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Cyclic Competition and Percolation in Grouping Predator-Prey Populations

Author

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  • Alessandra F. Lütz

    (Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil)

  • Annette Cazaubiel

    (Normale Supérieure, International Center of Fundamental Physics, 45 Rue d’Ulm, 75005 Paris, France)

  • Jeferson J. Arenzon

    (Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil)

Abstract

We study, within the framework of game theory, the properties of a spatially distributed population of both predators and preys that may hunt or defend themselves either isolatedly or in group. Specifically, we show that the properties of the spatial Lett-Auger-Gaillard model, when different strategies coexist, can be understood through the geometric behavior of clusters involving four effective strategies competing cyclically,without neutral states. Moreover, the existence of strong finite-size effects, a form of the survival of the weakest effect, is related to a percolation crossover. These results may be generic and of relevance to other bimatrix games.

Suggested Citation

  • Alessandra F. Lütz & Annette Cazaubiel & Jeferson J. Arenzon, 2017. "Cyclic Competition and Percolation in Grouping Predator-Prey Populations," Games, MDPI, vol. 8(1), pages 1-9, February.
    • Handle: RePEc:gam:jgames:v:8:y:2017:i:1:p:10-:d:89247
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    References listed on IDEAS

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    1. J. Cremer & T. Reichenbach & E. Frey, 2008. "Anomalous finite-size effects in the Battle of the Sexes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(3), pages 373-380, June.
    2. Guy Beauchamp, 2008. "What is the magnitude of the group-size effect on vigilance?," Behavioral Ecology, International Society for Behavioral Ecology, vol. 19(6), pages 1361-1368.
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    Cited by:

    1. Szolnoki, Attila & Chen, Xiaojie, 2020. "Strategy dependent learning activity in cyclic dominant systems," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

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