Quantifying spatio-temporal variation of invasion spread

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 novelway 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 woolly adelgid (Adelges tsugae) in North America. We provide an R-package that automates the calculations for any spatially referenced waiting time data.