Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System

¹ Centre d'Océanologie de Marseille, UMR CNRS 6117, Laboratoire de Microbiologie, de Géochimie et d'Ecologie Marines, Université de la Méditerranée, Campus de Luminy Case 901, 13288 Marseille Cedex 9 - France
² UR GEODES – IRD Bondy - 32, Av Henri Varagnat 93143 Bondy Cedex - France

Corresponding author: jean-christophe.poggiale@univmed.fr

Abstract

This paper is devoted to the study of a predator-prey model in a patchy environment. The model represents the interactions between phytoplankton and zooplankton in the water column. Two patches are considered with respect to light availability: one patch is associated to the surface layer, the second patch describes the bottom layer. We show that this spatial heterogeneity may destabilize the predator-prey system, even in oligotrophic system where the nutrient is low enough to avoid ”paradox-enrichment” phenomenon. Indeed, in this case, an heterogeneity index can be used as a bifurcation parameter, leading to a Hopf bifurcation. Moreover, we assume that individuals can be dispersed in both patches via hydrodynamism processes, like in a mixed layer. The effect of mixing intensity is analysed as well as interactions between dispersion and enrichment. We also show that, in some cases, spatial heterogeneity has a stabilizing effect. These contrasted results are examined by considering the non linear interaction between heterogeneity, dispersal and enrichment and some mechanisms leading to stabilization/destabilization are exhibited.