Invasion controlled pattern formation in a generalized multi-species predator-prey system

Abstract

Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator-prey-like dominance a balanced or peer relation can emerge between some competitors. By utilizing this possibility in the present work we generalize a four-state predator-prey type model where we establish two groups of species labeled by even and odd numbers. In particular, we introduce different invasion probabilities between and within these groups, which results in a tunable intensity of bidirectional invasion among peer species. Our study reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion. The related transition points can be identified with the help of appropriate order parameters based on the spatial autocorrelation decay, on the fraction of empty sites, and on the variance of the species density. Furthermore, the application of diverse, alliance-specific inner invasion rates for different groups may result in the extinction of the pair of species where this inner invasion is moderate. These observations highlight that beyond the well-known and intensively studied cyclic dominance there is an additional source of complexity of pattern formation that has not been explored earlier.

8 pages, 8 figures. To appear in PRE

References in corpus (37)

• Evolutionary games on graphs
• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Cyclic dominance in evolutionary games: A review
• Rock-scissors-paper game on regular small-world networks
• Oscillatory Dynamics in Rock-Paper-Scissors Games with Mutations
• Stochastic population dynamics in spatially extended predator-prey systems
• Cyclical interactions with alliance-specific heterogeneous invasion rates
• Spatial Rock-Paper-Scissors Models with Inhomogeneous Reaction Rates
• Junctions and spiral patterns in Rock-Paper-Scissors type models
• Dynamically generated cyclic dominance in spatial prisoner's dilemma games
• Phase transition and selection in a four-species cyclic Lotka-Volterra model
• Diverging fluctuations in a spatial five-species cyclic dominance game
• Zealots tame oscillations in the spatial rock-paper-scissors game
• Characterization of spiraling patterns in spatial rock-paper-scissors games
• Vortices determine the dynamics of biodiversity in cyclical interactions with protection spillovers
• Self-organizing patterns maintained by competing associations in a six-species predator-prey model
• Reentrant phase transitions and defensive alliances in social dilemmas with informed strategies
• Competing associations in six-species predator-prey models
• Cyclic competition of four species: domains and interfaces
• Biodiversity in models of cyclic dominance is preserved by heterogeneity in site-specific invasion rates
• Intransitivity and coexistence in four species cyclic games
• Phase transitions induced by variation of invasion rates in spatial cyclic predator-prey models with four or six species
• Costly hide and seek pays: Unexpected consequences of deceit in a social dilemma
• Interfaces with internal structures in generalized rock-paper-scissors models
• How directional mobility affects biodiversity in rock-paper-scissors models
• String networks in Z_N Lotka-Volterra competition models
• Spatial patterns and biodiversity in off-lattice simulations of a cyclic three-species Lotka-Volterra model
• A theoretical approach to understand spatial organization in complex ecologies
• Globally synchronized oscillations in complex cyclic games
• The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games
• Hamming distance and mobility behavior in generalized rock-paper-scissors models
• The Beneficial Role of Mobility for the Emergence of Innovation
• Coarsening with non-trivial in-domain dynamics: correlations and interface fluctuations
• Perturbing cyclic predator-prey systems: how a six-species coarsening system with non-trivial in-domain dynamics responds to sudden changes
• String networks with junctions in competition models
• Spatial organization and cyclic dominance in asymmetric predator-prey spatial games
• Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system

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• Mortality makes coexistence vulnerable in evolutionary game of rock-paper-scissors
• Influence of the neighborhood on cyclic models of biodiversity
• Performance of weak species in the simplest generalization of the rock-paper-scissors model to four species
• Breaking unidirectional invasions jeopardizes biodiversity in spatial May-Leonard systems
• Equal partners do better in defensive alliances
• Oppressed species can form a winning pair in a multi-species ecosystem
• Spatiotemporal Patterns in Active Four-State Potts Models
• Dynamics of one-dimensional spin models under the line-graph operator
• Impact of reproduction-mobility trade-off on biodiversity in rock-paper-scissors models in changing environmental conditions
• Dynamic modes of active Potts models with factorizable numbers of states