Does mutual interference always stabilize predator-prey dynamics? A comparison of models

Comptes Rendus - Biologies

Volumn 327, Issue 11, 2004, Pages 1037-1057

  Arditi, Roger ^a   Callois, Jean Marc ^a   Tyutyunov, Yuri ^a,b   Jost, Christian ^a,c  

^a AGROPARISTECH   (France)

^b SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

^c UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Enrichment; Functional response; Population dynamics; Predator dependence; Ratio dependence; Trophic interactions

Indexed keywords

FUNCTIONAL RESPONSE; POPULATION DYNAMICS; PREDATOR-PREY INTERACTION; TROPHIC INTERACTION;

ARTICLE; COMPARATIVE STUDY; ECOSYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; NONHUMAN; POPULATION DYNAMICS; PREDATION; PREDATOR PREY INTERACTION; QUALITATIVE ANALYSIS; TROPHIC LEVEL;

ANIMALS; LOGISTIC MODELS; MATHEMATICS; MODELS, BIOLOGICAL; POPULATION DENSITY; POPULATION GROWTH; PREDATORY BEHAVIOR;

EID: 8744272237     PISSN: 16310691     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crvi.2004.06.007     Document Type: Article

References (43)

1. V. Volterra Leçons sur la théorie mathématique de la lutte pour la vie 1931 Gauthier-Villars Paris
2. M.P. Hassell G.C. Varley New inductive population model for insect parasites and its bearing on biological control Nature 223 1969 1133-1137
3. C.A. Free J.R. Beddington J.H. Lawton On the inadequacy of simple models of mutual interference for parasitism and predation J. Anim. Ecol. 36 1977 375-389
4. C.S. Holling The components of predation as revealed by a study of small mammal predation of the European pine sawfly Can. Entomol. 91 1959 293-320
5. R. Arditi H.R. Akçakaya Underestimation of mutual interference of predators Oecologia 83 1990 358-361
6. J.R. Beddington Mutual interference between parasites or predators and its effect on searching efficiency J. Anim. Ecol. 45 1975 331-340
7. D.L. DeAngelis R.A. Goldstein R.V. O'Neill A model for trophic interaction Ecology 56 1975 881-892
8. M.P. Hassell D.J. Rogers Insect parasite responses in the development of population models J. Anim. Ecol. 41 1972 661-676
9. M.P. Hassell R.M. May Stability in insect host-parasite models J. Anim. Ecol. 42 1973 693-726
10. D. Rogers M.P. Hassell General models for insect parasite and predator searching behaviour: Interference J. Anim. Ecol. 43 1974 239-253
11. T.W. Hwang Global analysis of the predator-prey system with Beddington-DeAngelis functional response J. Math. Anal. Appl. 281 2003 395-401
12. T.W. Hwang Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response J. Math. Anal. Appl. 290 2004 113-122
13. M. Fan Y. Kuang Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response J. Math. Anal. Appl. 295 2004 15-39
14. R.S. Cantrell C. Cosner On the dynamics of predator-prey models with the Beddington-DeAngelis functional response J. Math. Anal. Appl. 257 2001 206-222
15. R.S. Cantrell C. Cosner Effects of domain size on the persistence of populations in a diffusive food chain model with DeAngelis-Beddington functional response Nat. Resour. Model. 14 2001 335-367
16. M. Begon M. Mortimer D.J. Thompson Population Ecology: A Unified Study of Animals and Plants third ed. 1996 Blackwell Science Oxford, UK
17. M.G. Neubert H. Caswell Alternatives to resilience for measuring the responses of ecological systems to perturbations Ecology 78 1997 653-665
18. M.P. Hassell The Dynamics of Arthropod Predator-Prey Systems 1978 Princeton University Press Princeton, NJ, USA
19. M.L. Rosenzweig Paradox of enrichment: Destabilization of exploitation ecosystem in ecological time Science 171 1971 385-387
20. R. Arditi L.R. Ginzburg Coupling in predator-prey dynamics: ratio-dependence J. Theor. Biol. 139 1989 311-326
21. J.R. Beddington C.A. Free J.H. Lawton Characteristics of successful natural enemies in models of biological control of insect pest Nature (Lond.) 273 1978 513-519
22. C. Jost O. Arino R. Arditi About deterministic extinction in ratio-dependent predator-prey models Bull. Math. Biol. 61 1999 19-32
23. F. Berezovskaya G. Karev R. Arditi Parametric analysis of the ratio-dependent predator-prey model J. Math. Biol. 43 2001 221-246
24. G.F. Gause Experimental demonstrations of Volterra's periodic oscillations in the numbers of animals J. Exp. Biol. 12 1935 44-48
25. L.S. Luckinbill Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum Ecology 54 1973 1320-1327
26. M.L. Rosenzweig R.H. MacArthur Graphical representation and stability conditions of predator-prey interactions Am. Natural. 97 1963 217-223
27. M.R. Myerscough M.J. Darwen W.L. Hogarth Stability, persistence and structural stability in a classical predator-prey model Ecol. Modelling 89 1996 31-42
28. Y. Kuang E. Beretta Global qualitative analysis of a ratio-dependent predator-prey system J. Math. Biol. 36 1998 389-406
29. Y. Kuang Rich dynamics of Gause-type ratio-dependent predator-prey system Fields Inst. Commun. 21 1999 325-337
30. R.M. May Stability and Complexity in Model Ecosystems 1973 Princeton University Press Princeton, NJ, USA
31. D. Tilman Secondary succession and the pattern of plant dominance along experimental nutrient gradients Ecol. Monogr. 57 1987 189-214
32. R.L. Haedrich G.T. Rowe P.T. Poloni The megabenthic fauna in the deep-sea south of New England, USA Mar. Biol. 57 1980 165-179
33. J.F. Owen On productivity as predictor of rodent and carnivore diversity Ecology 69 1988 1161-1165
34. M.L. Rosenzweig Species Diversity in Space and Time 1993 Cambridge University Press Cambridge
35. J.F. Riebesell Paradox of enrichment in competitive systems Ecology 55 1974 183-187
36. K.J. Griffiths C.S. Holling A competition submodel for parasites and predators Can. Entomol. 101 1969 785-818
37. M. Munster-Swendsen G. Nachman Asincrony in insect host-parasite interaction and its effect on stability, studied by a population model J. Anim. Ecol. 47 1978 159-171
38. S. Ponsard R. Arditi C. Jost Assessing top-down and bottom-up control in a litter-based soil macroinvertebrate food chain Oikos 89 2000 524-540
39. C. Jost R. Arditi From pattern to process: Identifying predator-prey interactions Popul. Ecol. 43 2001 229-243
40. W.J. Sutherland From Individual Behaviour to Population Ecology 1996 Oxford University Press Oxford, UK
41. J. Monod Recherches sur la croissance des cultures bactériennes 1942 Hermann Paris
42. C. Jost Predator-prey theory: Hidden twins in ecology and microbiology Oikos 90 2000 202-208
43. M.P. Hassel The Spatial and Temporal Dynamics of Host-Parasitoid Interactions 2000 Oxford University Press Oxford, UK