Zero-One Survival Behavior of Cyclically Competing Species

Maximilian Berr, Tobias Reichenbach, Martin Schottenloher, and Erwin Frey
Phys. Rev. Lett. 102, 048102 – Published 28 January 2009

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.

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  • Received 2 August 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.048102

©2009 American Physical Society

Authors & Affiliations

Maximilian Berr1,2, Tobias Reichenbach1, Martin Schottenloher2, and Erwin Frey1

  • 1Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), LMU München, Theresienstraße 37, 80333 München, Germany
  • 2Mathematisches Institut der LMU München, Theresienstraße 39, 80333 München, Germany

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Vol. 102, Iss. 4 — 30 January 2009

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