Predicting dynamics of spatial automata models using Hamiltonian equations

Ecological Modelling

Volumn 96, Issue 1-3, 1997, Pages 293-303

  Michael Childress, W ^a,b  

^a Department of Environmental and Radiological Health Sciences   (United States)

^b UNIVERSITY OF TEXAS AT EL PASO   (United States)

Author keywords

Cellular automata; Grid based models; Hamiltonian; Spatial dynamics

Indexed keywords

CELLULAR AUTOMATA; HAMILTONIAN EQUATIONS; MODELLING; SPATIAL DYNAMICS;

EID: 0030619533     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3800(96)00071-3     Document Type: Article

References (30)

1. Barkham, J.P. and Hance, C.E., 1982. Population dynamics of the wild daffodil (Narcissus pseudonarcissus). III. Implications of a computer model of 1000 years of population change. J. Ecol., 70: 323-344.
2. Caswell, H. and Eiter, R.E., 1993. Ecological interactions in patchy environments: From patch occupancy models to cellular automata. In: S.A. Levin, T.M. Powell and J.H. Steele (Editors), Patch Dynamics. Springer-Verlag, Berlin, pp. 93109.
3. Chiang. C.L., 1968. An Introduction to Stochastic Processes and Their Applications. Robert E. Krieger Publishing. Huntington, New York.
4. Childress, W.M., 1993. Primary succession on the Pumice Plain at Mount St. Helens, Washington: Resolving the significance of individual-level interactions to community-level dynamics using grid-based analysis and simulation. Ph.D. dissertation. Texas A&M University, College Station, USA.
5. Childress. W.M.. 1996. A hierarchically-explicit model of landscape dynamics. Landscape Ecol., submitted.
6. Colasanti, R.L. and Grime. J.P., 1993. Resource dynamics and vegetation processes: a deterministic model using two-dimensional cellular automata. Funct. Ecol., 7: 169-176.
7. Crawley, M.J. and May, R.M., 1987. Population dynamics and plant community structure: Competition between annuals and perennials. J. Theor. Biol., 125: 475-489.
8. Cullinan, V.l. and Thomas, J.M., 1992. A comparison of quantitative methods for examining landscape pattern and scale. Landscape Ecol., 7: 211-227.
9. DeAngelis, D.L. and Gross, L.J. (Editors), 1992. Individual-Based Models and Approaches in Ecology. Chapman & Hall, New York.
10. Doak, D.F. and Mills, L.S., 1994. A useful role for theory in conservation. Ecology, 75: 615-626.
11. Gao, W. and Li, B.-L., 1993. Wavelet analysis of coherent structures at the atmosphere-forest interface. J. Appl. Meteorol., 32: 1717-1725.
12. Gardner, R.H., Milne, B.T., Turner, M.G. and O'Neill, R.V. 1987. Neutral models for the analysis of broad-scale landscape pattern. Landscape Ecol., 1: 19-28.
13. Grassberger, P.. 1984. Chaos and diffusion in deterministic cellular automata. Physica D, 10: 52-58.
14. Hanski, I., 1991. Single-species metapopulation dynamics: Concepts, models and observations. Biol. J. Linn. Soc., 42: 17-38.
15. Hanski, I. and Gilpin, M., 1991. Metapopulation dynamics: Brief history and conceptual domain. Biol. J. Linn. Soc., 42: 3-16.
16. Hastings, A., Horn, C.L., Ellner, S., Turchin, P. and Godfrey, H.C.J. 1993. Chaos in ecology: Is Mother Nature a strange attractor? Ann. Rev. Ecol. Syst., 24: 1-33.
17. Hogeweg, P., 1988. Cellular automata as a paradigm for ecological modelling. Appl. Math. Comput., 27: 81-100.
18. Inghe, O., 1989. Genet and ramet survivorship under different mortality regimes - A cellular automata model. J. Theor. Biol., 138: 257-270.
19. Karieva, P., 1994. Space: The final frontier for ecological theory. Ecology, 75: 1.
20. Legcndre, P. and Fortin, M.-J., 1989. Spatial pattern and ecological analysis. Vegetatio, 47: 107-138.
21. Li, H. and Reynolds, J.E., 1994. A simulation experiment to quantify spatial heterogeneity in categorical maps. Ecology, 75: 2446-2455.
22. Molofsky, J., 1994. Population dynamics and pattern formation in theoretical populations. Ecology, 75: 30-39.
23. Nisbet, R.M. and Gurney, W.S.C., 1982. Modelling Fluctuating Populations. John Wiley & Sons, Chichester.
24. Ord, J.K., 1979. Time-series and spatial patterns in ecology. In: R.M. Cormack and J.K. Ord (Editors), Spatial and Temporal Analysis in Ecology. International Co-operative Publishing House, Fairland, MD, pp. 1-94.
25. Palmer, D., 1989. Broken ergodicity. In: D. Stein (Editor), Complex Systems. Addison-Wesley Longman, Redwood City, CA, pp. 275-300.
26. Rossi, R.E., Mulla, D.J., Journel, A.C. and Franz, E.H. 1992. Geostatistical tools for modeling and interpreting ecological spatial distance. Ecol. Monogr., 62: 277-314.
27. Silvertown, J., Holtier, S., Johnson, J. and Dale, P. 1992. Cellular automaton models of interspecific competition for space - The effect of pattern on process. J. Ecol., 80: 527-534.
28. Stein, D., 1989. Disordered systems: Mostly spin glasses. In: D. Stein (Editor), Complex Systems. Addison-Wesley Longman, Redwood City, CA, pp. 301-352.
29. Turner, M.G., 1990. Spatial and temporal analysis of landscape patterns. Landscape Ecol., 4: 21-30.
30. Wissel, C., 1991. A model for the mosaic-cycle concept. In: H. Remmert (Editor), The Mosaic-Cycle Concept of Ecosystems. Springer-Verlag, Berlin, pp. 22-45.