How does lake primary production scale with lake size? - Cael, B. B.; Seekell, David A. (Frontiers in Environmental Science, 2023)
Kleiber’s 3/4-scaling Law for metabolism with mass is one of the most striking regularities in the biological sciences. Kleiber's Law has been shown to apply not only to individual organisms, but also to communities and even whole-ecosystem properties such as the productivity of estuaries. Might Kleiber's Law also then apply to lake ecosystems? Here we show that for a collection of whole-lake primary production measurements, production scales to the 3/4-power of lake volume, consistent with Kleiber’s Law. However, this relationship is not explicable by analogy to theories developed for individual organisms. Instead, we argue that dimensional analysis offers a simple explanation. After accounting for latitudinal gradients in temperature and insolation, whole-lake primary production scales isometrically with lake area. Because the Earth's topography is self-affine, meaning there are global-scale differences between vertical and horizontal scaling of topography, lake volume scales super-linearly with lake surface area. 3/4-scaling for primary production by volume then results from these other two scaling relationships. The identified relationship between primary production and temperature-and-insolation-adjusted area may be useful for constraining lakes' global annual productivity and photosynthetic efficiency. More generally, this suggests there are multiple paths to realizing 3/4-scaling of metabolism rather than a single unifying law, at least when comparing across levels of biological organization.