Speed of invasion in lattice population models: pair-edge approximation
Generate an AI Snapshot to get a quick, structured summary of this paper.
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
A simple approach to approximating the speed of invasion in lattice population models by using quasi-steady-state pair approximations to describe the leading edge of the wave front, finding very good agreement between the approximation and simulation results.
Abstract
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 ordinary pair approximation, and using quasi-steady-state pair approximations to describe the leading edge of the wave front. We illustrate this idea using the basic contact process on the 1 and 2 dimensional lattice (with and without nearest-neighbor migration), finding very good agreement between the approximation and simulation results. The approximate critical values obtained by our approximation are significantly more accurate than those obtained by the ordinary pair approximation.