Dynamic body acceleration as a proxy to predict the cost of locomotion in bottlenose dolphins

Animals expend energy in four physiological processes: maintenance, growth, reproduction and physical activity. One component of physical activity is movement (Gleiss et al., 2011). The energy allocated to movement, also termed the cost of locomotion (COL), can vary greatly depending on life history and activity level, and is the primary source of energy use in many vertebrates (Karasov, 1992). For example, cheetahs (Acinonyx jubatus) may expend up to 100 W kg⁻¹ during a sprint (Wilson et al., 2013), although the short duration of such activity means that sprints have a negligible impact on their daily energy budget (Scantlebury et al., 2014). In contrast, African wild dogs (Lycaon pictus) spend hours hunting at a lower energetic cost (35 W kg⁻¹), so this activity comprises a large portion of their daily energy budget (Gorman et al., 1998). Because energy expenditure is linked to fitness (Grémillet et al., 2018), estimates of COL underpin many ecological questions, including understanding the effects of anthropogenic impacts. For example, COL can help parameterize population consequences of disturbance (PCoD) models to quantify the impacts of cumulative, sublethal threats to marine mammals (Pirotta et al., 2018).

Several methods exist to estimate COL, although there is considerable debate over which method is best for different species and contexts. The doubly labeled water method uses labeled isotopes to estimate field metabolic rate (FMR) and can be linked to activity budgets to estimate COL (Jeanniard-du-Dot et al., 2017b). Although doubly labeled water has been used in two cetacean species (Costa et al., 2013; Rimbach et al., 2021; Rojano-Doñate et al., 2018), proper validation and logistical considerations make this method difficult to use with large, free-ranging mammals (Butler et al., 2004; Speakman, 1997). Respiration has also been used as a proxy for FMR (Sumich, 2021; Villegas-Amtmann et al., 2015), although variation in tidal volume and end-tidal gas concentrations can cause significant uncertainty, especially over short time scales (Fahlman et al., 2016; Roos et al., 2016). Owing to the logistical constraints of working with large, aquatic, air-breathing animals, published estimates of COL are more limited for marine mammals than for terrestrial taxa.

Recent advances in biologging technology have facilitated the development of two additional proxies for COL: heart rate and activity (Wilmers et al., 2015; Wilson et al., 2020). In many taxa, heart rate correlates with energy use (Green, 2011). However, marine mammals exhibit cardiorespiratory changes related to submergence that are believed to be under conditioned control in at least some species (Fahlman et al., 2020; McDonald et al., 2018). Therefore, marine mammals may be able to temporally decouple heart rate from energy expenditure (Williams et al., 2017). An additional challenge to using heart rate as an energetic proxy is the logistical complexity of attaching external heart rate monitors to free-ranging marine mammals. In contrast, some short-duration, high-resolution archival tags include tri-axial accelerometers that can be used to measure activity level. Activity level (e.g. stroke rate, body acceleration, speed) has been used to predict fine-scale COL in many taxa, including marine mammals (Wilson et al., 2020).

Activity metrics generated from biologging tags include stroke frequency, dynamic body acceleration (DBA) calculated either as vectorial (VeDBA) or as an overall measure (ODBA; Qasem et al., 2012; Wilson et al., 2020, 2006), and, less frequently, speed (Gabaldon et al., 2019). When most of the measured acceleration is due to mechanical work performed by locomotor muscles, higher activity metric values indicate greater energy expenditure (Gleiss et al., 2011). Converting DBA to COL requires species-specific calibration experiments which often employ respirometry – the measurement of expired gases – because the rate of oxygen consumption (V̇_O2) is related to aerobic metabolism and allows fine-scale estimation of metabolic rate (Wilson et al., 2020; Withers, 1977). Activity–energetics calibration studies have been conducted in many terrestrial taxa (Halsey et al., 2009), but only a few exist for cetaceans and pinnipeds owing to logistical challenges: Steller sea lions (Eumetopias jubatus; Fahlman et al., 2013, 2008), Antarctic fur seals (Arctocephalus gazella; Jeanniard-du-Dot et al., 2017a; Skinner et al., 2014), northern elephant seals (Mirounga angustirostris; Maresh et al., 2014), Weddell seals (Leptonychotes weddellii; Williams et al., 2004), harbor porpoises (Phocoena phocoena; Otani et al., 2001) and common bottlenose dolphins (Tursiops truncatus; Williams et al., 1993, 2017; Yazdi et al., 1999).

Numerous factors can affect the relationship between activity metrics and energy expenditure, including tag position on the animal, locomotion type, non-movement-based energy expenditure, and experimental/analytical design (for reviews, see Gleiss et al., 2011; Halsey, 2017; Halsey et al., 2009; Wilson et al., 2020). Several studies have found no relationship between activity and energy expenditure in diving animals (Halsey et al., 2011a; Ladds et al., 2017) and some have argued that some correlations may not be as strong as they appear because of the type of metric used (Halsey, 2017; although see Wilson et al., 2020 for a response). However, activity is relatively straightforward to measure in many taxa using biologging devices, and movement may serve as a robust estimate of energy expenditure for some species and under certain circumstances.

To our knowledge, only one other study has attempted to correlate ODBA with energy expenditure in common bottlenose dolphins (John, 2020). Our study sought to determine this correlation with five dolphins of different body sizes. We measured breath-by-breath V̇_O2 in trained common bottlenose dolphins across a range of activity levels. The dolphins wore kinematic tags while swimming subsurface laps. We modeled ODBA–V̇_O2 after normalizing by mass. We developed this activity–energetics calibration across a range of body sizes to improve predictions of COL from movement data collected from free-ranging cetaceans and to demonstrate the utility of activity as a proxy for energy use.

We studied six male common bottlenose dolphins (Tursiops truncatus Montagu 1821) at Dolphin Quest Oahu, a public display zoological facility located on Oahu, Hawaii, accredited by the Alliance of Marine Mammal Parks and Aquariums and certified by American Humane. The dolphins resided in four natural seawater lagoons totaling ∼1420 m². The swim trial area was between 1.5 and 3.0 m in depth. Water temperatures during the trials were 25–26°C with an annual range of 24–28°C.

Swim trials were conducted in May 2017, 2018 and 2019. Trials were conducted in the morning following an over-night fast, with each animal completing one trial per day. In each trial the tag was placed between the blowhole and dorsal fin. The dolphin remained relaxed at station for ∼1 min before the pneumotachometer was placed over the blowhole. The dolphin breathed into the pneumotachometer for 1.2–10.3 min (median=2.3 min, IQR=2–3.1 min) to measure resting metabolic rate (RMR). The dolphin was then asked to swim to a trainer ∼30 m away and return to station, while remaining below the surface and without stopping (Fig. 1). Twelve trials contained speed data; assuming individuals swam the same distances in trials without speed data, individual mean lap distance (LD) traveled varied between 78 and 86 m owing to variable curvature at the turn around (Table 1). Upon returning to station, the dolphin breathed several times into the pneumotachometer (median=3 breaths, IQR=3–4 breaths), before swimming another lap, and repeating this process for 8–12 total laps before recovery (Fig. 2). Thus, each trial consisted of a pre-swim rest period, 8–12 laps of active swimming (median=10 laps, IQR=9–10 laps), and a recovery period (2.7–9.1 min). The dolphins primarily used consistent stroking, with minimal gliding at the lap mid-point and during the last several seconds before reaching station.

In each trial, animals were asked to swim each lap at approximately the same speed, but were asked to vary speed between trials to obtain inter-trial variation in swim speed. Lap and station durations varied slightly among individuals (Table 1). All breaths were spontaneous – the animals were not cued to breathe. All resting and swim trials were conducted post-absorptive (i.e. no food consumed for >12 h). This protocol was approved by Duke University's Institutional Animal Care & Use Committee (protocol no. A045-17-02).

We measured respiratory flows using a custom-made Fleisch type pneumotachometer (adm+ engineering, Valencia, Spain) equipped with a low-resistance laminar flow matrix (item Z9A887–2, Merriam Process Technologies, Cleveland, OH, USA). A differential pressure transducer (Spirometer Pod, ML 311, ADInstruments, Colorado Springs, CO, USA) was connected to the pneumotachometer with two 310 cm lengths of 2 mm I.D., firm-walled, flexible tubing. The differential pressure transducer was connected to a data acquisition system (Powerlab 8/35, ADInstruments) and the data were captured at 400 Hz and displayed on a laptop computer running LabChart (v. 8.1, ADInstruments). The differential pressure was used to determine flow rate and was calibrated using a 7.0 liter calibration syringe (Series 4900, Hans-Rudolph Inc., Shawnee, KS, USA).

Gas concentrations (O₂ and CO₂) were subsampled via a port in the pneumotachometer and passed through a 310 cm length of 2 mm I.D., firm-walled, flexible tubing and a 30 cm length of 1.5 mm I.D. Nafion tubing, to a fast-response O₂ and CO₂ analyzer (Gemini respiratory monitor, CWE Inc., with a 95% response time below 200 ms at a flow rate of 200 ml min⁻¹). The gas analyzer was connected to the data acquisition system and sampled at 400 Hz. The gas analyzer was calibrated before each day's first trial using a commercial mixture of 5% O₂, 5% CO₂ and 90% N₂ (product no. 17 L-340, GASCO, Oldsmar, FL, USA). We used ambient air to check the calibration before and after each trial.

We used three combinations of sensor packages and instrument housings. All contained tri-axial accelerometers, magnetometers, and temperature and pressure sensors. We conducted four trials using a digital acoustic recording tag (DTAG, version 3; Johnson and Tyack, 2003), 19 trials with an IMU sensor (ActiGraph, Pensacola, FL, USA) and 12 trials with an MTag containing an OpenTag3 sensor (Loggerhead Instruments, Sarasota, FL, USA). Both the IMU and MTag housings closely approximated the shape, profile and attachment mechanism of a DTAG, and both contained gyroscopes in addition to the DTAG sensor types. The MTag also measured speed (Gabaldon et al., 2019).

Body mass was measured every 2 weeks using an Altralite scale (Rice Lake Weighing Systems, USA) with a GSE 250SS indicator (GSE Scale Systems, USA; ±0.1 kg).

Methods used to process respirometry data are described in detail in Appendix 1.

We calculated RMR (ml O₂ min⁻¹) as the V̇_O2 during the last 70 s of each pre-swim rest phase of a trial. We chose 70 s because it was the duration of the shortest rest phase of the 62 trials we used for resting calculations (Table 1). We also calculated V̇_CO2 over the same duration (Table 1). We predicted basal metabolic rate (BMR) using Kleiber's allometric equation for mature terrestrial mammals (Fahlman et al., 2013; Kleiber, 1975) and divided the observed mean individual RMR (Table 1) by predicted BMR to obtain Kleiber ratios.

We performed a segmented linear regression to identify the number of laps required to reach steady-state V̇_O2 (Appendix 2). Dolphins usually reached steady-state by lap 4, so we chose the start of lap 5 as the beginning of steady-state for all animals. We made exceptions for four trials in which dolphins missed a breath (i.e. took a breath outside of the pneumotachometer) during lap 5 and, in these trials, steady-state instead began at lap 6. The steady-state period ended at the beginning of the last lap of each trial, as the O₂ consumed following this lap included recovery of the O₂ debt.

We calculated total energy expenditure by dividing V_O2 by the total steady-state duration (D_SS,Lap+D_SS,Station) and converted to W using a conversion factor of 20.1 J ml⁻¹ O₂, which assumes the animal is using a representative mixture of carbohydrates, lipids and proteins (Hill et al., 2012; Williams et al., 2017).

We calculated ODBA following Wilson and colleagues (2006), using a running mean of 2 s to filter out static acceleration based on our average fluking rate (1.2 Hz). We calculated per-trial ODBA in two ways. To compare against total energy expenditure, we took the mean ODBA during the rest period before the first lap, and the mean ODBA during each trial's entire steady-state period (D_SS,Lap+D_SS,Station). Tag data were unavailable for 19 of the 58 RMR trials included in the total energy expenditure analysis; mean individual ODBA during rest was used in place of measured values for those RMR trials. In the COL analysis, we calculated mean ODBA during only the submerged portion of the steady-state period (the periods at station were excluded), to match the COL calculations (Fig. 2). We processed tag data and calculated pitch using custom-written scripts in MATLAB (v. 2018a), available at soundtags.org. We computed lap distance traveled values from the MTag trials using calibration parameters and estimation methods detailed in Gabaldon et al. (2019).

We calculated power (W kg⁻¹) using two methods, both using only the 12 trials (five individuals) that used Mtags to record speed. Speed was defined as the distance (m) traveled during steady-state, divided by the time spent swimming during steady-state (D_SS,Lap). To compare with Yazdi et al. (1999), we divided steady-state V_O2 by the entire steady-state duration (D_SS,Lap+D_SS,Station), and termed this method ‘average power’. To compare with Williams et al. (1993), we estimated RMR at station by multiplying individual mean RMR by the steady-state station duration (D_SS,Station), and subtracted this resting station V_O2 from steady-state V_O2, before dividing the remainder by duration spent swimming (D_SS,Lap). We termed this method ‘station RMR subtracted’. We fit regressions to both power datasets, as described below.

Total cost of transport (COT; here in J kg⁻¹ m⁻¹) is power (W kg⁻¹) divided by speed (m s⁻¹), and is the amount of energy required to move 1 kg of M_b over 1 m (Schmidt-Nielsen, 1995). We divided both power regressions by speed to obtain COT fits, and compared against the ‘station RMR subtracted’ per-trial power values divided by speed.

To calculate stroke frequency, we used the pitch signal to count fluke strokes and defined stroke frequency as the sum of fluke strokes during steady-state divided by the duration the animal was submerged (i.e. not at station) during steady-state. We compared stroke frequency with V̇_O2 calculated as the steady-state V_O2 divided by the same steady-state submerged duration, in order to compare with Williams et al. (2017).

We performed all statistical analyses in R 4.0.2 (https://www.r-project.org/), except for the intraclass correlation coefficient (ICC) analysis described below. The breakpoint analysis we used to determine the beginning of steady-state V̇_O2 is described in Appendix 2.

In the total energy expenditure analysis, we used a linear regression from the nlme package (https://CRAN.R-project.org/package=nlme), with mass-specific energy expenditure (using both RMR and steady-state expenditure; W kg⁻¹) as the response variable and mean ODBA (calculated either during the RMR period or during the entire steady-state period) as the predictor variable, with individual dolphin as a random effect (random intercept only). Mixed-effects models are widely used when interpretations are desired for a population outside of those sampled (individuals in this instance; Ramsey and Schafer, 2013), and ‘represent a compromise between assuming no effects and fully independent effects of the levels of a factor’ (Kéry, 2010). We performed a likelihood ratio test (LRT) on the fixed effect (ODBA) against a reduced model without ODBA.

For the COL analysis, we used weighted linear regression from the nlme package with COL_norm as the response variable, mean ODBA (g) as the predictor variable, and individual dolphin as a random effect (fixed intercept, random slope). A fixed intercept was used because with RMR subtracted, each individual's COL should increase with activity level from a similar starting point (intercept). Random slopes were used to account for potential individual differences in the relationship between COL and activity. We compared this model against a random intercept, fixed slope model in Appendix 3. Mean ODBA squared was included as a fixed variance term [using weights=varFixed(∼ODBA²) inside the lme() function] to account for heteroscedasticity because the residual variance was proportional to ODBA². We performed identical LRTs on the COL models as described above.

ICC is a reliability index that reflects both the degree of correlation and agreement between measurements (Koo and Li, 2016). ICC can be used to assess reliability in test–retest situations; in this case, we calculated ICC by comparing each trial's measured COL with each trial's predicted COL using single measures statistics. We used a third-party MATLAB toolbox to facilitate ICC statistics computation (https://www.mathworks.com/matlabcentral/fileexchange/22099-intraclass-correlation-coefficient-icc).

For the power and COT analyses, we conducted nonlinear least squares regressions using third degree polynomials, with all terms constrained to be positive, as increasing speed should result in increasing energy expenditure. All statistics are means±s.d. unless stated otherwise. All confidence intervals were calculated to estimate the population response [i.e. using ‘level=0’ inside predict()], though given the mixed-effect framework it is important to note that the uncertainty estimate of the fixed effect (i.e. ODBA) is dependent on the estimates of the random effect variance.

Models were fit with maximum likelihood for LRTs, while reported coefficients, confidence intervals and figures are the restricted maximum likelihood fits. We visually analyzed model residuals to assess assumptions of homoscedasticity, linearity and normality. We used an alpha level of 0.05 for all statistical tests.

Post-absorptive resting V̇_O2 (N=62 trials) and V̇_CO2 (N=60 trials) varied among individuals (Table 1). The median individual Kleiber ratio was 0.99 (range=0.71–1.42).

Thirty-five swim trials were included in the steady-state breakpoint, total energy expenditure and COL analyses (representing five individuals; S, Table 1). Ten of the 35 trials had 1–3 breaths replaced before the analyses: in 6 trials the missed breath(s) occurred before steady-state; 4 trials had one missed breath during steady state. In these 4 trials, replacing the missed breath by the trial's median breath V_O2 increased the steady-state V̇_O2 by 1.2–7.4%. Replacing the missed breath by the trial's maximum breath V_O2 would have increased the steady-state V̇_O2 by 13.5–23.9%.

There was a significant (LRT=157.6, P<0.0001), positive, linear relationship between energy expenditure and ODBA (intercept=0.79, 95% CI=0.51–1.07, t=5.56; slope=8.69, 95% CI=7.83–9.55, t=20.07; d.f.=87; N=93 trials: 58 rest periods and 35 steady-state periods; Fig. 3).

There was a significant (LRT=14.9, P=0.0001), positive, linear relationship between COL_norm and ODBA (intercept=0.09, 95% CI=−1.24–1.42, t=0.14; slope=9.01, 95% CI=5.61–12.40, t=5.42; d.f.=29; N=35 trials; Fig. 4A).

Predicted COL were compared with measured values (Fig. 4B, Fig. A3). The results from the ICC analysis indicate that the COL model fit overestimates COL at lower effort levels and underestimates COL at higher effort levels compared with the measured values (Fig. 5). The one-way random, single measures ICC was 0.76 (95% CI=0.58–0.87, P=2.7×10⁻⁸), indicating moderate to good agreement between measured and predicted COL (Koo and Li, 2016). The fit is also visualized using Bland–Altman plots in Appendix 3 (Fig. A3C).

‘Average power’ was modeled as power (W kg⁻¹)=0.010v³+0.144 v²+0.378v+R (N=17, d.f.=14, s.e. of the regression=0.77; Fig. 6A), where v is swimming speed (m s⁻¹) and R is mean RMR (0.958±0.276 W kg⁻¹). ‘Station RMR subtracted’ power was modeled as power (W kg⁻¹)=0.087v³+0.228v²+0v+R (N=17, d.f.=14, s.e. of the regression=1.22; Fig. 6B), where v and R are the same as above.

Minimum COT (J kg⁻¹ min⁻¹) was similar between the ‘average power’ method (1.18 J kg⁻¹ min⁻¹; 2.3 m s⁻¹) and the ‘station RMR subtracted’ method (1.17 J kg⁻¹ min⁻¹; 1.4 m s⁻¹), although speed at minimum COT differed (Fig. 6C).

Per-trial COL versus mean stroke frequency (range=49–106 strokes min⁻¹) was compared with values from Williams et al. (2017); overall, there was a positive, non-linear relationship between V̇_O2,sCOL and stroke frequency when the two studies were combined (Fig. 6D).

Here, we show that ODBA and COL are correlated during experimental, aerobic, subsurface swim trials with common bottlenose dolphins. The strength of the correlation between ODBA and COL varied among individuals, so predictions regarding individual dolphins should be interpreted cautiously. This is perhaps unsurprising, given the limited number of trials for each individual. However, there was a significant linear relationship between ODBA and energy expenditure when all individuals were considered together (Figs 3 and 4A). Some other studies have been unable to find a relationship between DBA and COL. Below, we discuss factors that may confound the relationship between DBA and COL and discuss the implications of enhanced COL estimates.

Some individuals reached higher steady-state activity levels than others (Fig. 4), which is not unexpected given individual differences in fitness and swimming efficiencies related to morphometrics. Individual predictions largely tracked individual measurements (Fig. 4B). One individual (9ON6) had higher than predicted COL values (Fig. 4), suggesting that some individual differences may remain, even after accounting for variation in M_b. All dolphins remained submerged while swimming, but it is likely that some individuals may have incurred variable wave drag if they swam close to the surface during parts of the trial. Wave drag occurs when swimmers are within three body diameters of the surface or bottom (Fish, 1993a; Hertel, 1969). Although DBA metrics should account for the effect of wave drag, acceleration and V̇_O2 should increase with increased drag as the animal compensates with greater effort. Mechanical modeling would help further determine the relative impact of wave drag on activity–energetics correlations.

Tag stability, tag placement and gait changes can affect the DBA–V̇_O2 relationship (Gleiss et al., 2011; Wilson et al., 2020). We expect these effects to be minimal in the present study: tag placement was consistent among trials and close to the center of gravity, suction cups kept the tags firmly attached, and the dolphins used consistent stroking.

The mass-specific steady-state V̇_O2 (5.5–16.4 ml O₂ kg⁻¹ min⁻¹), calculated as in a previous study to estimate the lactate threshold in dolphins (20–29 ml O₂ kg⁻¹ min⁻¹; Williams et al., 1993), suggests that the exercise in the present study was primarily aerobic (i.e. submaximal) and therefore a valid measure of aerobic energy expenditure (Wasserman et al., 1967).

To allow comparisons of energy requirements across species, Kleiber (1975) defined a set of criteria for measurements of BMR: adult animals should be in a non-reproductive state, at rest, post-absorptive and thermoneutral. Many early measurements of marine mammals did not conform to these criteria. As a result, it has been suggested that marine mammals, in general, have resting metabolisms higher than those of terrestrial mammals. More recent studies suggest that BMR across marine mammals may be closer to values in terrestrial taxa, especially considering the sampling bias toward smaller, more active marine mammal species (for a review, see Maresh, 2014). BMR criteria were developed in terrestrial animals, and many marine mammal studies use the term ‘resting’ metabolic rate rather than ‘basal’, to acknowledge the challenges in applying these criteria to marine mammals (Maresh, 2014).

We believe that the RMR measurements in the present study met BMR criteria, including thermoneutrality (Williams et al., 2001). Among studies that met BMR criteria, our RMR values (1.9–4.1 ml O₂ kg⁻¹ min⁻¹; calculated from Table 1) were consistent with those from some previous studies (2.7–5.0 ml O₂ kg⁻¹ min⁻¹; Noren et al., 2013; Pedersen et al., 2020; van der Hoop et al., 2014; Yeates and Houser, 2008), and lower than others (6.4–7.4 ml O₂ kg⁻¹ min⁻¹; Williams et al., 1993; Williams et al., 2001; Williams et al., 2017). Even when the criteria for measuring BMR are met, other factors can influence mass-specific RMR estimates, including body condition, the duration of measurement of RMR, and the animal's familiarity and comfort with the experimental protocol (Fahlman et al., 2018). Individual Kleiber ratios in the present study suggest that BMR in bottlenose dolphins, at least in some studies, may be closer to that of terrestrial mammals than previously thought.

Energy expenditure increased linearly with ODBA, both when measuring total energy expenditure (Fig. 3) and after subtracting RMR to isolate COL (Fig. 4). Past studies have shown that both swim speed and stroke frequency increase exponentially with COL (Fig. 6D) as the effect of hydrodynamic drag increases with increasing speed (Williams et al., 1993). However, regarding the relationship between ODBA and metabolic work, Gleiss et al. (2011) note that ‘if ODBA scales linearly with mechanical work, the resultant relationship should be linear, given that mechanical work equals metabolic work (above RMR)’. A linear relationship has been found between DBA and metabolic work in all species tested so far (Wilson et al., 2020), including fish (Wright et al., 2014), pinnipeds (Fahlman et al., 2008), shellfish (Robson et al., 2012), amphibians (Halsey and White, 2010), reptiles (Halsey et al., 2011b), and many terrestrial mammals and birds (Halsey et al., 2009).

Previous marine mammal studies have reported conflicting results; some agree with our finding of a correlation between ODBA and V̇_O2 (i.e. a DBA–COL relationship), while others failed to detect a correlation. For example, Ladds et al. (2017) found no relationship between DBA or stroke frequency and V̇_O2 in fur seals or Steller sea lions. This could have been caused by thermal substitution, in which the confounding effect of thermal heat loss in cold water interferes with the relationship (Wilson et al., 2020). In our study, animals were housed in a thermoneutral environment (Williams et al., 2001). This may, in part, explain why our results showed a correlation, and why studies investigating homeotherms that operate both in air and cold water need to account for thermal substitution (Wilson et al., 2020).

It is important to note that activity–energetics correlations which use two cumulative metrics can produce a strong correlation between uncorrelated variables because time is on both axes – termed the ‘time trap’ (Halsey, 2017; Ladds et al., 2017). It has been argued that some activity–energetics correlations appear stronger than they are owing to using two cumulative metrics. This does not necessarily invalidate a correlation, but it is best to use at least one mean value (Wilson et al., 2020). In the present study we used two mean values to avoid this issue: mean ODBA and V̇_O2.

The dolphins' mean lap speeds (2.3–4.2 m s⁻¹) were similar to the observed swim speeds of bottlenose dolphins in both human care (1.2–6.0 m s⁻¹; Fish, 1993b) and in the wild (1.6–5.6 m s⁻¹; Rohr et al., 2002). Our power and COT values were lower at slower swim speeds than other studies owing to the lower RMR values in the present study (Fig. 6A–C). Our ‘average power’ method closely matched Yazdi et al. (1999) at speeds over 2 m s⁻¹ owing to their similar calculation (Fig. 6A). However, we feel that the’ station RMR subtracted’ method (Fig. 6B) more closely approximates the true relationship between power and speed by accounting (i.e. subtracting) for rest periods in between swimming periods. The ‘station RMR subtracted’ minimum COT (1.17 J kg⁻¹ min⁻¹) was close to the minimum identified by Williams et al. (1993; 1.29 J kg⁻¹ min⁻¹) but at a slower speed (1.4 m s⁻¹) than that of Williams et al. (1993; 2.1 m s⁻¹). The ‘station RMR subtracted’ COT fit is also higher than the fit of Yazdi et al. (1999) and lower than the fit of Williams et al. (1993) at speeds over 2 m s⁻¹ (Fig. 6C).

The mass-specific V̇_O2,sCOL–stroke frequency correlation in the present study was similar to that reported in a previous study (Williams et al., 2017), despite differences in experimental design (Fig. 6D). Both V̇_O2 and stroke frequency were higher in the present study, extending the range of our knowledge of the relationship between V̇_O2 and stroke frequency.

Estimates of COL are necessary to address fundamental ecological questions associated with foraging, migration and other life history events (Goldbogen et al., 2019; Williams et al., 2020). Such estimates are also needed to measure the impacts of sublethal threats to marine mammals (Williams et al., 2017). Several efforts are currently underway to determine whether anthropogenic disturbance of marine mammals can have population-level fitness consequences. Estimates of the increased metabolic cost of a response (e.g. swimming rapidly away from a perceived threat) are required to parameterize PCoD models. In the most acute cases, anthropogenic sounds may result in changes in physiology and behavior that cause direct or indirect trauma (Fahlman et al., 2021), but sub-acute changes in behavior and physiology may result in cumulative long-term consequences for fitness. For example, under the predation risk framework, an animal may perceive a human-caused disturbance as a predator and modify their physiology or behavior to reduce predation risk (Frid and Dill, 2002). Scaling the responses of individuals to population-level impacts requires measuring a response and integrating the response with the population's physiology, energetics and life history (King et al., 2015; Nabe-Nielsen et al., 2018; Nowacek et al., 2016; Schwacke et al., 2017; Williams et al., 2016). Owing to knowledge gaps, few PCoD models have explicitly incorporated the physiological consequences of disturbance, including COL (Pirotta et al., 2018).

Dolphins use a variety of swimming gaits that incorporate different proportions of stroking and gliding to maximize efficiency (Skrovan et al., 1999). The energetic cost of a stroke and of a dive has been shown to be influenced by gait changes (Williams et al., 2017). Future studies should examine the predictive power of different calibration studies on longer duration deployments that include different gaits and dive depths. Similarly, ODBA–V̇_O2 predictions from this study should only be applied to free-ranging cetaceans in which the tag is in a similar position and has not slid over the body. Future studies should compare the present study's COL prediction with stroke-based predictions at longer time scales to validate their ability to determine daily energy expenditure. COL estimates will need to be combined with RMR and specific dynamic action estimates to estimate daily FMR. This could be compared with other daily FMR estimates from ingested calories and labeled isotopes.

Although the strength of the correlation between ODBA and energy expenditure varied among individuals, overall, ODBA and energy expenditure are linearly correlated in common bottlenose dolphins, both when examining total energy expenditure and when isolating the COL. Activity–energetics proxies will benefit from including biomechanical modeling that incorporates drag effects and further refines differences owing to morphometrics and locomotory mode. Further studies are underway to test the ODBA–COL proxy in the present study, and stroke frequency–COL proxies from other studies, on longer duration deployments to quantify their ability to predict daily costs. The approach demonstrated here shows that ODBA may be a useful proxy for the energetic cost of physical activity in bottlenose dolphins; our goal is to apply these techniques to understand locomotion costs in free-ranging cetaceans.

To account for the delay caused by the time it takes the subsampled air to travel through the tubing and reach the gas analyzer, we shifted both gas signals to align with the flow rate (Arieli and Van Liew, 1981; Fahlman et al., 2015). We converted all gas volumes to standard temperature and pressure for dry air (STPD; Quanjer et al., 1993). We multiplied the expiratory flow rate by the expired O₂ and CO₂ to calculate V̇_O2 and CO₂ production rate (V̇_CO2), before integrating V̇_O2 and V̇_CO2 over each breath to yield the volume of O₂ consumed (V_O2) or CO₂ (V_CO2) produced during each breath (Fahlman et al., 2015). Additionally, the respiratory exchange ratio (V_CO2/V_O2) at rest and during the swim trials is reported in Fig. S1.

Fig. A2 demonstrates that even with mean ODBA remaining relatively stable within a trial (Fig. A2B), there was a ramp up in energy expenditure (Fig. A2A), demonstrating that it took several laps to reach steady-state energy expenditure. Lap duration (Fig. A2C) and station duration (Fig. A2D) remained relatively consistent within a trial. We expected between trials to vary in ODBA and lap duration, owing to asking animals for different activity levels between trials.

Although we believe that the fixed intercept, random slope model (Fig. 4A) is the best approach, we also performed a random intercept, fixed slope model, with all other model parameters staying the same. Just as in the fixed intercept model, there was a significant (LRT=15.8, P=0.0001), positive, linear relationship between COL_norm and ODBA (intercept=0.62, 95% CI=−1.03–2.29, t=0.77; slope=7.95, 95% CI=4.59–11.32, t=4.84; d.f.=29; N=35 trials; Fig. A3A).

Fig. A3A,B demonstrates that the random intercept model predicts greater COL at lower ODBA values than the fixed intercept model, and predicts lower COL at higher ODBA values. We performed Bland–Altman graphical procedures to examine agreement and evaluate the presence of proportional systemic bias; limits of agreement were calculated as the mean difference between predicted and measured COL±1.96×SD of the differences (Bland and Altman, 1986). For each pairwise comparison, we plotted the residuals between the predicted and measured COL. Because most trials fall in the middle of the ODBA range, the Bland–Altman plots (Fig. A3C,D) show little difference between predicted and measured COL between the two models. Potentially, the fixed intercept model better predicts individual 9FL3's COL (Fig. A3D) than in the random intercept model (Fig. A3C). Given the minimal difference between the models, we believe the fixed intercept, random slope model is the better choice; RMR was subtracted from steady-state energy expenditure to obtain COL values, thus each individual's COL should increase from a similar intercept (near zero COL at zero ODBA).

The authors thank the marine mammal specialists and veterinarians at Dolphin Quest, as well as the dolphins for their participation. We thank Sam Kelly, Charles Ward, Ben Bedard and Warwick Bayly for assistance with gas analyzer calibration and correction. We also thank David Rosen, Michael Moore, Lewis Halsey, Rory Wilson and Robert Schick for discussions regarding experimental design and methodology. We are grateful to Ding Zhang and Julie van der Hoop, who assisted with data collection. We also thank two anonymous reviewers whose comments/suggestions helped improve and clarify the manuscript.