Content area
Full Text
J Comp Physiol B (2009) 179:175182 DOI 10.1007/s00360-008-0300-x
ORIGINAL PAPER
A comparison of methods for tting allometric equations to eld metabolic rates of animals
Gary C. Packard Thomas J. Boardman
Received: 28 May 2008 / Revised: 30 July 2008 / Accepted: 1 September 2008 / Published online: 17 September 2008 Springer-Verlag 2008
Abstract We re-examined data for eld metabolic rates of varanid lizards and marsupial mammals to illustrate how different procedures for tting the allometric equation can lead to very different estimates for the allometric coefcient and exponent. A two-parameter power function was obtained in each case by the traditional method of back-transformation from a straight line tted to logarithms of the data. Another two-parameter power function was then generated for each data-set by non-linear regression on values in the original arithmetic scale. Allometric equations obtained by non-linear regression described the metabolic rates of all animals in the samples. Equations estimated by back-transformation from logarithms, on the other hand, described the metabolic rates of small species but not large ones. Thus, allometric equations estimated in the traditional way for eld metabolic rates of varanids and marsupials do not have general importance because they do not characterize rates for species spanning the full range in body size. Logarithmic transformation of predictor and response variables creates new distributions that may enable investigators to perform statistical analyses in compliance with assumptions underlying the tests. However, statistical models tted to transformations should not be used to estimate parameters of equations in the arithmetic domain because such equations may be seriously
biased and misleading. Allometric analyses should be performed on values expressed in the original scale, if possible, because this is the scale of interest.
Keywords Allometry Body size Field metabolic rates
Power functions Scaling
Introduction
The mathematical expression underlying the typical allo-metric analysis is the two-parameter power function
Y aXb 1
where Y is a measure of the character of interest and X is a measure of body size (Calder 1984; LaBarbera 1989; Peters 1983; Schmidt-Nielsen 1984). The parameters a and b are known more generally as the allometric coefcient and allometric exponent, respectively. Most investigators, however, choose to work with logarithmic transformations of the original data (LaBarbera 1989; Manaster and Manaster 1975; Smith 1984; Zar 1968), so the...