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 covering nearly an order of magnitude difference in body length from 1.3 m harbour porpoises to 12 m sperm whales.

We show that the motions measured by ODBA can be fundamentally different in small compared to 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., changes in orientation that accompany swimming and manoeuvring) can dominate the measured acceleration.

As body rotations do not necessarily increase in magnitude as swimming speed increases, ODBA may under-estimate 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.

Data was collected on 6 sperm whales (Physeter macrocephalus, Pm), 6 Blainville´s beaked whales (Mesoplodon densirostris, Md) and 6 harbour porposise (Phocoena phocoena, Pp) using suction cup attached multi-sensor tags (DTAGs version 2 and 3). Tags were attached to sperm whales between 2003-2010 in Norway, Italy, the U.S. North Atlantic, and the Azores, to Blainville's beaked whales between 2003-2010 off the coast of El Hierro (Canary Islands, Spain) and to harbour porpoises, which were bycaught in a pound net fishery in inner Danish waters between 2012-2014 and tagged upon release. The tags included a pressure sensor, triaxial magnetometers, and triaxial accelerometers sampled at 50-200 Hz with 16-bit resolution. These sensor streams were decimated to a common 25 Hz sampling rate in post processing. The triaxial accelerometer and magnetometer signals were rotated to correct for the orientation of the tag on the whale which was estimated at each surfacing from the stereotypical movements during respiration. Software tools from www.animaltags.org in Matlab R2019a were used for data processing.

Here we present a different nc-file for each of the 18 tagged animals, 6 individuals per species. nc files are named after the tag ID, i.e., the code comprises the first letter for each species initials in Latin, the year it was tagged (two digits), the Julian day, and the tag deployment of the day (a single letter). Each nc-file contains "P", "A" and "M" variables sampled at 25Hz for 10 randomly-selected data blocks ("block") of 10 consecutive swimming strokes.

"P" corresponds to depth in meters.

"A" corresponds to the measured animal-frame triaxial accelerometer signal in g; columns correspond to the acceleration components a_x, a_y and a_z, which correspond to the longitudinal, lateral and dorso-vental axis, respectively.

"M" corresponds to the measured animal-frame triaxial magnetometer signal in μT; columns correspond to the magnetometer components m_x, m_y and m_z, which correspond to the longitudinal, lateral and dorso-vental axis, respectively. "block" corresponds to the each of the randomnly selected blocks of 10 consecutive swimming strokes.

In addition each nc.file contains information regarding the data owner and data provider of each database.