Allometric law

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

or in a logarithmic form:

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

allometric law of cruising speed vs body mass

Some examples of allometric laws:

• Kleiber's law, the proportionality between metabolic rate q₀ and body mass M raised to the power 3 / 4:

• the proportionality between breathing and heart beating times t and body mass M raised to the power 1 / 4:

• mass transfer contact area A and body mass M:

• 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:

See also

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

References

• A. Bejan (2000). Shape and Structure, from Engineering to Nature. Cambridge UK: Cambridge University Press. ISBN 0-521-79388-2. 
• A. Bejan (2002). "Constructal theory of organization in nature: dendritic flows, allometric laws and flight". in CA Brebbia, L Sucharov & P Pascola. International Conference on Design and Nature (1st : 2002 : Udine, Italy). Design and Nature: comparing design in nature with science and engineering. Southampton: WIT. ISBN 1-85312-901-1.