title: Coexistence in a one-dimensional cyclic dominance process.
abstract: Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and nonequilibrium processes in the stationary state. We exploit these insights to obtain asymptotically exact descriptions of the emerging reactive steady state in the regimes of high and low mutation rates. The results are compared to stochastic lattice simulations. Our methods and findings are potentially relevant for the spatiotemporal evolution of other nonequilibrium stochastic processes.
authors.affiliation: Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333 München, Germany.
authors.forename: Anton A
authors.initials: AA
authors.lastname: Winkler
authors.forename: Tobias
authors.initials: T
authors.lastname: Reichenbach
authors.forename: Erwin
authors.initials: E
authors.lastname: Frey
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D005716:Game Theory; D015233:Models, Statistical; D008962:Models, Theoretical; D009154:Mutation; D011336:Probability; D013269:Stochastic Processes; D013997:Time Factors