Skip to main content

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Barenblatt, G. I. 1996. Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press, Cambridge.

    Google Scholar 

  • Becker, A., and P. Braun. 1999. Disaggregation, aggregation and spatial scaling in hydrological modelling. Journal of Hydrology 217:239-252.

    Google Scholar 

  • Belyea, L. R., and J. Lancaster. 2002. Inferring landscape dynamics of bog pools from scaling relationships and spatial patterns. Journal of Ecology 90:223-234.

    Google Scholar 

  • Berntson, G. M., and P. Stoll. 1997. Correcting for finite spatial scales of self-similarity when calculating the fractal dimensions of real-world structures. Proceedings of the Royal Society of London Series B-Biological Sciences 264:1531-1537.

    Google Scholar 

  • Beven, K. 2000. On the future of distributed modelling in hydrology. Hydrological Processes 14: 3183-3184.

    Google Scholar 

  • Bierkens, M. F. P., P. A. Finke, and P. de Willigen. 2000. Upscaling and Downscaling Methods for Environmental Research. Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Binney, J. J., N. J. Dowrick, A. J. Fisher, and M. E. Newman. 1993. The Theory of Critical Phenomena: An Introduction to the Renormalization Group. Oxford Science, Oxford.

    Google Scholar 

  • Blöschl, G., and M. Sivapalan. 1995. Scale issues in hydrological modelling: A review. Hydrological Processes 9:251-290.

    Google Scholar 

  • Bokma, F. 2004. Evidence against universal metabolic allometry. Functional Ecology 18:184-187.

    Google Scholar 

  • Brown, J. H., V. K. Gupta, B.-L. Li, B. T. Milne, C. Restrepo, and G. B. West. 2002. The fractal nature of nature: power laws, ecological complexity and biodiversity. Philosophical Transactions of the Royal Society (London B) 357:619-626.

    Google Scholar 

  • Brown, J. H., G. B. West, and B. J. Enquist. 2000. Patterns and processes, causes and consequences. Pages 1-24 in J. H. Brown and G. B. West, editors. Scaling in Biology. Oxford University Press, New York.

    Google Scholar 

  • Bull, W. B. 1975. Allometric change of landforms. Geological Society of America Bulletin 86:1489-1498.

    Google Scholar 

  • Burnett, C., and T. Blaschke. 2003. A multi-scale segmentation/object relationship modeling methodology for landscape analysis. Ecological Modelling 168:233-249.

    Google Scholar 

  • Calder, W. A. 1983. Ecological scaling: mammals and birds. Annual Review of Ecology and Systematics 14:213-230.

    Google Scholar 

  • Cale, W. G. 1995. Model Aggregation - Ecological perspectives. Pages 230-241 in B. C. Patten, S. E. Jorgensen, and S. I. Auerbach, editors. Complex Ecology. Prentice-Hall, Englewood Cliffs.

    Google Scholar 

  • Carbone, C., and J. L. Gittleman. 2002. A common rule for the scaling of carnivore density. Science 295:2273-2276.

    CAS  PubMed  Google Scholar 

  • Chave, J., and S. A. Levin. 2003. Scale and scaling in ecological and economic systems. Environmental and Resource Economics 26:527-557.

    Google Scholar 

  • Church, M., and D. M. Mark. 1980. On size and scale in geomorphology. Progress in Physical Geography 4:342-390.

    Google Scholar 

  • Crane, R. G., B. Yarnal, E. J. Barron, and B. Hewitson. 2002. Scale interactions and regional climate: examples from the Susquehanna River Basin. Human and Ecological Risk Assessment 8:147-158.

    Google Scholar 

  • Crawley, M. J., and J. E. Harral. 2001. Scale dependence in plant biodiversity. Science 291:864-868.

    CAS  PubMed  Google Scholar 

  • Cyr, H., and S. C. Walker. 2004. An illusion of mechanistic understanding. Ecology 85:1802-1804.

    Google Scholar 

  • de Vries, W., J. Kros, C. van der Salm, J. E. Groenenberg, and G. J. Reinds. 1998. The use of upscaling procedures in the application of soil acidification models at different spatial scales. Nutrient Cycling in Agroecosystems 50:223-236.

    CAS  Google Scholar 

  • Dolman, A. J., and E. A. Blyth. 1997. Patch scale aggregation of heterogeneous land surface cover for mesoscale meteorological model. Journal of Hydrology 190:252-268.

    Google Scholar 

  • Enquist, B. J., J. H. Brown, and G. B. West. 1998. Allometric scaling of plant energetics and population density. Nature 395:163-165.

    CAS  Google Scholar 

  • Gardner, R. H., B. T. Milne, M. G. Turner, and R. V. O’Neill. 1987. Neutral models for the analysis of broad-scale landscape pattern. Landscape Ecology 1:19-28.

    Google Scholar 

  • Goovaerts, P. 1997. Geostatistics for Natural Resources Evaluation. Oxford University Press, New York.

    Google Scholar 

  • Gould, S. J. 1966. Allometry and size in ontogeny and phylogeny. Biological Review 41:587-640.

    CAS  Google Scholar 

  • Griffith, G. E., J. M. Omernik, and A. J. Woods. 1999. Ecoregions, watersheds, basins, and HUCs: how state and federal agencies frame water quality. Journal of Soil and Water Conservation 54:666-677.

    Google Scholar 

  • Gunther, B. 1975. Dimensional analysis and theory of biological similarity. Physiological Reviews 55:659-699.

    CAS  PubMed  Google Scholar 

  • Hall, O., G. J. Hay, A. Bouchard, and D. J. Marceau. 2004. Detecting dominant landscape objects through multiple scales: an integration of object-specific methods and watershed segmentation. Landscape Ecology 19:59-76.

    Google Scholar 

  • Hanski, I., editor. 1999. Metapopulation Ecology. Oxford University Press, New York.

    Google Scholar 

  • Harte, J., A. Kinzig, and J. Green. 1999. Self-similarity in the distribution and abundance of species. Science 284:334-336.

    CAS  PubMed  Google Scholar 

  • Hastings, H. M., and G. Sugihara. 1993. Fractals: A User’s Guide for the Natural Sciences. Oxford University Press, Oxford.

    Google Scholar 

  • Haverkamp, R., J.-Y. Parlange, R. Cuenca, P. J. Ross, and T. S. Steenhuis. 1998. Scale analyses for land-surface hydrology. Pages 190-223 in G. Sposito, editor. Scale Dependence and Scale Invariance in Hydrology. Cambridge University Press, Cambridge.

    Google Scholar 

  • Hay, G., D. J. Marceau, P. Dubé, and A. Bouchard. 2001. A multiscale framework for landscape analysis: object-specific analysis and upscaling. Landscape Ecology 16:471-490.

    Google Scholar 

  • Hay, G. J., T. Blaschke, D. J. Marceau, and A. Bouchard. 2003. A comparison of three image-object methods for the multiscale analysis of landscape structure. ISPRS Journal of Photogrammetry and Remote Sensing 57:327-345.

    Google Scholar 

  • Hewitson, B. C., and R. G. Crane. 1996. Climate downscaling: techniques and application. Climate Research 7:85-95.

    Google Scholar 

  • Hood, W. G. 2002. Application of landscape allometry to restoration of tidal channels. Restoration Ecology 10:213-222.

    Google Scholar 

  • Iwasa, Y., S. A. Levin, and V. Andreasen. 1989. Aggregation in model ecosystems: II. approximate aggregation. IMA Journal of Mathematics Applied in Medicine & Biology 6:1-23.

    Google Scholar 

  • Jarvis, P. G. 1995. Scaling processes and problems. Plant, Cell and Environment 18:1079-1089.

    Google Scholar 

  • King, A. W. 1991. Translating models across scales in the landscape. Pages 479-517 in M. G. Turner and R. H. Gardner, editors. Quantitative Methods in Landscape Ecology. Springer-Verlag, New York.

    Google Scholar 

  • King, A. W., A. R. Johnson, and R. V. O’Neill. 1991. Transmutation and functional representation of heterogeneous landscapes. Landscape Ecology 5:239-253.

    Google Scholar 

  • Kozlowski, J., and M. Konarzewski. 2004. Is West, Brown and Enquist’s model of allometric scaling mathematically correct and biologically relevant? Functional Ecology 18:283-289.

    Google Scholar 

  • Kunin, W. E. 1998. Extrapolating species abundance across spatial scales. Science 281:1513-1515.

    CAS  PubMed  Google Scholar 

  • L’homme, J. P., A. Chehbouni, and B. A. Monteny. 1996. Canopy to region scale translation of surface fluxes. Pages 161-182 in J. B. Stewart, E. T. Engman, R. A. Feddes, and Y. Kerr, editors. Boundary-Layer Meteorology. Wiley, Chichester.

    Google Scholar 

  • LaBarbera, M. 1989. Analyzing body size as a factor in ecology and evolution. Annual Review of Ecology and Systematics 20:97-117.

    Google Scholar 

  • Lam, N. S. 1983. Spatial interpolation methods: a review. The American Cartographer 10:129-149.

    Google Scholar 

  • Levin, S. A. 1976. Population dynamic models in heterogeneous environments. Annual Review of Ecology and Systematics 7:287-310.

    Google Scholar 

  • Levin, S. A. 1992. The problem of pattern and scale in ecology. Ecology 73:1943-1967.

    Google Scholar 

  • Levin, S. A., and S. W. Pacala. 1997. Theories of simplification and sclaing of spatially distributed processes. Pages 271-295 in D. Tilman and P. Kareiva, editors. Spatial Ecology. Princeton University Press, Princeton.

    Google Scholar 

  • Levin, S. A., and R. T. Paine. 1974. Disturbance, patch formation and community structure. Proceedings of the National Academy of Sciences 71:2744-2747.

    CAS  Google Scholar 

  • Li, H., and J. Wu. 2004. Use and misuse of landscape indices. Landscape Ecology 19:389-399.

    Google Scholar 

  • Li, H., J. F. Franklin, F. J. Swanson, and T. A. Spies. 1993. Developing alternative forest cutting patterns: a simulation approach. Landscape Ecology 8:63-75.

    Google Scholar 

  • Lomolino, M. V. 2000. Ecology’s most general, yet protean pattern: the species-area relationship. Journal of Biogeography 27:17-26.

    Google Scholar 

  • Lonsdale, W. M. 1990. The self-thinning rule: dead or alive? Ecology 71:1373-1388.

    Google Scholar 

  • Magnani, F. 1999. Plant energetics and population density. Nature 398:572.

    Google Scholar 

  • Mandelbrot, B. B. 1982. The Fractal Geometry of Nature. W. H. Freeman and Company, New York.

    Google Scholar 

  • Mandelbrot, B. B. 1999. Multifractals and1/f Noise Wild Self-Affinity in Physics(1963-1976). Springer-Verlag, New York.

    Google Scholar 

  • Marceau, D. J. 1999. The scale issue in social and natural sciences. Canadian Journal of Remote Sensing 25:347-356.

    Google Scholar 

  • Miller, E. E., and R. D. Miller. 1956. Physical theory for capillary flow phenomena. Journal of Applied Physics 27:324-332.

    CAS  Google Scholar 

  • Milne, B. T. 1991. Heterogeneity as a multiscale characteristic of landscapes. Pages 69-84 in J. Kolasa and S. T. A. Pickett, editors. Ecological Heterogeneity. Springer-Verlag, New York.

    Google Scholar 

  • Milne, B. T. 1998. Motivation and benefits of complex systems approaches in ecology. Ecosystems 1:449-456.

    Google Scholar 

  • Niklas, K. J. 1994. Plant Allometry: The Scaling of Form and Process. University of Chicago Press, Chicago.

    Google Scholar 

  • Nikora, V. I., C. P. Pearson, and U. Shankar. 1999. Scaling properties in landscape patterns: New Zealand experience. Landscape Ecology 14:17-33.

    Google Scholar 

  • O’Neill, R. V. 1979. Natural variability as a source of error in model predictions. Pages 23-32 in G. S. Innis and R. V. O’Neill, editors. Systems Analysis of Ecosystems. International Co-operative Publishing House, Fairland, MD.

    Google Scholar 

  • O’Neill, R. V., and B. Rust. 1979. Aggregation error in ecological models. Ecological Modelling 7: 91-105.

    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 J. Kolasa and S. T. A. Pickett, editors. Ecological Heterogeneity. Springer-Verlag, New York.

    Google Scholar 

  • Omernik, J. M. 2003. The misuse of hydrologic unit maps for extrapolation, reporting, and ecosystem management. Journal of American Water Resources Association 39:563-573.

    Google Scholar 

  • Peters, R. H. 1983. The Ecological Implications of Body Size. Cambridge University Press, Cambridge.

    Google Scholar 

  • Peterson, G. D. 2000. Scaling ecological dynamics: Self-organization, hierarchical structure, and ecological resilience. Climatic Change 44:291-309.

    Google Scholar 

  • Phillips, J. D. 1999. Earth Surface Systems: Complexity, Order and Scale. Blackwell Publishers Ltd., Malden, Massachusetts.

    Google Scholar 

  • Pielke, R. A., and R. Avissar. 1990. Influence of landscape structure on local and regional climate. Landscape Ecology 4:133-155.

    Google Scholar 

  • Poole, G. C. 2002. Fluvial landscape ecology: addressing uniqueness within the river discontinuum. Freshwater Biology 47:641-660.

    Google Scholar 

  • Prothero, J. 1986. Methodological aspects of scaling in biology. Journal of Theoretical Biology 118:259-286.

    PubMed  Google Scholar 

  • Quattrochi, D. A., and M. F. Goodchild, editors. 1997. Scale in Remote Sensing and GIS. CRC Lewis Publishers, Boca Raton.

    Google Scholar 

  • Raupach, M. R., D. D. Baldocchi, H.-J. Bolle, L. Dümenil, W. Eugster, F. X. Meixner, J. A. Olejnik, R. A. Pielke, J. D. Tenhunen, and R. Valentin. 1999. How is the atmospheric coupling of land surfaces affected by topography, complexity in landscape patterning, and the vegetation mosaic? Pages 177-196 in J. D. Tenhunen and P. Kabat, editors. Integrating Hydrology, Ecosystem Dynamics, and Biogeochemistry in Complex Landscapes. Wiley, Chichester.

    Google Scholar 

  • Reynolds, J. F., and J. Wu. 1999. Do landscape structural and functional units exist? Pages 273-296 in J. D. Tenhunen and P. Kabat, editors. Integrating Hydrology, Ecosystem Dynamics, and Biogeochemistry in Complex Landscapes. Wiley, Chichester.

    Google Scholar 

  • Rodriguez-Iturbe, I., and A. Rinaldo. 1997. Fractal River Networks. Cambridge University Press, New York.

    Google Scholar 

  • Sailor, D., T. Hu, X. Li, and J. N. Rosen. 2000. A neural network approach to local downscaling of GCM output for assessing wind power implications of climate change. Renewable Energy 19:359-378.

    Google Scholar 

  • Scheurer, D. L., D. C. Schneider, and L. P. Sanford. 2001. Scaling issues in marine experimental ecosystems. Pages 330-360 in R. H. Gardner, W. M. Kemp, V. S. Kennedy, and J. E. Petersen, editors. Scaling Relations in Experimental Ecology. Columbia University Press, New York.

    Google Scholar 

  • Schmid, P. E., M. Tokeshi, and J. M. Schmid-Araya. 2000. Relation between population density and body size in stream communities. Science 289:1557-1560.

    CAS  PubMed  Google Scholar 

  • Schmidt-Nielsen, K. 1984. Scaling: Why Is Animal Size So Important? Cambridge University Press, Cambridge.

    Google Scholar 

  • Schneider, D. C. 2001a. Spatial allometry. Pages 113-153 in R. H. Gardner, W. M. Kemp, V. S. Kennedy, and J. E. Petersen, editors. Scaling Relations in Experimental Ecology. Columbia University Press, New York.

    Google Scholar 

  • Schneider, D. C. 2001b. The rise of the concept of scale in ecology. Bioscience 51:545-553.

    Google Scholar 

  • Schoener, T. W., D. A. Spiller, and J. B. Losos. 2001. Natural restoration of the species-area relation for a lizard after a hurricane. Science 294:1525-1528.

    CAS  PubMed  Google Scholar 

  • Schroeder, M. 1991. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. W.H. Freeman and Company, New York.

    Google Scholar 

  • Schweitzer, F., editor. 1997. Self-Organization of Complex Structures: From Individual to Collective Dynamics. Gordon and Breach Science Publishers, Amsterdam.

    Google Scholar 

  • Shmida, A., and M. Wilson. 1985. Biological determinants of species diversity. Journal of Biogeography 12:1-20.

    Google Scholar 

  • Sposito, G., editor. 1998. Scale Dependence and Scale Invariance in Hydrology. Cambridge University Press, Cambridge.

    Google Scholar 

  • Stanley, and H. E. P. Meakin. 1988. Multifractal phenomena in physics and chemistry. Nature 335: 405-409.

    Google Scholar 

  • Tenhunen, J. D., and P. Kabat, editors. 1999. Integrating Hydrology, Ecosystem Dynamics, and Biogeochemistry in Complex Landscapes. Wiley, Chichester.

    Google Scholar 

  • Turcotte, D. L. 1995. Scaling in geology: landforms and earthquakes. Proceedings of the National Academy of Science 92:6697-6704.

    CAS  Google Scholar 

  • Turner, M. G., V. H. Dale, and R. H. Gardner. 1989. Predicting across scales: theory development and testing. Landscape Ecology 3:245-252.

    Google Scholar 

  • Urban, D. L., M. F. Acevedo, and S. L. Garman. 1999. Scaling fine-scale processes to large-scale patterns using models derived from models: meta-models. Pages 70-98 in D. J. Mladenoff and W. L. Baker, editors. Spatial Modeling of Forest Landscape Change: Approaches and Applications. Cambridge University Press, Cambridge, UK.

    Google Scholar 

  • Urban, D. L., R. V. O’Neill, and H. H. Shugart. 1987. Landscape ecology: a hierarchical perspective can help scientists understand spatial patterns. Bioscience 37:119-127.

    Google Scholar 

  • Weller, D. E. 1987. A reevaluation of the -3/2 power rule of plant self-thinning. Ecological Monographs 57:23-43.

    Google Scholar 

  • West, G. B., J. H. Brown, and B. J. Enquist. 1997. A general model for the origin of allometric scaling laws in biology. Science 276:122-126.

    CAS  PubMed  Google Scholar 

  • Whittaker, R. J., K. J. Willis, and R. Field. 2001. Scale and species richness: towards a general, hierarchical theory of species diversity. Journal of Biogeography 28:453-470.

    Google Scholar 

  • Wilby, R. L., T. M. L. Wigley, D. Conway, P. D. Jones, B. C. Hewitson, J. Main, and D. S. Wilks. 1998. Statistical downscaling of general circulation model output: a comparison of methods. Water Resources Research 34:2995-3008.

    Google Scholar 

  • Wilson, K. G. 1975. Renormalization group methods. Advances in Mathematics 16:170-186.

    Google Scholar 

  • Woldenberg, M. J. 1969. Spatial order in fluvial systems: Horton’s laws derived from mixed hexagonal hierarchies of drainage basin areas. Geological Society of America Bulletin 80:97-112.

    Google Scholar 

  • Wood, E. F. 1998. Scale analyses for land-surface hydrology. Pages 1-29 in G. Sposito, editor. Scale Dependence and Scale Invariance in Hydrology. Cambridge University Press, Cambridge.

    Google Scholar 

  • Woodmansee, R. G. 1990. Biogeochemical cycles and ecological hierarchies. Pages 57-71 in I. S. Zonneveld and R. T. T. Forman, editors. Changing Landscapes: An Ecological Perspective. Springer-Verlag, New York.

    Google Scholar 

  • Wu, J. 1990. Modelling the energy exchange processes between plant communities and environment. Ecological Modelling 51:233-250.

    Google Scholar 

  • Wu, J. 1999. Hierarchy and scaling: extrapolating information along a scaling ladder. Canadian Journal of Remote Sensing 25:367-380.

    Google Scholar 

  • Wu, J. 2004. Effects of changing scale on landscape pattern analysis: scaling relations. Landscape Ecology 19:125-138.

    Google Scholar 

  • Wu, J., and J. L. David. 2002. A spatially explicit hierarchical approach to modeling complex ecological systems: theory and applications. Ecological Modelling 153:7-26.

    Google Scholar 

  • Wu, J., and R. Hobbs. 2002. Key issues and research priorities in landscape ecology: an idiosyncratic synthesis. Landscape Ecology 17:355-365.

    Google Scholar 

  • Wu, J., and S. A. Levin. 1997. A patch-based spatial modeling approach: conceptual framework and simulation scheme. Ecological Modelling 101:325-346.

    Google Scholar 

  • Wu, J., and O. L. Loucks. 1995. From balance-of-nature to hierarchical patch dynamics: a paradigm shift in ecology. Quarterly Review of Biology 70:439-466.

    Google Scholar 

  • Wu, J., D. Jelinski, M. Luck, and P. Tueller. 2000. Multiscale analysis of landscape heterogeneity. Geographic Information Sciences 6:6-19.

    Google Scholar 

  • Zeide, B. 1987. Analysis of the 3/2 power law of self-thinning. Forest Science 33:517-537.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this chapter

Cite this chapter

WU, J., LI, H. (2006). PERSPECTIVES AND METHODS OF SCALING. In: WU, J., JONES, K.B., LI, H., LOUCKS, O.L. (eds) SCALING AND UNCERTAINTY ANALYSIS IN ECOLOGY. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4663-4_2

Download citation

Publish with us

Policies and ethics