Invariance in species-abundance distributions

Arnošt L. Šizling, David Storch, Jiří Reif, Kevin J. Gaston

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)89-103
Number of pages15
JournalTheoretical Ecology
Issue number2
Publication statusPublished - 2009
Externally publishedYes


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

Cite this