Spatial Instabilities within the Diffusive Lotka-Volterra System: Individual-Based Simulation Results

A predator-prey system is studied via an individual-based simulation technique involving discrete Lotka-Volterra-type predator and prey individuals occupying a two-dimensional lattice of up to 256 sites by 256 sites, encompassing up to 65,536 predators and 65,536 prey. Spatial instabilities are found that break the system into "asynchronous regions" that can stabilize the "global" populations. These spatial heterogeneities are determined to be the result of discretizing space, time, and the population. Agreement is found with analytic results for the non-spatial Lotka-Volterra model and the spatial Lolka-Volterra model with diffusion when the discretizations are scaled to zero. It is argued from an individual-based modelling perspective, however, that this limiting procedure is biologically untenable. The conclusion is that under an individual-based model formulation of the Lotka-Volterra system, spatially heterogeneous population distributions are allowed. The specific form of these spatial distributions are shown to be strongly dependent on the prey diffusion rate and the specifics of implementing individual stochasticity.