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Measuring Ecosystem Patterns and Processes through Fractals
Changes in ecosystems are highly complex, heterogeneous and are extremely difficult to measure through single scale. Fractal geometry has been used to quantitatively estimate the extent of irregularity in ecosystem changes. However, in some cases it has been overly used giving misleading results. To avoid this, other metrics are also being used in studying changes in forest ecosystems. In this article, we review use of fractal geometry in measuring ecosystem components in a range of ecological conditions. Further, case studies from forest fragmentation and soil aggregates stability in different Indian tropical ecosystems with respect to management practices and environmental change have been described using fractal dimension. We have tried to point out some instances where fractals can more appropriately be used in assessing ecosystems properties and where it could not be successfully used. Characterization of ecological situations where fractals can effectively be used in general remains an important issue.
Keywords
Ecosystem Complexity, Ecosystem Patterns, Fractal Dimension, Landscape Change, Soil Processes.
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- Pianka, E. R., Evolutionary Ecology, Harper and Row, New York, 1998.
- Levin, S. A., The problem of pattern and scale in ecology. Ecology, 1992, 73, 1943–1967.
- Jiang, B., The fractal nature of maps and mapping. Int. J. Geogra. Inf. Sci., 2015, 29, 159–174.
- Rahbek, C. and Graves, G. R., Multiscale assessment of patterns of avian species richness. Proc. Natl. Acad. Sci. USA, 2001, 98, 4534–4539.
- Johnson, M. P., Frost, N. J., Mosley, M. W. J., Roberts, M. F. and Hawkins, S. J., The area-independent effects of habitat complexity on biodiversity vary between regions. Ecol. Lett., 2003, 6, 126–132.
- Kelaher, B. P., Changes in habitat complexity negatively affect diverse gastropod assemblages in coralline algal turf. Oecologia, 2003, 135, 431–441.
- Leon, J. X., Roelfsema, C. M., Saunders, M. I. and Phinn, S. R., Measuring coral reef terrain roughness using ‘Structure-fromMotion’ close range photogrammetry. Geomorphology, 2015, 242, 21–28.
- Kostylev, V. E., Erlandsson, J., Ming, M. Y. and Williams, G. A., The relative importance of habitat complexity and surface area in assessing biodiversity: Fractal application on rocky shores. Ecol. Complex., 2005, 2, 272–286.
- Mandelbrot, B. B., How long is the coastline of Britain? Statistical self-similarity and fractional dimension. Science, 1967, 156, 636– 638.
- Sugihara, G. and May, R. M., Applications of fractals in ecology. Trends Ecol. Evol., 1990, 5, 79–86.
- Halley, J. M., Hartley, S., Kallimanis, A. S., Kunin, W. E., Lennon, J. J. and Sgardelis, S. P., Uses and abuses of fractal methodology in ecology. Ecol. Lett., 2004, 7, 254–271.
- Tripathi, S. K., Kushwaha, C. P. and Basu, S. K., Application of fractal theory in assessing soil aggregates in Indian tropical ecosystems. J. For. Res., 2012, 23, 355–364.
- Mandelbrot, B. B., The Fractal Geometry of Nature, Freeman, San Francisco, 1992.
- Schroeder, M., Fractals, Chaos, Power Laws. Minutes from an Infinite Paradise, Freeman, New York, 1991.
- Kenkel, N. C. and Walker, D. J., Fractals in biological sciences. Coenoses, 1996, 11, 77–100.
- Jelinek, H. F. and Fernandez, E., Neurons and fractals: how reliable and useful are calculations of fractal dimensions? J. Neurosci. Methods, 1998, 81, 9–18.
- Murray, J. D., Mathematical Biology, Springer, New York, 2002.
- Williamson, M. H. and Lawton, J. H., Measuring habitat structure with fractal geometry. In Habitat Structure: the Physical Arrangement of Objects in Space (eds Bell, S., McCoy, E. D. and Mushinsky, H. R.), Chapman and Hall, London, 1991, pp. 69–86.
- Kenkel, N. C. and Walker, D. J., Fractals and ecology. Abst. Bot., 1993, 17, 53–70.
- Morse, D. R., Lawton, J. H., Dodson, M. M. and Williamson, M. H., Fractal dimension of vegetation and the distribution of arthropod body lengths. Nature, 1985, 314, 731–733.
- Basnou, C., Iguzquiza, J. and Pino, J., Examining the role of landscape structure and dynamics in alien plant invasion from urban Mediterranean coastal habitats. Landsc. Urban Planning, 2015, 136, 156–164.
- Schmid, P. E., Fractal properties of habitat and patch structure in benthic ecosystems. Adv. Ecol. Res., 2000, 30, 339–401.
- Gee, J. M. and Warwick, R. M., Body-size distribution in a marine metazoan community and the fractal dimensions of macroalgae. J. Exp. Mar. Biol. Ecol., 1994, 178, 247–259.
- Gee, J. M. and Warwick, R. M., Metazoan community structure in relation to the fractal dimensions of marine macroalgae. Mar. Ecol. Prog. Ser., 1994, 103, 141–150.
- Saunders, M. I. et al., Interdependency of tropical marine ecosystems in response to climate change. Nat. Clim. Change, 2014, 4, 724–729.
- Kostylev, V., Erlandsson, J. and Johannesson, K., Microdistribution of the polymorphic snail Littorina saxatilis (Olivi) in a patchy rocky shore habitat. Ophelia, 1997, 47, 1–12.
- Li, B. L., Fractal dimensions. In Encyclopedia of Environmetrics, vol. 2 (eds El-Shaarawi, A. H. and Piegorsch, W. W.), John Wiley & Sons Ltd., Chichester, 2002, pp. 821–825.
- Krummel, J. R., Gardner, R. H., Sugihara, G., O’Neill, R. V. and Colman, P. R., Landscape patterns in a distributed environment. Oikos, 1987, 48, 321–324.
- Lam, S. N. S., Description and measurement of Landsat TM images using fractals, Photogram. Eng. Remote Sens., 1990, 56, 187–195.
- Meltzer, M. I. and Hastings, H. M., The use of fractals to assess the ecological impact of increased cattle population: case study from the Runde Communal Land, Zimbabwe. J. Appl. Ecol., 1992, 29, 635–646.
- Lam, S. N. S. and Quattrochi, D. A., On the issues of scale, resolution and fractal analysis in the mapping sciences. Prof. Geogr., 1992, 44, 88–98.
- O’Neill, R. V., Hunsaker, R. V., Timmins, S. P. and Jackson, B. L., Scale problems in reporting landscape patterns at the regional scale. Landsc. Ecol., 1996, 11, 169–180.
- De Cola, L., Fractal analysis of classified Landsat scene. Photogram. Eng. Remote Sens., 1989, 55, 601–610.
- Frohn, R. C., Remote Sensing for Landscape Ecology, Lewis Publishers, New York, 1997.
- Cox, L. B. and Wang, J. S. Y., Fractal surfaces: measurement and application in the earth sciences. Fractals, 1993, 1, 87–115.
- Bradbury, R. H., Reichelt, R. E. and Green, D. G., Fractals in ecology: methods and interpretation. Mar. Ecol. Prog. Ser., 1984, 14, 295–296.
- LeTourneux, F. and Bourget, B. E., Importance of physical and biological settlement cues used at different spatial scales by the larvae of Semibalanus balanoides. Mar. Biol., 1988, 97, 57– 66.
- Erlandsson, J., Kostylev, V. and Williams, G. A., A field technique for estimating the influence of surface complexity on movement tortuosity in the tropical limpet Cellana grata Gould. Ophelia, 1999, 50, 215–224.
- Commito, J. A. and Rusignuolo, B. R., Structural complexity in mussel beds: the fractal geometry of surface topography. J. Exp. Mar. Biol. Ecol., 2000, 255, 133–152.
- Voss, R. F., Fractals in nature: from characterization to simulation. In The Science of Fractal Images (eds Peitgen, H.-O. and Saupe, D.), Springer, New York, 1988, pp. 21–70.
- Falconer, K., Fractal Geometry: Mathematical Foundations and Applications, J. Wiley and Sons, New York, 1990.
- Tricot, C., Curves and Fractal Dimension, Springer-Verlag, New York, 1991.
- Hastings, H. M. and Sugihara, G., Fractals: A User’s Guide for the Natural Sciences, Oxford University Press, Oxford, 1993.
- Frontier, S., Applications of fractal theory to ecology. In Developments in Numerical Ecology (eds Legendre, P. and Legendre, L.), Springer, Berlin, 1987, pp. 335–378.
- Young, I. M. and Crawford, J. W., The fractal structure of soil aggregates: its measurements and interpretation. J. Soil Sci., 1991, 42, 187–192.
- Milne, B. T., Measuring the fractal geometry of landscapes. Appl. Math. Comp., 1988, 27, 67–79.
- Jiang, B. and Junjun, Y., H-index for quantifying the fractal or scaling structures of geographic features. Ann. Assoc. Am. Geogr., 2014, 104, 530–540.
- Klinkenberg, B., A review of methods used to determine the fractal dimension of linear features. Math. Geol., 1993, 25, 1003–1026.
- Nonnenmacher, T. F., Losa, G. A. and Weibel, E. R., Fractals in Biology and Medicine, Birkhäuser, Cambridge, 1994.
- Lorimer, N. D., Haight, R. G. and Leary, R. A., The fractal forest: fractal geometry and applications in forest science. US Department of Agriculture, Forest Service. North Central Forest Experimental Station, General Technical Report NC-170, 1994, p. 43.
- Johnson, G. D., Tempelm, A. and Patil, G. P., Fractal based methods in ecology: a review for analysis at multiple spatial scales. Coenoses, 1995, 10, 123–131.
- Normant, F. and Tricot, C., Methods for evaluating the fractal dimension of curves using convex hulls. Phys. Rev. A, 1991, 43, 6518–6525.
- Longley, P. A. and Batty, M., On the fractal measurement of geographical boundaries. Geogr. Anal., 1989, 21, 47–67.
- Peitgen, H.-O., Jürgensand, H. and Saupe, D., Fractals for the Classroom, Springer, New York, 1992.
- Appleby, S., Multifractal characterization of the distribution pattern of the human population. Geogr. Anal., 1996, 28, 147–160.
- Tatsumi, J., Yamauchi, A. and Kono, Y., Fractal analysis of plant ischolar_main systems. Ann. Bot., 1989, 64, 499–503.
- Zeide, B. and Gresham, C. A., Fractal dimensions of tree crowns in three loblolly pine plantations of coastal South Carolina. Can. J. For. Res., 1991, 21, 1208–1212.
- Sarcinelli, T. S., Schaefer, C. E. G. R., Fernandes, E. I., Mafia, R. G. and Neri, A. V., Soil vegetation in the Brazilian Atlantic rain forest. J. Trop. Ecol., 2013, 29, 439–448.
- Huang, J. and Turcotte, D. L., Fractal mapping of digitized images: application to the topography of Arizona and comparisons with synthetic images. J. Geophys. Res., 1989, 94, 7491–7495.
- Shorrocks, B., Marsters, J., Ward, I. and Evennett, P. J., The fractal dimension of lichens and the distribution of arthropod body lengths. Funct. Ecol., 1991, 5, 457–460.
- Gunnarsson, B., Fractal dimension of plants and body size distribution in spiders. Funct. Ecol., 1992, 6, 636–641.
- Burrough, P. A., Principles of Geographical Systems for Land Resources Assessment, Clarendon, Oxford, 1986.
- Milne, B., The utility of fractal geometry in landscape design. Landsc. Urban Planning, 1991, 21, 81–90.
- Olsen, E. R., Ramsey, R. D. and Winn, D. S., A modified fractal dimension as a measure of landscape diversity. Photogram. Eng. Remote Sens., 1993, 59, 1517–1520.
- Kemper, W. D. and Rosenau, R. C., Aggregate stability and size distribution. In Methods of Soil Analysis (ed. Klute, A.), Part I. Physical and Mineralogical Methods, Soil Science of America Agronomy Monograph No. 9, 1986, pp. 425–442.
- Kushwaha, C. P., Tripathi, S. K. and Singh, K. P., Soil organic matter and water stable aggregates under different tillage and residue conditions in a tropical dryland agroecosystem. Appl. Soil Ecol., 2001, 16, 229–241.
- Pirmoradian, N., Sepashkhah, A. R. and Hajabbasi, M. A., Application of fractal theory to quantify soil aggregates as influenced by tillage treatments. Biosyst. Eng., 2005, 2, 227–234.
- Singh, S. and Singh, J. S., Microbial biomass associated with water-stable aggregates in forest, savanna and cropland soils of seasonally dry tropical region, India. Soil Biol. Biochem., 1995, 27, 1027–1033.
- Tripathi, S. K., Kushwaha, C. P. and Singh, K. P., Tropical forest and savanna ecosystems show differential impact of N and P additions on soil organic matter and aggregate structure. Global Change Biol., 2008, 14, 2572–2581.
- Martin, M. A., Pachepsky, Y. A. and Perfect, E., Scaling, fractals and diversity in soils and ecohydrology. Ecol. Modell., 2005, 182, 217–220.
- Perfect, E. and Kay, B. D., Fractal theory applied to soil aggregation. Soil Sci. Soc. Am. J., 1991, 55, 1552–1558.
- Milne, B. T., Spatial aggregation and neutral models in fractal landscapes. Am. Nat., 1992, 139, 32–57.
- Keller, J. M., Chen, S. and Crownover, R. M., Texture description and segmentation through fractal geometry. Comp. Vision Graph. Image Process., 1989, 45, 150–166.
- Hastings, H. M., Pekelney, R., Monticciolo, R., Vun Kannon, D. and Del Monte, D., Time scales, persistence and patchiness. Biosystematics, 1982, 15, 281–289.
- Hurst, H. E., Long-term storage capacity of reservoirs. Trans. Am. Soc. Civil Eng., 1951, 116, 770–808.
- Peters, E. E., Fractal Market Analysis. Applying Chaos Theory to Investment and Economics, John Wiley and Sons, New York, 1994.
- Xu, G. C., Li, Z. B. and Li, P., Fractal features of soil particle-size distribution and total soil nitrogen distribution in a typical watershed in the source area of the middle Dan River, China. Catena, 2013, 101, 17–23.
- Baldock, J. A. and Kay, B. D., Influence of cropping history and chemical treatments on the water stable aggregation of a silt loam soil. Can. J. Soil Sci., 1987, 67, 501–511.
- Turcotte, D. L., Fractals and fragmentation. J. Geophys. Res., 1986, 91, 1921–1926.
- Perfect, E., Rasiah, V. and Kay, B. D., Fractal dimension of soil aggregate-size distributions calculated by number and mass. Soil Sci. Soc. Am. J., 1992, 56, 1407–1409.
- Tyler, S. W. and Wheatcraft, S. W., Application of fractal mathematics to soil water retention estimation. Soil Sci. Soc. Am. J., 1989, 53, 987–996.
- Rasiah, V., Kay, B. D. and Perfect, E., Evaluation of selected factors influencing aggregate fragmentation using fractal theory. Can. J. Soil Sci., 1992, 72, 97–106.
- Rasiah, V., Kay, B. D. and Perfect, E., New mass-based model for estimating fractal dimension of soil aggregates. Soil Sci. Soc. Am. J., 1993, 57, 891–895.
- Tyler, S. W. and Wheatcraft, S. W., Fractal scaling of soil particle size distribution: Analysis and limitations. Soil Sci. Soc. Am. J., 1992, 56, 362–369.
- McBratney, A. B., Comments on ‘Fractal dimension of soil aggregate size distribution calculated by number and mass’. Soil Sci. Soc. Am. J., 1993, 57, 1393.
- Rasiah, V., Perfect, E. and Kay, B. D., Linear and nonlinear estimates of fractal dimension for soil aggregate fragmentation. Soil Sci. Soc. Am. J., 1995, 59, 83–87.
- Perfect, E. and Blevins, R. L., Fractal characterization of soil aggregation and fragmentation as influenced by tillage treatment. Soil Sci. Soc. Am. J., 1997, 61, 896–900.
- Pachepsky, Y. A., Gimenez, D. and Rawls, W. J., Bibliography on applications of fractals in soil science. In Fractals in Soil Science (eds Pachepsky, Y. A., Crawford, J. and Rawls, W.), Elsevier, New York, 2000, pp. 273–295.
- Mandelbrot, B. B., Passaja, D. E. and Paulley, A. T., Fractal character of fractal surfaces of metals. Nature, 1984, 308, 721–722.
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