  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 first, second and third neighbors in three distinct
environments, one with equal probability and the others with probability
following the power law and exponential profiles. The results are different,
but they all show that increasing the neighbourhood increases the
characteristic length of the system in an important way. We have studied other
possibilities, in particular the case where one modifies the manner a specific
species competes, unveiling the interesting result in which the strongest
individuals may constitute the less abundant population.
