title: Zero-one survival behavior of cyclically competing species.
abstract: The coexistence of competing species is, due to unavoidable fluctuations, always transient. In this Letter, we investigate the ultimate survival probabilities characterizing different species in cyclic competition. We show that they often obey a surprisingly simple, though nontrivial behavior. Within a model where coexistence is neutrally stable, we demonstrate a robust zero-one law: When the interactions between the three species are (generically) asymmetric, the "weakest" species survives at a probability that tends to one for large population sizes, while the other two are guaranteed to extinction. We rationalize our findings from stochastic simulations by an analytic approach.
authors.affiliation: Arnold Sommerfeld Center for Theoretical Physics, Theresienstrasse 37, 80333 München, Germany.
authors.forename: Maximilian
authors.initials: M
authors.lastname: Berr
authors.forename: Tobias
authors.initials: T
authors.lastname: Reichenbach
authors.forename: Martin
authors.initials: M
authors.lastname: Schottenloher
authors.forename: Erwin
authors.initials: E
authors.lastname: Frey
mesh_terms: D003163:Competitive Behavior; D003198:Computer Simulation; D017753:Ecosystem; D053476:Extinction, Biological; D008954:Models, Biological; D011157:Population Dynamics