Models that explain the sustainability of an exploiter-victim ecosystem admit, generally, a coexistence state of both species in the well-mixed limit. Even if this state is unstable, the extinction-prone system may acquire stability on spatial domains where different patches oscillate incoherently around the coexistence state. New experiments, however, suggest that a spatially segregated system may be stable even in the absence of such a coexistence state. Here we revisit the hawk-dove (case 3) model of Durrett and Levin, which has been shown to support persistent population for system of interacting particles. It turns out that this model does not admit a (stable or unstable) coexistence state on a single habitat. We analyze the peculiar mechanism that leads to persistence in this case and the role of demographic stochasticity with and without self-interaction, using numerical simulations and exact solutions in the infinite diffusion limit.
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Acknowledgements This work was supported by the CO3 STREP of the Complexity Pathfinder of NEST (EC FP6). We thank Simon Levin and David Kessler for helpful discussions and comments. Adam Lampert provides the intuitive explanation for the difference between models with and without self-interactions in the infinite diffusion limit.
- Demographic stochasticity
- Population dynamics
- Victim-exploiter systems