Supplementary Methods: Hydrodynamic Modeling from Physical trade-offs shape the evolution of buoyancy control in sharks

Buoyancy control is a fundamental aspect of aquatic life that has major implications for locomotor performance and ecological niche. Unlike terrestrial animals, the densities of aquatic animals are similar to the supporting fluid, thus even small changes in body density may have profound effects on locomotion. Here, we analysed the body composition (lipid versus lean tissue) of 32 shark species to study the evolution of buoyancy. Our comparative phylogenetic analyses indicate that although lean tissue displays minor positive allometry, liver volume exhibits pronounced positive allometry, suggesting that larger sharks evolved bulkier body compositions by adding lipid tissue to lean tissue rather than substituting lean for lipid tissue, particularly in the liver. We revealed a continuum of buoyancy control strategies that ranged from more buoyant sharks with larger livers in deeper ecosystems to relatively denser sharks with small livers in epipelagic habitats. Across this eco-morphological spectrum, our hydrodynamic modelling suggests that neutral buoyancy yields lower drag and more efficient steady swimming, whereas negative buoyancy may be more efficient during accelerated movements. The evolution of buoyancy control in sharks suggests that ecological and physiological factors mediate the selective pressures acting on these traits along two major gradients, body size and habitat depth.