A new perspective on the static metabolic allometry of carabid beetles

Abstract

The conventional allometric method entails fitting a straight line to logarithmic transformations of the original bivariate data and then back‐transforming the resulting equation (at least implicitly) to form a two‐parameter power function, Y = a × Xb, on the arithmetic scale. Although the protocol is widely used in contemporary research, it commonly performs poorly and thereby leads investigators to form inaccurate impressions of the dominant pattern in their data. Here I re‐examine the metabolic allometry for six species of carabid beetle to illustrate the problem that arises when pattern in the original data can be described by two (or more) statistically equivalent equations with different functional form. Whereas conventional analyses of data for the beetles yielded only a single descriptive model for each dataset (i.e., the two‐parameter power equation), the more versatile protocol used here fitted two to four statistically equivalent equations (including the two‐parameter power function) to the same sets of observations. Conclusions based on just the power equation estimated by conventional allometry would be misleading because the equation does not afford a unique description for pattern in the data.

Biological scaling analyses are more than statistical line fitting

“…et al, 2018) have not used the traditional method 'uncritically' or by 'rote', as claimed by some (e.g. Smith, 1980;Lovett and Felder, 1989;Packard, 2013Packard, , 2017Packard, , 2020a. Packard (2017, p. 116) also states without evidence or adequate justification that proponents of the traditional method have used 'ill-defined arguments' and 'misunderstanding of various statistical methods', merely to protect 'a large body of published research'.…”

“…Some or all of the several practical and theoretical advantages of using logarithms are ignored or dismissed without adequate justification by critics of the traditional method (e.g. Lovett and Felder, 1989;Packard, 2017Packard, , 2020aGeraert, 2016;Chen et al, 2020). Two widely recognized, statistically important advantages (among others) include normalizing data with multiplicative error (or heteroscedastic variation) and unequal body mass spacing (though it is also possible to incorporate multiplicative error into non-linear analyses based on arithmetic data: e.g.…”