Quantifying Spatio-Temporal Variation of Invasion Spread

TL;DR

This paper introduces a novel statistical approach using Gaussian processes to quantify and visualize the local speed and direction of invasive species spread, validated with simulations and applied to real case studies.

Contribution

It combines statistical methods in a new way to estimate invasion spread dynamics and links them to environmental factors, providing an R-package for practical application.

Findings

Accurate estimation of spread speed and direction at each location.

Successful application to case studies of gypsy moth and hemlock wolly adelgid.

Validated method with simulated diffusion models.

Abstract

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.