From individuals to population densities: Searching for the intermediate scale of nontrivial determinism

Ecology

Volumn 80, Issue 7, 1999, Pages 2225-2236

  Pascual, Mercedes ^a   Levin, Simon A ^b  

^a UNIVERSITY OF MARYLAND BIOTECHNOLOGY INSTITUTE   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Averaging scale; Chaos; Characteristic; Demographic noise; Determinism test; Individual based model; Model simplification; Nonlinearity; Predator prey model; Prediction algorithm; Spatial scale; Spatiotemporal model

Indexed keywords

ECOLOGICAL MODELING; POPULATION DENSITY; SPATIAL ANALYSIS; STOCHASTIC PROCESS;

EID: 0032863115     PISSN: 00129658     EISSN: None     Source Type: Journal    
DOI: 10.1890/0012-9658(1999)080[2225:FITPDS]2.0.CO;2     Document Type: Article

References (48)

1. Armstrong, R. A. 1994. Grazing limitation and nutrient limitation in marine ecosystems: steady-state solutions of an ecosystem model with multiple food chains. Limnology and Oceanography 39:597-608.
2. Bingham, S., and M. Kot. 1989. Multidimensional trees, range searching, and a correlation dimension algorithm of reduced complexity. Physics Letters A 140:327-330.
3. Bolker, B. M., and S. W. Pacala. 1997. Using moment equations to understand stochastically driven spatial pattern formation in ecological systems. Theoretical Population Biology 52:179-197.
4. Casdagli, M. 1989. Nonlinear prediction of chaotic time series. Physica D 35:335-356.
5. Caswell, H., and M. A. John. 1992. From the individual to the population in demographic models. Pages 36-61 in D. L. DcAngelis and L. J. Gross, editors. Individual-based models and approaches in ecology. Populations, Communities, and Ecosystems. Chapman and Hall, New York, New York, USA.
6. DeAngelis, D. L., and K. A. Rose. 1992. Which individual-based approach is most appropriate for a given problem. Pages 88-111 in D. L. DeAngelis and L. J. Gross, editors. Individual-based models and approaches in ecology. Populations, Communities, and Ecosystems. Chapman and Hall, New York, New York, USA.
7. De Roos, A. M., E. McCauley, and W. W. Wilson. 1991. Mobility vs. density-limited predator-prey dynamics on different spatial scales. Proceedings of the Royal Society of London Series B 246:117-122.
8. Dewdney, A. K. 1984. Computer Recreations column. Scientific American December: 14-22.
9. Durrett, R., and S. A. Levin. 1994. Stochastic spatial models: a user's guide to ecological applications. Philosophical Transactions of the Royal Society of London Series B. 343: 329-350.
10. Ellner, S. P., B. A. Bailey, G. V. Bobashev, A. R. Gallant, B. T. Grenfell, and D. W. Nychka. 1998. Noise and nonlinearity in measles epidemics: combining mechanistic and statistical approaches to population modeling. The American Naturalist 151:425-440.
11. Ellner, S. P., and P. Turchin. 1995. Chaos in a noisy world: new methods and evidence from time series analysis. The American Naturalist 145:343-375.
12. Farmer, J. D. 1982. Chaotic attractors of an infinite-dimensional dynamical system. Physica D 4:366-393.
13. Farmer, J. D., and J. J. Sidorowich. 1987. Predicting chaotic time series. Physics Review Letters 59:845-848.
14. Flierl, G., D. Grunbaum, S. A. Levin, and D. Olson. 1999. From individuals to aggregations: the interplay between behavior and physics. Journal of Theoretical Biology 196: 397-454.
15. Grassberger, P., and I. Procaccia. 1983. Measuring the strangeness of strange attractors. Physica D 9:189-208.
16. Hay, M. E. 1994. Species as noise in community ecology: do seaweeds block our view of the kelp forest. Trends in Ecology and Evolution 9:414-416.
17. Huston, M., D. L. DeAngelis, and W. Post. 1988. New computer models unify ecological theory. Biosciences 38:682-691.
18. Judson, O. P. 1994. The rise of the individual-based model in ecology. Trends in Ecology and Evolution 9:9-14.
19. Kaplan, D., and L. Glass. 1995. Understanding nonlinear dynamics. Springer-Verlag, New York, New York, USA.
20. Keeling, M. J., I. Mezic, R. J. Hendry, J. McGlade, and D. A. Rand. 1997. Characteristic length scales of spatial models in ecology via fluctuation analysis. Philosophical Transactions of the Royal Society of London Series B 352:1589-1601.
21. King, A. W. 1992. Translating models across scales in the landscape. Pages 479-514 in C. G. Jones and J. H. Lawton, editors. Linking species and ecosystems. Chapman and Hall, New York, New York, USA.
22. Kot, M., W. M. Schaffer, G. L. Truly, D. J. Grase, and L. F. Olsen. 1988. Changing criteria for imposing order. Ecological Modelling 43:75-110.
23. Levin, S. A. 1988. Pattern, scale, and variability: an ecological perspective. Pages 1-12 in A. Hastings, editor. Community ecology. Lecture notes in biomathematics 77. Springer-Verlag, Heidelberg, Germany.
24. _. 1992. The problem of pattern and scale in ecology. Ecology 73:1943-1967.
25. Levin, S. A., and L. Buttel. 1987. Measures of patchiness in ecological systems. Ecosystems Research Center Report Number ERC-130. Cornell University Press, Ithaca, New York, USA.
26. Levin, S. A., and R. Durrett. 1996. From individuals to epidemics. Philosophical Transactions of the Royal Society of London Series B 351:1615-1621.
27. Levin, S. A., and S. W. Pacala. 1997. Theories of simplification and scaling of spatially distributed processes. Pages 271-296 in D. Tilman and P. Kareiva, editors. Spatial ecology: the role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton, New Jersey, USA.
28. Little, S. A., S. Ellner, M. Pascual, M. Neubert, D. T. Kaplan, T. Sauer, A. Solow, and H. Caswell. 1996. Detecting non-linear dynamics in spatiotemporal systems: examples from ecological models. Physica D 96:321-333.
29. Ma, S. 1976. Modern theory of critical phenomena. Addison-Wesley, New York, New York, USA.
30. McCauley, E., W. G. Wilson, and A. M. de Roos. 1993. Dynamics of age-structured and spatially structured predator-prey interactions: individual-based models and population-level formulations. The American Naturalist 142: 412-442.
31. Nisbet, R. M., and W. S. C. Gurney. 1982. Modelling fluctuating populations. John Wiley and Sons, Chichester, UK.
32. Pacala, S. W., and D. Deutchsman. 1996. Details that matter: the spatial distribution of individual trees maintains forest ecosystem function. Oikos 74:357-365.
33. Pacala, S. W., and S. A. Levin. 1997. Biologically generated spatial pattern and the coexistence of competing species. Pages 204-232 in D. Tilman and P. Kareiva, editors. Spatial ecology: the role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton, New Jersey, USA.
34. Pascual, M. 1993. Diffusion-induced chaos in a spatial predator-prey system. Proceedings of the Royal Society of London Series B 251:1-7.
35. Powell, T. 1989. Physical and biological scales of variability in lakes, estuaries, and the coastal ocean. Pages 157-176 in J. Roughgarden, R. M. May, and S. A. Levin, editors. Perspectives in ecological theory. Princeton University Press, Princeton, New Jersey, USA.
36. Rand, D. A., and H. B. Wilson. 1995. Using spatiotemporal chaos and intermediate-scale determinism to quantify spatially extended ecosystems. Proceedings of the Royal Society of London Series B 259:111-117.
37. Rastetter, E. B., A. W. King, B. J. Cosby, G. M. Hornberger, R. V. O'Neill, and J. E. Hobbie. 1992. Aggregating fine-scale ecological knowledge to model coarser scale attributes of ecosystems. Ecological Applications 2:55-70.
38. Sauer, T. 1993. Time series prediction by using delay coordinate embedding. Pages 175-193 in A. S. Weigend and N. A. Gershenfeld, editors. Time series prediction: forecasting the future and understanding the past. SFI Studies in the Sciences of Complexity, Proceedings Vol. XV. Addison Wesley, Reading, Massachusetts, USA.
39. Sherratt, J. A., B. T. Eagan, and M. A. Lewis. 1997. Oscillations and chaos behind predator-prey invasion: mathematical artifact or ecological reality? Philosophical Transactions of the Royal Society of London Series B 352:21-38.
40. Steneck, R. S., and M. N. Dethier. 1994. A functional group approach to the structure of algal-dominated communities. Oikos 69:476-498.
41. Sugihara, G. 1994. Nonlinear forecasting for the classification of natural time series. Philosophical Transactions of the Royal Society of London Series A 348:477-495.
42. Sugihara, G., B. Grenfell, and R. M. May. 1990. Distinguishing error from chaos in ecological time series. Philosophical Transactions of the Royal Society of London Series B 330:235-251.
43. Sugihara, G., and R. M. May. 1990. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344:734-741.
44. Takens, F. 1981. Detecting strange attractors in turbulence. Pages 366-381 in D. Rand and L. S. Young, editors. Dynamical systems and turbulence, Warwick 1980. Lecture Notes in Mathematics 898. Springer-Verlag, New York, New York, USA.
45. Turner, M. G., and R. V. O'Neill. 1992. Exploring aggregation in space and time. Pages 194-208 in C. G. Jones and J. H. Lawton, editors. Linking species and ecosystems. Chapman and Hall. New York, New York, USA.
46. Wilson, W. G. 1996. Lotka's game in predator-prey theory: linking populations to individuals. Theoretical Population Biology 50:368-393.
47. Wolf, A., J. B. Swift, H. L. Swinney, and J. A. Vastano. 1985. Determining Lyapunov exponents from a time series. Physica D 16:285-317.
48. Yao, Q., and H. Tong. 1994. On prediction and chaos in stochastic systems. Philosophical Transactions of the Royal Society of London Series A 348:357-369.