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