SPEED OF INVASION IN LATTICE POPULATION-MODELS - PAIR-EDGE APPROXIMATION

We propose a simple approach to approximating the speed of invasion in lattice population models. Approximate critical parameter values for successful invasion are then found by solving for zero wave speed. The approximation is based on describing the occupied region by the ordin ary pair approximation, and using quasi-steady-state pair approximatio ns to describe the leading edge of the wave front. We illustrate this idea using the basic contact process on the 1 and 2 dimensional lattic e (with and without nearest-neighbor migration), finding very good agr eement between the approximation and simulation results. The approxima te critical values obtained by our approximation are significantly mor e accurate than those obtained by the ordinary pair approximation.