Phylogenetically Informed Analysis of the Allometry of Mammalian Basal Metabolic Rate Supports Neither Geometric Nor Quarter-Power Scaling

The form of the relationship between the basal metabolic rate (BMR) and body mass (M) of mammals has been at issue for almost seven decades, with debate focusing on the value of the scaling exponent (b, where BMR &agr; Mb) and the relative merits of b = 0.67 (geometric scaling) and b = 0.75 (quarter-power scaling). However, most analyses are not phylogenetically informed (PI) and therefore fail to account for the shared evolutionary history of the species they consider. Here, we reanalyze the most rigorously selected and comprehensive mammalian BMR dataset presently available, and investigate the effects of data selection and phylogenetic method (phylogenetic generalized least squares and independent contrasts) on estimation of the scaling exponent relating mammalian BMR to M. Contrary to the results of a non-PI analysis of these data, which found an exponent of 0.67–0.69, we find that most of the PI scaling exponents are significantly different from both 0.67 and 0.75. Similarly, the scaling exponents differ between lineages, and these exponents are also often different from 0.67 or 0.75. Thus, we conclude that no single value of b adequately characterizes the allometric relationship between body mass and BMR.

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

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

[3]  David R. Anderson,et al.  Kullback-Leibler information as a basis for strong inference in ecological studies , 2001 .

[4]  D. Swanson,et al.  A comparative analysis of thermogenic capacity and cold tolerance in small birds , 2006, Journal of Experimental Biology.

[5]  onrad,et al.  Resolution of a Supertree / Supermatrix Paradox , 2002 .

[6]  Theodore Garland,et al.  Phylogenetic Analysis of Covariance by Computer Simulation , 1993 .

[7]  T. Garland,et al.  Effects of branch length errors on the performance of phylogenetically independent contrasts. , 1998, Systematic biology.

[8]  C. R. White,et al.  The scaling and temperature dependence of vertebrate metabolism , 2006, Biology Letters.

[9]  J. Chaui-Berlinck A critical understanding of the fractal model of metabolic scaling , 2006, Journal of Experimental Biology.

[10]  T. Garland,et al.  Phylogenetic approaches in comparative physiology , 2005, Journal of Experimental Biology.

[11]  J. Kozłowski,et al.  West, Brown and Enquist's model of allometric scaling again: the same questions remain , 2005 .

[12]  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.

[13]  D. Maddison,et al.  Mesquite: a modular system for evolutionary analysis. Version 2.6 , 2009 .

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

[15]  F J Rohlf,et al.  COMPARATIVE METHODS FOR THE ANALYSIS OF CONTINUOUS VARIABLES: GEOMETRIC INTERPRETATIONS , 2001, Evolution; international journal of organic evolution.

[16]  Geoffrey B. West,et al.  Scaling in Biology , 2000 .

[17]  P. Butler,et al.  Minimal Metabolic Rate, What It Is, Its Usefulness, and Its Relationship to the Evolution of Endothermy: A Brief Synopsis , 2004, Physiological and Biochemical Zoology.

[18]  R. Freckleton,et al.  Phenotypic plasticity in the scaling of avian basal metabolic rate , 2006, Proceedings of the Royal Society B: Biological Sciences.

[19]  PHYLOGENY AFFECTS ESTIMATION OF METABOLIC SCALING IN MAMMALS , 2002, Evolution; international journal of organic evolution.

[20]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[21]  J. Felsenstein Phylogenies and the Comparative Method , 1985, The American Naturalist.

[22]  K. L. Blaxter,et al.  The energy metabolism of ruminants. , 1962 .

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

[24]  M. Pagel Inferring the historical patterns of biological evolution , 1999, Nature.

[25]  M. Novacek,et al.  Cretaceous eutherians and Laurasian origin for placental mammals near the K/T boundary , 2007, Nature.

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

[27]  Ramón Díaz-Uriarte,et al.  TESTING HYPOTHESES OF CORRELATED EVOLUTION USING PHYLOGENETICALLY INDEPENDENT CONTRASTS: SENSITIVITY TO DEVIATIONS FROM BROWNIAN MOTION , 1996 .

[28]  L. Halsey,et al.  A Phylogenetic Analysis of the Allometry of Diving , 2006, The American Naturalist.

[29]  A. Grafen The phylogenetic regression. , 1989, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[30]  S. O’Brien,et al.  A Molecular Classification for the Living Orders of Placental Mammals and the Phylogenetic Placement of Primates , 2007 .

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

[32]  T. Garland,et al.  Why Not to Do Two-Species Comparative Studies: Limitations on Inferring Adaptation , 1994, Physiological Zoology.

[33]  Ross Ihaka,et al.  Gentleman R: R: A language for data analysis and graphics , 1996 .

[34]  M. Pagel,et al.  Phylogenetic Analysis and Comparative Data: A Test and Review of Evidence , 2002, The American Naturalist.

[35]  T. F. Hansen,et al.  Phylogenies and the Comparative Method: A General Approach to Incorporating Phylogenetic Information into the Analysis of Interspecific Data , 1997, The American Naturalist.

[36]  N. Gotelli,et al.  ALLOMETRIC EXPONENTS SUPPORT A 3/4-POWER SCALING LAW , 2005 .

[37]  Jan Kozłowski,et al.  Is West, Brown and Enquist's model of allometric scaling mathematically correct and biologically relevant? , 2004 .

[38]  Phillip Cassey,et al.  Allometric exponents do not support a universal metabolic allometry. , 2007, Ecology.

[39]  J. Speakman,et al.  Measurement of Basal Metabolic Rates: Don't Lose Sight of Reality in the Quest for Comparability , 1993, Physiological Zoology.

[40]  B. McNab On the Utility of Uniformity in the Definition of Basal Rate of Metabolism , 1997, Physiological Zoology.

[41]  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.

[42]  Mark S. Springer,et al.  Which Mammalian Supertree to Bark Up? , 2001, Science.

[43]  Geoffrey B. West,et al.  The origin of universal scaling laws in biology , 1999 .

[44]  Eric D. Green,et al.  Confirming the Phylogeny of Mammals by Use of Large Comparative Sequence Data Sets , 2008, Molecular biology and evolution.

[45]  Geoffrey B. West,et al.  The predominance of quarter-power scaling in biology , 2004 .

[46]  D. Wingate Comparative physiology of the vertebrate digestive system , 1989 .

[47]  C. R. White,et al.  The Influence of Foraging Mode and Arid Adaptation on the Basal Metabolic Rates of Burrowing Mammals , 2003, Physiological and Biochemical Zoology.

[48]  S. O’Brien,et al.  Placental mammal diversification and the Cretaceous–Tertiary boundary , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[49]  F. T. Jung The Fire of Life , 1962 .

[50]  B. O. Wolf,et al.  The Allometry of Avian Basal Metabolic Rate: Good Predictions Need Good Data , 2004, Physiological and Biochemical Zoology.

[51]  M. Elgar,et al.  Basal Metabolic Rates in Mammals: Allometry, Phylogeny and Ecology , 1987 .

[52]  B. McNab An analysis of the factors that influence the level and scaling of mammalian BMR. , 2008, Comparative biochemistry and physiology. Part A, Molecular & integrative physiology.

[53]  T. Fenchel,et al.  Bioenergetics and Growth , 2022 .

[54]  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.

[55]  C. R. White,et al.  Does Basal Metabolic Rate Contain a Useful Signal? Mammalian BMR Allometry and Correlations with a Selection of Physiological, Ecological, and Life‐History Variables , 2004, Physiological and Biochemical Zoology.

[56]  O. Bininda-Emonds,et al.  The evolution of supertrees. , 2004, Trends in ecology & evolution.

[57]  K. Gaston,et al.  Species‐energy relationships at the macroecological scale: a review of the mechanisms , 2005, Biological reviews of the Cambridge Philosophical Society.

[58]  M. Clauss,et al.  Mammalian metabolic rate scaling to 2/3 or 3/4 depends on the presence of gut contents , 2008 .

[59]  Paul S Agutter,et al.  Metabolic scaling: consensus or controversy? , 2004, Theoretical Biology and Medical Modelling.

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

[61]  J. Speakman,et al.  Associations between energetics and over-winter survival in the short-tailed field vole Microtus agrestis , 2001 .

[62]  Kate E. Jones,et al.  Supertrees are a necessary not-so-evil: a comment on Gatesy et al. , 2003, Systematic biology.

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

[64]  Joseph B. Williams,et al.  Basal Metabolic Rate in Carnivores Is Associated with Diet after Controlling for Phylogeny , 2005, Physiological and Biochemical Zoology.

[65]  Craig R. White,et al.  Allometric scaling of mammalian metabolism , 2005, Journal of Experimental Biology.

[66]  D. S. Hinds,et al.  Scaling of Respiratory Variables and the Breathing Pattern in Birds: An Allometric and Phylogenetic Approach , 2001, Physiological and Biochemical Zoology.

[67]  F. Bozinovic,et al.  Passerines versus nonpasserines: so far, no statistical differences in the scaling of avian energetics. , 2002, The Journal of experimental biology.

[68]  M. Symonds The effects of topological inaccuracy in evolutionary trees on the phylogenetic comparative method of independent contrasts. , 2002, Systematic biology.

[69]  B. McNab The evolution of energetics in eutherian “insectivorans”: an alternate approach , 2006, Acta Theriologica.

[70]  J. Speakman The Cost of Living: Field Metabolic Rates of Small Mammals , 1999 .

[71]  C. R. White,et al.  Sample size and mass range effects on the allometric exponent of basal metabolic rate. , 2005, Comparative biochemistry and physiology. Part A, Molecular & integrative physiology.

[72]  Geoffrey B. West,et al.  Yes, West, Brown and Enquist"s model of allometric scaling is both mathematically correct and biologically relevant , 2005 .

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

[74]  T. Garland,et al.  Procedures for the Analysis of Comparative Data Using Phylogenetically Independent Contrasts , 1992 .

[75]  Kate E. Jones,et al.  The delayed rise of present-day mammals , 1990, Nature.

[76]  T. Garland,et al.  TESTING FOR PHYLOGENETIC SIGNAL IN COMPARATIVE DATA: BEHAVIORAL TRAITS ARE MORE LABILE , 2003, Evolution; international journal of organic evolution.

[77]  Simon Easteal,et al.  Rates of genome evolution and branching order from whole genome analysis. , 2007, Molecular biology and evolution.

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

[79]  D. S. Glazier Effects of metabolic level on the body size scaling of metabolic rate in birds and mammals , 2008, Proceedings of the Royal Society B: Biological Sciences.

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

[81]  E. Martins The Comparative Method in Evolutionary Biology, Paul H. Harvey, Mark D. Pagel. Oxford University Press, Oxford (1991), vii, + 239 Price $24.95 paperback , 1992 .

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

[83]  Gaston H. Gonnet,et al.  A Phylogenomic Study of Human, Dog, and Mouse , 2006, PLoS Comput. Biol..

[84]  José Guilherme Chaui-Berlinck,et al.  Response to `Comment on “A critical understanding of the fractal model of metabolic scaling'” , 2007, Journal of Experimental Biology.

[85]  B. Enquist,et al.  Comment on `A critical understanding of the fractal model of metabolic scaling' , 2007, Journal of Experimental Biology.

[86]  D. S. Glazier,et al.  Beyond the ‘3/4‐power law’: variation in the intra‐and interspecific scaling of metabolic rate in animals , 2005, Biological reviews of the Cambridge Philosophical Society.

[87]  Anthony R. Ives,et al.  An Introduction to Phylogenetically Based Statistical Methods, with a New Method for Confidence Intervals on Ancestral Values , 1999 .

[88]  M. Pagel A method for the analysis of comparative data , 1992 .

[89]  A. Purvis A composite estimate of primate phylogeny. , 1995, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[90]  J. Ackerman,et al.  Exploring Individual Quality: Basal Metabolic Rate and Reproductive Performance in Storm-petrels , 2005 .

[91]  Korbinian Strimmer,et al.  APE: Analyses of Phylogenetics and Evolution in R language , 2004, Bioinform..