Influence of the neighborhood on cyclic models of biodiversity

TL;DR

This study investigates how different neighborhood structures influence cyclic biodiversity models, revealing that larger neighborhoods increase system scale and that stronger competitors can be less abundant.

Contribution

It introduces a detailed analysis of neighborhood effects in rock-paper-scissors biodiversity models with various mobility rules and competition modifications.

Findings

Increasing neighborhood size enlarges the characteristic length of the system.

Different neighborhood probability profiles affect the system's dynamics.

Strongest competitors can be less abundant than weaker ones.

Abstract

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.