Model analysis of a simple aquatic ecosystems with sublethal toxic effects
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 m...
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AIMS Press
2008-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.771 |
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| author | B. W. Kooi D. Bontje M. Liebig |
| author_facet | B. W. Kooi D. Bontje M. Liebig |
| author_sort | B. W. Kooi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-58ff7ca7cbbb47199464215aef4c8822 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2008-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-58ff7ca7cbbb47199464215aef4c88222025-01-24T01:58:42ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-09-015477178710.3934/mbe.2008.5.771Model analysis of a simple aquatic ecosystems with sublethal toxic effectsB. W. Kooi0D. Bontje1M. Liebig2Department of Theoretical Biology, Faculty of Earth and Life Sciences, Vrije Universiteit, de Boelelaan 1087, 1081 HV AmsterdamDepartment of Theoretical Biology, Faculty of Earth and Life Sciences, Vrije Universiteit, de Boelelaan 1087, 1081 HV AmsterdamDepartment of Theoretical Biology, Faculty of Earth and Life Sciences, Vrije Universiteit, de Boelelaan 1087, 1081 HV AmsterdamThe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.771toxicological effectsbifurcation analysisecological factorsecosystem dynamics |
| spellingShingle | B. W. Kooi D. Bontje M. Liebig Model analysis of a simple aquatic ecosystems with sublethal toxic effects Mathematical Biosciences and Engineering toxicological effects bifurcation analysis ecological factors ecosystem dynamics |
| title | Model analysis of a simple aquatic ecosystems with sublethal toxic effects |
| title_full | Model analysis of a simple aquatic ecosystems with sublethal toxic effects |
| title_fullStr | Model analysis of a simple aquatic ecosystems with sublethal toxic effects |
| title_full_unstemmed | Model analysis of a simple aquatic ecosystems with sublethal toxic effects |
| title_short | Model analysis of a simple aquatic ecosystems with sublethal toxic effects |
| title_sort | model analysis of a simple aquatic ecosystems with sublethal toxic effects |
| topic | toxicological effects bifurcation analysis ecological factors ecosystem dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.771 |
| work_keys_str_mv | AT bwkooi modelanalysisofasimpleaquaticecosystemswithsublethaltoxiceffects AT dbontje modelanalysisofasimpleaquaticecosystemswithsublethaltoxiceffects AT mliebig modelanalysisofasimpleaquaticecosystemswithsublethaltoxiceffects |