Influence of consumer mutual interference on the stabilization of a three-level trophic system

Population Ecology

Volumn 49, Issue 2, 2007, Pages 155-163

  Zhang, Fengpan ^a   Li, Zi Zhen ^a   Zhang, Xinfeng ^a   Gao, Meng ^a  

^a LANZHOU UNIVERSITY   (China)

Author keywords

Beddington DeAngelis functional response; Mutual interference; Stabilizing influence; Three species food chain

Indexed keywords

CONSUMPTION BEHAVIOR; FOOD CHAIN; MUTUALISM; NUMERICAL MODEL; POPULATION DYNAMICS; POPULATION ECOLOGY; PREDATOR-PREY INTERACTION; TROPHIC LEVEL;

EID: 33947099014     PISSN: 14383896     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10144-006-0033-1     Document Type: Article

References (47)

1. Arditi R, Akçakaya HR (1990) Underestimation of mutual interference of predators. Oecologia 83:358-361
2. Arditi R, Jean-Marc C, Yuri T, Christian J (2004) Does mutual interference always stabilize predator-prey dynamics? A comparison of models. Biol Modell 327:1037-1057
3. Begon M, Mortimer M, Thompson DJ (1996) Population ecology: a unified study of animals and plants. Blackwell Science, Oxford
4. Cantrell RS, Cosner C (2001) On the dynamics of predator-prey models with the Beddington-DeAngelis functional response. J Math Anal Appl 257:206-222
5. DeAngelis DL, Goldstein RA, O'Neill RV (1975) A model for trophic interaction. Ecology 56:881-892
6. De Roos AM, McCauley E, Wilson WG (1991) Mobility versus density limited predator-prey dynamics on different spatial scales. Proc R Soc Lond B 246:117-122
7. Edelstein-Keshet L (1988)Models in biology. Random, New York
8. Eisenberg JN, Maszle DR (1995) The structural stability of a three-species food chain model. J Theor Biol 176:501-510
9. Elton C (1930) Animal ecology and evolution. Oxford University Press, New York
10. Free CA, Beddington JR, Lawton JH (1977) On the inadequacy of simple models of mutual interference for parasitism and predation. J Anim Ecol 36:375-389
11. Gonzalez-Andujar JL, Perry JN (1993a) The effect of dispersal between chaotic and non-chaotic populations within a metapopulation. Oikos 66:555-557
12. Gonzalez-Andujar JL, Perry JN (1993b) Chaos, metapopulations and dispersal. Ecol Modell 65:255-263
13. Hanski I, Turchin P, Korpimake E, Henttonen H (1993) Population oscillations of boreal rodents: regulation by mustelid predators leads to chaos. Nature 364:232-235
14. Hassell MP (1971) Mutual interference between searching insect parasites. J Anim Ecol 40:473-486
15. Hassell MP, May RM (1973) Stability in insect host-parasite models. J Anim Ecol 42:693-726
16. Hassell MP, Rogers DJ (1972) Insect parasite responses in the development of population models. J Anim Ecol 41:661-676
17. Hassell MP, Varley GC (1969) New inductive population model for insect parasites and its bearing on biological control. Nature 223:1133-1137
18. Hastings A, Powell T (1991) Chaos in a three-species food chain. Ecology 72:896-903
19. Hastings A, Hom CL, Ellner S, Turchin P, Godfray HCJ (1993) Chaos in ecology: is mother nature a strange attractor? Annu Rev Ecol Syst 34:1-33
20. Holling CS (1959) The components of predation as revealed by a study of small mammal predation of the European pine sawfly. Can Entomol 91:293-320
21. May RM (1974) Stability and complexity in model ecosystems, 2nd edn, vol 6. Monographs in population biology. Princeton University Press, Princeton, NJ
22. May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261:459-467
23. McCallum HI (1992) Effects of immigration on chaotic population dynamics. J Theor Biol 154:277-284
24. McCann K, Hastings A (1997) Re-evaluating the omnivorystability relationship in food webs. Proc R Soc Lond B 264:1249-1254
25. McCann K, Yodzis P (1994a) Biological condition for chaos in a three-species food chain. Ecology 75:561-564
26. McCann K, Yodzis P (1994b) Nonlinear dynamics and population disappearances. Am Nat 144:873-879
27. McCann K, Yodzis P (1995) Bifurcation structure of a threespecies food chain model. Theor Popul Biol 48:93-125
28. Murdoch W, Oaten A (1975) Predation and population stability. Adv Ecol Res 9:1-125
29. Muratori S, Rinaldi S (1992) Low- and high-frequency oscillations in three dimensional food chain systems. J Soc Ind Appl Math 52:1688-1706
30. Pahl-Wostl C (1997) Dynamic structure of a food web model: comparison with a food chain model. Ecol Modell 100:103-123
31. Peet AB, Deutsh PA, Peacock-Lopez E (2005) Complex dynamics in a three-level trophic system with intraspecies interaction. J Theor Biol 232:491-503
32. Rai V, Sreenivasan R (1993) Period-doubling bifurcation leading to chaos in a model food chain. Ecol Modell 69:63-77
33. Rohani P, Miramontes O, Hassell MP (1994) Quasiperiodicity and chaos in population models. Proc R Soc Lond B 258:17-22
34. Ruxton GD (1995) Short term refuge use and stability of predator-prey models. Theor Popul Biol 47:1-17
35. Ruxton GD (1996) Chaos in a three-species food chain with a low bound on the bottom population. Ecology 77:317-319
36. Salt GW (1967) Predation in an experimental protozoan population (Woodruffia Paramecium). Ecol Monogr 37:113-144
37. Salt GW (1974) Predator and prey densities as controls of the rate of capture by the predator Didinium nasutum. Ecology 55:434-439
38. Schaffer WM, DeBoer RJ (1995) Implications of spatial heterogeneity for the paradox of enrichment. Ecology 76:2270-2277
39. Stone L (1993) Period-doubling reversals and chaos in simple ecological models. Nature 365:617-620
40. Tilman D, Wedin D (1991) Oscillations and chaos in the dynamics of a perennial grass. Nature 353:653-655
41. Turchin P, Taylor AD (1992) Complex dynamics in ecological time series. Ecology 73:289-305
42. Varriale MC, Gomes AA (1998) A study of a three-species food chain. Ecol Modell 110:119-133
43. Vayenas DV, Pavlou S (2001) Chaotic dynamics of a microbial system of coupled food chains. Ecol Modell 136:285-295
44. Wolfram S (1991) Mathematica: a system for doing mathematics by computer. Addison-Wesley, Redwood City, CA
45. Wynne-Edwards VC (1962) Animal dispersion in relation to social behavior. Hafner, New York
46. Xu C, Li Z (2002) Influence of intraspecific density dependence on a three-species food chain with and without external stochastic disturbances. Ecol Modell 155:71-83
47. Yodzis P, Innes S (1992) Body size and consumer-resource dynamics. Am Nat 139:1151-1175