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Multiplicative by nature: Logarithmic transformation in allometry
Author(s) -
Packard Gary C.
Publication year - 2014
Publication title -
journal of experimental zoology part b: molecular and developmental evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.823
H-Index - 63
eISSN - 1552-5015
pISSN - 1552-5007
DOI - 10.1002/jez.b.22570
Subject(s) - allometry , multiplicative function , logarithm , mathematics , bivariate data , heteroscedasticity , bivariate analysis , statistics , transformation (genetics) , power function , ecology , mathematical analysis , biology , gene , biochemistry
The traditional allometric method, which is at the heart of research paradigms used by comparative biologists around the world, entails fitting a straight line to logarithmic transformations of the original bivariate data and then back‐transforming the resulting equation to form a two‐parameter power function in the arithmetic scale. The method has the dual advantages of enabling investigators to fit statistical models that describe multiplicative growth while simultaneously addressing the multiplicative nature of residual variation in response variables (heteroscedasticity). However, important assumptions of the traditional method seldom are assessed in contemporary practice. When the assumptions are not met, mean functions may fail to capture the dominant pattern in the original data and incorrect form for error may be imposed upon the fitted model. A worked example from metabolic allometry in doves and pigeons illustrates both the power of newer statistical procedures and limitations of the traditional allometric method. J. Exp. Zool. (Mol. Dev. Evol.) 322B: 202–207, 2014 . © 2014 Wiley Periodicals, Inc.