Math. Model. Nat. Phenom.
Volume 4, Number 6, 2009Ecology (Part 1)
|Page(s)||54 - 90|
|Published online||27 November 2009|
Evolutionary Games in Space
Department of Applied Mathematics, Holon Institute of Technology, Holon 58102, Israel
2 Department of Fisheries, Wildlife, and Conservation Biology, University of Minnesota, St. Paul, MN 55118
Corresponding author: email@example.com
The G-function formalism has been widely used in the context of evolutionary games for identifying evolutionarily stable strategies (ESS). This formalism was developed for and applied to point processes. Here, we examine the G-function formalism in the settings of spatial evolutionary games and strategy dynamics, based on reaction-diffusion models. We start by extending the point process maximum principle to reaction-diffusion models with homogeneous, locally stable surfaces. We then develop the strategy dynamics for such surfaces. When the surfaces are locally stable, but not homogenous, the standard definitions of ESS and the maximum principle fall apart. Yet, we show by examples that strategy dynamics leads to convergent stable inhomogeneous strategies that are possibly ESS, in the sense that for many scenarios which we simulated, invaders could not coexist with the exisiting strategies.
Mathematics Subject Classification: 35B30 / 35B20 / 91A22
Key words: mathematical modeling / game theory / reaction-diffusion equation / G-function / evolutionary ecology
© EDP Sciences, 2009
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