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The elimination of hierarchy in a completely cyclic competition system

Author

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  • Li, Yongming
  • Dong, Linrong
  • Yang, Guangcan

Abstract

Interactions among competing units are crucial to maintaining biodiversity, and non-hierarchical interactions can promote biodiversity in cyclic competing systems. In the present study, we explore the role of hierarchical interactions, existing ubiquitously in reality, in the co-evolution of a cyclic competing system. In systems composed of cyclic competing species with hierarchy interactions in which one predator species has more than one prey, we find that hierarchy disappears in a rather short evolving time. In the process of co-evolution, a hierarchical competing system tends to transit to a cyclic non-hierarchical competing system described by the rock–paper–scissors game. In other words, the cyclic competing interactions appear to eradicate hierarchy. This conclusion is analyzed by a mean-field approach and is tested by stochastic simulations.

Suggested Citation

  • Li, Yongming & Dong, Linrong & Yang, Guangcan, 2012. "The elimination of hierarchy in a completely cyclic competition system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 125-131.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:1:p:125-131
    DOI: 10.1016/j.physa.2011.08.019
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    Cited by:

    1. Muyinda, Nathan & Baetens, Jan M. & De Baets, Bernard & Rao, Shodhan, 2020. "Using intransitive triads to determine final species richness of competition networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Avelino, P.P. & de Oliveira, B.F. & Trintin, R.S., 2022. "Parity effects in rock-paper-scissors type models with a number of species NS≤12," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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