Self-formation of noisy patterns governs species coevolution in spatially extended, biodiverse ecosystems. Individuals that organize into such patterns are often mobile: bacteria run and tumble, and animals migrate from place to place. Interactions may be hierarchical (food chains) as well as non-hierarchical. We develop a framework to theoretically describe such systems, via individual-based simulations as well as stochastic partial differential equations.

Results/Conclusions

Employing a specific model for cyclic (rock-paper-scissors-type) competition of species, we show that, under the influence of mobility, surprisingly regular, geometric patterns form. Namely, a noisy entanglement of rotating spiral waves self-organizes in the course of time. A critical value of mobility separates this biodiverse scenario from a uniform one where only one species survives.