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Discriminating the effects of spatial extent and population size in cyclic competition among species

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Lamouroux,  David
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Eule,  Stephan
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Geisel,  Theo
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Nagler,  Jan
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Lamouroux, D., Eule, S., Geisel, T., & Nagler, J. (2012). Discriminating the effects of spatial extent and population size in cyclic competition among species. Physical Review E, 86: 021911. doi:10.1103/PhysRevE.86.021911.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-10A5-8
Abstract
We introduce a population model for species under cyclic competition. This model allows individuals to coexist and interact on single cells while migration takes place between adjacent cells. In contrast to the model introduced by Reichenbach, Mobilia, and Frey [ Reichenbach, Mobilia and Frey Nature (London) 448 1046 (2007)], we find that the emergence of spirals results in an ambiguous behavior regarding the stability of coexistence. The typical time until extinction exhibits, however, a qualitatively opposite dependence on the newly introduced nonunit carrying capacity in the spiraling and the nonspiraling regimes. This allows us to determine a critical mobility that marks the onset of this spiraling state sharply. In contrast, we demonstrate that the conventional finite size stability analysis with respect to spatial size is of limited use for identifying the onset of the spiraling regime.