RESEARCH ARTICLE Flipper bone distribution reveals flexible trailing edge in underwater flying marine tetrapods Mark C. DeBlois | Ryosuke Motani Department of Earth and Planetary Sciences, University of California, Davis, California Correspondence Email: mcdeblois@ucdavis.edu Funding information University of California, Davis Abstract 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 experimen- tal 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 signifi- cantly 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. KEYWORDS flexible trailing edge, flipper functional morphology, secondarily marine tetrapods 1 | INTRODUCTION The invasion of marine environments by tetrapods occurred repeat- edly in many different lineages resulting in convergent morphology and two general swimming modes: axial swimming, in which thrust is produced predominantly by undulations or oscillations of the body axis (including the tail, tailfin, or fluke); and paraxial swimming, in which thrust is produced predominantly by oscillations of modified limbs (Bannasch, 1994; Kelley & Pyenson, 2015; Lighthill, 1969; Vermeij & Motani, 2018; Vogel, 1994). Modified limbs could be Received: 12 November 2018 Revised: 6 March 2019 Accepted: 26 March 2019 DOI: 10.1002/jmor.20992 Journal of Morphology. 2019;1–17. wileyonlinelibrary.com/journal/jmor © 2019 Wiley Periodicals, Inc. 1