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GEO-MATHEMATICAL MODELLING OF SPATIAL-ECOLOGICAL COMPLEX SYSTEMS: AN EVALUATION

https://doi.org/10.24057/2071-9388-2010-3-1-67-80

Abstract

Assessing the complexity of landscapes is one of the top research priorities for Physical Geography and Ecology.
This paper aims at a methodological evaluation of the discrete and analytical mathematical models hitherto available for quantitative assessments of spatial ecological complex systems.
These models are derived from cellular automata and nonlinear dynamics. They describe complex features and processes in landscapes, such as spatial ecological nonlinear interactions, unpredictability and chaos, self-organization and pattern formation.
Beginning with a distinction between two basic types of spatial ecological complexity (structural, functional), and after reviewing the quantitative methods so far available to assess it, the areas where the major challenges (and hence, difficulties) for future research arise are identified. These are: a) to develop measures of structural spatial-ecological complexity, b) to find Lyapunov functions for dynamical systems describing spatial interactions on the landscape (and related attractors), and c) to combine discrete time and continuous spatial data and models.

About the Author

Fivos Papadimitriou

Greece
Department of European Culture, Geography Unit, Hellenic Open University, 13a Aedonon street, Athens 11475


References

1. Barredo J.I., Kasanko, M., McCormick, N, Lavalle, C. (2003). Modelling dynamic spatial

2. processes: simulation of urban future scenarios through cellular automata. Landscape and

3. Urban Planning, 64(3), 145–160.

4. Baynes, T.M. (2009). Complexity in Urban Development and Management: Historical

5. Overview and Opportunities. Journal of Industrial Ecology, 13(2), 214–227.

6. Casado J.M. (2001). Coherence resonance in a washboard potential. Physics Letters A, 291(2,

7. , 82–86.

8. D’Ambrosio, D., Di Gregorio, S., Gabriele S., Gaudio R. (2001). A Cellular Automata model

9. for soil erosion by water. Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and

10. Atmosphere, 26(1), 33–39.

11. Duarte, J. (1997). Bushfire automata and their phase transitions. Int. J. Mod. Phys. C 8:171–

12.

13. Fonstad, M. (2006). Cellular automata as analysis and synthesis engines at the

14. geomorphology-ecology interface.Geomorphology, 7(7), 217–234.

15. Forman, R.T.T. & Godron, M. (1986). Landscape Ecology. New York: J.Wiley and sons.

16. Gabriel, D., Thies,C. & Tscharntke, T. (2005). Local diversity of arable weeds increases

17. with landscape complexity. Perspectives in Plant Ecology, Evolution and Systematics, 7(2),

18. –93.

19. Green, D.G. (1990). Landscapes, cataclysms and population explosions. Math.Comput.

20. Model. 13,75–82.

21. Guermond, Y., Delahaye, D., Dubos-Paillard, E., Langlois, P. (2004). From modelling to

22. experiment. GeoJournal, 59(3), 171–176.

23. Herzon, I. & O’Hara, R.B. (2006). Effects of landscape complexity on farmland birds in the

24. Baltic states. Agriculture, Ecosystems and Environment, 118(1–4), 297–306.

25. Klebanoff, A. & Hastings, A. (1994). Chaos in three species food chains. Journal of

26. Mathematical Biology, 32, 427–451.

27. Kolasa, J. (2005). Complexity, System integration and susceptibility to change: biodiversity

28. connection. Ecological Complexity, 2(4), 431–442.

29. Levins, R. (1969). Some demographic and genetic consequences of environmental

30. heterogeneity for biological control. Bulletin of the Entomological Society of America 15,

31. –240.

32. Loehle, C. (2004). Challenges of Ecological Complexity. Ecological Complexity, 1, 3–6.

33. Malamud, B.D., Turcotte,D.L. (1999). Self-organized criticality applied to natural hazards.

34. Natural Hazards 20, 93–116.

35. Manrubia, S.C., Sole,R.V. (1996). Self-organized criticality in rainforest dynamics. Chaos

36. Solitons and Fractals 7,523–541.

37. Matsuba, I., Namatame, M. (2003). Scaling behavior in urban development process of

38. Tokyo City and hierarchical dynamical structure. Chaos, Solitons and Fractals, 16(1), 151–

39.

40. May, R.M. & Leonard, W.J. (1975). Nonlinear aspects of competition between three species.

41. SIAM Journal of Applied Mathematics, 29, 243–253.

42. May, R.M. & Oster,G.F. (1976). Bifurcations and Dynamic Complexity in simple ecological

43. models. American Naturalist, 110, 573–599.

44. Murray, B. & Fonstad, M. (2007). Preface: Complexity (and simplicity) in landscapes.

45. Geomorphology, 91(3–4), 173–177.

46. Nee, S. & May, R.M. (1992). Dynamics of Metapopulations: Habitat destruction and

47. Competitive Coexistence. Journal of Animal Ecology 61, 37–40.

48. Pahl-Wostl, C. (1995). The dynamic nature of ecosystems: Chaos and order entwined. New

49. York: Wiley.

50. Phillips, J.D. (1993). Biophysical feedbacks and the risks of desertification. Annals of the

51. Association of American Geographers 83, 630–640.

52. Phillips, J. (1995). Nonlinear dynamics and the evolution of relief. Geomorphology, 14(1),

53. –64.

54. Pykh, Yu. (2002). Lyapunov functions as a measure of Biodiversity: Theoretical background.

55. Ecological Indicators, 2, 123–133.

56. Rohde, K. (2005). Cellular automata and ecology. Oikos, 110(1), 203–207.

57. Satulovsky,J.E. (1997). On the synchronizing mehcanism of a class of cellular automata.

58. Physica A 237, 52–58.

59. Sprott J.C., Bolliger, J., Mladenoff, D.J. (2002). Self-organized criticality in forest-landscape

60. evolution. Physics Letters A, 297(3), 267–271.

61. Turchin, P. & Taylor, A.D. (1992). Complex Dynamics in ecological time series. Ecology, 73,

62. –305.

63. Werner, B.T. (1999). Complexity in natural landform patterns. Science, 284(5411), pp.

64. –104.

65. Wu, J. & Hobbs, R. (2002). Key issues and research priorities


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For citations:


Papadimitriou F. GEO-MATHEMATICAL MODELLING OF SPATIAL-ECOLOGICAL COMPLEX SYSTEMS: AN EVALUATION. GEOGRAPHY, ENVIRONMENT, SUSTAINABILITY. 2010;3(1):67-80. https://doi.org/10.24057/2071-9388-2010-3-1-67-80

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