American Institute of Mathematical Sciences

Advanced
2008, 5(4): 771-787. doi: 10.3934/mbe.2008.5.771

Model analysis of a simple aquatic ecosystems with sublethal toxic effects

B. W. Kooi 1, , D. Bontje 1, and  M. Liebig 2,

1. 

Department of Theoretical Biology, Faculty of Earth and Life Sciences, Vrije Universiteit, de Boelelaan 1087, 1081 HV Amsterdam, Netherlands
2. 

ECT Oekotoxikologie GmbH, Böttgerstrasse 2-14, D-65439 Flörsheim/Main, Germany

Received  December 2007 Revised  March 2008 Published  October 2008

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.
Keywords: toxicological effects, Bifurcation analysis, ecological factors, ecosystem dynamics.
Mathematics Subject Classification: Primary: 92D25; Secondary: 34K18.
Citation: B. W. Kooi, D. Bontje, M. Liebig. Model analysis of a simple aquatic ecosystems with sublethal toxic effects. Mathematical Biosciences & Engineering, 2008, 5 (4) : 771-787. doi: 10.3934/mbe.2008.5.771
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