Spatial distribution of dispersing animals

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Abstract
A mathematical model for the dispersal of an animal population is presented for a system in which animals are initially released in the central region of a uniform field and migrate randomly, exerting mutually repulsive influences (population pressure) until they eventually become sedentary. The effect of the population pressure, which acts to enhance the dispersal of animals as their density becomes high, is modeled in terms of a nonlinear-diffusion equation. From this model, the density distribution of animals is obtained as a function of time and the initial number of released animals. The analysis of this function shows that the population ultimately reaches a nonzero stationary distribution which is confined to a finite region if both the sedentary effect and the population pressure are present. Our results are in good agreement with the experimental data on ant lions reported by Morisita, and we can also interpret some general features known for the spatial distribution of dispersing insects.