Zealots tame oscillations in the spatial rock-paper-scissors game

A. Szolnoki, MatjaŽ Perc

Research output: Contribution to journalArticle

39 Citations (Scopus)


The rock-paper-scissors game is a paradigmatic model for biodiversity, with applications ranging from microbial populations to human societies. Research has shown, however, that mobility jeopardizes biodiversity by promoting the formation of spiral waves, especially if there is no conservation law in place for the total number of competing players. First, we show that even if such a conservation law applies, mobility still jeopardizes biodiversity in the spatial rock-paper-scissors game if only a small fraction of links of the square lattice is randomly rewired. Secondly, we show that zealots are very effective in taming the amplitude of oscillations that emerge due to mobility and/or interaction randomness, and this regardless of whether the later is quenched or annealed. While even a tiny fraction of zealots brings significant benefits, at 5% occupancy zealots practically destroy all oscillations regardless of the intensity of mobility, and regardless of the type and strength of randomness in the interaction structure. Interestingly, by annealed randomness the impact of zealots is qualitatively the same as by mobility, which highlights that fast diffusion does not necessarily destroy the coexistence of species, and that zealotry thus helps to recover the stable mean-field solution. Our results strengthen the important role of zealots in models of cyclic dominance, and they reveal fascinating evolutionary outcomes in structured populations that are a unique consequence of such uncompromising behavior.

Original languageEnglish
Article number062307
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
Publication statusPublished - Jun 10 2016

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

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