A universal scaling relationship between body mass and proximal limb bone dimensions in quadrupedal terrestrial tetrapods

BackgroundBody size is intimately related to the physiology and ecology of an organism. Therefore, accurate and consistent body mass estimates are essential for inferring numerous aspects of paleobiology in extinct taxa, and investigating large-scale evolutionary and ecological patterns in the history of life. Scaling relationships between skeletal measurements and body mass in birds and mammals are commonly used to predict body mass in extinct members of these crown clades, but the applicability of these models for predicting mass in more distantly related stem taxa, such as non-avian dinosaurs and non-mammalian synapsids, has been criticized on biomechanical grounds. Here we test the major criticisms of scaling methods for estimating body mass using an extensive dataset of mammalian and non-avian reptilian species derived from individual skeletons with live weights.ResultsSignificant differences in the limb scaling of mammals and reptiles are noted in comparisons of limb proportions and limb length to body mass. Remarkably, however, the relationship between proximal (stylopodial) limb bone circumference and body mass is highly conserved in extant terrestrial mammals and reptiles, in spite of their disparate limb postures, gaits, and phylogenetic histories. As a result, we are able to conclusively reject the main criticisms of scaling methods that question the applicability of a universal scaling equation for estimating body mass in distantly related taxa.ConclusionsThe conserved nature of the relationship between stylopodial circumference and body mass suggests that the minimum diaphyseal circumference of the major weight-bearing bones is only weakly influenced by the varied forces exerted on the limbs (that is, compression or torsion) and most strongly related to the mass of the animal. Our results, therefore, provide a much-needed, robust, phylogenetically corrected framework for accurate and consistent estimation of body mass in extinct terrestrial quadrupeds, which is important for a wide range of paleobiological studies (including growth rates, metabolism, and energetics) and meta-analyses of body size evolution.

[1]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[2]  F. Jenkins Limb posture and locomotion in the Virginia opossum (Didelphis marsupialis) and in other non‐cursorial mammals , 2009 .

[3]  M. Benton,et al.  Body size evolution in Mesozoic birds , 2008, Journal of evolutionary biology.

[4]  S. Finnegan,et al.  Body size, energetics, and the Ordovician restructuring of marine ecosystems , 2008, Paleobiology.

[5]  M. Westoby,et al.  Bivariate line‐fitting methods for allometry , 2006, Biological reviews of the Cambridge Philosophical Society.

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

[7]  Olaf Hellwich,et al.  A new body mass estimation ofBrachiosaurus brancaiJanensch, 1914 mounted and exhibited at the Museum of Natural History (Berlin, Germany) , 2008 .

[8]  R. Blob Interspecific scaling of the hindlimb skeleton in lizards, crocodilians, felids and canids: does limb bone shape correlate with limb posture? , 2000 .

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

[10]  Sara Taskinen,et al.  smatr 3– an R package for estimation and inference about allometric lines , 2012 .

[11]  G. Cawley,et al.  On allometric equations for predicting body mass of dinosaurs , 2010 .

[12]  B. MacFadden,et al.  Body size in mammalian paleobiology : estimation and biological implications , 2005 .

[13]  E. H. Colbert The Weights of Dinosaurs , 2004 .

[14]  Y. Kumazawa,et al.  Mitochondrial DNA sequences of the Afro-Arabian spiny-tailed lizards (genus Uromastyx; family Agamidae) : phylogenetic analyses and evolution of gene arrangements , 2005 .

[15]  J. Hopson Relative Brain Size and Behavior in Archosaurian Reptiles , 1977 .

[16]  The weights of dinosaurs. American Museum novitates ; no. 2076 , 1962 .

[17]  M. Carrano,et al.  Scaling of reproductive turnover in archosaurs and mammals : why are large terrestrial mammals so rare? , 1991 .

[18]  Harry J. Jerison,et al.  Brain Evolution and Dinosaur Brains , 1969, The American Naturalist.

[19]  M. Norell,et al.  Avian Paternal Care Had Dinosaur Origin , 2008, Science.

[20]  C. McClain,et al.  Biodiversity and body size are linked across metazoans , 2009, Proceedings of the Royal Society B: Biological Sciences.

[21]  H. Gunga,et al.  Body mass estimations for Plateosaurus engelhardti using laser scanning and 3D reconstruction methods , 2007, Naturwissenschaften.

[22]  J. Fröbisch Locomotion in derived dicynodonts (Synapsida, Anomodontia): a functional analysis of the pelvic girdle and hind limb of Tetragonias njalilus , 2006 .

[23]  R. J. Smith Allometric scaling in comparative biology: problems of concept and method. , 1984, The American journal of physiology.

[24]  G. C. Packard,et al.  Allometric equations for predicting body mass of dinosaurs , 2009 .

[25]  A. Purvis,et al.  Macroevolutionary trends in the Dinosauria: Cope's rule , 2005, Journal of evolutionary biology.

[26]  A. Biewener,et al.  In vivo locomotor strain in the hindlimb bones of alligator mississippiensis and iguana iguana: implications for the evolution of limb bone safety factor and non-sprawling limb posture , 1999, The Journal of experimental biology.

[27]  R. Bakker,et al.  Anatomical and Ecological Evidence of Endothermy in Dinosaurs , 1972, Nature.

[28]  Taane G. Clark,et al.  Lack of Association of Interferon Regulatory Factor 1 with Severe Malaria in Affected Child-Parental Trio Studies across Three African Populations , 2009, PloS one.

[29]  K. Gaston,et al.  Range size-body size relationships: evidence of scale dependence , 1996 .

[30]  Jerrold H. Zar,et al.  Calculation and Miscalculation of the Allometric Equation as a Model in Biological Data , 1968 .

[31]  M. Carrano What, if anything, is a cursor? Categories versus continua for determining locomotor habit in mammals and dinosaurs , 1999 .

[32]  William I. Sellers,et al.  Estimating Mass Properties of Dinosaurs Using Laser Imaging and 3D Computer Modelling , 2009, PloS one.

[33]  J. Ast Mitochondrial DNA Evidence and Evolution in Varanoidea (Squamata) , 2001, Cladistics : the international journal of the Willi Hennig Society.

[34]  A. Biewener,et al.  Mechanics of limb bone loading during terrestrial locomotion in the green iguana (Iguana iguana) and American alligator (Alligator mississippiensis). , 2001, The Journal of experimental biology.

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

[36]  C. Raxworthy,et al.  A molecular phylogeny of tortoises (Testudines: Testudinidae) based on mitochondrial and nuclear genes. , 2006, Molecular phylogenetics and evolution.

[37]  H. Shaffer,et al.  Multiple data sets, high homoplasy, and the phylogeny of softshell turtles (Testudines: Trionychidae). , 2004, Systematic biology.

[38]  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.

[39]  S. Gould,et al.  Evolution of the brain and intelligence. , 1974, Science.

[40]  Kristian Remes,et al.  Biology of the Sauropod Dinosaurs: Understanding the Life of Giants , 2011 .

[41]  T. F. Hansen,et al.  Interpreting the evolutionary regression: the interplay between observational and biological errors in phylogenetic comparative studies. , 2012, Systematic biology.

[42]  D. Henderson BURLY GAITS: CENTERS OF MASS, STABILITY, AND THE TRACKWAYS OF SAUROPOD DINOSAURS , 2006 .

[43]  R. M. Alexander,et al.  Dynamics of dinosaurs and other extinct giants , 1989 .

[44]  D Curran-Everett,et al.  Multiple comparisons: philosophies and illustrations. , 2000, American journal of physiology. Regulatory, integrative and comparative physiology.

[45]  J. J. Flynn,et al.  Ancestral state reconstruction of body size in the Caniformia (Carnivora, Mammalia): the effects of incorporating data from the fossil record. , 2006, Systematic biology.

[46]  A. Casinos,et al.  Allometry of the limb long bones of insectivores and rodents , 1987, Journal of morphology.

[47]  M. Carrano The Evolution of Sauropod Locomotion: Morphological Diversity of a Secondarily Quadrupedal Radiation , 2005 .

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

[49]  Michael J. Benton,et al.  The phylogeny and classification of tetrapods , 1986 .

[50]  R. Butler,et al.  Body size evolution in Mesozoic birds: little evidence for Cope’s rule , 2008, Journal of evolutionary biology.

[51]  M. Taper,et al.  Evolution of Body Size: Consequences of an Energetic Definition of Fitness , 1993, The American Naturalist.

[52]  M. Butcher,et al.  In vivo strains in the femur of river cooter turtles (Pseudemys concinna) during terrestrial locomotion: tests of force-platform models of loading mechanics , 2008, Journal of Experimental Biology.

[53]  F. H. Pough,et al.  Metabolism of Squamate Reptiles: Allometric and Ecological Relationships , 1985, Physiological Zoology.

[54]  R. McN. Alexander,et al.  Allometry of the limb bones of mammals from shrews (Sorex) to elephant (Loxodonta) , 2009 .

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

[56]  J. Finarelli Hierarchy and the reconstruction of evolutionary trends: evidence for constraints on the evolution of body size in terrestrial caniform carnivorans (Mammalia) , 2008, Paleobiology.

[57]  A. Farke,et al.  Femoral Strength and Posture in Terrestrial Birds and Non‐Avian Theropods , 2009, Anatomical record.

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

[59]  P. Christiansen,et al.  Mass Prediction in Theropod Dinosaurs , 2004 .

[60]  John R. Hutchinson,et al.  The evolution of locomotion in archosaurs , 2006 .

[61]  P. Marquet,et al.  Scaling and power-laws in ecological systems , 2005, Journal of Experimental Biology.

[62]  F. Seebacher,et al.  A NEW METHOD TO CALCULATE ALLOMETRIC LENGTH-MASS RELATIONSHIPS OF DINOSAURS , 2001 .

[63]  P. Christiansen Long bone scaling and limb posture in non-avian theropods: Evidence for differential allometry , 1999 .

[64]  D. Henderson,et al.  MY THEROPOD IS BIGGER THAN YOURS … OR NOT: ESTIMATING BODY SIZE FROM SKULL LENGTH IN THEROPODS , 2007 .

[65]  J. Damuth,et al.  Population density and body size in mammals , 1981, Nature.

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

[67]  A. Hall-Martin,et al.  Long‐bone circumference and weight in mammals, birds and dinosaurs , 2009 .

[68]  Yasuhisa Okajima,et al.  articleMitochondrial genomes of acrodont lizards : timing of gene rearrangements and phylogenetic and biogeographic implications , 2010 .

[69]  D. M. Power Biometry. The Principles and Practice of Statistics in Biological Research; Statistical Tables , 1970 .

[70]  A. Woodward,et al.  Maximum Size of the Alligator (Alligator mississippiensis) , 1995 .

[71]  R. Blob Evolution of hindlimb posture in nonmammalian therapsids: biomechanical tests of paleontological hypotheses , 2001, Paleobiology.

[72]  Yasuhisa Okajima,et al.  Mitogenomic perspectives into iguanid phylogeny and biogeography: Gondwanan vicariance for the origin of Madagascan oplurines. , 2009, Gene.

[73]  E. Louis,et al.  Molecular phylogenetics of squamata: the position of snakes, amphisbaenians, and dibamids, and the root of the squamate tree. , 2004, Systematic biology.

[74]  G. Erickson Assessing dinosaur growth patterns: a microscopic revolution. , 2005, Trends in ecology & evolution.

[75]  M. Carrano Body-size evolution in the Dinosauria , 2006 .

[76]  P. M. Sander,et al.  Long and Girdle Bone Histology of Stegosaurus: Implications for Growth and Life History , 2009 .

[77]  M. Köhler,et al.  New equations for body mass estimation in bovids: Testing some procedures when constructing regression functions , 2011 .

[78]  Kate E. Jones,et al.  The delayed rise of present-day mammals (vol 446, pg 507, 2007) , 2008 .

[79]  G. Amato,et al.  Evolutionary relationships of marine turtles: A molecular phylogeny based on nuclear and mitochondrial genes. , 2008, Molecular phylogenetics and evolution.

[80]  Jeffrey A. Wilson,et al.  The Sauropods: Evolution and Paleobiology , 2005 .

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

[82]  H. J. Jerison,et al.  Evolution of the Brain and Intelligence , 1973 .

[83]  J. Bertram,et al.  Differential scaling of the long bones in the terrestrial carnivora and other mammals , 1990, Journal of morphology.

[84]  S. Yerby,et al.  Dinosaurian growth patterns and rapid avian growth rates , 2001, Nature.

[85]  L E Lanyon,et al.  Dynamic strain similarity in vertebrates; an alternative to allometric limb bone scaling. , 1984, Journal of theoretical biology.

[86]  D. Henderson,et al.  Estimating the masses and centers of mass of extinct animals by 3-D mathematical slicing , 1999, Paleobiology.

[87]  Jan Paul Medema,et al.  Betulin Is a Potent Anti-Tumor Agent that Is Enhanced by Cholesterol , 2009, PloS one.

[88]  John M. Harris,et al.  Body size of Smilodon (Mammalia: Felidae) , 2005, Journal of morphology.

[89]  J. Hutchinson,et al.  Biomechanics of Running Indicates Endothermy in Bipedal Dinosaurs , 2009, PloS one.

[90]  K. Kirsch,et al.  Body size and body volume distribution in two sauropods from the Upper Jurassic of Tendaguru (Tanzania) , 1999 .

[91]  P. Christiansen Scaling of mammalian long bones: small and large mammals compared , 1999 .

[92]  M. Carrano,et al.  Implications of limb bone scaling, curvature and eccentricity in mammals and non‐avian dinosaurs , 2001 .

[93]  M. Mendoza,et al.  Body mass estimation in xenarthra: A predictive equation suitable for all quadrupedal terrestrial placentals? , 2008, Journal of morphology.

[94]  J. Borkowski,et al.  Nest and egg clutches of the dinosaur Troodon formosus and the evolution of avian reproductive traits , 1997, Nature.

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

[96]  Gregory M. Erickson,et al.  A Basal Dromaeosaurid and Size Evolution Preceding Avian Flight , 2007, Science.

[97]  P. Gingerich Prediction of Body Mass in Mammalian Species from Long Bone Lengths and Diameters , 1990 .

[98]  Brent H. Breithaupt,et al.  Dynamics of Dinosaurs and Other Extinct Giants, R. McNeill Alexander, R. McNeill Alexander. Columbia University Press, New York (1989), 167, Price $30.00 , 1990 .

[99]  M. Kleiber Body size and metabolic rate. , 1947, Physiological reviews.

[100]  R. Benson,et al.  Air‐filled postcranial bones in theropod dinosaurs: physiological implications and the ‘reptile’–bird transition , 2012, Biological reviews of the Cambridge Philosophical Society.

[101]  A. Biewener Allometry of quadrupedal locomotion: the scaling of duty factor, bone curvature and limb orientation to body size. , 1983, The Journal of experimental biology.

[102]  G. Paul DINOSAUR MODELS : THE GOOD , THE BAD , AND USING THEM TO ESTIMATE THE MASS OF DINOSAURS , 2022 .

[103]  R. Motani Estimating body mass from silhouettes: testing the assumption of elliptical body cross-sections , 2001, Paleobiology.

[104]  P. Makovicky AMNIOTE PALEOBIOLOGY: PERSPECTIVES ON THE EVOLUTION OF MAMMALS, BIRDS, AND REPTILES , 2007, Copeia.

[105]  A. Casinos Bipedalism and quadrupedalism in Megatheriurn: an attempt at biomechanical reconstruction , 1996 .

[106]  D. Henderson Pterosaur Body Mass Estimates from Three-Dimensional Mathematical Slicing , 2010 .

[107]  R. Zardoya,et al.  Effect of taxon sampling on recovering the phylogeny of squamate reptiles based on complete mitochondrial genome and nuclear gene sequence data. , 2009, Gene.

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

[109]  T. Lehman,et al.  Modeling growth rates for sauropod dinosaurs , 2008, Paleobiology.

[110]  Richard J. Smith Estimation of Body Mass in Paleontology , 2002 .

[111]  H. Shaffer,et al.  Assessing Concordance of Fossil Calibration Points in Molecular Clock Studies: An Example Using Turtles , 2004, The American Naturalist.

[112]  Grant R. Hurlburt Comparison of body mass estimation techniques, using Recent reptiles and the pelycosaur Edaphosaurus boanerges , 1999 .

[113]  J. Wiens,et al.  WHY DOES A TRAIT EVOLVE MULTIPLE TIMES WITHIN A CLADE? REPEATED EVOLUTION OF SNAKELIKE BODY FORM IN SQUAMATE REPTILES , 2006, Evolution; international journal of organic evolution.

[114]  A. Janke,et al.  Extended mitogenomic phylogenetic analyses yield new insight into crocodylian evolution and their survival of the Cretaceous-Tertiary boundary. , 2007, Molecular phylogenetics and evolution.

[115]  E. Charnov,et al.  Dinosaur Fossils Predict Body Temperatures , 2006, PLoS biology.

[116]  M. Carrano,et al.  Locomotion in non-avian dinosaurs: integrating data from hindlimb kinematics, in vivo strains, and bone morphology , 1998, Paleobiology.

[117]  M. Wedel Vertebral pneumaticity, air sacs, and the physiology of sauropod dinosaurs , 2003, Paleobiology.

[118]  J. Diamond,et al.  Dinosaurs, dragons, and dwarfs: The evolution of maximal body size , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[119]  A. C. Economos Elastic and/or geometric similarity in mammalian design? , 1983, Journal of theoretical biology.

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

[121]  W. Jetz,et al.  Biogeography of body size in Pacific island birds , 2010 .

[122]  S. Hedges,et al.  The phylogeny of squamate reptiles (lizards, snakes, and amphisbaenians) inferred from nine nuclear protein-coding genes. , 2005, Comptes rendus biologies.

[123]  M. Young,et al.  Body size estimation and evolution in metriorhynchid crocodylomorphs: Implications for species diversification and niche partitioning , 2011 .

[124]  M. Fortelius,et al.  The largest land mammal ever imagined , 1993 .

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

[126]  H. Shaffer,et al.  Conflicting mitochondrial and nuclear phylogenies for the widely disjunct Emys (Testudines: Emydidae) species complex, and what they tell us about biogeography and hybridization. , 2009, Systematic biology.

[127]  James O. Farlow,et al.  A Consideration of the Trophic Dynamics of a Late Cretaceous Large-Dinosaur Community (Oldman Formation) , 1976 .

[128]  J. Rayner,et al.  Flight characteristics of Triassic and Jurassic Pterosauria: an appraisal based on wing shape , 1992, Paleobiology.

[129]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[130]  R. Rustad,et al.  Movements of echinochrome granules during the early development of sea urchin eggs. , 1972, Nature: New biology.

[131]  T. McMahon Using body size to understand the structural design of animals: quadrupedal locomotion. , 1975, Journal of applied physiology.

[132]  D. Henderson Tipsy punters: sauropod dinosaur pneumaticity, buoyancy and aquatic habits , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[133]  Alexander K. Hastings,et al.  Giant boid snake from the Palaeocene neotropics reveals hotter past equatorial temperatures , 2009, Nature.

[134]  Kate E. Jones,et al.  PanTHERIA: a species‐level database of life history, ecology, and geography of extant and recently extinct mammals , 2009 .

[135]  M. Laurin The evolution of body size, Cope's rule and the origin of amniotes. , 2004, Systematic biology.

[136]  John R. Hutchinson,et al.  A Computational Analysis of Limb and Body Dimensions in Tyrannosaurus rex with Implications for Locomotion, Ontogeny, and Growth , 2011, PloS one.

[137]  J. Peczkis Implications of body-mass estimates for dinosaurs , 1995 .

[138]  William I. Sellers,et al.  HOW BIG WAS 'BIG AL'? QUANTIFYING THE EFFECT OF SOFT TISSUE AND OSTEOLOGICAL UNKNOWNS ON MASS PREDICTIONS FOR ALLOSAURUS (DINOSAURIA:THEROPODA) , 2009 .

[139]  L. Lanyon,et al.  Limb mechanics as a function of speed and gait: a study of functional strains in the radius and tibia of horse and dog. , 1982, The Journal of experimental biology.

[140]  Victor Ng-Thow-Hing,et al.  A 3D interactive method for estimating body segmental parameters in animals: application to the turning and running performance of Tyrannosaurus rex. , 2007, Journal of theoretical biology.

[141]  L. M. Gosling,et al.  Habitat primary production and the evolution of body size within the hartebeest clade , 2007 .

[142]  H. Gunga,et al.  Allometry of visceral organs in living amniotes and its implications for sauropod dinosaurs , 2009, Proceedings of the Royal Society B: Biological Sciences.

[143]  D. Lloyd,et al.  Evolution of limb bone loading and body size in varanid lizards , 2011, Journal of Experimental Biology.

[144]  A. Biewener Scaling body support in mammals: limb posture and muscle mechanics. , 1989, Science.

[145]  P Christiansen,et al.  Scaling of the limb long bones to body mass in terrestrial mammals , 1999, Journal of morphology.

[146]  Helene C. Bovy,et al.  When teeth and bones disagree: body mass estimation of a giant extinct rodent , 2010 .

[147]  Jafferson K. L. da Silva,et al.  Interspecific allometry of bone dimensions: A review of the theoretical models , 2006 .