Multi-layered model for rock-paper-scissors game: A swarm intelligence sustains biodiversity

Abstract Much literature exists for rock-paper-scissors (RPS) game. It is well known in a single habitat that spatial models are more stable than well-mixed population. However, the mechanism of spatial stabilization has been unclear. In the present article, we study multilayer model of RPS game in a patchy environment; respective patches are set as lattices. The predation probability of one of three species is assumed to be reduced as a parameter. Simulations on two-layer system reveal the opposite result to those on a single-habitat system. Namely, the well-mixed population becomes stable. In contrast, extinction occurs by random migration in spatially-explicit model, when the reduced predation probability is below a certain critical value. The extinction in spatial model is found to be caused by the collapse of a kind of swarm intelligence (SI). In RPS system, large swarms of each species are automatically protected from its predator. Such a self-organized protection is one of the simplest examples of SI. We also discuss some serious problems for random migration.