The geometry of life: testing the scaling of whole-organism surface area and volume using sharks.

The ratio of surface area to volume is a key biological parameter that underpins our understanding of physiology across all levels of biological organization. Surfaces control the rate of key reactions and processes operating within the body and between organisms and their environment. Our understanding of surface area to volume ratios is embedded in the 2/3 scaling law, stating that surface area scales with volume raised to a power of 0.66. However, most empirical studies of surface area and volume scaling in animals focus on individual cells or tissues. Comparatively few studies have addressed these scaling relationships among species or ontogenetic stages at the whole-organism level. This study uncovers quantitative support for the 2/3 scaling law in an interspecific dataset at the whole-organism level. We find that the scaling of surface area to volume across 54 shark species (exhibiting an approx. 19 000-fold variation in body mass) is nearly identical to the isometric prediction of the 2/3 scaling law. There is no evidence that this relationship is driven by ecological or physiological characteristics. One plausible explanation is the presence of developmental constraints on tissue allocation that could influence the range of possible surface areas or volumes at any given body size.