title: Intransitivity and coexistence in four species cyclic games.
abstract: Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We consider here a generalization with four species, the minimum number of species allowing other interactions beyond the single loop (one predator, one prey). We show that, contrary to the mean field prediction, on a square lattice the model presents a transition, as the parameter setting the rate at which one species invades another changes, from a coexistence to a state in which one species gets extinct. Such a dependence on the invasion rates shows that the interaction graph structure alone is not enough to predict the outcome of such models. In addition, different invasion rates permit to tune the level of transitiveness, indicating that for the coexistence of all species to persist, there must be a minimum amount of intransitivity.
authors.affiliation: Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre, RS, Brazil. sandiflutz@gmail.com
authors.forename: Alessandra F
authors.initials: AF
authors.lastname: Lütz
authors.forename: Sebastián
authors.initials: S
authors.lastname: Risau-Gusman
authors.forename: Jeferson J
authors.initials: JJ
authors.lastname: Arenzon
mesh_terms: D003163:Competitive Behavior; D003198:Computer Simulation; D003299:Cooperative Behavior; D017753:Ecosystem; D005716:Game Theory; D011156:Population Density; D013045:Species Specificity; D013997:Time Factors