Physica A 295 (2001) 53–57 www.elsevier.com/locate/physa Self-organized spatial structures in a ratio-dependent predator–prey model Fede Bartumeus a ; ∗ , David Alonso a; b , Jordi Catalan a a Dept. of Ecology, Facultat de Biologia, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spain b Complex Systems Research Group, Universitat Polit ecnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain Abstract Using linear stability analysis we demonstrate that a simple reaction-diusion predator–prey model with a ratio-dependent functional response for the predator, can develop diusion driven instabilities, also known as Turing structures. The ratio-dependent predator functional response assumes that predator density has a negative eect, due to mutual interference between predators, on the rate of prey consumption by an average predator. We suggest that this mechanism is the most convincing hypothesis for the spontaneous generation of patchiness through diusion and trophic interaction in a homogeneous environment and add a new feature in the controversial issue of ratio and prey dependent predator–prey models in ecology. c  2001 Elsevier Science B.V. All rights reserved. PACS: 87.10.+e; 05.70.Ln; 47.54.+r Keywords: Predator–prey models; Ratio-dependent functional response; Diusion driven instability; Turing structures 1. Introduction: the ratio-dependent model with diusion It is now accepted that precise prey dependence or ratio dependence functional re- sponses in predator–prey models will likely both be rare in nature [1]. However, since the inuential paper [2] comparing prey versus ratio-dependent functional responses within general predator–prey models, a lot of eort has been devoted to understand the divergent consequences of assuming one of the two idealized forms of functional response. In fact, the sort of functional response assumed strongly inuences dynamic * Corresponding author. Fax: +34-93-4111438. E-mail address: fbartu@porthos.bio.ub.es (F. Bartumeus). 0378-4371/01/$ - see front matter c  2001 Elsevier Science B.V. All rights reserved. PII:S0378-4371(01)00051-6