When can noise induce chaos and why does it matter: A critique

Oikos

Volumn 111, Issue 3, 2005, Pages 620-631

  Ellner, S P ^a   Turchin, P ^b  

^a Department of Obstetrics Gynecology   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC DYNAMICS; ECOLOGICAL APPROACH; ECOLOGICAL THEORY; NOISE;

RODENTIA;

EID: 29144481903     PISSN: 00301299     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1600-0706.2005.14129.x     Document Type: Review

References (53)

1. Bailey, B. A., Ellner, S. and Nychka, D. W. 1997. Chaos with confidence: asymptotics and applications of local Lyapunov exponents. - In: Cutler, C. D. and Kaplan, D. T. (eds), Nonlinear dynamics and time series: building a bridge between the natural and statistical sciences. Fields Inst Comm., vol 110. Am. Math. Soc., Providence RI, pp. 115-133.
2. Billings, L. and Schwartz, I. B. 2002. Exciting chaos with noise: unexpected dynamics in epidemic outbreaks. - J. Math. Biol. 44: 31-48.
3. Bjørnstad, O. N., Sait, S. M., Stenseth, N. C. et al. 2001. The impact of specialised enemies on the dimensionality of host dynamics. - Nature 401: 1001-1006.
4. Bjørnstad, O. N., Nisbet, R. M. and Fromentin, J.-M. 2004. Trends and cohort resonant effects in age-structured populations. - J. Anim. Ecol. 73: 1157-1167.
5. Bolker, B. M. and Pacala, S. W. 1999. Spatial moment equations for plant competition: understanding spatial strategies and the advantages of short dispersal. - Am. Nat. 153: 575-602.
6. Costantino, R. F., Desharnais, R. A., Cushing, J. M. et al. 1997. Chaotic dynamics in an insect population. Science 275: 389-391.
7. Coulson, T., Milner-Gulland, E. J. and Clutton-Brock, T. 2000. The relative roles of density and climatic variation on population dynamics and fecundity rates in three contrasting ungulate species. - Proc. R. Soc. B. 267: 1171-1179.
8. Coulson, T., Catchpole, E. A., Albon, S. D. et al. 2001. Age, sex, density, winter weather and population crashes in Soay sheep. - Science 292: 1528-1531.
9. Coulson, T., Rohani, P. and Pascual, M. 2004. Skeletons, noise and population growth: the end of an old debate? - Trends Ecol. Evol. 19: 359-364.
10. Dennis, B., Desharnais, R. A., Cushing, J. M. et al. 2001. Estimating chaos and complex dynamics in an insect population. - Ecol. Monogr. 71: 277-303.
11. Dennis, B., Desharnais, R. A., Cushing, J. M. et al. 2003. Can noise induce chaos? - Oikos 102: 329-340.
12. Desharnais, R. A., Costantino, R. F., Cushing, J. M. et al. 1997. Estimating chaos in an insect population. - Science 276: 1881-1882.
13. Dieckmann, U., Law, R. and Metz, J. A. J. (eds) 2000. The geometry of ecological interactions: simplifying spatial complexity. - Cambridge Univ. Press.
14. Durrett, R. T. and Levin, S. A. 1994. The importance of being discrete (and spatial). - Theor. Popul. Biol. 46: 363-394.
15. Ellner, S. and Turchin, P. 1995. Chaos in a noisy world: new methods and evidence from time series analysis. - Am. Nat. 145: 343-375.
16. Ellner, S. P., Bailey, B. A., Bobashev, G. V. et al. 1998. Noise and nonlinearity in measles epidemics: combining mechanistic and statistical approaches to population modeling. - Am. Nat. 151: 425-440.
17. Faisst, H. and Eckhardt, B. 2003. Lifetimes of noisy repellors. - Phys. Rev. E 68: 026215.
18. Ginzburg, L. and Colyvan, M. 2004. Ecological orbits: how planets move and populations grow. - Oxford Univ. Press.
19. Hanski, I. and Henttonen, H. 1996. Predation on competing rodent species: a simple explanation of complex patterns. - J. Anim. Ecol. 65: 220-232.
20. Hanski, I., Hansson, L. and Henttonen, H. 1991. Specialist predators, generalist predators, and the microtine rodent cycle. - J. Anim. Ecol. 60: 353-367.
21. Hanski, I., Turchin, P., Korpimäki, H. et al. 1993. Population oscillations of boreal rodents: regulation by mustelid predators leads to chaos. - Nature 364: 232-235.
22. Hanski, I., Henttonen, H., Korpimäki, E. et al. 2001. Small rodent dynamics and predation. - Ecology 82: 1505-1520.
23. Hassell, M. P., Lawton, J. H. and May, R. M. 1976. Patterns of dynamical behaviour in single-species populations. - J. Anim. Ecol. 45: 471-486.
24. Hurlburt, S. H. 1990. Spatial distribution of the montane unicorn. - Oikos 58: 257-271.
25. Kendall, B. E. 2001. Chaos, cycles and noise in predator-prey dynamics. - Chaos Solitons Fractals 12: 321-332.
26. Kendall, B. E., Prendergast, J. and Bjornstad, O. N. 1998. The macroecology of population cycles: taxonomic and biogeographic patterns in population cycles. - Ecol. Lett. 1: 160-164.
27. Kendall, B. E., Briggs, C. J., Murdoch, W. W. et al. 1999. Why do populations cycle? a synthesis of statistical and mechanistic modeling approaches. - Ecology 80: 1789-1805.
28. Kraut, S. and Feudel, U. 2002. Multistability, noise, and attractor hopping: the crucial role of chaotic saddles. - Phys. Rev. E 66, 015207.
29. Kraut, S. and Feudel, U. 2003. Noise-induced escape through a chaotic saddle: lowering of the activation energy. - Physica D 181: 222-234.
30. Lai, Y.-C., Liu, Z., Billings, L. et al. 2003. Noise-induced unstable dimension variability and transition to chaos in random dynamical systems. - Phys. Rev. E 67: 026210.
31. Lima, M., Stenseth, N. C. and Jaksic, F. 2002. Food web structure and climate effects in the dynamics of small mammals and owls in semiarid Chile. - Ecol. Lett. 5: 273-284.
32. May, R. M. 1974. Biological populations with nonoverlapping generations - stable points, stable cycles and chaos. - Science 186: 645-647.
33. May, R. M. 1976. Simple mathematical models with very complicated dynamics. - Nature 261: 459-467.
34. Owen-Smith, R. N. 2002. Adaptive herbivore ecology: from resources to populations in variable environments. - Cambridge Univ. Press.
35. Post, E. and Stenseth, N. C. 1998. Large-scale climatic fluctuation and population dynamics of moose and white-tailed deer. - J. Anim. Ecol. 67: 537-543.
36. Post, E. and Stenseth, N. C. 1999. Climatic variability, plant phenology, and northern ungulates. - Ecology 80: 1322-1339.
37. Post, E., Peterson, R. O., Stenseth, N. C. et al. 1999. Ecosystem consequences of wolf behavioural response to climate. - Nature 401: 905-907.
38. Ruelle, D. 1989. Chaotic evolution and strange attractors. - Cambridge Univ. Press.
39. Rand, D. A. and Wilson, H. B. 1991. Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics. - Proc. R. Soc. B 246: 179-184.
40. Snyder, R. E. and Chesson, P. 2004. How the spatial scales of dispersal, competition, and environmental heterogeneity interact to affect coexistence. - Am. Nat. 164: 633-650.
41. Tél, T. 1990. Transient chaos. - In: Bailin, H. (ed.), Directions in chaos, Vol. 3: Experimental study and characterization of chaos. World Scientific, Singapore, pp. 149-211.
42. Tél, T. 1991. Controlling transient chaos. - J. Physics A: Math. Gen. 24: L1359-L1368.
43. Tong, H. 1997. Some comments on nonlinear time series analysis. - In: Cutler, C. D. and Kaplan, D. T. (eds), Nonlinear dynamics and time series (Fields Inst. Comm., Vol. 11). Am. Math. Soc., pp. 17-27.
44. Turchin, P. 1993. Chaos and stability in rodent population dynamics: evidence from nonlinear time-series analysis. - Oikos 68: 167-172.
45. Turchin, P. 1996. Nonlinear time-series modeling of vole population fluctuations. - Res. Popul. Ecol. 38: 121-132.
46. Turchin, P. 2003. Complex population dynamics: a theoretical/empirical synthesis. - Princeton Univ. Press.
47. Turchin, P. and Ellner, S. P. 2000a. Time-series modeling of population fluctuations. - In: Perry, J. N., Smith, R. H., Woiwod, I. P. et al. (eds), Chaos in real data: analysis of non-linear dynamics from short ecological time series. Kluwer, pp. 33-48.
48. Turchin, P. and Ellner, S. P. 2000b. Living on the edge of chaos: population dynamics of Fennoscandian voles. - Ecology 81: 3099-3116.
49. Turchin, P. and Hanski, I. 1997. An empirically-based model for the latitudinal gradient in vole population dynamics. - Am. Nat. 149: 842-874.
50. Turchin, P., Wood, S. N., Ellner, S. P. et al. 2003. Dynamical effects of plant quality and parasitism on population cycles of larch budmoth. - Ecology 84: 1207-1214.
51. Wood, S. 2004. mgcv: GAMs with GCV smoothness estimation and GAMMs by REML/PQL. R package version 1.2-3. URL www.R-project.org.
52. Yoshida, T., Jones, L. E., Ellner, S. P. et al. 2003. Rapid evolution drives ecological dynamics in a predator-prey system. - Nature 424: 303-306.
53. Zimmer, C. 1999. Life after chaos. - Science 284: 83-86.