Modelling allometry: statistical and biological considerations – a reply to Packard

Abstract

Allometry studies describe how phenotypic traits increase relative to the increase of the size of the organism. Given that the increase in size of an organism is attributable to growth, a multiplicative process, allometric relationships are often analysed on a proportional scale (e.g. a log-log scale) to account for the multiplicative nature of the data. Nonetheless, the logarithmic transformation of the data when estimating allometric relationships has been the subject of debate. In a series of replies to various case studies of allometry, G. C. Packard has repeatedly criticized this approach under the premise that the logarithmic transformation of the data alters the estimate of the allometric exponent and obscures the biological meaning of the allometric parameters. Recently, Packard (2018) reanalysed data from our study on horn length allometry in bovids (Tidiere et al., 2017) and reached conclusions that contrasted with those reported in our original study. Echoing many authors before us, we argue here that logarithmic transformation of the data in allometric studies is justified by the expected distribution of the residual variation in ontogenetic, static and evolutionary allometry. We also point out that allometric slopes thus obtained have a direct biological interpretation in terms of elasticities. Finally, we show that Packard's criticism is based on qualitative and not quantitative assessment of the models fitted on different scales, and his conclusions disregard statistical and biological evidence supporting models fitted on a log-log scale. ADDITIONAL KEYWORDS: biological error-elasticity-fitness function-measurement error-scale.