Overall dynamic body acceleration measures activity differently on large versus small aquatic animals

Understanding the kinematics and costs of locomotion is fundamental to unravelling how animals exploit resources resolve life-history trade-offs, as well in assessing potential disturbance. Early insights into terrestrial, aerial aquatic were obtained using cinematographic recording on treadmills (Taylor et al., 1970) wind tunnels (Tucker, or water flumes (Schmidt-Nielsen, 1972). In addition providing high-resolution data full body movement, these captive test environments offered possibility also measuring forces, cardiac rate oxygen consumption at a range speeds. This resulted energetics models that account for both mechanical power expended metabolic required different levels steady activity (Schmidt-Wellenburg 2008; Williams, 1999). However, limited size facilities precludes larger even experiments with smaller must be often performed under conditions little ecological relevance. An alternative approach has been instrument bio-logging devices have provided fine-scale biomechanics behaviour free-ranging fauna (Brown 2013). High-resolution archival tags containing sensors such pressure, speed triaxial accelerometers magnetometers deployed many terrestrial species but especially valuable cetaceans spend most time underwater A major area research interest infer energetic cost animal activities from accelerometer data. Accelerometers measure mass-specific force via Newton's second law, f = ma. As work (i.e. energy) integral over product speed, there direct link between acceleration done by an animal, least respect movements reach tag (Gleiss, Wilson, 2011). Based this, Wilson al. (2006) developed proxy energy expenditure termed overall dynamic (ODBA) defined sum reference interval magnitude after removal running mean. Although other proxies proposed, ODBA its variants are far widely used methods. number studies demonstrated clear individual-specific relationship (VO2) ODBA, showing can during tested (Wilson 2020). important caveat acceleration-based only quantify use cannot directly consumed physiological processes thermoregulation Concerns raised about errors resulting so-called time-trap involving trivial correlation increasing functions (Halsey, 2017; Ladds, 2017), this avoided dividing observation duration, mean rather than accumulating one. despite some testing effort, reliability remains largely unknown when extrapolated individuals size, ontogenetic state species, behaviours, locomotory modes placements (Gleiss 2010; recent effort address uncertainty (Byrnes 2021) mass scaling effect VO2–ODBA (max. 17 kg) highlighting importance validating representative conditions. validation challenge large studied setting, yet increasingly targeted function natural disturbed behaviour. But, though VO2 may animals, could useful relative it consistent, is, if change movement results comparable ODBA. Such consistency argued theoretical level 2020) implicitly assumed compare Gleiss, Jorgensen, 2011; Norman, 2011), not verified animals. Here, we toothed whale cover order difference length. We show assumption borne out because fundamentally aspect does small On measures muscle-generated making effective work, bigger 3 m, influenced rotations generated which scale consistently use. To first consider what animal-attached actually develop simple mathematical model then predictions recordings cetaceans. Animal-attached sensitive orientation gravity non-isometric muscle action. latter component specific just (SA) strapdown inertial navigation literature (Savage, 1998) linked muscles consume contract so generate Even typically measured attached single location body, contractions throughout give rise accelerations coupled tag, greater lesser extent, through frame. Thus, single-point measurements tool monitoring activity. Metabolic maintaining changing (e.g. isometric slow contractions), complex indirect. For example, statically extended fin similar rudder boat cause continual turning easily inferred orientation. Consequently, information conveyed SA, characterise signal, necessary remove component. The beautiful idea behind filter attenuate recognises that, compared contractions, generally slowly due rotational inertia. filtering appropriately chosen high-pass reduces term while leaving SA unaffected (Shepard 2008). high-pass-filtered acceleration, DA, although interchangeably papers fully removing Shepard Shiomi Williams 2017). distinction two terms analysis therefore propose following definitions ambiguity literature: actual wish energetics; DA signal on-animal contains any remnant effect, hidden within equal completely removes gravitational) definition implemented steps: first, centralised moving average (MA) computed each axis outputs subtracted original acceleration. scheme efficient compute low-power microprocessor tag. frequency response varying sensitivity passband attenuates relatively weakly low frequencies. recommend longer symmetric finite impulse (FIR) advantages flatter increased attenuation lower frequencies expense more computation (see Figure S1 Supporting Information). Whichever used, cut-off above signals passed unattenuated) should selected pass orientation-related signal. active represents involves largest body. contraction inversely related fibre length (Medler, 2002), tend lowest components SA. It seems logical set fraction dominant stride wingbeat birds stroke swimmers). swimming several marine vertebrates, (2008) suggest MA s one cycle whichever longer, equating half-power 0.15 Hz lower. being changes agile avoid consistent 40%–60%) subject Information details design issues). final step computing summed desired interval. Variants differ way calculated. taken absolute value axis. lead overestimation circumstances 2009) leading proposal Vectorial Dynamic Body Acceleration (VeDBA) usual vector square-root squares) VeDBA advantage insensitive (Qasem 2012) otherwise gives Another variant, partial (PDBA, Halsey 2009), uses subset axes follows same computational steps followed summation. critical underpinning costly produce 2010). extremities induces cyclic posture. readily visualised propulsive wave passes down fish mammals (Lindsey, 1978). Swimmers caudal undulations broadly classified according induced rotation cyclical angular displacement associated swimming, see glossary further explanations term) reaches anteriorly (Lighthill, 1971) anguiliform (large length) thunniform (rotations decrease strongly anteriorly). instantaneous reflects posture postural dive angle banking turn) displacements inevitable (Martín López 2016; occur rate, they contribute oscillatory separated included call added (DOA, glossary). (from contractions) DOA locomotion), constituent without resorting additional information, sensor gyroscope focus here undulating (Kilbourne & Hoffman, 2013) meaning taxa, combination action signals. presence complicates vary ways. increases stroking propulsor extension but, confirm below, higher DOA. imply no cost, problem resolved sensor, either (Ware 2016) magnetometer 2016), provide independent estimate removed yielding drawbacks: Gyroscopes significant power, method restricted styles involve around 2016). developing assume negligible contribution 2011) reasonable assumption. substantial multiplied gravitational (9.8 m/s2) determine really ignored, accurate towards answering simplified assess contributions locomotion. Overall calculated At summing Our goal much Equation 1 contributes DA. length, BL, influence fs d. given style, thunniform, assuming placed α fairly BL geometric similarity motion. Conversely, d proportional geometrically shown approximately wide seabirds (Sato 2007). our heave predicts decreases part locomotion, style. cetaceans, appears (Gough 2019) suggesting ||SA|| asymptote continuing increases. massive asymptotic almost certainly below typical values ||DOA||. likely dominate high rates. contrast, enough will dominated rotations, DOA, (unless accompanied amplitude) ||DOA|| rate. These thus fail capture transport section, empirical define rough limits provides prediction 5b phocid seals transverse propulsion, steep descent ascent swimming. During horizontal do occurs plane orthogonal vector. means aspects motion depending problematic apparent parts dives. makes assumptions cetacean require chose three lengths appear styles. dataset comprised recorded suction cup multi-sensor (DTAGs version 2 3) Phocoena phocoena harbour porpoises (Pp), Mesoplodon densirostris Blainville's beaked whales (Md) Physeter macrocephalus sperm (Pm). Tags (n 6) 2003 2010 Norway, Italy, U.S. North Atlantic Azores cantilevered pole mounted bow rigid hulled inflatable (Miller 2004). tagged off coast El Hierro (Canary Islands, Spain) handheld (Johnson Harbour bycaught pound net fishery inner Danish waters 2012 2014 upon release (Wisniewska positioned blowhole Pp, dorsal Md Pm. all cases, released autonomously float surface recovered radio tracking. See ethics permits tagging was conducted. pressure sampled 50–200 16-bit resolution. streams decimated common 25-Hz sampling post processing applying anti-alias raw downsampling rate). decimation serves standardise rates high-frequency vibration flow (Cade 2018). rotated correct estimated surfacing stereotypical respiration Tyack, 2003). Software tools www.animaltags.org Matlab R2019a (Mathworks Inc.) processing. periods continuous strokes phase 10 randomly blocks consecutive analysed. 0.4 separate separately (Table Information) Pp visual observations porpoise anterior locations had closely (RMS 4.7° 3.9° Pm, respectively), RMS surge SAs 12 times bigger, respectively, Pp: 2.7 1.9 m/s2; Pm: 0.26 0.11 1). Results 18 (Figure 2) sharply (due decreasing fluking rate), roughly constant. intraspecies variation parameters Pm variable differences individual fact, less across S1) supporting expectation placements. But notwithstanding measurement artefacts, evident predicted, constitute proportion whales. comparison, porpoises, extent considered interchangeable Fitting Sato (2007) dominates twice DOA) m. specifically evaluated inequality 5 estimates (fs, Hz), perpendicular amplitude (d, m) (α, radians) species. dorsoventral experienced travels along shows up allowing us filtered depth. d, near-horizontal (Pm) S2 constant (4.5, 6.3 5.7 0-to-peak degrees, positions bodies. decreased (fs 1.5, 0.44 0.17 (d 1.6, 20.0 25.2 cm respectively). √(α/2d) slightly considerably whale. Quantifying expend reliable would improve understanding efficiency perform vital allow quantification human Due complexity unlikely nonetheless increase corresponding proxy. metric, supported strong basis metric lacking beyond basic physical production core underlying contents acknowledge argue impact (DOA) small. assertion modelling measurements. confirms offer quantifying, limitations measurement, contractions. (DA) close justifying usage papers. motions track energy. demonstrate conclusion apply applies PDBA steps. Swimming, like forms complicated array synchronous relies simplifying tractable. Nonetheless, comparison spanning 10:1 demonstrates captures relationships skin offers quantifies swimmers examine following. undulation varies modulate meet needs, drag extensions make adjust output (Saadat If case unreliable particular situation misleading behavioural (Tyack locomotor intervals experimental swim exposure, inconsistency sharks propulsion. quantified pitch angle: tracks accurately, vertical exceed effort. orientation-dependent matters comparing behaviours angles, deep-divers elephant considerable near-vertical (Le Boeuf 1992). rarely ascend descend angles (Andrzejaczek 2020; pronounced. Given misinterpretation key question problems become manifest. depends difficult predict general, rule thumb arrived intended formulation, ⪆ 2||DOA|| case, model, fs, √(α/2d). Estimating found nearly met 1.1 m missed margin 10-m approximate magnitudes determines matched. mid-sized gait potentially comparisons gaits 2015). pinnipeds reflect produced highlights sizes population, mum–calf pairs. their Extrapolation possible treated caution. whether cautions walking steeply need oppose forces lifting limbs (Alexander, concerns beg universal movement. issue filtering. minimum (MSA) introduced Simon (2012) avoids exploiting calibration underestimate central trend interpret. subtract Methods proposed gyroscopes (Kawabata 2014; Martín Ware ODBA-like derived APBA (averaged OSA (overall should, design, sizes, neither validated against Moreover, methods useful, accuracy achieve moderate estimation established, unclear beneficial. practical drawback significantly accelerometer, reducing batteries. free-living solution elusive. By sensing force, seem hold promise quantifying use, confounds this. While minor result, variants, fauna. caution independently validated. thank researchers involved collection. Thanks C. Botelho de Oliveira P. Tyack data, J. Teilmann D. Wisniewska F. Fish A. Biewener helpful advice. reviewers handling editor insightful critique. Data collection Canary Islands funded Office Naval Research (ONR), National Oceanographic Partnership Program Spanish Ministry Science (CGL2009-13112). Ligurian sea Gulf Mexico ONR, Minerals Management Service Cooperative Agreements 1435-01-02-CA-85186 NA87RJ0445 grant #N00014-99-1-0819. Andenes Carlsberg Foundation, ONR Strategic Environmental Development Program. Work Council, Fundação para Ciência e Tecnologia Fundo Regional da Ciência, (TRACE-PTDC/MAR/74071/2006 MAPCET-M2.1.2/F/012/2011). L.M.M.L. St. Andrews University Knowledge Exchange Impact N.A.d.S. Ramón y Cajal Fellowship Government. M.J. Aarhus Foundation EU H2020 Innovation Programme Marie Skłodowska-Curie 754513. Kattegat, Denmark German Federal Agency Nature Conservation contracts 5330/2010/14 BfN -Cluster 7 'Effects noise vertebrates'. None authors conflict interest. conceived ideas designed methodology; M.J., N.A.d.S., P.T.M. collected data; analysed interpreted led writing manuscript. All contributed critically drafts gave approval publication. peer review history article available https://publons.com/publon/10.1111/2041-210X.13751. paper deposited Dryad Digital Repository https://doi.org/10.5061/dryad.ns1rn8prc 2021). Please note: publisher responsible content functionality supplied authors. Any queries (other missing content) directed author article.