B. B. Cael, David Seekell

Kleiber’s ¾-scaling Law for metabolism with mass is one of the most striking regularities in the biological sciences. We demonstrate that whole-lake primary production scales to the ¾-power of lake volume, consistent with Kleiber’s Law but not explicable by analogy to theories developed for individual organisms. Instead, dimensional analysis offers a simple explanation. Because Earth's topography is self-affine and whole-lake primary production scales isometrically with lake area after accounting for latitudinal gradients in temperature and insolation, sub-linear scaling for primary production by volume emerges; the ¾ scaling exponent derives from global-scale differences between vertical and horizontal scaling of topography. From these patterns we make novel inferences about lakes' global annual productivity, photosynthetic efficiency, trophic structure, and role in the carbon cycle. More generally, our study suggests there are multiple paths to realizing ¾-scaling of metabolism rather than a single unifying law, at least when comparing across levels of biological organization.