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We consider a two-dimensional model of three species in rock-paper-scissorscompetition and study the self-organisation of the population into fascinatingspiraling patterns. Within our individual-based metapopulation formulation, thepopulation composition changes due to cyclic dominance (dominance-removal anddominance-replacement), mutations, and pair-exchange of neighboringindividuals. Here, we study the influence of mobility on the emerging patternsand investigate when the pair-exchange rate is responsible for spiral waves tobecome elusive in stochastic lattice simulations. In particular, we show thatthe spiral waves predicted by the system's deterministic partial equations arefound in lattice simulations only within a finite range of the mobility rate.We also report that in the absence of mutations and dominance-replacement, theresulting spiraling patterns are subject to convective instability andfar-field breakup at low mobility rate. Possible applications of theseresolution and far-field breakup phenomena are discussed.

The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games