Performance of weak species in the simplest generalization of the rock-paper-scissors model to four species

Abstract

We investigate the problem of the predominance and survival of "weak" species in the context of the simplest generalization of the spatial stochastic rock-paper-scissors model to four species by considering models in which one, two, or three species have a reduced predation probability. We show, using lattice based spatial stochastic simulations with random initial conditions, that if only one of the four species has its probability reduced then the most abundant species is the prey of the "weakest" (assuming that the simulations are large enough for coexistence to prevail). Also, among the remaining cases, we present examples in which "weak" and "strong" species have similar average abundances and others in which either of them dominates -- the most abundant species being always a prey of a "weak" species with which it maintains a unidirectional predator-prey interaction. However, in contrast to the three-species model, we find no systematic difference in the global performance of "weak" and "strong" species, and we conjecture that the same result will hold if the number of species is further increased. We also determine the probability of single species survival and coexistence as a function of the lattice size, discussing its dependence on initial conditions and on the change to the dynamics of the model which results from the extinction of one of the species.

7 pages, 6 figures. arXiv admin note: text overlap with arXiv:1907.11280

References in corpus (14)

• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Cyclic dominance in evolutionary games: A review
• Junctions and spiral patterns in Rock-Paper-Scissors type models
• Self-organizing patterns maintained by competing associations in a six-species predator-prey model
• Segregation process and phase transition in cyclic predator-prey models with even number of species
• 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
• Interplay between partnership formation and competition in generalized May-Leonard games
• Globally synchronized oscillations in complex cyclic games
• Hamming distance and mobility behavior in generalized rock-paper-scissors models
• Coarsening with non-trivial in-domain dynamics: correlations and interface fluctuations
• Four-state rock-paper-scissors games on constrained Newman-Watts networks
• Invasion controlled pattern formation in a generalized multi-species predator-prey system
• Apex predator and the cyclic competition in a rock-paper-scissors game of three species

Cited by in corpus (5)

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• Competition among alliances of different sizes
• Oppressed species can form a winning pair in a multi-species ecosystem
• Spatial patterns and biodiversity in rock-paper-scissors models with regional unevenness