My watch list  

Allometric law

An allometric law describes the relationship between two attributes of living organisms, and is usually expressed as a power-law:

y \propto x^{a} \,\! or in a logarithmic form: \log y \sim a \log x \,\!

where a is the scaling exponent of the law. Methods for estimating this exponent from data tend to involve a particular kind of principal component analysis.


 Some examples of allometric laws:

  • Kleiber's law, the proportionality between metabolic rate q0 and body mass M raised to the power 3 / 4:
q_{0} \sim M^{\frac 3 4}
  • the proportionality between breathing and heart beating times t and body mass M raised to the power 1 / 4:
t \sim M^{\frac 1 4}
  • mass transfer contact area A and body mass M:
A \sim M^{\frac 7 8}
  • the proportionality between the optimal cruising speed Vopt of flying bodies (insects, birds, airplanes) and body mass M in kg raised to the power 1 / 6:
V_{opt} \sim 30.M^{\frac 1 6} m.s^{-1}

See also

  • allometry
  • constructal law
  • power law
  • Rensch's rule
  • scaling law
  • square-cube law
  • Metabolic theory of ecology


  • A. Bejan, Shape and Structure, from Engineering to Nature, Cambridge University Press, Cambridge, UK, 2000. ISBN 0-521-79388-2
  • A. Bejan, Constructal theory of organization in nature: dendritic flows, allometric laws and flight, Design and Nature, CA Brebbia, L Sucharov & P Pascola (Editors). ISBN 1-85312-901-1
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Allometric_law". A list of authors is available in Wikipedia.
Your browser is not current. Microsoft Internet Explorer 6.0 does not support some functions on Chemie.DE