Beyond the ideal free distribution: More general models of predator distribution

The ideal free distribution model which relates the spatial distribution of mobile consumers to that of their resource is shown to be a limiting case of a more general model which we develop using simple concepts of diffusion. We show how the ideal free distribution model can be derived from a more general model and extended by incorporating simple models of social influences on predator spacing. First, a free distribution model based on patch switching rules, with a power-law interference term, which represents instantaneous biased diffusion is derived. A social bias term is then introduced to represent the effect of predator aggregation on predator fitness, separate from any effects which act through intake rate. The social bias term is expanded to express an optimum spacing for predators and example solutions of the resulting biased diffusion models are shown. The model demonstrates how an empirical interference coefficient, derived from measurements of predator and prey densities, may include factors expressing the impact of social spacing behaviour on fitness. We conclude that empirical values of log predator/log prey ratio may contain information about more than the relationship between consumer and resource densities. Unlike many previous models, the model shown here applies to conditions without continual input. (C) 1997 Academic Press Limited.