Our results show that intermittent locomotion, analogous to undulating flight, is found in a range of marine species, such as sharks and seals (Fig. 1; also see Kawabe et al.17).This high degree of similarity in the movement patterns of the different species is surprising considering their distinct evolutionary history and differing modes of propulsion; fur seals swim by pectoral propulsion, elephant seals use modified hind limbs as flippers and sharks propel themselves using a caudal fin. The intermittent locomotion observed was associated with changes in depth, thus resembling undulating flight described in birds (Fig. 1; Supplementary Movie 1).

Mechanical models have shown that modest to significant savings of metabolic power can be achieved by undulating flight in both air and water9,10,23. Most aquatic studies have focused on the metabolic savings that are achieved while animals are assisted by buoyancy13,14,15, thus losing potential energy that has to be repaid (but see Davis & Weihs16). Indeed, such studies have focused on locomotory adjustments to changing buoyant forces as pulmonary and fur associated air is compressed with increasing depth, resulting in less stroking and more gliding. In contrast, our study shows that intermittent locomotion is also an effective mode of locomotion when the net change in potential energy is zero, that is, no net change of depth (Figs 1 and 3) and buoyancy remains near constant, as the amplitude of individual undulations is too small to elicit a significant change in the volume of respiratory and fur-associated air.

As ODBA has been shown to correlate linearly with oxygen consumption in the exercising marine and terrestrial animals examined thus far19,20,22, our treatise demonstrates that muscular work is more pronounced in continuous locomotion than in intermittent locomotion. The kinematics of undulating flight vary according to travel speed and morphology in birds11 and we observed a similar relationship in our marine vertebrates (Table 2; Fig. 3). Indeed, similar to the elephant seal in this study (Fig. 3), birds performing undulating flight have been shown to increase duty factor with flight speed. It is thought that this modulation of duty factor permits birds to maintain relatively constant wing-beat kinematics resulting in maximum efficiency11, although it is still debated whether birds perform undulating flight because of kinematic and muscular constraints, rather than purely to save mechanical work10,11. It is therefore interesting that the elephant seal was able to satisfy mechanical power requirements for the same range of speeds using continuous and intermittent stroking, suggesting that intermittent locomotion primarily serves energy conservation in this species. However, the resultant saving is presumably a combination of efficiently converting muscular power into thrust, which relies on the interaction of an efficient muscle working stroke, coupled with limb kinematics that maximize the overall economy of converting fuel into forward locomotion.

Whereas the kinematics of individual undulations where relatively invariant in the pinnipeds, vertical movement during undulation in sharks displayed larger plasticity (Table 2). This variance was likely due to varying motivation of movement, given that large scale vertical movements serve both the purpose of travel and search in sharks23,24, which are characterized by different optima25. Indeed, the amplitude of individual undulations by sharks occurred over a wide vertical range (2–70 m, Fig. 1), whereas amplitudes were far more constrained in the two species of seal (Table 2). Despite the large variability in diving patterns of whale sharks, a recent study was able to show that continuous bounce diving utilized descent and ascent angles, which optimize the horizontal cost of transport25, supporting the notion that sharks also move through the water column in order to cover horizontal distance efficiently. These lines of evidence substantiate theoretical evidence of the efficacy of intermittent locomotion for the reduction of the cost of transport. Marine animals are often neutrally buoyant at depth, which yields insights into undulating flight as a gait in air and water. We found no evidence of intermittent locomotion by elephant seals at depths shallower than ∼15 m (Figs 2 and 3), probably as a result of animals being near neutral buoyancy (Fig. 2)26, whereas at deeper depths seals would swim intermittently, likely due to their increased overall density (Fig. 2). The lack of gas-spaces in sharks results in a fixed body density greater than that of water, irrespective of depth27,28. Thus, sharks can exhibit larger amplitudes in individual undulations than the two species of pinnipeds (Table 2). In fact, the amplitudes of the undulations in seals were so small that variations in body density are likely to be inconsequential within peaks and troughs of each undulation (Table 2 and Fig. 2), in a manner similar to the fixed negative buoyancy of sharks. However, there were significant differences in the depth at which the two elephant seals started to swim intermittently, likely resulting from differing body density (Fig. 2)29. Swimming gaits have been shown to relate to body condition in a number of species, such as baikal seals (Pusa sibirica) and weddel seals (Leptonychotes weddellii), with seals of higher body density adopting more gliding behaviour during descent30,31. It is, however, possible that a shift in behavioural mode, rather than buoyancy alone, triggered a change in the gait pattern of the elephant seals. For instance, some species of primate adopt intermittent locomotion to scan the environment, which may enable more efficient prey detection8. Against this, our elephant seal was on the outward leg of its migration moving rapidly over the Patagonian Shelf towards the shelf edge using u-shaped dives characteristic of directed travelling, whereas deep dives indicating foraging only occur once off-shelf waters are reached32 supporting the notion that energy conservation is the prime reason for intermittent locomotion.

Our results suggest that effective intermittent locomotion may require potential energy to be translated into horizontal distance and that seals have to exceed a critical body density to undulate effectively. Indeed, whereas duty factor increased systematically with depth in fur seals, which are characterized by appreciable air in their pelage, no such pattern was evident in whale sharks, presumably due to the lack of airspaces in sharks. Sharks, with their depth-independent negative buoyancy, appear to be able to glide continuously throughout the water column, whereas seals appear to be constrained to the depths were they attain negative buoyancy30. These results are at odds with 'burst and coast' swimming in small teleost fish, which may occur as a consequence of the profound difference in size between the fish observed thus far, and our study subjects. Indeed, it is possible that the cost of the burst acceleration phase is mass-specific33 and larger animals may benefit from less deceleration during the coast phase, which may be enhanced by negative buoyancy. In addition, locomotory activity during the active phase shows complete overlap with continuous locomotion, suggesting that undulating flight in large marine vertebrates is aerobic, unlike burst-coast swimming in smaller fish. The advantage of negative buoyancy as shown by our study has profound implications for our understanding of optimal body density in aquatic animals, where historically neutral buoyancy is often considered advantageous. In all likelihood, there is probably no single density that is optimal under all circumstances. Adjustment of density is likely highly adaptive, such that aquatic animals that exploit a prey patch at a given depth will benefit from neutral buoyancy34, while travelling animals may benefit from negative buoyancy (Figs. 2, 3). While many of the pelagic fish species have a reduced swim-bladder, there remains fine volume control over the size of the gas bladder.

Our findings indicate that intermittent locomotion in marine environments may be a common mode of transport that in all likelihood favours a lowering of aerobic costs due to efficient locomotion. By using animal-attached technologies to study submerged marine vertebrates, we demonstrate that this strategy operates in water across taxonomic clades as well as in air. Indeed, the species studied here all have to complete large-scale migrations between patches of productivity35,36,37, which would make efficient transiting particularly important. Any reduction in the cost of transport is expected to be highly selected for in natural populations and similar constraints are presumed to result in a convergence of morphological or behavioural solutions38. Given that animal movement is shaped by universal physical and physiological principles; such as commonalities regarding muscle efficiency39 and hydrodynamic interactions with the fluid environment40, common solutions might be expected to increase energetic efficiency even in differing media41. Indeed, sufficient lift-production during glides is the main criterion allowing birds to undulate11,42, whereas marine animals appear at times to face the opposite problem of not having enough 'effective weight' to undulate.