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Space promotes the coexistence of species: Effective medium approximation for rock-paper-scissors system

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  • Nagatani, Takashi
  • Sato, Kazunori
  • Ichinose, Genki
  • Tainaka, Kei-ichi

Abstract

Stochastic cellular automata for rock-paper-scissors games are related to Lotka-Volterra model. Simulations are usually performed by two methods local and global interactions. It is well known that the population dynamics with local interaction is stable, where all species coexist. In contrast, global interaction leads to extinction. So far, theories such as mean-field theory and pair approximation have been presented, but they never explained the stable dynamics in local simulation. In the present article, we apply effective medium approximation (EMA) which has been developed in Physics. The effective medium is determined in a self-consistent way. The EMA theory well predicts the stability of population dynamics. Moreover, it fairly explains the aggregation of each species observed in the stationary state.

Suggested Citation

  • Nagatani, Takashi & Sato, Kazunori & Ichinose, Genki & Tainaka, Kei-ichi, 2017. "Space promotes the coexistence of species: Effective medium approximation for rock-paper-scissors system," Ecological Modelling, Elsevier, vol. 359(C), pages 240-245.
    • Handle: RePEc:eee:ecomod:v:359:y:2017:i:c:p:240-245
    DOI: 10.1016/j.ecolmodel.2017.06.001
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    References listed on IDEAS

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    1. Gatti, Roberto Cazzolla & Hordijk, Wim & Kauffman, Stuart, 2017. "Biodiversity is autocatalytic," Ecological Modelling, Elsevier, vol. 346(C), pages 70-76.
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    Cited by:

    1. Bazeia, D. & de Oliveira, B.F. & Silva, J.V.O. & Szolnoki, A., 2020. "Breaking unidirectional invasions jeopardizes biodiversity in spatial May-Leonard systems," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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