  The spread of invasive species can have far reaching environmental and
ecological consequences. Understanding invasion spread patterns and the
underlying process driving invasions are key to predicting and managing
invasions. We combine a set of statistical methods in a novel way to
characterize local spread properties and demonstrate their application using
simulated and historical data on invasive insects. Our method uses a Gaussian
process fit to the surface of waiting times to invasion in order to
characterize the vector field of spread. Using this method we estimate with
statistical uncertainties the speed and direction of spread at each location.
Simulations from a stratified diffusion model verify the accuracy of our
method. We show how we may link local rates of spread to environmental
covariates for two case studies: the spread of the gypsy moth (Lymantria
dispar), and hemlock wolly adelgid (Adelges tsugae) in North America. We
provide an R-package that automates the calculations for any spatially
referenced waiting time data.
