Geodesic
Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System
J.-C. Poggiale1 ; M. Gauduchon1 ; P. Auger2
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
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 3, pp. 87-102.

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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.
DOI : 10.1051/mmnp:2008065

J.-C. Poggiale 1 ; M. Gauduchon 1 ; P. Auger 2

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 
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     title = {Enrichment {Paradox} {Induced} by {Spatial} {Heterogeneity} in a {Phytoplankton} - {Zooplankton} {System}},
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J.-C. Poggiale; M. Gauduchon; P. Auger. Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 3, pp. 87-102. doi : 10.1051/mmnp:2008065. http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008065/

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