Enrichment and foodchain stability: The impact of different forms of predator-prey interaction

Journal of Theoretical Biology

Volumn 227, Issue 3, 2004, Pages 349-358

  Gross, Thilo ^a   Ebenhöh, Wolfgang ^a   Feudel, Ulrike ^a  

^a ICBM   (Germany)

Author keywords

Bifurcation; Dynamics; Ecosystem stability; Enrichment; Foodchain

Indexed keywords

BIFURCATION; ECOLOGICAL MODELING; ENRICHMENT; FOOD CHAIN; PREDATOR-PREY INTERACTION;

ANALYTIC METHOD; ARTICLE; ECOLOGY; FOOD CHAIN; MOLECULAR INTERACTION; MOLECULAR MODEL; PREDATOR PREY INTERACTION; PRIORITY JOURNAL; QUALITATIVE ANALYSIS;

ANIMALS; ECOSYSTEM; FOOD CHAIN; MODELS, BIOLOGICAL;

EID: 1542358782     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jtbi.2003.09.020     Document Type: Article

References (29)

1. Argyris J., Faust G., Haase M. An Exploration of Chaos: An Introduction for Natural Scientists and Engineers. 1994;North-Holland, Amsterdam.
2. Boer M.P., Kooi B.W., Kooijman S.A.L.M. Food chain dynamics in the chemostat. Math. Biosci. 150:1998;43-62. doi:10.1016/S0025-5564(98)00010-8.
3. Busenberg S., Kumar S.K., Austin P., Wake G. The dynamics of a model of plankton-nutrient interaction. Bull. Math. Biol. 52:1990;677-696.
4. DeAngelis D.L. Dynamics of Nutrient Cycling and Food Webs. 1st Edition:1992;Chapman & Hall, London.
5. Ebenhöh W. Coexistence of an unlimited number of algal species in a model system. J. Theor. Popul. Biol. 34:1988;130.
6. Edwards A.M., Brindley J. Oscillatory behaviour in a three-component plankton population model. Dynam. Stability Syst. 11:1996;347-370.
7. Freedman H.I., So J.W.-H. Global stability and persistence of simple foodchains. Math. Biosci. 76:1985;69-86. doi:10.1016/0025-5564(85)90047-1.
8. Gard T.C. Persistence in foodchains with general interactions. Math. Biosci. 51:1980;165-174. doi:10.1016/0025-5564(80)90096-6.
9. Glendinning P. Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations. 1994;Cambridge University Press, Cambridge.
10. Gragnani A., De Feo O., Rinaldi S. Food chain in the chemostat. relationships between mean yield and complex dynamics Bull. Math. Biol. 60:1998;703-719. doi:10.1006/bulm.1997.0039.
11. Gross, T., Feudel, U., 2003. Analytical search for bifurcation surfaces in parameter space. Physica D, submitted.
12. Guckenheimer J., Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. 7th Edition:2002;Springer, Berlin.
13. Guckenheimer J., Myers M., Sturmfels B. Computing Hopf bifurcations i. SIAM J. Numer. Anal. 34:1997;1-33.
14. Hopf E. Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialgleichungssystems. Ber. Math. Phys. Sächs. Akad. Wiss. 94:1942;1-22.
15. Ivlev V. Experimental Ecology and Feeding of Fishes. 1961;Yale University Press, New Haven, CI.
16. Kirk K.L. Enrichment can stabilize population dynamics. autotoxins and density dependence Ecology. 79:1998;2456-2462.
17. Kuznetsov Y.A. Elements of Applied Bifurcation Theory. 1995;Springer, Berlin.
18. Lotka A.J. Elements of Physical Biology. 1st Edition:1925;Williams and Wilkens, Baltimore.
19. Luckinbill L.S. The effect of space and enrichment on a predator-prey system. Ecology. 55:1974;1142-1147.
20. McCauley E., Murdoch W.W. Predator-prey dynamics in environments rich and poor in nutrients. Nature. 343:1990;455-457. doi:10.1038/343455a0.
21. McCauley E., Nisbet R.M., Murdoch W.W., Roos A.M.D., Gurney W.S.C. Large-amplitude cycles of daphnia and its algal prey in enriched environments. Nature. 402:1999;653-656. doi:10.1038/45223.
22. Moloney C.L., Field J.G. General allometric equations for rates of nutrient uptake, ingestion and respiration in plankton organisms. Limnol. Oceanogr. 34:1989;1290-1299.
23. Morin P.J., Lawler S.P. Food web architecture and population dynamics. theoretical and empirical evidence Ann. Rev. Ecol. Syst. 26:1995;505-529.
24. Ott E. Chaos in Dynamical Systems. 1997;Cambridge University Press, Cambridge.
25. Rosenzweig M.L. Paradox of enrichment. destabilization of exploitation ecosystems in ecological time Science. 171:1971;385-387.
26. Saunders P.T., Bazin M.J. On the stability of foodchains. J. Theor. Biol. 52:1974;121-142.
27. Sommer U. The paradox of plankton. fluctuations of phosphorus availability maintain diversity of phytoplankton in flow-through cultures Limnol. Oceanogr. 29:1984;633.
28. Tilman D., Wedin D. Oscillations and chaos in the dynamics of perennial grasses. Nature. 353:1991;653-655. doi:10.1038/353653A0.
29. Volterra V. Fluctuations in the abundance of a species considered mathematically. Nature. 118:1926;558-560.