1Centre 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 2UR GEODES – IRD Bondy - 32, Av Henri Varagnat 93143 Bondy Cedex - France
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 3, pp. 87-102
Cet article a éte moissonné depuis la source EDP Sciences
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.
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
@article{10_1051_mmnp:2008065,
author = {J.-C. Poggiale and M. Gauduchon and P. Auger},
title = {Enrichment {Paradox} {Induced} by {Spatial} {Heterogeneity} in a {Phytoplankton} - {Zooplankton} {System}},
journal = {Mathematical modelling of natural phenomena},
pages = {87--102},
year = {2008},
volume = {3},
number = {3},
doi = {10.1051/mmnp:2008065},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008065/}
}
TY - JOUR
AU - J.-C. Poggiale
AU - M. Gauduchon
AU - P. Auger
TI - Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System
JO - Mathematical modelling of natural phenomena
PY - 2008
SP - 87
EP - 102
VL - 3
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UR - http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008065/
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%J Mathematical modelling of natural phenomena
%D 2008
%P 87-102
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%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008065/
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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
