Intransitivity and coexistence in four species cyclic games

LÜTZ, ALESSANDRA; RISAU GUSMAN, SEBASTIAN; ARENZON, JEFERSON

JOURNAL OF THEORETICAL BIOLOGY

ACADEMIC PRESS LTD-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2013 vol. 317 p. 286 - 292

0022-5193

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.