Effect of diffusion and spatially varying predation risk on the dynamics and equilibrium density of a predator-prey system

Journal of Theoretical Biology

Volumn 219, Issue 1, 2002, Pages 73-82

  Cai Lin, Xu ^a   Zi Zhen, Li ^a  

^a LANZHOU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; HETEROGENEITY; PREDATION RISK; PREDATOR-PREY INTERACTION; SPATIAL DISTRIBUTION;

ARTICLE; BEHAVIORAL SCIENCE; FLOW RATE; PLANKTON; PREDATION; PREDATOR PREY INTERACTION; PRIORITY JOURNAL; REGULATORY MECHANISM; RISK; THEORY;

EID: 0036418574     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5193(02)93110-3     Document Type: Article

References (47)

1. Abrams, P. A. (1993). Effect of increased productivity on the abundances of trophic levels. Am. Nat. 141, 351-371.
2. Abrams, P. A. (1994). The fallacies of "ratio-dependent" predations. Ecology 75, 1842-1850.
3. Abrams, P. A. & Walters, C. J. (1996). Invulnerable prey and the paradox of enrichment. Ecology 75, 1125-1133.
4. Beddington, J. R. (1975). Mutual interference between parasites or predator and its effect on searching efficiency. J. Anim. Ecol. 51, 597-624.
5. Bohannan, B. J. M. & Lenski, R. E. (1999). Effect of prey heterogeneity on the response of a model food chain to resource enrichment. Am. Nat. 153, 73-82.
6. Colebrook, J. M. (1960. Some observations of Zooplankton swarms in Windermere. J. Anim. Ecol. 29, 241-242.
7. Crowley, P. H. (1981). Dispersal and the stability of predator-prey interactions. Am. Nat. 118, 673-701.
8. DeAngelis, D. L., Goldstein, R. A. & O'Neill, R. V. (1975). A model for trophic interaction. Ecology 56, 881-892.
9. De Roos, A. M., McCauley, E. & Wilson, W. G. (1991). Mobility versus density limited predator-prey dynamics on different spatial scales. Proc. R. Soc. London Ser B 246, 117-122.
10. Freedman, H. I. & Takeuchi, Y. (1989a). Global stability and predator dynamics in a model of prey dispersal in a patchy environment. Non-linear Analy. Theor. Meth. Appl. 13, 993-1002.
11. Freedman, H. I. & Takeuchi, Y. (1989b). Predator survival versus extinction as a function of dispersal in a predator-prey model with patchy environment. Appl. Anal. 31, 247-266.
12. Gadgil M. (1971). Dispersal: Population consequences and evolution. Ecology 52, 253-261.
13. Gatto, M. (1991). Some remarks on models of plankton densities in lakes. Am. Nat. 137, 264-267.
14. Gilpin, M. E. (1972). Enriched prey-predator systems: Theoretical stability. Science 177, 902-904.
15. Gonzalez-Andujar, J. L. & Perry, J. N. (1993). Chaos, metapopulations and dispersal. Ecol. Model. 65, 255-263.
16. Gurney, W. S. C. & Nisbet, R. M. (1978). Predator-prey fluctuations in patchy environments. J. Anim. Ecol. 47, 85-102.
17. Hanski, I. (1985). Single-species spatial dynamics may contribute to long term rarity and commonness. Ecology 66, 335-343.
18. Harris, G. P. (1986). Phytoplankton ecology: Structure, function and fluctuation. Chapman and Hall, London.
19. Hassell, M. P. & May, R. M. (1973). Stability in insect host-parasites and its effect on stability. J. Anim. Ecol. 42, 693-726.
20. Hassell, M. P. & May, R. M. (1974). Aggregation in predators and insect parasites and its effect on stability. J. Anim. Ecol. 43, 567-594.
21. Hastings, A. (1993). Complex interactions between dispersal and dynamics: Lessons from coupled logistic equations. Ecology 74, 1362-1377.
22. Holling, C. S. (1959). The components of predation as revealed by a study of small-mammal predations of the European pine sawfly. Can. Entomol. 91, 293-320.
23. Jakobsen, P. J. & Johnsen, G. H. (1988). The influence of food limitation on swarming behaviour of the waterflea Daphnia longispina. Anim. Behav. 36, 991-995.
24. Jenkins, G. P. (1988). Micro- and fine-scale distribution of microplankton in the feeding environment of larval flounder. Mar. Ecol. Prog. Ser. 43, 233-244.
25. Johnson, D. S. & Chua, T. E. (1973). Remarkable schooling behaviour of a waterflea Moina Sp. (Clado-cera). Crustaceana 24, 332-333.
26. Klemetsen, A. (1970). Plankton swarms in Lake Gjökvatn, East Finmark, Astarte 3, 83-85.
27. Kretzschmar, M., Nisbet, R. M. & McCauley, E. (1993). A predator-prey model for zooplankton grazing on competing algal populations. Theor. Popul. Biol. 44, 32-66.
28. Kuenne, C. (1925). Uber schwarmbildung bei Bosmina longirostris O.F.M. Arch. Hydrobiol. 16, 508.
29. Lei, G. C. Vikberg, V., Nieminen, M. & Kuussaari, M. (1997). The parasitoid complex attacking Finnish populations of the Glanville fritillary Melitaea cinxia (Lep: Nymphalidae), an endangered butterfly. J. Nat. Hist. 31, 635-648.
30. Malone, B. J. & McQueen, D. J. (1983). Horizontal patchiness in Zooplankton populations in two Ontario kettle lakes. Hydrobiologia 99, 101-124.
31. McCauley, E. & Murdoch, W. W. (1987). Cyclic and stable populations: Plankton as a paradigm. Am. Nat. 129, 98-121.
32. McCauley, E. & Murdoch, W. W. (1990). Predator-prey dynamics in environments rich and poor in nutrients. Nature 343, 455-457.
33. McCauley, E. & Murdoch, W. W. & Watson, S. (1988). Simple models and variation in plankton densities among lakes. Am. Nat. 132, 383-403.
34. Nisbet, R. M., Gurney, W. S. C., Murdoch, W. W. & McCauley, E. F. (1989). Structured population models: A tool for linking effects at individual and population level. Biol. J. Linn. Soc. 37, 79-99.
35. Pacala, P. & Hassell, M. P. (1991). The persistence of the host-parasitoid associations in patchy environments. II. Evaluation of field data. Am. Nat. 138, 584-605.
36. Polis, G. A. & Strong, D. R. (1996). Food web complexity and community dynamics. Am. Nat. 147, 813-846.
37. Rose, K. A. & Swartzman, G. L. (1988). Stepwise iterative calibration of a multi-species phytoplankton-zooplankton simulation model using laboratory data. Ecol. Model. 42, 1-32.
38. Rosenzweig, M. L. (1971). Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time. Science 171, 385-387.
39. Ruxton, G. D. (1994). Low levels of immigration between chaotic populations can reduce system extinctions by inducing asychronous regular cycles. Proc. R. Soc. London Ser B 256, 189-193.
40. Ruxton, G. D., Gurney, W. S. C. & De Roos, A. M. (1992). Interference and generation cycles. Theor. Popul. Biol. 42, 235-253.
41. Sarnelle, O. (1992). Nutrient enrichment and grazer effects on phytoplankton in lakes. Ecology 73, 551-560.
42. Sarnelle, O. (1994). Inferring process from pattern: Trophic level abundances and imbedded interactions. Ecology 75, 1835-1841.
43. Scheffer, M. (1992). Fish and nutrient determines algal biomass: A minimal model. Oikos 62, 271-282.
44. Scheffer, M. & De Boer, R. J. (1995). Implications of spatial heterogeneity for the paradox of enrichment. Ecology 76, 2270-2277.
45. Scheuring, I. & JaLnosi, I. M. (1996). When two and two make four: A structured population without chaos. J. Theor. Biol. 178, 89-97.
46. Scott, J. D., Chalker-Scott, L., Foreman, A. E. & D'Angelo, M. (1999). Daphnia Pulex Fed UVB-irradiated Chlamydomonas reinhardtii show decreased survival and fecundity. Photochem. Photobiol. 70, 308-313.
47. Taylor, A. D. (1990). Metapopulation, dispersal, and predator-prey dynamics: An overview. Ecology 71, 429-433.