American Institute of Mathematical Sciences

Advanced
2005, 2(2): 345-362. doi: 10.3934/mbe.2005.2.345

Two-Species Competition with High Dispersal: The Winning Strategy

S.A. Gourley 1, and  Yang Kuang 2,

1. 

Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH
2. 

Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804

Received  January 2005 Revised  March 2005 Published  March 2005

This paper is motivated by the following simple question: how does diffusion affect the competition outcomes of two competing species that are identical in all respects other than their strategies on how they spatially distribute their birth rates. This may provide us with insights into how species learn to compete in a relatively stable setting, which in turn may point out species evolution directions. To this end, we formulate some extremely simple two- species competition models that have either continuous or discrete diffusion mechanisms. Our analytical work on these models collectively and strongly suggests the following in a fast diffusion environment: where different species have the same birth rates on average, those that do well are those that have greater spatial variation in their birth rates. We hypothesize that this may be a possible explanation for the evolution of grouping behavior in many species. Our findings are confirmed by extensive numerical simulation work on the models.
Keywords: stability, patch population model, competition, evolution, reaction diffusion, bifurcation..
Mathematics Subject Classification: 92D25, 35K5.
Citation: S.A. Gourley, Yang Kuang. Two-Species Competition with High Dispersal: The Winning Strategy. Mathematical Biosciences & Engineering, 2005, 2 (2) : 345-362. doi: 10.3934/mbe.2005.2.345
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