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Deterministic evolutionary game dynamics in finite populations

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons56574

Altrock,  Philipp M.
Department Evolutionary Ecology, Max Planck Institute for Evolutionary Biology, Max Planck Society;
Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons56973

Traulsen,  Arne
Department Evolutionary Ecology, Max Planck Institute for Evolutionary Biology, Max Planck Society;
Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Zitation

Altrock, P. M., & Traulsen, A. (2009). Deterministic evolutionary game dynamics in finite populations. Physical Review E, 80(1): 011909. doi:10.1103/PhysRevE.80.011909.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-D598-4
Zusammenfassung
Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic such that the dynamics becomes deterministic only in infinitely large populations. Here, we present a microscopic birth-death process that has a fully deterministic strong selection limit in well-mixed populations of any size. Additionally, under weak selection, from this process the frequency-dependent Moran process is recovered. This makes it a natural extension of the usual evolutionary dynamics under weak selection. We find simple expressions for the fixation probabilities and average fixation times of the process in evolutionary games with two players and two strategies. For cyclic games with two players and three strategies, we show that the resulting deterministic dynamics crucially depends on the initial condition in a nontrivial way.