On the Significance of the Constant b in the Law of Allometry y = bxa

• Published in: The American naturalist 1942-07, Vol.76 (765), p.364-375
• Main Authors: Lumer, H., Anderson, B. G., Hersh, A. H.
• Format: Article
• Language: English
• Subjects: Allometry; Approximation; Body size; Coefficients; Coordinate systems; Correlation coefficients; Data ranges; Mathematical constants; Skull; Wolves
• ISSN: 0003-0147; 1537-5323

The constants b and a of the law of allometry frequently are found to be inversely related for a given set of relative growth curves, which means that the curves in question intersect approximately at a common point. Since the numerical value of b depends on the units of measurement employed, the relationship between the constants can be arbitrarily varied (by selecting suitable units), so as to vary from inverse to direct, or vice versa, for the same set of data. It is shown further that the existence of a relationship between b and a in many cases arises simply from the requirement, made by the data, that the relative growth curves pass through a restricted area, coupled with a choice of units which places the value of b some distance outside this area. In addition, where b lies considerably beyond the range of the data, comparisons of this constant for different curves may be misleading. These obscuring arbitrary factors can best be ruled out by expressing b in terms of a unit given by the data, such as the size of a standard part at a particular developmental stage, or at least in terms of a unit which places b within the lower limit of the range.