Coexistence in a one-dimensional cyclic dominance process

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.