Background/Question/Methods   Biological invasions are a global phenomenon that affects the functioning and composition of ecosystems. Numerous studies have sought to understand the spread dynamics of invasive species to facilitate the development of management strategies. However, most statistical or mathematical models often assume radial spread without incorporating heterogeneity, consequently reporting a single speed across large areas. Here we present a new method to calculate not only local rates of spread but also the direction of movement. The method involves wombling of the surface of the waiting times to species establishment to generate a field of speed vectors that describe local invasion spread across a landscape.

Results/Conclusions   We use a theoretical example and empirical data on the gypsy moth invasion of the USA to show how local rates of spread can be calculated using wombling and subsequently correlated with local habitat features. Our results show how heterogeneity in spread rates can serve to increase the overall speed of range expansion. Finally we apply the wombling method to understand and characterize outbreak patterns using a theoretical host-parasitoid model and Larch budmoth and gypsy moth data.