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The Mouse‐To‐Elephant Metabolic Curve: Historical Overview

Jacopo P. Mortola

10.1002/cphy.c220003

Source: Volume 13, Issue 2, April 2023

Published online: March 2023

Full Article on Wiley Online Library



Abstract

Although it is intuitive that large mammals need more food than smaller ones, it is not so obvious that, relative to their body mass, larger mammals consume less than smaller ones. In fact, on a per kg basis, the resting metabolic rate of a mouse is some 50 times higher than that of an elephant. The fact that metabolism could not be proportional to the mass of the animal was suggested by Sarrus and Rameaux in 1838. The first indication that oxygen consumption (or other indices of metabolic rate, Y) related to the animal body mass (M) according to an exponential of the type Y = a · Mb, where b was about 0.75, was presented by Max Kleiber in 1932. Two years later Samuel Brody had collected sufficient data to construct the first “mouse‐to‐elephant” metabolic curve. The physiological basis of the relationship has been the object of many hypotheses, often accompanied by a great deal of controversy. This historical essay traces the origin of the mouse‐to‐elephant metabolic function, recalling the earliest concepts of metabolism and its measurements to understand the body size dependency, which is still one of the most elusive phenomena in comparative physiology. A brief look at the metabolic scaling of nonmammalian organisms will be included to frame the mouse‐to‐elephant curve into a broader context and to introduce some interesting interpretations of the mammalian function. © 2023 American Physiological Society. Compr Physiol 13:4513‐4558, 2023.

Figure 1. Figure 1. Santorio Sanctorius (1561–1636). Reused, with permission, from History and Art Collection/Alamy Images.
Figure 2. Figure 2. Germain Hess (1802–1850). Reused, with permission, from /Wikimedia Commons/Public domain.
Figure 3. Figure 3. August Krogh (1874–1949). Reused, with permission, from A. B. Lagrelius/Wikimedia Commons/Public domain.
Figure 4. Figure 4. D'Arcy Wentworth Thompson (1860–1948) and some of his geometric transformations.
Figure 5. Figure 5. Georges Teissier (1900–1972).
Figure 6. Figure 6. (A) Allometric relations in absolute values (Y = Mb) or (B) mass‐specific values (Y/M = Mb) for volumes, areas, and linear dimensions.
Figure 7. Figure 7. Pierre Frédéric Sarrus (1798–1861). Reused, with permission, from Unknown Source/Wikimedia Commons/Public domain.
Figure 8. Figure 8. Thermographs of a Patagonian mara (A) and a White rhinoceros (B) at approximately 21°C ambient temperature. At top are the corresponding standard digital pictures. Note the differences in radiant temperature among body surface regions. Reused, with permission, from Mortola JP, The Zoological Society of Japan. 2013 163.
Figure 9. Figure 9. Body temperature (top) and body surface radiant temperature (at the ambient temperatures Ta of about 21, 23.5, and 26°C) in mammals of different body size. Each symbol is the average value of a species. Reused, with permission, from Mortola JP, The Zoological Society of Japan. 2013 163.
Figure 10. Figure 10. (A) Samuel A. Brody (1890–1956). (B) The allometric plot of metabolism covered the range in body size from mouse to elephant. Reused, with permission, from Brody S, et al., Curators of the University of Missouri. 1934 35.
Figure 11. Figure 11. (A) Francis G. Benedict (1870–1957). Reused, with permission, from Unknown Source/Wikimedia Commons/CC BY 4.0. (B) Figure 44 from Benedict's monograph “Vital Energetics”. The units of the Y‐axis are Cal/m2 surface area. Reused, with permission, from Benedict FG, Carnegie Inst. Washington Publication. 1938 20.
Figure 12. Figure 12. Double‐log plot of oxygen consumption against body mass in eutherian species. Dashed line indicates the best fit through all species. Red and blue symbols refer to species with body weight, respectively, smaller or greater than 100 g. Constructed by combining the lists compiled by Brody 35, Benedict 20, Hayssen and Lacy 91, Elgar and Harvey 58, Frappell et al. 70, and White and Seymour 247.
Figure 13. Figure 13. Allometric plot (double‐log representation) of oxygen consumption (mL/min) against body mass (M, kg) for 65 species of nonpasserines (blue circles) and 62 species of passerines (red triangles). The dashed lines are the extrapolated linear regressions through the data points, the slope of which is indicated in brackets. The thicker black continuous line is the linear regression through all bird species combined (M0.67). Adapted, with permission, from McKechnie AE and Wolf BO, Physiol Biochem Zool. 2004 149.
Figure 14. Figure 14. The slopes of the regression lines of the three groups of organisms (0.75 for all) were parallel to each other, with the intercept becoming progressively higher from unicellular, to poikilotherms, to homeotherms. Reused, with permission, from Hemmingsen AM, ScienceOpen, Inc. 1960 95.
Figure 15. Figure 15. Otto Heinrich Warburg (1883–1970). Reused, with permission, from Georg Pahl/Wikimedia Commons/CC BY‐SA 3.0.
Figure 16. Figure 16. Allometric curve of the surface areas (solid lines) of summated organs (liver, kidney, brain, and heart) and of the summated organs plus skeletal muscles. The two dashed lines are the allometric curves of resting and maximal oxygen consumption (V˙O2) for the species studied. Adapted, with permission, from Else PL and Hulbert AJ, Am J Physiol. 1985 60.
Figure 17. Figure 17. Diagram of the multi‐contributor model of metabolic allometry proposed by Darveau et al. 48. Each contributor to energy demand (left) and supply (right) has its own allometric scaling (intercept c and slope b in Eq. 16); their individual c and b can vary depending on extrinsic and intrinsic regulation. ATP‐utilizing processes can be considered linked in parallel, while the supply processes are linked in series. Reused, with permission, Hochachka PW, et al. Comp Biochem Physiol A. 2003/Elsevier 99.


Figure 1. Santorio Sanctorius (1561–1636). Reused, with permission, from History and Art Collection/Alamy Images.


Figure 2. Germain Hess (1802–1850). Reused, with permission, from /Wikimedia Commons/Public domain.


Figure 3. August Krogh (1874–1949). Reused, with permission, from A. B. Lagrelius/Wikimedia Commons/Public domain.


Figure 4. D'Arcy Wentworth Thompson (1860–1948) and some of his geometric transformations.


Figure 5. Georges Teissier (1900–1972).


Figure 6. (A) Allometric relations in absolute values (Y = Mb) or (B) mass‐specific values (Y/M = Mb) for volumes, areas, and linear dimensions.


Figure 7. Pierre Frédéric Sarrus (1798–1861). Reused, with permission, from Unknown Source/Wikimedia Commons/Public domain.


Figure 8. Thermographs of a Patagonian mara (A) and a White rhinoceros (B) at approximately 21°C ambient temperature. At top are the corresponding standard digital pictures. Note the differences in radiant temperature among body surface regions. Reused, with permission, from Mortola JP, The Zoological Society of Japan. 2013 163.


Figure 9. Body temperature (top) and body surface radiant temperature (at the ambient temperatures Ta of about 21, 23.5, and 26°C) in mammals of different body size. Each symbol is the average value of a species. Reused, with permission, from Mortola JP, The Zoological Society of Japan. 2013 163.


Figure 10. (A) Samuel A. Brody (1890–1956). (B) The allometric plot of metabolism covered the range in body size from mouse to elephant. Reused, with permission, from Brody S, et al., Curators of the University of Missouri. 1934 35.


Figure 11. (A) Francis G. Benedict (1870–1957). Reused, with permission, from Unknown Source/Wikimedia Commons/CC BY 4.0. (B) Figure 44 from Benedict's monograph “Vital Energetics”. The units of the Y‐axis are Cal/m2 surface area. Reused, with permission, from Benedict FG, Carnegie Inst. Washington Publication. 1938 20.


Figure 12. Double‐log plot of oxygen consumption against body mass in eutherian species. Dashed line indicates the best fit through all species. Red and blue symbols refer to species with body weight, respectively, smaller or greater than 100 g. Constructed by combining the lists compiled by Brody 35, Benedict 20, Hayssen and Lacy 91, Elgar and Harvey 58, Frappell et al. 70, and White and Seymour 247.


Figure 13. Allometric plot (double‐log representation) of oxygen consumption (mL/min) against body mass (M, kg) for 65 species of nonpasserines (blue circles) and 62 species of passerines (red triangles). The dashed lines are the extrapolated linear regressions through the data points, the slope of which is indicated in brackets. The thicker black continuous line is the linear regression through all bird species combined (M0.67). Adapted, with permission, from McKechnie AE and Wolf BO, Physiol Biochem Zool. 2004 149.


Figure 14. The slopes of the regression lines of the three groups of organisms (0.75 for all) were parallel to each other, with the intercept becoming progressively higher from unicellular, to poikilotherms, to homeotherms. Reused, with permission, from Hemmingsen AM, ScienceOpen, Inc. 1960 95.


Figure 15. Otto Heinrich Warburg (1883–1970). Reused, with permission, from Georg Pahl/Wikimedia Commons/CC BY‐SA 3.0.


Figure 16. Allometric curve of the surface areas (solid lines) of summated organs (liver, kidney, brain, and heart) and of the summated organs plus skeletal muscles. The two dashed lines are the allometric curves of resting and maximal oxygen consumption (V˙O2) for the species studied. Adapted, with permission, from Else PL and Hulbert AJ, Am J Physiol. 1985 60.


Figure 17. Diagram of the multi‐contributor model of metabolic allometry proposed by Darveau et al. 48. Each contributor to energy demand (left) and supply (right) has its own allometric scaling (intercept c and slope b in Eq. 16); their individual c and b can vary depending on extrinsic and intrinsic regulation. ATP‐utilizing processes can be considered linked in parallel, while the supply processes are linked in series. Reused, with permission, Hochachka PW, et al. Comp Biochem Physiol A. 2003/Elsevier 99.
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Article Title: The Mouse‐To‐Elephant Metabolic Curve: Historical Overview
 

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Jacopo P. Mortola. The Mouse‐To‐Elephant Metabolic Curve: Historical Overview. Compr Physiol 2023, 13: 4513-4558. doi: 10.1002/cphy.c220003