A comparison of methods for fitting allometric equations to field metabolic rates of animals.
We re-examined data for field metabolic rates of varanid lizards and marsupial mammals to illustrate how different procedures for fitting the allometric equation can lead to very different estimates for the allometric coefficient and exponent. A two-parameter power function was obtained in each case by the traditional method of back-transformation from a straight line fitted 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 field 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 fitted 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.
Packard
Gary C
GC
Department of Biology, Colorado State University, Fort Collins, CO 80523-1878, USA. Packard@lamar.colostate.edu
Boardman
Thomas J
TJ
D000818:Animals; D003625:Data Collection; D003627:Data Interpretation, Statistical; D004734:Energy Metabolism / Q000502:physiology*; D008116:Lizards; D008394:Marsupialia; D008954:Models, Biological; D012044:Regression Analysis
J Exp Biol. 2005 May;208(Pt 9):1611-9
15855392
Annu Rev Nutr. 1999;19:247-77
10448524
Am J Physiol. 1984 Feb;246(2 Pt 2):R152-60
6696141
J Exp Biol. 2005 May;208(Pt 9):1575-92
15855389
Physiol Biochem Zool. 2008 Jul-Aug;81(4):496-507
18513152
J Theor Biol. 2007 Nov 7;249(1):168-77
17720203
J Exp Biol. 2005 May;208(Pt 9):1621-5
15855393
Physiol Biochem Zool. 2006 May-Jun;79(3):665-74
16691531
J Morphol. 1975 Nov;147(3):299-307
1185789