Acceleration-based proxies for activity and energy expenditure are widely used in bio-logging studies of animal movement and locomotion to explore biomechanical strategies, energetic costs of behaviour, habitat use and the impact of anthropogenic disturbance. The foremost such proxy is overall dynamic body acceleration (ODBA) along with variants VeDBA and PDBA. This technique, which involves summing the magnitude of high-pass-filtered acceleration signals (the so-called dynamic acceleration) over a reference interval, has been applied to animals as diverse as shags, lobsters, humans and whales. The relationship between ODBA and energy use has been tested empirically on animals small enough to house in laboratory facilities and arguments have been offered for why the method should be generally applicable; however, validations on larger animals are scant. Here, we examine how body size impacts ODBA and its variants under steady locomotion in large aquatic animals, using cetaceans as model species. To do this, we first develop a simplified mathematical model for the acceleration signals that would be measured by a tag on a swimming animal. We then test this model with empirical data gathered using bio-logging tags on whale species spanning 1.3 m harbour porpoises to 12-m sperm whales. We show that the motions measured by ODBA can be fundamentally different in small versus large aquatic animals. Whereas dynamic acceleration in small animals is predominantly due to specific acceleration (i.e. actual accelerative motions generated by muscle action), in larger aquatic animals, body rotations (i.e. cyclical angular displacements associated with swimming) can dominate the measured acceleration. As body rotations do not necessarily increase in magnitude as swimming speed increases, ODBA may underestimate the relative cost of behaviours or responses to disturbance in large aquatic animals. This does not lessen the value of ODBA for small animals, but it raises a caution against uncritical use on larger animals. For large aquatic animals, activity proxies that specifically remove body rotations using gyroscopes or magnetometers may provide more consistent estimates of energy use although these methods are yet to be validated.
