From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature

William J. Reed and Barry D. Hughes
Phys. Rev. E 66, 067103 – Published 20 December 2002
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Abstract

We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law tails in the distributions of the sizes of incomes, cities, internet files, biological taxa, and in gene family and protein family frequencies.

  • Received 5 August 2002

DOI:https://doi.org/10.1103/PhysRevE.66.067103

©2002 American Physical Society

Authors & Affiliations

William J. Reed

  • Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4

Barry D. Hughes

  • Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia

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Vol. 66, Iss. 6 — December 2002

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