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Testing the power law model for discrete size data.

Andrew R Solow1, Christopher J Costello, Michael Ward

  • 1Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA. asolow@whoi.edu

The American Naturalist
|November 18, 2003
PubMed
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Biological size data rarely follows a power law distribution. A new statistical test shows that for discrete biological size data, the power law is typically rejected, challenging common assumptions in scientific research.

Area of Science:

  • Ecology
  • Evolutionary Biology
  • Biostatistics

Background:

  • Power law distributions are frequently hypothesized for biological size data.
  • However, rigorous statistical validation for discrete biological datasets is often lacking.

Purpose of the Study:

  • To develop and apply a formal statistical test for power law distributions in discrete biological size data.
  • To evaluate the prevalence of power law distributions in empirical biological datasets.

Main Methods:

  • Developed a nonparametric statistical test embedding the power law within distributions where frequency decreases with size.
  • Utilized a parametric bootstrap approach to determine statistical significance.
  • Applied the test to four empirical datasets on the frequency of genera by size.

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Main Results:

  • The developed statistical test was applied to four biological size datasets.
  • The power law distribution was rejected in three out of the four tested datasets.
  • This indicates that power law models are not universally applicable to discrete biological size data.

Conclusions:

  • The common claim that biological size data follows a power law is often not supported by rigorous statistical testing.
  • The developed test provides a robust method for assessing power law adherence in discrete biological data.
  • Further research is needed to explore alternative distributions that better model biological size variation.