Patchiness in the Spatial Distribution of a Population Caused by Stochastic Fluctuations in Resources

This paper presents a model for a simple and possibly very common mechanism to produce patchiness. It is shown that patchiness is an inevitable consequence simply of dispersal in a randomly fluctuating environment. The paper discusses the measurement of patchiness using the variance spectrum. A linearized model for population dynamics in a spatially and temporally varying environment is introduced and analyzed. Explicit formulae are obtained for the equilibrium spatial pattern of the population as a function of the spatial pattern of the resource abundance and of the population's rate of increase and dispersal characteristics.