The regulation of inhomogeneous populations

A number of authors have argued that dispersal may play a key role in the regulation of populations of some species. In this paper we examine, on an ecological time scale, mechanisms whereby a population existing in an inhomogeneous environment may use dispersal to regulate its size below the carrying capacity set by the supply of available nutrients. We show that dispersal produced by wholly random motion is incapable of exerting any stabilizing influence, but that the introduction of a suitable non-linearity into the dispersal behaviour of a species whose characteristics are otherwise wholly linear can lead to stabilization under a wide range of conditions.