Chaos in natural populations: Edge or wedge?

Ecological Complexity

Volumn 1, Issue 2, 2004, Pages 127-138

  Rai, Vikas ^a  

^a DELHI TECHNOLOGICAL UNIVERSITY   (India)

Author keywords

Edge of chaos; Model systems; Natural populations; Predator prey interaction; Pseudo prey method; Short term recurrent chaos; Simulation experiments; Specialist and generalist predators

Indexed keywords

MURIDAE;

EID: 1642395722     PISSN: 1476945X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecocom.2004.02.002     Document Type: Article

References (35)

1. Abrams, P.A., 1994. The fallacies of ratio-dependent predation. Ecology 75, 1842-1850.
2. Allee, W.C., Emerson, A.E., Park, O., Schmidt, T., 1949. Principles of Animal Ecology. Saunders, London.
3. Bjornstad, O.N., Grenfell, B.T., 2001. Noisy clockwork: time series analysis of population fluctuations in animals. Science 293, 638-643.
4. Costantino, R.F., Desharnais, R.A., Cushing, J.M., Dennis, B., 1997. Chaotic dynamics in an insect population. Science 257, 389-391.
5. Dixon, P.A., Milicich, M.J., Sugihara, G., 1999. Episodic fluctuations in larval supply. Science 283, 1528-1530.
6. Ellner, S., Turchin, P., 1995. Chaos in a noisy world: new methods and evidence from time-series analysis. Am. Nature 145, 343-375.
7. Higgins, K., Hastings, A., Sarvela, J.N., Botsfort, L.W., 1997. Stochastic dynamics and deterministic skeletons: population behavior of Dungeness crab. Science 276, 1431-1435.
8. Ikegami, T., Kaneko, K., 1992. Evolution of host-parasitoid network through homeochaotic dynamics. Chaos 2, 397-407.
9. Jorgensen, S.E., (Ed.) 1979. Handbook of Environmental Data and Ecological Parameters. Pergamon Press, Amsterdam, pp. 142-216.
10. Jorgensen, S.E., 1995. The growth rate of Zooplankton at the edge of chaos: ecological models. J. Theor. Biol. 175, 13-21.
11. Kaitala, V., Ylikarjula, J., Heino, M., 2000. Non-unique population dynamics: basic patterns. Ecol. Modell. 135, 127-134.
12. Kaufmann, S.A., 1993. Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, Oxford.
13. Kaufmann, S.A., Jonsen, S., 1990. Coevolution to the edge of chaos: coupled fitness landscapes, poised states, and coevolutionary avalanches. Santa Fe Institute working paper 90-013. Santa Fe Institute, Santa Fe, NM.
14. Kaneko, K., Ikegami, T., 1992. Homeochaos: dynamic stability of a symbiolic network with population dynamics and evolving mutation rates. Physica D 56, 406-429.
15. Lande, R., 1988. Genetics and demography in biological conservation. Science 241, 1455-1460.
16. Leslie, P.H., 1948. Some further notes on the use of matrices in population mathematics. Biometrica 35, 213-245.
17. Leslie, P.H., Gower, J.C., 1960. The properties of a stochastic model for the predator-prey type of interaction between two species. Biometrica 47, 219-234.
18. May, R.M., 1976. Simple mathematical models with very complicated dynamics. Nature 261, 459-467.
19. May, R.M., 2001. Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, NJ, USA.
20. Medvinsky, A.B., Tikhonova, I.A., Aliev, R.R., Li, B.-L., Lin, Z.-S., Malchow, H., 2001. Patchy Environment as a Factor of Complex Plankton Dynamics, Physical Review E 64, 021915 (7 pages).
21. Mitchell, M., Harber, P.T., Crutchfield, J.P., 1993. Revisiting the edge of chaos: evolving cellular automata to perform computations. Complex Syst. 7, 89-130.
22. Ott, E., 1993. Chaotic Dynamical Systems. Cambridge University Press, Cambridge, UK.
23. Pielou, E.C., 1977. Mathematical Ecology. Wiley, New York.
24. Ricker, W.E., 1954. Stock and recruitment. J. Fish Res. Bd. Can. 11, 559-623.
25. Rinaldi, S., De Feo, O., 1999. Top-predator abundance and chaos in tritrophic food chains. Ecol. Lett. 2, 6-10.
26. Rosenzweig, M.L., MacArthur, R.H., 1963. Graphical representation and stability conditions of predator-prey interactions. Am. Nature 97, 205-223.
27. Smith R.H., Daniels S., Simkiss K. Bell, E.D., Ellner S.P., Forest, M.B., 2000. Blowflies as a case study in non-linear population dynamics. In: Perry, J.N., Smith, R.H., Woiwod, I.P., Morse, D. (Eds.), Chaos in Real Data. Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 137-172.
28. Turchin, P., Ellner, S.P., 2000. Living on the edge of chaos: population dynamics of Fennoscandian voles. Ecology 81, 3099-3116.
29. Turchin, P., Hanski, I., 1997. An empirically based model for latitudinal gradient in vole population dynamics. Am. Nature 149 (5), 842-874.
30. Turchin, P., Oksanen, L., Ekerholm, P., Oksanen, T., Hentonnen, H., 2000. Are lemmings prey or predator? Nature 405, 562-565.
31. Upadhyay, R.K., Rai, V., 1997. Why chaos is rarely observed in natural populations? Chaos, Solitons Fractals 8, 1933-1939.
32. Upadhyay, R.K., Iyengar, S.R.K., Rai, V., 1998. Chaos: an ecological reality? Int. J. Bifur. Chaos 8, 1325-1333.
33. Upadhyay, R.K., Rai, V., Iyengar, S.R.K., 2001. Species extinction problem: genetic vs. ecological factors. Appl. Math. Model. 25, 937-951.
34. Yodziz, P., 1994. Predator-prey theory and management of multispecies fisheries. Ecol. Appl. 4 (1), 51-58.
35. Yodzis, P., 1989. Introduction to Theoretical Ecology. Harper and Row, New York.