Abstract
Use of scaling terminology and concepts in ecology evolved rapidly from rare occurrences in the early 1980s to a central idea by the early 1990s (Allen and Hoekstra 1992; Levin 1992; Peterson and Parker 1998). In landscape ecology, use of “scale” frequently connotes explicitly spatial considerations (Dungan et al. 2002), notably grain and extent. More generally though, scaling refers to the systematic change of some biological variable with time, space, mass, or energy. Schneider (2001) further specifies ecological scaling sensu Calder (1983) and Peters (1983) as “the use of power laws that scale a variable (e.g., respiration) to body size, usually according to a nonintegral exponent” while noting that this is one of many equally common technical definitions. He further notes that “the concept of scale is evolving from verbal expression to quantitative expression” (p. 545), and will continue to do so as mathematical theory matures along with quantitative methods for extrapolating across scales.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Wikipedia contributors, “Emergence,” Wikipedia, the Free Encyclopedia, http://en.wikipedia.org/wiki/Emergence. Accessed 25 Jan 2010.
References
Adamic, L.A., and B.A. Huberman. 2000. The nature of markets in the World Wide Web. Quarterly Journal of Electronic Commerce 1: 512.
Agee, J.K. 1993. Fire ecology of Pacific Northwest forests. Washington: Island Press.
Allen, T.F.H., and T.W. Hoekstra. 1992. Toward a unified ecology. New York: Columbia University Press.
Bak, P., C. Tang, and K. Wiesenfeld. 1988. Self-organized criticality. Physical Review A 38: 364–374.
Bak, P.C., K. Chen, and C. Tang. 1990. A forest-fire model and some thoughts on turbulence. Physics Letters A 147: 297–300.
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 B 357: 619–626.
Calder, W.A. 1983. Ecological scaling: mammals and birds. Annual Review of Ecology and Systematics 14: 213–230.
Carlson, J.M., and J. Doyle. 2002. Complexity and robustness. Proceedings of the National Academy of Sciences 99: 2538–2545.
Cello, G., and B.D. Malamud. eds. 2006. Fractal analysis for natural hazards. Special publication 261. London: Geological Society.
Clauset, A., C.R. Shalizi, and M.E.J. Newman. 2007. Power law distributions in empirical data. (http://arXiv:0706.1062v1).
Cohen, J.D., and J.E. Deeming. 1985. The national fire danger rating system: basic equations. General Technical Report PSW-82. Berkeley: Forest Service.
Collins, B.M., J.D. Miller, A.E. Thode, M. Kelly, J.W. van Wagtendonk, and S.L. Stephens. 2009. Interactions among wildland fires in a long-established Sierra Nevada natural fire area. Ecosystems 12: 114–128.
Cumming, S.G. 2001. A parametric model of the fire-size distribution. Canadian Journal of Forest Research 31: 1297–1303.
Diggle, P.J. 2003. Statistical analysis of spatial point patterns, 2nd ed. London: Arnold.
Doyle, J., and J.M. Carlson. 2000. Power laws, HOT, and generalized source coding. Physics Review Letters 84: 5656–5659.
Dungan, J.L., J.N. Perry, M.R.T. Dale, P. Legendre, S. Citron-Pousty, M.-J. Fortin, A. Jakomulska, M. Miriti, and M.S. Rosenberg. 2002. A balanced view of scale in spatial statistical analysis. Ecography 25: 626–640.
Evans, M., N. Hastings, and B. Peacock. 2000. Statistical distributions, 3rd ed. New York: Wiley.
Everett, R.L., R. Schelhaas, D. Keenum, D. Spubeck, and P. Ohlson. 2000. Fire history in the ponderosa pine/Douglas-fir forests on the east slope of the Washington Cascades. Forest Ecology and Management 129: 207–225.
Falk, D.A. 2004. Scale dependence of probability models for fire intervals in a ponderosa pine ecosystem. Ph.D. dissertation. Tucson: University of Arizona.
Falk, D.A., C. Miller, D. McKenzie, and A.E. Black. 2007. Cross-scale analysis of fire regimes. Ecosystems 10: 809–823.
Gardner, R.H., and D.L. Urban. 2007. Neutral models for testing landscape hypotheses. Landscape Ecology 22: 15–29.
Gwozdz, R., and D. McKenzie. (unpublished data) Effects of topography, humidity, and model parameters on the spatial structure of simulated fine-fuel moisture. Seattle: Pacific Wildland Fire Sciences Lab, U.S. Forest Service (manuscript on file with: Don McKenzie).
Habeeb, R.L., J. Trebilco, S. Witherspoon, and C.R. Johnson. 2005. Determining natural scales of ecological systems. Ecological Monographs 75: 467–487.
Hessburg, P.F., and J.K. Agee. 2005. Dry forests and wildland fires of the inland Northwest USA: contrasting the landscape ecology of the pre–settlement and modern eras. Forest Ecology and Management 211: 117–139.
Hessl, A.E., D. McKenzie, and R. Schellhaas. 2004. Drought and Pacific decadal oscillation linked to fire occurrence in the inland Pacific Northwest. Ecological Applications 14: 425–442.
Hessl, A.E., J. Miller, J. Kernan, and D. McKenzie. 2007. Mapping wildfire boundaries from binary point data: comparing approaches. Professional Geographer 59: 87–104.
Isaaks, E.H., and R.M. Srivastava. 1989. An introduction to applied geostatistics. New York: Oxford University Press.
Johnson, E.A., and S.L. Gutsell. 1994. Fire frequency models, methods, and interpretations. Advances in Ecological Research 25: 239–287.
Kellogg, L.-K.B., D. McKenzie, D.L. Peterson, and A.E. Hessl. 2008. Spatial models for inferring topographic controls on low-severity fire in the eastern Cascade Range of Washington, USA. Landscape Ecology 23: 227–240.
Kennedy, M.C., and D. McKenzie. 2010. Using a stochastic model and cross-scale analysis to evaluate controls on historical low-severity fire regimes. Landscape Ecology. doi:10.1007/s10980-010-9527-5.
Legendre, P., and L. Legendre. 1998. Numerical ecology, 2nd ed. Amsterdam: Elsevier Science B.V.
Levin, S.A. 1992. The problem of pattern and scale in ecology. Ecology 73: 1943–1967.
Levin, S.A. 2005. Self-organization and the emergence of complexity in ecological systems. Bioscience 55: 1075–1079.
Littell, J.S., D. McKenzie, D.L. Peterson, and A.L. Westerling. 2009. Climate and wildfire area burned in western U.S. ecoprovinces, 1916–2003. Ecological Applications 19: 1003–1021.
Loehle, C. 2004. Applying landscape principles to fire hazard reduction. Forest Ecology and Management 198: 261–267.
Malamud, B.D., G. Morein, and D.L. Turcotte. 1998. Forest fires: an example of self-organized critical behavior. Science 281: 1840–1842.
Malamud, B.D., Millington, J.D.A., and G.L.W. Perry. 2005. Characterizing wildfire regimes in the United States. Proceedings of the National Academy of Sciences, USA 102:4694–4699.
McKenzie, D. [N.d.]. Unpublished data. Seattle: Pacific Wildland Fire Sciences Lab (On file with: Don McKenzie).
McKenzie, D., D.L. Peterson, and E. Alvarado. 1996. Extrapolation problems in modeling fire effects at large spatial scales: a review. International Journal of Wildland Fire 6: 65–76.
McKenzie, D., D.L. Peterson, and J.K. Agee. 2000. Fire frequency in the Columbia River Basin: building regional models from fire history data. Ecological Applications 10: 1497–1516.
McKenzie, D., A.E. Hessl, and Lara-Karena B. Kellogg. 2006a. Using neutral models to identify constraints on low-severity fire regimes. Landscape Ecology 21: 139–152.
McKenzie, D., L-K.B. Kellogg, D.A. Falk, C. Miller, and A.E. Black. 2006b. Scaling laws and fire-size distributions in historical low-severity fire regimes. Geophysical Research Abstracts, 8: 1607–7962/gra/EGU06–A–01436.
Miller, J.R., M.G. Turner, E.A.H. Smithwick, C.L. Dent, and E.H. Stanley. 2004. Spatial extrapolation: the science of predicting ecological patterns and processes. Bioscience 54: 310–320.
Millington, J.D.A., G.L.W. Perry, and B.D. Malamud. 2006. Models, data, and mechanisms: quantifying wildfire regimes. In Fractal analysis for natural hazards, eds. G. Cello, and B.D. Malamud, 155–167. Special Publication 261. London: Geological Society.
Milne, B.T. 1998. Motivation and benefits of complex systems approaches in ecology. Ecosystems 1: 449–456.
Minnich, R.A. 1983. Fire mosaics in southern California and northern Baja California. Science 219: 1287–1294.
Moritz, M.A. 2003. Spatio-temporal analysis of controls of shrubland fire regimes: age dependency and fire hazard. Ecology 84: 351–361.
Moritz, M.A., M.E. Morais, L.A. Summerell, J.M. Carlson, and J. Doyle. 2005. Wildfires, complexity, and highly optimized tolerance. Proceedings of the National Academy of Sciences 102: 17912–17917.
National Geophysical Data Center. 2010. NGDC: natural hazards databases at NGDC. http://www.ngdc.noaa.gov/hazard/hazards.shtml. Accessed 25 Jan 2010.
NOAA. 2010. International multiproxy paleofire database. http://www.ncdc.noaa.gov/paleo/impd/paleofire.html. Accessed 25 Jan 2010.
Newman, M.E.J. 2005. Power laws, Pareto distributions, and Zipf’s law. Contemporary Physics 46: 323–351.
O’Neill, R.V., D.L. deAngelis, J.B. Waide, and T.F.H. Allen. 1986. A hierarchical concept of ecosystems. Princeton: Princeton University Press.
Parody, J.M., and B.T. Milne. 2004. Implications of rescaling rules for multi-scaled habitat models. Landscape Ecology 19: 691–701.
Pascual, M., and F. Guichard. 2005. Criticality and disturbance in spatial ecological systems. Trends in Ecology & Evolution 20: 88–95.
Peters, R.H. 1983. The ecological implications of body size. Cambridge: Cambridge University Press.
Peterson, G.D. 2002. Contagious disturbance, ecological memory, and the emergence of landscape pattern. Ecosystems 5: 329–338.
Peterson, D.L., and V.T. Parker, eds. 1998. Ecological scale: theory and applications. New York: Columbia University Press.
R Foundation. 2003. The R Project for statistical computing. http://www.r-project.org. Accessed 25 Jan 2010.
Rastetter, E.B., A.W. King, B.J. Cosby, G.M. Hornberger, R.V. O’Neill, and J.E. Hobbie. 1992. Aggregating finescale ecological knowledge to model coarser scale attributes of ecosystems. Ecological Applications 2: 55–70.
Redner, S. 1998. How popular is your paper? An empirical study of the citation distribution. The European Physical Journal B 4: 131–134.
Reed, W.J. 2001. The Pareto, Zipf, and other power laws. Economics Letters 74: 15–19.
Reed, W.J. 2006. A note on fire frequency concepts and definitions. Canadian Journal of Forest Research 36: 1884–1888.
Reed, W.J., and E.A. Johnson. 2004. Statistical methods for estimating historical fire frequency from multiple fire-scar data. Canadian Journal of Forest Research 34: 2306–2313.
Reed, W.J., and K.S. McKelvey. 2002. Power-law behaviour and parametric models for the size distribution of forest fires. Ecological Modelling 150: 239–254.
Ricotta, C. 2003. Fractal size distributions of wildfires in hierarchical landscapes: Natura facit saltus? Comments on Theoretical Biology 8: 93–101.
Roberts, D.C., and D.L. Turcotte. 1998. Fractality and self-organized criticality of wars. Fractals 6: 351–357.
Rossi, R.E., D.J. Mulla, A.G. Journel, and E.H. Franz. 1992. Geostatistical tools for modeling and interpreting spatial dependence. Ecological Monographs 62: 277–314.
Scanlon, T.M., K.K. Caylor, S.A. Levin, and I. Rodriguez-Iturbe. 2007. Positive feedbacks promote power-law clustering of Kalahari vegetation. Nature 449: 209–213.
Schneider, D.C. 2001. The rise of the concept of scale in ecology. Bioscience 51: 545–553.
Simard, A.J. 1991. Fire severity, changing scales, and how things hang together. International Journal of Wildland Fire 1: 23–34.
Sole, R. 2007. Scaling laws in the drier. Nature 447: 151–152.
Solow, A.R. 2005. Power laws without complexity. Ecology Letters 8: 361–363.
Song, W., F. Weicheng, W. Binghong, and Z. Jianjun. 2001. Self-organized criticality of forest fire in China. Ecological Modelling 145: 61–68.
Stauffer, D., and A. Aharony. 1994. Introduction to percolation theory, 2nd ed. London: Taylor and Francis.
Turcotte, D.L., B.D. Malamud, F. Guzzetti, and P. Reichenbach. 2002. Self-organization, the cascade model, and natural hazards. Proceedings of the National Academy of Sciences 99: 2530–2537.
Turner, M.G., and W.H. Romme. 1994. Landscape dynamics in crown fire ecosystems. Landscape Ecology 9: 59–77.
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.
West, G.B., J.H. Brown, and B.J. Enquist. 1999. A general model for the structure of plant vascular systems. Nature 400: 664–667.
West, G.B., W.H. Woodruff, and J.H. Brown. 2002. Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals. Proceedings of the National Academy of Sciences 99: 2473–2478.
White, E.P., B.J. Enquist, and J.L. Green. 2008. On estimating the exponent of power-law frequency distributions. Ecology 89: 905–912.
Wu, J. 1999. Hierarchy and scaling: extrapolating information along a scaling ladder. Canadian Journal of Remote Sensing 25: 367–380.
Zipf, G.K. 1949. Human behavior and the principle of least effort: an introduction to human ecology. Reading: Addison-Wesley.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
McKenzie, D., Kennedy, M.C. (2011). Scaling Laws and Complexity in Fire Regimes. In: McKenzie, D., Miller, C., Falk, D. (eds) The Landscape Ecology of Fire. Ecological Studies, vol 213. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0301-8_2
Download citation
DOI: https://doi.org/10.1007/978-94-007-0301-8_2
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0300-1
Online ISBN: 978-94-007-0301-8
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)