2002
DOI: 10.2307/3078974
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Species-Area Curves, Diversity Indices, and Species Abundance Distributions: A Multifractal Analysis

Abstract: Although fractals have been applied in ecology for some time, multifractals have, in contrast, received little attention. In this article, we apply multifractals to the species-area relationship and species abundance distributions. We highlight two results: first, species abundance distributions collected at different spatial scales may collapse into a single curve after appropriate renormalization, and second, the power-law form of the species-area relationship and the Shannon, Simpson, and Berger-Parker dive… Show more

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Cited by 9 publications
(14 citation statements)
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“…One of the most popular approaches for multifractal analysis is the conjunction of the moment method with so-called boxcounting algorithm (Borda-de-Á gua et al, 2002). The method consists of two steps: dividing the object of study (i.e.…”
Section: Multifractal Analysismentioning
confidence: 99%
See 1 more Smart Citation
“…One of the most popular approaches for multifractal analysis is the conjunction of the moment method with so-called boxcounting algorithm (Borda-de-Á gua et al, 2002). The method consists of two steps: dividing the object of study (i.e.…”
Section: Multifractal Analysismentioning
confidence: 99%
“…For q ) 1, regions with a high degree of concentration are amplified, while regions with a small degree of concentration are magnified for q ( À1. However, as recognized by many researchers (Feeny, 2000;Borda-de-Á gua et al, 2002;Lopes and Betrouni, 2009), the empirical density function associated to the q-order moment is very noisy at the distribution tails, due to the lack of enough sampling. So the D q values are only reliable for small q (i.e.…”
Section: Multifractal Analysismentioning
confidence: 99%
“…Both the Shannon index and Fractal analyses have been widely used in ecology to understand spatial complexity (Pielou 1966;Frontier 1987;Krummel et al 1987;Brooks and Wiley 1988;Palmer 1988;Cohen et al 1990;Milne 1992;Loehle and Wein 1994;Li 2000;Alados et al 2003). In addition, the Shannon index and the Fractal Dimension are closely related (Farmer et al 1983;Borda-de-Agua et al 2002;Alados et al 2003). Scaling relationships and fractals provide a powerful analytical framework for simplifying ecological complexity and understanding its dynamic (Brown et al 2002).…”
Section: Introductionmentioning
confidence: 98%
“…The spectrum of generalized dimensions or Rényi spectrum (Grassberger, 1985) generalizes the notion of entropy dimension by introducing entropies of order q. This spectrum summarizes a number of commonly used diversity indexes by the exponent of their scaling behaviors (Borda-de-Agua et al, 2002). This paper focuses primarily on two main questions related to pedodiversity at the planetary scale when complexity and environmental heterogeneity (of earth soil systems) are understood as a by-product of deterministic chaotic dynamics.…”
Section: Introductionmentioning
confidence: 99%
“…In order to characterize fractal objects and strange sets of nonlinear physics, multifractal theory was elaborated under the ideas of thermodynamical formalism (Frisch and Parisi, 1985;Halsey et al, 1986). Multifractal structures have been described for very different fields as DLA patterns investigation (Mandelbrot and Everstz, 1991), earthquake distribution analysis (Hirata and Imoto, 1991), signal processing (Lévy Véhel and Mignot, 1994), internet data traffic modeling (Lévy Véhel and Riedi, 1997), characterization of mineral deposits (Cheng et al, 1994), analysis of vegetation patterns (Scheuring and Riedi, 1994;Borda-de-Agua et al, 2002) zooplankton biomass time series (Pascual et al, 1995), soil porosity and particle size distributions (Caniego et al, 2001;Martín and Montero, 2002) and soil spatial variability (Kravchenko et al, 1999;Caniego et al, 2005).…”
Section: Introductionmentioning
confidence: 99%