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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received 4 September 1996
Rights and permissions
About this article
Cite this article
Ellner, S., Sasaki, A., Haraguchi, Y. et al. Speed of invasion in lattice population models: pair-edge approximation. J Math Biol 36, 469–484 (1998). https://doi.org/10.1007/s002850050109
Issue Date:
DOI: https://doi.org/10.1007/s002850050109