allometry

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Allometry is the study of the relationship between size and shape,^[1] first outlined by Otto Snell in 1892^[2] and Julian Huxley in 1932.^[3] Allometry is a well-known study, particularly in statistical shape analysis for its theoretical developments, as well as in biology for practical applications to the differential growth rates of the parts of a living organism's body. One application is in the study of various insect species (e.g., the Hercules Beetle), where a small change in overall body size can lead to an enormous and disproportionate increase in the dimensions of appendages such as legs, antennae, or horns.

Allometry studies shape differences in terms of ratios of the objects' dimensions. Two objects of different size but common shape will have their dimensions in the same ratio. Take, for example, a biological object that grows as it matures. Its size changes with age but the shapes are similar. Studies of ontogenetic allometry often use lizards or snakes as model organisms because they lack parental care after birth or hatching and because they exhibit a large range of body size between the juvenile and adult stage. Lizards often exhibit allometric changes during their ontogeny.^[4]

Isometric scaling and geometric similarity

Isometric scaling occurs when changes in size (during growth or over evolutionary time) do not lead to changes in proportion. An example is found in frogs - aside from a brief period during the few weeks after metamorphosis, frogs grow isometrically.^[5] Therefore, a frog whose legs are as long as its body will retain that relationship throughout its life, even if the frog itself increases in size tremendously.

Isometric scaling is governed by the square-cube law. An organism which doubles in length isometrically will find that the surface area available to it will increase fourfold, while its volume and mass will increase by a factor of eight. This can present problems for organisms. In the case of above, the animal now has eight times the biologically active tissue to support, but the surface area of its respiratory organs has only increased fourfold, creating a mismatch between scaling and physical demands. Similarly, the organism in the above example now has eight times the mass to support on its legs, but the strength of its bones and muscles is dependent upon their surface area, which has only increased fourfold. Therefore, this hypothetical organism would experience twice the bone and muscle loads of its smaller version. This mismatch can be avoided either by being "overbuilt" when small or by changing proportions during growth, called allometry.

Isometric scaling is often used as a null hypothesis in scaling studies, with 'deviations from isometry' considered evidence of physiological factors forcing allometric growth.

Allometric scaling

Allometric scaling is any growth with deviates from isometry. A classic example is the skeleton of mammals, which becomes much more robust and massive relative to the size of the body as the body size increases. Allometry is often expressed in terms of a scaling exponent based on mass. An isometrically scaling organism would see all volume-based properties change with mass to the first power, all surface area-based properties change with mass to the 2/3 power, and all length-based properties change with mass to the 1/3 power. If, for example, a volume-based property was found to scale to mass to the 0.9 power, this would be called "negative allometry", as the values are smaller than predicted by isometry. Conversely, if a surface area based property scales to mass to the 0.8 power, the values are higher than predicted by isometry and the organism is said to show "positive allometry".

Physiological scaling

Many biochemical processes (such as the respiration rate, or the maximum reproduction rate) show scaling, mostly associated with the ratio between surface area and mass in the animal. Overall metabolic rate in animals is generally accepted to show negative allometry, scaling to mass to a power 0.75, known as Kleiber's law.

For inter-species parameters related to ecological variables such as maximal reproduction rate, attempts have been made to explain scaling within the context of dynamic energy budget theory. However, such ideas have been less successful.

See also

• Allometric law
• Constructal theory
• Evolutionary physiology
• Metabolic theory of ecology
• Phylogenetic comparative methods
• Power law (also known as a scaling law)

References

Further reading

• Calder, W. A. (1984). Size, function and life history. Cambridge, Mass.: Harvard University Press. ISBN 0674810708. 
• McMahon, T. A. and J. T. Bonner (1983). On Size and Life. New York: Scientific American Library. ISBN 0716750007. 
• Niklas, K. J. (1994). Plant allometry: The scaling of form and process. Chicago: University of Chicago Press. ISBN 0226580814. 
• Peters, R. H. (1983). The ecological implications of body size. Cambridge: Cambridge University Press. ISBN 052128886X. 
• Reiss, M. J. (1989). The allometry of growth and reproduction. Cambridge: Cambridge University Press. ISBN 0521423589. 
• Schmidt-Nielsen, K. (1984). Scaling: why is animal size so important?. Cambridge: Cambridge University Press. ISBN 0521319870. 
• Samaras, Thomas T. (2007). Human body size and the laws of scaling: physiological, performance, growth, longevity and ecological ramifications. Nova Publishers. ISBN 1600214088.  book entry at Google Book Search

External links

• FDA Guidance for Estimating Human Equivalent Dose (For "first in human" clinical trials of new drugs)