Why bears hibernate? Redefining the scaling energetics of hibernation

Abstract

Hibernation is a natural state of suspended animation that many mammals experience and has been interpreted as an adaptive strategy for saving energy. However, the actual amount of savings that hibernation represents, and particularly its dependence on body mass (the ‘scaling’) has not been calculated properly. Here, we estimated the scaling of daily energy expenditure of hibernation (DEE_H), covering a range of five orders of magnitude in mass. We found that DEE_H scales isometrically with mass, which means that a gram of hibernating bat has a similar metabolism to that of a gram of bear, 20 000 times larger. Given that metabolic rate of active animals scales allometrically, the point where these scaling curves intersect with DEE_H represents the mass where energy savings by hibernation are zero. For BMR, these zero savings are attained for a relatively small bear (approx. 75 kg). Calculated on a per cell basis, the cellular metabolic power of hibernation was estimated to be 1.3 × 10⁻¹² ± 2.6 × 10⁻¹³ W cell⁻¹, which is lower than the minimum metabolism of isolated mammalian cells. This supports the idea of the existence of a minimum metabolism that permits cells to survive under a combination of cold and hypoxia.

1. Introduction

In a hypothetical 120-year space voyage, a hibernating astronaut is mistakenly awakened by the computer that monitors her vital signs, unable to resume hibernation, after 30 years of travel. Desperate, the astronaut realizes that living her remaining life on the ship will also condemn the rest of the passengers to die of starvation, as she will consume all the food on the ship before dying of old age. How realistic is this science fiction story?

In naturally hibernating mammals (e.g. bats, several marsupials, rodents, echidnas and mouse lemurs [1,2]), energy expenditure can be reduced by 98% of normal levels [2,3]. These animals rely almost exclusively on body fats during hibernation [2,3]; therefore, a hypothetical 70 kg hibernating human consuming 12 500 kJ d⁻¹ would reduce this expenditure to 250 kJ d⁻¹. In other words, an awake person would consume the energy of 50 hibernating humans in a single day. At this rate, an astronaut travelling interstellar distances in hibernation (the typical sci-fi story) [4] would spend 6.3 g of fat per day, which requires them to have 2.2 kg of fat to survive a year hibernating, and 204 kg for 90 years. Thus, even if a human was able to hibernate as natural hibernators do, the problem of fuel stores precludes such long-term dormancy [5].

An additional problem comes from the fact that hibernation seems to be beneficial only at small sizes [6]. Black and brown bears (approx. 80–400 kg) are the largest known hibernators and reduce their resting metabolism by as much as 75% (as percentage of basal metabolic rate (BMR), the standard comparison, see [2,3,7]) during hibernation [8,9]. This is a relatively small saving compared with the 95–98% metabolic reduction of a little brown bat [10,11], a pigmy possum [12] or a jumping mouse [13]. In fact, hibernating metabolism seems to be isometrically related with body mass [2], but active metabolism scales allometrically, with an exponent (i.e. the slope of the curve, in a log–log plot) that is below 1.0. This is known as Kleiber's rule [14] (the actual exponent is a matter of debate, see [15–18]).

Therefore, theoretically, where the allometric curve of metabolism in active animals (i.e. not torpid) intersects the isometric curve of hibernating metabolism, the endothermic cost of maintenance equals the energy consumption in hibernation. At this point, the energetic saving of hibernation becomes zero. Two variables are important for describing the energy expenditure of active mammals: BMR (representing the minimum cost of euthermic maintenance) [19] and daily energy expenditure (DEE), the average energy consumption of a free-ranging individual during 24 h [20–22]. Whereas DEE (also known as field metabolic rate) includes all activities (i.e. resting, running, sleep, foraging, digestion etc), the BMR represents the energy consumption of a resting animal, excluding all other costs. Thus, BMR represents the minimum cost of maintenance in euthermia [23] and is considered the standard criterion for calculating the energy savings of hibernation and daily torpor [2,3,7,24]. With these considerations, the hibernation energy saving becomes zero at a body mass above about 15 tons [3]. Understandably, no hibernator is known of this size [4,25].

Despite hibernation being historically recognized as an adaptation for energy economy [26], a general rule predicting how much energy is saved during these episodes of metabolic depression is still pending. Some authors calculated allometric equations using the minimum mass-specific metabolism during torpor in several hibernators, but results were mixed: whereas some authors did not find a significant scaling [2,27], others reported a slight (R² = 0.13), but significant, relationship with mass [3,7]. Additionally, we argue that, in order to have meaningful values (in terms of the energy budget of the animals), the energy saved by hibernation should be calculated based on a long-term averaged reduction in energy consumption (not minimum values). Such a number, expressed as a daily rate of energy expenditure in hibernation (DEE_H), would be useful to calculate either how long hypothetical astronauts will last in the space, or the limiting size at which hibernation becomes inefficient.

For the calculation of DEE_H, we took advantage of the fact that most hibernators rely exclusively on their body reserves during hibernation [12,28]. Thus, determining initial and final body composition (mass of fat and lean tissue) over a fixed period in torpor, it is possible to factorize the amount of energy consumed by the animal during this time lapse. Then, comparing the theoretical predictions with the metabolic scaling of BMR, we show that the energy savings of hibernation are zero for a bear of about 100 kg. We also used the allometry for DEE, for which the energy savings of hibernation become zero for an animal of about 1500 kg. Our results also highlight the intriguing question of why a cell of a hibernating bat has a similar metabolism to a cell of hibernating bear, an animal that is 20 000 times larger.

2. Material and methods

(a) . Statistical analyses

We performed ordinary least-squares linear regressions on log₁₀-transformed variables, where the abscissa is body mass, M_B (g), and the ordinate is metabolic rate (kJ d⁻¹). All regressions were done using Statistica (v. 6.1) software [29] and repeated in GraphPad Prism v. 8.0.0 for Mac (GraphPad Software, San Diego, California, USA, www.graphpad.com). Scaling exponents were obtained from the linear equation for regression, where log₁₀(MR) = exponent × log₁₀(M_B) + intercept. This is equivalent to MR = intercept × M^exponent_B. The analyses are reproduced in a single R-script, provided with the data deposited at Dryad [30].

(b) . Reanalysis of previous work

Previous authors compiled the torpor minimum metabolic rate (TMR), using mass-specific units, and expressing the values on a per-gram basis, thus reporting negative allometric slopes [2,3]. In our opinion, this has two problems. First, calculating ratios of two random variables amplifies the error term [31,32], thus reducing the statistical power of the test, and the precision of the estimated parameters. That is probably the reason for the large dispersion observed in such plots, and the low obtained R² values of these resulting regressions (below 0.20, see [2,3]). Second, mass-specific units of metabolism assume isometric scaling, which could produce downwardly biased estimations of metabolism at large sizes, if the allometric slope is less than 1. Fortunately, Ruf & Geiser [3] published the whole dataset of minimum torpor metabolism for hibernators, which we reanalysed here (n = 50 species, including one bird) and expressed TMR as kJ d⁻¹, and M_B in grams (mean value for the species, according to [3, pp. 893]). Given that the original study was already controlled by phylogenetic effects (the phylogenetic signal for TMR was low and non-significant) [3], we did not repeat the phylogenetic analysis here. Our reanalysis of Ruf & Geiser's dataset gave a highly significant allometric regression for TMR, close to an isometric scaling (slope = 0.90 ± 0.036, intercept = −1.62 ± 0.074, R² = 0.96, p << 0.001, electronic supplementary material, figures S1 and S2).

(c) . Our compilation

In order to estimate average energy consumption during hibernation, we analysed the reduction in body fat after a hibernation period. We averaged M_B of females and males and/or fat consumption when reported separately. When provided, we also averaged M_B before and after the hibernation. Given that hibernators are a small subset of mammalian species, biased to small M_B values, we tried to cover a representative sample including large species. This left us with a limited dataset, but covering five orders of magnitude in mass. We first selected studies where body composition (lean and fat mass) was measured individually in animals before and after hibernation, for a minimum of 30 days, and without access to food. As expected, studies that met these stringent criteria were rare (n = 5) and limited to works where authors applied either isotopic dilution measurements, impedance methods or the recently developed quantitative magnetic resonance. These works were done in the leaf-eared bat, Myotis myotis (24.7 g) [11], the marsupial monito del monte, Dromiciops gliroides (45 g) [33], the Arctic ground squirrel, Spermophilus parryii (820 g) [34], and the bears Ursus americanus (74.5 kg) [35] and Ursus arctos (179 kg) [9] (see electronic supplementary material, table S1). Using these five datapoints, the resulting logarithmic regression with M_B was highly significant (R² = 0.98, intercept = −0.04 ± 0.3, slope = 0.94 ± 0.09, p = 0.002; electronic supplementary material, figure S3). We then expanded the dataset to include studies where energy consumption during hibernation was inferred only from body mass reductions, always taking care to filter for a minimum of 30 days of hibernation, and experiments where animals were not allowed to ingest food. With this, we could include small species such as the little brown bat (Myotis lucifugus, 8.5 g) [10] and species of intermediate sizes such as woodchucks (Marmota monax, 2.2 kg) [36] and also a monotreme, the short-beaked echidna (Tachyglossus aculeatus, 4.7 kg) [37]. However, these new datapoints did not change the result (i.e. a significant log–log regression with a slope close to 1; see Results).

In most cases, measurements were conducted in the field under natural conditions of hibernation, but in a few cases, animals were held in the laboratory with natural photoperiod and temperature [12,36]. We first calculated DEE_H only using fat consumption, which was more often reported. In a few cases (see electronic supplementary material, table S1), both lean and fat mass changes were available, thus we recalculated DEE_H using both variables for these species. For species in which changes in lean mass were not measured, we estimated them using the proportional contribution reported in the studies in which it was measured. That is, a proportional contribution to the hibernation energy consumption of 21% lean mass and 79% fat mass (presented in electronic supplementary material, table S1). Although the results remained qualitatively similar, this adjustment improved the fit of the log–log regression from R² = 0.95 (adjusted R-value, using only fat mass) to R² = 0.96 (using both fat and lean mass) and increased the regression slope from 0.98 to 1.0. The daily amount of energy consumed during each period of hibernation was calculated as DEE_H = (39.7 kJ g⁻¹ × (fat mass consumed, in grams) + 23.6 kJ g⁻¹ × (lean mass consumed, in grams))/(duration of the experiment, in days), which considers the respiratory quotient or RQ of each nutrient [35,38].

(d) . Q₁₀, isometric scaling and hibernation

Previously, some authors reported isometric scaling for isolated mammalian cells [17], for torpor metabolism in large mammals [39], or for heterothermic birds and mammals [2]; but some others did not find such isometry [7]. A particular mention is deserved by the comprehensive review of these latter authors, who reported a scaling exponent for TMR of 0.80 (Fig. 6 in Guppy & Withers [7]), which is different from our findings of isometric scaling. This discrepancy, as we explain below, in our opinion is due to a high sensitivity of the allometric slope to Q₁₀ corrections, especially at large body masses. The problems of applying this correction to endothermic metabolism had already been mentioned by Heldmaier & Ruf [27], which we explain here briefly.

For making data comparable across different types of organisms (i.e. ecto- and endotherms, uni- and multicellular organisms, marine and terrestrial animals), Guppy & Withers [7] and other authors apply a Q₁₀ standardization to a fixed temperature [7,15,16]. This is certainly needed for comparing very different organisms under resting conditions (e.g. ectotherms versus endotherms, unicellular versus multicellular organisms, and aquatic versus terrestrial animals), where the thermal sensibility of metabolic reactions is approximately constant. However, there is controversy about what would be the actual Q₁₀ during hibernation (for instance Geiser [40] reported Q₁₀ for hibernators ranging from 2.85 to 4.11, which was questioned by [7,27]). This is probably because animals actively suppress metabolism when entering torpor, thus experiencing passive cooling until reaching a critical lower temperature, where they start thermoregulating (in torpor) [2,27,41]. We recalculated each of our allometric equations using a range of different Q₁₀, observing that the best fit is obtained without the Q₁₀ correction, and that an inverse relationship is obtained between the scaling exponent and the magnitude of Q₁₀ (electronic supplementary material, figure S4). Thus, the application of Q₁₀ for the metabolic rate of endotherms seems inadequate, as previously indicated [27].

(e) . Predicting energy savings

There is some debate regarding the appropriate exponent for metabolic scaling, which increases with M_B (see Kolokotrones et al. [18]. According to these authors (see also [15]), the most appropriate scaling exponent for our range of sizes (M_B < 10⁵ g) is ⅔ (0.67) (see Fig. 2 in [18]). Then, to contrast our estimations with theoretical predictions, we estimated BMR using the equation: BMR = 4.34M^0.67_B [15], which is in ml O₂ h⁻¹, and converted BMR values to kJ d⁻¹ using the conversion factor 19.8 J (ml O₂), which assumes RQ = 0.71 [38]. We also included in the comparison the expected value of DEE, using the equation of Speakman & Krol [22]: DEE = 6.29M^0.67_B. In the final allometric curve, we included a few studies where the energy savings of hibernation were estimated with techniques other than fat/lean mass consumption (e.g. respirometry). All these additional datapoints (denoted in red in figures 2 and 3) fell within the 95% confidence interval of the original regression, thus supporting our main conclusion.

Figure 2.

Semi-log plot showing the predicted percentage of energy saved by hibernation computed as 100 (BMR − DEE_H)/BMR for the species in electronic supplementary material, table S1 (black dots). Red dots represent datapoints added a posteriori, where energy savings were estimated empirically by each author, from oxygen consumption values for yellow-bellied marmots [42] and 60 kg black bears [8], by direct calorimetry for Richardson's ground squirrel [43], and by using doubly labelled water for the golden-mantled ground squirrel [44]. Regression equation: savings (%) = −0.0015M_B + 86.4 (R² = 0.94, p < 0.001). Regression line plus 95% confidence intervals are shown (see text for details; all data are provided in the electronic supplementary material, table S1). (Online version in colour.)

Figure 3.

Predicted energy savings of hibernation, calculated for our dataset (electronic supplementary material, table S1) as in figure 2 but using DEE according to the allometric equation of Speakman & Krol [22]. Red dots represent datapoints added a posteriori, where energy savings were estimated empirically by each author, from oxygen consumption values for yellow-bellied marmots [42] and 60 kg black bears [8], by direct calorimetry for Richardson's ground squirrel [43], and by using doubly labelled water for the golden-mantled ground squirrel [44]. Regression equation: savings (%) = −0.0004M_B + 94.9 (R² = 0.97, p < 0.001). Regression line plus 95% confidence intervals are shown (see text for details; all data are provided in the electronic supplementary material, table S1). (Online version in colour.)

3. Results

Our compilation and the reanalysis of Ruf & Geiser [3] dataset gave similar results, as did the unified dataset (electronic supplementary material, figures S1 and S2). Here, for simplicity, we discuss our own results (DEE_H presented in electronic supplementary material, table S1). The linear regression between log₁₀(DEE_H) and log₁₀M_B was significant (slope = 1.02 ± 0.05, intercept = −1.40 ± 0.15, adjusted R² = 0.96, p << 0.001; figure 1). Comparing the obtained curve for DEE_H with the theoretical expectation for a resting animal (i.e. BMR) [15], it was found that the energy savings due to hibernation are maximum in very small species (the distance between the solid and dotted line in figure 1). For instance, a 45 g monito del monte (D. gliroides) has a DEE_H of 6.32 kJ d⁻¹ but a predicted BMR of 26.4 kJ d⁻¹, thus giving a net saving of 76%. Similarly, for a large grizzly bear (U. arctos) of 180 kg, the predicted BMR is 6823.9 kJ d⁻¹, which is below DEE_H, thus giving a negative energy saving (−124%, figure 2). Equating our empirical allometric equation of DEE_H with the equation of BMR gives M_B = 75.2 kg. This is the point where the hibernation energy saving becomes zero. A similar calculation using expected DEE indicates that energy savings of hibernation become zero at M_B = 1549.7 kg.

Figure 1.

Relationship between DEE_H (kJ d⁻¹), estimated from fat and lean mass consumption during hibernation (n = 17), and the expected BMR [15] and DEE [22] (both having the standard ⅔ exponent). At body sizes above 75 kg (i.e. brown bears, U. arctos), DEE_H approaches BMR, but for the case of DEE both curves intersect at approximately 1.5 tons.) MR, metabolic rate (kJ d⁻¹).

4. Discussion

(a) . Hibernation energy savings: calculating the limits

Whereas the exact value of the slope of the allometry is debated (for mammals, the allometric exponent for BMR increases with size [18]), there is no doubt that the scaling exponent of metabolism in active animals is less than 1 [7,15,18,45]. Thus, our findings of isometric scaling of DEE_H have several implications. Compared with the estimation of Heldmaier et al. [2] and also previous authors showing that the metabolic rate in hibernation is constant per unit body mass [27], our analysis of the metabolic scaling of hibernation based on changes in body composition raised the intercept fourfold (i.e. from 0.014 to 0.054 kJ g⁻¹ d⁻¹, using mass-specific units) [2]. This implies that in large hibernators of 75 kg or above, the energy savings by hibernation approaches zero (using BMR as comparison), or 1.5 tons (using DEE as comparison). Given that mammalian metabolism in activity is typically 2–3 times BMR [46], it could be argued that it is more appropriate to use DEE rather than BMR to calculate energy savings of hibernation. However, most authors have used BMR (see compilations in [2,3,7]), because a torpid animal is in a resting state, in which the only difference from an active animal is that it is not paying the cost of endothermy. Reanalysing our data using DEE gives the regression line presented in figure 3, which shows a slightly better adjustment, and a similar trend to using BMR (i.e. that energy savings of hibernation are reduced at large sizes).

(b) . Why bears hibernate?

Classic physiology textbooks affirm that bears (i.e. black bears, U. americanus, and brown bears, U. arctos) do not hibernate, owing to the relatively small drop in body temperature they experience (from 37° to 32–34°C in hibernation [47] (but this claim was questioned in [48]). However, the molecular and physiological evidence accumulated during the last decade revealed that bears experience a profound and extended dormancy, as in other hibernators [8,39,49–53]. Although they do not experience large reductions in temperature, black bears experience a complete metabolic suppression during torpor [52], which represents acute reductions to about 25% of BMR [8]. Bears do not urinate nor defaecate during the 4–6 months of their hibernation (they recycle nitrogen from urea) [54], which is preceded by a long fast that could last several months [9,55]. This denning period (i.e. fasting plus hibernation) is coincident with the fetal and neonatal growth of the cub [49], overall representing an enormous energetic challenge to the mother. Thus, females consume themselves to feed their cubs, starting by consuming fat stores and following with lean mass [39,49]. According to Lopez-Alfaro et al. [49], in brown bears, the protein transferred from the mother to the cubs accounts for 73% of body mass loss that occurred above the maternal maintenance costs. Then, protein turnover in these large mammals is more important for survival than energy stored as fats. Thus, reducing the cost of euthermia (which, as we discussed, is small for large endotherms) also reduces the metabolic load on lean tissue, the limiting resource of females with offspring. Then, recalling the allocation principle [56], the optimal strategy for a wintering bear would be to turn off the euthermia tap and to prioritize resources (protein and energy) to offspring.

(c) . Implications of isometric scaling

Our results also posit the intriguing question of why a cell of a hibernating bat has a similar metabolism to a cell of a hibernating bear, an animal that is 20 000 times larger. Indeed, a hibernating mammal expends 2.24 ± 0.56 J h⁻¹ per gram of tissue, which is equivalent to 6.2 × 10⁻⁴ ± 1.6 × 10⁻⁴ W g⁻¹. Thus, considering that a standard 70 kg human has on average nearly 3.72 × 10¹³ cells [57] (5.3 × 10⁸ cells g⁻¹), the cellular metabolic power of hibernation would be 1.2 × 10⁻¹² ± 1.6 × 10⁻¹³ W cell⁻¹. This allometric scaling, the slope of which is non-significantly different from 0, is presented for our data by figure 4, and also compiled in the electronic supplementary material, table S1, showing together bears, bats and woodchucks. Of course, this averaging represents a rough approximation, since animals differ in the proportional composition of different cell types. But the y-intercept of this curve has a very small standard error (1.11 × 10⁻¹² ± 1.7 × 10⁻¹³, n = 17, p << 0.001), and the value falls below the metabolic power of isolated mammalian cells in cultures (approx. 10⁻¹⁰, see Fig. 4 in West et al. [17]). It seems, then, that at this very low level of metabolism, the networks of vascularization and transport of oxygen and nutrients become unnecessary. According to West et al. ([17], their Fig. 4), for mammalian cells scaling is isometric and goes downwards until isolated mitochondria, at approximately 10⁻¹⁵ W cell⁻¹ and mass = 10⁻¹³ g. Thus, the cellular power of hibernating cells is near the minimum viable cell metabolism proposed by these authors. We believe this is an interesting finding that deserves further exploration, for instance, with single-cell measurements of metabolic rates under dormancy.

Figure 4.

Cellular metabolic power of hibernation, calculated for the dataset in figure 1. Common names are defined in electronic supplementary material, table S1. See text for details.

(d) . The adaptive significance of physiological dormancy

The fact that hibernation and daily torpor has appeared many times independently in the phylogeny of mammals and birds [2] would suggest that this is an evolutionary convergence [3,5]. However, many kinds of physiological dormancies have been described in an enormous range of organisms, from unicellular to multicellular, and also in ecto- and endotherms, suggesting that facultative metabolic depression is a general capacity of eukaryotic cells [7]. Thus, and understandably, several authors have struggled with inferring the evolutionary origin of heterothermy, as it could be considered an ‘ancient’ trait (since it is a basic property of organisms) [2], but it is also considered an independent adaptation (since it has appeared independently several times) [28,58,59]. Perhaps a more parsimonious interpretation of physiological dormancy is that this is an ancestral capacity of living beings, which is adaptively reactivated under a certain combination of climatic and ecological conditions. This would explain the common molecular basis for metabolic depression in anoxia-tolerant vertebrates and invertebrates, hibernation in endotherms, and aestivation in some terrestrial ectotherms [60].

Data availability

Data are available in the electronic supplementary material [61] and from the Dryad Digital Repository: https://doi.org/10.5061/dryad.0cfxpnw4j [30].

A reanalysis of data from the following reference is included [3].

Authors' contributions

R.F.N.: conceptualization, data curation, formal analysis, funding acquisition, methodology, and writing—original draft; F.B.: conceptualization, funding acquisition, investigation, methodology, and writing—review and editing; C.M.: conceptualization and data curation.

All authors gave final approval for publication and agreed to be held accountable for the work performed herein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

This work was funded by ANID – Millennium Science Initiative Program – centre code NCN2021-050 and ANID PIA/BASAL Center FB0002; and FONDECYT 1221073.