  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.
