Allometric equations for predicting body mass of dinosaurs: a comment on Cawley & Janacek (2010)

‘In the statistics of today, transformations . . . [aid] in the analysis of data by bending the data nearer the Procrustean bed of the assumptions underlying conventional analyses’ (Tukey, 1957). This letter is in response to Cawley & Janacek (2010), who take exception with our critique of a widely used procedure for estimating bodymass of dinosaurs and other giant animals in extinct lineages (Packard, Boardman & Birchard, 2009). Although the mass of dinosaurs certainly was at issue in our critique, the article actually was a general indictment of the traditional method for estimating parameters in two-parameter allometric equations. Thus, in their challenge to our analysis, Cawley and Janacek essentially mount a defense for the traditional way of doing things (see also their reference to Kerkhoff & Enquist, 2009). This defense is flawed, however, by their failure to balance their excellent analysis of the assumptions (and shortcomings) of nonlinear regression with an equally thorough analysis of the assumptions (and shortcomings) of the traditional approach to allometric research. We focus our response on assumptions underlying the traditional approach because resolving the larger question about statistical modeling of allometric data is key to resolving disagreement concerning estimates for mass of dinosaurs. The allometric equation is widely assumed to take the form of a two-parameter power function