Self-Organization and Scaling in a Lattice Predator-Prey Model
B. R. Sutherland
D.A.M.T.P., University of Cambridge,
Cambridge, England CB3 9EW
A. E. Jacobs
Department of Physics,
University of Toronto,
Toronto, Canada M5S 1A7
Abstract
We propose that self-organization may provide a mechanism by which power-law cluster distributions of mobile prey (i.e., fish, phytoplankton) may develop; in contrast, such distributions have often been attributed to scaling of the background environment. Evidence supporting our proposal is provided by examining the dynamics of a cellular automaton-like model of a predator-prey system. The model, which is discrete in space and time, is robust and evolves to a state with oscillatory, phase-shifted populations for a large range of parameter values, namely the predator and prey breeding times and the predator starvation time. The distribution function of the prey cluster sizes
has roughly power-law form,
, over a range of moderately large sizes but is cut off at large
. The exponent
depends only weakly on the parameters of the model.