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

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

Mathematical Modelling of Natural Phenomena (2008)

- Volume: 3, Issue: 3, page 87-102
- ISSN: 0973-5348

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topPoggiale, J.-C., Gauduchon, M., and Auger, P.. "Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System." Mathematical Modelling of Natural Phenomena 3.3 (2008): 87-102. <http://eudml.org/doc/222337>.

@article{Poggiale2008,

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.
},

author = {Poggiale, J.-C., Gauduchon, M., Auger, P.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {spatial heterogeneity; enrichment paradox; singular perturbations; bifurcations},

language = {eng},

month = {11},

number = {3},

pages = {87-102},

publisher = {EDP Sciences},

title = {Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System},

url = {http://eudml.org/doc/222337},

volume = {3},

year = {2008},

}

TY - JOUR

AU - Poggiale, J.-C.

AU - Gauduchon, M.

AU - Auger, P.

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

JO - Mathematical Modelling of Natural Phenomena

DA - 2008/11//

PB - EDP Sciences

VL - 3

IS - 3

SP - 87

EP - 102

AB -
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.

LA - eng

KW - spatial heterogeneity; enrichment paradox; singular perturbations; bifurcations

UR - http://eudml.org/doc/222337

ER -

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