Species-area curves, diversity indices, and species abundance distributions: a multifractal analysis

The American Naturalist
Luís Borda-de-AguaMurdoch McAllister

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 diversity indices belong to a family of equations relating the species number, species abundance, and area through the moments of the species abundance-probability density function. Explicit formulas for these diversity indices, as a function of area, are derived. Methods to obtain the multifractal spectra from a data set are discussed, and an example is shown with data on tree and shrub species collected in a 50-ha plot on Barro Colorado Island, Panama. Finally, we discuss the implications of the multifractal formalism to the relationship between species range and abundance and the relation between the shape of the species abundance distribution and area.

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Citations

Apr 4, 2012·PloS One·Leonardo Ariel SaraviaFernando Momo
Nov 6, 2014·Doklady Biological Sciences : Proceedings of the Academy of Sciences of the USSR, Biological Sciences Sections·B N YakimovD B Gelashvili
Nov 5, 2013·Journal of Theoretical Biology·Basil N YakimovDavid B Gelashvili
Dec 9, 2009·Mathematical Biosciences·Petr KůrkaJames Rosindell
May 13, 2006·The Journal of Animal Ecology·Kevin J GastonClara Gaspar
Mar 27, 2010·Ecology Letters·Brian J McGill
Sep 28, 2005·Mathematical Biosciences·Alfonso Garmendia, Adela Salvador
May 5, 2012·FEMS Microbiology Letters·Peter E LarsenJack A Gilbert
Feb 24, 2009·Brazilian Journal of Biology = Revista Brasleira De Biologia·F C Ferreira, M Petrere
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Mar 9, 2004·Proceedings. Biological Sciences·Stephen HartleyMichael J O Pocock
Feb 28, 2015·Ontogenez·V N IakimovD B Gelashvili
Jul 31, 2013·The International Journal of Biostatistics·Abbas Golestani, Robin Gras

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