The predominance of quarter-power scaling in biology

Summary 1. Recent studies have resurrected the debate over the value for the allometric scaling exponent that relates whole-organism metabolic rate to body size. Is it 3 / 4 or 2 / 3 ? This question has been raised before and resolved in favour of 3 / 4 . Like previous ones, recent claims for a value of 2 / 3 are based almost entirely on basal metabolic rate (BMR) in mammals. 2. Here we compile and analyse a new, larger data set for mammalian BMR. We show that interspecific variation in BMR, as well as field metabolic rates of mammals, and basal or standard metabolic rates for many other organisms, including vertebrates, invertebrates, protists and plants, all scale with exponents whose confidence intervals include 3 / 4 and exclude 2 / 3 . Our analysis of maximal metabolic rate gives a slope that is greater than and confidence intervals that exclude both 3 / 4 and 2 / 3 . 3. Additionally, numerous other physiological rates that are closely tied to metabolism in a wide variety of organisms, including heart and respiratory rates in mammals, scale as M − 1/4 . 4. The fact that quarter-power allometric scaling is so pervasive in biology suggests that different allometric relations have a common, mechanistic origin and provides an empirical basis for theoretical models that derive these scaling exponents.

[1]  Geoffrey B. West,et al.  Effects of Body Size and Temperature on Population Growth , 2004, The American Naturalist.

[2]  Ethan P. White,et al.  Thermodynamic and metabolic effects on the scaling of production and population energy use , 2003 .

[3]  C. R. White,et al.  Mammalian basal metabolic rate is proportional to body mass2/3 , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Karl J. Niklas,et al.  A general model for mass-growth-density relations across tree-dominated communities , 2003 .

[5]  B. G. Lovegrove,et al.  The influence of climate on the basal metabolic rate of small mammals: a slow-fast metabolic continuum , 2003, Journal of Comparative Physiology B.

[6]  B. Enquist.  Universal scaling in tree and vascular plant allometry: toward a general quantitative theory linking plant form and function from cells to ecosystems. , 2002, Tree physiology.

[7]  Andrea Belgrano,et al.  Allometric scaling of maximum population density: a common rule for marine phytoplankton and terrestrial plants , 2002 .

[8]  Andrea Rinaldo,et al.  Supply–demand balance and metabolic scaling , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Bernard Sapoval,et al.  Smaller is better—but not too small: A physical scale for the design of the mammalian pulmonary acinus , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[10]  James H. Brown,et al.  Effects of size and temperature on developmental time , 2002, Nature.

[11]  Karl J Niklas,et al.  On the Vegetative Biomass Partitioning of Seed Plant Leaves, Stems, and Roots , 2002, The American Naturalist.

[12]  Karl J Niklas,et al.  Global Allocation Rules for Patterns of Biomass Partitioning in Seed Plants , 2002, Science.

[13]  James H Brown,et al.  Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[14]  James H. Brown,et al.  The Physiological Ecology of Vertebrates: A View from Energetics , 2002 .

[15]  James H. Brown,et al.  A general model for ontogenetic growth , 2001, Nature.

[16]  James H. Brown,et al.  Effects of Size and Temperature on Metabolic Rate , 2001, Science.

[17]  Karl J. Niklas,et al.  Invariant scaling relations across tree-dominated communities , 2001, Nature.

[18]  K J Niklas,et al.  Invariant scaling relationships for interspecific plant biomass production rates and body size , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[19]  J. Weitz,et al.  Re-examination of the "3/4-law" of metabolism. , 2000, Journal of theoretical biology.

[20]  J. Nelson,et al.  Energy, water balance and the roost microenvironment in three Australian cave-dwelling bats (Microchiroptera) , 2000, Journal of Comparative Physiology B.

[21]  Barry G Lovegrove,et al.  The Zoogeography of Mammalian Basal Metabolic Rate , 2000, The American Naturalist.

[22]  Sebastiaan A.L.M. Kooijman,et al.  Dynamic Energy and Mass Budgets in Biological Systems , 2000 .

[23]  Anthony R. Ives,et al.  Using the Past to Predict the Present: Confidence Intervals for Regression Equations in Phylogenetic Comparative Methods , 2000, The American Naturalist.

[24]  Charles M. Bishop.  The maximum oxygen consumption and aerobic scope of birds and mammals: getting to the heart of the matter , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[25]  James H. Brown,et al.  Allometric scaling of production and life-history variation in vascular plants , 1999, Nature.

[26]  James H. Brown,et al.  A general model for the structure and allometry of plant vascular systems , 1999, Nature.

[27]  James H. Brown,et al.  The fourth dimension of life: fractal geometry and allometric scaling of organisms. , 1999, Science.

[28]  Amos Maritan,et al.  Size and form in efficient transportation networks , 1999, Nature.

[29]  K. Nagy,et al.  Energetics of free-ranging mammals, reptiles, and birds. , 1999, Annual review of nutrition.

[30]  James H. Brown,et al.  Allometric scaling of plant energetics and population density , 1998, Nature.

[31]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[32]  Don E. Wilson,et al.  The Mammal Species of the World , 2009 .

[33]  M. Patterson,et al.  A Mass Transfer Explanation of Metabolic Scaling Relations in Some Aquatic Invertebrates and Algae , 1992, Science.

[34]  B. McNab.  A statistical analysis of mammalian rates of metabolism , 1992 .

[35]  Heusner Aa,et al.  Size and power in mammals. , 1991 .

[36]  A. Heusner,et al.  Size and power in mammals. , 1991, The Journal of experimental biology.

[37]  M. Pagel,et al.  The comparative method in evolutionary biology , 1991 .

[38]  M. Pagel,et al.  The Taxon-Level Problem in the Evolution of Mammalian Brain Size: Facts and Artifacts , 1988, The American Naturalist.

[39]  W. Calder.  Size, Function, and Life History , 1988 .

[40]  H. Hoppeler,et al.  Matching O2 delivery to O2 demand in muscle: II. Allometric variation in energy demand. , 1988, Advances in experimental medicine and biology.

[41]  A. Heusner.  What does the power function reveal about structure and function in animals of different size? , 1987, Annual review of physiology.

[42]  R. Macmillen,et al.  Scaling of Energy Metabolism and Evaporative Water Loss in Heteromyid Rodents , 1985, Physiological Zoology.

[43]  K. Schmidt-Nielsen,et al.  Scaling, why is animal size so important? , 1984 .

[44]  R. Peters.  The Ecological Implications of Body Size , 1983 .

[45]  Similarity principles for the biology of pelagic animals. , 1983, Proceedings of the National Academy of Sciences of the United States of America.

[46]  H. Feldman,et al.  The 3/4 mass exponent for energy metabolism is not a statistical artifact. , 1983, Respiration physiology.

[47]  John Tyler Bonner,et al.  On size and life , 1983 .

[48]  A. Heusner.  Energy metabolism and body size. II. Dimensional analysis and energetic non-similarity. , 1982, Respiration physiology.

[49]  A. Heusner.  Energy metabolism and body size. I. Is the 0.75 mass exponent of Kleiber's equation a statistical artifact? , 1982, Respiration physiology.

[50]  E R Weibel,et al.  Design of the mammalian respiratory system. III Scaling maximum aerobic capacity to body mass: wild and domestic mammals. , 1981, Respiration physiology.

[51]  W. Calder,et al.  Body Size, Physiological Time, and Longevity of Homeothermic Animals , 1981, The Quarterly Review of Biology.

[52]  G. Maloiy,et al.  Thermoregulation and Standard Metabolism of the Slender Mongoose (Herpestes sanguineus) , 1979, Physiological Zoology.

[53]  J. Prothero.  Maximal oxygen consumption in various animals and plants , 1979 .

[54]  A. Lechner,et al.  The scaling of maximal oxygen consumption and pulmonary dimensions in small mammals. , 1978, Respiration physiology.

[55]  J. Weiner.  Energy Metabolism of the Roe Deer , 1977 .

[56]  J J Blum,et al.  On the geometry of four-dimensions and the relationship between metabolism and body mass. , 1977, Journal of theoretical biology.

[57]  M. E. El Halawani,et al.  The relative importance of monoamine oxidase and catechol-O-methyl transferase on the physiologic response to administered norepinephrine in the turkey. , 1975, Comparative biochemistry and physiology. C: Comparative pharmacology.

[58]  Thomas A. McMahon,et al.  Allometry and Biomechanics: Limb Bones in Adult Ungulates , 1975, The American Naturalist.

[59]  W. G. Bradley,et al.  Thermoregulatory responses in the plains pocket gopher, Geomys bursarius. , 1975, Comparative biochemistry and physiology. A, Comparative physiology.

[60]  T. McMahon,et al.  Size and Shape in Biology , 1973, Science.

[61]  Knut Schmidt-Nielsen,et al.  How Animals Work , 1972 .

[62]  Claud L. Brown,et al.  Growth and Form , 1971 .

[63]  P. Pasquis,et al.  Maximal oxygen uptake in four species of small mammals. , 1970, Respiration physiology.

[64]  B. McNab.  The economics of temperature regulation in neotropical bats. , 1969, Comparative biochemistry and physiology.

[65]  W. Calder.  Respiratory and Heart Rates of Birds at Rest , 1968 .

[66]  W. R. Stahl,et al.  Scaling of respiratory variables in mammals. , 1967, Journal of applied physiology.

[67]  R. C. Lasiewski,et al.  A Re-Examination of the Relation between Standard Metabolic Rate and Body Weight in Birds , 1967 .

[68]  S. Hemmingsen,et al.  Energy metabolism as related to body size and respiratory surfaces, and its evolution , 1960 .

[69]  L. Walford,et al.  Bioenergetics and Growth , 1947 .

[70]  S. Brody,et al.  Growth and development with special reference to domestic animals. 34. Basal metabolism, endogenous nitrogen, creatinine and neutral sulphur excretions as functions of body weight. , 1934 .

[71]  M. Kleiber.  Body size and metabolism , 1932 .

[72]  D'arcy W. Thompson,et al.  On Growth and Form , 1917, Nature.

[73]  C. R. Stockard.  The influence of alcohol and other anesthetics on developing embryos , 1909 .

[74]  M. Rubner,et al.  Ueber den Einfluss der Körpergrösse auf Stoff- und Kraftwechsel , 1883 .