Allometric law

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.

Examples

Some examples of allometric laws:
* Kleiber's law, the proportionality between metabolic rate q_{0} 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 V_{opt} of flying bodies (insects, birds, airplanes) and body mass M in "kg" raised to the power 1/6:: V_{opt} sim 30 cdot M^{frac 1 6} m cdot s^{-1}

ee also

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

References

* 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


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