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

TL;DR

This study explores how long-range connections in constrained Newman-Watts networks influence species coexistence in a four-state rock-paper-scissors game, revealing that increased long-range interactions lead to larger spiral waves, instability, and biodiversity loss.

Contribution

It introduces a four-state variant of the rock-paper-scissors game on constrained Newman-Watts networks, analyzing the impact of long-range connections on species dynamics and stability.

Findings

Long-range connections increase spiral wave size.

Higher connection probability leads to system instability.

Long-range interactions promote species extinction.

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 $R_{max}$ in Newman-Watts networks with the long-rang 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 $R_{max}$, 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 $R_{max}$. These results are similar to recent results of Reichenbach \textit{et al.} [Nature (London) \textbf{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.