Threefold way to extinction in populations of cyclically competing species - Rulands, Steffen; Reichenbach, Tobias; Frey, Erwin (Journal of Statistical Mechanics-Theory and Experiment, 2011)
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can vary broadly and provide information on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic population model where three species exhibit cyclic competition. The cyclic dynamics reflects the non-equilibrium nature of the species interactions. While previous work focuses on the coarsening process as a mechanism that drives the system to extinction, we found that unexpectedly the dynamics in going to extinction is much richer. We observed dynamics of three different types. In addition to coarsening, in the evolutionarily relevant limit of large times, oscillating traveling waves and heteroclinic orbits play a dominant role. The weights of the different processes depend on the degree of mixing and the system size. By means of analytical arguments and extensive numerical simulations we provide the full characteristics of scenarios leading to extinction in one of the most surprising models of ecology. © 2011 IOP Publishing Ltd and SISSA.
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Keywords: Coarsening processes (theory); Phase transitions into absorbing states (theory); Population dynamics (theory); Stochastic processes