Allometry is the study of the relationship of body size to
shape,
anatomy,
physiology and finally behaviour, first outlined by Otto Snell in 1892,
D'Arcy Thompson in 1917 in
On Growth and Form and
Julian Huxley in 1932. 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. The relationship between the two measured quantities is often expressed as a
power law:
or in a logarithmic form: ![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=1634)
where
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=3017)
is the
scaling exponent of the law. Methods for estimating this exponent from data use type 2 regressions such as major axis regression or reduced major axis regression as these account for the variation in both variables, contrary to
least squares regression, which does not account for error variance in the independent variable (e.g., log body mass). Other methods include
measurement error models and a particular kind of principal component analysis.