Re-examination of the "3/4-law" of Metabolism

Abstract

We examine the scaling law $B \propto M^α$ which connects organismal metabolic rate $B$ with organismal mass $M$, where $α$ is commonly held to be 3/4. Since simple dimensional analysis suggests $α=2/3$, we consider this to be a null hypothesis testable by empirical studies. We re-analyze data sets for mammals and birds compiled by Heusner, Bennett and Harvey, Bartels, Hemmingsen, Brody, and Kleiber, and find little evidence for rejecting $α=2/3$ in favor of $α=3/4$. For mammals, we find a possible breakdown in scaling for larger masses reflected in a systematic increase in $α$. We also review theoretical justifications of $α=3/4$ based on dimensional analysis, nutrient-supply networks, and four-dimensional biology. We find that present theories for $α=3/4$ require assumptions that render them unconvincing for rejecting the null hypothesis that $α=2/3$.