Hamming distance and mobility behavior in generalized rock-paper-scissors models

TL;DR

This paper investigates how Hamming distance behaves in generalized rock-paper-scissors models and how species mobility impacts biodiversity, revealing universal patterns and the potential for mobility to threaten diversity.

Contribution

It extends the analysis of rock-paper-scissors models to multiple species and lattice sizes, highlighting universal Hamming distance behavior and the impact of mobility on biodiversity.

Findings

Hamming distance shows universal behavior regardless of species number and lattice size.

Increased mobility can lead to the loss of biodiversity.

The study confirms mobility's role in jeopardizing species coexistence.

Abstract

This work reports on two related investigations of stochastic simulations which are widely used to study biodiversity and other related issues. We first deal with the behavior of the Hamming distance under the increase of the number of species and the size of the lattice, and then investigate how the mobility of the species contributes to jeopardize biodiversity. The investigations are based on the standard rules of reproduction, mobility and predation or competition, which are described by specific rules, guided by generalization of the rock-paper-scissors game, valid in the case of three species. The results on the Hamming distance indicate that it engenders universal behavior, independently of the number of species and the size of the square lattice. The results on the mobility confirm the prediction that it may destroy diversity, if it is increased to higher and higher values.