Four-state rock-paper-scissors games in constrained Newman-Watts networks

Abstract

We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance R[sub max] in Newman-Watts networks with the long-range connection probability p, we depict more realistically the stochastic interactions among species within ecosystems. When we fix mobility and vary the value of p or R[sub max], the Monte Carlo simulations show that the spiral waves grow in size, and the system becomes unstable and biodiversity is lost with increasing p or R[sub max]. These results are similar to recent results of Reichenbach et al. Nature (London) 448 1046 (2007)], in which they increase the mobility only without including long-range interactions. We compared extinctions with or without long-range connections and computed spatial correlation functions and correlation length. We conclude that long-range connections could improve the mobility of species, drastically changing their crossover to extinction and making the system more unstable.