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7 - Scale and scaling: a cross-disciplinary perspective

Published online by Cambridge University Press:  12 January 2010

By
Jianguo Wu
Edited by
Jianguo Wu  and
Richard J. Hobbs
Jianguo Wu
Affiliation:
Professor of Ecology, Evolution, and Environmental Science, Arizona State University, Tempe, Arizona, USA
Jianguo Wu
Affiliation:
Arizona State University
Richard J. Hobbs
Affiliation:
Murdoch University, Western Australia
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Summary

Introduction

Scale and heterogeneity are two key concepts in landscape ecology which are inherently related. Scale would matter little in a world where entities and relationships remain invariant across space or time, or in a landscape that is spatially or temporally homogeneous (i.e., uniform or random). However, real landscapes are heterogeneous biophysically and socioeconomically, and they must be treated as such for most questions and problems that interest us as scientists or citizens. Spatial heterogeneity – the diversity of entities and their spatial arrangement – is one of the most essential and unifying features of all natural and anthropogenic systems. Landscape heterogeneity is the manifestation of patchiness (discrete patterns) and gradients (continuous variations) that are intertwined across multiple spatial scales. Thus, scale is indispensable for describing and understanding landscape pattern.

It is not surprising, therefore, that scale has become one of the most fundamental concepts in landscape ecology, a field that focuses prominently on spatial heterogeneity and its ecological consequences (Risser et al. 1984, Forman and Godron 1986, Forman 1995, Turner et al. 2001). In fact, landscape ecology has been widely recognized by biologists, geographers, and even social scientists for its leading role in studying scale issues (McBratney 1998, Marceau 1999, Withers and Meentemeyer 1999, Meadowcroft 2002, Sayre 2005). However, it was not until the 1980s that the notion of scale began to gain its prominence in landscape ecology (and in ecology in general). Also, landscape ecology is not the only discipline that deals with scale and spatial pattern.

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Key Topics in Landscape Ecology , pp. 115 - 142
Publisher: Cambridge University Press
Print publication year: 2007

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References

Alker, H. R. 1969. A typology of ecological fallacies. Pages 69–86 in Dogan, M. and Rokkan, S. (eds.). Quantitative Ecological Analysis in the Social Sciences. Cambridge, MA: MIT Press.Google Scholar
Allardt, E. 1969. Aggregate analysis: the problem of its informative value. Pages 41–51 in Dogan, M. and Rokkan, S. (eds.). Quantitative Ecological Analysis in the Social Sciences. Cambridge, MA: MIT Press.Google Scholar
Allen, T. F. H., R. V. O'Neill, and T. W. Hoekstra. 1984. Interlevel Relations in Ecological Research and Management: Some Working Principles from Hierarchy Theory. USDA Forest Service General Technical Report RM-110. Fort Collins, Co: Rocky Mountain Forest and Range Experiment Station.
Allen, T. F. H. and Starr, T. B.. 1982. Hierarchy: Perspectives for Ecological Complexity. Chicago: University of Chicago Press.Google Scholar
Amrhein, C. G. 1995. Searching for the elusive aggregation effect: evidence from statistical simulations. Environment and Planning A 27, 105–19.CrossRefGoogle Scholar
Arbia, G. 1989. Spatial Data Configuration in the Statistical Analysis of Regional Economic and Related Problems. Dordrecht: Kluwer.CrossRefGoogle Scholar
Bak, P. 1996. How Nature Works: The Science of Self-Organized Criticality. New York: Copernicus.CrossRefGoogle Scholar
Barenblatt, G. I. 1996. Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Belyea, L. R. and Lancaster, J.. 2002. Inferring landscape dynamics of bog pools from scaling relationships and spatial patterns. Journal of Ecology 90, 223–34.CrossRefGoogle Scholar
Benson, B. J. and Mackenzie, M. D.. 1995. Effects of sensor spatial resolution on landscape structure parameters. Landscape Ecology 10, 113–20.CrossRefGoogle Scholar
Bierkens, M. F. P., Finke, P. A., and Willigen, P.. 2000. Upscaling and Downscaling Methods for Environmental Research. Dordrecht: Kluwer Academic Publishers.Google Scholar
Blöschl, G. and Sivapalan, M.. 1995. Scale issues in hydrological modelling: a review. Hydrological Processes 9, 251–90.CrossRefGoogle Scholar
Bokma, F. 2004. Evidence against universal metabolic allometry. Functional Ecology 18, 184–7.CrossRefGoogle Scholar
Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M., and West, G. B.. 2004. Toward a metabolic theory of ecology. Ecology 85, 1771–89.CrossRefGoogle Scholar
Brown, J. H., Gupta, V. K., B.-L. Li, et al. 2002. The fractal nature of nature: Power laws, ecological complexity and biodiversity. Philosophical Transactions of the Royal Society (London B) 357, 619–26.CrossRefGoogle ScholarPubMed
Brown, J. H. and West, G. B. (eds.). 2000. Scaling in Biology. New York: Oxford University Press.Google Scholar
Brutsaert, W. 1982. Evaporation into Atmosphere: Theory, History, and Applications. Dordrecht: D. Reidel Publishing Company.CrossRefGoogle Scholar
Calder, W. A. 1983. Ecological scaling: mammals and birds. Annual Reviews Ecology and Systematics 14, 213–30.CrossRefGoogle Scholar
Ciret, C. and Henderson-Sellers, A.. 1998. Sensitivity of ecosystem models to the spatial resolution of the NCAR community climate model CCM2. Climate Dynamics 14, 409–29.CrossRefGoogle Scholar
Clark, W. C. 1985. Scales of climate impacts. Climatic Change 7, 5–27.CrossRefGoogle Scholar
Cowan, G. A., Pines, D., and Meltzer, D. (eds.). 1994. Complexity: Metaphors, Models, and Reality. Reading, MA: Perseus Books.Google Scholar
Crane, R. G., Yarnal, B., Barron, E. J., and Hewitson, B.. 2002. Scale interactions and regional climate: examples from the Susquehanna River Basin. Human and Ecological Risk Assessment 8, 147–58.CrossRefGoogle Scholar
Cullinan, V. I., Simmons, M. A., and Thomas, J. M.. 1997. A Bayesian test of hierarchy theory: scaling up variability in plant cover from field to remotely sensed data. Landscape Ecology 12, 273–85.CrossRefGoogle Scholar
Cyr, H. and Walker, S. C.. 2004. An illusion of mechanistic understanding. Ecology 85, 1802–4.CrossRefGoogle Scholar
Dale, M. R. T. 1999. Spatial Pattern Analysis in Plant Ecology. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Delcourt, H. R. and Delcourt, P. A.. 1988. Quaternary landscape ecology: relevant scales in space and time. Landscape Ecology 2, 23–44.CrossRefGoogle Scholar
Dodds, P. S., Rothman, D. H., and Weitz, J. S.. 2001. Re-examination of the “3/4-law” of metabolism. Journal of Theoretical Biology 209, 9–27.CrossRefGoogle Scholar
Dogan, M. and Rokkan, S. (eds.). 1969. Quantitative Ecological Analysis in the Social Sciences. Cambridge, MA: MIT Press.Google Scholar
Foody, G. M. 2000. Estimation of sub-pixel land cover composition in the presence of untrained classes. Computers and Geosciences 26, 469–78.CrossRefGoogle Scholar
Forman, R. T. T. 1995. Land Mosaics: The Ecology of Landscapes and Regions. Cambridge: Cambridge University Press.Google Scholar
Forman, R. T. T. and Godron, M.. 1986. Landscape Ecology. New York: John Wiley & Sons, Inc.Google Scholar
Fotheringham, A. S. and Wong, D.. 1991. The modifiable areal unit problem in multivariate statistical analysis. Environment and Planning A 23, 1026–44.CrossRefGoogle Scholar
Freedman, D. A. 2001. Ecological inference and the ecological fallacy. International Encyclopedia for the Social and Behavioral Sciences 6, 4027–30.CrossRefGoogle Scholar
Freedman, D. A., Klein, S. P., Ostland, M., and Roberts, M. R.. 1998. A solution to the ecological inference problem (book review). Journal of the American Statistical Association 93, 1518–22.CrossRefGoogle Scholar
Freedman, D. A., Klein, S. P., Sacks, J., Smyth, C. A., and Everett, C. G.. 1991. Ecological regression and voting rights. Evaluation Review 15, 673–711.CrossRefGoogle Scholar
Freedman, D. A., Ostland, M., Roberts, M. R., and Klein, S. P.. 1999. Response to King's comment. Journal of the American Statistical Association 94, 355–7.CrossRefGoogle Scholar
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 Ecology 1, 19–28.CrossRefGoogle Scholar
Gardner, R. H., O'Neill, R. V., Turner, M. G., and Dale, V. H.. 1989. Quantifying scale-dependent effects of animal movement with simple percolation models. Landscape Ecology 3, 217–27.CrossRefGoogle Scholar
Gehlke, C. E. and Biehl, K.. 1934. Certain effects of grouping upon the size of the correlation coefficient in census tract material. Journal of the American Statistical Association 29, 169–70.Google Scholar
Goodchild, M. F. and Gopal, S. (eds.). 1989. Accuracy of Spatial Databases. London: Taylor and Francis.Google Scholar
Goodman, L. 1953. Ecological regression and the behavior of individuals. American Sociological Review 18, 663–4.CrossRefGoogle Scholar
Greig-Smith, P. 1952. The use of random and contiguous quadrats in the study of the structure of plant communities. Annals of Botany 16, 293–316.CrossRefGoogle Scholar
Haggett, P. 1965. Scale components in geographical problems. Pages 164–185 in Chorley, R. J. and Hagget, P. (eds.). Frontiers in Geographical Teaching. London: Methuen.Google Scholar
Hall, O., Hay, G. J., Bouchard, A., and Marceau, D. J.. 2004. Detecting dominant landscape objects through multiple scales: an integration of object-specific methods and watershed segmentation. Landscape Ecology 19, 59–76.CrossRefGoogle Scholar
Harvey, D. W. 1968. Pattern, process and the scale problem in geographical research. Transactions of the Institute of British Geographers 45, 71–8.CrossRefGoogle Scholar
Hastings, H. M. and Sugihara, G.. 1993. Fractals: A User's Guide for the Natural Sciences. Oxford: Oxford University Press.Google Scholar
Hay, G., Marceau, D. J., Dubé, P., and Bouchard, A.. 2001. A multiscale framework for landscape analysis: object-specific analysis and upscaling. Landscape Ecology 16, 471–90.CrossRefGoogle Scholar
Heuvelink, G. B. M. 1998a. Error Propagation in Environmental Modelling with GIS. Bristol: Taylor & Francis Inc.Google Scholar
Heuvelink, G. B. M. 1998b. Uncertainty analysis in environmental modelling under a change of spatial scale. Nutrient Cycling in Agroecosystems 50, 255–64.CrossRefGoogle Scholar
Hewitson, B. C. and Crane, R. G.. 1996. Climate downscaling: techniques and application. Climate Research 7, 85–95.CrossRefGoogle Scholar
Hood, W. G. 2002. Application of landscape allometry to restoration of tidal channels. Restoration Ecology 10, 213–22.CrossRefGoogle Scholar
Jelinski, D. E. and Wu, J.. 1996. The modifiable areal unit problem and implications for landscape ecology. Landscape Ecology 11, 129–40.CrossRefGoogle Scholar
Jenerette, G. D. and Wu, J.. 2001. Analysis and simulation of land-use change in the central Arizona–Phoenix region, USA. Landscape Ecology 16, 611–26.CrossRefGoogle Scholar
Judson, O. P. 1994. The rise of the individual-based model in ecology. TREE 9, 9–14.Google ScholarPubMed
Kersebaum, K. C. and Wenkel, K.-O.. 1998. Modelling water and nitrogen dynamics at three different spatial scales: influence of different data aggregation levels on simulation results. Nutrient Cycling in Agroecosystems 50, 313–19.CrossRefGoogle Scholar
Kidson, J. W. and Thompson, C. S.. 1998. A comparison of statistical and model-based downscaling techniques for estimating local climate variations. Journal of Climate 11, 735–53.2.0.CO;2>CrossRefGoogle Scholar
King, A. W. 1991. Translating models across scales in the landscape. Pages 479–517 in Turner, M. G. and Gardner, R. H. (eds.). Quantitative Methods in Landscape Ecology. New York: Springer-Verlag.CrossRefGoogle Scholar
King, A. W., Johnson, A. R., and O'Neill, R. V.. 1991. Transmutation and functional representation of heterogeneous landscapes. Landscape Ecology 5, 239–53.CrossRefGoogle Scholar
King, G. 1997. A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data. Princeton: Princeton University Press.Google Scholar
King, G. 1999. The future of ecological inference research: a comment on Freedman et al. Journal of the American Statistical Association 94, 352–5.Google Scholar
Kozlowski, J. and Konarzewsk, M.. 2004. Is West, Brown and Enquist's model of allometric scaling mathematically correct and biologically relevant?Functional Ecology 18, 283–9.CrossRefGoogle Scholar
LaBarbera, M. 1989. Analyzing body size as a factor in ecology and evolution. Annual Reviews Ecology and Systematics 20, 97–117.CrossRefGoogle Scholar
Levin, S. A. 1992. The problem of pattern and scale in ecology. Ecology 73, 1943–67.CrossRefGoogle Scholar
Levin, S. A. 1999. Fragile Dominions: Complexity and the Commons. Reading, MA: Perseus Books.Google Scholar
Levin, S. A., Grenfell, B., Hastings, A., and Perelson, A. S.. 1997. Mathematical and computational challenges in population biology and ecosystems science. Science 275, 334–43.CrossRefGoogle ScholarPubMed
Levin, S. A. and S. W. Pacala. 1997. Theories of simplification and caling of spatially distributed processes. Pages 271–95 in Tilman, D. and Kareiva, P. (eds.). Spatial Ecology. Princeton: Princeton University Press.Google Scholar
Li, H. and J. Wu. 2005. Uncertainty and error analysis in ecological studies: an overview. In Wu, J., Jones, K. B., Li, H., and Loucks, O. L. (eds.). Scaling and Uncertainty Analysis in Ecology: Methods and Applications. New York: Columbia University Press.Google Scholar
Li, X. and Sailor, D.. 2000. Application of tree-structured regression for regional precipitation prediction using general circulation model output. Climate Research 16, 17–30.CrossRefGoogle Scholar
Ludwig, J. A., Wiens, J. A., and Tongway, D. J.. 2000. A scaling rule for landscape patches and how it applies to conserving soil resources in Savannas. Ecosystems 3, 84–97.CrossRefGoogle Scholar
Mandelbrot, B. B. 1982. The Fractal Geometry of Nature. New York: W. H. Freeman and Company.Google Scholar
Marceau, D. J. 1999. The scale issue in social and natural sciences. Canadian Journal of Remote Sensing 25, 347–56.CrossRefGoogle Scholar
McBratney, A. B. 1998. Some considerations on methods for spatially aggregating and disaggregating soil information. Nutrient Cycling in Agroecosystems 50, 51–62.CrossRefGoogle Scholar
Meadowcroft, J. 2002. Politics and scale: some implications for environmental governance. Landscape and Urban Planning 61, 169–79.CrossRefGoogle Scholar
Meentemeyer, V. 1989. Geographical perspectives of space, time, and scale. Landscape Ecology 3, 163–73.CrossRefGoogle Scholar
Mertens, K. C., Verbeke, L. P. C., Westra, T., and Wulf, R. R.. 2004. Sub-pixel mapping and sub-pixel sharpening using neural network predicted wavelet coefficients. Remote Sensing of Environment 91, 225–36.CrossRefGoogle Scholar
Miller, D. H. 1978. The factor of scale: ecosystem, landscape mosaic, and region. Pages 63–88 in Hammond, K. A., Macinio, G., and Fairchild, W. B. (eds.). Sourcebook on the Environment: A Guide to the Literature. Chicago: University of Chicago Press.Google Scholar
Miller, E. E. and Miller, R. D.. 1956. Physical theory for capillary flow phenomena. Journal of Applied Physics 27, 324–32.CrossRefGoogle Scholar
Milne, B. T. 1992. Spatial aggregation and neutral models in fractal landscapes. American Naturalist 139, 32–57.CrossRefGoogle Scholar
Murphy, J. 1999. An evaluation of statistical and dynamical techniques for downscaling local climate. Journal of Climate 12, 2256–84.2.0.CO;2>CrossRefGoogle Scholar
Murphy, J. 2000. Predictions of climate change over Europe using statistical and dynamical downscaling techniques. International Journal of Climatology 20, 489–501.3.0.CO;2-6>CrossRefGoogle Scholar
Niklas, K. J. 1994. Plant Allometry: The Scaling of Form and Process. Chicago: University of Chicago Press.Google Scholar
O'Neill, R. V., DeAngelis, D. L., Waide, J. B., and Allen, T. F. H.. 1986. A Hierarchical Concept of Ecosystems. Princeton: Princeton University Press.Google Scholar
O'Neill, R. V., R. H. Gardner, B. T. Milne, M. G. Turner, and B. Jackson. 1991. Heterogeneity and spatial hierarchies. Pages 85–96 in Kolasa, J. and Pickett, S. T. A. (eds.). Ecological Heterogeneity. New York: Springer-Verlag.CrossRefGoogle Scholar
O'Neill, R. V., Hunsaker, C. T., Timmins, S. P., et al. 1996. Scale problems in reporting landscape pattern at the regional scale. Landscape Ecology 11, 169–80.CrossRefGoogle Scholar
O'Neill, R. V. and A. W. King. 1998. Homage to St. Michael; or, why are there so many books on scale? Pages 3–15 in Peterson, D. L. and Parker, V. T. (eds.). Ecological Scale: Theory and Applications. New York: Columbia University Press.Google Scholar
Openshaw, S. 1984. The Modifiable Areal Unit Problem. Norwich: Geo Books.Google Scholar
Openshaw, S. and P. Taylor. 1979. A million or so correlation coefficients: three experiments on the modifiable areal unit problem. Pages 127–144 in Wrigley, N. (ed.). Statistical Application in the Spatial Sciences. London: Qion.Google Scholar
Pearce, N. 2000. Editorial: the ecological fallacy strikes back. Journal of Epidemiology and Community Health 54, 326–7.CrossRefGoogle ScholarPubMed
Peters, D. P. C., Herrick, J. E., Urban, D. L., Gardner, R. H., and Breshears, D. D.. 2004. Strategies for ecological extrapolation. Oikos 106, 627–36.CrossRefGoogle Scholar
Poole, C. 1994. Editorial: ecologic analysis as outlook and method. American Journal of Public Health 84, 715–16.CrossRefGoogle ScholarPubMed
Rastetter, E. B., Aber, J. D., Peters, D. P. C., Ojima, D. S., and Burke, I. C.. 2003. Using mechanistic models to scale ecological processes across space and time. BioScience 53, 68–76.CrossRefGoogle Scholar
Rastetter, E. B., King, A. W., Cosby, B. J., et al. 1992. Aggregating fine-scale ecological knowledge to model coarser-scale attributes of ecosystems. Ecological Applications 2, 55–70.CrossRefGoogle ScholarPubMed
Reynolds, J. F., D. W. Hilbert, and P. R. Kemp. 1993. Scaling ecophysiology from the plant to the ecosystem: a conceptual framework. Pages 127–40 in Ehleringer, J. R. and Field, C. B. (eds.). Scaling Physiological Processes: Leaf to Globe. San Diego: Academic Press.Google Scholar
Reynolds, J. F. and J. Wu. 1999. Do landscape structural and functional units exist? Pages 273–96 in Tenhunen, J. D. and Kabat, P. (eds.). Integrating Hydrology, Ecosystem Dynamics, and Biogeochemistry in Complex Landscapes. Chichester: John Wiley & Sons, Ltd.Google Scholar
Risser, P. G., Karr, J. R., and Forman, R. T. T.. 1984. Landscape Ecology: Directions and Approaches. Special Publication 2, Champaign, IL: Illinois Natural History Survey.Google Scholar
Robinson, W. S. 1950. Ecological correlations and the behavior of individuals. American Sociological Review 15, 351–7.CrossRefGoogle Scholar
Rosin, P. L. 2001. Robust pixel unmixing. IEEE Transactions on Geoscience and Remote Sensing 39, 1978–83.CrossRefGoogle Scholar
Saura, S. 2004. Effects of remote sensor spatial resolution and data aggregation on selected fragmentation indices. Landscape Ecology 19, 197–209.CrossRefGoogle Scholar
Sayre, N. F. 2005. Ecological and geographical scale: parallels and potential for integration. Progress in Physical Geography 29, 276–90.CrossRefGoogle Scholar
Schmidt-Nielsen, K. 1984. Scaling: Why is Animal Size so Important?Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Schneider, D. C. 2001. Spatial allometry. Pages 113–53 in Gardner, R. H., Kemp, W. M., Kennedy, V. S., and Petersen, J. E. (eds.). Scaling Relations in Experimental Ecology. New York: Columbia University Press.CrossRefGoogle Scholar
Schneider, D. C. 2002. Scaling theory: application to marine ornithology. Ecosystems 5, 736–48.CrossRefGoogle Scholar
Schwartz, S. 1994. The fallacy of the ecological fallacy: the potential misuse of a concept and the consequences. American Journal of Public Health 84, 819–24.CrossRefGoogle ScholarPubMed
Simon, H. A. 1962. The architecture of complexity. Proceedings of the American Philosophical Society 106, 467–82.Google Scholar
Song, C. 2005. Spectral mixture analysis for subpixel vegetation fractions in the urban environment: how to incorporate endmember variability?Remote Sensing of Environment 95, 248–63.CrossRefGoogle Scholar
Sposito, G. (ed.). 1998. Scale Dependence and Scale Invariance in Hydrology. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Stommel, H. 1963. Varieties of oceanographic experience. Science 139, 572–6.CrossRefGoogle ScholarPubMed
Tenhunen, J. D. and Kabat, P. (eds.). 1999. Integrating Hydrology, Ecosystem Dynamics, and Biogeochemistry in Complex Landscapes. Chichester: John Wiley & Sons, Ltd.Google Scholar
Turner, M. G., Dale, V. H., and Gardner, R. H.. 1989a. Predicting across scales: theory development and testing. Landscape Ecology 3, 245–52.CrossRefGoogle Scholar
Turner, M. G., Gardner, R. H., and O'Neill, R. V.. 2001. Landscape Ecology in Theory and Practice: Pattern and Process. New York: Springer-Verlag.Google Scholar
Turner, M. G., O'Neill, R. V., Gardner, R. H., and Milne, B. T.. 1989b. Effects of changing spatial scale on the analysis of landscape pattern. Landscape Ecology 3, 153–62.CrossRefGoogle Scholar
Urban, D. L., O'Neill, R. V., and Shugart, H. H.. 1987. Landscape ecology: a hierarchical perspective can help scientists understand spatial patterns. BioScience 37, 119–27.CrossRefGoogle Scholar
Watson, M. K. 1978. The scale problem in human geography. Geografiska Annaler 60B, 36–47.CrossRefGoogle Scholar
Wickham, J. D. and Riitters, K. H.. 1995. Sensitivity of landscape metrics to pixel size. International Journal of Remote Sensing 16, 3585–95.CrossRefGoogle Scholar
Wiens, J. A. 1989. Spatial scaling in ecology. Functional Ecology 3, 385–97.CrossRefGoogle Scholar
Wilby, R. L. and Wigley, T. M. L.. 1997. Downscaling general circulation model output: a review of methods and limitations. Progress in Physical Geography 21, 530–48.CrossRefGoogle Scholar
Wilby, R. L., Wigley, T. M. L., Conway, D., et al. 1998. Statistical downscaling of general circulation model output: a comparison of methods. Water Resources Research 34, 2995–3008.CrossRefGoogle Scholar
Withers, M. and V. Meentemeyer. 1999. Concepts of scale in landscape ecology. Pages 205–52 in Klopatek, J. M. and Gardner, R. H. (eds.). Landscape Ecological Analysis: Issues and Applications. New York: Springer.CrossRefGoogle Scholar
Wolfram, S. 1984. Cellular automata as models of complexity. Nature 311, 419–24.CrossRefGoogle Scholar
Wrigley, N. 1994. Revisiting the modifiable areal unit problem and the ecological fallacy. Pages 1–35 in Cliff, A. D., Goulc, P. R., and Hoare, A. G. (eds.). Festschrift for Peter Haggett. Oxford: Blackwell.Google Scholar
Wrigley, N., T. Holt, D. Steel, and M. Tranmer. 1996. Analyzing, modelling, and resolving the ecological fallacy. Pages 23–40 in Longley, P. and Batty, M. (eds.). Spatial Analysis: Modelling in a GIS Environment. Cambridge: GeoInformation International.Google Scholar
Wu, J. 1990. Modelling the energy exchange processes between plant communities and environment. Ecological Modelling 51, 233–50.CrossRefGoogle Scholar
Wu, J. 1999. Hierarchy and scaling: extrapolating information along a scaling ladder. Canadian Journal of Remote Sensing 25, 367–80.CrossRefGoogle Scholar
Wu, J. 2004. Effects of changing scale on landscape pattern analysis: Scaling relations. Landscape Ecology 19, 125–38.CrossRefGoogle Scholar
Wu, J. and David, J. L.. 2002. A spatially explicit hierarchical approach to modeling complex ecological systems: theory and applications. Ecological Modelling 153, 7–26.CrossRefGoogle Scholar
Wu, J. and Hobbs, R.. 2002. Key issues and research priorities in landscape ecology: an idiosyncratic synthesis. Landscape Ecology 17, 355–65.CrossRefGoogle Scholar
Wu, J. and Levin, S. A.. 1994. A spatial patch dynamic modeling approach to pattern and process in an annual grassland. Ecological Monographs 64(4), 447–64.CrossRefGoogle Scholar
Wu, J. and Levin, S. A.. 1997. A patch-based spatial modeling approach: conceptual framework and simulation scheme. Ecological Modelling 101, 325–46.CrossRefGoogle Scholar
Wu, J. and Loucks, O. L.. 1995. From balance-of-nature to hierarchical patch dynamics: a paradigm shift in ecology. Quarterly Review of Biology 70, 439–66.CrossRefGoogle Scholar

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