It is generally assumed that the body temperature of large animals is less likely to change because of their large body size, resulting in a high thermal inertia and a smaller surface area to volume ratio. The goal of this study was to investigate the stability of body temperature in large fish using data from field experiments. We measured the muscle temperatures of free-ranging whale sharks (Rhincodon typus), the largest extant fish globally, and investigated their ectothermic physiology and the stability of their body temperature. The muscle temperature changed substantially more slowly than the water temperature fluctuations associated with vertical movements, and the whole-body heat-transfer coefficients (HTCs) of whale sharks estimated using heat-budget models were lower than those of any other fish species measured to date. The heat-budget models also showed that internal heat production does not contribute to changes in muscle temperature. A comparative analysis showed that the HTC at cooling in various fish species including both ectothermic and endothermic species ranging from 10−4 to 103 kg was proportional to body mass−0.63. This allometry was present regardless of whether the fish were ectothermic or endothermic, and was an extension of the relationship observed in previous studies on small fish. Thus, large fish have the advantage of body temperature stability while moving in environments with large temperature variations. Our results suggest that the large body size of whale sharks aids in preventing a decrease in body temperature during deep excursions to more than 1000 m depths without high metabolic costs of producing heat.

Body temperature affects the fitness of organisms because it influences their activity, growth and metabolism through physiological processes (Huey and Stevenson, 1979). Most fish are ectotherms, i.e. their body temperatures are dependent on their external environment, with their activity levels changing with temperature (Lear et al., 2019; Payne et al., 2016). Since fish live in water, which has a high thermal conductivity, it has been assumed that they lose most of their metabolic heat through their gills during branchial respiration (Stevens et al., 1974; Stevens, 2011). However, some fishes, such as tunas and lamnid sharks, have evolved the ability to raise their body temperature (Carey et al., 1971). These fishes have a counter-current heat exchange system that efficiently transfers the heat produced by aerobic red muscles during exercise to cool blood returning from the body's surface or the gills where heat is lost to the environment (Brill et al., 1994; Dickson and Graham, 2004; Stevens, 2011). The strategy of maintaining relatively high body temperatures could generate benefits, such as elevated cruising speeds and large-scale migrations (Dickson and Graham, 2004; Watanabe et al., 2015). Regardless of the source of heat, from specific tissues and organs such as active muscles, or from whole-body endothermy, maintaining higher body temperatures is energetically expensive because metabolic thermoregulation requires a large amount of energy (Bennett and Ruben, 1979).

Empirical measurements of body temperature have indicated that the body temperatures of large fish, such as tunas, ocean sunfish and swordfish, decrease slowly when they move through a cold environment under the thermocline between mixed surface water of homogeneous temperatures and waters that are cooler at greater depths (Lawson et al., 2010; Nakamura et al., 2015; Stoehr et al., 2018). High thermal inertia due to large body size helps maintain higher body temperatures during swimming below the thermocline without the high metabolic cost of heat production. Fish with relatively large body sizes that temporarily swim below the thermocline show behavioural thermoregulation to ensure that their body temperature does not decrease to the same temperature as that of deep water (Carey and Scharold, 1990; Holland and Sibert, 1994; Lawson et al., 2010; Nakamura et al., 2015). Such behavioural thermoregulation is facilitated by the fact that different environmental temperatures are vertically close together in marine environments.

Behavioural thermoregulation is performed in order for animals to maintain an appropriate body temperature for activities. Temperature affects the activity level of animals, and the effect of temperature on activity levels can be understood by drawing a thermal performance curve (Huey and Stevenson, 1979; Huey and Kingsolver, 1989). Examining which temperature leads to the highest activity level is important to understand the significance of behavioural thermoregulation. The thermal performance curve of free-ranging fish has been estimated from their activities, which vary with water temperature (Lear et al., 2019; Payne et al., 2016, 2018). It was based on the assumption that water temperature and body temperature would be the same, but body temperature and water temperature may differ because of high thermal inertia, especially for large fish whose body temperature changes slowly. Therefore, it is necessary to draw a thermal performance curve against body temperature. Fish activity can be quantified by examining body movement using accelerometers (Tanaka et al., 2001; Kawabe et al., 2003), and recording of body temperature and activity simultaneously may provide a more accurate thermal performance curve for free-ranging fish.

Heat exchange between fish and their environment may manifest as changes in fish body temperature and rates of change in body temperature may be quantified by a coefficient that is often, though not strictly correctly, described as a ‘heat-transfer coefficient’ (HTC). For convenience and consistency with previous literature we continue to refer to this coefficient as a HTC (Kubb et al., 1980; Neill et al., 1976; Sorenson and Fromm, 1976; Stevens and Fry, 1974; Stevens and Sutterlin, 1976; Weller et al., 1984). The HTC is estimated using Newton's law of cooling, and represents the rate at which fish body temperature changes relative to changes in environmental temperature. It is derived from the overall thermal conductance, Ko (estimated in W °C−1 as seen in Bakken, 1976) by dividing Ko by the whole-body heat capacity of tissues, C (in J °C−1). Thus, the HTC includes the effects of heat capacity due to body size, the effects of thermal conductivity due to the components of the fish body, and the effects of differences in body shape. Previous studies have shown that larger fish generally have a smaller HTC; the HTC of very small fish (<10 g) was proportional to the power of −0.3; however, the HTC of fish weighing 100–5000 g was proportional to the power of −0.6 (Fechhelm and Neill, 1982; Spigarelli et al., 1977; Stevens and Fry, 1970, 1974; Stevens and Sutterlin, 1976). Since the range of body mass in these studies was for relatively small-sized fish, it is necessary to establish how HTC varies with body size by extending it to the largest extant fish. In addition, living animals cool (or warm) much faster than non-living animals because heat can diffuse more quickly in living animals as a result of blood flow (Pearse and Hall, 1928). This is why empirical measurements of changes in body temperature in the living state are required.

The whale shark (Rhincodon typus, Smith 1828) is the world's largest fish, and is mainly distributed in tropical and sub-tropical waters (Stevens, 2007). Whale sharks are often observed near the sea surface, although recent tracking studies have shown that they can dive to depths exceeding 1000 m below the sea surface (Brunnschweiler et al., 2009; Graham et al., 2006; Tyminski et al., 2015). Thums et al. (2012) suggested that behavioural thermoregulation exists in whale sharks; the colder temperatures experienced during diving increase the duration of subsequent surfacing behaviour. Meekan et al. (2015) suggested that the enormous size of whale sharks allows them to increase their foraging efficiency and to access food in deep, cold water. These studies suggest that the large body size of whale sharks causes high thermal inertia; however, no empirical studies have measured the body temperature of whale sharks to investigate this aspect.

This study aimed to investigate the existence of high thermal inertia in whale sharks, which can be identified by slow changes in their body temperature. Specifically, we collected behavioural data from free-ranging whale sharks and took direct measurements of their body temperature. We then evaluated the HTC of fish with different body sizes from the published literature in comparison to that of whale sharks to investigate the effect of body size on HTC.

Field experiments

The field experiments in this study were conducted around Okinawa Island, Japan. Two whale sharks (C1, C2) that were caught by a set-net in Yomitan, Okinawa, Japan (26°21.9′N, 127°43.1′E) in 1998 and 1997 were kept in a netted cage for 17 and 19 years, respectively. After this time, they were released near Ie Island, Okinawa, Japan (26°48.0′N, 127°48.0′E) on 22 June, 2015 and 10 October, 2016, respectively. A third whale shark (W1), which was caught by a set-net in Yomitan on 23 April, 2016, was released on 25 April, 2016. The length between the tip of the snout and the first dorsal fin in each of the sharks was measured and converted to total length (TL). We also measured the girth of the sharks in cm (Table 1).

Table 1.

Details of instrument deployments on the three whale sharks

Details of instrument deployments on the three whale sharks
Details of instrument deployments on the three whale sharks

An accelerometer-magnetometer data-logger (AMD) (W2000-3MPD3GT, Little Leonardo Co., Bunkyo-ku, Tokyo, Japan; diameter: 28 mm, length: 166 mm, mass: 180 g) was used to measure vertical movements and swimming activity. It recorded tri-axial acceleration at 16 Hz and tri-axial magnetism, swimming speed, depth, and water temperature at 1 Hz. To measure the temperature inside the body, a depth-temperature recorder (DTR) was used (LAT1810ST, Lotek Wireless Inc., Newmarket, ON, Canada; diameter: 11 mm, length: 35 mm, mass: 5 g, with a 150 mm stalk temperature sensor). It recorded depth and both internal and external temperatures at 1 Hz. These devices were combined on a single unit foam buoy with a retrieval system consisting of an auto-release timer (RT-4, Little Leonardo Co.; diameter: 16 mm, length: 25 mm, mass: 16 g), a VHF transmitter (MM130B, Advanced Telemetry Systems, NW Isanti, MN, USA; diameter: 16 mm, length: 60 mm, mass: 20 g), and a satellite transmitter (SPOT6, Wildlife Computers, Redmond, WA, USA; diameter: 10 mm, width: 20 mm, length: 80 mm, mass: 30 g). A pop-up satellite archival tag (PSAT) (MiniPAT, Wildlife Computers; diameter: 38 mm, length: 124 mm, mass: 60 g) was also deployed to collect long-term vertical movements. It recorded depth and water temperature every 5 to 10 min.

The instrument packages were secured by metal or plastic cable ties that were threaded through small holes that horizontally penetrated the skin on the dorsal (top) surface of the shark. Another vertical hole was pierced (we confirmed that it penetrated the skin by the presence of bleeding), and the stalk sensor of the DTR was inserted; thus, muscle temperature (Tm) at a depth of 15 cm from the body surface was measured (Fig. 1). Whale sharks have a layer of connective tissue under the skin, which functions as an insulation layer (Meekan et al., 2015). Their blood absorbs and distributes heat throughout the body, which is why their peripheral muscle temperature could be used as an indicator of body temperature. Notably the temperature of the blood collected from a whale shark kept at the aquarium was similar to the ambient water temperature (R.M., unpublished observations). The instrument packages automatically detached from each shark after several days of deployment. The packages then floated to the surface, were located using the satellite and VHF transmitters, and were retrieved by boat. The PSATs were deployed on the side of the first dorsal fin by an anchor with a nylon tether (Fig. 1) and detached from the sharks after the several months of deployment time. Data on the PSATs were retrieved via the ARGOS system. Detailed information on how the sharks were tagged is presented in Table 1. These procedures were approved by the Ethics Committee at the University of Tokyo, Japan (Institutional Animal Case and Use Committee Protocol P15-15, P16-8).

Fig. 1.

Attachment positions of an instrument package and a pop-up satellite tag on a whale shark. Enlarged image shows the devices contained in the package: an accelerometer–magnetometer data-logger (W2000-3MPD3GT), a depth temperature recorder (LAT1810ST) with a 15 cm stalk sensor, a time-release mechanism, a syntactic foam buoy, a VHF transmitter (MM130B) and a satellite transmitter (SPOT6). The instrument packages were attached via metal or plastic cable ties threaded through small holes (A) pierced in the back of the fish. Another vertical hole (B) was pierced, and a stalk sensor was inserted into the muscle under the skin.

Fig. 1.

Attachment positions of an instrument package and a pop-up satellite tag on a whale shark. Enlarged image shows the devices contained in the package: an accelerometer–magnetometer data-logger (W2000-3MPD3GT), a depth temperature recorder (LAT1810ST) with a 15 cm stalk sensor, a time-release mechanism, a syntactic foam buoy, a VHF transmitter (MM130B) and a satellite transmitter (SPOT6). The instrument packages were attached via metal or plastic cable ties threaded through small holes (A) pierced in the back of the fish. Another vertical hole (B) was pierced, and a stalk sensor was inserted into the muscle under the skin.

We set the auto-release timers of the instrument packages to detach after two days, three days and one day for whale shark C1, C2 and W1, respectively. However, the detachment of the packages on whale sharks C1 and C2 was delayed by 7 days and 5 days, respectively, because of a problem with the auto-release timer. The packages on whale sharks C1, C2 and W1 floated 78 km, 49 km and 6 km away from each release point, respectively, and all packages were retrieved. Owing to the limited recording duration of the AMD (7 days), caused by limited memory capacity, we obtained 7 days of data from whale sharks C1 and C2, and 1 day of data from whale shark W1 (Table 1). The stalk of the DTR inserted in whale sharks C1 and C2 fell out 2 and 4 days after release (the temperature change became synchronised with changes in water temperature), respectively. Therefore, we obtained 2 days of Tm data from whale shark C1 4 days from C2, and 1 day of data from W1 (Table 1). PSATs deployed on whale sharks C1 and C2 detached according to the scheduled time (3 and 6 months, respectively); however, the PSAT on whale shark C2 was retrieved directly when it landed on the coast of the Philippines after being detached as scheduled. The PSAT deployed on whale shark W1 was retrieved when the shark was recaptured by the same trap-net two weeks after release.

Data analysis

Swimming activity was measured by tailbeat frequency. We used the ‘Ethographer’ software from Igor Pro (v.6.34, Wave Metrics, Portland, OR, USA) to generate spectrograms for frequency spectrum analyses using wavelet transforms (Sakamoto et al., 2009). The spectrum of lateral acceleration was calculated every 5 s and the frequency with the largest amplitude was assumed to be the tailbeat frequency (TBF). TBF and Tm were compared to determine the relationship between activity and body temperature. A Gaussian curve was fitted for the thermal performance curve to establish changes in activity with temperature (Payne et al., 2016). Note that since a decrease in TBF at higher temperatures has not been well confirmed, only the portion below the optimal temperature (the temperature with the highest activity) section of the Gaussian curve was fitted, indicating that the Tm of the whale shark might not have reached the optimal temperature.

Changes in the HTC of the whole body provide information on the observed rates of body warming and cooling, and were estimated using a function of heat exchange with the environment and internal heat production (Holland and Sibert, 1994; Kitagawa et al., 2001). Since fish live in water and there is no evaporative heat lost, an intuitive heat balance equation is:
formula
(1)
where M is metabolic heat production, Ko is thermal conductance (an integrated parameter describing the rate of total heat flow between the body and the environment), Tb is the body temperature, Te is the environmental temperature, C is the whole-body heat capacity and dTb/dt is the rate of body temperature change over time. In the case of ectothermic fish, however, most metabolic heat is lost to water through their gills (Stevens, 2011); thus, the greatest part of body temperature change should be explained by the heat exchange with the water. Dividing both sides of Eqn 1 by C and rearranging it gives:
formula
(2)
Since we measured muscle temperature as body temperature and environmental temperature as ambient water temperature, assuming Tm=Tb and Ta=Te, making , k=−Ko/C, and adding observation noise, we have the following heat-budget model:
formula
(3)
where k is the HTC of the whole body (°C min−1 °C−1), Ta(t) is the ambient water temperature (°C) as a function of time t (min), Tm(t) is the muscle temperature as a function of time t, is the rate of temperature change due to internal heat production (°C min−1), and ε is white Gaussian noise. Since there was a time difference between when each shark entered the water with Ta<Tm and when Tm began to decrease, τ (min) was added as the response time lag against Ta(t):
formula
(4)
Since Ko varies with blood circulation in living animals (Pearse and Hall, 1928), the coefficient k includes both physiological conditions and physical thermal inertia and represents the sum of physical thermal conductivity and physiological factors (Kitagawa and Kimura, 2006). Since k is known to vary with ambient temperature (Kitagawa and Kimura, 2006), fixed and variable conditions were assumed for k:
formula
(5)
formula
(6)
where k1 and k2 are two alternative values for HTC (at cooling and at warming). The parameters for each model were estimated using a maximum likelihood method. We used the function optim in R v.3.4.1 (https://www.r-project.org/) to maximize the likelihood by adjusting all parameters. It was also used to calculate the Bayesian information criterion (BIC) values of the fixed HTC models (Eqn 5) and the variable HTC model (Eqn 6). The model that had the lowest BIC value was regarded as the more parsimonious model. To investigate the contribution of to the changes in Tm, we compared the BIC value between the model with and the model without .

Comparative analysis

To compare the HTC at cooling of a range of fishes in relation to body size, we collected data from the published literature on body mass and HTCs that had been estimated using heat-budget models similar to those used in this study (coefficients related to temperature differences between body and water, with the dimension being the reciprocal of time). Both endothermic and ectothermic fishes were included, because the HTC contributes to the physical component of body temperature change caused by temperature differences with the surroundings of each fish. Note that the body parts where temperature was measured varied because different measurement methods were used in each study. Body mass was used as an index of body size because the fish species used in the dataset varied greatly in body shape, with mass being a better predictor of heat capacity. When body mass was not reported, it was estimated from body length using published length–mass relationships for a given species. All Thunnus species, swordfish and Mako sharks were regarded as endothermic (including regionally endothermic), but Pacific bluefin tuna weighing less than 500 g were classified as ectothermic because individuals in this species develop endothermy when their body mass ≥500 g (Kubo et al., 2008). Since we collected data on both ectothermic and endothermic species, we used generalised linear mixed models (GLMMs) and a likelihood ratio test to test whether ectothermy or endothermy affected the relationship between body mass and HTC. To use linear models, both body mass and HTC were logarithmically transformed. We used GLMMs with a Gaussian distribution, and fish species were set as a random effect. We used the function lmer from the lme4 package (https://cran.r-project.org/web/packages/lme4/index.html; Bates et al., 2015) in R to estimate the parameters of each model. We configured two GLMMs: one that included separate categories of ectothermy or endothermy and one that excluded these categories. We set the logarithm of HTC as a response variable in the model, and the logarithm of body mass and the categories of ectothermy or endothermy as explanatory variables.

We found that the maximum Tm was similar to the sea surface temperature (SST), that is, the water temperature when the sharks were swimming near the sea surface (depth <1 m), in all three whale sharks (Fig. 2). Tm fluctuated less than the water temperature and changes in Tm were less than 0.1°C min−1 in water with a temperature difference of >10°C (Fig. 2). After being released, whale shark C1 dived to 390 m, where the water temperature was 14°C, and returned to the surface after 12 h (Fig. 2B). The Tm of this shark decreased to a minimum of 19°C after the time spent at 390 m (Fig. 2B). This shark showed lower TBF when Tm decreased, as seen with the fitted Gaussian curve (R2=0.84), which peaked above 27°C (Fig. 3).

Fig. 2.

The time-series depth, water temperature and muscle temperature obtained from whale shark C1. (A) Data captured from the retrieved instrument package from whale shark C. (B,C) Enlargements of the boxed regions in A. Green and orange lines for temperature indicate water temperature and measured muscle temperature, respectively. The probe inserted into the whale shark detached 2 days after release, so the muscle temperature data were cut off at this time. Dotted blue and pink lines for temperature indicate estimated muscle temperature by fixed and variable HTC models, respectively. The variable HTC model shows a better fit, and the fixed HTC model shows slower muscle temperature recovery (B) and higher muscle temperature than the sea surface temperature (SST) (C).

Fig. 2.

The time-series depth, water temperature and muscle temperature obtained from whale shark C1. (A) Data captured from the retrieved instrument package from whale shark C. (B,C) Enlargements of the boxed regions in A. Green and orange lines for temperature indicate water temperature and measured muscle temperature, respectively. The probe inserted into the whale shark detached 2 days after release, so the muscle temperature data were cut off at this time. Dotted blue and pink lines for temperature indicate estimated muscle temperature by fixed and variable HTC models, respectively. The variable HTC model shows a better fit, and the fixed HTC model shows slower muscle temperature recovery (B) and higher muscle temperature than the sea surface temperature (SST) (C).

Fig. 3.

Relationship between muscle temperature (Tm) and tailbeat frequency (TBF) of whale shark C1. Lines in the boxes indicate the medians; the ends of the box represent the upper and lower quartiles. The most extreme lines show the highest and lowest values, excluding outliers. The red line indicates the fitted Gaussian curve estimated by the least squares method and the red dotted lines indicate 95% prediction interval.

Fig. 3.

Relationship between muscle temperature (Tm) and tailbeat frequency (TBF) of whale shark C1. Lines in the boxes indicate the medians; the ends of the box represent the upper and lower quartiles. The most extreme lines show the highest and lowest values, excluding outliers. The red line indicates the fitted Gaussian curve estimated by the least squares method and the red dotted lines indicate 95% prediction interval.

Calculated BIC values of the heat-budget models were at their minimum at the response time lag of 1–6 min, and the variable HTC model had a lower BIC value than the constant HTC model in whale sharks C1 and C2, but both models of whale shark W1 showed similar BIC values (Fig. 4, Table 2). In the fixed HTC model, the model with the rate of temperature change due to internal heat production showed lower BIC values in whale sharks C1 and C2, while the model without showed a lower BIC value in whale shark W1 (Fig. 4, Table 2). In the variable HTC model, since the version without yielded a lower BIC value than the version with in all whale sharks, the model without was adopted (Fig. 4, Table 2). All individuals had a higher HTC at warming (k2) than at cooling (k1) in the variable HTC models (Table 2). The Tm estimated from the variable HTC model provides a better fit, while the Tm estimated from the fixed HTC model with showed that the Tm recovered more slowly and was higher than the SST when the whale shark stayed near the sea surface, indicating that fast recovery of Tm and Tm not exceeding the SST cannot be achieved simultaneously only by the presence of (Fig. 2B,C).

Fig. 4.

Relationship between the response time lag (τ) and the Bayesian information criterion (BIC) for whale sharks. Data are shown for whale sharks C1 (A),C2 (B) andW1 (C). Filled and open symbols indicate the fixed heat-transfer coefficient (HTC) models and the variable HTC models, respectively. Red squares and blue circles indicate the models of temperature change with and without the rate of temperature change due to internal heat production, respectively.

Fig. 4.

Relationship between the response time lag (τ) and the Bayesian information criterion (BIC) for whale sharks. Data are shown for whale sharks C1 (A),C2 (B) andW1 (C). Filled and open symbols indicate the fixed heat-transfer coefficient (HTC) models and the variable HTC models, respectively. Red squares and blue circles indicate the models of temperature change with and without the rate of temperature change due to internal heat production, respectively.

Table 2.

Temperature information and estimatedparameters using the heat-budget models

Temperature information and estimated parameters using the heat-budget models
Temperature information and estimated parameters using the heat-budget models

The long-term data obtained by the PSATs showed that whale sharks C1 and C2 dived to depths greater than 800 m. These deep excursions were observed twice in whale shark C1, which dived to a maximum depth of 1427 m, and 13 times in whale shark C2, which dived to a maximum depth of 1368 m. Such deep excursions were never observed in whale shark W1. The coldest water temperatures experienced by whale sharks C1 and C2 during their deep excursions were 3.4°C and 3.6°C, respectively. During these deep excursions, the time spent at depths greater than 200 m, where the temperature was <20°C, ranged from 38 to 45 min in whale shark C1, and from 30 to 60 min in whale shark C2. The mean vertical speeds of these deep excursions were 1.02 m s−1 for descent and 0.67 m s−1 for ascent.

As a result of the comparative analysis, the estimated HTC of whale sharks was lower than that of any other fish species measured to date (Table 3). The HTC (k) at cooling was correlated with body mass (Mb) (Fig. 5). The GLMM excluding and including categories of ectothermy and endothermy had log likelihoods of −71.928 and −71.926, respectively, and there was no significant difference in the likelihood ratio test (χ2=0.0048, P=0.945). The relationship obtained from the GLMM excluding the categories of ectothermy or endothermy was: . The 95% confidence intervals ranged from −2.446 to −2.014 for the intercept (from 0.0866 to 0.1335 for the constant of the power function) and from −0.657 to −0.596 for the exponent.

Table 3.

Mass and heat-transfer coefficients of fishes from the published literature

Mass and heat-transfer coefficients of fishes from the published literature
Mass and heat-transfer coefficients of fishes from the published literature
Fig. 5.

Relationship between body mass (Mb) and heat-transfer coefficients (HTC: k) at cooling of various fish species. Blue and red colours indicate ectothermic species and endothermic species (including regionally endothermic species), respectively. Pacific bluefin tuna weighing less than 500 g are classified as ectothermic because this species develops endothermy when individuals weigh 500 g or more (Kubo et al., 2008). Open and filled symbols indicate freshwater and seawater species, respectively. The line through the data points was estimated using the generalised linear mixed model log k=−2.232−0.627log Mb (k=0.1073 Mb−0.627).

Fig. 5.

Relationship between body mass (Mb) and heat-transfer coefficients (HTC: k) at cooling of various fish species. Blue and red colours indicate ectothermic species and endothermic species (including regionally endothermic species), respectively. Pacific bluefin tuna weighing less than 500 g are classified as ectothermic because this species develops endothermy when individuals weigh 500 g or more (Kubo et al., 2008). Open and filled symbols indicate freshwater and seawater species, respectively. The line through the data points was estimated using the generalised linear mixed model log k=−2.232−0.627log Mb (k=0.1073 Mb−0.627).

Whale sharks may use thermal inertia, one of several elements required for ‘gigantothermy’ sensuPaladino et al. (1990) as a thermoregulatory strategy, because of their large body size, allowing them to conserve environmentally derived heat to access deep water food resources (Meekan et al., 2015). The present study confirmed body temperature stability in whale sharks by directly measuring their muscle temperature (Tm) under free-ranging conditions. The amplitudes of fluctuations in the Tm of the three whale sharks were much smaller than those of the water temperature experienced. The upper limits of the Tm in whale sharks were similar to those of the SST and the heat-budget models showed that internal heat production did not contribute to changes in body temperature, confirming that this species has an ectothermic physiology, in which the physiological heat is relatively small or negligible in thermoregulation. Our data suggest that the whale sharks maintained a relatively constant body temperature because of high thermal inertia without relying on metabolic heat as they swam in largely fluctuating water temperatures from the surface to the deep-sea.

Whale shark C1 swam at great depths immediately after release, possibly related to the trauma caused by tagging. During this period, this whale shark had the lowest recorded Tm (19°C). The lowest swimming activity was observed when Tm was low. The muscle temperature with the highest activity should exceed 27°C, falling within the highest probability range for whale sharks, which is around 27.5–29°C (Sequeira et al., 2012). However, sightings of whale sharks at higher latitudes (44°N) with SSTs of around 20–21°C, have been reported (Tomita et al., 2014). This study confirmed that whale sharks can withstand body temperatures below 20°C, at least for a short period. Note that it was not possible to detect the upper limit of temperature because their swimming activity did not appear to decline even at the highest temperature (28°C) in this study.

The heat-budget models estimated in this study showed that all whale sharks had a higher HTC during warming compared with cooling. Carey and Scharold (1990) suggested a difference in the cooling and warming rates of blue sharks (Prionace glauca): the HTCs of the blue sharks in their study, which differs by one order of magnitude between warming and cooling, was later quantified by Kitagawa and Kimura (2006), and the alternative HTCs could be separated linearly based on the thermal conductivity of tissue outside the isothermal core and the quantity of heat carried to the gills from the isothermal core. This suggests that recovery of body temperature is not due to the generation of metabolic heat, but rather is due to the regulation of heat flow by blood (Kitagawa and Kimura, 2006). Increasing perfusion flow through the gills increased heat exchange in the gills and 60% of the total heat exchange was accounted for by the gills (Sorenson and Fromm, 1976). The ratio of HTC of the whale sharks was within one order of magnitude, similar to that of the blue sharks, whereas bigeye tunas, which have retia mirabilia for metabolic heat conservation, can change the ratio of HTC by two orders of magnitude (Holland and Sibert, 1994). Fish may have the ability to increase heat gain or decrease heat loss from the surrounding water by altering the flow of heat via their blood through thermoregulation, although elucidating the mechanism of thermoregulation by blood flow requires further measurements such as heart rate.

The HTC at cooling for fish of various sizes was strongly correlated with body mass, and was not related to whether that fish was ectothermic or endothermic (Fig. 5). The obtained exponent (−0.63) was similar to −2/3 (−0.67), and was consistent with previous studies [−0.59 for 18–146 g fish (Fechhelm and Neill, 1982); −0.64 for 10–7958 g fish (Spigarelli et al., 1977); −0.57 for 1–1194 g fish (Stevens and Sutterlin, 1976); −0.51 for 515–2710 g fish (Weller et al., 1984); −0.695 for 1–3900 g fish (Kubo et al., 2008)]. The HTC in these studies included the effects of both body size and body shape, as well as thermal conductivity. Although variations among species might reflect differences in body shape and thermal conductivity, allometry proportional to the power of −2/3 in terms of body mass was maintained across a range of fish species. Heat capacity is proportional to volume and heat loss is proportional to body surface area (Schmidt-Nielsen, 1984). The body mass of fish is proportional to the cube of its length, with this relationship being confirmed in multiple sharks and ocean sunfish (Kohler et al., 1995; Watanabe and Sato, 2008), and swimming fish do not deviate much from their streamlined shape. If a fish has a similar shape to that described here, then its body surface area would be proportional to the power of 2/3 of its body mass. Then, its rate of decrease in body temperature (HTC at cooling) should be proportional to the power of −1/3 of its body mass. In addition, larger sharks had relatively larger gill surface areas; their gill surface area was proportional to the power of 0.85 (>2/3) of their body mass (Bigman et al., 2018), suggesting that the slope should become more gentle than −1/3 if most heat exchange occurs at the gills. Stevens and Fry (1974) suggested that the exponent is −2/3 because the measuring point of body temperature was further from the body surface in larger fish. This explanation is reasonable because the temperature change inside the cylinder will be slow in inverse proportion to the square of the radius (i.e. the 2/3 power of the volume), and the relative distance from the body surface will be greater in larger fish when the temperature of anatomically symmetrical sites is measured; thus, the heat of the body may be less likely to be transferred to the surrounding water in larger fish. However, in order to further investigate heat flow in the body of fish, it is necessary to simultaneously measure the temperature of multiple parts of the body. Our results suggest that the exponent of −2/3 is maintained even when body mass exceeds several hundred kilograms, with larger body size possibly being more advantageous for maintaining a relatively stable body temperature.

Various studies have documented excursions to depths greater than 1000 m in whale sharks and other large fish species such as basking sharks and ocean sunfish (Brunnschweiler et al., 2009; Gore et al., 2008; Graham et al., 2006; Rowat and Gore, 2007; Thys et al., 2017; Tyminski et al., 2015). From the long tracking data using the PSAT in this study, the whale sharks experienced water temperatures of around 4°C at the bottom of their deep excursions; however, these excursions did not exceed 60 min. The relationship between HTC and body mass indicates that the body temperature of fish weighing 1000 kg should decrease by <1°C after swimming down 1000 m and back up again, while that of 100 kg fish should decrease by approximately 4°C (Fig. 6). Indeed, larger fish should take a longer time to recover their body temperature, but it takes more than 40 min to travel to depths of 1000 m and back, so it is difficult for smaller fish to approach to such a great depth while maintaining their body temperature. In order to approach to such a great depth for smaller fish, it is also possible for them to increase their vertical velocities; bigeye tunas had higher vertical velocities of 1–2 m s−1 (Malte et al., 2007) and Chilean devil rays had a descent rate of up to 6 m s−1 (Thorrold et al., 2014). The limited duration of deep excursions of the whale sharks might be to avoid reduced activity because of decreased body temperature, while their high thermal inertia should help them access the deep-sea environment.

Fig. 6.

Estimated body temperature changes of fish as a function of body mass when travelling to a depth of 1000 m and back. The vertical speed and the vertical profile of water temperature were obtained from the pop-up satellite tags attached to the whale sharks. The coloured lines indicate the changes in body temperature of fish of each body mass. The heat-transfer coefficients (k) at cooling of fish of each body mass (Mb) were estimated from the allometric equation k=0.1073Mb–0.627.

Fig. 6.

Estimated body temperature changes of fish as a function of body mass when travelling to a depth of 1000 m and back. The vertical speed and the vertical profile of water temperature were obtained from the pop-up satellite tags attached to the whale sharks. The coloured lines indicate the changes in body temperature of fish of each body mass. The heat-transfer coefficients (k) at cooling of fish of each body mass (Mb) were estimated from the allometric equation k=0.1073Mb–0.627.

The present study confirmed that the body temperature stability of whale sharks is due to their large body size, allowing them to perform deep excursions (to >1000 m). The large body size of the whale shark seems to be advantageous for maintaining a relatively stable body temperature without high metabolic costs for thermoregulation when moving between environments with different temperatures. The function of excursions to extreme depths remains unclear. Most previous studies assumed that such deep excursions are for foraging (Meekan et al., 2015; Thums et al., 2012); however, these excursions occur rarely (once per day, at most, in the present study). Further deployment of cameras during these deep excursions might reveal why whale sharks access the deep-sea environment.

We would like to thank Kiyomi Murakumo, Makio Yanagisawa and other Okinawa Churaumi Aquarium staff members for assisting with our fieldwork.

Author contributions

Conceptualization: I.N., R.M., K.S.; Methodology: I.N., R.M., K.S.; Validation: K.S.; Formal analysis: I.N.; Investigation: I.N., R.M.; Resources: I.N., R.M., K.S.; Data curation: I.N.; Writing - original draft: I.N.; Writing - review & editing: R.M., K.S.; Visualization: I.N.; Supervision: K.S.; Project administration: R.M.; Funding acquisition: I.N., K.S.

Funding

This study was funded by the Bio-Logging Science, the University of Tokyo (UTBLS), Grant-in-Aids for JSPS Fellows from the Japan Society for the Promotion of Science (JSPS) (16J00837, 17H00776), and the CREST funding program from the Japan Science and Technology Agency (JST) (JPMJCR13A5).

Data availability

The datasets used in this study are available from figshare: doi:10.6084/m9.figshare.12355955

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Competing interests

The authors declare no competing or financial interests.