Macroscopic dynamic effects of migrations in patchy predator-prey systems

Journal of Theoretical Biology

Volumn 185, Issue 4, 1997, Pages 459-474

  Michalski, J ^a,g   Poggiale, J Ch ^a,b,f   Arditi, R ^a,c,d   Auger, P M ^e  

^a UNIVERSITY OF LAUSANNE   (Switzerland)

^b UNIVERSITÉ DE BOURGOGNE   (France)

^c UNIVERSITÉ PARIS SUD   (France)

^d AGROPARISTECH   (France)

^e UNIVERSITÉ LYON 1   (France)

^f AIX MARSEILLE UNIVERSITY   (France)

^g EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL BEHAVIOR; ARTICLE; ECOSYSTEM; MATHEMATICAL MODEL; MIGRATION; POPULATION DYNAMICS; PREDATOR; PRIORITY JOURNAL;

ANIMALIA;

EID: 0031582205     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1996.0327     Document Type: Article

References (31)

1. ARDITI, R. (1979). Les composants de la prédation, les modèles proie-prédateur, et les cycles de populations naturelles. Thesis, Université Paris 7, Paris.
2. ARDITI, R., ABILLON, J. M. & VIEIRA DA SILVA, J. (1977). The effect of a time-delay in a predator-model. Mathematical Biosciences 33, 107-120.
3. ARDITI, R., ABILLON, J. M. & VIEIRA DA SILVA, J. (1978). A predator-prey model with satiation and intraspecific competition. Ecol. Modelling 5, 173-191.
4. ARDITI, R. & GINZBURG, L. R. (1989). Coupling in predator-prey dynamics: ratio-dependence. J. theor. Biol. 139, 311-326.
5. AUGER, P. (1989). Dynamics and Thermodynamics in Hierarchically Organised Systems. Oxford: Pergamon Press.
6. AUGER, P. & ROUSSARIE, R. (1994). Complex ecological models with simple dynamics: From individuals to populations. Acta Biotheor. 42, 111-136.
7. AUGER, P. & POGGIALE, J.-CH. (1996). Emergence of population growth models: fast migrations and slow growth. J. theor. Biol. 182, 99-108.
8. BEDDINGTON, J. R. (1975). Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44, 331-340.
9. BERRYMAN, A. A. (1981). Population Systems: A General Introduction. New York: Plenum Press.
10. BERRYMAN, A. A., MICHALSKI, J., GUTIERREZ, A. P. & ARDITI, R. (1995). Logistic theory of food web dynamics. Ecology 76, 336-343.
11. CARTAN, H. (1966). Calcul Différentiel. Hermann, Collection Méthodes.
12. CHOW, S. N., LIE, C. & WANG, D. (1994). Normal Forms and Bifurcation of Planar Vector Fields. Cambridge: Cambridge Press University.
13. DEANGELIS, D. L., GOLDSTEIN, R. A. & O'NEILL, R. V. (1975). A model for trophic interaction. Ecology 56, 881-892.
14. FENICHEL, N. (1971). Persistence and smoothness of invariant manifolds for flows. Indiana University Mathematical Journal 21, 193-226.
15. GOMATAM, J. (1974). A new model for interacting populations I. Two-species systems. Bull. Math. Biol. 36, 347-353.
16. HASSELL, M. P. & VARLEY, G. C. (1969). New inductive population model for insect parasites and its bearing on biological control. Nature 223, 1133-1137.
17. HASSELL, M. P. & ROGERS, D. J. (1972). Insect parasite responses in the development of population models. J. Anim. Ecol. 41, 661-676.
18. HOLLING, C. S. (1959). Some characteristics of simple types of predation and parasitism. Can. Entomol. 91, 385-398.
19. IVLEV, V. S. (1961). Experimental Ecology of the Feeding of Fishes. New Haven: Yale University Press.
20. JOST, J. L., DRAKE, J. F., TSUCHIYA, H. M. & FREDRICKSON, A. G. (1973). Microbial food chains and food webs. J. theor. Biol. 41, 461-484.
21. MCCARTHY, M. A., GINZBURG, L. R. & AKÇAKAYA, H. R. (1995). Predator interference across trophic chains. Ecology 76, 1310-1319.
22. POGGIALE, J.-CH., AUGER, P. & ROUSSARIE, R. (1995). Perturbations of Lotka-Volterra systems by behavioural sequences. Acta Biotheor. 43, 27-39.
23. POGGIALE, J.-CH. & AUGER, P. (1996). Fast Oscillating Migration in a Predator-Prey Model. Math. Models Methods Applied Sci. 6, 217-226.
24. REAL, L. A. (1977). The kinetics of functional response. Amer. Naturalist 111, 289-300.
25. ROGERS, D. J. & HASSELL, M. P. (1974). General models for insect parasite and predator searching behaviour: interference. J. Anim. Ecol. 43, 239-253.
26. ROSENZWEIG, M. L. (1971). Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171, 385-387.
27. RUXTON, G. D., GURNEY, W. S. C. & DE ROOS, A. M. (1992). Interference and population cycles. Theor. Popul. Biol. 42, 235-253.
28. STREBEL, D. E. & GOEL, N. S. (1973). On the isocline methods for analysing prey-predator interactions. J. theor. Biol. 39, 211-234.
29. TAKAHASHI, F. (1964). Reproduction curve with two equilibrium points: a consideration on the fluctuation of insect population. Res. Popul. Ecol. (Kyoto) 6, 28-36.
30. TOSTOWARYK, W. (1972). The effect of prey defence on the functional response of Podisus modestus (Hemiptera: Pentatomidae) to densities of the sawflies Neodiprion swainei and N. pratti banksianae (Hymenoptera: Neodiprionidae). Can. Entomol. 104, 61-69.
31. WATT, K. E. F. (1959). A mathematical model for the effect of densities of attacked and attacking species on the number attacked. Can. Entomol. 91, 129-144.