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Theoretical Ecology

, Volume 2, Issue 2, pp 89–103 | Cite as

Invariance in species-abundance distributions

  • Arnošt L. ŠizlingEmail author
  • David Storch
  • Jiří Reif
  • Kevin J. Gaston
Original paper

Abstract

Many attempts to explain the species-abundance distribution (SAD) assume that it has a universal functional form which applies to most assemblages. However, if such a form does exist, then it has to be invariant under changes in the area of the study plot (the addition of neighboring areas or subdivision of the original area) and changes in taxonomic composition (the addition of sister taxa or subdivision to subtaxa). We developed a theory for such an area-and-taxon invariant SAD and derived a formula for such a distribution. Both the log-normal and our area-and-taxon invariant distribution fitted data well. However, the log-normal distributions of two adjoined sub-assemblages cannot be composed into a log-normal distribution for the resulting assemblage, and the SAD composed from two log-normal distributions fits the SAD for the assemblage poorly in comparison to the area-and-taxon invariant distribution. Observed abundance patterns therefore reveal area-and-taxon invariant properties absent in log-normal distributions, suggesting that multiplicative models generating log-normal-like SADs (including the power-fraction model) cannot be universally valid, as they necessarily apply only to particular scales and taxa.

Keywords

Scale invariance Area invariance Taxon invariance Population sizes Frequency distributions Relative abundances 

Notes

Acknowledgement

We thank J. Mourková and J. Cepák for their help with the fieldwork. We are grateful to M. Williamson, J. Nekola, B. J. McGill, F. He and anonymous referees for their comments. A.L.Š. was supported by the Marie Curie Fellowship no. 039576-RTBP-EIF. K.J.G. holds a Royal Society-Wolfson Research Merit Award. This work was supported by grants from the Czech Ministry of Education No. LC06073 and MSM0021620845, and Grant agency of the AS CR (IAA601970801).

Supplementary material

12080_2008_31_MOESM1_ESM.doc (2.2 mb)
ESM 1 (DOC 2.18 MB)

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Arnošt L. Šizling
    • 1
    • 2
    Email author
  • David Storch
    • 2
    • 3
  • Jiří Reif
    • 3
  • Kevin J. Gaston
    • 1
  1. 1.Biodiversity and Macroecology Group, Department of Animal and Plant SciencesUniversity of SheffieldSheffieldUK
  2. 2.Center for Theoretical StudyCharles University in Prague and the Academy of Sciences of the Czech RepublicPraha 1Czech Republic
  3. 3.Department of Ecology, Faculty of ScienceCharles UniversityPraha 2Czech Republic

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