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 the 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 (~100 kg). Calculated on a per-cell basis, the cellular metabolic power of hibernation was estimated to be 1.3x10^-12 ± 2.6x10^-13 W/cell, 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.

This is a compilation from literature, where fat consumption during hibernation, in a fixed period of time was measured in several mammalian species. We averaged M_B (in grams) 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’s, 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 (24.7g)[1], the marsupial monito del monte Dromiciops gliroides (45g)[2], the arctic ground squirrel Spermophilus parryii (820g)[3], and the bears: Ursus americanus (74.5kg)[4], and Ursus arctos (179kg)[5] (see Table S1). We then expanded the data set 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, 8.5g)[6], and species of intermediate sizes such as woodchucks (Marmota monax, 2.2kg)[7] and also a monotreme, the short-beaked echidna (Tachyglossus aculeatus, 4.7kg)[8]. The whole compilation is presented in Table S1. The data reproducing each figure of the paper are presented in the attached Excel file, with each tab denoted as each Figure of the paper.

In most cases, measurements were conducted in the field under natural conditions of hibernation, but in few cases animals were held in the laboratory with natural photoperiod and temperature [7, 9]. We calculated the daily energy expenditure of hibernation (DEE_H, in kJ/day; see the formula below) using fat consumption, which was more often reported. In a few cases (see 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 hibernation energy consumption of 21% lean mass and 79% fat mass (presented in 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 (see Results in [10]). The daily amount of energy consumed during each period of hibernation was calculated as DEE_H=[39.7kJg^-1 * (fat mass consumed, in grams) + 23.6kJg^-1*(lean mass consumed, in grams)]/duration of the experiment, in days; which considers the respiratory quotient or RQ of each nutrient [4, 11]. Given that DEE_H presented an isometric scaling (i.e., a gram of a hibernating bat of 8g has a similar metabolism of a gram of hibernating bear of 180kg), we divided DEE_H by M_B, and calculated the cellular metabolic rate (cel_met, in tab “Fig 4”) as W/cell, assuming that a standard 70 kg human has in average nearly 3.72x10¹³ cells [12], (=5.3x10⁸ cells per gram). In tab “Fig S1” we recalculate data of minimum torpor metabolic rate (TMR_min), presented in the review of Ruf and Geiser (2015)[13], and expressed in kJ/day, together with our own data of DEE_H in another column named DEE_H.

Predicting energy savings

There is some debate regarding the appropriate exponent for metabolic scaling, which increases with M_B [14]. According to these authors (see also [15]), the most appropriate scaling exponent for our range of sizes (M_B<10⁵g) is 2/3 (see Fig 2 in [14]). Then, to contrast our estimations with theoretical predictions, we estimated BMR (kJ/day) using the equation: BMR= 4.34M_B^0.67[15], which is in mlO₂ h^-1 and converted BMR values to kJd^-1 using the conversion factor 19.8 J mlO₂^-1, which assumes RQ=0.71[11].  We also included in the comparison, the expected value of daily energy expenditure (DEE), using the equation of Speakman and Krol (2010)[16]: DEE = 6.29M_B^0.67. In the final allometric curve, we included a few studies where the energy savings of hibernation was estimated with techniques other than fat/lean mass consumption (e.g., respirometry). All these additional datapoints (denoted in red in Figs 2 and 3) fell within the 95% confidence interval of the original regression, thus supporting our main conclusion.

Literature 

1.         Koteja P., Jurczyszyn M., Woloszyn B.W. 2001 Energy balance of hibernating mouse-eared bat Myotis myotis: a study with a TOBEC instrument. Acta Theriologica 46(1), 1-12. (doi:10.1007/bf03192411).

2.         Mejias C., J. N., Sabat P., Franco L.M., Bozinovic F., Nespolo R.F. 2022 Body composition and energy savings by hibernation in the South American marsupial Dromiciops gliroides: a field study applying quantitative magnetic resonance. Physiological and Biochemical Zoology (in press) (xx), 1-10.

3.         Buck C.L., Barnes B.M. 1999 Annual cycle of body composition and hibernation in free-living arctic ground squirrels. Journal of Mammalogy 80(2), 430-442. (doi:10.2307/1383291).

4.         Harlow H.J., Lohuis T., Grogan R.G., Beck T.D.I. 2002 Body mass and lipid changes by hibernating reproductive and nonreproductive black bears (Ursus americanus). Journal of Mammalogy 83(4), 1020-1025. (doi:10.1644/1545-1542(2002)083<1020:Bmalcb>2.0.Co;2).

5.         Hilderbrand G.V., Schwartz C.C., Robbins C.T., Hanley T.A. 2000 Effect of hibernation and reproductive status on body mass and condition of coastal brown bears. Journal of Wildlife Management 64(1), 178-183. (doi:10.2307/3802988).

6.         Jonasson K.A., Willis C.K.R. 2012 Hibernation energetics of free-ranging little brown bats. J Exp Biol 215(12), 2141-2149. (doi:10.1242/jeb.066514).

7.         Bailey E.D., Davis D.E. 1965 The utilization of body fat during hibernation in woodchucks. Canadian Journal of Zoology 43, 701-707.

8.         Falkenstein F., Kortner G., Watson K., Geiser F. 2001 Dietary fats and body lipid composition in relation to hibernation in free-ranging echidnas. Journal of Comparative Physiology B-Biochemical Systemic and Environmental Physiology 171(3), 189-194. (doi:10.1007/s003600000157).

9.         Geiser F. 2007 Yearlong hibernation in a marsupial mammal. Naturwissenschaften 94(11), 941-944. (doi:10.1007/s00114-007-0274-7).

10.       Nespolo R.F., Mejias C., Bozinovic F. 2022 Why bears hibernate? Redefining the scaling energetics of hibernation. Proceedings of the Royal Society B (in press).

11.       Walsberg G.E., Wolf B.O. 1995 Variation in the respiratory quotient of birds and implications for indirect calorimetry using measurements of carbon-dioxide production. J Exp Biol 198(1), 213-219.

12.       Bianconi E., Piovesan A., Facchin F., Beraudi A., Casadei R., Frabetti F., Vitale L., Pelleri M.C., Tassani S., Piva F., et al. 2013 An estimation of the number of cells in the human body. Annals of Human Biology 40(6), 463-471. (doi:10.3109/03014460.2013.807878).

13.       Ruf T., Geiser F. 2015 Daily torpor and hibernation in birds and mammals. Biol Rev 90(3), 891-926. (doi:10.1111/brv.12137).

14.       Kolokotrones T., Savage V., Deeds E.J., Fontana W. 2010 Curvature in metabolic scaling. Nature 464(7289), 753-756. (doi:10.1038/nature08920).

15.       White C.R., Seymour R.S. 2003 Mammalian basal metabolic rate is proportional to body mass 2/3 Proceedings of the National Academy of Science of USA 100(7), 4046-4049.

16.       Speakman J.R., Krol E. 2010 Maximal heat dissipation capacity and hyperthermia risk: neglected key factors in the ecology of endotherms. J Anim Ecol 79(4), 726-746. (doi:10.1111/j.1365-2656.2010.01689.x).

Put the files in a single folder and run the R-script. Results will appear in the order presented in the paper.