Spatial patterns and biodiversity in off-lattice simulations of a cyclic three-species Lotka-Volterra model

¹ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP - Rua das Estrelas, PT4150-762 Porto, Portugal
² Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto - Rua do Campo Alegre 687, PT4169-007 Porto, Portugal
³ Departamento de Física, Universidade Federal da Paraíba - 58051-900 João Pessoa, PB, Brazil
⁴ Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte - Caixa Postal 1524, 59072-970, Natal, RN, Brazil
⁵ Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Science Park 904 1098 XH Amsterdam, The Netherlands
⁶ Departamento de Física, Universidade Estadual de Maringá - Av. Colombo 5790, 87020-900 Maringá, PR, Brazil

Received: 24 January 2018
Accepted: 29 March 2018

Abstract

Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest-neighbour interactions starting from random initial conditions. In this letter we describe the results of off-lattice Lotka-Volterra stochastic simulations, showing that the emergence of spiral patterns does occur for sufficiently high values of the (conserved) total density of individuals. We also investigate the dynamics in our simulations, finding an empirical relation characterizing the dependence of the characteristic peak frequency and amplitude on the total density. Finally, we study the impact of the total density on the extinction probability, showing how a low population density may jeopardize biodiversity.