Minimal wave speed and spread speed of competing pioneer and climax species

Abstract

In this article, for a diffusive population model describing interaction of pioneer-climax species, we explore the issues of spreading speed, linear determinacy and traveling wave fronts. Applying the theory developed by Weinberger et al. [J. Math. Biol. 2002;45:183–218], we identify some ranges of model parameters within which, the model is shown to have a single spreading speed which is linearly determinate and coincides with the corresponding minimal speed for the traveling wave fronts connecting two relevant equilibria, one being a boundary equilibrium and the other being a coexistence equilibrium.

Keywords:

• single spreading speed
• linear determinacy
• traveling wave front
• reaction-diffusion system
• pioneer and climax species

AMS Subject Classifications:

• 35K57
• 34C12
• 92D25

Acknowledgments

We would like to thank the two anonymous referees for their valuable comments which have led to an improvement of the presentation of the paper.