DOI: 10.5061/dryad.0cfxpnw4j
title: Why bears hibernate? Redefining the scaling energetics of hibernation

description: 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 (DEEH), covering a range of five orders of
 magnitude in mass. We found that DEEH 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 DEEH 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.
description: 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<sub>B</sub> (in grams) of females and males and/or fat
 consumption when reported separately. When provided, we also averaged
 M<sub>B</sub> before and after the hibernation. Given that
 hibernators are a small subset of mammalian species, biased to small
 M<sub>B</sub>’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
 <em>Myotis myotis</em> (24.7g)[1], the marsupial monito del monte
 <em>Dromiciops gliroides</em> (45g)[2], the arctic ground squirrel
 <em>Spermophilus parryii</em> (820g)[3], and the bears: <em>Ursus
 americanus</em> (74.5kg)[4], and <em>Ursus arctos
 </em>(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 (<em>Myotis lucifugus</em>,
 8.5g)[6], and species of intermediate sizes such as
 woodchucks (<em>Marmota monax</em>,
 2.2kg)[7] and also a monotreme, the short-beaked echidna
 (<em>Tachyglossus aculeatus</em>, 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<sub>H</sub>, 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<sub>H</sub> 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 R<sup>2</sup>=0.95 (adjusted R-value,
 using only fat mass) to R<sup>2</sup>=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<sub>H</sub>=[39.7kJg<sup>-1</sup> * (fat mass
 consumed, in grams) + 23.6kJg<sup>-1</sup>*(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<sub>H</sub>
 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<sub>H</sub> by M<sub>B</sub>, 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
 3.72x10<sup>13</sup> cells [12], (=5.3x10<sup>8</sup> cells per
 gram). In tab “Fig S1” we recalculate data of minimum torpor metabolic
 rate (TMR<sub>min</sub>), presented in the review of Ruf and
 Geiser (2015)[13], and expressed in kJ/day, together with our own
 data of DEE<sub>H</sub> in another column named
 DEE<sub>H</sub>.  
 <em>Predicting energy
 savings</em> There is some debate regarding the appropriate
 exponent for metabolic scaling, which increases with
 M<sub>B</sub> [14]. According to these authors (see also
 [15]), the most appropriate scaling exponent for our
 range of sizes
 (M<sub>B</sub>&lt;10<sup>5</sup>g) 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<sub>B</sub><sup>0.67</sup>[15], which is in mlO<sub>2</sub> h<sup>-1</sup> and converted BMR values to kJd<sup>-1</sup> using the conversion factor 19.8 J mlO<sub>2</sub><sup>-1</sup>, 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<sub>B</sub><sup>0.67</sup>. 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.   <em>Literature</em>  1.         Koteja P., Jurczyszyn M., Woloszyn B.W. 2001 Energy balance of hibernating mouse-eared bat Myotis myotis: a study with a TOBEC instrument. <em>Acta Theriologica </em><strong>46</strong>(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 <em>Dromiciops gliroides</em>: a field study applying quantitative magnetic resonance. <em>Physiological and Biochemical Zoology</em> (<strong>in press</strong>) (xx), 1-10. 3.         Buck C.L., Barnes B.M. 1999 Annual cycle of body composition and hibernation in free-living arctic ground squirrels. <em>Journal of Mammalogy</em> <strong>80</strong>(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). <em>Journal of Mammalogy</em> <strong>83</strong>(4), 1020-1025. (doi:10.1644/1545-1542(2002)083&lt;1020:Bmalcb&gt;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. <em>Journal of Wildlife Management</em> <strong>64</strong>(1), 178-183. (doi:10.2307/3802988). 6.         Jonasson K.A., Willis C.K.R. 2012 Hibernation energetics of free-ranging little brown bats. <em>J Exp Biol</em> <strong>215</strong>(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. <em>Canadian Journal of Zoology</em> <strong>43</strong>, 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. <em>Journal of Comparative Physiology B-Biochemical Systemic and Environmental Physiology</em> <strong>171</strong>(3), 189-194. (doi:10.1007/s003600000157). 9.         Geiser F. 2007 Yearlong hibernation in a marsupial mammal. <em>Naturwissenschaften</em> <strong>94</strong>(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. <em>Proceedings of the Royal Society B</em> (<strong>in press</strong>). 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. <em>J Exp Biol</em> <strong>198</strong>(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. <em>Annals of Human Biology</em> <strong>40</strong>(6), 463-471. (doi:10.3109/03014460.2013.807878). 13.       Ruf T., Geiser F. 2015 Daily torpor and hibernation in birds and mammals. <em>Biol Rev</em> <strong>90</strong>(3), 891-926. (doi:10.1111/brv.12137). 14.       Kolokotrones T., Savage V., Deeds E.J., Fontana W. 2010 Curvature in metabolic scaling.<em> Nature</em> <strong>464</strong>(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 <em>Proceedings of the National Academy of Science of USA</em> <strong>100</strong>(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. <em>J Anim Ecol</em> <strong>79</strong>(4), 726-746. (doi:10.1111/j.1365-2656.2010.01689.x).
description: Put the files in a single folder and run the R-script. Results
 will appear in the order presented in the paper.