Long-Distance Dispersal and Spread

Abstract

Long-distance dispersal is a key factor driving rapid spread of invasive species. In this chapter, we develop models for dispersal kernels, which describe the spatial distribution of propagules relative to their parent. Dynamical systems that couple dispersal kernels with population growth can be formulated in either discrete time (integrodifference equations) or continuous time (integrodifferential equations). We show that, when long-distance dispersal via the dispersal kernel is incorporated into a dynamical system, the population can spread an order of magnitude faster than predicted by the equivalent reaction–diffusion models of the sort seen in Chap. 3 Indeed, when dispersal kernels are fat-tailed, the population spread can actually accelerate continually, leading to theoretically infinite asymptotic spreading speeds. We show how the concept of rapid invasive spread has applications not only to invasive species but also to the spread of infectious disease. The idea of an accelerating invasion can also be understood via the concept of stratified diffusion, where a spatially implicit model is used to keep track of the size distribution of localized invasion processes. Finally, the results regarding rapid spread implicitly assume that there are no Allee effects. We show how Allee effects obstruct rapid and accelerating invasions, bringing the spreading speed down to much lower levels.