Effects of competition on pattern formation in the rock-paper-scissors game

Abstract

We investigate the impact of cyclic competition on pattern formation in the rock-paper-scissors game. By separately considering random and prepared initial conditions, we observe a critical influence of the competition rate $p$ on the stability of spiral waves and on the emergence of biodiversity. In particular, while increasing values of $p$ promote biodiversity, they may act detrimental on spatial pattern formation. For random initial conditions, we observe a phase transition from biodiversity to an absorbing phase, whereby the critical value of mobility grows linearly with increasing values of $p$ on a log-log scale, but then saturates as $p$ becomes large. For prepared initial conditions, we observe the formation of single-armed spirals, but only for values of $p$ that are below a critical value. Once above, the spirals break up and form disordered spatial structures, mainly because of the percolation of vacant sites. Thus, there exists a critical value of the competition rate $p_c$ for stable single-armed spirals in finite populations. Importantly though, $p_c$ increases with increasing system size, because noise reinforces the disintegration of ordered patterns. In addition, we also find that $p_c$ increases with the mobility. These phenomena are reproduced by a deterministic model that is based on nonlinear partial differential equations. Our findings indicate that competition is vital for the sustenance of biodiversity and emergence of pattern formation in ecosystems governed by cyclical interactions.

arXiv comment7 two-column pages, 7 figures; accepted for publication in Physical Review E

References in corpus (25)

• Evolutionary games on graphs
• Coevolutionary games - a mini review
• Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• The outbreak of cooperation among success-driven individuals under noisy conditions
• Does mobility decrease cooperation?
• Effects of mobility in a population of Prisoner's Dilemma players
• Noise and Correlations in a Spatial Population Model with Cyclic Competition
• Disordered Environments in Spatial Games
• Cyclic dominance and biodiversity in well-mixed populations
• Spatial organization in cyclic Lotka-Volterra systems
• Cyclical interactions with alliance-specific heterogeneous invasion rates
• Zero-one survival behavior of cyclically competing species
• Theoretical Analysis and Simulations of the Generalized Lotka-Volterra Model
• Instability of spatial patterns and its ambiguous impact on species diversity
• Noise-guided evolution within cyclical interactions
• Dynamically generated cyclic dominance in spatial prisoner's dilemma games
• Phase transition and selection in a four-species cyclic Lotka-Volterra model
• Defensive alliances in spatial models of cyclical population interactions
• Self-organizing patterns maintained by competing associations in a six-species predator-prey model
• Mobility and asymmetry effects in one-dimensional rock-paper-scissors games
• Phase transitions induced by variation of invasion rates in spatial cyclic predator-prey models with four or six species
• Emergence of target waves in paced populations of cyclically competing species
• Cyclic competition of four species: mean field theory and stochastic evolution
• Coexistence in a One-Dimensional Cyclic Dominance Process

Cited by in corpus (34)

• Cyclic dominance in evolutionary games: A review
• Stochastic population dynamics in spatially extended predator-prey systems
• Diverging fluctuations in a spatial five-species cyclic dominance game
• Characterization of spiraling patterns in spatial rock-paper-scissors games
• A novel route to cyclic dominance in voluntary social dilemmas
• Optimal cooperation-trap strategies for the iterated Rock-Paper-Scissors game
• Cyclic competition of four species: domains and interfaces
• Adaptive long-range migration promotes cooperation under tempting conditions
• Intransitivity and coexistence in four species cyclic games
• Interplay between partnership formation and competition in generalized May-Leonard games
• How directional mobility affects biodiversity in rock-paper-scissors models
• From pairwise to group interactions in games of cyclic dominance
• Mobility restores the mechanism which supports cooperation in the voluntary prisoner's dilemma game
• Spatial patterns and biodiversity in off-lattice simulations of a cyclic three-species Lotka-Volterra model
• A novel procedure for the identification of chaos in complex biological systems
• Global attractors and extinction dynamics of cyclically competing species
• A theoretical approach to understand spatial organization in complex ecologies
• Labyrinthine clustering in a spatial rock-paper-scissors ecosystem
• Hamming distance and mobility behavior in generalized rock-paper-scissors models
• Stochastic evolution of four species in cyclic competition
• Extinction in four species cyclic competition
• Spirals and coarsening patterns in the competition of many species: A complex Ginzburg-Landau approach
• Coevolutionary dynamics of a variant of the cyclic Lotka-Volterra model with three-agent interactions
• Apex predator and the cyclic competition in a rock-paper-scissors game of three species
• Mortality makes coexistence vulnerable in evolutionary game of rock-paper-scissors
• Spatial Pattern Dynamics due to the Fitness Gradient Flux in Evolutionary Games
• Influence of the neighborhood on cyclic models of biodiversity
• Synchronization and extinction in cyclic games with mixed strategies
• Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system
• Emergence of anti-coordinated patterns in snowdrift game by reinforcement learning
• Interface networks in models of competing alliances
• Intransitive Machines
• Non-Markovian Rock-Paper-Scissors games
• Monitoring biodiversity on highly reactive rock-paper-scissors models