© 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.     The file attached is the published version of the article

Charlotte A. Brassey

Kilbourne BM

Mallison H

Mazzetta G

Paul M. Barrett

Susannah C. R. Maidment

Biology Letters

English

PubMed

Brassey, Charlotte

Maidment, Susannah

Barrett, Paul

University of Brighton Research Portal

 on May 6, 2015http://rsbl.royalsocietypublishing.org/Downloaded from rsbl.royalsocietypublishing.orgResearchCite this article: Brassey CA, Maidment SCR,Barrett PM. 2015 Body mass estimates of anexceptionally complete Stegosaurus(Ornithischia: Thyreophora): comparingvolumetric and linear bivariate mass estimationmethods. Biol. Lett. 11: 20140984.http://dx.doi.org/10.1098/rsbl.2014.0984Received: 21 November 2014Accepted: 10 February 2015Subject Areas:palaeontology, biomechanicsKeywords:Stegosaurus, body mass, scaling equations,volumetric model, photogrammetryAuthor for correspondence:Charlotte A. Brasseye-mail: c.brassey@nhm.ac.ukElectronic supplementary material is availableat http://dx.doi.org/10.1098/rsbl.2014.0984 orvia http://rsbl.royalsocietypublishing.org.& 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons AttributionLicense http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the originalauthor and source are credited.PalaeontologyBody mass estimates of an exceptionallycomplete Stegosaurus (Ornithischia:Thyreophora): comparing volumetric andlinear bivariate mass estimation methodsCharlotte A. Brassey1, Susannah C. R. Maidment2 and Paul M. Barrett11Department of Earth Sciences, The Natural History Museum, Cromwell Road, London SW7 5DB, UK2Department of Earth Science and Engineering, Imperial College, South Kensington Campus,London SW7 2AZ, UKBody mass is a key biological variable, but difficult to assess from fossils.Various techniques exist for estimating body mass from skeletal parameters,but few studies have compared outputs from different methods. Here, weapply several mass estimation methods to an exceptionally complete skel-eton of the dinosaur Stegosaurus. Applying a volumetric convex-hullingtechnique to a digital model of Stegosaurus, we estimate a mass of 1560 kg(95% prediction interval 1082–2256 kg) for this individual. By contrast,bivariate equations based on limb dimensions predict values between 2355and 3751 kg and require implausible amounts of soft tissue and/or highbody densities. When corrected for ontogenetic scaling, however, volumetricand linear equations are brought into close agreement. Our results raise con-cerns regarding the application of predictive equations to extinct taxa withno living analogues in terms of overall morphology and highlight the sensi-tivity of bivariate predictive equations to the ontogenetic status of thespecimen. We emphasize the significance of rare, complete fossil skeletonsin validating widely applied mass estimation equations based on incompleteskeletal material and stress the importance of accurately determiningspecimen age prior to further analyses.1. IntroductionIn extant taxa, body mass is an indicator of fundamental ecological and physi-ological traits such as population density, metabolism and cost-of-transport [1].Key evolutionary transitions in deep time, such as the origin of avian flight [2]and the adaptive radiation of mammals around the Cretaceous-Paleogeneboundary [3], have been interpreted in the context of body size: thus bodymass reconstruction in extinct species is of considerable interest.Ideally, mass estimates for extinct taxa would be based upon completespecimens, but such material is rare. Consequently, many mass estimation tech-niques for fossil taxa rely upon measurements taken from commonly preservedskeletal elements. Recently, the sum of femoral and humeral circumferenceswas shown to correlate strongly with mass in extant taxa [4]. However, theapplicability of this equation to fossil groups with unusual morphological fea-tures, overly robust/gracile limb elements or lying outside of the size range ofextant taxa, remains to be tested. Additionally, application of bivariate predic-tive equations to specimens of uncertain ontogenetic status is potentiallyproblematic given evidence of allometric scaling of limb dimensions with ageamong dinosaur taxa [5].(a) (b)(c) (d )(g)(e) ( f )Figure 1. Reconstructions of Stegosaurus stenops (NHMUK R36730) and associated convex hulls. (a,b) Cvol(min); (c,d) Cvol( pref ); (e,f ) Cvol(max); (g) Cvol(C&E). (Onlineversion in colour.)rsbl.royalsocietypublishing.orgBiol.Lett.11:201409842 on May 6, 2015http://rsbl.royalsocietypublishing.org/Downloaded from When specimens are complete, volumetric methods of massestimation can be used [6,7]. Such methods incorporate all of theavailable data from the specimen and are not biased by theproblem of unexpectedly robust/gracile elements, nor do theyrely on regressions that are extrapolated beyond empiricallybased body mass data. Nevertheless, the reconstruction processinvolves a degree of subjectivity and sensitivity analyses areessential to quantify the effects of anatomical uncertainties [6].Convex hulling [7] circumvents this problem by fitting ‘shrink-wrap’ convex polytopes around the three-dimensional skeletonand deriving a mass estimate based on the relationship betweenconvex hull volume (Cvol) and body mass in modern species.Using a three-dimensional computer model of an excep-tionally complete Stegosaurus specimen, we compare massestimation techniques based on volumetric and traditionalbivariate regressions to test if estimates generated from limbbone dimensions alone are biologically plausible for taxawith morphologies lacking close modern analogues or forspecimens that have not attained full adult size.2. Material and methodsThe specimen is a Stegosaurus stenops (NHMUK (Natural HistoryMuseum, London) R36730) from the Upper Jurassic MorrisonFormation near Shell, Wyoming. It is substantially complete, withall body regions represented except the left forelimb and part ofthe tail. NHMUK R36730 is classified as a ‘young adult’ based onhistological sampling [8,9] (electronic supplementary material, S1).The specimen was digitized as disarticulated bones using photo-grammetry [10] and the freely available software ‘VisualSFM’(http://ccwu.me/vsfm) and ‘Meshlab’ (http://meshlab.source-forge.net) (electronic supplementary material, S2).The skeleton was posed in 3DsMax (www.autodesk.com/3dsmax) and a convex hull model produced (Cvol(pref)) represent-ing our preferred articulation of the elements based oncomparative dinosaur anatomy and information from the extantphylogenetic bracket (crocodilians/birds). A sensitivity analysisquantified the effect of rearticulation on Cvol. Intervertebralspacing, rib flaring and scapula position were altered to define aminimum (Cvol(min)) and maximum (Cvol(max)) volume pose forthe skeleton (electronic supplementary material, S3). Modelswere subdivided into functional units: head, neck, trunk(sacrum and thorax), tail, upper arm, forearm, hand, thigh,shank and foot. The cervical series was subdivided to ensure atight fit of the hulls around the neck. Convex hulls were fittedto functional units using the ‘convhulln’ function in MATLAB(www.mathworks.com) implementing the ‘qhull’ algorithm [11].Total Cvol was calculated as the sum of segment values, andbody mass estimated using the relationship between Cvol andbody mass published elsewhere [7,12] (electronic supplementarymaterial, S4). By directly converting Cvol into a mass estimate, a0Cvol(min)Cvol(pref)Cvol(max)Cvol(C&E)CE2012bCE2012mAn1985M2004EYPM1856EYPM18532000estimated mass (kg)400060008000rsbl.royalsocietypublishing.orgBiol.Lett.11:201409843 on May 6, 2015http://rsbl.royalsocietypublishing.org/Downloaded from body density value is not explicitly assigned. However, there is anassumption that the density of the fossil species falls within therange of those species from which the predictive equation isderived, in this case modern quadrupedal mammals.We expanded our ‘maximum’ convex hull model (Cvol(max)) tomatch the body mass value predicted when applying a recentlypublished scaling equation (Cvol(C&E)) [4]. Dermal armour masswas determined separately and added to each volumetric massestimate (electronic supplementary material, table S1). Mass esti-mates based on femoral and/or humeral circumference werecalculated using the MASSTIMATE package in R [13] and raw dataavailable from previous studies [14,15] (electronic supplementarymaterial, S4). The potential effect of ontogenetic scaling was inves-tigated using Developmental Mass Extrapolation (DME), wherebythe mass of a ‘known’ adult individual (in this case StegosaurusYPM (Peabody Museum of Natural History, Yale University)1853 and YPM 1856) is estimated using the bivariate equation inquestion, and subsequently scaled isometrically on the basis offemoral length to the subadult individual [16] (electronicsupplementary material, S5).Table 1. Volume data (m3) for convex hull reconstructions of Stegosaurusstenops (NHMUK R36730).body segment Cvol( pref ) Cvol(min) Cvol(max) Cvol(C&E)head 0.0056 0.0056 0.0056 0.0119neck 0.0177 0.0152 0.0199 0.0425trunk 1.0786 0.8724 1.3686 2.9174left upper arm 0.0098 0.0098 0.0098 0.0208left forearm 0.0046 0.0046 0.0046 0.0099left hand 0.0021 0.0021 0.0021 0.0046left thigh 0.0159 0.0159 0.0159 0.0339left shank 0.0084 0.0084 0.0084 0.0178left foot 0.0018 0.0018 0.0018 0.0038right upper arm 0.0084 0.0084 0.0084 0.0180right forearm 0.0042 0.0042 0.0042 0.0091right hand 0.0020 0.0020 0.0020 0.0043right thigh 0.0166 0.0166 0.0166 0.0354right shank 0.0091 0.0091 0.0091 0.0194right foot 0.0014 0.0014 0.0014 0.0031DMDMFigure 2. Volumetric mass estimates for NHMUK R36730 calculated herecompared with those derived from proximal limb circumference. For abbrevi-ations, see table 2. (Online version in colour.)3. ResultsThe convex hull reconstruction of our preferred model(Cvol(pref )) provides a mass estimate of 1560 kg (95% predic-tion interval (PI) 1082–2256 kg), including 34 kg of dermalarmour (electronic supplementary material, table S1).Values for Cvol(min) of 1311 kg (95% PI ¼ 916–1884 kg) andCvol(max) of 1894 kg (95% PI ¼ 1303–2760 kg) derived fromthe rearticulation sensitivity analysis provide upper andlower bounds to our convex hull mass estimate (figure 1and table 1). Prior to accounting for ontogeny, mass estimatesbased on proximal limb bone circumferences [5] were consist-ently higher than those based on convex hulls (figure 2),ranging between 2355 and 3751 kg (table 2). The predictionintervals of Cvol(pref ) do not overlap those of either of the pre-dictive equations of Campione & Evans (C&E) [4] (figure 2).To achieve the 3752 kg estimate derived from the C&E bivari-ate equation [4], the convex hulls fitted to the Cvol(max) modelrequired considerable rescaling, resulting in a total convexhull volume of 3.378 m3 for the Cvol(C&E) model and an esti-mated body mass of 3745 kg (figure 1g and table 1).However, accounting for possible ontogenetic scalingbrought volumetric and linear bivariate predictions intoclose agreement. Based on DME using adult Stegosaurusspecimens (YPM1853, 1856) as endpoints, predicted massesfor NHMUK R36730 using the C&E bivariate equations [4]were 1823 kg and 2158 kg, respectively, and fall within theconfidence intervals of our volumetric models.tail 0.0936 0.0781 0.1061 0.2262total 1.2800 1.0558 1.5848 3.37814. DiscussionThis is the first study to apply both volumetric and linearbivariate mass estimation techniques to the same Stegosaurusindividual. Prior to accounting for ontogenetic scaling, volu-metric mass estimates for Stegosaurus were considerablylower than those predicted on the basis of limb bone dimen-sions. The Cvol(min), Cvol(pref ) and Cvol(max) model predictionsare 35, 42 and 50%, respectively, of the 3752 kg estimatedby the C&E bivariate predictive equation [4], which wasbased on adult individuals. Previous studies on other stego-saur specimens also found that volumetric mass estimateswere consistently lower than those based on limb bonescaling (electronic supplementary material, tables S2 and S3).The Cvol(C&E) model created to reconstruct the bodydimensions required to meet the original 3752 kg mass esti-mation of Campione & Evans [4] represents a 165%increase in volume from the Cvol(pref ) model. Outwardly,the convex hull volumes appear extremely large (figure 1g)and, given the excessive soft tissue volume that would needto be placed outside the skeleton in order to reach a bodymass of more than 3700 kg, we consider that the CETable 2. Mass estimates (kg) for Stegosaurus stenops (NHMUK R36730)based on proximal limb circumference. ‘An1985’ and ‘M2004’ equationshave been modified from those originally published (electronicsupplementary material, S4). CE2012b and CE2012m refer to bivariate andmultivariate equations in [4].equation mean lower 95% PI upper 95% PICE2012b [4] 3752 2790 4713CE2012m [4] 3329 2499 4159An1985 [15] 3632 2089 6316M2004 [16] 2355 971 5717DMEYPM1853 [4] 1823 1356 2290DMEYPM1856 [4] 2158 1605 2712rsbl.royalsocietypublishing.orgBiol.Lett.11:201409844 on May 6, 2015http://rsbl.royalsocietypublishing.org/Downloaded from predictive equation [5] overestimates body mass in Stego-saurus when applied in this manner (i.e. without correctionfor the ontogenetic stage of the specimen).The convex hull mass estimates for NHMUK R36730 arelower than those calculated for other Stegosaurus specimens(e.g. USNM (United States National Museum of NaturalHistory, Washington, DC, USA) 4934) using alternativevolumetric techniques (electronic supplementary material,table S1). NHMUK R36730 was not osteologically mature attime of death and is smaller than USNM 4934 (electronic sup-plementary material, table S4). It is therefore expected thatthe convex hull estimates calculated here should be lowerthan previous volumetric reconstructions. This differencehighlights the importance of generating specimen-specificmass values prior to subsequent biomechanical analysesrather than applying species-means.Although a ‘young adult’ [8,9], NHMUK R36730 was stillgrowing at the time of death (electronic supplementarymaterial, S1). When DME was applied to the specimenusing ‘known’ adult Stegosaurus as a baseline (electronic sup-plementary material, S5), the two mass estimation techniquesconverged significantly. Importantly, correction for ontogen-etic stage resulted in the original mass estimates derivedusing the CE equations [4] falling within the confidenceintervals of all volumetric estimates (figure 2 and table 2).Much of the discrepancy between the two techniques may,therefore, be attributed to the age of the specimen.Discrepancies between volumetric and linear mass esti-mates have been noted for other dinosaurs [7], and ourresults suggest that ontogeny is a potential explanation. Byconsidering NHMUK R36730 as subadult rather than adult,previous mass estimates [4] more than halve (from 3752 to1823 kg; table 2). This highlights the sensitivity of linear bivari-ate equations to ontogenetic status and urges caution ininstances when the age of the specimen is unclear (e.g. inthe absence of histological information or for fragmentarymaterial). While important palaeoecological studies of broadtaxonomic scope must necessarily include as large a samplesize as possible, our results suggest that authors should restrictthemselves to sampling the largest individual of a given taxonin order to minimize this effect [17].In summary, our volumetric mass estimates of Stegosaurusfall outside the prediction intervals of commonly used massprediction equations based on proximal limb dimensions, apattern seen in other dinosaurs [7]. Ontogenetic scaling is apossible explanation for this discrepancy. Rare finds ofexceptionally complete specimens should play a crucial rolein validating widely applied mass estimations based onincomplete skeletal material. It is possible that important size-related shifts in palaeoecology or physiology in fossil taxa arebeing misinterpreted owing to the inappropriate applicationof mass prediction equations. Our results urge caution whenestimating the mass of extinct species, particularly when theontogenetic status of the specimen is difficult to determine.Data accessibility. Convex hull models are downloadable from Dryad(doi:10.5061/dryad.2307m).Acknowledgements. We are grateful to Jeremy Herrmann and the otherdonors who made the purchase of this exceptional specimen possible.We thank D. Evans for discussion and two anonymous reviewers forcomments.Author contributions. C.A.B. collected and analysed the data, and wrotethe manuscript. S.C.R.M. and P.M.B. assisted with data analysisand helped draft the manuscript.Conflict of interest. The authors declare that they have no competinginterests.References1. Schmidt-Nielsen K. 1984 Scaling: why is animal sizeso important? Cambridge, UK: Cambridge UniversityPress.2. Turner AH, Pol D, Clarke JA, Erickson GM, Norell MA.2007 A basal dromaeosaurid and size evolutionpreceding avian flight. Science 317, 1378 – 1381.(doi:10.1126/science.1144066)3. Wilson GP, Evans AR, Corfe IJ, Smits PD, Fortelius M,Jernvall J. 2012 Adaptive radiation ofmultituberculate mammals before the extinction ofdinosaurs. Nature 483, 457 – 460. (doi:10.1038/nature10880)4. Campione NE, Evans DC. 2012 A universal scalingrelationship between body mass and proximal limbbone dimensions in quadrupedal terrestrialtetrapods. BMC Biol. 10, 60. (doi:10.1186/1741-7007-10-60)5. Kilbourne BM, Makovicky PJ. 2010 Limb boneallometry during postnatal ontogeny in non-aviandinosaurs. J. Anat. 217, 135 – 152. (doi:10.1111/j.1469-7580.2010.01253.x)6. Bates KT, Manning PL, Hodgetts D, Sellers WI. 2009Estimating mass properties of dinosaurs using laserimaging and 3D computer modelling. PLoS ONE 4,e4532. (doi:10.1371/journal.pone.0004532)7. Sellers WI, Hepworth-Bell J, Falkingham PL, BatesKT, Brassey CA, Egerton VM, Manning PL. 2012Minimum convex hull mass estimations of completemounted skeletons. Biol. Lett. 8, 842 – 845. (doi:10.1098/rsbl.2012.0263)8. Redelstorff R, Sander PM. 2009 Long and girdlebone histology of Stegosaurus: implications forgrowth and life history. J. Vertebr. Paleontol. 29,1087 – 1099. (doi:10.1671/039.029.0420)9. Hayashi S, Carpenter K, Suzuki D. 2009 Differentgrowth patterns between the skeleton andosteoderms of Stegosaurus (Ornithischia:Thyreophora). J. Vertebr. Paleontol. 29, 123 – 131.(doi:10.1080/02724634.2009.10010366)10. Mallison H, Wings O. 2014 Photogrammetry inpaleontology—a practical guide. J. Paleontol. Tech.12, 1 – 31. (http://www.jpaleontologicaltechniques.org/pasta3/JPT%20N12/Bulletin.html)11. Barber CB, Dobkin DP, Huhdanpaa HT. 1996 TheQuickhull algorithm for convex hulls. ACM Trans. Math.Softw. 22, 469 – 483. (doi:10.1145/235815.235821)12. Brassey C, Sellers WI. 2014 Scaling of convexhull volume to body mass in modernprimates, non-primate mammals and birds.PLoS ONE 9, e91691. (doi:10.1371/journal.pone.0091691)rsbl.royalsocietypublishing5 on May 6, 2015http://rsbl.royalsocietypublishing.org/Downloaded from 13. Campione NE, Evans DC, Brown CM, Carrano MT.2014 Body mass estimation in non-avian bipedsusing a theoretical conversion to quadrupedstylopodial proportions. Methods Ecol. Evol. 5,913 – 923. (doi:10.1111/2041-210X.12226)14. Anderson JF, Hall-Martin A, Russell DA. 1985 Long-bone circumference and weight in mammals, birdsand dinosaurs. J. Zool. 207, 53 – 61. (doi:10.1111/j.1469-7998.1985.tb04915.x)15. Mazzetta G, Christiansen P, Farina R. 2004Giants and bizarres: body size of somesouthern south American Cretaceous dinosaurs.Hist. Biol. 1 – 13. (doi:10.1080/08912960410001715132)16. Erickson GM, Tumanova TA. 2000 Growthcurve of Psittacosaurus mongoliensis Osborn(Ceratopsia: Psittacosauridae) inferred fromlong bone histology. Zool. J. Linn. Soc.130, 551 – 566. (doi:10.1111/j.1096-3642.2000.tb02201.x)17. Benson RBJ, Campione NE, Carrano MT, MannionPD, Sullivan C, Upchurch P, Evans DC. 2014Rates of dinosaur body mass evolutionindicate 170 million years of sustainedecological innovation on the avian stem lineage.PLoS Biol. 12, e1001853. (doi:10.1371/journal.pbio.1001853).orgBiol.Lett.11:20140984

Body mass estimates of an exceptionally complete Stegosaurus (Ornithischia: Thyreophora): comparing volumetric and linear bivariate mass estimation methods


            Body mass is a key biological variable, but difficult to assess from fossils. Various techniques exist for estimating body mass from skeletal parameters, but few studies have compared outputs from different methods. Here, we apply several mass estimation methods to an exceptionally complete skeleton of the dinosaur
            Stegosaurus
            . Applying a volumetric convex-hulling technique to a digital model of
            Stegosaurus
            , we estimate a mass of 1560 kg (95% prediction interval 1082–2256 kg) for this individual. By contrast, bivariate equations based on limb dimensions predict values between 2355 and 3751 kg and require implausible amounts of soft tissue and/or high body densities. When corrected for ontogenetic scaling, however, volumetric and linear equations are brought into close agreement. Our results raise concerns regarding the application of predictive equations to extinct taxa with no living analogues in terms of overall morphology and highlight the sensitivity of bivariate predictive equations to the ontogenetic status of the specimen. We emphasize the significance of rare, complete fossil skeletons in validating widely applied mass estimation equations based on incomplete skeletal material and stress the importance of accurately determining specimen age prior to further analyses.
          </jats:p

Crossref

Body mass estimates of an exceptionally complete
            <i>Stegosaurus</i>
            (Ornithischia: Thyreophora): comparing volumetric and linear bivariate mass estimation methods

Body mass is a key biological variable, but difficult to assess from fossils.
Various techniques exist for estimating body mass from skeletal parameters,
but few studies have compared outputs from different methods. Here, we
apply several mass estimation methods to an exceptionally complete skeleton
of the dinosaur Stegosaurus. Applying a volumetric convex-hulling
technique to a digital model of Stegosaurus, we estimate a mass of 1560 kg
(95% prediction interval 1082–2256 kg) for this individual. By contrast,
bivariate equations based on limb dimensions predict values between 2355
and 3751 kg and require implausible amounts of soft tissue and/or high
body densities. When corrected for ontogenetic scaling, however, volumetric
and linear equations are brought into close agreement. Our results raise concerns
regarding the application of predictive equations to extinct taxa with
no living analogues in terms of overall morphology and highlight the sensitivity
of bivariate predictive equations to the ontogenetic status of the
specimen. We emphasize the significance of rare, complete fossil skeletons
in validating widely applied mass estimation equations based on incomplete
skeletal material and stress the importance of accurately determining
specimen age prior to further analyses

Brassey, CA

Maidment, SCR

Barrett, PM

Spiral - Imperial College Digital Repository

rsbl.royalsocietypublishing.orgResearchCite this article: Brassey CA, Maidment SCR,Barrett PM. 2015 Body mass estimates of anexceptionally complete Stegosaurus(Ornithischia: Thyreophora): comparingvolumetric and linear bivariate mass estimationmethods. Biol. Lett. 11: 20140984.http://dx.doi.org/10.1098/rsbl.2014.0984Received: 21 November 2014Accepted: 10 February 2015Subject Areas:palaeontology, biomechanicsKeywords:Stegosaurus, body mass, scaling equations,volumetric model, photogrammetryAuthor for correspondence:Charlotte A. Brasseye-mail: c.brassey@nhm.ac.ukElectronic supplementary material is availableat http://dx.doi.org/10.1098/rsbl.2014.0984 orvia http://rsbl.royalsocietypublishing.org.& 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons AttributionLicense http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the originalauthor and source are credited.PalaeontologyBody mass estimates of an exceptionallycomplete Stegosaurus (Ornithischia:Thyreophora): comparing volumetric andlinear bivariate mass estimation methodsCharlotte A. Brassey1, Susannah C. R. Maidment2 and Paul M. Barrett11Department of Earth Sciences, The Natural History Museum, Cromwell Road, London SW7 5DB, UK2Department of Earth Science and Engineering, Imperial College, South Kensington Campus,London SW7 2AZ, UKBody mass is a key biological variable, but difficult to assess from fossils.Various techniques exist for estimating body mass from skeletal parameters,but few studies have compared outputs from different methods. Here, weapply several mass estimation methods to an exceptionally complete skel-eton of the dinosaur Stegosaurus. Applying a volumetric convex-hullingtechnique to a digital model of Stegosaurus, we estimate a mass of 1560 kg(95% prediction interval 1082–2256 kg) for this individual. By contrast,bivariate equations based on limb dimensions predict values between 2355and 3751 kg and require implausible amounts of soft tissue and/or highbody densities. When corrected for ontogenetic scaling, however, volumetricand linear equations are brought into close agreement. Our results raise con-cerns regarding the application of predictive equations to extinct taxa withno living analogues in terms of overall morphology and highlight the sensi-tivity of bivariate predictive equations to the ontogenetic status of thespecimen. We emphasize the significance of rare, complete fossil skeletonsin validating widely applied mass estimation equations based on incompleteskeletal material and stress the importance of accurately determiningspecimen age prior to further analyses.1. IntroductionIn extant taxa, body mass is an indicator of fundamental ecological and physi-ological traits such as population density, metabolism and cost-of-transport [1].Key evolutionary transitions in deep time, such as the origin of avian flight [2]and the adaptive radiation of mammals around the Cretaceous-Paleogeneboundary [3], have been interpreted in the context of body size: thus bodymass reconstruction in extinct species is of considerable interest.Ideally, mass estimates for extinct taxa would be based upon completespecimens, but such material is rare. Consequently, many mass estimation tech-niques for fossil taxa rely upon measurements taken from commonly preservedskeletal elements. Recently, the sum of femoral and humeral circumferenceswas shown to correlate strongly with mass in extant taxa [4]. However, theapplicability of this equation to fossil groups with unusual morphological fea-tures, overly robust/gracile limb elements or lying outside of the size range ofextant taxa, remains to be tested. Additionally, application of bivariate predic-tive equations to specimens of uncertain ontogenetic status is potentiallyproblematic given evidence of allometric scaling of limb dimensions with ageamong dinosaur taxa [5].(a) (b)(c) (d )(g)(e) ( f )Figure 1. Reconstructions of Stegosaurus stenops (NHMUK R36730) and associated convex hulls. (a,b) Cvol(min); (c,d) Cvol( pref ); (e,f ) Cvol(max); (g) Cvol(C&E). (Onlineversion in colour.)rsbl.royalsocietypublishing.orgBiol.Lett.11:201409842When specimens are complete, volumetric methods of massestimation can be used [6,7]. Such methods incorporate all of theavailable data from the specimen and are not biased by theproblem of unexpectedly robust/gracile elements, nor do theyrely on regressions that are extrapolated beyond empiricallybased body mass data. Nevertheless, the reconstruction processinvolves a degree of subjectivity and sensitivity analyses areessential to quantify the effects of anatomical uncertainties [6].Convex hulling [7] circumvents this problem by fitting ‘shrink-wrap’ convex polytopes around the three-dimensional skeletonand deriving a mass estimate based on the relationship betweenconvex hull volume (Cvol) and body mass in modern species.Using a three-dimensional computer model of an excep-tionally complete Stegosaurus specimen, we compare massestimation techniques based on volumetric and traditionalbivariate regressions to test if estimates generated from limbbone dimensions alone are biologically plausible for taxawith morphologies lacking close modern analogues or forspecimens that have not attained full adult size.2. Material and methodsThe specimen is a Stegosaurus stenops (NHMUK (Natural HistoryMuseum, London) R36730) from the Upper Jurassic MorrisonFormation near Shell, Wyoming. It is substantially complete, withall body regions represented except the left forelimb and part ofthe tail. NHMUK R36730 is classified as a ‘young adult’ based onhistological sampling [8,9] (electronic supplementary material, S1).The specimen was digitized as disarticulated bones using photo-grammetry [10] and the freely available software ‘VisualSFM’(http://ccwu.me/vsfm) and ‘Meshlab’ (http://meshlab.source-forge.net) (electronic supplementary material, S2).The skeleton was posed in 3DsMax (www.autodesk.com/3dsmax) and a convex hull model produced (Cvol(pref)) represent-ing our preferred articulation of the elements based oncomparative dinosaur anatomy and information from the extantphylogenetic bracket (crocodilians/birds). A sensitivity analysisquantified the effect of rearticulation on Cvol. Intervertebralspacing, rib flaring and scapula position were altered to define aminimum (Cvol(min)) and maximum (Cvol(max)) volume pose forthe skeleton (electronic supplementary material, S3). Modelswere subdivided into functional units: head, neck, trunk(sacrum and thorax), tail, upper arm, forearm, hand, thigh,shank and foot. The cervical series was subdivided to ensure atight fit of the hulls around the neck. Convex hulls were fittedto functional units using the ‘convhulln’ function in MATLAB(www.mathworks.com) implementing the ‘qhull’ algorithm [11].Total Cvol was calculated as the sum of segment values, andbody mass estimated using the relationship between Cvol andbody mass published elsewhere [7,12] (electronic supplementarymaterial, S4). By directly converting Cvol into a mass estimate, a0Cvol(min)Cvol(pref)Cvol(max)Cvol(C&E)CE2012bCE2012mAn1985M2004EYPM1856EYPM18532000estimated mass (kg)400060008000rsbl.royalsocietypublishing.orgBiol.Lett.11:201409843body density value is not explicitly assigned. However, there is anassumption that the density of the fossil species falls within therange of those species from which the predictive equation isderived, in this case modern quadrupedal mammals.We expanded our ‘maximum’ convex hull model (Cvol(max)) tomatch the body mass value predicted when applying a recentlypublished scaling equation (Cvol(C&E)) [4]. Dermal armour masswas determined separately and added to each volumetric massestimate (electronic supplementary material, table S1). Mass esti-mates based on femoral and/or humeral circumference werecalculated using the MASSTIMATE package in R [13] and raw dataavailable from previous studies [14,15] (electronic supplementarymaterial, S4). The potential effect of ontogenetic scaling was inves-tigated using Developmental Mass Extrapolation (DME), wherebythe mass of a ‘known’ adult individual (in this case StegosaurusYPM (Peabody Museum of Natural History, Yale University)1853 and YPM 1856) is estimated using the bivariate equation inquestion, and subsequently scaled isometrically on the basis offemoral length to the subadult individual [16] (electronicsupplementary material, S5).Table 1. Volume data (m3) for convex hull reconstructions of Stegosaurusstenops (NHMUK R36730).body segment Cvol( pref ) Cvol(min) Cvol(max) Cvol(C&E)head 0.0056 0.0056 0.0056 0.0119neck 0.0177 0.0152 0.0199 0.0425trunk 1.0786 0.8724 1.3686 2.9174left upper arm 0.0098 0.0098 0.0098 0.0208left forearm 0.0046 0.0046 0.0046 0.0099left hand 0.0021 0.0021 0.0021 0.0046left thigh 0.0159 0.0159 0.0159 0.0339left shank 0.0084 0.0084 0.0084 0.0178left foot 0.0018 0.0018 0.0018 0.0038right upper arm 0.0084 0.0084 0.0084 0.0180right forearm 0.0042 0.0042 0.0042 0.0091right hand 0.0020 0.0020 0.0020 0.0043right thigh 0.0166 0.0166 0.0166 0.0354right shank 0.0091 0.0091 0.0091 0.0194right foot 0.0014 0.0014 0.0014 0.0031DMDMFigure 2. Volumetric mass estimates for NHMUK R36730 calculated herecompared with those derived from proximal limb circumference. For abbrevi-ations, see table 2. (Online version in colour.)3. ResultsThe convex hull reconstruction of our preferred model(Cvol(pref )) provides a mass estimate of 1560 kg (95% predic-tion interval (PI) 1082–2256 kg), including 34 kg of dermalarmour (electronic supplementary material, table S1).Values for Cvol(min) of 1311 kg (95% PI ¼ 916–1884 kg) andCvol(max) of 1894 kg (95% PI ¼ 1303–2760 kg) derived fromthe rearticulation sensitivity analysis provide upper andlower bounds to our convex hull mass estimate (figure 1and table 1). Prior to accounting for ontogeny, mass estimatesbased on proximal limb bone circumferences [5] were consist-ently higher than those based on convex hulls (figure 2),ranging between 2355 and 3751 kg (table 2). The predictionintervals of Cvol(pref ) do not overlap those of either of the pre-dictive equations of Campione & Evans (C&E) [4] (figure 2).To achieve the 3752 kg estimate derived from the C&E bivari-ate equation [4], the convex hulls fitted to the Cvol(max) modelrequired considerable rescaling, resulting in a total convexhull volume of 3.378 m3 for the Cvol(C&E) model and an esti-mated body mass of 3745 kg (figure 1g and table 1).However, accounting for possible ontogenetic scalingbrought volumetric and linear bivariate predictions intoclose agreement. Based on DME using adult Stegosaurusspecimens (YPM1853, 1856) as endpoints, predicted massesfor NHMUK R36730 using the C&E bivariate equations [4]were 1823 kg and 2158 kg, respectively, and fall within theconfidence intervals of our volumetric models.tail 0.0936 0.0781 0.1061 0.2262total 1.2800 1.0558 1.5848 3.37814. DiscussionThis is the first study to apply both volumetric and linearbivariate mass estimation techniques to the same Stegosaurusindividual. Prior to accounting for ontogenetic scaling, volu-metric mass estimates for Stegosaurus were considerablylower than those predicted on the basis of limb bone dimen-sions. The Cvol(min), Cvol(pref ) and Cvol(max) model predictionsare 35, 42 and 50%, respectively, of the 3752 kg estimatedby the C&E bivariate predictive equation [4], which wasbased on adult individuals. Previous studies on other stego-saur specimens also found that volumetric mass estimateswere consistently lower than those based on limb bonescaling (electronic supplementary material, tables S2 and S3).The Cvol(C&E) model created to reconstruct the bodydimensions required to meet the original 3752 kg mass esti-mation of Campione & Evans [4] represents a 165%increase in volume from the Cvol(pref ) model. Outwardly,the convex hull volumes appear extremely large (figure 1g)and, given the excessive soft tissue volume that would needto be placed outside the skeleton in order to reach a bodymass of more than 3700 kg, we consider that the CETable 2. Mass estimates (kg) for Stegosaurus stenops (NHMUK R36730)based on proximal limb circumference. ‘An1985’ and ‘M2004’ equationshave been modified from those originally published (electronicsupplementary material, S4). CE2012b and CE2012m refer to bivariate andmultivariate equations in [4].equation mean lower 95% PI upper 95% PICE2012b [4] 3752 2790 4713CE2012m [4] 3329 2499 4159An1985 [15] 3632 2089 6316M2004 [16] 2355 971 5717DMEYPM1853 [4] 1823 1356 2290DMEYPM1856 [4] 2158 1605 2712rsbl.royalsocietypublishing.orgBiol.Lett.11:201409844predictive equation [5] overestimates body mass in Stego-saurus when applied in this manner (i.e. without correctionfor the ontogenetic stage of the specimen).The convex hull mass estimates for NHMUK R36730 arelower than those calculated for other Stegosaurus specimens(e.g. USNM (United States National Museum of NaturalHistory, Washington, DC, USA) 4934) using alternativevolumetric techniques (electronic supplementary material,table S1). NHMUK R36730 was not osteologically mature attime of death and is smaller than USNM 4934 (electronic sup-plementary material, table S4). It is therefore expected thatthe convex hull estimates calculated here should be lowerthan previous volumetric reconstructions. This differencehighlights the importance of generating specimen-specificmass values prior to subsequent biomechanical analysesrather than applying species-means.Although a ‘young adult’ [8,9], NHMUK R36730 was stillgrowing at the time of death (electronic supplementarymaterial, S1). When DME was applied to the specimenusing ‘known’ adult Stegosaurus as a baseline (electronic sup-plementary material, S5), the two mass estimation techniquesconverged significantly. Importantly, correction for ontogen-etic stage resulted in the original mass estimates derivedusing the CE equations [4] falling within the confidenceintervals of all volumetric estimates (figure 2 and table 2).Much of the discrepancy between the two techniques may,therefore, be attributed to the age of the specimen.Discrepancies between volumetric and linear mass esti-mates have been noted for other dinosaurs [7], and ourresults suggest that ontogeny is a potential explanation. Byconsidering NHMUK R36730 as subadult rather than adult,previous mass estimates [4] more than halve (from 3752 to1823 kg; table 2). This highlights the sensitivity of linear bivari-ate equations to ontogenetic status and urges caution ininstances when the age of the specimen is unclear (e.g. inthe absence of histological information or for fragmentarymaterial). While important palaeoecological studies of broadtaxonomic scope must necessarily include as large a samplesize as possible, our results suggest that authors should restrictthemselves to sampling the largest individual of a given taxonin order to minimize this effect [17].In summary, our volumetric mass estimates of Stegosaurusfall outside the prediction intervals of commonly used massprediction equations based on proximal limb dimensions, apattern seen in other dinosaurs [7]. Ontogenetic scaling is apossible explanation for this discrepancy. Rare finds ofexceptionally complete specimens should play a crucial rolein validating widely applied mass estimations based onincomplete skeletal material. It is possible that important size-related shifts in palaeoecology or physiology in fossil taxa arebeing misinterpreted owing to the inappropriate applicationof mass prediction equations. Our results urge caution whenestimating the mass of extinct species, particularly when theontogenetic status of the specimen is difficult to determine.Data accessibility. Convex hull models are downloadable from Dryad(doi:10.5061/dryad.2307m).Acknowledgements. We are grateful to Jeremy Herrmann and the otherdonors who made the purchase of this exceptional specimen possible.We thank D. Evans for discussion and two anonymous reviewers forcomments.Author contributions. C.A.B. collected and analysed the data, and wrotethe manuscript. S.C.R.M. and P.M.B. assisted with data analysisand helped draft the manuscript.Conflict of interest. The authors declare that they have no competinginterests.References1. Schmidt-Nielsen K. 1984 Scaling: why is animal sizeso important? Cambridge, UK: Cambridge UniversityPress.2. Turner AH, Pol D, Clarke JA, Erickson GM, Norell MA.2007 A basal dromaeosaurid and size evolutionpreceding avian flight. Science 317, 1378 – 1381.(doi:10.1126/science.1144066)3. Wilson GP, Evans AR, Corfe IJ, Smits PD, Fortelius M,Jernvall J. 2012 Adaptive radiation ofmultituberculate mammals before the extinction ofdinosaurs. Nature 483, 457 – 460. (doi:10.1038/nature10880)4. Campione NE, Evans DC. 2012 A universal scalingrelationship between body mass and proximal limbbone dimensions in quadrupedal terrestrialtetrapods. BMC Biol. 10, 60. (doi:10.1186/1741-7007-10-60)5. Kilbourne BM, Makovicky PJ. 2010 Limb boneallometry during postnatal ontogeny in non-aviandinosaurs. J. Anat. 217, 135 – 152. (doi:10.1111/j.1469-7580.2010.01253.x)6. Bates KT, Manning PL, Hodgetts D, Sellers WI. 2009Estimating mass properties of dinosaurs using laserimaging and 3D computer modelling. PLoS ONE 4,e4532. (doi:10.1371/journal.pone.0004532)7. Sellers WI, Hepworth-Bell J, Falkingham PL, BatesKT, Brassey CA, Egerton VM, Manning PL. 2012Minimum convex hull mass estimations of completemounted skeletons. Biol. Lett. 8, 842 – 845. (doi:10.1098/rsbl.2012.0263)8. Redelstorff R, Sander PM. 2009 Long and girdlebone histology of Stegosaurus: implications forgrowth and life history. J. Vertebr. Paleontol. 29,1087 – 1099. (doi:10.1671/039.029.0420)9. Hayashi S, Carpenter K, Suzuki D. 2009 Differentgrowth patterns between the skeleton andosteoderms of Stegosaurus (Ornithischia:Thyreophora). J. Vertebr. Paleontol. 29, 123 – 131.(doi:10.1080/02724634.2009.10010366)10. Mallison H, Wings O. 2014 Photogrammetry inpaleontology—a practical guide. J. Paleontol. Tech.12, 1 – 31. (http://www.jpaleontologicaltechniques.org/pasta3/JPT%20N12/Bulletin.html)11. Barber CB, Dobkin DP, Huhdanpaa HT. 1996 TheQuickhull algorithm for convex hulls. ACM Trans. Math.Softw. 22, 469 – 483. (doi:10.1145/235815.235821)12. Brassey C, Sellers WI. 2014 Scaling of convexhull volume to body mass in modernprimates, non-primate mammals and birds.PLoS ONE 9, e91691. (doi:10.1371/journal.pone.0091691)rsbl.royalsocietypublishing513. Campione NE, Evans DC, Brown CM, Carrano MT.2014 Body mass estimation in non-avian bipedsusing a theoretical conversion to quadrupedstylopodial proportions. Methods Ecol. Evol. 5,913 – 923. (doi:10.1111/2041-210X.12226)14. Anderson JF, Hall-Martin A, Russell DA. 1985 Long-bone circumference and weight in mammals, birdsand dinosaurs. J. Zool. 207, 53 – 61. (doi:10.1111/j.1469-7998.1985.tb04915.x)15. Mazzetta G, Christiansen P, Farina R. 2004Giants and bizarres: body size of somesouthern south American Cretaceous dinosaurs.Hist. Biol. 1 – 13. (doi:10.1080/08912960410001715132)16. Erickson GM, Tumanova TA. 2000 Growthcurve of Psittacosaurus mongoliensis Osborn(Ceratopsia: Psittacosauridae) inferred fromlong bone histology. Zool. J. Linn. Soc.130, 551 – 566. (doi:10.1111/j.1096-3642.2000.tb02201.x)17. Benson RBJ, Campione NE, Carrano MT, MannionPD, Sullivan C, Upchurch P, Evans DC. 2014Rates of dinosaur body mass evolutionindicate 170 million years of sustainedecological innovation on the avian stem lineage.PLoS Biol. 12, e1001853. (doi:10.1371/journal.pbio.1001853).orgBiol.Lett.11:20140984

© 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.     The file attached is the published version of the article.NHM Repositor

Maidment, SC

Natural History Museum Repository

 on July 19, 2016http://rsbl.royalsocietypublishing.org/Downloaded from rsbl.royalsocietypublishing.orgResearchCite this article: Brassey CA, Maidment SCR,Barrett PM. 2015 Body mass estimates of anexceptionally complete Stegosaurus(Ornithischia: Thyreophora): comparingvolumetric and linear bivariate mass estimationmethods. Biol. Lett. 11: 20140984.http://dx.doi.org/10.1098/rsbl.2014.0984Received: 21 November 2014Accepted: 10 February 2015Subject Areas:palaeontology, biomechanicsKeywords:Stegosaurus, body mass, scaling equations,volumetric model, photogrammetryAuthor for correspondence:Charlotte A. Brasseye-mail: c.brassey@nhm.ac.ukElectronic supplementary material is availableat http://dx.doi.org/10.1098/rsbl.2014.0984 orvia http://rsbl.royalsocietypublishing.org.& 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons AttributionLicense http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the originalauthor and source are credited.PalaeontologyBody mass estimates of an exceptionallycomplete Stegosaurus (Ornithischia:Thyreophora): comparing volumetric andlinear bivariate mass estimation methodsCharlotte A. Brassey1, Susannah C. R. Maidment2 and Paul M. Barrett11Department of Earth Sciences, The Natural History Museum, Cromwell Road, London SW7 5DB, UK2Department of Earth Science and Engineering, Imperial College, South Kensington Campus,London SW7 2AZ, UKBody mass is a key biological variable, but difficult to assess from fossils.Various techniques exist for estimating body mass from skeletal parameters,but few studies have compared outputs from different methods. Here, weapply several mass estimation methods to an exceptionally complete skel-eton of the dinosaur Stegosaurus. Applying a volumetric convex-hullingtechnique to a digital model of Stegosaurus, we estimate a mass of 1560 kg(95% prediction interval 1082–2256 kg) for this individual. By contrast,bivariate equations based on limb dimensions predict values between 2355and 3751 kg and require implausible amounts of soft tissue and/or highbody densities. When corrected for ontogenetic scaling, however, volumetricand linear equations are brought into close agreement. Our results raise con-cerns regarding the application of predictive equations to extinct taxa withno living analogues in terms of overall morphology and highlight the sensi-tivity of bivariate predictive equations to the ontogenetic status of thespecimen. We emphasize the significance of rare, complete fossil skeletonsin validating widely applied mass estimation equations based on incompleteskeletal material and stress the importance of accurately determiningspecimen age prior to further analyses.1. IntroductionIn extant taxa, body mass is an indicator of fundamental ecological and physi-ological traits such as population density, metabolism and cost-of-transport [1].Key evolutionary transitions in deep time, such as the origin of avian flight [2]and the adaptive radiation of mammals around the Cretaceous-Paleogeneboundary [3], have been interpreted in the context of body size: thus bodymass reconstruction in extinct species is of considerable interest.Ideally, mass estimates for extinct taxa would be based upon completespecimens, but such material is rare. Consequently, many mass estimation tech-niques for fossil taxa rely upon measurements taken from commonly preservedskeletal elements. Recently, the sum of femoral and humeral circumferenceswas shown to correlate strongly with mass in extant taxa [4]. However, theapplicability of this equation to fossil groups with unusual morphological fea-tures, overly robust/gracile limb elements or lying outside of the size range ofextant taxa, remains to be tested. Additionally, application of bivariate predic-tive equations to specimens of uncertain ontogenetic status is potentiallyproblematic given evidence of allometric scaling of limb dimensions with ageamong dinosaur taxa [5].(a) (b)(c) (d )(g)(e) ( f )Figure 1. Reconstructions of Stegosaurus stenops (NHMUK R36730) and associated convex hulls. (a,b) Cvol(min); (c,d) Cvol( pref ); (e,f ) Cvol(max); (g) Cvol(C&E). (Onlineversion in colour.)rsbl.royalsocietypublishing.orgBiol.Lett.11:201409842 on July 19, 2016http://rsbl.royalsocietypublishing.org/Downloaded from When specimens are complete, volumetric methods of massestimation can be used [6,7]. Suchmethods incorporate all of theavailable data from the specimen and are not biased by theproblem of unexpectedly robust/gracile elements, nor do theyrely on regressions that are extrapolated beyond empiricallybased body mass data. Nevertheless, the reconstruction processinvolves a degree of subjectivity and sensitivity analyses areessential to quantify the effects of anatomical uncertainties [6].Convex hulling [7] circumvents this problem by fitting ‘shrink-wrap’ convex polytopes around the three-dimensional skeletonand deriving amass estimate based on the relationship betweenconvex hull volume (Cvol) and body mass in modern species.Using a three-dimensional computer model of an excep-tionally complete Stegosaurus specimen, we compare massestimation techniques based on volumetric and traditionalbivariate regressions to test if estimates generated from limbbone dimensions alone are biologically plausible for taxawith morphologies lacking close modern analogues or forspecimens that have not attained full adult size.2. Material and methodsThe specimen is a Stegosaurus stenops (NHMUK (Natural HistoryMuseum, London) R36730) from the Upper Jurassic MorrisonFormation near Shell, Wyoming. It is substantially complete, withall body regions represented except the left forelimb and part ofthe tail. NHMUK R36730 is classified as a ‘young adult’ based onhistological sampling [8,9] (electronic supplementary material, S1).The specimen was digitized as disarticulated bones using photo-grammetry [10] and the freely available software ‘VisualSFM’(http://ccwu.me/vsfm) and ‘Meshlab’ (http://meshlab.source-forge.net) (electronic supplementary material, S2).The skeleton was posed in 3DsMax (www.autodesk.com/3dsmax) and a convex hull model produced (Cvol(pref)) represent-ing our preferred articulation of the elements based oncomparative dinosaur anatomy and information from the extantphylogenetic bracket (crocodilians/birds). A sensitivity analysisquantified the effect of rearticulation on Cvol. Intervertebralspacing, rib flaring and scapula position were altered to define aminimum (Cvol(min)) and maximum (Cvol(max)) volume pose forthe skeleton (electronic supplementary material, S3). Modelswere subdivided into functional units: head, neck, trunk(sacrum and thorax), tail, upper arm, forearm, hand, thigh,shank and foot. The cervical series was subdivided to ensure atight fit of the hulls around the neck. Convex hulls were fittedto functional units using the ‘convhulln’ function in MATLAB(www.mathworks.com) implementing the ‘qhull’ algorithm [11].Total Cvol was calculated as the sum of segment values, andbody mass estimated using the relationship between Cvol andbody mass published elsewhere [7,12] (electronic supplementarymaterial, S4). By directly converting Cvol into a mass estimate, a0C vol(min)C vol(pref)C vol(max)C vol(C&E)CE2012bCE2012mAn1985M2004E YPM1856E YPM18532000estimated mass (kg)400060008000rsbl.royalsocietypublishing.orgBiol.Lett.11:201409843 on July 19, 2016http://rsbl.royalsocietypublishing.org/Downloaded from body density value is not explicitly assigned. However, there is anassumption that the density of the fossil species falls within therange of those species from which the predictive equation isderived, in this case modern quadrupedal mammals.We expanded our ‘maximum’ convex hull model (Cvol(max)) tomatch the body mass value predicted when applying a recentlypublished scaling equation (Cvol(C&E)) [4]. Dermal armour masswas determined separately and added to each volumetric massestimate (electronic supplementary material, table S1). Mass esti-mates based on femoral and/or humeral circumference werecalculated using the MASSTIMATE package in R [13] and raw dataavailable from previous studies [14,15] (electronic supplementarymaterial, S4). The potential effect of ontogenetic scaling was inves-tigated using Developmental Mass Extrapolation (DME), wherebythe mass of a ‘known’ adult individual (in this case StegosaurusYPM (Peabody Museum of Natural History, Yale University)1853 and YPM 1856) is estimated using the bivariate equation inquestion, and subsequently scaled isometrically on the basis offemoral length to the subadult individual [16] (electronicsupplementary material, S5).Table 1. Volume data (m3) for convex hull reconstructions of Stegosaurusstenops (NHMUK R36730).body segment Cvol(pref ) Cvol(min) Cvol(max) Cvol(C&E)head 0.0056 0.0056 0.0056 0.0119neck 0.0177 0.0152 0.0199 0.0425trunk 1.0786 0.8724 1.3686 2.9174left upper arm 0.0098 0.0098 0.0098 0.0208left forearm 0.0046 0.0046 0.0046 0.0099left hand 0.0021 0.0021 0.0021 0.0046left thigh 0.0159 0.0159 0.0159 0.0339left shank 0.0084 0.0084 0.0084 0.0178left foot 0.0018 0.0018 0.0018 0.0038right upper arm 0.0084 0.0084 0.0084 0.0180right forearm 0.0042 0.0042 0.0042 0.0091right hand 0.0020 0.0020 0.0020 0.0043right thigh 0.0166 0.0166 0.0166 0.0354right shank 0.0091 0.0091 0.0091 0.0194right foot 0.0014 0.0014 0.0014 0.0031DMDMFigure 2. Volumetric mass estimates for NHMUK R36730 calculated herecompared with those derived from proximal limb circumference. For abbrevi-ations, see table 2. (Online version in colour.)3. ResultsThe convex hull reconstruction of our preferred model(Cvol(pref )) provides a mass estimate of 1560 kg (95% predic-tion interval (PI) 1082–2256 kg), including 34 kg of dermalarmour (electronic supplementary material, table S1).Values for Cvol(min) of 1311 kg (95% PI ¼ 916–1884 kg) andCvol(max) of 1894 kg (95% PI ¼ 1303–2760 kg) derived fromthe rearticulation sensitivity analysis provide upper andlower bounds to our convex hull mass estimate (figure 1and table 1). Prior to accounting for ontogeny, mass estimatesbased on proximal limb bone circumferences [5] were consist-ently higher than those based on convex hulls (figure 2),ranging between 2355 and 3751 kg (table 2). The predictionintervals of Cvol(pref ) do not overlap those of either of the pre-dictive equations of Campione & Evans (C&E) [4] (figure 2).To achieve the 3752 kg estimate derived from the C&E bivari-ate equation [4], the convex hulls fitted to the Cvol(max) modelrequired considerable rescaling, resulting in a total convexhull volume of 3.378 m3 for the Cvol(C&E) model and an esti-mated body mass of 3745 kg (figure 1g and table 1).However, accounting for possible ontogenetic scalingbrought volumetric and linear bivariate predictions intoclose agreement. Based on DME using adult Stegosaurusspecimens (YPM1853, 1856) as endpoints, predicted massesfor NHMUK R36730 using the C&E bivariate equations [4]were 1823 kg and 2158 kg, respectively, and fall within theconfidence intervals of our volumetric models.tail 0.0936 0.0781 0.1061 0.2262total 1.2800 1.0558 1.5848 3.37814. DiscussionThis is the first study to apply both volumetric and linearbivariate mass estimation techniques to the same Stegosaurusindividual. Prior to accounting for ontogenetic scaling, volu-metric mass estimates for Stegosaurus were considerablylower than those predicted on the basis of limb bone dimen-sions. The Cvol(min), Cvol(pref ) and Cvol(max) model predictionsare 35, 42 and 50%, respectively, of the 3752 kg estimatedby the C&E bivariate predictive equation [4], which wasbased on adult individuals. Previous studies on other stego-saur specimens also found that volumetric mass estimateswere consistently lower than those based on limb bonescaling (electronic supplementary material, tables S2 and S3).The Cvol(C&E) model created to reconstruct the bodydimensions required to meet the original 3752 kg mass esti-mation of Campione & Evans [4] represents a 165%increase in volume from the Cvol(pref ) model. Outwardly,the convex hull volumes appear extremely large (figure 1g)and, given the excessive soft tissue volume that would needto be placed outside the skeleton in order to reach a bodymass of more than 3700 kg, we consider that the CETable 2. Mass estimates (kg) for Stegosaurus stenops (NHMUK R36730)based on proximal limb circumference. ‘An1985’ and ‘M2004’ equationshave been modiﬁed from those originally published (electronicsupplementary material, S4). CE2012b and CE2012m refer to bivariate andmultivariate equations in [4].equation mean lower 95% PI upper 95% PICE2012b [4] 3752 2790 4713CE2012m [4] 3329 2499 4159An1985 [15] 3632 2089 6316M2004 [16] 2355 971 5717DMEYPM1853 [4] 1823 1356 2290DMEYPM1856 [4] 2158 1605 2712rsbl.royalsocietypublishing.orgBiol.Lett.11:201409844 on July 19, 2016http://rsbl.royalsocietypublishing.org/Downloaded from predictive equation [5] overestimates body mass in Stego-saurus when applied in this manner (i.e. without correctionfor the ontogenetic stage of the specimen).The convex hull mass estimates for NHMUK R36730 arelower than those calculated for other Stegosaurus specimens(e.g. USNM (United States National Museum of NaturalHistory, Washington, DC, USA) 4934) using alternativevolumetric techniques (electronic supplementary material,table S1). NHMUK R36730 was not osteologically mature attime of death and is smaller than USNM 4934 (electronic sup-plementary material, table S4). It is therefore expected thatthe convex hull estimates calculated here should be lowerthan previous volumetric reconstructions. This differencehighlights the importance of generating specimen-specificmass values prior to subsequent biomechanical analysesrather than applying species-means.Although a ‘young adult’ [8,9], NHMUK R36730 was stillgrowing at the time of death (electronic supplementarymaterial, S1). When DME was applied to the specimenusing ‘known’ adult Stegosaurus as a baseline (electronic sup-plementary material, S5), the two mass estimation techniquesconverged significantly. Importantly, correction for ontogen-etic stage resulted in the original mass estimates derivedusing the CE equations [4] falling within the confidenceintervals of all volumetric estimates (figure 2 and table 2).Much of the discrepancy between the two techniques may,therefore, be attributed to the age of the specimen.Discrepancies between volumetric and linear mass esti-mates have been noted for other dinosaurs [7], and ourresults suggest that ontogeny is a potential explanation. Byconsidering NHMUK R36730 as subadult rather than adult,previous mass estimates [4] more than halve (from 3752 to1823 kg; table 2). This highlights the sensitivity of linear bivari-ate equations to ontogenetic status and urges caution ininstances when the age of the specimen is unclear (e.g. inthe absence of histological information or for fragmentarymaterial). While important palaeoecological studies of broadtaxonomic scope must necessarily include as large a samplesize as possible, our results suggest that authors should restrictthemselves to sampling the largest individual of a given taxonin order to minimize this effect [17].In summary, our volumetric mass estimates of Stegosaurusfall outside the prediction intervals of commonly used massprediction equations based on proximal limb dimensions, apattern seen in other dinosaurs [7]. Ontogenetic scaling is apossible explanation for this discrepancy. Rare finds ofexceptionally complete specimens should play a crucial rolein validating widely applied mass estimations based onincomplete skeletal material. It is possible that important size-related shifts in palaeoecology or physiology in fossil taxa arebeing misinterpreted owing to the inappropriate applicationof mass prediction equations. Our results urge caution whenestimating the mass of extinct species, particularly when theontogenetic status of the specimen is difficult to determine.Data accessibility. Convex hull models are downloadable from Dryad(doi:10.5061/dryad.2307m).Acknowledgements. We are grateful to Jeremy Herrmann and the otherdonors who made the purchase of this exceptional specimen possible.We thank D. Evans for discussion and two anonymous reviewers forcomments.Author contributions. C.A.B. collected and analysed the data, and wrotethe manuscript. S.C.R.M. and P.M.B. assisted with data analysisand helped draft the manuscript.Conflict of interest. The authors declare that they have no competinginterests.References1. Schmidt-Nielsen K. 1984 Scaling: why is animal sizeso important? Cambridge, UK: Cambridge UniversityPress.2. Turner AH, Pol D, Clarke JA, Erickson GM, Norell MA.2007 A basal dromaeosaurid and size evolutionpreceding avian flight. Science 317, 1378–1381.(doi:10.1126/science.1144066)3. Wilson GP, Evans AR, Corfe IJ, Smits PD, Fortelius M,Jernvall J. 2012 Adaptive radiation ofmultituberculate mammals before the extinction ofdinosaurs. Nature 483, 457–460. (doi:10.1038/nature10880)4. Campione NE, Evans DC. 2012 A universal scalingrelationship between body mass and proximal limbbone dimensions in quadrupedal terrestrialtetrapods. BMC Biol. 10, 60. (doi:10.1186/1741-7007-10-60)5. Kilbourne BM, Makovicky PJ. 2010 Limb boneallometry during postnatal ontogeny in non-aviandinosaurs. J. Anat. 217, 135–152. (doi:10.1111/j.1469-7580.2010.01253.x)6. Bates KT, Manning PL, Hodgetts D, Sellers WI. 2009Estimating mass properties of dinosaurs using laserimaging and 3D computer modelling. PLoS ONE 4,e4532. (doi:10.1371/journal.pone.0004532)7. Sellers WI, Hepworth-Bell J, Falkingham PL, BatesKT, Brassey CA, Egerton VM, Manning PL. 2012Minimum convex hull mass estimations of completemounted skeletons. Biol. Lett. 8, 842–845. (doi:10.1098/rsbl.2012.0263)8. Redelstorff R, Sander PM. 2009 Long and girdlebone histology of Stegosaurus: implications forgrowth and life history. J. Vertebr. Paleontol. 29,1087–1099. (doi:10.1671/039.029.0420)9. Hayashi S, Carpenter K, Suzuki D. 2009 Differentgrowth patterns between the skeleton andosteoderms of Stegosaurus (Ornithischia:Thyreophora). J. Vertebr. Paleontol. 29, 123–131.(doi:10.1080/02724634.2009.10010366)10. Mallison H, Wings O. 2014 Photogrammetry inpaleontology—a practical guide. J. Paleontol. Tech.12, 1–31. (http://www.jpaleontologicaltechniques.org/pasta3/JPT%20N12/Bulletin.html)11. Barber CB, Dobkin DP, Huhdanpaa HT. 1996 TheQuickhull algorithm for convex hulls. ACM Trans. Math.Softw. 22, 469–483. (doi:10.1145/235815.235821)12. Brassey C, Sellers WI. 2014 Scaling of convexhull volume to body mass in modernprimates, non-primate mammals and birds.PLoS ONE 9, e91691. (doi:10.1371/journal.pone.0091691)rsbl.royalsocietypublishing5 on July 19, 2016http://rsbl.royalsocietypublishing.org/Downloaded from 13. Campione NE, Evans DC, Brown CM, Carrano MT.2014 Body mass estimation in non-avian bipedsusing a theoretical conversion to quadrupedstylopodial proportions. Methods Ecol. Evol. 5,913–923. (doi:10.1111/2041-210X.12226)14. Anderson JF, Hall-Martin A, Russell DA. 1985 Long-bone circumference and weight in mammals, birdsand dinosaurs. J. Zool. 207, 53–61. (doi:10.1111/j.1469-7998.1985.tb04915.x)15. Mazzetta G, Christiansen P, Farina R. 2004Giants and bizarres: body size of somesouthern south American Cretaceous dinosaurs.Hist. Biol. 1–13. (doi:10.1080/08912960410001715132)16. Erickson GM, Tumanova TA. 2000 Growthcurve of Psittacosaurus mongoliensis Osborn(Ceratopsia: Psittacosauridae) inferred fromlong bone histology. Zool. J. Linn. Soc.130, 551–566. (doi:10.1111/j.1096-3642.2000.tb02201.x)17. Benson RBJ, Campione NE, Carrano MT, MannionPD, Sullivan C, Upchurch P, Evans DC. 2014Rates of dinosaur body mass evolutionindicate 170 million years of sustainedecological innovation on the avian stem lineage.PLoS Biol. 12, e1001853. (doi:10.1371/journal.pbio.1001853).orgBiol.Lett.11:20140984

A basal dromaeosaurid and size evolution preceding avian flight.

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

Adaptive radiation of multituberculate mammals before the extinction of dinosaurs.

Estimating mass properties of dinosaurs using laser imaging and 3D computer modelling.

Growth curve of Psittacosaurus mongoliensis Osborn (Ceratopsia: Psittacosauridae) inferred from long bone histology.

Long and girdle bone histology of Stegosaurus: implications for growth and life history.

Longbone circumference and weight in mammals, birds and dinosaurs.

Minimum convex hull mass estimations of complete mounted skeletons.

Photogrammetry in paleontology—a practical guide.

Rates of dinosaur body mass evolution indicate 170 million years of sustained ecological innovation on the avian stem lineage.

The Quickhull algorithm for convex hulls.

 on May 6, 2015http://rsbl.royalsocietypublishing.org/Downloaded from rsbl.royalsocietypublishing.orgResearchCite this article: Brassey CA, Maidment SCR,Barrett PM. 2015 Body mass estimates of anexceptionally complete Stegosaurus(Ornithischia: Thyreophora): comparingvolumetric and linear bivariate mass estimationmethods. Biol. Lett. 11: 20140984.http://dx.doi.org/10.1098/rsbl.2014.0984Received: 21 November 2014Accepted: 10 February 2015Subject Areas:palaeontology, biomechanicsKeywords:Stegosaurus, body mass, scaling equations,volumetric model, photogrammetryAuthor for correspondence:Charlotte A. Brasseye-mail: c.brassey@nhm.ac.ukElectronic supplementary material is availableat http://dx.doi.org/10.1098/rsbl.2014.0984 orvia http://rsbl.royalsocietypublishing.org.& 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons AttributionLicense http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the originalauthor and source are credited.PalaeontologyBody mass estimates of an exceptionallycomplete Stegosaurus (Ornithischia:Thyreophora): comparing volumetric andlinear bivariate mass estimation methodsCharlotte A. Brassey1, Susannah C. R. Maidment2 and Paul M. Barrett11Department of Earth Sciences, The Natural History Museum, Cromwell Road, London SW7 5DB, UK2Department of Earth Science and Engineering, Imperial College, South Kensington Campus,London SW7 2AZ, UKBody mass is a key biological variable, but difficult to assess from fossils.Various techniques exist for estimating body mass from skeletal parameters,but few studies have compared outputs from different methods. Here, weapply several mass estimation methods to an exceptionally complete skel-eton of the dinosaur Stegosaurus. Applying a volumetric convex-hullingtechnique to a digital model of Stegosaurus, we estimate a mass of 1560 kg(95% prediction interval 1082–2256 kg) for this individual. By contrast,bivariate equations based on limb dimensions predict values between 2355and 3751 kg and require implausible amounts of soft tissue and/or highbody densities. When corrected for ontogenetic scaling, however, volumetricand linear equations are brought into close agreement. Our results raise con-cerns regarding the application of predictive equations to extinct taxa withno living analogues in terms of overall morphology and highlight the sensi-tivity of bivariate predictive equations to the ontogenetic status of thespecimen. We emphasize the significance of rare, complete fossil skeletonsin validating widely applied mass estimation equations based on incompleteskeletal material and stress the importance of accurately determiningspecimen age prior to further analyses.1. IntroductionIn extant taxa, body mass is an indicator of fundamental ecological and physi-ological traits such as population density, metabolism and cost-of-transport [1].Key evolutionary transitions in deep time, such as the origin of avian flight [2]and the adaptive radiation of mammals around the Cretaceous-Paleogeneboundary [3], have been interpreted in the context of body size: thus bodymass reconstruction in extinct species is of considerable interest.Ideally, mass estimates for extinct taxa would be based upon completespecimens, but such material is rare. Consequently, many mass estimation tech-niques for fossil taxa rely upon measurements taken from commonly preservedskeletal elements. Recently, the sum of femoral and humeral circumferenceswas shown to correlate strongly with mass in extant taxa [4]. However, theapplicability of this equation to fossil groups with unusual morphological fea-tures, overly robust/gracile limb elements or lying outside of the size range ofextant taxa, remains to be tested. Additionally, application of bivariate predic-tive equations to specimens of uncertain ontogenetic status is potentiallyproblematic given evidence of allometric scaling of limb dimensions with ageamong dinosaur taxa [5].(a) (b)(c) (d )(g)(e) ( f )Figure 1. Reconstructions of Stegosaurus stenops (NHMUK R36730) and associated convex hulls. (a,b) Cvol(min); (c,d) Cvol( pref ); (e,f ) Cvol(max); (g) Cvol(C&E). (Onlineversion in colour.)rsbl.royalsocietypublishing.orgBiol.Lett.11:201409842 on May 6, 2015http://rsbl.royalsocietypublishing.org/Downloaded from When specimens are complete, volumetric methods of massestimation can be used [6,7]. Suchmethods incorporate all of theavailable data from the specimen and are not biased by theproblem of unexpectedly robust/gracile elements, nor do theyrely on regressions that are extrapolated beyond empiricallybased body mass data. Nevertheless, the reconstruction processinvolves a degree of subjectivity and sensitivity analyses areessential to quantify the effects of anatomical uncertainties [6].Convex hulling [7] circumvents this problem by fitting ‘shrink-wrap’ convex polytopes around the three-dimensional skeletonand deriving amass estimate based on the relationship betweenconvex hull volume (Cvol) and body mass in modern species.Using a three-dimensional computer model of an excep-tionally complete Stegosaurus specimen, we compare massestimation techniques based on volumetric and traditionalbivariate regressions to test if estimates generated from limbbone dimensions alone are biologically plausible for taxawith morphologies lacking close modern analogues or forspecimens that have not attained full adult size.2. Material and methodsThe specimen is a Stegosaurus stenops (NHMUK (Natural HistoryMuseum, London) R36730) from the Upper Jurassic MorrisonFormation near Shell, Wyoming. It is substantially complete, withall body regions represented except the left forelimb and part ofthe tail. NHMUK R36730 is classified as a ‘young adult’ based onhistological sampling [8,9] (electronic supplementary material, S1).The specimen was digitized as disarticulated bones using photo-grammetry [10] and the freely available software ‘VisualSFM’(http://ccwu.me/vsfm) and ‘Meshlab’ (http://meshlab.source-forge.net) (electronic supplementary material, S2).The skeleton was posed in 3DsMax (www.autodesk.com/3dsmax) and a convex hull model produced (Cvol(pref)) represent-ing our preferred articulation of the elements based oncomparative dinosaur anatomy and information from the extantphylogenetic bracket (crocodilians/birds). A sensitivity analysisquantified the effect of rearticulation on Cvol. Intervertebralspacing, rib flaring and scapula position were altered to define aminimum (Cvol(min)) and maximum (Cvol(max)) volume pose forthe skeleton (electronic supplementary material, S3). Modelswere subdivided into functional units: head, neck, trunk(sacrum and thorax), tail, upper arm, forearm, hand, thigh,shank and foot. The cervical series was subdivided to ensure atight fit of the hulls around the neck. Convex hulls were fittedto functional units using the ‘convhulln’ function in MATLAB(www.mathworks.com) implementing the ‘qhull’ algorithm [11].Total Cvol was calculated as the sum of segment values, andbody mass estimated using the relationship between Cvol andbody mass published elsewhere [7,12] (electronic supplementarymaterial, S4). By directly converting Cvol into a mass estimate, a0C vol(min)C vol(pref)C vol(max)C vol(C&E)CE2012bCE2012mAn1985M2004E YPM1856E YPM18532000estimated mass (kg)400060008000rsbl.royalsocietypublishing.orgBiol.Lett.11:201409843 on May 6, 2015http://rsbl.royalsocietypublishing.org/Downloaded from body density value is not explicitly assigned. However, there is anassumption that the density of the fossil species falls within therange of those species from which the predictive equation isderived, in this case modern quadrupedal mammals.We expanded our ‘maximum’ convex hull model (Cvol(max)) tomatch the body mass value predicted when applying a recentlypublished scaling equation (Cvol(C&E)) [4]. Dermal armour masswas determined separately and added to each volumetric massestimate (electronic supplementary material, table S1). Mass esti-mates based on femoral and/or humeral circumference werecalculated using the MASSTIMATE package in R [13] and raw dataavailable from previous studies [14,15] (electronic supplementarymaterial, S4). The potential effect of ontogenetic scaling was inves-tigated using Developmental Mass Extrapolation (DME), wherebythe mass of a ‘known’ adult individual (in this case StegosaurusYPM (Peabody Museum of Natural History, Yale University)1853 and YPM 1856) is estimated using the bivariate equation inquestion, and subsequently scaled isometrically on the basis offemoral length to the subadult individual [16] (electronicsupplementary material, S5).Table 1. Volume data (m3) for convex hull reconstructions of Stegosaurusstenops (NHMUK R36730).body segment Cvol(pref ) Cvol(min) Cvol(max) Cvol(C&E)head 0.0056 0.0056 0.0056 0.0119neck 0.0177 0.0152 0.0199 0.0425trunk 1.0786 0.8724 1.3686 2.9174left upper arm 0.0098 0.0098 0.0098 0.0208left forearm 0.0046 0.0046 0.0046 0.0099left hand 0.0021 0.0021 0.0021 0.0046left thigh 0.0159 0.0159 0.0159 0.0339left shank 0.0084 0.0084 0.0084 0.0178left foot 0.0018 0.0018 0.0018 0.0038right upper arm 0.0084 0.0084 0.0084 0.0180right forearm 0.0042 0.0042 0.0042 0.0091right hand 0.0020 0.0020 0.0020 0.0043right thigh 0.0166 0.0166 0.0166 0.0354right shank 0.0091 0.0091 0.0091 0.0194right foot 0.0014 0.0014 0.0014 0.0031DMDMFigure 2. Volumetric mass estimates for NHMUK R36730 calculated herecompared with those derived from proximal limb circumference. For abbrevi-ations, see table 2. (Online version in colour.)3. ResultsThe convex hull reconstruction of our preferred model(Cvol(pref )) provides a mass estimate of 1560 kg (95% predic-tion interval (PI) 1082–2256 kg), including 34 kg of dermalarmour (electronic supplementary material, table S1).Values for Cvol(min) of 1311 kg (95% PI ¼ 916–1884 kg) andCvol(max) of 1894 kg (95% PI ¼ 1303–2760 kg) derived fromthe rearticulation sensitivity analysis provide upper andlower bounds to our convex hull mass estimate (figure 1and table 1). Prior to accounting for ontogeny, mass estimatesbased on proximal limb bone circumferences [5] were consist-ently higher than those based on convex hulls (figure 2),ranging between 2355 and 3751 kg (table 2). The predictionintervals of Cvol(pref ) do not overlap those of either of the pre-dictive equations of Campione & Evans (C&E) [4] (figure 2).To achieve the 3752 kg estimate derived from the C&E bivari-ate equation [4], the convex hulls fitted to the Cvol(max) modelrequired considerable rescaling, resulting in a total convexhull volume of 3.378 m3 for the Cvol(C&E) model and an esti-mated body mass of 3745 kg (figure 1g and table 1).However, accounting for possible ontogenetic scalingbrought volumetric and linear bivariate predictions intoclose agreement. Based on DME using adult Stegosaurusspecimens (YPM1853, 1856) as endpoints, predicted massesfor NHMUK R36730 using the C&E bivariate equations [4]were 1823 kg and 2158 kg, respectively, and fall within theconfidence intervals of our volumetric models.tail 0.0936 0.0781 0.1061 0.2262total 1.2800 1.0558 1.5848 3.37814. DiscussionThis is the first study to apply both volumetric and linearbivariate mass estimation techniques to the same Stegosaurusindividual. Prior to accounting for ontogenetic scaling, volu-metric mass estimates for Stegosaurus were considerablylower than those predicted on the basis of limb bone dimen-sions. The Cvol(min), Cvol(pref ) and Cvol(max) model predictionsare 35, 42 and 50%, respectively, of the 3752 kg estimatedby the C&E bivariate predictive equation [4], which wasbased on adult individuals. Previous studies on other stego-saur specimens also found that volumetric mass estimateswere consistently lower than those based on limb bonescaling (electronic supplementary material, tables S2 and S3).The Cvol(C&E) model created to reconstruct the bodydimensions required to meet the original 3752 kg mass esti-mation of Campione & Evans [4] represents a 165%increase in volume from the Cvol(pref ) model. Outwardly,the convex hull volumes appear extremely large (figure 1g)and, given the excessive soft tissue volume that would needto be placed outside the skeleton in order to reach a bodymass of more than 3700 kg, we consider that the CETable 2. Mass estimates (kg) for Stegosaurus stenops (NHMUK R36730)based on proximal limb circumference. ‘An1985’ and ‘M2004’ equationshave been modiﬁed from those originally published (electronicsupplementary material, S4). CE2012b and CE2012m refer to bivariate andmultivariate equations in [4].equation mean lower 95% PI upper 95% PICE2012b [4] 3752 2790 4713CE2012m [4] 3329 2499 4159An1985 [15] 3632 2089 6316M2004 [16] 2355 971 5717DMEYPM1853 [4] 1823 1356 2290DMEYPM1856 [4] 2158 1605 2712rsbl.royalsocietypublishing.orgBiol.Lett.11:201409844 on May 6, 2015http://rsbl.royalsocietypublishing.org/Downloaded from predictive equation [5] overestimates body mass in Stego-saurus when applied in this manner (i.e. without correctionfor the ontogenetic stage of the specimen).The convex hull mass estimates for NHMUK R36730 arelower than those calculated for other Stegosaurus specimens(e.g. USNM (United States National Museum of NaturalHistory, Washington, DC, USA) 4934) using alternativevolumetric techniques (electronic supplementary material,table S1). NHMUK R36730 was not osteologically mature attime of death and is smaller than USNM 4934 (electronic sup-plementary material, table S4). It is therefore expected thatthe convex hull estimates calculated here should be lowerthan previous volumetric reconstructions. This differencehighlights the importance of generating specimen-specificmass values prior to subsequent biomechanical analysesrather than applying species-means.Although a ‘young adult’ [8,9], NHMUK R36730 was stillgrowing at the time of death (electronic supplementarymaterial, S1). When DME was applied to the specimenusing ‘known’ adult Stegosaurus as a baseline (electronic sup-plementary material, S5), the two mass estimation techniquesconverged significantly. Importantly, correction for ontogen-etic stage resulted in the original mass estimates derivedusing the CE equations [4] falling within the confidenceintervals of all volumetric estimates (figure 2 and table 2).Much of the discrepancy between the two techniques may,therefore, be attributed to the age of the specimen.Discrepancies between volumetric and linear mass esti-mates have been noted for other dinosaurs [7], and ourresults suggest that ontogeny is a potential explanation. Byconsidering NHMUK R36730 as subadult rather than adult,previous mass estimates [4] more than halve (from 3752 to1823 kg; table 2). This highlights the sensitivity of linear bivari-ate equations to ontogenetic status and urges caution ininstances when the age of the specimen is unclear (e.g. inthe absence of histological information or for fragmentarymaterial). While important palaeoecological studies of broadtaxonomic scope must necessarily include as large a samplesize as possible, our results suggest that authors should restrictthemselves to sampling the largest individual of a given taxonin order to minimize this effect [17].In summary, our volumetric mass estimates of Stegosaurusfall outside the prediction intervals of commonly used massprediction equations based on proximal limb dimensions, apattern seen in other dinosaurs [7]. Ontogenetic scaling is apossible explanation for this discrepancy. Rare finds ofexceptionally complete specimens should play a crucial rolein validating widely applied mass estimations based onincomplete skeletal material. It is possible that important size-related shifts in palaeoecology or physiology in fossil taxa arebeing misinterpreted owing to the inappropriate applicationof mass prediction equations. Our results urge caution whenestimating the mass of extinct species, particularly when theontogenetic status of the specimen is difficult to determine.Data accessibility. Convex hull models are downloadable from Dryad(doi:10.5061/dryad.2307m).Acknowledgements. We are grateful to Jeremy Herrmann and the otherdonors who made the purchase of this exceptional specimen possible.We thank D. Evans for discussion and two anonymous reviewers forcomments.Author contributions. C.A.B. collected and analysed the data, and wrotethe manuscript. S.C.R.M. and P.M.B. assisted with data analysisand helped draft the manuscript.Conflict of interest. The authors declare that they have no competinginterests.References1. Schmidt-Nielsen K. 1984 Scaling: why is animal sizeso important? Cambridge, UK: Cambridge UniversityPress.2. Turner AH, Pol D, Clarke JA, Erickson GM, Norell MA.2007 A basal dromaeosaurid and size evolutionpreceding avian flight. Science 317, 1378–1381.(doi:10.1126/science.1144066)3. Wilson GP, Evans AR, Corfe IJ, Smits PD, Fortelius M,Jernvall J. 2012 Adaptive radiation ofmultituberculate mammals before the extinction ofdinosaurs. Nature 483, 457–460. (doi:10.1038/nature10880)4. Campione NE, Evans DC. 2012 A universal scalingrelationship between body mass and proximal limbbone dimensions in quadrupedal terrestrialtetrapods. BMC Biol. 10, 60. (doi:10.1186/1741-7007-10-60)5. Kilbourne BM, Makovicky PJ. 2010 Limb boneallometry during postnatal ontogeny in non-aviandinosaurs. J. Anat. 217, 135–152. (doi:10.1111/j.1469-7580.2010.01253.x)6. Bates KT, Manning PL, Hodgetts D, Sellers WI. 2009Estimating mass properties of dinosaurs using laserimaging and 3D computer modelling. PLoS ONE 4,e4532. (doi:10.1371/journal.pone.0004532)7. Sellers WI, Hepworth-Bell J, Falkingham PL, BatesKT, Brassey CA, Egerton VM, Manning PL. 2012Minimum convex hull mass estimations of completemounted skeletons. Biol. Lett. 8, 842–845. (doi:10.1098/rsbl.2012.0263)8. Redelstorff R, Sander PM. 2009 Long and girdlebone histology of Stegosaurus: implications forgrowth and life history. J. Vertebr. Paleontol. 29,1087–1099. (doi:10.1671/039.029.0420)9. Hayashi S, Carpenter K, Suzuki D. 2009 Differentgrowth patterns between the skeleton andosteoderms of Stegosaurus (Ornithischia:Thyreophora). J. Vertebr. Paleontol. 29, 123–131.(doi:10.1080/02724634.2009.10010366)10. Mallison H, Wings O. 2014 Photogrammetry inpaleontology—a practical guide. J. Paleontol. Tech.12, 1–31. (http://www.jpaleontologicaltechniques.org/pasta3/JPT%20N12/Bulletin.html)11. Barber CB, Dobkin DP, Huhdanpaa HT. 1996 TheQuickhull algorithm for convex hulls. ACM Trans. Math.Softw. 22, 469–483. (doi:10.1145/235815.235821)12. Brassey C, Sellers WI. 2014 Scaling of convexhull volume to body mass in modernprimates, non-primate mammals and birds.PLoS ONE 9, e91691. (doi:10.1371/journal.pone.0091691)rsbl.royalsocietypublishing5 on May 6, 2015http://rsbl.royalsocietypublishing.org/Downloaded from 13. Campione NE, Evans DC, Brown CM, Carrano MT.2014 Body mass estimation in non-avian bipedsusing a theoretical conversion to quadrupedstylopodial proportions. Methods Ecol. Evol. 5,913–923. (doi:10.1111/2041-210X.12226)14. Anderson JF, Hall-Martin A, Russell DA. 1985 Long-bone circumference and weight in mammals, birdsand dinosaurs. J. Zool. 207, 53–61. (doi:10.1111/j.1469-7998.1985.tb04915.x)15. Mazzetta G, Christiansen P, Farina R. 2004Giants and bizarres: body size of somesouthern south American Cretaceous dinosaurs.Hist. Biol. 1–13. (doi:10.1080/08912960410001715132)16. Erickson GM, Tumanova TA. 2000 Growthcurve of Psittacosaurus mongoliensis Osborn(Ceratopsia: Psittacosauridae) inferred fromlong bone histology. Zool. J. Linn. Soc.130, 551–566. (doi:10.1111/j.1096-3642.2000.tb02201.x)17. Benson RBJ, Campione NE, Carrano MT, MannionPD, Sullivan C, Upchurch P, Evans DC. 2014Rates of dinosaur body mass evolutionindicate 170 million years of sustainedecological innovation on the avian stem lineage.PLoS Biol. 12, e1001853. (doi:10.1371/journal.pbio.1001853).orgBiol.Lett.11:20140984

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Body mass estimates of an exceptionally complete Stegosaurus (Ornithischia: Thyreophora): comparing volumetric and linear bivariate mass estimation methods

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