Heart rate as a predictor of energy expenditure in undisturbed fasting and incubating penguins

In order to understand behavioural strategies in free-living birds, especially during breeding periods, it is important to be well informed about the energy costs related to various activities such as foraging, parental care, incubation, territory defence and self-maintenance. The calculation of energy budgets from time budgets directly implies the measurement of energy expenditure (EE) associated with each specific activity. Such measurements are challenging to obtain under field conditions, which explains why the vast majority of energy budgets have been estimated from EE measured under laboratory conditions. Unfortunately, such EE estimates often differ widely from those obtained in the field (Flint and Nagy, 1984).

During the last decade, numerous studies have estimated field EE from heart rate (f_H) measurements, especially in birds (Woakes and Butler, 1983; Nolet et al., 1992; Bevan et al., 1994; Bevan et al., 1995; Boyd et al., 1999; Ward et al., 2002; Weimerskirch et al., 2002; Green et al., 2003; Fahlman et al., 2004; Froget et al., 2004). The use of f_H as a predictor of EE relies on the relationship between the O₂ consumption rate () and f_H as formulated in the Fick equation for O₂ convection in the cardiovascular system (Dejours, 1981). The recording of f_H provides an accurate correlation of O₂ consumption (Boyd et al., 1995; Butler et al., 2004), and is also a relatively non-invasive technique offering the possibility to monitor metabolism with a fine time-resolution. Precaution is however necessary, as this relationship is species-specific, and may be affected by several factors such as gender (Froget et al., 2001; Green et al., 2001), type and level of activity (Nolet et al., 1992; Butler et al., 2000; Froget et al., 2002), physiological and nutritional state (Froget et al., 2001; Green et al., 2001) and seasonal changes (Holter et al., 1976; Speakman, 1997).

The relationship between O₂ consumption and f_H, as well as the influence of various factors on this relationship have been investigated in great detail for the king penguin Aptenodytes patagonicus (Froget et al., 2001; Froget et al., 2002; Fahlman et al., 2004). These previous studies, carried out on regularly manipulated captive king penguins, have shown that the relationship slope (i.e. the O₂ pulse, the volume of O₂ used per one heart beat), which depends on body condition (Froget et al., 2001), is three times higher during walking than while resting (Froget et al., 2002). Whether the relationship is affected by gender, however, was not clearly established (Froget et al., 2001).

These studies also showed that fasting affects the relationship during exercise but not during resting periods (Fahlman et al., 2004). For measurements, birds were kept in a metabolic chamber and forced to walk on a treadmill. As stress-related f_H variations do not always correspond to metabolic variations (McPhee et al., 2003), these relationships may be affected by handling and confinement. Moreover, the ‘HRDDL Loggers’ used to measure f_H in previous studies (Woakes et al., 1995), have yet to be validated in king penguins, and a limited number of individuals have been used for calibration in this species. The use of previously established relationships to estimate EE from f_H in free-living king penguins undergoing normal activities while breeding therefore remains controversial (Halsey et al., 2007).

Whereas continuous recording of f_H in free-living king penguins breeding ashore is not a major technical difficulty, estimating EE is more challenging. Doubly labelled water could be used but would be expensive given the large size of king penguins and the number of individuals required for an accurate calibration (Nagy, 1983). Alternatively, as king penguins fast ashore for weeks during the breeding season their EE can be derived from body mass (M_b) loss measured under freely living conditions if the energy equivalent of M_b loss is known. Interestingly, the composition of M_b loss, and thus its energy equivalent, is constant in phase II fasting animals. This observation is consistent for seabirds (Groscolas, 1988; Groscolas et al., 1991) and for animals with different body composition (Cherel and Groscolas, 1999) and levels of metabolic rate (Cherel et al., 1995).

The present study aims to determine the relationship between EE, as estimated from M_b loss, and f_H in undisturbed, freely incubating king penguins. Measurements were performed on both male and female incubating penguins to test for a gender effect. In order to detect a potential effect of incubation on the EE/f_H relationship, the same measurements were also carried out in naturally fasting but non-incubating males and females acclimatized to captivity. In contrast to previous studies, f_H and EE variations were not induced by potentially stressful experimental challenges, such as walking on a treadmill or exposure to various ambient temperatures when kept in a metabolic chamber. Here, EE/f_H variations were due to natural inter- and intra-individual differences in resting metabolic rate and activity levels throughout the course of natural fasting. This study can therefore be considered to provide an accurate estimate of the EE/f_H relationship free of the effect of stress.

Fieldwork was undertaken during the 2002–2003 and 2003–2004 breeding seasons in the king penguin colony (Aptenodytes patagonicus Miller 1778) (ca. 20,000 breeding pairs) of ‘Baie du Marin’, Possession Island, Crozet Archipelago (46°25′ S; 51°52′ E). The study was approved by the Ethical Committee of the Institut Polaire Français-Paul Emile Victor (IPEV) and complies with current French laws. The authorization to enter the colony and handle birds was obtained from Terres Australes et Antarctiques Françaises.

In the king penguin, both genders alternate shifts of incubation, with males consistently performing the first shift. Birds were therefore sexed by their breeding behaviour. Incubation lasts an average of 53 days and individual shifts last approximately 15 days (Stonehouse, 1960; Weimerskirch et al., 1992). A few days prior to laying, experimental birds were randomly chosen from among 80 pairs then marked and banded at the flipper (plastic band). Bands were removed at the end of the study. To determine the onset of each incubation shift, banded birds were checked twice daily. A total of 51 males and 23 females were observed during one of their incubation shifts and their f_H and M_b loss were measured. To ensure that f_H and M_b loss measurements were performed while birds were in phase II fasting, these measurements started after day three of an incubation shift and stopped at least four days before its end (Le Ninan et al., 1988; Gauthier-Clerc et al., 2001; Groscolas and Robin, 2001; Robin et al., 2001). The minimum M_b measured in our study was 9.8 kg, i.e. above the 9.6 kg M_b threshold recorded in fasting, incubating king penguins at the transition between phases II and III (Cherel et al., 1988; Gauthier-Clerc et al., 2001). The mean fasting duration and M_b of incubating birds were also well within the previously reported ranges for phase II fasting king penguins [M_b is 10.3–12.9 kg for males and 9.7–11.9 kg for females (Gauthier-Clerc et al., 2001); Table 1]. f_H and M_b loss were recorded over four-day periods and the same individuals were monitored for 1–3 periods. A total of 65 and 26 data points were obtained for incubating males and females, respectively.

During the courting period, breeding penguins fasting ashore were captured and marked on the breast using a dye (Raidex GmbH, Dettingen, Germany). Gender was determined from differences in body size and singing behaviour (Jouventin, 1982). Birds were left fasting in the colony for a further 2–3 days. Then, a total of 18 males and 11 females were penned (two birds per pen), within 3 m × 3 m wooden fences located in the vicinity of the colony and under natural weather conditions. A preliminary study on king penguins showed that penning initially resulted in a f_H increase, which then returned to basal levels within five days. Thus, f_H and M_b loss measurements were started after five consecutive days of penning in order to ensure that the birds were used to captivity and had begun phase II fasting. M_b loss and f_H were measured over four-day consecutive periods, up to a maximum fasting duration of 25 days. Only data obtained before the beginning of phase III fasting were considered, the latter state being characterised by an increase in daily M_b loss (Groscolas, 1988). Mean total fasting duration and M_b during measurement periods are presented in Table 1. Depending on individuals, M_b loss and f_H were recorded over 1–6 periods, yielding a total of 102 and 32 data points for males and females, respectively. All birds were released at the end of the experiment and usually departed to feed at sea within 1–3 days.

f_H was recorded using a Polar® S810 f_H logger (Polar Electro Oy, Kempele, Finland) adapted for use in king penguins. This logger has a 20–235 beats per min (beats min^–1) resolution range and is composed of a transmitter and a receiver/logger. The whole unit weighed 80 g. The transmitter contains a f_H processor that filters electronic signals received by the electrodes and allows the distinction of heart beats from other electric activities (e.g. muscle or electrode noises). It was supplied with two 15 cm wires to which a gold-plated safety pin electrode was attached. The f_H logger was glued in the middle of the bird's back using adhesive tape. Dorsal electrodes were placed approximately 0.5 cm under the skin. The upper electrode was placed on the upper back and the lower electrode was approximately 30 cm below, just above the tail. Loggers were programmed to record f_H every minute during a four-day period so that mean daily f_H was calculated at ±0.5 beats min^–1 from a total of 5760 measurements. The length of the recording period depended on the storage capacity of the logger and had to be long enough to allow an accurate determination of M_b loss (see below).

A calibration study was performed to validate the use of the Polar® S810 logger for f_H measurements on king penguins. f_H was simultaneously measured using a Polar® logger and a stethoscope. Forty incubating birds (males and females) were equipped with f_H loggers, and heart beats were immediately counted for 30 s using both methods in restrained birds that were either at rest or moving slightly (see Results).

For incubating birds, the egg was temporarily replaced by a plaster dummy egg before being transferred from the incubating position to a nearby shelter. The birds were equipped with an f_H logger and weighed on a platform scale at ±4 g. The whole procedure lasted less than 10 min. The bird was then put back into the colony, where it continued incubating. The same procedure, without the use of a dummy egg, was used for captive birds. Thereafter, the equipped birds were left undisturbed. They behaved normally, spending most of the time resting (around 70%) or showing aggressive or comfort behaviours. Birds were recaptured four days later and weighed after switching off the logger. The durations of f_H and M_b loss measurements were therefore strictly identical. Given that f_H returned to normal levels less than half an hour after handling, f_H values obtained during the four-day recording period can be considered to be representative of undisturbed birds in over 99% of cases. When weighing was performed on a rainy day, birds were first dried using a cloth and a hairdryer to avoid any inaccuracy in M_b values. Given the accuracy of M_b measurements (±4 g) and the total M_b loss throughout the four-day recording period (at least 220 g), the relative error for total and daily M_b loss was estimated at less than 3.6%. No egg desertions or losses were observed in equipped incubating birds.

Daily EE was calculated by multiplying daily M_b loss by its energy equivalent (the latter having been determined in a complementary study performed during the 2003–2004 breeding season). The body composition of 81 unsexed, breeding king penguins was determined from the measurement of their total body water (TBW) using tritiated water, as described and validated previously in another seabird species, the great-winged petrel Pterodroma macroptera (Groscolas et al., 1991). At the time of TBW measurement, penguins had been fasting ashore for 6–30 days, and their M_b (which mostly differed because of different fasting durations) ranged from 9.7 to 17.0 kg (see Fig. 1). They were therefore considered to be in phase II of fasting. Lean body mass (LM_b) was calculated as TBW/0.73, where 0.73 is the fractional water content of LM_b (Groscolas et al., 1991). Lipid and protein masses were calculated as M_b–LM_b and LM_b–TBW, respectively. Total body energy content (TBE) of birds was the sum of the energy contained in lipids and proteins, assuming that the energy density of lipids and proteins are 39.3 kJ g^–1 (Schmidt-Nielsen, 1979; Groscolas et al., 1991) and 17.8 kJ g^–1 (Schmidt-Nielsen, 1979), respectively. A significant relationship was found between TBE (kJ) and M_b (g), the best fit being linear (Fig. 1). The slope of this relationship (23.9±1.3 kJ g^–1) represents the energy equivalent of M_b loss in phase II fasting king penguins.

A linear regression was conducted in order to compare f_H measured with both Polar® loggers and a stethoscope, and to relate total TBE to M_b. The Student's t-test or a multi-way repeated-measures analysis of variance (ANOVA) followed by multiple-comparisons (LSD method) were performed to compare the difference between the means of two populations or more than two populations, respectively. After testing variables for normality with the Kolmogorov–Smirnov test, a mixed generalized linear model (GLMM) with individuals as a random factor was used to assess the relationship between f_H and EE. When necessary, variables were corrected with the appropriate transformations to meet the assumption of normality. The GLMM took into account the dependence between observations from the same bird with a compound symmetry structure. Firstly, a saturated model with all fixed effects, fasting duration and M_b, and two-way interactions was explored to examine the effect of fasting duration and M_b on the EE/f_H relationship. Secondly, using a backward procedure, fitted variables were manually dropped depending on their P value. Collinearity diagnostics for all analyses indicated no multicollinearity problems between variables, as the highest condition index obtained was 1.6. Multicollinearity can affect parameter estimates when condition indices are ≥20 (Belsley et al., 1980). Squared correlation coefficients explaining the amount of variation in the models include both fixed and random effects. Similar R² values were calculated when relating EE to f_H or log EE to log f_H. The Williams' test was used to compare correlation coefficients of EE/f_H relationships obtained from alternative methods. This test is suggested when correlation coefficients are dependent and sample sizes are between 50 and 500 (Neill and Dunn, 1975). To compare the slopes of these relationships, the heterogeneous regression slopes with the Johnson–Neyman technique (Huitema, 1980) was used. This technique allowed the estimation of f_H values where heterogenic slopes differed significantly. All statistical analyses were performed with SAS statistical software (SAS Institute, Cary, NC, USA; version 9.1). All values are reported ± 1 s.e.m., and the statistical significance was set at 0.05 for all statistical procedures.

Fig. 2 shows that f_H data from the logger and the stethoscope were strongly correlated (R²=0.98). The data ranged from 53 to 176 beats min^–1 and the slope and intercept were very close to 1 and 0, respectively. In incubating and captive king penguins, the range of mean daily f_H (Table 1) was close to the above range. Also, their minimum and maximum instantaneous f_H (28 and 235 beats min^–1, respectively) was within the Polar® logger resolution range.

When considering all data points (N=225), daily M_b loss varied from 55 to 247 g day^–1, i.e. a 4.5-fold range. The corresponding range for EE was from 1315 to 5903 kJ day^–1. Mean daily f_H varied from 39 to 111 beats min^–1, i.e. a 2.8-fold range. Within a gender, the mean daily M_b loss and f_H did not differ significantly between incubating and non-incubating captive birds (Table 1). Daily M_b loss was significantly higher for females than males, by 42% in incubating birds and by 22% in captive ones (Table 1). Similarly, f_H was significantly higher in females than in males, by 31% in incubating birds and 22% in captive ones (Table 1).

Equation 1 in Fahlman et al. (Fahlman et al., 2004) is currently considered to be the most suitable equation for estimating EE from f_H in king penguins for all locomotory and nutritional states (Halsey et al., 2007). This equation [log() =–0.279 + 1.24 × log(f_H) + 0.0237 × t – 0.0157 × log(f_H) × t], with in ml min^–1, f_H in beats min^–1 and t in days, was determined by measuring O₂ consumption and f_H in captive male king penguins fasting for various durations during the breeding season. The EE predicted using eqn 1 in Fahlman et al. (Fahlman et al., 2004) were compared with those of Eqn 2, by applying each equation to the f_H and t dataset obtained in the present study (N=225, f_H=38–111 beast min^–1, t=3–25 days). Oxygen consumption was converted into EE using the energy equivalent of 20.11 J ml^–1 O₂ determined in fasting birds (Schmidt-Nielsen, 1997).

Predicted EE were related to f_H for both equations (Fig. 4) and the correlation coefficients were not significantly different (R²=0.85 for Eqn 2 in our study and R²=0.84 for eqn 1 in Fahlman et al. (Fahlman et al., 2004); Williams' test: t₂₂₂=0.134, P=0.89). For f_H values lower than 103 beats min^–1, predicted values differed significantly between the two equations for both the slopes (F_1,207=10.05, P=0.0012) and the intercept (F_1,207=31.12, P<0.0001). Eqn 2 from our study yielded predicted EE values on average 26% higher than eqn 1 in Fahlman et al. (Fahlman et al., 2004). The difference increased with decreasing f_H, reaching 75% (t₃₅₆=21.49, P<0.0001) for f_H=40 beats min^–1. In other words, for a given EE the corresponding f_H is higher for eqn 1 in Fahlman et al. (Fahlman et al., 2004) than for our Eqn 2, and even more so when EE is low.

This study is the first to successfully calibrate the relationship between EE and f_H using a large sample of free-ranging animals during natural and undisturbed behaviours. We determined two equations for predicting EE from f_H, with and without fasting duration. Although females had a f_H 22–31% higher than males, gender did not affect these relationships. Finally, we observed that EE values predicted from f_H and fasting duration were higher than values obtained in previous studies, mostly when f_H was low.

Numerous studies have been conducted to estimate field energetics for penguins based on f_H measurements (Bevan et al., 1994; Boyd et al., 1999; Froget et al., 2001; Froget et al., 2002, Froget et al., 2004; Green et al., 2003; Fahlman et al., 2004; Fahlman et al., 2005; Fahlman et al., 2006). Unfortunately, this huge piece of work was performed without knowing the accuracy of loggers [‘HRDDL Logger’ (Woakes et al., 1995)] for f_H measurements over the f_H range commonly found in free-living birds. Actually, there is evidence that this logger may overestimate f_H because some electrical spikes corresponding to muscular activity are counted as heart beats (Y.H., unpublished data). Our calibration study showed that the Polar® logger yielded highly accurate f_H measurements, within a f_H range close to that documented in free-living or captivity-acclimatized king penguins fasting ashore, for restrained birds which were either resting or moving slightly. This conclusion is therefore at least valid for birds with limited physical activity, as it is the case during incubation; incubating king penguins in fact spend most of their time resting (60–75%) and have a mean level of EE only slightly higher (approximately 14%) than their resting metabolic rate (V.V., R.G. and S.D.C., unpublished data).

The error made for M_b loss measurements was lower than 3.6% (see Materials and methods). The validity of EE estimates therefore depended mostly on the energy equivalent of M_b loss. We found that the best fit for the relationship between total energy content and M_b was linear (Fig. 1). The constant level of the M_b loss energy equivalent throughout phase II fasting in king penguins is therefore illustrated, as previously observed in other fasting seabirds (Groscolas, 1988; Groscolas et al., 1991). The use of the same M_b loss energy equivalent to calculate EE whatever the duration of phase II fasting, as carried out in our study, was therefore appropriate. The value (23.9 kJ g^–1) calculated and used in the present study only differs by ±7% from those previously determined by direct analysis of body composition in two other species of long-term fasting seabirds during phase II, the great-winged petrel [Pterodroma macroptera: 22.3 kJ g^–1 (Groscolas et al., 1991)] and the emperor penguin [Aptenodytes forsteri: 25.5 kJ g^–1 (Groscolas, 1988)]. Applying the latter values to the calculation of EE from M_b loss would have decreased the intercept or increased the slope of Eqn 1 by only 5.4%. The use of the 23.9 kJ g^–1M_b loss energy equivalent can therefore be considered to have yielded a reliable estimate of EE and its relationships with f_H.

Our results showed that f_H explained 85 (Eqn 1) to 91% (Eqn 2) of EE variability, i.e. at least as well as for the relationships between f_H and in previous studies on penguins [46–91% (Green et al., 2001; Froget et al., 2002; Fahlman et al., 2004; Halsey et al., 2007)]. The unexplained variation in EE could be linked to inter-individual differences in stroke volume and/or tissue oxygen extraction reflecting inter-individual variations in physical fitness. Changes in the allometry of the circulatory system (McPhee et al., 2003) or differences in structural size and shape (Fahlman et al., 2006) are other potential contributors to variations in EE. Considering the accuracy of our predictive equations, it was also at least as good as those of previously reported equations obtained from the measurements of O₂ consumption. For example, the mean residual error and the absolute mean error were –2.2 and 10.9% for Eqn 2 from the present study, which compares with the 3.0 and 19.3% respective values reported for eqn 1 in Fahlman et al. (Fahlman et al., 2004). From our validation tests, we determined that the absolute mean error of the prediction was 10.2% for Eqn 2, which is slightly lower that values reported for predictive equations in king [12.6–46.1% (Halsey et al., 2007)] and macaroni [24.9% (Green et al., 2001)] penguins.

We found that EE and f_H decrease during fasting, and that fasting affects EE/f_H relationships. These findings are similar to those previously reported by Fahlman et al. (Fahlman et al., 2004) for king penguins, except that these authors observed an effect of fasting on the relationship for exercising (walking) but not for resting birds. Because birds in our study spent most of the time either resting or in moderate activity, we suggest that there is actually an effect of fasting for both resting and exercising penguins. This meets the conclusion of Halsey et al. (Halsey et al., 2007): an equation including fasting time and the interaction term f_H × fasting time, as for eqn 1 in Fahlman et al. (Fahlman et al., 2004) and for our Eqn 2, is the most suitable equation to estimate EE from f_H in fasting king penguins from different activity and nutritional states. Fasting affects the EE/f_H relationship through a decrease in the energy (or oxygen) pulse. This decrease is illustrated in Fig. 4, both for eqn 1 in Fahlman et al. (Fahlman et al., 2004) and for our Eqn 2. Indeed, the best fits for these EE/f_H relationships including the fasting duration are curvilinear, showing that for decreasing f_H (due mostly to increasing fasting duration) the relationship slope (i.e. the energy pulse) progressively decreases. As previously suggested (Froget et al., 2001; Fahlman et al., 2004), a decrease in the oxygen pulse during fasting [the product of stroke volume by the () difference in Fick's equation] could be due to a decrease in systolic volume linked to a decrease in heart mass and to a decrease in the capacity of tissues to extract oxygen due to inactivity. A greater decrease in heart protein mass compared with total body protein mass has indeed been observed in fasting king penguins (Cherel et al., 1994).

The EE/f_H relationship was similar for freely incubating and captive non-incubating birds, demonstrating that incubation per se does not affect this relationship. Furthermore, we did not find a gender effect on the EE/f_H relationship (Eqn 1 and 2), although f_H was 22–31% higher in females than in males. To date, contradictory results have been reported regarding a gender effect on the relationship in penguins. Gender differences have been reported in the king penguin by Froget et al. (Froget et al., 2001) but these differences were later shown to disappear when M_b and fasting duration were included in the model relating to f_H (Fahlman et al., 2004). In exercising macaroni penguins, the relationship was seen to differ greatly between males and females (Green et al., 2001). However, in this case, the comparison was between breeding males and a pool of breeding or moulting females, meaning that the difference between genders may simply be the result of moulting vs breeding states. Our results support the hypothesis that there is no difference in their relationship for male and female penguins, providing that they are in a similar physiological state.

Fig. 4 shows that eqn 1 in Fahlman et al. (Fahlman et al., 2004) yields predicted EE lower than those predicted from our Eqn 2. This difference could partially be due to a potential overestimation of the energy equivalent of M_b loss in our study. However, the 95% confidence interval of our estimate was small (±1.3 kJ g^–1, i.e. ±5.4% of the 23.9 kJ g^–1 estimate) and, as discussed above, this estimate only differed by ±7% from those previously obtained in other naturally fasting seabirds (Groscolas, 1988; Groscolas et al., 1991). It is therefore unlikely that the use of a 23.9 kJ g^–1 energy equivalent of M_b loss could have led to an average 26% overestimate of EE. Furthermore, we observed that differences between both predictions did not remain constant for the entire f_H range of measured in king penguins but increased progressively as f_H decreased. How could this discrepancy be explained?

Previous measurements of f_H (with HRDDL loggers) and in king penguins have been conducted with males placed in a respirometer or wearing a respiratory mask. Males were caught during courtship and kept fasting in a pen, in the same way as captive males in the present study. We found that for a mean M_b of 12.3 kg and a mean fasting duration of 12 days, f_H of captive and undisturbed males averaged 62 beats min^–1. By comparison and for similar M_b and fasting durations, f_H values averaged 93 (Froget et al., 2001) or 91 to 107 beats min^–1 (Fahlman et al., 2004) when birds were kept resting in a respirometer. These values were 47–72% higher than for our captive undisturbed birds spending most, but not all, of their time resting. They are also similarly higher than for freely incubating males (see Table 1). As recently recognised by Halsey et al. (Halsey et al., 2008), confinement in a respirometer and repeated handling to measure undoubtedly cause stress in individuals. Stress is known to enhance f_H (Blix et al., 1974; Wilhelm and Roth, 1998; McPhee et al., 2003), which could most probably explain the marked over-estimation of resting f_H in previous studies. Moreover, the increase in f_H during stress is generally beyond levels that can be predicted from measured oxygen uptake (Blix et al., 1974; Steptoe, 2000; McPhee et al., 2003). This ‘additional f_H’ is used as an indicator of emotional activation or arousal in humans (Stromme et al., 1978; Wilhelm and Roth, 1998). We suggest that this type of disproportionate stress effect on f_Hvs EE may explain why the f_H corresponding to a given EE was higher in previous studies (Fahlman et al., 2004) than in the present study. In addition, the stress-induced ‘additional f_H’ could be proportionally higher when EE and f_H is low, explaining why the difference between our study and that of Fahlman et al. (Fahlman et al., 2004) is particularly marked for low EE and f_H. Lastly, confinement and walking in a respirometer (or when wearing a respirometry mask) may induce hyperthermia. Under such conditions, we recently observed a 0.5°C increase in the body temperature (stomach) of king penguins after a 15 min walk (R.G., J. Tornos and J.-L. Rouanet, unpublished data). It is known that under an extreme heat load, f_H increases to improve heat dissipation and that the oxygen pulse decreases (Brosh, 2007). Thus, heat load may also have contributed to the disproportionate increase in f_Hvs in previous studies. We therefore conclude that previously calibrated EE/f_H relationships have no doubt been affected by stress (and possibly by heat load), leading to underestimations of EE from f_H, particularly at low f_H and EE levels. As a result, the use of our Eqn 2 yields a more accurate estimate of EE and could therefore be an indispensable tool for the determination of EE from f_H in incubating and moderately active king penguins fasting ashore. Whether and how stress could have affected previous determinations of EE/f_H relationships in other animal species should be considered in further studies.

 
• EE

  energy expenditure

 
• f_H

  heart rate

 
• LM_b

  lean body mass

 
• M_b

  body mass

 
• TBE

  total body energy

 
• TBW

  total body water

 
• 

  rate of oxygen consumption