Stochastic patterns in a 1D Rock–Paper–Scissor model with mutation

In the framework of a 1D cyclic competition model, the Rock–Paper–Scissor model, where bacteria are allowed to mutate and move in space, we study the formation of stochastic patterns, where all the bacteria species do coexist. We modelled the problem using an individual–based setting and using the system size van Kampen expansion to deal with the Master Equation, we have been able to characterise the spatio–temporal patterns using the power spectrum of the fluctuations. We proved that such patterns are robust against the intrinsic noise and they can be found for parameters values beyond the ones fixed by the deterministic approach. We complement such analytical results with numerical simulations based on the Gillespie’s algorithm.