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

¹ Departamento de Física, Universidade Federal da Paraíba - 58051-970 João Pessoa, Paraíba, Brazil
² Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte - Caixa Postal 1524, 59072-970, Natal, Rio Grande do Norte, Brazil
³ Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam - Science Park 904, 1098 XH Amsterdam, The Netherlands
⁴ Departamento de Física, Universidade Estadual de Maringá - 87020-900 Maringá, Paraná, Brazil

^(a) bazeia@fisica.ufpb.br (corresponding author)

Received: 2 August 2017
Accepted: 3 November 2017

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.