Pattern formation in a predator-prey system characterized by a spatial scale of interaction

¹  Centro Brasileiro de Pesquisas Físicas - Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brasil
²  Instituto de Física, Universidade Federal Fluminense - Campus da Praia Vermelha, 24210-340, Niterói, RJ, Brasil
³  Facultad de Física, Universidad de La Habana - Ave. Universidad y Ronda, Vedado, 10400, Havana, Cuba
⁴  Instituto Mexicano del Petróleo - Eje Central Lázaro Cárdenas Norte 152, Gustavo A. Madero, 07730 DF, México
⁵  Centro de Investigaciones en Modelado Oceanográfico y Biológico Pesquero, IMARPE - Apartado 22, Callao, Perú
⁶  Institut des Sciences de l'Evolution - Place Eugene Bataillon, CC 065, 34095 Montpellier, France, EU

Corresponding author: edgardo@cbpf.br

Received: 20 August 2009
Accepted: 18 November 2009

Abstract

We describe pattern formation in ecological systems using a version of the classical Lotka-Volterra model characterized by a spatial scale which controls the predator-prey interaction range. Analytical and simulational results show that patterns can emerge in some regions of the parameters space where the instability is driven by the range of the interaction. The individual-based implementation captures realistic ecological features. In fact, spatial structures emerge in an erratic oscillatory regime which can contemplate predators' extinction.