Evolutionary games and two species population dynamics |
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Authors: | R. Cressman A. T. Dash E. Akin |
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Affiliation: | (1) Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada;(2) Department of Mathematics and Statististics, University of Guelph, N1G 2W1 Guelph, Ontario, Canada;(3) Department of Mathematics, The City University of New York, 10031 New York, NY, USA |
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Abstract: | Competition between species has long been modeled by population dynamics based on total numbers of each species. Recently, the evolution of strategy frequencies has been used successfully for competition models between individuals. In this paper, we illustrate that these two views of competition are compatible. It is shown that the rate of intra and interspecific competitions between individuals largely determines the population dynamics. Competition models over a single common resource and predator-prey models are developed from this individual competition approach. In particular, the equilibrium strategies in a co-evolving predator-prey system are shown to be more stable than the predicted strategy cycling of standard evolutionary game theory. |
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Keywords: | Haploid species Polymorphisms Frequency independent Interspecific and intraspecific contests Payoff matrices Dynamical equations Global stability |
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