Zero-one survival behavior of cyclically competing species
arXiv:0812.4191 · doi:10.1103/PhysRevLett.102.048102
Abstract
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 non-trivial 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 extinct. We rationalize our findings from stochastic simulations by an analytic approach.
4 pages, 3 figures
References in corpus (5)
- Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
- Coevolutionary Dynamics: From Finite to Infinite Populations
- Noise and Correlations in a Spatial Population Model with Cyclic Competition
- Instability of spatial patterns and its ambiguous impact on species diversity
- Anomalous finite-size effects in the Battle of the Sexes