Influence of the neighborhood on cyclic models of biodiversity

This work deals with the influence of the neighborhood in simple rock-paper-scissors models of biodiversity. We consider the case of three distinct species which evolve under the standard rules of mobility, reproduction and competition. The rule of competition follows the guidance of the rock-paper-scissors game, with the prey being annihilated, leaving an empty site in accordance with the May-Leonard proposal for the predator and prey competition. We use the von Neumann neighborhood, but we consider mobility under the presence of the nearest, next nearest and next to next nearest neighbors in three distinct environments, one with equal probability and the others with probability following power law and exponential profiles. The results are different, but they all show that increasing the neighborhood increases the characteristic length of the system in an important way. We have studied other models, in particular the case where one modifies the manner a specific species competes, breaking the cyclic evolution and unveiling the interesting result in which the strongest individuals may constitute the less abundant population.