A formal derivation of the 'Beddington' functional response

Journal of Theoretical Biology

Volumn 185, Issue 3, 1997, Pages 389-400

  Huisman, Gert ^a   De Boer, Rob J ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL BEHAVIOR; ARTICLE; ECOSYSTEM; MATHEMATICAL MODEL; POPULATION DENSITY; POPULATION MODEL; PREDATOR; PRIORITY JOURNAL;

EID: 0031557670     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1996.0318     Document Type: Article

References (27)

1. ABRAMS, P. A. (1994). The fallacies of ratio-dependent predation. Ecology 75, 1842-1850.
2. ARDITI, R. & AKÇAKAYA, H. R. (1990). Underestimation of mutual interference of predators. Oecologia 83, 358-361.
3. ARDITI, R. & GINZBURG, L. R. (1989). Coupling in predator-prey dynamics: Ratio-dependence. J. theor. Biol. 139, 311-326.
4. BAKER, G. A. & GRAVIS-MORRIS, P. R. (1984). Encyclopedia of Mathematics and its Applicants, chapter Padé approximants. New York: Cambridge University Press.
5. BEDDINGTON, J. R. (1975). Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 51, 597-624.
6. BERRYMAN, A. A. (1992). The origins and evolution of predator prey theory. Ecology 73, 1530-1535.
7. BORGHANS, J. A. M., DE BOER, R. J. & SEGEL, L. A. (1996). Extending the quasi-steady state approximation by changing variables. Bull. Math. Biol. 58, 43-63.
8. DE BOER, R. J. & PERELSON, A. S. (1995). Toward a general function describing T cell proliferation. J. theor. Biol. 175, 567-576.
9. DE ROOS, A. M., METZ, J. A. J., EVERS, E. & LEIPOLDT, A. (1990). A size dependent predator-prey interaction: who pursues whom? J. math. Biol. 28, 609-643.
10. DIEHL, S., LUNDBERG, P. A., GARDFJELL, H., OKSANEN, L. & PERSSON, L. (1993). Daphnia-phytoplankton interactions in lakes: is there a need for ratio-dependent consumer-resource models. Am. Nat. 142, 1052-1061.
11. GINZBURG, L. R. & AKÇAKAYA, H. R. (1994). consequences of ratio-dependent predation for steady-state properties of ecosystems. Ecology 73, 1536-1543.
12. GLEESON, S. K. (1994). Density-dependence is better than ratio dependence. Ecology 75, 1834-1835.
13. HANSKI, I. & KORPIMÄKI, E. (1995). Microtine rodent dynamics in northern Europe: Parameterized models for the predator-prey interaction. Ecology 76, 840-850.
14. ROLLING, C. S. (1959). The components of predation as revealed by a study of small mammal predation of the European pine sawfly. Can. Ent. 91, 293-320.
15. LEIBOLD, M. (1989). Resource edibility and the effects of predator productivity on the outcome of trophic interactions. Am. Nat. 134, 922-949.
16. MCCAULEY, E. & MURDOCH, W. W. (1987). Cyclic and stable populations: plankton as a paradigm. Am. Nat. 129, 98-121.
17. MCCAULEY, E. & MURDOCH, W. W. (1990). Predator-prey dynamics in environments rich and poor in nutrients. Nature 343, 455-457.
18. MCCAULEY, E., MURDOCH, W. W. & WATSON, S. (1988). Simple models and variation in plankton models in lakes. Am. Nat. 132, 383-403.
19. METZ, J. A. J. & DIEKMANN, O. (1986). The dynamics of physiologically structured populations In: Lecture Notes in Biomathematics, Vol. 68. p6. Berlin: Springer-Verlag.
20. MITTELBACH, G. G., OSENBERG, C. W. & LEIBOLD, M. A. (1988). Trophic relations and ontogenic niche shift in aquatic ecosystems. In: Size-structured Populations, (Ebenman, B. & Perrson, L., eds), pp. 219-235. Berlin: Springer-Verlag.
21. OKSANEN, L., MOEN, J. & LUNDBERG, P. A. (1992). The time-scale problem in exploiter-victim models: does the solution lie in ratio-dependent exploitation? Am. Nat. 140, 938-960.
22. PERSSON, L., DIEHL, S., JOHANSSON, L., ANDERSON, G. & HAMRIN, S. F. (1992). Trophic interactions in temperate lake ecosystems: a test of food chain theory. Am. Nat. 140, 59-84.
23. ROSENZWEIG, M. L. (1971). Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171, 385-387.
24. RUXTON, G. D., GURNEY, W. S. C. & DE ROOS A. M. (1992). Interference and generation cycles. Theor. Popul. Biol. 42, 235-254.
25. SCHEFFER, M. & DE BOER, R. J. (1995). Implications of spatial heterogeneity for the paradox of enrichment. Ecology 76, 2270-2277.
26. STEPHENS, D. W. & KREBS, J. R. (1986). Foraging Theory. In: Monographs in Behavior and Ecology, (Krebs, J. R. & Clutton-Brock, T., eds) Vol. 4. Princeton, NJ: Princeton University Press.
27. YODSIS, P. (1989). Introduction to Theoretical Ecology. New York: Harper & Row Publishers.