Scaling laws relating body mass to species characteristics are among the most universal quantitative patterns in biology. Within major taxonomic groups, the 4 key ecological variables of metabolism, abundance, growth, and mortality are often well described by power laws with exponents near 3/4 or related to that value, a commonality often attributed to biophysical constraints on metabolism. However, metabolic scaling theories remain widely debated, and the links among the 4 variables have never been formally tested across the full domain of eukaryote life, to which prevailing theory applies. Here we present datasets of unprecedented scope to examine these 4 scaling laws across all eukaryotes and link them to test whether their combinations support theoretical expectations. We find that metabolism and abundance scale with body size in a remarkably reciprocal fashion, with exponents near ±3/4 within groups, as expected from metabolic theory, but with exponents near ±1 across all groups. This reciprocal scaling supports "energetic equivalence" across eukaryotes, which hypothesizes that the partitioning of energy in space across species does not vary significantly with body size. In contrast, growth and mortality rates scale similarly both within and across groups, with exponents of ±1/4. These findings are inconsistent with a metabolic basis for growth and mortality scaling across eukaryotes. We propose that rather than limiting growth, metabolism adjusts to the needs of growth within major groups, and that growth dynamics may offer a viable theoretical basis to biological scaling.

Center for Theoretical Study Charles University and the Academy of Sciences of the Czech Republic 110 00 Praha Czech Republic Department of Ecology Faculty of Science Charles University 128 44 Praha Czech Republic

Centre for Biodiversity Theory and Modelling Theoretical and Experimental Ecology Station CNRS 09200 Moulis France

Department of Ecology and Evolutionary Biology Princeton University Princeton NJ 08544

Department of Ecology and Evolutionary Biology Princeton University Princeton NJ 08544 Santa Fe Institute Santa Fe NM 87501

ICREA Universitat Autonoma de Barcelona 08193 Barcelona Spain Department of Earth and Planetary Sciences McGill University Montreal QC H3A 0G4 Canada

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