Pushing the Boundaries: Models for the Spatial Spread of Ecosystem Engineers.

Ecosystems engineers are species that can substantially alter their abiotic environment and thereby enhance their population growth. The net growth rate of obligate engineers is even negative unless they modify the environment. We derive and analyze a model for the spread and invasion of such species. Prior to engineering, the landscape consists of unsuitable habitat; after engineering, the habitat is suitable. The boundary between the two types of habitat is moved by the species through their engineering activity. Our model is a novel type of a reaction-diffusion free boundary problem. We prove the existence of traveling waves and give upper and lower bounds for their speeds. We illustrate how the speed depends on individual movement and engineering behavior near the boundary.