Zealots tame oscillations in the spatial rock-paper-scissors game
arXiv:1607.04269 · doi:10.1103/PhysRevE.93.062307
Abstract
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. Firstly, 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.
arXiv comment6 two-column pages, 4 figures; accepted for publication in Physical Review E
References in corpus (37)
- Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
- Cyclic dominance in evolutionary games: A review
- Critical behavior of propagation on small-world networks
- Does a Single Zealot Affect an Infinite Group of Voters ?
- Resolving social dilemmas on evolving random networks
- Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
- Defense mechanisms of empathetic players in the spatial ultimatum game
- Correlation of positive and negative reciprocity fails to confer an evolutionary advantage: Phase transitions to elementary strategies
- Rock-scissors-paper game on regular small-world networks
- Oscillatory Dynamics in Rock-Paper-Scissors Games with Mutations
- Zero-one survival behavior of cyclically competing species
- Instability of spatial patterns and its ambiguous impact on species diversity
- Spatial Rock-Paper-Scissors Models with Inhomogeneous Reaction Rates
- Junctions and spiral patterns in Rock-Paper-Scissors type models
- Noise-guided evolution within cyclical interactions
- Coexistence and Survival in Conservative Lotka-Volterra Networks
- Fluctuations and Correlations in Lattice Models for Predator-Prey Interaction
- Phase transitions for rock-scissors-paper game on different networks
- Statistical Physics of the Spatial Prisoner's Dilemma with Memory-Aware Agents
- Characterization of spiraling patterns in spatial rock-paper-scissors games
- Von-Neumann's and related scaling laws in Rock-Paper-Scissors type models
- Vortices determine the dynamics of biodiversity in cyclical interactions with protection spillovers
- Evolutionary games of condensates in coupled birth-death processes
- Cyclic competition of four species: domains and interfaces
- When does cyclic dominance lead to stable spiral waves?
- Ecosystems with mutually exclusive interactions self-organize to a state of high diversity
- Interplay between partnership formation and competition in generalized May-Leonard games
- Interfaces with internal structures in generalized rock-paper-scissors models
- From pairwise to group interactions in games of cyclic dominance
- A theoretical approach to understand spatial organization in complex ecologies
- Globally synchronized oscillations in complex cyclic games
- Vortex dynamics in a three-state model under cyclic dominance
- Labyrinthine clustering in a spatial rock-paper-scissors ecosystem
- Complementarity and diversity in a soluble model ecosystem
- Clonal selection prevents tragedy of the commons when neighbors compete in a rock-paper-scissors game
- Stability and robustness analysis of cooperation cycles driven by destructive agents in finite populations
- Oscillations and patterns in interacting populations of two species
Cited by in corpus (25)
- Zealots in the mean-field noisy voter model
- Pattern formations driven by cyclic interactions: a brief review of recent developments
- Biodiversity in models of cyclic dominance is preserved by heterogeneity in site-specific invasion rates
- Predominance of the weakest species in Lotka-Volterra and May-Leonard implementations of the rock-paper-scissors model
- Mobility restores the mechanism which supports cooperation in the voluntary prisoner's dilemma game
- A novel procedure for the identification of chaos in complex biological systems
- A Heterogeneous Out-of-Equilibrium Nonlinear -Voter Model with Zealotry
- Critical mass effect in evolutionary games triggered by zealots
- Hamming distance and mobility behavior in generalized rock-paper-scissors models
- Invasion controlled pattern formation in a generalized multi-species predator-prey system
- Competition of alliances in a cyclically dominant eight-species population
- Coevolutionary dynamics of a variant of the cyclic Lotka-Volterra model with three-agent interactions
- Basin entropy behavior in a cyclic model of the rock-paper-scissors type
- Risk and interaction aversion: screening mechanisms in the Prisoner's Dilemma game
- Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system
- How multiple weak species jeopardise biodiversity in spatial rock-paper-scissors models
- Emerging solutions from the battle of defensive alliances
- Lotka-Volterra versus May-Leonard formulations of the spatial stochastic Rock-Paper-Scissors model: the missing link
- The Host-Pathogen Game: an evolutionary approach to biological competitions
- Equal partners do better in defensive alliances
- Effects of a pestilent species on the stability of cyclically dominant species
- -player game formulation of the majority-vote model of opinion dynamics
- Trade-off between reproduction and mobility prolongs organisms' survival in rock-paper-scissors models
- Role of predator-prey reversal in Rock-Paper-Scissors models
- Characterization of phase transitions in a model ecosystem of sessile species