Scaling metabolic rate with body mass and inverse body temperature: a test of the Arrhenius fractal supply model


*Correspondence author. E-mail:


  • 1How body mass and body temperature influence metabolic rate has been of interest for decades. Today that interest can be seen in the form of debates over the proper scaling coefficients, and the mechanistic underpinnings of allometric models for metabolic rate in relation to body mass and body temperature. We tested explicit assumptions built into what we term the Arrhenius fractal supply (AFS) model of these relationships. This model, and its assumptions, is foundational to the controversial Metabolic Theory of Ecology.
  • 2In addition to predicting that the scaling exponent for body mass is 3/4, the AFS model originally predicted that metabolic responses to body temperature, measured as activation energies, should fall between 0·2 and 1·2 eV. More recently, the latter range was narrowed to 0·6 and 0·7 eV.
  • 3To test the AFS's predictions, we used multiple regression of ln(metabolic rate) as a function of ln(body mass) and 1/(body temperature) to fit the best scaling exponent for body mass to nine data sets of many diverse species.
  • 4For the majority of the data sets, in addition to not supporting a scaling exponent of 3/4, the analyses indicated that effects of body temperature sometimes fell outside the range of 0·6–0·7 eV, indicating that the predictions of the AFS model do not hold universally.
  • 5Effects of body temperature, however, did fall within the range of 0·2–1·2 eV. To aid interpretation of these results, we transformed activation energies into Q10s. At ecologically realistic temperatures, the values of Q10 that approximate activation energies of 0·2–1·2 eV ranged from c. 1·4 to 6·1 (where 6·1 is clearly unreasonably high). Hence, any model that predicts activation energies between 0·2 and 1·2 eV does not appear to be an informative scaling model at the organismal level.
  • 6The AFS model is foundational for the Metabolic Theory of Ecology. While we commend the attempt to incorporate scaling of metabolism into ecological theory, and the research it has inspired, we caution against using untested, and likely incorrect, assumptions as a foundation to a general theory of ecology. We recommend that scientists allow the data to determine the best model for incorporating energetics into ecological theory.