Food quality in producer-grazer models: A generalized analysis

American Naturalist

Volumn 176, Issue 3, 2010, Pages 367-380

  Stiefs, Dirk ^a,b   Van Voorn, George A K ^c   Kooi, Bob W ^d   Feudel, Ulrike ^a   Gross, Thilo ^b  

^a UNIVERSITY OF OLDENBURG   (Germany)

^b MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^c WAGENINGEN UNIVERSITY   (Netherlands)

^d VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Bifurcation analysis; Food quality; Generalized model; Paradox of enrichment; Stoichiometry; Variable efficiency

Indexed keywords

BIOMASS; FOOD QUALITY; INTRASPECIFIC COMPETITION; POPULATION DYNAMICS; PRODUCER-SCROUNGER INTERACTION; STOICHIOMETRY;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOMASS; ENERGY METABOLISM; FOOD; FOOD CHAIN; PLANT PHYSIOLOGY; STANDARD; STANDARDS;

ANIMALS; BIOMASS; ENERGY METABOLISM; FOOD; FOOD CHAIN; MODELS, BIOLOGICAL; PLANT PHYSIOLOGICAL PHENOMENA;

EID: 77955601235     PISSN: 00030147     EISSN: None     Source Type: Journal    
DOI: 10.1086/655429     Document Type: Article

References (40)

1. Andersen, T. 1997. Pelagic nutrient cycles: herbivores as sources and sinks. Vol. 129. Ecological Studies Series. Springer, Berlin.
2. Andersen, T., J. Elser, and D. Hessen. 2004. Stoichiometry and population dynamics. Ecology Letters 7:884-900.
3. DeAngelis, D. L. 1975. Stability and connectance in food web models. Ecology 56:238-243.
4. -. 1992. Dynamics of nutrient cycling and food webs. Population and Community Biology Series. Chapman & Hall, London.
5. Deng, B., and I. Loladze. 2007. Competitive coexistence in stoichiometric chaos. Chaos 17:1-14.
6. Diehl, S. 2007. Paradoxes of enrichment: effects of increased light versus nutrient supply on pelagic producer-grazer systems. American Naturalist 169: E173-E191.
7. Doedel, E. J., and B. Oldeman. 2009. Auto 97: continuation and bifurcation software for ordinary differential equations (with homcont). Technical report. Concordia University, Montreal.
8. Doedel, E. J., A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. Wang. 1997. Auto 97: continuation and bifurcation software for ordinary differential equations (with homcont). Technical report. Concordia University, Montreal.
9. Fell, D. A., and H. M. Sauro. 1985. Metabolic control and its analysis: additional relationships between elasticities and control coefficients. European Journal of Biochemistry 148:555-561.
10. Gardner, M. R., and W. R. Ashby. 1970. Connectance of large dynamic (cybernetic) systems: critical values for stability. Nature 228:784.
11. Gross, T., and U. Feudel. 2006. Generalized models as a universal approach to nonlinear dynamical systems. Physical Review E 73, 016205.
12. Gross, T., W. Ebenhöh, and U. Feudel. 2004. Enrichment and foodchain stability: the impact of different forms of predator-prey interaction. Journal of Theoretical Biology 227:349-358.
13. Gross, T., L. Rudolf, S. A. Levin, and U. Dieckmann. 2009. Generalized models reveal stabilizing factors in food webs. Science 325:747-750.
14. Grover, J. P. 2003. The impact of variable stoichiometry on predatorprey interactions: a multinutrient approach. American Naturalist 162:29-43.
15. Guckenheimer, J., and P. Holmes. 2002. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Vol. 42. Applied Mathematical Sciences. 7th ed. Springer, Berlin.
16. Guckenheimer, J., M. Myers, and B. Sturmfels. 1997. Computing Hopf bifurcations I. SIAM Journal of Numerical Analysis 34:1.
17. Hall, S. R. 2004. Stoichiometrically explicit competition between grazers: species replacement, coexistence, and priority effects along resource supply gradients. American Naturalist 164:157-172.
18. Hendriks, A. J. 1999. Allometric scaling of rate, age and density parameters in ecological models. Oikos 86:293-310.
19. Huxel, G. 1999. On the influence of food quality in consumerresource interactions. Ecology Letters 2:256-261.
20. Kooijman, S. A. L. M. 2010. Dynamic energy budget theory for metabolic organisation. Cambridge University Press, Cambridge.
21. Kooijman, S. A. L. M., T. Andersen, and B. W. Kooi. 2004. Dynamic energy budget representations of stoichiometric constraints on population dynamics. Ecology 85:1230-1243.
22. Kooijman, S. A. L. M., J. Grasman, and B. W. Kooi. 2007. A new class of non-linear stochastic population models with mass conservation. Mathematical Biosciences 210:378-394.
23. Kuznetsov, Y. A. 2004. Elements of applied bifurcation theory. Vol. 112. Applied Mathematical Sciences. 3rd ed. Springer, New York.
24. Levin, S. A. 1977. A more functional response to predator-prey stability. American Naturalist 111:381-383.
25. Loladze, I., Y. Kuang, and J. J. Elser. 2000. Stoichiometry in producergrazer systems: linking energy flow with element cycling. Bulletin of Mathematical Biology 62:1137-1162.
26. Loladze, I., Y. Kuang, J. Elser, and W. Fagan. 2004. Competition and stoichiometry: coexistence of two predators on one prey. Theoretical Population Biology 65:1-15.
27. May, R. M. 1972. Will a large complex system be stable? Nature 238:413-414.
28. Miller, C., Y. Kuang, W. Fagan, and J. Elser. 2004. Modeling and analysis of stoichiometric two-patch consumer-resource systems. Mathematical Biosciences 189:153-184.
29. Morin, P. J., and S. P. Lawler. 1995. Food web architecture and population dynamics: theory and empirical evidence. Annual Review of Ecology and Systematics 26:505-529.
30. Muller, E. B., R. M. Nisbet, S. A. L. M. Kooijman, J. J. Elser, and E. McCauley. 2001. Stoichiometric food quality and herbivore dynamics. Ecology Letters 4:519-529.
31. Murdoch, W., and A. Oaten. 1975. Predation and population stability. Pages 1-131 in Advances in ecological research. Vol. 9. Academic Press, New York.
32. Murdoch, W. W. 1977. Stabilizing effects of spatial heterogeneity in predator-prey systems. Theoretical Population Biology 11:252-273.
33. Qian, C., and D. E. Giles. 2007. The bias of elasticity estimators in linear regression: some analytic results. Economics Letters 94:185-191.
34. Rosenzweig, M. L. 1971. Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171:385-387.
35. Rosenzweig, M. L., and R. H. MacArthur. 1963. Graphical representation and stability conditions of predator-prey interactions. American Naturalist 97:209-223.
36. Scheffer, M., S. Carpenter, J. Foley, C. Folke, and B. Walker. 2001. Catastrophic shifts in ecosystems. Nature 413:591-596.
37. Sterner, R. W. 1986. Herbivores' direct and indirect effects on algal populations. Science 231:605-607.
38. Sterner, R. W., and J. J. Elser. 2002. Ecological stoichiometry: the biology of elements from molecules to the biosphere. Princeton University Press, Princeton, NJ.
39. Stiefs, D., T. Gross, R. Steuer, and U. Feudel. 2008. Computation and visualization of bifurcation surfaces. International Journal of Bifurcation and Chaos 18:2191-2206.
40. Wollkind, D., A. Hastings, and J. Logan. 1982. Age structure in predator-prey systems. II. Functional response and stability and the paradox of enrichment. Theoretical Population Biology 21:57-68.