Spreading speed and linear determinacy for two-species competition models (original) (raw)

Abstract

One crucial measure of a species' invasiveness is the rate at which it spreads into a competitor's environment. A heuristic spread rate formula for a spatially explicit, two-species competition model relies on `linear determinacy' which equates spread rate in the full nonlinear model with spread rate in the system linearized about the leading edge of the invasion. However, linear determinacy is not always valid for two-species competition; it has been shown numerically that the formula only works for certain values of model parameters when the model is diffusive Lotka-Volterra competition [2]. This paper derives a set of sufficient conditions for linear determinacy in spatially explicit two-species competition models. These conditions can be interpreted as requiring sufficiently large dispersal of the invader relative to dispersal of the out-competed resident and sufficiently weak interactions between the resident and the invader. When these conditions are not satisfied, spread rate may exceed linearly determined predictions. The mathematical methods rely on the application of results established in a companion paper [11].

Access this article

Log in via an institution

Subscribe and save

• Starting from 10 chapters or articles per month
• Access and download chapters and articles from more than 300k books and 2,500 journals
• Cancel anytime View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Author information

Authors and Affiliations

1. Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA, , , , , , US
   Mark A. Lewis & Bingtuan Li
2. School of Mathematics, University of Minnesota, 514 Vincent Hall, 206 Church Street S.E., Minneapolis, Minnesota 55455, USA, , , , , , US
   Hans F. Weinberger

Authors

1. Mark A. Lewis
2. Bingtuan Li
3. Hans F. Weinberger

Additional information

Received: 7 August 2000 / Revised version: 5 January 2002 / Published online: 17 July 2002

Rights and permissions

About this article

Cite this article

Lewis, M., Li, B. & Weinberger, H. Spreading speed and linear determinacy for two-species competition models.J Math Biol 45, 219–233 (2002). https://doi.org/10.1007/s002850200144

Download citation

• Issue date: September 2002
• DOI: https://doi.org/10.1007/s002850200144

Keywords