The amplification of environmental noise in population models: Causes and consequences

American Naturalist

Volumn 161, Issue 2, 2003, Pages 225-239

  Greenman, J V ^a   Benton, T G ^a  

^a UNIVERSITY OF STIRLING   (United Kingdom)

Author keywords

Color; LPA and Turchin models; Noise amplification; Periodicity; Stochastic chaos; Threshold

Indexed keywords

AMPLIFICATION; DENSITY DEPENDENCE; NOISE; POPULATION DYNAMICS; POPULATION MODELING;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; ENVIRONMENT; EVOLUTION; POPULATION DYNAMICS; STATISTICS;

ANIMALS; ENVIRONMENT; EVOLUTION; MODELS, BIOLOGICAL; POPULATION DYNAMICS; STOCHASTIC PROCESSES;

ANIMALIA;

EID: 0037323968     PISSN: 00030147     EISSN: None     Source Type: Journal    
DOI: 10.1086/345784     Document Type: Article

References (50)

1. Aparicio, J. P., and H. G. Solari. 2001. Sustained oscillations in stochastic systems. Mathematical Biosciences 169:15-25.
2. Benton, T. G., C. T. Lapsley, and A. P. Beckerman. 2001. Population synchrony and environmental variation: an experimental demonstration. Ecology Letters 4:236-243.
3. Bjornstad, O. N. 2000. Cycles and synchrony: two historical "experiments" and one experience. Journal of Animal Ecology 69:869-873.
4. Bjornstad, O. N., and B. T. Grenfell. 2001. Noisy clock-work: time series analysis of population fluctuations in animals. Science (Washington, D.C.) 293:638-643.
5. Blasius, B., A. Huppert, and L. Stone. 1999. Complex dynamics and phase synchronization in spatially extended ecological systems. Nature 399:354-359.
6. Bourgine, P., and D. Snyers. 1996. Lotka Volterra coevolution at the edge of chaos. Artificial Evolution 1063: 131-144.
7. Burnside, W. S., and A. W. Panton. 1901. The theory of equations. Vol. 2. Longman, London.
8. Costantino, R. F., R. A. Desharnais, J. M. Cushing, and B. Dennis. 1997. Chaotic dynamics in an insect population. Science (Washington, D.C.) 275:389-391.
9. Coulson, T., E. A. Catchpole, S. D. Albon, B. J. T. Morgan, J. M. Pemberton, T. H. Clutton-Brock, M. J. Crawley, and B. T. Grenfell. 2001. Age, sex, density, winter weather and population crashes in Soay sheep. Science (Washington, D.C.) 292:1528-1531.
10. Cuddington, K. M., and P. Yodzis. 1999. Black noise and population persistence. Proceedings of the Royal Society of London B, Biological Sciences 266:969-973.
11. Cushing, J. M., B. Dennis, R. A. Desharnais, and R. F. Costantino. 1998. Moving toward an unstable equilibrium: saddle nodes in population systems. Journal of Animal Ecology 67:298-306.
12. Cushing, J. M., S. M. Henson, R. A. Desharnais, B. Dennis, R. F. Costantino, and A. King. 2001. A chaotic attractor in ecology: theory and experimental data. Chaos Solitons and Fractals 12:219-234.
13. Dennis, B., R. A. Desharnais, J. M. Cushing, and R. F. Costantino. 1995. Nonlinear demographic dynamics: mathematical models, statistical methods and biological experiments. Ecological Monographs 65:261-281.
14. de Oliveira, P. M. 2001. Why do evolutionary systems stick to the edge of chaos. Theory in Biosciences 120:1-19.
15. Doebeli, M., and G. D. Ruxton. 1997. Controlling spatial chaos in metapopulations with long-range dispersal. Bulletin of Mathematical Biology 59:497-515.
16. Ellner, S. 1985. The accuracy of Bartlett's small-fluctuation approximation for stochastic-difference-equation population models. Mathematical Biosciences 74:233-246.
17. Ellner, S., and P. Turchin. 1995. Chaos in a noisy world: new methods and evidence from time-series analysis. American Naturalist 145:343-375.
18. Ellner, S. P. 2000. Defining chaos for real, noisy data: local Lyapunov exponents and sensitive response to perturbations. Pages 1-32 in J. N. Perry, R. H. Smith, I. P. Woiwod, and D. R. Morse, eds. Chaos in real data: the analysis of non-linear dynamics from short ecological time series. Kluwer Academic, Dordrecht.
19. Ellner, S. P., B. A. Bailey, G. V. Bobashev, A. R. Gallant, B. T. Grenfell, and D. W. Nychka. 1998. Noise and non-linearity in measles epidemics: combining mechanistic and statistical approaches to population modeling. American Naturalist 151:425-440.
20. Finkenstadt, B. F., and B. T. Grenfell. 2000. Time series modelling of childhood diseases: a dynamical systems approach. Journal of the Royal Statistical Society Series C, Applied Statistics 49:187-205.
21. Gragnani, A., O. De Feo, and S. Rinaldi. 1998. Food chains in the chemostat: relationships between mean yield and complex dynamics. Bulletin of Mathematical Biology 60: 703-719.
22. Grenfell, B. T., K. Wilson, B. F. Finkenstadt, T. N. Coulson, S. Murray, S. D. Albon, J. M. Pemberton, T. H. Clutton-Brock, and M. J. Crawley. 1998. Noise and determinism in synchronized sheep dynamics. Nature 394:674-677.
23. Gurney, W. S. C., R. M. Nisbet, and J. H. Lawton. 1983. The systematic formulation of tractable single species population models incorporating age structure. Journal of Animal Ecology 52:479-495.
24. Heino, M., V. Kaitala, E. Ranta, and J. Lindstrom. 1997. Synchronous dynamics and rates of extinction in spatially structured populations. Proceedings of the Royal Society of London B, Biological Sciences 264:481-486.
25. Hellriegel, B. 2000. Single- or multistage regulation in complex life cycles: does it make a difference? Oikos 88: 239-249.
26. Higgins, K., A. Hastings, and L. W. Botsford. 1997a. Density dependence and age structure: nonlinear dynamics and population behavior. American Naturalist 149: 247-269.
27. Higgins, K., A. Hastings, J. N. Sarvela, and L. W. Botsford. 1997b. Stochastic dynamics and deterministic skeletons: population behavior of Dungeness crab. Science (Washington, D.C.) 276:1431-1435.
28. Jorgensen, S. E. 1995. The growth-rate of zooplankton at the edge of chaos: ecological models. Journal of Theoretical Biology 175:13-21.
29. Kaitala, V., and E. Ranta. 2001. Is the impact of environmental noise visible in the dynamics of age-structured populations? Proceedings of the Royal Society of London B, Biological Sciences 268:1769-1774.
30. Kaitala, V., E. Ranta, and J. Lindstrom. 1996. Cyclic population dynamics and random perturbations. Ecology 65:249-251.
31. Kaitala, V., J. Ylikarjula, E. Ranta, and P. Lundberg. 1997. Population dynamics and the colour of environmental noise. Proceedings of the Royal Society of London B, Biological Sciences 264:943-948.
32. Kendall, B. E., J. Prendergast, and O. N. Bjornstad. 1998. The macroecology of population dynamics: taxonomic and biogeographic patterns in population cycles. Ecology Letters 1:160-164.
33. Lauwerier, H. A., and J. A. J. Metz. 1986. Hopf bifurcation in host-parasitoid models. IMA Journal of Mathematics Applied in Medicine and Biology 3:191-210.
34. Leslie, P. H. 1945. On the use of matrices in certain population mathematics. Biometrika 33:213-245.
35. _. 1959. The properties of a certain lag type of population growth and the influence of an external random factor on a number of such populations. Physiological Zoology 32:151-159.
36. Nisbet, R. M., and W. S. C. Gurney. 1976. A simple mechanism for population cycles. Nature 263:319-320.
37. _. 1982. Modelling fluctuating populations. Wiley, New York.
38. Nisbet, R. M., and L. C. Onyiah. 1994. Population dynamic consequences of competition within and between age classes. Journal of Mathematical Biology 32:329-344.
39. Nychka, D., P. D. Haaland, M. O'Connell, and S. Ellner. 1998. FUNFITS: data analysis and statistical tools for estimating functions. Pages 159-179 in D. Nychka, W. W. Piegorsch, and L. H. Cox, eds. Lecture notes in statistics. Vol. 132. Springer, New York.
40. Palmqvist, E., and P. Lundberg. 1998. Population extinctions in correlated environments. Oikos 83:359-367.
41. Pascual, M., P. Mazzega, and S. A. Levin. 2001. Oscillatory dynamics and spatial scale: the role of noise and unresolved pattern. Ecology 82:2357-2369.
42. Rand, D. A., and H. B. Wilson. 1991. Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics. Proceedings of the Royal Society of London B, Biological Sciences 246:179-184.
43. Ranta, E., P. Lundberg, V. Kaitala, and J. Laakso. 2000. Visibility of the environmental noise modulating population dynamics. Proceedings of the Royal Society of London B, Biological Sciences 267:1851-1856.
44. Rinaldi, S., and O. De Feo. 1999. Top-predator abundance and chaos in tritrophic food chains. Ecology Letters 2: 6-10.
45. Ripa, J. 2000. Analysing the Moran effect and dispersal: their significance and interaction in synchronous population dynamics. Oikos 89:175-187.
46. Ripa, J., and M. Heino. 1999. Linear analysis solves two puzzles in population dynamics: the route to extinction and extinction in coloured environments. Ecology Letters 2:219-222.
47. Smith, R. H., S. Daniels, K. Simkiss, E. D. Bell, S. P. Ellner, and M. B. Forrest. 2000. Blowflies as a case study in non-linear population dynamics. Pages 137-172 in J. N. Perry, R. H. Smith, I. P. Woiwod, and D. R. Morse, eds. Chaos in real data: the analysis of non-linear dynamics from short ecological time series. Kluwer Academic, Dordrecht.
48. Suarez, I. 1999. Mastering chaos in ecology. Ecological Modelling 117:305-314.
49. Turchin, P. 1990. Rarity of density dependence or population regulation with lags? Nature 344:660-663.
50. Turchin, P., and S. P. Ellner. 2000. Living on the edge of chaos: population dynamics of Fennoscandian voles. Ecology 81:3099-3116.