Model analysis of a simple aquatic ecosystems with sublethal toxic effects

Mathematical Biosciences and Engineering

Volumn 5, Issue 4, 2008, Pages 771-787

  Kooi, B W ^a   Bontje, D ^a   Liebig, M ^b  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b ECT OEKOTOXIKOLOGIE GMBH   (Germany)

Author keywords

Bifurcation analysis; Ecological factors; Ecosystem dynamics; Toxicological effects

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; ECOSYSTEM; ECOTOXICOLOGY; FOOD CHAIN; PREDATION; WATER POLLUTION;

ANIMALS; ECOSYSTEM; ECOTOXICOLOGY; FOOD CHAIN; MODELS, BIOLOGICAL; PREDATORY BEHAVIOR; WATER POLLUTION;

EID: 58949104334     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2008.5.771     Document Type: Article

References (30)

1. A. D. Bazykin. Nonlinear dynamics of interacting populations. World Scientific, Singapore (1998).
2. B. Boldin. Introducing a population into a steady community: The critical case, the center manifold, and the direction of bifurcation. SIAM Journal on Applied Mathematics, 66 (2006) 1424-1453.
3. K. E. Clark, F. A. P. C. Gobas, and D. Mackay. Model of organic chemical uptake and clearance by Fish from food and water. Environmental Science Technology, 24 (1990) 1203-1213.
4. D. L. DeAngelis. Dynamics of Nutrient Cycling and Food Webs. Number 9 in Population and Community Biology series. Chapman & Hall, London (1992).
5. E. J. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. Wang. Auto 97: Continuation and bifurcation software for ordinary differential equations. Technical report, Concordia University, Montreal, Canada (1997).
6. J. W. Fleeger, K. R. Carman, and R. M. Nisbet. Indirect effects of contaminants in aquatic ecosystems. The Science of the Total Environment, 317 (2003) 207-233.
7. F. A. P. C. Gobas. A model for predicting the bioaccumulation of hydrophobic organic chemicals in aquatic food-webs: application to Lake Ontario. Ecological Modelling, 69 (1992) 1-17.
8. V. Grimm and C. Wissel. Babel, or the ecological stability discussion: an inventory and analysis of terminology and a guide for avoiding confusion. Oecologia, 109 (1997) 323-334.
9. J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, volume 42 of Applied Mathematical Sciences. Springer-Verlag, New York, 2 edition (1985).
10. W. S. C. Gurney and R. M. Nisbet. Ecological Dynamics. Oxford University Press (1998).
11. C. R. Gwaltney and M. A. Stadtherr. Reliable computation of equilibrium states and bifurcations in ecological systems analysis. Computers & Chemical Engineering, 31 (2007) 993-1005.
12. T. G. Hallam, G. A. Canziani, and R. R. Lassiter. Sublethal narcosis and population persistence: A modelling study on growth effects. Environmental Toxicology and Chemistry, 12 (1993) 947-954.
13. T. G. Hallam, R. R. Lassiter, J. Li, and W. McKinney. Toxicant-induced mortality in models of Daphnia populations. Environmental Toxicology and Chemistry, 9 (1990) 597-621.
14. T. G. Hallam, R. R. Lassiter, J. Li, and W. McKinney. An approach for modelling populations with continuous structured models. In Individual-based Models and Approaches in Ecology (eds. D. L. DeAngelis and L. J. Gross), Chapman & Hall, New York (1992) 312-337, 312-337.
15. T. G. Hallam, R. R. Lassiter, J. Li, and L. A. Suarez. Modelling individuals employing an integrated energy response: Application to Daphnia. Ecology, 71 (1990) 938-954.
16. A. I. Khibnik, Y. A. Kuznetsov, V. V. Levitin, and E. V. Nikolaev. Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps. Physica D, 62 (1993) 360-371.
17. H. L. Koh, T. G. Hallam, and H. L. Lee. Combined effects of environmental and chemical stressors on a model Daphnia population. Ecological Modelling, 103 (1997) 19-32.
18. B. W. Kooi. Numerical bifurcation analysis of ecosystems in a spatially homogeneous environment. Acta Biotheoretica, 51 (2003) 189-222.
19. B. W. Kooi, D. Bontje, G. A. K. van Voorn, and S. A. L. M. Kooijman. Sublethal toxic effects in a simple aquatic food chain. Ecological Modelling, 212 (2008) 304-318.
20. B. W. Kooi, L. D. J. Kuijper, M. P. Boer, and S. A. L. M. Kooijman. Numerical bifurcation analysis of a tri-trophic food web with omnivory. Mathematical Biosciences, 177 (2002) 201-228.
21. B. W. Kooi, L. D. J. Kuijper, and S. A. L. M. Kooijman. Consequence of symbiosis for food web dynamics. Journal of Mathematical Biology, 49 (2004) 227-271.
22. B. W. Kooi, J. C. Poggiale, P. Auger, and S. A. L. M. Kooijman. Aggregation methods in food chains with nutrient recycling. Ecological Modelling, 157 (2002) 69-86.
23. S. A. L. M. Kooijman. Dynamic Energy and Mass Budgets in Biological Systems. Cambridge University Press, Cambridge (2000).
24. S. A. L. M. Kooijman and J. J. M. Bedaux. The analysis of aquatic toxicity data. VU University Press, Amsterdam (1996).
25. Y. A. Kuznetsov. Elements of Applied Bifurcation Theory, volume 112 of Applied Mathematical Sciences. Springer-Verlag, New York, 3 edition (2004).
26. M. Loreau, S. Naeem, P. Inchausti, J. Bengtsson, J. P. Grime, H. A., D. U. Hooper, M. A. Huston, D. Raffaelli, B. Schmid, D. Tilman, and D. A. Wardle. Ecology - biodiversity and ecosystem functioning: Current knowledge and future challenges. Science, 294 (2001) 804-808.
27. S. Sharpe and D. Mackay. A framework for evaluating bioaccumulation in food webs. Environmental Science Technology, 34 (2000) 1203-1213.
28. H. L. Smith and P. Waltman. The Theory of the Chemostat. Cambridge University Press, Cambridge (1994).
29. R. V. Thomann and J. A. Mueller. Principles of surface water quality modeling and control. Harper & Row, Publ., New York (1987).
30. S. Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos, volume 2 of Texts in Applied Mathematics. Springer-Verlag, New York (1990).