Mathematical Biosciences and Engineering (MBE)

Two-Species Competition with High Dispersal: The Winning Strategy

Pages: 345 - 362, Volume 2, Issue 2, April 2005      doi:10.3934/mbe.2005.2.345

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S.A. Gourley - Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom (email)
Yang Kuang - Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, United States (email)

Abstract: 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:  competition, evolution, reaction diffusion, patch population model, stability, bifurcation.
Mathematics Subject Classification:  92D25, 35K57.

Received: January 2005;      Accepted: March 2005;      Available Online: March 2005.