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8 - Body size and scale invariance: multifractals in invertebrate communities

Published online by Cambridge University Press:  02 December 2009

By
Peter E. Schmid  and
Jenny M. Schmid-Araya
Edited by
Alan G. Hildrew ,
David G. Raffaelli  and
Ronni Edmonds-Brown
Peter E. Schmid
Affiliation:
Queen Mary University of London; University of Vienna
Jenny M. Schmid-Araya
Affiliation:
Queen Mary University of London
Alan G. Hildrew
Affiliation:
Queen Mary University of London
David G. Raffaelli
Affiliation:
University of York
Ronni Edmonds-Brown
Affiliation:
University of Hertfordshire
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Summary

Introduction

As ecologists seek conceptual syntheses to understand the mechanistic and functional processes that underlie empirical community patterns in different ecosystems, they are developing concepts that depict complexity on a number of universal themes. General patterns in the statistical distributions of species and individuals within and across ecosystems provide information about the organizing principles underlying ecosystem structure. Interrelations between species richness, population density, body-size and distribution ranges are of central concern in ecology and have been widely debated (Brown, 1995; Brown, Allen & Gillooly, this volume). To represent the structure of ecosystems adequately, species composition and population size are the most appropriate attributes containing information that is closely correlated with the organism's size.

Attributes of body size may affect many ecological characteristics, such as resource use and allocation in communities, reflecting their complex internal structure. Feeding patterns that result in resource partitioning among species of a benthic species assemblage demonstrate strong body-size dependence (Schmid & Schmid-Araya, 1997; Woodward & Warren, this volume). Information on species population and body-size distribution (BSD) of communities is frequently given for the larger or is toxonomically not well resolved, organisms inhabiting an ecosystem, therefore resulting in veiled, often highly scattered and incomplete, distributions. In contrast, the size distribution of well-resolved species communities may reflect the different evolutionary traits underlying diverse scaling domains. Therefore, more realistic expectations for real-world species and abundance distributions are obtained using scale-dependent definitions of individual species' spatial and/or size structure within communities.

Type
Chapter
Information
Body Size: The Structure and Function of Aquatic Ecosystems , pp. 140 - 166
Publisher: Cambridge University Press
Print publication year: 2007

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References

Ankersmid, B. V. (2002). Particle size of certified standards using the time-of-transition method. Ankersmid Application Note, 1.1, 1.Google Scholar
Bittelli, M., Campbell, G. S. & Flury, M. (1999). Characterization of particle-size distribution in soils with a fragmentation model. Soil Science Society America Journal, 63, 782–788.CrossRefGoogle Scholar
Borda-de-Áqua, L., Hubbell, S. P. & McAllister, M. (2002). Species-area curves, diversity indices, and species abundance distributions: a multifractal analysis. The American Naturalist, 159, 138–155.Google Scholar
Brown, J. H. (1995). Macroecology. Chicago: University of Chicago Press.Google Scholar
Brown, J. H. & West, G. B. (2000). Scaling in Biology. Santa Fe Institute Studies in the Science of Complexity. Oxford: Oxford University Press.Google Scholar
Brown, J. H., Gupta, V. K., Li, B.-L.et al. (2002). The fractal nature of nature: power laws, ecological complexity and biodiversity. Philosophical Transactions of the Royal Society London B, 357, 619–626.CrossRefGoogle ScholarPubMed
Brown, J. H., Gillooly, J. F., Allan, A. P., Savage, V. M. & West, G. B. (2004). Towards a metabolic theory of ecology. Ecology, 85, 1771–1789.CrossRefGoogle Scholar
Calder, W. A. III (1996). Size, Function, and Life History. Mineola, New York: Dover Publications, Inc.Google Scholar
Chhabra, A. & Jensen, R. V. (1989). Direct determination of the f(α) singularity spectrum. Physical Review Letters, 62, 1327–1330.CrossRefGoogle Scholar
Bartolo, S. D., Gabriele, S. & Gaudio, R. (2000). Multifractal behaviour of river networks. Hydrology and Earth System Sciences, 4, 105–112.CrossRefGoogle Scholar
Dodds, P. S., Rothman, D. H. & Weitz, J. S. (2001). Re-examination of the ‘3/4 law’ of metabolism. Journal of Theoretical Biology, 209, 9–27.CrossRefGoogle Scholar
Dornelas, M., Connolly, S. R. & Hughes, T. P. (2006). Coral reef diversity refutes the neutral theory of biodiversity. Nature, 440, 80–82.CrossRefGoogle ScholarPubMed
Drake, J. B. & Weishampel, J. F. (2000). Multifractal analysis of canopy height measures in a longleaf pine savanna. Forest Ecology and Management, 128, 121–127.CrossRefGoogle Scholar
Enquist, B. J. & Niklas, K. J. (2001). Invariant sclaing relations across tree-dominated communities. Nature, 410, 655–660.CrossRefGoogle ScholarPubMed
Etienne, R. S. (2005). A new sampling formula for neutral biodiversity. Ecology Letters, 8, 253–260.CrossRefGoogle Scholar
Evertsz, C. J. G. & Mandelbrot, B. B. (1992). Multifractal measures. In Chaos and Fractals. New Frontiers of Science, ed. Peitgen, H., Jürgens, H. and Saupe, D.. New York: Springer Verlag, pp. 921–953.CrossRefGoogle Scholar
Feder, H. (1988). Fractals. New York: Plenum Press.CrossRefGoogle Scholar
Fesl, C. (2002). Niche-oriented species-abundance models: different approaches of their application to larval chironomid (Diptera) assemblages in a large river. Journal of Animal Ecology, 71, 1085–1094.CrossRefGoogle Scholar
Finlay, B. J. (2002). Global dispersal of free-living microbial eukaryote species. Science, 296, 1061–1063.CrossRefGoogle ScholarPubMed
Gisiger, T. (2001). Scale invariance in biology: coincidence or footprint of a universal mechanism? Biological Review, 76, 161–209.CrossRefGoogle ScholarPubMed
Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I. & Shraiman, B. I. (1986). Fractal measures and their singularities: the characterization of strange sets. Physical Review A, 33, 1141–1151.CrossRefGoogle ScholarPubMed
Harte, J., Kinzig, A. & Green, J. (1999). Self-similarity in the distribution and abundance of species. Science, 284, 334–336.CrossRefGoogle ScholarPubMed
Hentschel, H. & Procaccia, I. (1983). The infinite number of generalized dimensions of fractal and strange attractors. Physica D, 8, 435–444.CrossRefGoogle Scholar
Hubbell, S. P. (2001). A Unified Neutral Theory of Biodiversity and Biogeography. Princeton, NJ: Princeton University Press.Google Scholar
Jeffries, M. (1993). Invertebrate colonization of artificial pond weeds of differing fractal dimension. Oikos, 67, 142–148.CrossRefGoogle Scholar
Johnson, G. D., Tempelman, A. & Patil, G. P. (1995). Fractal based methods in ecology: a review for analysis at multiple spatial scales. Coenosis, 10, 123–131.Google Scholar
Keylock, C. J. (2005). Simpson diversity and the Shannon-Wiener index as special cases of a generalized entropy. Oikos, 101, 205–207.Google Scholar
Kolmogorov, A. N. (1959). Entropy per unit time as a metric invariant of automorphisms. Mathemathical Review, 21, 2035.Google Scholar
Kravchenko, A. N., Boast, C. W. & Bullock, D. G. (1999). Multifractal analysis of soil spatial variability. Agronomy Journal, 91, 1033–1041.CrossRefGoogle Scholar
Kropp, J., von Bloh, W., Block, A., Klenke, Th. & Schellnhuber, H.-J. (1994). Characteristic multifractal element distributions in recent bioactive marine sediments. In Fractals and Dynamic Systems in Geosciences, ed. Kruhl, J. H.. Berlin: Springer, pp. 369–375.CrossRefGoogle Scholar
Kunin, W. E. (1998). Extrapolating species abundance across spatial scales. Science, 281, 1513–1515.CrossRefGoogle ScholarPubMed
Lennon, J. J., Kunin, W. E. & Hartley, S. (2002). Fractal species distributions do not produce power-law species-area relationships. Oikos, 97, 378–386.CrossRefGoogle Scholar
Mandelbrot, B. B. (1974). Intermittent turbulence in self similar cascades: divergence of high moments and dimension of the carrier. Journal of Fluid Mechanics, 62, 331–358.CrossRefGoogle Scholar
Mandelbrot, B. B. (1989). Multifractal measures, especially for the geophysicist. Pure Applied Geophysics, 131, 5–42.CrossRefGoogle Scholar
Manrubia, S. C. & Solé, R. V. (1996). Self-organized criticality in rainforest dynamics. Chaos, Solutions and Fractals, 7, 523–541.CrossRefGoogle Scholar
Margalef, R. (1996). Information and uncertainty in living systems, a view from ecology. BioSystems, 38, 141–146.CrossRefGoogle ScholarPubMed
Margalef, R. (1997). Our Biosphere, ed. Kinne, O.. Oldendorf/Luhe, Germany: Ecology Institute.Google Scholar
Marquet, P. A., Quiñones, R. A., Abades, S.et al. (2005). Scaling and power-laws in ecological systems. The Journal of Experimental Biology, 208, 1749–1769.CrossRefGoogle ScholarPubMed
McGill, B. J. (2003). A test of the unified neutral theory of biodiversity. Nature, 422, 881–884.CrossRefGoogle ScholarPubMed
Milne, B. T. (1998). Motivation and beliefs of complex system approaches in ecology. Ecosystems, 1, 449–456.CrossRefGoogle Scholar
Nee, S., Read, A. F., Greenwood, J. J. D. & Harvey, P. H. (1991). The relationship between abundance and body size in British birds. Nature, 351, 312–313.CrossRefGoogle Scholar
Pascual, M., Ascioti, F. A. & Caswell, H. (1995). Intermittency in the plankton: a multifractal analysis of zooplankton biomass variability. Journal of Plankton Research, 17, 1209–1232.CrossRefGoogle Scholar
Peters, R. H. (1983). The Ecological Implications of Body Size. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Posadas, A. N. D., Giménez, D., Bittelli, M., Vaz, C. M. P. & Flury, M. (2001). Multifractal characterization of soil particle-size distributions. Soil Science Society America Journal, 65, 1361–1367.CrossRefGoogle Scholar
Rényi, A. (1955). On a new axiomatic theory of probability. Acta Mathematica Hungarica, 6, 285–335.CrossRefGoogle Scholar
Rodriguez-Iturbe, I. & Rinaldo, A. (2001). Fractal River Basins. Chance and Self-Organisation. Cambridge, UK: Cambridge University Press.Google Scholar
Rosenzweig, M. L. (1995). Species Diversity in Space and Time. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Schmid, P. E. (1997). Stochasticity in resource utilization by a larval Chironomidae (Diptera) community in the bed sediments of a gravel stream. In Groundwater/Surfacewater Ecotones: Biological and Hydrological Interactions and Management Options, ed. Gilbert, J., Mathieu, J. & Fournier, F.. Cambridge: Cambridge University Press, pp. 21–29.CrossRefGoogle Scholar
Schmid, P. E. (2000). The fractal properties of habitat and patch structure in benthic ecosystems. Advances in Ecological Research, 30, 339–401.CrossRefGoogle Scholar
Schmid, P. E. & Schmid-Araya, J. M. (1997). Predation on meiobenthic assemblages: resource use of a tanypod guild (Chironomidae, Diptera) in a gravel stream. Freshwater Biology, 38, 67–91.CrossRefGoogle Scholar
Schmid, P. E. & Schmid-Araya, J. M. (2002). Trophic relationships in temporary and permanent freshwater meiofauna. In Freshwater Meiofauna: Biology and Ecology, ed. Rundle, S. D., Robertson, A. L. and Schmid-Araya, J. M.. Leiden, The Netherlands: Backhuys Publisher, pp. 295–319.Google Scholar
Schmid, P. E., Tokeshi, M. & Schmid-Araya, J. M. (2000). Relation between population density and body size in stream communities. Science, 289, 1557–1560.CrossRefGoogle ScholarPubMed
Schmid, P. E., Tokeshi, M. & Schmid-Araya, J. M. (2002). Scaling in stream communities. Proceedings of the Royal Society London B, 269, 2587–2594.CrossRefGoogle ScholarPubMed
Schmitt, F. G. & Seuront, L. (2001). Multifractal random walk in copepod behavior. Physica A, 301, 375–396.CrossRefGoogle Scholar
Schroeder, M. (1991). Fractals, Chaos, Power Laws. Minutes from an Infinite Paradise. New York: W. H. Freeman and Company.Google Scholar
Sugihara, G. (1980). Minimal community structure: an explanation of species abundance patterns. The American Naturalist, 116, 770–787.CrossRefGoogle ScholarPubMed
Stanley, H. E., Amaral, L. A. N., Gopikrishnan, P.et al. (2000). Scale invariance and universality: organising principles in complex systems. Physica A, 281, 60–68.CrossRefGoogle Scholar
Taniguchi, H. & Tokeshi, M. (2004). Effects of habitat complexity on benthic assemblages in a variable environment. Freshwater Biology, 49, 1164–1178.CrossRefGoogle Scholar
Tokeshi, M (1993). Species abundance patterns and community structure. Advances in Ecological Research, 24, 111–186.CrossRefGoogle Scholar
Tokeshi, M. (1996). Power fraction: a new explanation of relative abundance patterns in species-rich assemblages. Oikos, 75, 543–550.CrossRefGoogle Scholar
Tokeshi, M. (1999). Species Coexistence. Ecological and Evolutionary Perspectives. Oxford: Blackwell Science.Google Scholar
Turcotte, D. L. (1986). Fractals and fragmentation. Journal of Geophysical Research, 91, 1921–1926.CrossRefGoogle Scholar
West, G. B., Brown, J. H. & Enquist, B. J. (1999). The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science, 284, 1677–1679.CrossRefGoogle ScholarPubMed

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