Commentary: Glazier, D. Multiphasic allometry: the reality and significance of ontogenetic shifts in the body-mass scaling of metabolic rate. Acad. Biol. 2024, 2, 7411 - Gary C. Packard (Academia Biology)
A recent article in this journal presented a new analysis of ontogenetic variation in metabolic rate vs. body mass in tobacco hornworms (Manduca sexta) as part of an overall defense of the concept of polyphasic, loglinear allometry. The analysis applied a method that is widely used in contemporary studies of allometric variation: transform the original measurements for body mass and metabolic rate to logarithms, fit straight lines to observations for larval instars 3, 4, and 5, and then compare slopes for the several lines. The slope for the line describing observations for third-instar larvae was greater than slopes for the other two lines, thereby pointing to polyphasic, loglinear allometry. However, fitting a straight line to logarithmic transformations is merely the first step in a procedure for estimating parameters in a two-parameter power function describing variation on the untransformed scale, so the analysis is incomplete until that power function is validated analytically and graphically in the arithmetic domain. I repeated and extended the analysis to illustrate the conceptual and analytical problems associated with a reliance on logarithmic transformations in allometric research. Further analysis by linear and nonlinear regression revealed that untransformed data for metabolic rate vs. body mass are well described by a single power equation that characterizes variation for all three instars as well as the combined distribution. The perception that metabolic allometry in larval hornworms is polyphasic and loglinear is based on incomplete analysis of logarithmic transformations.