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The Lotka-Volterra model of predator-prey interaction is based on the assumption of mass action, a concept borrowed from the traditional theory of chemical kinetics in which reactants are assumed to be homogeneously mixed. In order to explore the effect of spatial heterogeneity on predator-prey dynamics, we constructed a lattice-based reaction-diffusion model corresponding to the Lotka-Volterra equations. Spatial heterogeneity was imposed on the system using percolation maps, gradient percolation maps, and fractional Brownian surfaces. In all simulations where diffusion distances were short, anomalously low reaction orders and aggregated spatial patterns were observed, including traveling wave patterns. In general, the estimated reaction order decreased with increasing degrees of spatial heterogeneity. For simulations using percolation maps with p-values varying between 1.0 (all cells available) to 0.5 (50% available), order estimates varied from 1.27 to 0.47. Gradient percolation maps and fractional Brownian surfaces also resulted in anomalously low reaction orders. Increasing diffusion distances resulted in reaction order estimates approaching the expected value of 2. Analysis of

Author

Timothy H. Keitt; Alan R. Johnson

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-5193)

Published

1995

Language

EN