Over the course of an epidemic, many viral pathogens are known to evolve rapidly, leaving an imprint of the pattern of spread in their genomes. Uncovering the molecular footprint of this transmission process is a key goal of phylodynamic inference. Phylogeography takes dated and spatially referenced sequences to analyse the spatial spread of the epidemics, trying to answer questions such as how fast the virus is spreading, or where did it emerge or was introduced originally. Given a dated phylogenetic tree, phylogeography models the spatial spread as a continuous space and time stochastic process on the tree, that splits into independent processes at each tree bifurcation. The so-called relaxed random walk is widely popular in the domain. It can be shown to be equivalent, under some assumptions, to a pure jump process. Just as the regular Brownian motion, it has infinite variations, making any speed estimation based on it inconsistent, a phenomenon that has been observed in the literature. The integrated Brownian and Ornstein–Uhlenbeck processes, by definition, have more regularity, and therefore can be better suited to model a spatial spread. We show how the likelihood of such processes can be computed in a linear time in the number of observations, making Bayesian inference possible. We apply our results to the study of the spread of the West Nile Virus in North America in the early 2000s.
Joint work with Gilles Didier and Stéphane Guindon.
References: https://doi.org/10.1093/sysbio/syad053, https://doi.org/10.1073/pnas.2411582121
