9780521861724htl 1..2

(Jacob Rumans) #1
known as multifractal. Thus, through the examination of multifractal measures,
subtle differences in spatial and size structure can be explored. Fine-scale patterns
embedded within coarser patterns apparently reflect ecological processes operat-
ing across a wide size spectrum and spatial scales, such as the resource utilization
among invertebrate species in streams. The fact that multifractals can mirror
compound phenomena may prove increasingly useful in the characterization,
modelling and understanding of complex phenomena in ecology.

Acknowledgements
This work has been supported by grants from NERC (NER/A/S/2001/00566), the
Royal Society, and in parts from the Austrian Science Fund FWF: P15597-B03.
We thank Dr Luı ́s Borda-de-A ́gua and an anonymous reviewer for valuable com-
ments and suggestions on an early draft of this chapter.

References
Ankersmid, B. V. (2002). Particle size of certified
standards using the time-of-transition
method.Ankersmid Application Note,1.1,1.
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.
Borda-de-A ́qua, 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.
Brown, J. H. (1995).Macroecology. Chicago:
University of Chicago Press.
Brown, J. H. & West, G. B. (2000).Scaling in Biology.
Santa Fe Institute Studies in the Science of
Complexity. Oxford: Oxford University
Press.
Brown, J. H., Gupta, V. K., Li, B.-L.et al. (2002). The
fractal nature of nature: power laws, eco-
logical complexity and biodiversity.
Philosophical Transactions of the Royal Society
London B, 357 , 619–626.
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.

Calder, W. A. III (1996).Size, Function, and Life
History. Mineola, New York: Dover
Publications, Inc.
Chhabra, A. & Jensen, R. V. (1989). Direct deter-
mination of the f(a) singularity spectrum.
Physical Review Letters, 62 , 1327–1330.
De Bartolo, S. D., Gabriele, S. & Gaudio, R. (2000).
Multifractal behaviour of river networks.
Hydrology and Earth System Sciences, 4 , 105–112.
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.
Dornelas, M., Connolly, S. R. & Hughes, T. P. (2006).
Coral reef diversity refutes the neutral theory
of biodiversity.Nature, 440 , 80–82.
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.
Enquist, B. J. & Niklas, K. J. (2001). Invariant
sclaing relations across tree-dominated
communities.Nature, 410 , 655–660.
Etienne, R. S. (2005). A new sampling formula for
neutral biodiversity.Ecology Letters, 8 , 253–260.
Evertsz, C. J. G. & Mandelbrot, B. B. (1992).
Multifractal measures. InChaos and Fractals.
New Frontiers of Science, ed. H. Peitgen,

164 P.E. SCHMID AND J. M. SCHMID-ARAYA

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