Invasions with density-dependent ecological parameters.

The speed and the minimum carrying capacity needed for a successful population expansion into new territory are addressed using a reaction-diffusion model. The model is able to encapsulate a rich collection of ecological behaviours, including the Allee effect, resource depletion due to consumption, dispersal adaptation due to population pressure, biological control agents, and a range of breeding suppression mechanisms such as embryonic diapause, delayed development and sperm storage. It is shown how many of these phenomena can be characterised as density-dependence in a few fundamental ecological parameters. With the help of a powerful mathematical technique recently developed by Balasuriya and Gottwald (J. Math. Biol. 61, pp. 377-399, 2010), explicit formulae for the effect on the speed and minimum carrying capacity are obtained.