Flipper bone distribution reveals flexible trailing edge in underwater flying marine tetrapods

Hydrofoil-shaped limbs (flipper-hydrofoils) have evolved independently several times in secondarily marine tetrapods and generally fall into two functional categories: (1) those that produce the majority of thrust during locomotion (propulsive flipper-hydrofoils); (2) those used primarily to steer and resist destabilizing movements such as yaw, pitch, and roll (controller flipper-hydrofoils). The morphological differences between these two types have been poorly understood. Theoretical and experimental studies on engineered hydrofoils suggest that flapping hydrofoils with a flexible trailing edge are more efficient at producing thrust whereas hydrofoils used in steering and stabilization benefit from a more rigid one. To investigate whether the trailing edge is generally more flexible in propulsive flipper-hydrofoils, we compared the bone distribution along the chord in both flipper types. The propulsive flipper-hydrofoil group consists of the forelimbs of Chelonioidea, Spheniscidae, and Otariidae. The controller flipper-hydrofoil group consists of the forelimbs of Cetacea. We quantified bone distribution from radiographs of species representing more than 50% of all extant genera for each clade. Our results show that the proportion of bone in both groups is similar along the leading edge (0-40% of the chord) but is significantly less along the trailing edge for propulsive flipper-hydrofoils (40-80% of the chord). Both flipper-hydrofoil types have little to no bony tissue along the very edge of the trailing edge (80-100% of the chord). This suggests a relatively flexible trailing edge for propulsive flipper-hydrofoils compared to controller flipper-hydrofoils in line with findings from prior studies. This study presents a morphological correlate for inferring flipper-hydrofoil function in extinct taxa and highlights the importance of a flexible trailing edge in the evolution of propulsive flipper-hydrofoils in marine tetrapods.