Some fishes and sea turtles are distinct from ectotherms by having elevated core body temperatures and metabolic rates. Quantifying the energetics and activity of the regionally endothermic species will help us understand how a fundamental biophysical process (i.e. temperature-dependent metabolism) shapes animal ecology; however, such information is limited owing to difficulties in studying these large, highly active animals. White sharks, Carcharodon carcharias, are the largest fish with regional endothermy, and potentially among the most energy-demanding fishes. Here, we deployed multi-sensor loggers on eight white sharks aggregating near colonies of long-nosed fur seals, Arctocephalus forsteri, off the Neptune Islands, Australia. Simultaneous measurements of depth, swim speed (a proxy for swimming metabolic rate) and body acceleration (indicating when sharks exhibited energy-efficient gliding behaviour) revealed their fine-scale swimming behaviour and allowed us to estimate their energy expenditure. Sharks repeatedly dived (mean swimming depth, 29 m) and swam at the surface between deep dives (maximum depth, 108 m). Modal swim speeds (0.80–1.35 m s−1) were slower than the estimated speeds that minimize cost of transport (1.3–1.9 m s−1), a pattern analogous to a ‘sit-and-wait’ strategy for a perpetually swimming species. All but one shark employed unpowered gliding during descents, rendering deep (>50 m) dives 29% less costly than surface swimming, which may incur additional wave drag. We suggest that these behavioural strategies may help sharks to maximize net energy gains by reducing swimming cost while increasing encounter rates with fast-swimming seals.

The metabolic rate of organisms plays fundamental roles in physiological ecology by setting the ‘pace of life’ (Brown et al., 2004). Ectotherms (invertebrates, fishes, amphibians and reptiles) generally have lower body temperatures and, hence, lower metabolic rates than similar-sized endotherms (birds and mammals). Consequently, ectotherms are considered to ‘live life in the slow lane’ (e.g. move slower, eat less and grow slower), whereas endotherms have more active lifestyles, eat more food and grow more rapidly. The dichotomy of ectotherms and endotherms has long been a basis for understanding the lifestyles of diverse animals and their broad-scale ecological implications (Buckley et al., 2012); however, remarkable intermediate forms exit. Some fishes (tunas, opah and some sharks) and leatherback sea turtles have elevated core body temperatures and metabolic rates (Dickson and Graham, 2004; Paladino et al., 1990; Wegner et al., 2015), and exhibit highly active lifestyles (e.g. swim faster and migrate longer distances) (Watanabe et al., 2015) with elevated growth rates (Grady et al., 2014) compared with their ectothermic counterparts. The thermal physiology of these animals, referred to as regional endothermy (Dickson and Graham, 2004), is distinct from the true endothermy of birds and mammals owing to their confined warmed organs and incomplete abilities of regulating body temperature (Clarke and Portner, 2010). To stress their intermediate thermal physiology between true ectotherms and endotherms, some authors proposed the term ‘mesothermy’ (Grady et al., 2014). Quantifying the energetics and activity of regionally endothermic species in the wild will lead to a better understanding of how a fundamental biophysical process (i.e. temperature-dependent metabolism) shapes the ecology of diverse animals. However, such information is still limited, primarily because of difficulties in studying these large, highly active animals.

White sharks, Carcharodon carcharias (Linnaeus 1758), the largest fish with regional endothermy (typical adult body mass, 300–800 kg), are likely to have unusually high energy expenditure for a fish. Although they eat a variety of foods, including teleosts, other sharks and cephalopods (Estrada et al., 2006; Hussey et al., 2012), they seasonally aggregate near pinniped colonies in temperate waters to hunt weaned pups or adult seals. Once caught, a seal will become a disproportionally energy-rich food, equivalent to hundreds of teleosts or cephalopods, owing to its large body size and high fat content. However, seals, especially otariids (fur seals and sea lions), are fast swimmers with remarkable manoeuvrability (Fish et al., 2003; Watanabe et al., 2011). To maximize net energy gains, white sharks are expected to employ behavioural strategies that increase prey encounter rates while reducing the energetic cost of swimming. Despite previous studies on the movement patterns of white sharks near seal colonies (recorded by acoustic telemetry) (Goldman and Anderson, 1999; Huveneers et al., 2013; Jewell et al., 2014; Klimley et al., 2001; Towner et al., 2016), spatiotemporal distributions of seal-predation attempts (directly observed from a boat) (Martin et al., 2005, 2009) and the estimates of daily energy expenditure (Carey et al., 1982; Semmens et al., 2013), the potential behavioural strategies and their consequence on energetics in white sharks have not been sufficiently addressed.

In this study, we attached a package of recording devices, consisting of an accelerometer (with a speed, depth and temperature sensor) and video camera, to white sharks aggregating near the colonies of long-nosed fur seals, Arctocephalus forsteri (formally New Zealand fur seals), off the Neptune Islands, Australia. The direct measurements of swim speed (a proxy for swimming metabolic rate) and body acceleration (indicating when sharks exhibited energy-efficient gliding behaviour) not only revealed their fine-scale swimming behaviour, but also allowed us to estimate their instantaneous field metabolic rates (FMR). Based on this information, we tested two hypotheses regarding shark swimming strategies. First, we hypothesized that white sharks swim slower than the speed that minimizes the cost of transport (hereafter, UCOT-min, where COT is the energy needed to move a unit body mass over a unit distance). According to a theoretical model (Papastamatiou et al., 2018), sharks should do so to maximize net energy gain when the average speed of prey is comparable to that of the sharks (such as our white shark and seal system). This is because, in such systems, the probability of prey arriving at the predator’s location without the predator moving is relatively high, and predators do not need to find prey through active searching at the cost of increased metabolic rates. In other words, UCOT-min, which minimizes energy expenditure per unit distance rather than per unit time, is not optimal when predators can ‘sit and wait’. Second, we hypothesized that cost-efficient gliding behaviour with negative buoyancy, exhibited by white sharks during descending phases of dives (Gleiss et al., 2011a), has substantial effects on their overall swimming costs. More specifically, we would expect that a series of deep dives (passive descents followed by active ascents) shown by white sharks is associated with decreased FMR compared with surface swimming shown by sharks between deep dives. By testing these two hypotheses, we aim to better understand the energy management strategies of this evolutionarily interesting, regionally endothermic species.

Fieldwork and instrumentation

The fieldwork was conducted at the Neptune Islands Group (Ron and Valerie Taylor) Marine Park in Australia (35°14′S, 136°04′E) during August–September 2014, October–November 2015 and January 2016. The island system is composed of two groups of small, rocky islands (the North and South Neptune Islands), which are approximately 10 km apart. In this area, commercial cage-diving tours are operated, in which customers can watch white sharks underwater from cages (Huveneers et al., 2017). Off the North Neptune Islands, sharks were attracted to a boat using bait and chum. When sharks swam past the boat, a metal clamp (to which an electronic biologging package was attached) was placed on the first dorsal fin of the sharks using a deployment pole (Customized Animal Tracking Solutions) (Chapple et al., 2015) (Fig. 1A). This remote attachment method has a great advantage over the conventional method of hooking and catching sharks, where, owing to stress, animals can exhibit unusual behaviour after being released (Sundström and Gruber, 2002; Whitney et al., 2016b). The package was programmed to detach from the clamp 1–2 days later by a time-scheduled release mechanism (Little Leonardo), float to the surface, and be located and recovered using signals from a satellite transmitter (Wildlife Computers) and VHF transmitter (Advanced Telemetry Systems) (Watanabe et al., 2004, 2008). The clamp had a corrodible section, and was designed to come off the dorsal fin after approximately 1 week (that is, nothing would remain attached to the sharks after the research was finished). For each shark tagged, sex was determined by underwater observation, and total length (TL, in m) was visually estimated in relation to the length of several parts of the boat (Table 1). The estimated TL was converted to precaudal length (PCL, in m; PCL=−0.09+0.85×TL) and then body mass [Mb, in kg; ln(Mb)=2.83+2.95×ln(PCL)] using published relationships for this species (Mollet and Cailliet, 1996). However, our estimates of body size may be inaccurate, and sensitivities were tested in the energetic modelling (see below).

The package included a PD3GT accelerometer (21 mm diameter, 115 mm length, 60 g; Little Leonardo), which recorded depth, swim speed (measured by a propeller sensor) and temperature at 1-s intervals, and triaxial acceleration (along longitudinal, lateral and dorso-ventral axes) at 1/16- or 1/32-s intervals throughout the deployment periods (1–2 days). The package on three individuals also included a DVL400M camera (21 mm width, 22 mm height, 68 mm length, 47 g; Little Leonardo), which recorded video (1440×1080 pixels at 30 frames s−1) for approximately 6 h. The camera was programmed with a 3–12 h delay start to target daytime periods when cage-diving operators were not present.

All necessary permits were obtained from the Department of Environment, Water and Natural Resources (DEWNR) (M26292), Marine Parks (MR00047), PIRSA Exemption (9902693 and 9902777) and the Flinders University ethics committee (E398).

Swim speed measurement

Relative swim speed, measured by the number of rotations per second of the propeller sensor, was converted to actual swim speed (m s−1) using equations obtained from a flow tank calibration experiment. In the experiment, a PD3GT accelerometer was set in the tank and flow speed was increased from 0.3 to 1.1 m s−1 at intervals of 0.1 m s−1. The relationship obtained was linear (R2>0.99, N=9 data points). Although the upper speed range was limited to 1.1 m s−1 by the capacity of the tank, a linear relationship between propeller rotation and swim speed has been validated for up to approximately 3.8 m s−1 (Aoki et al., 2012). Inevitable differences between the pitch angles of the sharks and those of the accelerometers (calculated from low-pass filtered longitudinal accelerations) were estimated for each shark using the within-data calibration method (Kawatsu et al., 2010). This ‘attachment angle’ was accounted for in the conversion of swim speed by dividing the raw speed estimate by the cosine of the attachment angle. To validate this correction method, another set of flow tank experiments was conducted. A PD3GT accelerometer was set in the tank at angles of 15, 30 and 45 deg relative to flow, and the flow speed was increased from 0.4 to 1.0 m s−1 at intervals of 0.2 m s−1 for each angle. Using the correction method, errors in the speed estimates (i.e. difference between the true and estimated speeds, expressed as percentages of the true speeds) were reduced (average error across the four different speeds was 1%, 8% and 9% for angles of 15, 30 and 45 deg, respectively). Therefore, the correction method was considered valid, as long as the attachment angle was moderate (<45 deg). By contrast, the differences between the yaw angles of the sharks and those of the accelerometers were assumed to be zero, because the packages were firmly attached to the side of the dorsal fins (Fig. 1A). The package was accidentally set vertically on the dorsal fin for shark 8, and the propeller sensor did not rotate properly. Swim speed and field metabolic rate (FMR) were not estimated for this individual.

Depth and acceleration data analyses

Behavioural data were analysed using the software Igor Pro (WaveMetrics) with the Ethographer extension (Sakamoto et al., 2009). The periods during which sharks interacted with the boat, representing unnatural behaviour (Huveneers et al., 2018), were excluded from the analyses. Based on the depth profiles, shark behaviour was categorized into three groups: (i) shallow dives, when the sharks undertook repeated up-and-down movements at <50 m depth without extended surfacing periods; (ii) deep dives, when the sharks dived from the surface to >50 m depth and returned to the surface within 1 h; and (iii) surface swimming, when the shark kept swimming at the surface (0–2 m depth) for >5 min (Fig. 1C). Although some intermediate patterns (e.g. continuous deep dives without surfacing) were also observed, 80% of our 150-h records was covered by the three categories (Table 2).

Gliding periods during descending phases of dives were determined by the lateral acceleration records as the periods showing no cyclic changes. This method was confirmed to be valid by the simultaneously recorded video footage (Movie 1). Overall dynamic body acceleration (ODBA) (Wilson et al., 2006), a proxy for energy expenditure of the animals, was calculated as the sum of the absolute values of high-pass filtered acceleration over three axes.

Field metabolic rate

Instantaneous FMR of individual sharks was estimated based on swim speed, water temperature and whether the shark was actively swimming versus passively gliding. A previous experiment with swim-tunnel respirometry for short-fin mako sharks, Isurus oxyrinchus (6.1 kg body mass; 18°C water temperature), a species with regional endothermy closely related to white sharks, showed that their FMR (in mg O2 kg−1 h−1) during active swimming is approximated by:
formula
(1)

where SMR is standard (or resting) metabolic rate in mg O2 kg−1 h−1 and U is swim speed in TL s−1 (Sepulveda et al., 2007). Although this equation was obtained from sharks smaller than the white sharks tagged in the present study, the effects of body size on swimming metabolic rates in fishes can be removed by using swim speed relative to body length (Beamish, 1978). More specifically, log swimming metabolic rates plotted against swim speed relative to body length produce similar straight lines independently of body size of the fish (Beamish, 1978). Owing to the lack of direct measurements of swimming metabolic rates for larger fishes with regional endothermy, Eqn 1 was regarded as the best available information.

The SMR of short-fin mako sharks, estimated by an extrapolation of the relationship between swim speed and metabolic rate to zero speed, is 124 mg O2 kg−1 h−1 (Sepulveda et al., 2007). The SMR of white sharks was estimated by scaling up the short-fin mako shark value to the body mass of white sharks using a scaling exponent of 0.79 (Payne et al., 2015), and adjusted for the water temperature experienced by the sharks using a Q10 value of 2.42, a typical value reported for sharks (Whitney et al., 2016a) (see below for sensitivity analyses). Instantaneous FMR during active swimming periods was estimated based on swim speed and total length of the sharks using Eqn 1. All but one shark exhibited gliding behaviour during descending phases of dives, and FMR during gliding periods was set at SMR. FMR was smoothed using a 1-min running average to obtain a physiologically appropriate time scale for changes in metabolic rate (Williams et al., 2014). The units of FMR were converted from mg O2 kg−1 h−1 to W by assuming that 1 mol O2 equates to the utilization of 434 kJ.

We are aware of the limitations of scaling up a 6 kg short-fin mako shark to model 200–700 kg white sharks (see Payne et al., 2015); therefore, our focus in this study was to compare FMR among different behavioural categories and to estimate UCOT-min for individual sharks, rather than compare FMR of white sharks with that of other species.

Hypothesis testing

To test the hypothesis that white sharks swim slower than UCOT-min, the relationship between swim speed and COT was constructed for individual sharks based on Eqn 1 and the estimates of SMR as explained above (Fig. 2). COT (J m−1 kg−1) was calculated by dividing FMR (W) by swim speed (m s−1) and body mass (kg). The mean water temperature experienced by individual sharks was used in the calculation of FMR (Table 1). However, FMR and COT are sensitive to several parameters, especially body mass (estimated from visually determined body length), the scaling exponent of metabolic rates (set at 0.79) and Q10 values. To address these uncertainties, four additional scenarios were considered. In the first and second scenarios, the TL of each shark was assumed to be 0.3 m shorter and longer, respectively, than our estimate. A recent study conducted at the same site (C. May, unpublished data) showed that the mean difference between white shark TL visually estimated by scientists and that measured by stereo-video cameras is approximately 0.2 m. Our choice of 0.3 m, therefore, represents a conservative case, encompassing likely biases in size estimates. In the third scenario, the scaling exponent of metabolic rates was set at 0.84 (Sims, 2000). In the fourth scenario, the Q10 value was set at 1.67, which was reported for endothermic tunas (Dewar and Graham, 1994).

To test the hypothesis that deep diving behaviour (passive descents followed by active ascent) is cost-efficient, mean FMR and ODBA was calculated for each behavioural event, including shallow dives, deep dives and surface swimming. Because shallow dive events continued for hours without clear breaks, these events were split into 15-min segments to calculate mean FMR and ODBA. Then, the effects of behavioural categories on FMR and ODBA were examined with linear mixed-effect models with shark ID as a random factor, using the software R with the lme4 extension (Bates et al., 2014). Statistical significance was tested by comparing the full models and the models without behavioural categories using the likelihood ratio test.

High ODBA values for surface swimming events (0–2 m depth; Fig. 3B) may overestimate the swimming costs, because dorsal fins of the sharks (and the accelerometers attached) may oscillate while breaking the surface. To test this possibility, deeper portions of surface swimming events (1–2 m depth for >10 s) were subsampled, in which dorsal fins (approximately 0.5 m length) are unlikely to break the surface. The depth sensors had a sufficient resolution (0.097 m) and accuracy (calibrated to zero when they were floating at the surface) for this subsampling. Statistical analysis was repeated with the subsamples.

We attached the biologging packages to 10 sharks over three research cruises; however, in two individuals, the clamp came off prematurely and the recording durations were <2.5 h. Excluding these individuals and all periods during which sharks interacted with the boat (0–13 h), the effective sample size was eight, with recording durations of 9–37 h (total duration, 150 h) (Table 1). Despite considerable variation among individuals, the behaviour of all eight sharks was composed of shallow dives (60%), deep dives (11%), surface swimming (9%) and other behaviours (20%) (Table 2). Surface swimming mostly occurred between deep dives (Fig. 1C), but some surface swimming was observed between shallow dives. Based on the acceleration data, all but one (shark 3) shark exhibited gliding behaviour during descending phases of dives (Fig. 1C, Movie 1). Deep dives had more consistent dive profiles and proportionally longer gliding periods (20% of total durations) than shallow dives (8% of total durations). Video footage was obtained for three of the eight sharks, but one shark interacted with the boat throughout the footage. In the video footage obtained from shark 5, a seal was seen three times, once on the sea floor during shallow dives, and twice during surface swimming (Fig. 1B).

The modal, sustained swim speed (calculated as the 5-min average of swim speed) for individual sharks ranged from 0.80 to 1.35 m s−1 (overall average, 0.94 m s−1), which was slower than the estimated UCOT-min (range 1.3–1.9 m s−1; Fig. 2A–G). Under the scenarios that the TL of each shark is 0.3 m shorter and longer than our estimates, respectively, UCOT-min shifted to a lower range (1.1–1.8 m s−1) and a higher range (1.4–2.1 m s−1), respectively (black dotted and dashed curves in Fig. 2A–G). Nevertheless, the recorded modal swim speeds were still slower than the UCOT-min values. Under the additional two scenarios that (i) the scaling exponent is 0.84 rather than 0.79, and (ii) Q10 is 1.67 rather than 2.42, the COT curves shifted upward without affecting UCOT-min (red dotted and dashed curves in Fig. 2A–G). In addition, the recorded speeds were slower than the predicted speeds for the body mass and regionally endothermic physiology of white sharks, based on a published allometric relationship (Watanabe et al., 2015) (Fig. 2H). However, shark 5 had a higher subpeak at 2.05 m s−1, which was close to its UCOT-min (Fig. 2E) and the predicted speed from allometry (Fig. 2H). This subpeak corresponded to the period when the shark exhibited surface swimming with elevated speeds for 1 h (Fig. 1C). We know that this shark moved from the North Neptune Islands (where it was tagged) to the South Neptune Islands (where it was re-observed the next day and the tag was manually recovered, approximately 10 km away from the North Neptune Islands) during the deployment period. As such, the fast surface swimming period might represent travel between the islands.

Linear mixed-effects models based on the data for seven (for FMR, expressed as multiples of SMR) and eight sharks (for ODBA) showed that behavioural categories (shallow dives, deep dives and surface swim) affected both FMR (χ22=157.1, P<0.0001) and ODBA (χ22=564.4, P<0.0001), with deep dives being the least energetically expensive (Fig. 3). Based on FMR and ODBA, shallow dives were 13% and 11% more costly, respectively, whereas surface swimming was 29% and 155% more costly, respectively, than deep dives. Interestingly, surface swimming was 19% and 146% more costly (based on FMR and ODBA, respectively) than the non-gliding, ascending phase of deep dives (FMR, χ21=54.0, P<0.0001; ODBA, χ21=153.0, P<0.0001). When surface swimming events were replaced by deeper subsamples of the events (1–2 m depth), the estimate of ODBA for surface swimming decreased by 28% (in the model including shallow dives, deep dives and surface swimming) and 37% (in the model including surface swimming and the ascending phase of deep dives), but remained significantly higher than that of deep and shallow dives (χ22=84.7, P<0.0001) and the ascending phase of deep dives (χ21=19.4, P<0.0001). The results for FMR changed little.

Slow swim speed

Using propeller speed sensors, we showed that white sharks sustain swim speeds of 0.80–1.35 m s−1, which are slower than the estimated UCOT-min values. Our results were robust to some uncertainties in shark body size, the scaling exponent of metabolic rates and Q10 values, as shown by the sensitivity analyses (Fig. 2A–G). In addition, the recorded swim speeds were slower than the predicted speeds for the body mass and regionally endothermic physiology of white sharks (Fig. 2H). Our swim speed records are lower than the previous estimates based on acoustic telemetry [median 1.34 m s−1 (Klimley et al., 2001); median 2.25 m s−1, mean 2.91 m s−1 (Semmens et al., 2013)]; however, swim speed may have been overestimated in those studies, which relied on a positioning system with significant error. Our findings agree with a theoretical model (Papastamatiou et al., 2018) that states that sharks should swim slower than their UCOT-min to maximize net energy gain when the average prey speed is comparable to the average predator speed (such as our white shark and seal system). Largemouth bass in the wild also swim slower than its UCOT-min, presumably to increase foraging efficiency rather than maximize travel efficiency (Han et al., 2017). Another, but not mutually exclusive, interpretation is that white sharks might reduce energy expenditure by swimming at the minimum speed at which the forces acting on them, including hydrodynamic lift and negative buoyancy, are balanced (Gleiss et al., 2015; Iosilevskii and Papastamatiou, 2016). This interpretation is supported by our observation that shark 3, which swam the slowest compared with its UCOT-min (Fig. 2C), is the only individual that did not exhibit gliding behaviour during descents. That is, shark 3, which is a female, might have a buoyancy close to neutral owing to its high fat content, and could balance forces at slower swim speeds compared with other individuals. Overall, our results support our hypothesis that white sharks aggregating near seal colonies adopt slow speeds that may be optimized to increase encounter rates with fast-swimming seals while reducing swimming costs. This strategy is as close to a ‘sit-and-wait’ strategy as is possible for perpetual swimmers such as white sharks.

Interestingly, however, we also showed that a shark (shark 5) swam at a high speed (2 m s−1) at the surface for 1 h, presumably when it travelled from the North Neptune Islands to the South Neptune Islands. This sustained speed is among the highest values recorded for fishes (Watanabe et al., 2015), and close to the predicted speed for their body mass and regionally endothermic physiology. Moreover, the speed is close to UCOT-min of the shark, indicating that this shark adopted a different, faster optimal speed when travelling rather than foraging. Although we need more data to confirm our observations, this finding suggests that white sharks may use different swim speeds depending on the context to optimize their energy use, as previously reported for flight speeds of a bat (Grodzinski et al., 2009).

Cost-efficient gliding behaviour

Gliding behaviour during descending phases of dives was previously reported for white sharks (Gleiss et al., 2011a), but quantitative assessments of the energetic benefit based on field data have never been made. In theory, passive gliding descents followed by active ascents with negative buoyancy could lead to substantial energy savings compared with continuous horizontal swimming, because animals incur decreased drag during passive gliding for a given swim speed (Weihs, 1973). Moreover, cost-efficient intermittent swimming was experimentally validated using a pitching foil operated in a water tunnel at variable duty cycles (Floryan et al., 2017). In accordance with the previous studies, we showed that deep dives (which had proportionally longer gliding periods than shallow dives) were the least expensive, followed by shallow dives, with surface swimming the most expensive, based on our FMR estimates (Fig. 3A). One may argue that sharks are expected to work harder for a given swim speed during ascending phases of deep dives compared with horizontal swimming, and that the costs of deep dives are underestimated. Although this possibility cannot be fully assessed by our FMR estimates, ODBA, a proxy for energy expenditure that quantifies the relative body movements of the animals, showed a trend similar to that of FMR (Fig. 3B), supporting our argument that deep dives are the least expensive. Unexpectedly, even ascending phases of deep dives had lower FMR and ODBA than surface swimming. Therefore, the absence of gliding behaviour is not the only factor that explains the higher costs of surface swimming. Another factor is the relatively high speed during surface swimming, especially in shark 5 (Fig. 2). Additionally, when moving at the surface, animals inevitably create waves and incur increased drag (called wave drag, which may increase body movements and ODBA), even when they are fully submerged (Alexander, 2003). To avoid wave drag, animals may need to swim deeper than approximately 2.5 body diameters (Alexander, 2003), which is approximately 2 m for white sharks. Particularly high ODBA during surface swimming (Fig. 3B) could be due to the dorsal fins breaking the surface rather than high activities of the whole bodies. In fact, ODBA decreased by 28–37% when surface swimming events were replaced by deeper subsamples, in which dorsal fins are unlikely to break the surface. However, the subsamples still had higher ODBA than deep dives, shallow dives and ascending phases of deep dives, indicating that high energetic cost of surface swimming is a robust result.

The main function of deep-diving behaviour might be foraging rather than energy saving, as suggested by some burst swimming events observed during deep dives (Y. Y. Watanabe, unpublished data). In addition, five of the eight sharks did not exhibit deep diving behaviour during our limited recording periods (Table 2). Nevertheless, a large difference in FMR between deep dives and surface swimming, as well as the commonness of deep diving behaviour in both coastal and offshore habitats reported for this species from longer-term satellite telemetry data (Domeier and Nasby-Lucas, 2008; Sims et al., 2012; Weng et al., 2007), suggests that gliding behaviour has substantial effects on the overall swimming costs of white sharks. Among large-bodied sharks, prolonged gliding during descents has also been reported for whale sharks (Gleiss et al., 2011b), but not for tiger or Greenland sharks (Nakamura et al., 2011; Watanabe et al., 2012), despite their negative buoyancy. As apparently rare cases, prolonged gliding during ascents with positive buoyancy was reported for bluntnose sixgill and prickly sharks (Nakamura et al., 2015). How the interspecific variation in gliding behaviour is linked to species-specific foraging strategies would be an interesting question for future research. In addition, it is intriguing that surface swimming is costly for white sharks, given that they have a strong preference for surface swimming during oceanic migrations (Bonfil et al., 2005; Domeier and Nasby-Lucas, 2008; Sims et al., 2012). If surface swimming during long travels is for navigation purposes (e.g. using celestial cues) (Bonfil et al., 2005), it would mean a trade-off between navigation and energy saving, a topic that would merit further investigations.

In conclusion, by using modern biologging technologies, we provided support for the two hypotheses regarding behavioural strategies of white sharks aggregating near seal colonies. First, they swim slower than UCOT-min, presumably to increase encounter rates with fast-swimming seals while reducing swimming costs, as predicted by theoretical models. White sharks can be considered ‘sit-and-wait’ predators in this sense, although they are continuous swimmers. Second, sharks exhibit gliding behaviour during descending phases of dives, rendering diving behaviour less costly than horizontal surface swimming, which presumably incurs additional wave drag. This study highlights some new aspects of energy management strategies for white sharks, a species with unique eco-physiology among vertebrates.

We thank R. Hall, L. Meyer, R. Mulloy, L. Nazimi, S. Payne, W. Robbins, A. Schilds, M. Ward and S. Whitmarsh for their support during fieldwork, N. Miyata and T. Mori for their help with the flow tank experiment, and two anonymous reviewers for thoughtful comments.

Author contributions

Conceptualization: Y.Y.W., N.P., J.S., A.F., C.H.; Methodology: Y.Y.W., N.L.P., J.M.S., A.F., C.H.; Formal analysis: Y.Y.W.; Investigation: Y.Y.W., N.L.P., J.M.S., A.F., C.H.; Writing - original draft: Y.Y.W.; Writing - review & editing: N.L.P., J.M.S., C.H.

Funding

This work was funded by Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS) (25850138 and 16H04973), the Winifred Violet Scott Foundation, the Neiser Foundation, Nature Films Production, and supporters of the study through the crowdfunding campaign on Pozible. J.M.S. held a JSPS Invitation Fellowship for Research in Japan (L15560) during part of this work.

Data availability

Data used in the linear mixed-effect model analyses are available from the figshare repository: 10.6084/m9.figshare.7671836

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Competing interests

The authors declare no competing or financial interests.

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