Complex dynamics in stochastic tritrophic models

Ecology

Volumn 79, Issue 3, 1998, Pages 1039-1052

  Ives, Anthony R ^a   Jansen, Vincent A A ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b NATURAL ENVIRONMENT RESEARCH COUNCIL   (United Kingdom)

Author keywords

Chaos; Density dependence; Host; Hyperparasitoid; Parasitoid; Resilience; Stochastic population dynamics; Time series analysis; Tritrophic interactions

Indexed keywords

MODELING; POPULATION DYNAMICS; STOCHASTIC PROCESS; TRITROPHIC INTERACTION;

EID: 0031871060     PISSN: 00129658     EISSN: None     Source Type: Journal    
DOI: 10.1890/0012-9658(1998)079[1039:CDISTM]2.0.CO;2     Document Type: Article

References (63)

1. Abrams, P. A., and J. D. Roth. 1994. The effects of enrichment of three-species food chains with nonlinear functional responses. Ecology 75:1118-1130.
2. Beddington, J. R., and P. S. Hammond. 1977. On the dynamics of host-parasite-hyperparasite interactions. Journal of Animal Ecology 46:811-821.
3. Bloomfield, P. 1976. Fourier analysis of time series: an introduction. John Wiley & Sons, New York, New York, USA.
4. Boerlijst, M. C., and P. Hogeweg. 1991. Spiral wave structure in pre-biotic evolution: hypercycles stable against parasites. Physica D 48:17-28.
5. Box, G. E. P., G. M. Jenkins, and G. C. Reinsel. 1994. Time series analysis: forecasting and control. Prentice Hall, Englewood Cliffs, New Jersey, USA.
6. Chesson, P. L., and W. W. Murdoch. 1986. Aggregation of risk: relationships among host-parasitoid models. American Naturalist 127:696-715.
7. Dennis, B., R. A. Desharnais, J. M. Gushing, and R. F. Costantino. 1995. Nonlinear demographic dynamics: mathematical models, statistical methods, and biological experiments. Ecological Monographs 65:261-281.
8. Dennis, B., and B. Taper. 1994. Density dependence in time series observations of natural populations: estimation and testing. Ecological Monographs 64:205-224.
9. Ellner, S., and P. Turchin. 1995. Chaos in a "noisy" world: new methods and evidence from time series analysis. American Naturalist 145:343-375.
10. Engbert, R., and F. R. Drepper. 1994. Quantitative analysis of unpredictability: a case study for childhood epidemics. Pages 204-215 in J. Grasman and G. van Straten, editors. Predictability and nonlinear modeling in natural sciences and economics. Kluwer Academic Press, Dordrecht, The Netherlands.
11. Godfray, H. C. J., and M. P. Hassell. 1992. Long lime series reveal density dependence. Nature 359:673-674.
12. Guckcnheimer, J., and P. Holmes. 1983. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer-Verlag, New York, New York, USA.
13. Hassell, M. P 1978. The dynamics of arthropod predatorprey systems. Princeton University Press, Princeton, New Jersey, USA.
14. _. 1986. Detecting density dependence. Trends in Ecology and Evolution 1:90-93.
15. Hassell, M. P., H. N. Comins, and R. M. May. 1991. Spatial structure and chaos in insect population dynamics. Nature 353:255-258.
16. Hassell, M. P., and R. M. May. 1973. Stability in insect host-parasite models. Journal of Animal Ecology 42:693-736.
17. Hastings, A., and K. Higgins. 1994. Persistence of transients in spatially structured ecological models. Science 263:1133-1135.
18. Hastings, A., C. L. Hom, S. Ellner, P. Turchin, and H. C. J. Godfray. 1993. Chaos in ecology: is Mother Nature a strange attractor? Annual Review of Ecology and Systematics 34:1-33.
19. Hastings, A., and T. J. Powell. 1991. Chaos in a three-species food chain. Ecology 72:896-903.
20. Hochberg, M. E., and B. A. Hawkins. 1992. Refuges as a predictor of parasitoid diversity. Science 255:973-976.
21. Hogeweg, P., and B. Hesper. 1978. Interactive instructions on population dynamics. Comput 8:319-327.
22. Rolling, C. S. 1959. Some characteristics of simple types of predation and parasitism. Canadian Entomologist 91:385-398.
23. Holyoak, M. 1993. Identifying delayed density dependence in time-series data. Oikos 79:296-304.
24. Ives, A. R. 1995a. Measuring resilience in stochastic systems. Ecological Monographs 65:217-233.
25. _. 1995b. Predicting the response of populations to environmental change. Ecology 76:926-941.
26. Jansen, V. A. A. 1995. Effects of dispersal in a tri-trophic metapopulation model. Journal of Mathematical Biology 34:195-224.
27. Kareiva, P. 1989. Renewing the dialogue between theory and experiments in population ecology. Pages 68-88 in J. Roughgarden, R. M. May, and S. A. Levin, editors. Perspectives in ecological theory. Princeton University Press, Princeton, New Jersey, USA.
28. Khibnik, A. I., Y. A. Kuznctsov, V. V. Levitin, and E. V. Nikolav. 1993. Continuation techniques and interactive software for bifurcation analysis of ODE's and iterative maps. Physica D 62:360-371.
29. Klebanoff, A., and A. Hastings. 1994. Chaos in three-species food chains. Journal of Mathematical Biology 32:427-451.
30. Kuznetsov, Y. A., and S. Rinaldi. 1996. Remarks on food-chain dynamics. Mathematical Biosciences 134:1-33.
31. Mackauer, M., and W. Voelkl. 1993. Regulation of aphid population by aphidiid wasps: does parasitoid foraging behavior or hyperparasitism limit impact? Oecologia 94:339-350.
32. May, R. M. 1973. Stability in randomly fluctuating vs. deterministic environments. American Naturalist 107:621-650.
33. _. 1974. Biological populations with nonoverlapping generations: stable points, stable cycles, chaos. Science 186:645-647.
34. _. 1976. Simple mathematical models with very complicated dynamics. Nature 261:459-467.
35. _. 1978. Host-parasitoid systems in patchy environments: a phenomenological model. Journal of Animal Ecology 47:833-843.
36. May, R. M., and M. R Hassell. 1981. The dynamics of multiparasitoid-host interactions. American Naturalist 117:234-261.
37. May, R. M., and G. F. Oster. 1976. Bifurcations and dynamic complexity in simply ecological models. American Naturalist 110:573-599.
38. McCann, K., and P. Yodzis. 1994. Biological conditions for chaos in a three-species food chain. Ecology 75:561-564.
39. Morris, R. F. 1959. Single-factor analysis in population dynamics. Ecology 40:580-588.
40. Muratori, S., and S. Rinaldi. 1992. Low- and high-frequency oscillations in three dimensional food chain systems. Journal of the Society for Industrial and Applied Mathematics 52:1688-1706.
41. Murray, J. D. 1989. Mathematical biology. Springer-Verlag, New York, New York, USA.
42. Nowak, M. A., and R. M. May. 1992. Evolutionary games and spatial chaos. Nature 359:826-829.
43. Pimm, S. L. 1984. Food chains and return times. Pages 397-412 in D. R. Strong, D. Simberloff, L. G. Abele, and A. B. Thistle, editors. Ecological communities: conceptual issues and the evidence. Princeton University Press, Princeton, New Jersey, USA.
44. Rand, D. A., and H. B. Wilson. 1991. Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics. Proceedings of the Royal Society of London 6246:179-184.
45. Rand, D. A., and H. B. Wilson. 1995. Using spatio-temporal chaos and intermediate-scale determinism to quantify spatially extended ecosystems. Proceedings of the Royal Society of London 8259:111-117.
46. Renshaw, E. 1991. Modelling biological populations in space and time. Cambridge University Press, Cambridge, UK.
47. Rohani, P., O. Miramontes, and M. P. Hassell. 1994. Quasiperiodicity and chaos in population models. Proceedings of the Royal Society of London 8258:17-22.
48. Royama, T. 1971. A comparative study of models for predation and parasitism. Researches on Population Ecology Supplement 1:1-91.
49. Schaffer, W. M., S. Ellner, and M. Kot. 1986. Effects of noise on some dynamical models in ecology. Journal of Mathematical Biology 24:479-523.
50. Schaffer, W. M., and M. Kot. 1985. Do strange attractors govern ecological processes? BioScience 35:342-350.
51. Sharov, A. A. 1992. The life-system approach: a system paradigm in population ecology. Oikos 63:485-494.
52. Smith, H. R., and R. Mead. 1980. The dynamics of discrete stochastic models of population growth. Journal of The-oretical Biology 86:607-627.
53. Sugihara, G. 1994. Nonlinear forecasting for the classification of natural time series. Philosophical Transactions of the Royal Society of London A348:477-495.
54. Taylor, A. D. 1992. Deterministic stability analysis can predict the dynamics of some stochastic population models. Journal of Animal Ecology 61:241-248.
55. Tuda, M., and M. Shimada. 1995. Developmental schedules and persistence of experimental host-parasitoid systems at two different temperatures. Oecologia 103:283-291.
56. Turchin, P. 1990. Rarity of density dependence or population regulation with lags? Nature 344:660-663.
57. _. 1995. Population regulation: old arguments and a new synthesis. Pages 19-40 in N. Cappuccino and P. W. Price, editors. Population dynamics: new approaches and synthesis. Academic Press, San Diego, California, USA.
58. Turehin, P., and A. D. Taylor. 1992. Complex dynamics in ecological time series. Ecology 73:289-305.
59. Turelli, M. 1977. Random environmental and stochastic calculus. Theoretical Population Biology 12:140-178.
60. Turing, A. M. 1952. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London B237:37-72.
61. Utida, S. 1957. Cyclic fluctuations of population density intrinsic to the host-parasite system, Ecology 38:442-449.
62. Vandermeer, J. 1993. Loose coupling of predator-prey cycles: entrainment. chaos, and intermittency in the classic MacArthur consumer-resource equations. American Naturalist 141:687-716.
63. Varley, G. C., G. R. Gradwell, and M. R Hassell. 1973. Insect population ecology. Blackwell Scientific. Oxford, UK.