Model analysis of a simple aquatic ecosystems with sublethal toxic effects
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1.
Department of Theoretical Biology, Faculty of Earth and Life Sciences, Vrije Universiteit, de Boelelaan 1087, 1081 HV Amsterdam
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2.
ECT Oekotoxikologie GmbH, Böttgerstrasse 2-14, D-65439 Flörsheim/Main
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Received:
01 December 2007
Accepted:
29 June 2018
Published:
01 October 2008
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MSC :
Primary: 92D25; Secondary: 34K18
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The dynamic behaviour of simple aquatic ecosystems with nutrient
recycling in a chemostat, stressed by limited food availability
and a toxicant, is analysed. The aim is to find effects of toxicants
on the structure and functioning of the ecosystem. The starting point is
an unstressed ecosystem model for nutrients, populations, detritus
and their intra- and interspecific interactions, as well as the
interaction with the physical environment. The fate of the toxicant
includes transport and exchange between the water and the
populations via two routes, directly from water via diffusion over
the outer membrane of the organism and via consumption of
contaminated food. These processes are modelled using mass-balance
formulations and diffusion equations. At the population level the
toxicant affects different biotic processes such as assimilation,
growth, maintenance, reproduction, and survival, thereby changing their
biological functioning. This is modelled by taking the parameters
that described these processes to be dependent on the internal
toxicant concentration. As a consequence, the structure of the
ecosystem, that is its species composition, persistence, extinction
or invasion of species and dynamics behaviour, steady state
oscillatory and chaotic, can change. To analyse the long-term
dynamics we use the bifurcation analysis approach. In
ecotoxicological studies the concentration of the toxicant in the
environment can be taken as the bifurcation parameter. The value of
the concentration at a bifurcation point marks a structural change
of the ecosystem. This indicates that chemical stressors are
analysed mathematically in the same way as environmental (e.g.
temperature) and ecological (e.g. predation) stressors. Hence,
this allows an integrated approach where different type of
stressors are analysed simultaneously. Environmental regimes and
toxic stress levels at which no toxic effects occur and where the
ecosystem is resistant will be derived. A numerical continuation
technique to calculate the boundaries of these regions will be
given.
Citation: B. W. Kooi, D. Bontje, M. Liebig. Model analysis of a simple aquatic ecosystems with sublethal toxic effects[J]. Mathematical Biosciences and Engineering, 2008, 5(4): 771-787. doi: 10.3934/mbe.2008.5.771
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Abstract
The dynamic behaviour of simple aquatic ecosystems with nutrient
recycling in a chemostat, stressed by limited food availability
and a toxicant, is analysed. The aim is to find effects of toxicants
on the structure and functioning of the ecosystem. The starting point is
an unstressed ecosystem model for nutrients, populations, detritus
and their intra- and interspecific interactions, as well as the
interaction with the physical environment. The fate of the toxicant
includes transport and exchange between the water and the
populations via two routes, directly from water via diffusion over
the outer membrane of the organism and via consumption of
contaminated food. These processes are modelled using mass-balance
formulations and diffusion equations. At the population level the
toxicant affects different biotic processes such as assimilation,
growth, maintenance, reproduction, and survival, thereby changing their
biological functioning. This is modelled by taking the parameters
that described these processes to be dependent on the internal
toxicant concentration. As a consequence, the structure of the
ecosystem, that is its species composition, persistence, extinction
or invasion of species and dynamics behaviour, steady state
oscillatory and chaotic, can change. To analyse the long-term
dynamics we use the bifurcation analysis approach. In
ecotoxicological studies the concentration of the toxicant in the
environment can be taken as the bifurcation parameter. The value of
the concentration at a bifurcation point marks a structural change
of the ecosystem. This indicates that chemical stressors are
analysed mathematically in the same way as environmental (e.g.
temperature) and ecological (e.g. predation) stressors. Hence,
this allows an integrated approach where different type of
stressors are analysed simultaneously. Environmental regimes and
toxic stress levels at which no toxic effects occur and where the
ecosystem is resistant will be derived. A numerical continuation
technique to calculate the boundaries of these regions will be
given.
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