemiology. Our model is based on the coalescent, a stochastic process that relates phylogenies to population dynamics. We enforce temporal smoothing of inferred trajectories via a Gaussian Markov random field prior. Notably, our framework incorporates data from multiple genetic loci to achieve improved inference of population dynamics. Next, we turn to phylogenetic trait evolution. Modeling the processes giving rise to nonsequence traits associated with molecular sequence data is crucial in comparative studies of phenotypic traits as well as in phylogeographic analyses that reconstruct the spatiotemporal spread of viruses. A popular, yet restrictive approach to modeling such processes is Brownian diffusion along a phylogeny. We relax a major restriction by introducing a nontrivial estimable drift vector into the Brownian diffusion. Importantly, we implement a relaxed drift process that permits the drift vector to vary along the phylogeny. We showcase improved trait evolutionary inference in three viral examples. Finally, we return to effective population size inference and extend our framework to include covariates, enabling modeling of associations between past population dynamics and external factors. 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. 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