Zero-One Survival Behavior of Cyclically Competing Species

Berr, Maximilian; Reichenbach, Tobias; Schottenloher, Martin and Frey, Erwin (January 2009): Zero-One Survival Behavior of Cyclically Competing Species. In: Physical Review Letters, Vol. 102, No. 4: 048102-1

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.

• Item Type: Journal article
• Form of publication: Publisher's Version
• Faculties: Physics
• Subjects: 500 Science > 530 Physics
• ISSN: 0031-9007
• Place of Publication: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
• Language: English