The Speed of Spatial Spread

Abstract

When a population can persist in a certain environment, we expect that it will spread through that environment if it is initially spatially confined to some small region. How fast will this spatial spread occur? How does the speed depend on movement behavior? These questions are particularly relevant for understanding and managing biological invasions. Spreading nonnative species can cause great damage to existing local ecosystems, e.g., by replacing native species or introducing pathogens. We need insights that help us decide between different management options to slow or contain the spread of harmful species. IDEs are particularly well suited to addressing the question of how different dispersal patterns influence the speed of spread. We begin this chapter with two different scenarios for spatial spread and explicit calculations for the linear growth function. We denote these as the point-release scenario and the traveling-front scenario. Then we define the asymptotic spreading speed and present the results for the nonlinear theory. Throughout the chapter, we assume that there is no Allee effect; we will devote Chap. 6 to it.