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Parity effects in rock-paper-scissors type models with a number of species NS≤12

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  • Avelino, P.P.
  • de Oliveira, B.F.
  • Trintin, R.S.

Abstract

We investigate the impact of parity on the abundance of weak species in the context of the simplest generalization of the rock-paper-scissors model to an arbitrary number of species — we consider models with a total number of species (NS) between 3 and 12, having one or more (weak) species characterized by a reduced predation probability (by a factor of Pw with respect to the other species). We show, using lattice based spatial stochastic simulations with random initial conditions, large enough for coexistence to prevail, that parity effects are significant. We find that the performance of weak species is dependent on whether the total number of species is even or odd, especially for NS≤8, with odd numbers of species being on average more favourable to weak species than even ones. We further show that, despite the significant dispersion observed among individual models, a weak species has on average a higher abundance than a strong one if Pw is sufficiently smaller than unity — the notable exception being the four species case.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010924
    DOI: 10.1016/j.chaos.2021.111738
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    References listed on IDEAS

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    1. 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.
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    3. Tobias Reichenbach & Mauro Mobilia & Erwin Frey, 2007. "Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games," Nature, Nature, vol. 448(7157), pages 1046-1049, August.
    4. Michael J. Liao & Arianna Miano & Chloe B. Nguyen & Lin Chao & Jeff Hasty, 2020. "Survival of the weakest in non-transitive asymmetric interactions among strains of E. coli," Nature Communications, Nature, vol. 11(1), pages 1-8, December.
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    Cited by:

    1. Szolnoki, Attila & Perc, Matjaž, 2023. "Oppressed species can form a winning pair in a multi-species ecosystem," Applied Mathematics and Computation, Elsevier, vol. 438(C).

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