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Cautionary tales on the use of proxies to estimate body size and form of extinct animals

Ecology and Evolution

September 2024
14(9):70218

DOI:10.1002/ece3.70218

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CC BY 4.0

Authors:

Joel Harrison Gayford

James Cook University

Russell Engelman

Case Western Reserve University

Phillip Sternes

Shark Measurements

Wayne Itano

University of Colorado Boulder

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Body size is of fundamental importance to our understanding of extinct organisms. Physiology, ecology and life history are all strongly influenced by body size and shape, which ultimately determine how a species interacts with its environment. Reconstruction of body size and form in extinct animals provides insight into the dynamics underlying community composition and faunal turnover in past ecosystems and broad macroevolutionary trends. Many extinct animals are known only from incomplete remains, necessitating the use of anatomical proxies to reconstruct body size and form. Numerous limitations affecting the appropriateness of these proxies are often overlooked, leading to controversy and downstream inaccuracies in studies for which reconstructions represent key input data. In this perspective, we discuss four prominent case studies (Dunkleosteus, Helicoprion, Megalodon and Perucetus) in which proxy taxa have been used to estimate body size and shape from fragmentary remains. We synthesise the results of these and other studies to discuss nuances affecting the validity of taxon selection when reconstructing extinct organisms, as well as mitigation measures that can ensure the selection of the most appropriate proxy. We argue that these precautionary measures are necessary to maximise the robustness of reconstructions in extinct taxa for better evolutionary and ecological inferences.

Examples of reconstructions of extinct megafauna, showing early estimates of body size/form now thought to be inaccurate (grey silhouettes), and more recent estimates, the validity of which remain uncertain (black silhouettes). Original work and sources of these reconstructions are listed in the Data S1, and we do not necessarily endorse any particular reconstruction over others. Credit for the original silhouettes used to produce this figure are as follows: Guillame Dera, CC0 1.0 (Enchoteuthis before), Tyler Greenfield with input from Dirk Fuchs, CC‐BY 3.0 (Enchoteuthis after), Scott Hartman, CC‐BY 3.0 (Seismosaurus), JF Studios, CC0 (Pliosauridae), T. K. Robinson CC‐BY 3.0 (Mosasaurus), Nobu Tamura (Josephoartigasia body), Gustavo Lecuona (Josephoartigasia head), both CC‐BY 3.0, Andrews (1985) (Rhizodus), Pimiento et al. (2024) (Glyptapsis), Nobu Tamura (modified by T. Michael Keesey; Beelzebufo), Granger et al. (1936) (Paraceratherium before), Larramendi (2015) (Paraceratherium after), Russell Engelman, modified from Hodnett et al., 2021, CC‐BY 4.0 (Ctenacanthus), Scott Hartman, CC‐BY 3.0 (Machimosaurus), Mark P. Witton and Darren Naish, CC‐BY 3.0 (Quetzalcoatlus), Dal Sasso et al. (2005) (Spinosaurus before), Tasman Dixson, CC0 (Spinosaurus after), Dan Niel, CC0 (Argentavis), T. Michael Keesey, CC0 (Gigantopithecus), Anton et al. (2004) (Megalictis). Jagged Fang Designs, CC0 (Ekrixinatosaurus), Ferran Sayol, CC0 (Mourasuchus, body) and Langston (1965, Mourasuchus, head).

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Fossil (or cast) material for each of the four case studies (skull and trunk armour from a cast of Dunkleosteus terrelli, (a); tooth whorl from Helicoprion spp, (b); tooth from Otodus megalodon, (c); and vertebra from Perucetus colossus, (d); respectively), along with silhouettes representing reconstructions of body size and form, where grey silhouettes are past reconstructions now thought to be inaccurate and black silhouettes are recent reconstructions, the validity of which remains uncertain. Scale bars = 5 cm for fossil/cast material and 2 m for silhouettes. Image credits for fossil/cast material are as follows: Archival Photograph GEO82014 of cast CMNH 5768, Field Museum of Natural History, Chicago, Illinois, USA (a), Helicoprion bessonowi Karpinsky, 1899, holotype specimen, F.N. Chernyshev Central Scientific Research Geological Prospecting Museum, St. Petersburg, Russia, 1/1865 (b), Otodus megalodon tooth MUSM 2093, Sacaco, Museo de Historia Natural (UNMSM) Peru (c), Perucetus colossus holotype MUSM 3248, Museo de Historia Natural (UNMSM) Peru. Silhouette images were modified from image used with permission by Yang Song (grey, a) created by Russell Engelman (black, a), used with permission from William Snyder under a CC BY‐SA 4.0 licence (b), or modified from Sternes et al. (2024) (c) and Bianucci et al. (2023) (d).

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Ecology and Evolution. 2024;14:e70218.  

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https://doi.org/10.1002/ece3.70218

www.ecolevol.org

Received:8May2024

Revised:3August2024

Accepted:12August2024

DOI: 10.1002/ece 3.70 218

VIEWPOINT

Cautionary tales on the use of proxies to estimate body size

and form of extinct animals

Joel H. Gayford1,2,3 | Russell K. Engelman4 | Phillip C. Sternes3,5 |

Wayne M. Itano6 | Mohamad Bazzi7 | Alberto Collareta8,9 |

Rodolfo Salas- Gismondi10,11 | Kenshu Shimada12,13,14

1DepartmentofLifeSciences,SilwoodParkCampus,ImperialCollegeLondon,London,UK

2Depar tmentofMarineBiologyandAquaculture,JamesCookUniversity,Douglas,Queensland,Australia

3SharkMeasurements,London,UK

4Depar tmentofBiolog y,CaseWesternReserveUniversity,Cleveland,Ohio,USA

5Depar tmentofEvolution,Ecolog yandOrganismalBiology,UniversityofCalifornia,Riverside,California,USA

6MuseumofNaturalHistor y,UniversityofColorado,Boulder,Colorado,USA

7Depar tmentofEarthandPlanetar ySciences,StanfordUniversity,Stanford,California,USA

8DipartimentodiScienzeDellaTerra,UniversitàdiPisa,Pisa,Italy

9MuseodiStoriaNaturale,UniversitàdiPisa,Pisa,Italy

10LaboratoriosdeInvestigaciónyDesarrollo,FacultaddeCienciasyFilosofía/CentrodeInvestigaciónParaelDesarrolloIntegralySostenible,Universit ad

PeruanaCayetanoHerediaLima,Lima,Peru

11Depar tamentodePaleontologíadeVertebrados,MuseodeHistoriaNatural-UniversidadNacionalMayordesanMarcos,Lima,Peru

12DepartmentofEnvironmentalScienceandStudies,DePaulUniversit y,Chicago,Illinois,USA

13Depar tmentofBiologicalSciences,DePaulUniver sity,Chicago,Illinois,USA

14SternbergMuseumofNaturalHistory,For tHaysStateUniversity,Hays,Kansas,USA

ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttributionLicense,whichpermitsuse,distributionandreproductioninanymedium,

provide d the original wor k is properly cited.

©2024TheAuthor(s).Eco logy an d EvolutionpublishedbyJohnWiley&SonsLtd.

Correspondence

JoelH.Gayford,DepartmentofLife

Sciences,SilwoodParkCampus,Imperial

CollegeLondon,6NewRoadLewes,BN7

1YW,UK.

Email: jhg19@ic.ac.uk

Funding information

ItalianMinisterodell'Universitàe

dellaRicerca,Grant/AwardNumber:

2022MAM9ZB

Abstract

Bodysizeisoffundamental importancetoourunderstandingofextinct organisms.

Physiology, ecology and life history are all strongly influenced by body size and

shape, which ultimately determine how a species interacts with its environment.

Reconstructionofbodysizeandforminextinctanimalsprovidesinsightintothedy-

namics underlyingcommunity composition and faunal turnover in past ecosystems

andbroadmacroevolutionarytrends.Manyextinctanimalsareknownonlyfromin-

complete remains, necessitating theuse of anatomicalproxiesto reconstruct body

sizeandform.Numerous limitationsaffecting theappropriateness of theseproxies

areoftenoverlooked,leadingtocontroversyanddownstreaminaccuraciesinstudies

forwhich reconstructionsrepresentkey inputdata.In thisperspective,we discuss

fourprominent casestudies(Dunkleosteus, Helicoprion, Megalodon and Perucetus)in

which proxy taxa have been used toestimate body sizeand shape from fragmen-

taryremains.Wesynthesisetheresultsoftheseandotherstudiestodiscussnuances

affecting thevalidity of taxon selection when reconstructing extinct organisms, as

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1 | INTRODUC TION

AswrittenbyBartholomew(1981),‘itisonlyaslightoverstatement

tosay thatthe most importantattribute of an animal, bothphysi-

callyandecologically,isitssize’.Thisisbecausebodysize(measured

either as lengthorasmass) and form (i.e.,body shape)fundamen-

tally define the r ange of ecological niches an animal can occupy

(Blanckenhorn,2000; Dalponti et al., 2018;Schmidt-Nielsen,1984).

Reconstructingthebody size andformofextinctanimalscanthus

helpusunderstandtheirpalaeobiologyandpalaeoecology(O'Keefe

et al., 2011; Sander et al., 2021; Sternes et al., 2024).This can in-

cludebasic biologicalinformationlikephysiology,dietary,locomo-

tor,spatialand reproductivebiology(Ferrónetal.,2018; Finnegan

&Droser,20 08; Grogan & Lund, 2011; Pyenson & Vermeij, 2016)

orbroaderevolutionaryand ecologicalpatternslikepredator–prey

relationships,pastecosystemdynamicsandmass extinctionselec-

tivit y (Farlow & Planka, 2002; F innegan & Droser, 2008; G rogan

&Lund,2011; Monarrez et al., 2021; Morgan et al., 19 95; Payne&

Heim,2020; Pyenson & Vermeij,2016; Sallan&Galimberti,2015).

However, estimating the body size and form in extinct species

isoften challenging. Many taxa of interest areknownonly from a

handful of anatomically incomplete specimens, which may exhibit

highlyidiosyncraticbodyplans (Bianuccietal.,2023)or leave little

directevidence(pertainingfromthefossilrecord)ofhowmorphol-

ogyshouldscalewithbodysize.

Thebody sizeand shapeof variousiconic,large-bodied extinct

taxa have b een estimated by combining fossil data with physic al

measurements taken from extant or extinctproxies (Table 1)pre-

sumedtobecloselyrelatedtothetaxoninquestion(Millien,2008;

Millien & Bov y, 2010) and/or to displ ay significant e cological and

morphological similarities (Ferrón et al., 2017). This ‘extant scal-

ing’ approach typically relies on regression equations generated

from modern species or well-preserved fossil taxa, creating allo-

metric scaling relationships that are then applied to homologous

(or superficially similar) features on the extinct study species.

Many studies do not even use regression equations at all, instead

selec ting a single prox y taxon (either a si ngle specimen o r a rep-

resent ative reconst ruction of a sin gle taxon) and th en scaling th e

proxyupordowntothesizeoftheincompletefossilmaterialusing

the proportional size of an anatomical measurement assumed

to scale isometrically (Lingham-Soliar, 1995; Lomax et al., 2024;

Molnar, 2004; Savage, 1973).Importantly,thetermproxy refersto

both taxo n or taxa, and th e specific anato mical or morph ometric

characterthatistypically assumedtobehomologousbetween the

proxytaxonandthetaxonofinterest.Nomethodofreconstructing

bodyformorsizeinextincttaxaisflawless(Nelsonetal.,2023),and

many recent s tudies have proven highly controversial, prompting

thepublicationofrebuttalsandrevisions(Engelman,2022b, 2023a;

Grillo&Delcourt,2017; Millien, 2008;Millien&Bovy,2010; Motani

&Pyenson, 2024; Romano & Manucci, 2021; Sternes et al., 2023,

2024).Differencesinestimated bodysizeacross these studies are

notminor(Figure 1),with revisedsizeestimatesoftenbeinghalfor

lessthantheiroriginallyproposedvalue(e.g.,Cidadeetal.,2019; see

Table S2).These situations feed into a broader problem regarding

scepticismandmistrusttowardsscientists–the‘deathofexpertise’

(Nichols,2017 ).Thefrequencyandmagnitudewithwhichsizeesti-

matesformegafaunaneedtoberevisitedposesdifficultyforscien-

tistsinmaintainingpublictrustandconfidence,potentiallybleeding

intopublicopiniononothermattersofimportanceincludingclimate

changeandconservationissues.

Despite this, palaeobiologists generally agree that some infor-

mationfromextantorextinctproxiesisnecessarytoestimatebody

form and/orsize in extinct animals. Even multivariate or volumet-

ricmodels,whichsome authors regardasmoreaccuratethan sim-

plelinear regressions (Bateset al.,2015; Brassey, 2016;Romano&

Manucci,2021),stillrely ondata andunderlyingassumptionsfrom

modern taxa such as soft-tissue distribution and density (Bates

et al., 2009;Bianuccietal.,2023;Campione&Evans,2020;Motani&

Pyenson, 2024).Volumetricmodelsalsorequiresilhouettesorskele-

talreconstructionsasinputdata(Brassey,2016;Henderson,2010;

Motani, 20 01)–outsideofrarecasesinwhich theentire skeleton

isknown–relyingonpre-existingestimatesofbodysize(e.g.,total

length)andform.Optimisationofbodysizeandformestimatesthus

dependsontheselection of appropriate proxies and mathematical

models while acknowledging the intrinsic limitations of estimations

basedondatafromextantspecies.

Inthisreview, weconsiderfourprominentcase studies ofbody

sizeestimationinextinctorganisms,focusingonmarinemegafauna

(Figure 2).Thesecasestudieswerechosenastheyrepresentarange

of body sizes, ecomorphological niches and geological time inter vals.

well as mitigation measures that can ensure the selection of the most appropriate

proxy.Wearguethat theseprecautionary measuresare necessarytomaximisethe

robustnessofreconstructionsin extincttaxafor betterevolutionary and ecological

inferences.

KEY WORDS

allometricscaling,bodyshape,evolution,fossil,morphology,palaeobiology

TAXONOMY CLASSIFICATION

Paleoecology,Phylogenetics,Taxonomy

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GAY FO RD et al .

TAB LE 1 Taxaofunusuallylargesize(1)whichhavebeenthesubjectofattemptstoestimatetheirbodysizeand/orformfrom

fragmentarymaterial,(2)whichhavereceivedasignificantamountofresearchorpopularattentionduetotheirunusualsize,or(3)forwhich

previousestimatesofsize/shapehavebeencontroversial(denotedwithanasterisk).

Higher taxa Example taxa

Cephalopoda:Nautiloidea Endoceras/Cameroceras*, Rayonnoceras

Cephalopoda: Belemnitida Megateuthis

Cephalopoda: Coleoidea Enchoteuthis(‘Tusoteuthis’)*

Arthropoda:Radiodonta Anomalocaris*

Arthropoda:Eurypterida Jaekelopterus*, Pterygotus

Arthropoda:Myriapoda Arthropleura

Arthropoda:Insecta Meganeura*, Meganeuropsis*

Placodermi:Arthrodira Dunkleosteus*, Titanichthys*, Glyptaspis*

Chondrichthyes:Eugeneodontiformes Helicoprion, Edestus, Parahelicoprion*

Chondrichthyes: Orodontiformes Orodus*

Chondrichthyes: Ctenacanthiformes Ctenacanthus*, Saivodus,the‘TexasSupershark’

Chondrichthyes: Lamniformes Megalodon(Otodus megalodon)*

Osteichthyes: Pachycormiformes Leedsichthys*

Osteichthyes: Salmoniformes Oncorhynchus rastrosus

Sarcopterygii Rhizodus*, Hyneria, Mawsonia*

Temnospondyli Prionosuchus*, Eryops,Mastodonsauridae,the‘PreciousofLesotho’

Anura Beelze bufo*

Squamata:terrestrialtaxa megalania(Varanus priscus)*,Barbaturex

Squamata:Serpentes Titanoboa, Vasuki

Squamata:Mosasauridae Mosasaurus*, Tylosaurus

Testudines Stupendemys, Caninemys, Peltocephalus maturin,Meolaniidae,gianttortoises(Megalochelys atlas*)

Crocodyliformes:Thallatosuchia Machimosaurus*, Metriorhynchidae*

Crocodyliformes:Notosuchia Barinasuchus, Kaprosuchus*

Crocodyliformes:stemNeosuchia Aegisuchus*, Sarcosuchus*

Crocodyliformes: Crocodylia Deinosuchus*, Purussaurus*, Mourasuchus*

Ichthyopterygia Cymbospondylus, Shonisaurus*,‘Shastasaurus’ sikanniensis*,Ichthyotitan*,the‘AustColossus’

Sauropterygia Liopleurodon*, Kronosaurus* Pliosaurus*

Pterosauria Pteranodon, Quetzalcoatlus*, Arambourgiana*Hatzegopteryx*

Dinosauria:flightlessAvialae Dinornithidae*,Aepyornithidae,Dromornithidae*,Gastornithidae*,Phorusrhacidae

Dinosauria:volantAvialae Pelagornithidae*,Argentavis*

Dinosauria:Sphenisciformes Anthropornis*,Pachydyptes*,Kairuku

Dinosauria:non-avianTheropoda Many, e.g., Tyrannosaurus, Spinosaurus*,severalAbelisauridae( Abelisaurus*,Ekrixinatosaurus*)

Dinosauria:Sauropoda Many, e.g., Dreadnoughtus*,‘Seismosaurus’*,Futalognkosaurus*,Bruhathkayosaurus*,Maraapunisaurus*

Dinosauria:Ornithischia Many, e.g., Triceratops, Stegosaurus

Synapsida: Dicynodontia Lisowicia*

Mammalia:Dasyuromorphia Thylacinus cynocephalus*,T. p otens*

Mammalia: Diprotodontia Diprotodon, Thylacoleo*, Procoptodon*

Mammalia: Proboscidea Palaeoloxodon*, Mammuthus

Mammalia: Rhinoceratoidea Paraceratherium*, Elasmotherium*

Mammalia: Cetacea Perucetus*, Livyatan*

Mammalia:Hyaenodonta Megistotherium*, Hyainailouros*, Simbakubwa

Mammalia: Carnivora Arctotherium, Arctodus, Smilodon, Megalictis*

Mammalia: Rodentia Josephoartigasia*, Phoberomys*, Telic o my s*,Casteroides

Mammalia: Primates Gigantopithecus*

Note:KeyreferencesforeachtaxonarelistedinTa b le S1 ,wherefurtherdetailsregardingbodysizeestimatesinthesetaxaarealsoprovided.

Asterisks(*)denotetaxainwhichestimatesofbodysize/formhaveprovencontroversial.

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Moreover,thequalityandextentofthefossilrecordofeachofthese

taxa d i f f ermar k e dly,asdo t h eappro a c h e susedt oestima t etheir b o d y

size and form. Otodus megalodon is largely known only from isolated

teethandanincompletevertebralcolumn,anddespitetheexistence

ofmodernrelatives(lamniformsharks),there isdebatesurrounding

thevalidityoftheserelativesasproxies(Sterneset al., 2023, 2024).

Perucetus colossusalsohasmodernrelatives(whales)butisknown

only from vertebrae, ribs and the incomplete pelvis of a single in-

dividual(Bianucci et al.,2023).Bycontrast, Dunkleosteus terrelli is a

Palaeozoicfishthatisalmostexclusivelyknownfromdermalarmour

thatcoveredtheheada ndanteriort runkandhasn omoder nrelative s

(Engelman, 2023b, 2024), and Helicoprion spp., another Palaeozoic

fish,isevenmorechallengingtoreconstruct;notonlydoesithaveno

modern relatives whatsoever but is knownonlyfromisolatedtooth

whorlsofcontentiouspositionandfunction(Karpinsky,1899).Thus,

eachofthesetaxarepresentsaunique‘enigma’inthepalaeontolog-

icalliterature,wherebodysizehasbeenestimatedusingnecessarily

different approaches based on the available data. It is important to

notewhileallofthesecase studies are marinemegafauna,thecon-

cepts and principleswediscuss throughoutthe perspectiveare ap-

plicabletoallextinctanimals(Figure 1; Table 1; Data S1).Weexplore

howandonwhat datathese size estimates were produced andthe

resultingcontroversy in the literature. Subsequently,weusethese

case studies to synthesise broadthematiclimitations in palaeobiol-

ogy and theuse of extant andextinct proxy taxatoestimatebody

size and form i n extinct ani mals, including m athematical , phyloge-

neticandsocialissues.

2 | CASE STUDIES

2.1 | Dunkleosteus terrelli (Placodermi: Arthrodira)

Dunkleosteus terrelli is a large late Devonian arthrodire placoderm,

knownforitsbonyarmourandguillotine-likejaws.However,out-

side of its b ony head and trunk a rmour (Figure 2a), the rest of

its body was composed of perichondrally ossified cartilage. This

material rarely preserves, complicating estimates of body size

and morphology (Carr, 2010; Ferrón et al., 2017). Additionally,

Dunkleosteushasnocloselivingrelativesthatcanbeusedtoin-

terpret its anatomy. Complete remains are known for some smaller

arthrodires(Jobbinsetal.,2022;Miles&Westoll,1968),butthese

FIGURE 1 Examplesofreconstructionsofextinctmegafauna,showingearlyestimatesofbodysize/formnowthoughttobeinaccurate

(greysilhouettes),andmorerecentestimates,thevalidityofwhichremainuncertain(blacksilhouettes).Originalworkandsourcesof

thesereconstructionsarelistedintheDataS1,andwedonotnecessarilyendorseanyparticularreconstructionoverothers.Creditforthe

originalsilhouettesusedtoproducethisfigureareasfollows:GuillameDera,CC01.0(Enchoteuthisbefore),TylerGreenfieldwithinputfrom

DirkFuchs,CC-BY3.0(Enchoteuthisafter),ScottHartman,CC-BY3.0(Seismosaurus),JFStudios,CC0(Pliosauridae),T.K.RobinsonCC-BY

3.0(Mosasaurus),NobuTamura(Josephoartigasiabody),GustavoLecuona(Josephoartigasiahead),bothCC-BY3.0,Andrews(198 5)(Rhizodus),

Pimientoetal.(2024)(Glyptapsis),NobuTamura(modifiedbyT.MichaelKeesey;Beelzebufo),Grangeretal.(1936)(Paraceratheriumbefore),

Larramendi(2015)(Paraceratheriumafter),RussellEngelman,modifiedfromHodnettetal.,2021,CC-BY4.0(Ctenacanthus),ScottHartman,

CC-BY3.0(Machimosaurus),MarkP.WittonandDarrenNaish,CC-BY3.0(Quetzalcoatlus),DalSassoetal.(2005)(Spinosaurusbefore),

TasmanDixson,CC0(Spinosaurusafter),DanNiel,CC0(Argentavis),T.MichaelKeesey,CC0(Gigantopithecus),Antonetal.(20 04)(Megalictis).

JaggedFangDesigns,CC0(Ekrixinatosaurus),FerranSayol,CC0(Mourasuchus,body)andLangston(1965, Mourasuchus,head).

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taxa like ly differed fro m D. terrelli in ecological niche and body

shape(Ferrónetal.,2 017).

Dunkleosteus has been tr aditional ly cited as reach ing 5–10 m

in total length (TL). However, these are generally speculative

estimates that omit key methodological details as to how they

were produced, including what taxa or anatomical elements

were used as proxies, what specimensof Dunkleosteuswereex-

aminedand the measurementsusedtoproduce theseestimates

(see Engelman, 2023b; Ferrón et al., 2017 for details), making

these estimates non-reproducible and highlyquestionable. One

exception was Ferrónetal.(2 017),whichcalculatedtheTLofD.

terrelliusingtheupperjawperimeterofselectlarge,nektonicex-

tant sharks to estimateits caudal fin shape, as their method re-

quiredbodysizeasanindependentpredictorvariable.Thisstudy

assumed m outh and bod y size likely correl ate in fishes be cause

predatorsizeiscorrelatedwithpreysize,whichinturncorrelated

with gap e, meaning mo uth size and bod y size may be indire ctly

linked (Ferr ón et al., 2017). However, this st udy did not test if

sharksandarthrodiresshowedcomparablemouthproportionsor

cross-examinetheaccuracyoftheresultingbodylengthestimates

(Engelman, 2023b; Ferrón et al., 2017). Testing this me thod on

complete arthrodires finds arthrodires have proportionally larger

mouths t han sharks , producing over estimates of T L 2–2. 5 times

the actual value (Engelman, 2023a, 2023b). Traditionally cited

lengths for Dunkleosteusalsorequireahyper-elongatetrunk,with

a head of only ~8%TL(seeFigure 1),andhead–bodyproportions

thataremoreextremethaneveneels.Notonlyarethesepropor-

tionsimplausible,buttheyarealsounlikecompletearthrodiresor

non-anguilliformfishes(inwhichheadlengthisgenerally~17–3 0 % 

TL; Engelman, 2023b).

Becauseoftheinabilityofmouthdimensionstoreliablyestimate

thesizeofarthrodires,Engelman(2023a)attemptedtoestimatethe

size of Dunkleosteusbasedonthecombinedlengthoftheneuro-

cranial a nd branchial reg ions of the head (i.e ., head length m inus

preorbital length; Engelman, 2023a), reas oning that the s caling of

these ar eas with body si ze was likely stro ngly constr ained due to

their function. This study (Engelman, 2023a) selected a variable

basedonhomologouslandmarksbetweenDunkleosteus and a wide

range of extant proxies. It also tested the initial assumption of

correlat ion to ensure that sca ling patter ns were consiste nt across

taxa. Fur thermore, it used complete arthrodires as case studies

to ensure th at the method accu rately predict ed body size in this

FIGURE 2 Fossil(orcast)materialforeachofthefourcasestudies(skullandtrunkarmourfromacastofDunkleosteus terrelli,(a);

tooth whorl from Helicoprionspp,(b);toothfromOtodus megalodon,(c);andvertebrafromPerucetus colossus,(d);respectively),along

withsilhouettesrepresentingreconstructionsofbodysizeandform,wheregreysilhouettesarepastreconstructionsnowthoughtto

beinaccurateandblacksilhouettesarerecentreconstructions,thevalidityofwhichremainsuncertain.Scalebars = 5 cmforfossil/cast

materialand2 mforsilhouettes.Imagecreditsforfossil/castmaterialareasfollows:ArchivalPhotographGEO82014ofcastCMNH5768,

FieldMuseumofNaturalHistory,Chicago,Illinois,USA(a),Helicoprion bessonowiKarpinsky,1899,holotypespecimen,F.N.Chernyshev

CentralScientificResearchGeologicalProspectingMuseum,St.Petersburg,Russia,1/1865(b),Otodus megalodontoothMUSM2093,

Sacaco,MuseodeHistoriaNatural(UNMSM)Peru(c),Perucetus colossusholotypeMUSM3248,MuseodeHistoriaNatural(UNMSM)Peru.

SilhouetteimagesweremodifiedfromimageusedwithpermissionbyYangSong(grey,a)createdbyRussellEngelman(black,a),usedwith

permissionfromWilliamSnyderunderaCCBY-SA4.0licence(b),ormodifiedfromSternesetal.(2024)(c)andBianuccietal.(2023)(d).

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group,suggestingthatthismethodshouldproducereliablesizesfor

Dunkleosteusintheabsenceofcompletespecimens.Thisresultedin

lengthsofonly 3.4–4.1 mfor largeD. terrelli individuals, with even

the upperends of the marginof errorbarely overlapping with the

smallestlengthsinpreviousstudies(Engelman,2023a).Independent

testsbyscalingfromotherarthrodiresproducedsimilarresults,and

thereconstructedbodyshapeforDunkleosteus better agrees with

thecomparativeanatomy of otherarthrodires(e.g., in fin location/

sizerelative toTLandtrunk armourdimensions;Engelman,2023a,

2024).Arthrodires, actinopterygians and chondrichthyansshowed

significant, clade-specific differences in overall body form, with

complete arthrodires exhibiting a much stockier body plan com-

paredtochondrichthyans(Engelman,2023a).

2.2 | Helicoprion spp.: (Chondrichthyes:

Eugeneodontidiformes)

Helicoprion,foundgloballyinPermiandeposits,isarguablythemost

widely recognised Palaeozoic chondrichthyan. Its notoriety stems

from theunique nature ofits spiraliform toothwhorls(Figure 2b),

which constitutepractically the only known remains of thetaxon.

The lack of any r easonable ex tant or ex tinct proxi es to the tooth

whorls of Helicoprion has presented significant difficultiesininfer-

ring its body size and form. For some time af ter the description of

HelicoprionbyKarpinsky(1899),therewas no agreement as to the

position of the tooth whorl on the body of the animal or even its

nature (e.g., dermal spine or oral teeth), making inference of body

sizeorformimpossibl e.AlthoughKarpinsk y(1899)consideredother

interpre tations, he f avoured a locati on of the tooth whor l mostly

externalto the mouthandextendedfromtheupperjaw.However,

basedonexaminationof IMNH (IdahoMuseumofNaturalHistory)

37899,auniquespecimenofH. davisii from the Permian Phosphoria

FormationofIdaho,USA,withremainsofcranialcartilagepreserved,

Bendix-Almgreen(1966)concludedthe toothwhorl was located at

thesymphysisofthelowerjaw,internaltothebuccalcavity,andthat

nosimilartoothwhorlwasintheupperjaw.

Subsequently,Lebedev(2009)madethefirstqua ntitativerecon-

structionofthe bodysizeandshapeofHelicoprion,using(1)extant

odontocetes(toothedwhales)and(2)extincteugeneodontsknown

from nearly completeremains (Caseodus, Romerodus, and Fadenia)

as proxies . The first p roxy was base d on a presumed si milarity in

size, diet (fish and cephalopods)and habitat (pelagic) andthe sec-

ond on phylogenetic proximity.Lebedev's reconstruction featured

an elongated lower jaw, with the tooth whorl placed near the distal

end,andconventionalfusiformfishbodyproportions.Basedonthe

eugeneo dont proxies, Leb edev inferred a hea d length of 2.5–4 .0

times the toothwhorldiameter.An assumption ofa ratio of body

lengt h to head lengt h of 5.0 (conventional f ish body propo rtions)

yieldsabodylength(TL)of12.5–20timesthetooth-whorldiameter.

Foratoothwhorlwithadiameterof 0.56 m(the largestone listed

inTapanila&Pruitt,2013),thiscorrespondstoarangeof7.0–11.2 m

TL. Later examination by Tapanilaetal. (2013) of IMNH 37899by

X-CT(X-raycomputedtomography)showedthatHelicoprion's lower

jaw was shor ter than Lebedev envisioned and that the ratio of the

head length to the tooth-whorl diameter was approximately 2.5

(Tapanilaetal.,2020, figure3), resultinginaninferredbody length

ofapproximately7.0 mTL.

2.3 | Otodus megalodon (Chondrichthyes:

Lamniformes)

The megatooth shark, Otodus megalodon,isani conicextinctel asmo-

branchrepresentedprimarilybygiganticteeth(Figure 2c)commonly

foundfromthemid-MiocenetotheEarlyPliocenenearlyworldwide

(Boessenecker et al.,2 019; Cappetta, 2012; Cooper et al., 2020,

2022; Gott fried et al., 1996; Sternes et al., 2023). The biolog y of

O. megalodon has remained difficult to decipher. Although some

vertebral remains, placoid scales, and fragments of tessellated car-

tilage of O. megalodonhavebeenreported(Bendix-Almgreen,1983;

Leriche, 1926; Shimada et al., 2023), the li mited fossil recor d has

hampered attempts to estimate its true size and to reconstruct

body form.When such attemptsaremade,theextantwhite shark

(Carcharodon carcharias)hasbeenassumedtobealogicalecological

proxyduetoitssimilartoothformandtrophicecologytoO. megalo-

don(Collaretaetal.,2017;Gottfriedetal.,1996).

The most common size estimation method for O. megalodon has

beenextrapolationfromscalingrelationshipsbetweendentalmea-

surementsandtotalbodylengthsinC. carcharias(Perezetal.,2021;

Randall, 1973; Shimada, 2002, 2019).These studiesgenerallysug-

gestamaximum lengthof15–20 mforO. megalodon.Alternatively,

theallometricrelationshipofvertebraldiametersinextantC. carch-

arias(Gottfriedetal.,19 96)hasbeenusedtoextrapolatebodysize

based on incremental growth bands preser ved in a set of vertebral

specimens of O. megalodon,producingalength estimateatbirth of

2 m(Shimadaetal.,2021).

Likewise, the body form of O. megalodon has traditionally been

modelledafterextantC. carcharias(Bendix-Almgreen,1982; Cooper

et al., 2020, 2022;G ottfrie d et al., 1996). This see med logica l es-

peciallyinearlierstudies(Applegate&Espinosa-Arrubarrena,1996;

Gottfriedetal.,1996),duetothesimilarlyserrateddentalmorphol-

ogy,thefossilsharkwasplacedinthegenusCarcharodon(Lamnidae)

with the interpretation that‘C.’ megalodon was the direct ancestor

ofextantC. carcharias.Asofnow,thefossilspeciesisconsideredto

belong to Otodus(Otodontidae)ratherthanCarcharodon (Shimada

et al., 20 17). DespiteC. carcharias and O. megalodon likely not hav-

inganydirectphylogeneticlinkwithinLamniformes(Shimada,2022;

Shimada et al., 2017; Sternes et al., 2023, 2024),theuseofC. carcha-

riasasaproxyhascontinuedbasedontheassumptionthatO. mega-

lodonwasanactive,regionallyendothermic(Ferrón,2017)predator

liketheextantlamnids(Cooperetal.,2020, 2022).

Geochemical evidence has subsequently confirmed that O.

megalodon was a ‘warm-blooded’ shark (Griffiths et al., 2023)

occupyin g a high trophic p osition (Kas t et al., 2022; McCormack

et al., 2022). However, the assumption that O. megalodon must

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haveresembledextantC. carchariashasbeencalledintoquestion.

Supportfortherelationshipbetweenbodyformandthermophysi-

ologyinsharkshasweakened(Dolton,Jackson,etal.,2023; Dolton,

Snelling, et al., 2023; Sternes et al., 2023),andtheabsenceofkeels

onitsscalessuggeststhatO. megalodon was likely not a fast swim-

mer like ex tant lamnids. Add itionally, the total com bined length

of a parti al vertebra l column of O. megalodon from the Miocene

ofBelgium, previously estimated tobefrom a9.2-m-TLindividual

based on comparisonsof vertebral diameters in extant C. carch-

arias(Gottfried etal., 19 96), was measured to be11.1 m(Cooper

et al., 2022).Thisdiscrepancy–thatis,theactualmeasuredlength

ofthe incomplete vertebral column (not considering the head or

caudal fin)beingsubstantiallylongerthantheTLestimateforthis

specimenbasedontheextantC. carcharias(9.2 mTL)–stronglyin-

dicates that O. megalodonwasnotmerelyalargerversionofextant

C. carchariasbutratheraproportionatelyslender,more elongate

shark(Sternesetal.,2024).Theexact bodymorphologyandmax-

imum TL of O. megalodon remain uncer tain, but the implications

aresignificant.NotonlymaytheuseofextantC. carcharias not be

appropriate for deciphering the body form and body size of O. meg-

alodon,buttheobservationalsostronglyindicatesthatallprevious

TLestimatesbased ondental proportions of extant C. carcharias,

which conc luded a maximu m TL of at least 15 m for th e species

(Shimada,2019),maybeunderestimates.

2.4 | Perucetus colossus (Mammalia: Artiodactyla)

Perucetus colossus is a recently described, large-bodied archae-

ocete(stemcetacean)fromthelatemiddleEoceneofPeru(Bianucci

et al., 2023). Thistaxon is only represented by the holotype, con-

sistingof13vertebrae(Figure 2d),4ribs,and therightinnominate.

Perucetus is considered a member of Basilosauridae, the derived

group of ful ly aquatic archa eocetes that may re present the sis ter

group of crow n Cetacea. Perucetus exhibits extreme pachyostosis

and osteosclerosis, traits generally associated with shallow diving in

modernaquaticmammals(Buffréniletal.,2010).

Despite belonging to a clade with modern representatives

(crownCetacea),therearenoclose extantanaloguesforthe large,

serpen tiform body pla n of basilosaurid s. Thus, to recon struct the

body size of Perucetus,Bianuccietal.(2023)utilisedmultipleproxies

includingsirenians and neocetes.Bianuccietal. (2023) firstscaled

upanddilatedadigital3Dmodeloftheskeletonofthebasilosaurid

Cynthiacetus peruvianussuchthatthe volumeof itsbones equalled

that of the corresponding skeletal elements of P. colossus(produc-

ingmultiplemodelstoaccountfortheuncertainpositionofthelat-

ter's ver tebrae and var iable verteb ral count among b asilosaurids),

yieldin g estimates of s keletal leng th and volum e ranging bet ween

~17–20 mand2.9–4.1 m3,respectively.Bodymassvalueswerethen

calculatedfortheP. colossus holotype based on the range of skele-

talfraction(SF)observedinextantmarinemammals,yieldingmini-

mumandmaximumestimatesof85 t(assumingthemeanSFoflarge

Trichechus manatus and the minimum skeletal volume) and 340 t

(assumingtheSFofMesoplodon europaeusandt hemaximumskel eta l

volume),respectively(Bianuccietal.,2023).

Subsequently,Motani and Pyenson (2024) raised severa l criti-

cisms of Bianucci et al. (2023)'s analysis. Forexample, Motaniand

Pyenson(2024)suggested that itwould be impossible to fit 180–

340 t of bio mass (correspon ding to the upper p ortion of Bia nucci

etal. (2023)'srange ofbody mass estimates)into thevolume of a

20 mwhale, withtheir volumetricmethods instead producing esti-

matesof60–114 tusing volumetricmethods.Theyalsoquestioned

Bianuccietal.(2023)'suseofasimpleSFratioasopposedtoanal-

lometricregressionequation,arguingthatacrossmarineandterres-

trialmammals(includingbothneocetesandsirenians),SFappearsto

scalewithpositiveallometryratherthanisometry.Usingregression

equations,MotaniandPyenson(2024)producedestimatesof135–

193 tassuming aneocete-likeSF and 40.0–54.6 t using a sirenian-

likeSF (Motani & Pyenson, 2024).Nevertheless,thisrevisedbody

mass estimate is not free of limitations either, namely, reliance on a

modelcreatedfroma2Dpalaeoartisticreconstructionthatwasnot

depicted in direc t lateral view. This method is by no means intrin-

sically flawedbut is heavilydependent on approximationofthree-

dimensionalbodyproportions.Alternatively,asilhouettecouldhave

beenproducedfromthemodifiedCynthiacetus model presented by

Bianuccietal.(2023),whichcouldhaveyieldedadifferentresult.

3 | WHY ESTIMATING THE BODY

SIZE AND FORM OF EXTINCT ANIMALS

MAT TER S

The body size and form estimates presented in each of the case

studiesdiscussedherehavesignificantconsequencesforourunder-

standing of vertebrate macroevolution, beyond thepalaeoecology

ofthe individualtaxa themselves. Inthe case of Dunkleosteus, the

Devonianwaslongthoughttobeaperiodofexplosivebodysizeex-

pansioninver tebrates,inpart,becauseoftheabruptappearanceof

largeplacoderms(includingDunkleosteus; Dahl et al., 2010 ;Sallan&

Galimberti,2015).However,thesamemethodologythatdownsized

thisiconictaxon (Engelman,2023a)also produceslengths<5 m for

other large Devonian placoderms like Gorgonichthys and Titanichthys.

Other Devonian and early Carboniferous vertebrates like ctena-

canthsandsarcopterygiansappeartohavereachedsimilarmaximal

sizes (Engelm an, 2023a; Jeffer y, 1998 ; Young et al., 2013), imply-

ing that ver tebrates likely did not reach the size of modern marine

megafauna(i.e.,whitesharks,baskingsharks,whalesharksandce-

taceans)until wellintotheCarboniferous(Engelman,2023a),much

laterthan traditionallythought.This is ofgreat importanceforour

understandingofgigantism and bodysizeevolution invertebrates,

aswellasthestructureandfunctionofPalaeozoicecosystems.

Similar insights into macroevolutionary trends can be de-

ciphered from Perucetus, which indicates at least two distinct

periods of cetacean gigantism (Bianucci et al., 2023). Despite

the controve rsy over its we ight, both Bi anucci et al. (2023) a nd

Motani andPyenson(2024)agree that Perucetus was ver y large,

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comparableinsizetomodernphyseteridsandrorqualsandatleast

anorder ofmagnitudeheavierthanthe next largestPalaeogene

whale(Basilosaurus;seeMotani&Pyenson,2024:p.18).Crucially,

Eocenebasilosauridsevolved giant bodysizesincoastalsettings

with high seafloor productivityand globalcoolingratherthan in

thepelagic,open-marinerealmliketheirmodernmysticeterela-

tives(Bianucciet al., 2019).Similarly,alongwiththeriseof apo-

tentialecologicalcompetitor(whiteshark,Carcharodon carcharias:

Boessenecker et al., 2019; McCormack et al., 2022),lateNeogene

global cooling and restructuring of ocean circulation coincides

with the demise of O. megalodon, w hich may have been e xacer-

batedbyitslargesize(Condamineetal.,20 19).

Body size es timates of ext inct tax a also contribu te to our un-

derstanding of trophic dynamics within past ecosystems, as body

size and form are critic al in determining the range of predator and

preyspecieswith whicha species caninteract.DuringthePermo-

Carboniferous,mostlargemarinevertebrateswerechondrichthyans

(Schnetzetal.,2024),manyofwhich(e.g.,Petalodontiformes)can-

not easily be compared to modern chondrichthyans in terms of their

dental a natomy or body sha pe (Ginter et al., 2010). T his included

variouswhorl-toothedeugeneodonts,includingHelicoprion, Edestus

giganteus (Newberry, 1889) and Karpinskiprion ivanovi (Lebedev

et al., 2022), which were among the largestorganismsintheir re-

spective ecosystems. Without reliable estimates of body size in

Helicoprionand related eugeneodonts,it is difficult to reconstruct

thestructureofPermo-Carboniferousmarinefoodwebsordeter-

mineifpatternsofbodysizeevolutioncorrelate withother events

such as the Carboniferous Rainforest Collapse (McGhee, 2018;

Schnetz et al., 2024)orgigantismproposedformarineinvertebrates

(McGhee,2018).

Several s tudies identif ying likely spurious size estim ates have

alsodiscussedtheirimmediatedownstreamconsequenceson our

understanding of evolutionary history (Engelman, 2023a, 2023b;

Forteli us & Kappelman , 1993; G rilo & Delcour t, 2017; Roma no &

Manucci,2021; Rovinsk y et al., 2020).Inparticular,because many

ofthesetaxaexistattheextremes ofthe variationseen in nature,

spurioussizeestimateshavethepotentialtobiasdiscussionsabout

biomechanical and physiological limits of animal size (Witton &

Habib,2010)orpatternsofbodysizeevolutioninevolutionaryhis-

tory (Engelman,2023a, 2023b;Grillo&Delcourt, 2017;Romano&

Manucci,2021). One exampl e of this is estim ating the bod y mass

of large Late Cretaceous azdarchid pterosaurs such as Pterodon

longiceps and Quetzalcoatlus northropi. These are some of the larg-

est known flying organisms and thus provide key information to

discussions of possible biomechanical limits in powered flight. As

notedbyWittonandHabib (2010: p.2)‘[a]ccuratelymodellingthe

size of giant forms is essential to appreciating their flight abilit y as

evenrelativelysmallover-predictionsofwingspansmaytranslateto

consider able over-estima tes of mass and subseq uently inaccur ate

appreci ation of flight pe rformance’. Sever al biomecha nical studi es

concludedthese taxa wereincapable of powered flight, at leastin

part onthe basis of estimatedbody mass (Henderson, 2010; Sato

et al., 2008).However,subsequent research hasshown thatthese

values arelikelyoverestimates and/ortheresult of incorrectmod-

ellingofbodyforminavolumetricmodel (Witton,2008;Witton&

Habib,2010). Alter natively, work into th e launch mecha nics of Q.

northropiassumedflightcapabilityunderabipedal,bird-likelaunch-

ingmodel(Chatterjee&Templin,2004), resultinginanuppermass

estimateof75 kg, thatwould require theanimaltobe nearly 80%

airbyvolume(Witton,2008).Hadextremesizeestimatesforthese

taxa been upheld bysubsequent studies, it would have enormous

consequences for our understanding of flight biomechanics and

macroevolutionarytransitionsinflightcapabilityinallvolanttaxa.

Theissueinsuchcasesisnotthatsizeestimatessometimeshave

to be revise d. This is genera lly a natural con sequence of work ing

with fra gmentar y taxa often m uch larger than p otential compl ete

anatomicalproxies(seebelow).Theissueisthatvariationinsizees-

timatesbet weenstudiesismassive,withestimatesinonestudyfre-

quently half (ortwice) thosepresented inothers(seeDataS1),and

these differences seem to be driven by methodological problems

and data p ractices r ather than tr ue unknowns in es timating bo dy

size and/or form. This results in a potentiallymajor and pervasive

source of error in palaeoecological and evolutionary studies given

that many relyto someextent onbody size/form estimates of ex-

tincttaxa.Furthermore,becausethebodysizeofextinctorganisms

isa quality oftenimmediatelyvisible to the public, extremely large

swings in size estimates reduce public confidence in the ability of

pal ae ontologist stosp eakauthoritati velyaboutextinctlife.Apoten-

tialriskorconsequenceisthatthisphenomenonmayleadtopublic

disillusionmentwithpalaeontologyandanerroneousorunfounded

beliefthatpalaeontologistsdeliberatelyexaggeratethesizeoftheir

subjectsforprestigeinresponsetohigh-profilestudiesrevisingsize

estimates.

4 | LIMITATI ON S

4.1 | Modelling and extrapolation

Themostfundamentalrequirementforpredictingbodysizeand/or

formofanextinctspeciesisthattheproxyaccuratelypredictsbody

size in the fi rst place (Bate s et al., 2009). This mi ght seem trivia l,

butdifferentphysicalfeatures exhibit diverse scaling relationships

acrosstaxa,and theselectionofspecificanatomicalunits tomodel

bodysizerequirescarefulexaminationandabundantdata(e.g.,Field

et al., 2013). Nelso n eta l .(2023)foundthatlimbbonecross-sectional

dimensions (diameters and circumferences), long considered the

strongest predictors of body size among terrestrial vertebrates

(Anderson et al., 1985; Campione& Evans, 2012;Ruff,19 90 ), had

significant,non-randombiasindependent of phylogenybutseem-

ingly correlated withbodyrobustness – a factor that is difficultto

controlformathematicallywithoutcircularlogic.Unfortunately,ex-

istingstudiesoftendonotexplorepossiblesourcesofallometricbias

oruncertainty whenselectingsizeproxies, butassumeacloseand

consistentrelationship withbody sizebetweentheproxyandfocal

taxaapriori(Cooperetal.,2020, 2022; Ferrón et al., 2017;Gottfried

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et al., 1996).This issueis exemplifiedbyinitial bodysizeestimates

for Dunkleosteus, which were based on scaling relationships of the

upperjawinextantsharks(Ferrónetal.,2 017)despitealackofevi-

dence for similar jaw proportions between ar throdires and sharks

(Engelman, 2023b). While post hoc analysis of arthrodire cranial

scaling improved size estimates for Dunkleosteus(Engelman,2023a,

2023b),itisextremelychallengingifnotimpossibletoverifytheva-

lidity ofproposedscalingtrendsin othertaxawithfewor noliving

(or well-p reserved fos sil) relatives, s uch as Helicoprion. Whenever

possible,proposedscalingrelationshipsshouldbetestedempirically

using close relatives of the focal taxon to ensure model reliability

(Engelman,2023b) orcross-testingsize/form estimates usingmul-

tiple proxiesand/orscalingmethods(Bianuccietal., 2023; Motani

&Pyenson,2024).Wherethisisnotpossible,weurgescepticismof

resultingbodysizeandformestimates.

Ano t h erco m m o niss u eise x t r a p o latio n error.Wh e n using r egres -

sionequationstoestimatebodysize,imprecisiontypicallyincreases

asthesizeofanatomicalelementsfromthefocaltaxonextendsbe-

yondthatofthetrainingdata(Batesetal.,2009; Engelman, 2023a;

Schmidt-Nielsen,198 4).Thisisaparticularproblemiftaxaofinter-

est to palaeontologists are significantly larger or smaller than their

nearestextant proxies or occupy sizeranges where only a limited

number ofsimilar-sizedmodern proxiesexist(i.e.,megafauna).This

can be mitigated if taxa in the training data span a wide range of

bodysizes(Campione,2017 ) butsuch widesamples are often not

available . Perhaps, the best examp le of the effect s of extrapola-

tion erro r on body mass es timates can b e seen in the ex tinct ro-

dent Josephoartigasia(Engelman,2023a; Millien, 2008),althoughit

alsoappliestoothertaxa,includingPerucetus(Bianuccietal.,2023;

Motani&Pyenson,2024).

Manysizeestimates run intoproblemswiththe ever-present

spectreofpositiveornegativeallometry(Schmidt-Nielsen,1984),

eitherassuming theiranatomicalproxiesscaleisometricallywith

body size or c alculating t heir estim ates via simple s caling rati os

withaproxytaxon(whichimplicitlyassumesisometry).However,

isometr yistypicallytheexception,nottherule,amongscalingre-

lationships(Raup&Stanley,1978:p.61).Regressionmodelstend

tobe more robustto this kindofbiasduetotheirvariableslope,

whereas simple scaling ratios can be biased by even slight devi-

ations from isometryor if the size proxy chosen does not show

astrong correlation with body size (Grillo & Delcourt, 2017).As

withextrapolati oner ror,samplingawidearr ayofbodysizesinthe

training dataset is one of the best ways to detect positive or neg-

ativeallometry.Bodysizeestimatesshouldalwaysbemadebased

onregressionequationsorvolumetricmodelswheneverpossible.

Estimating body size via simple scaling ratios from one or a few

proxy specimensortaxashould beconsidered as a lastresort if

appropriateregressionmodelsarenotavailable,andtheresulting

sizeand/or form estimates considered verytentative until more

robustestimatesofsizecanbeproduced.

Other issues arise fromthe fact thatmost variables in allome-

tric scaling relationships are logarithmically distributed and thus

log-transformedbefore analyses.Itisoften assumed thatrelation-

ships between variables are completely linearised by log transforma-

tion(Engelman,2022b;Schmidt-Nielsen,1984).However,thisisnot

alwaysthe case,andfurtherinspection has shownsomebiological

relationships previously thought to be log-linearmay,in fact, scale

log-curvilinearly (Bertram & Biewener, 1990 ; Engelman, 2022a;

Knell, 2009; Venditti et al., 2024) with their curvature implying

treating these variables log-linearly may overestimate body size.

This is problematic as the biological significance of log-curvilinear

relationshipsisnotwellunderstood,nordotheirmathematicalcon-

stantshave a ready explanation (Knell, 2009; Manger et al., 1999)

incontrasttolog-linearmodelswhichfollowapowerlaw(Schmidt-

Nielsen,19 84 ). Until we have an improved understanding of non-

linear allometry, the validity of linear approximations to these

allometricrelationships cannot be known.Forthis reason, we sug-

gest future studies at least consider the possibility of non-linear

allometryintheirdatasetsandreportsuspectedlog-curvilinearre-

lationshipsiffound.

Log-transformationcreatesotherissuesinmodelevaluationand

predic tion. Most regre ssion models meas ure the streng th of cor-

relationsbetweenvariables using the coefficientofdetermination

(r2), but for log-trans formed models (e specially ones i ntended for

prediction), r2 is actua lly a poor measu re of relationshi p strengt h.

Coefficientsof determination tendto unilaterally increase asdata

spreadincreases,andlog-transformationexacerbatesthis problem

becaus e it compresses the scatter of data points around the re-

gression line (Smith,1984;VanValkenburgh,199 0),inflatingr2 val-

ues. Thi s means that even lo g-scaled m odels with r2 greater than

0.9 can have poor prediction accuracy in practice (Smith, 198 4;

VanValkenburgh, 1990). For this re ason, percen t error (%PE) and

percent standarderror ofthe estimate (%SEE) are of ten preferred

asmeasures ofpredictive accuracy becausethey directlymeasure

the accuracy of the predicted values (Campione & Evans, 2020;

Engelman, 2022a, 2023a;VanValkenburgh,19 90 ).

Log-transformedregressionequationsalsotendtoproduce un-

reasonably large prediction inter vals, often on the scale of orders of

magnitude.Thisisbecauseantilogtransformationturnsthenormally

distributed residualsof a log-scaled regression equation into non-

normallydistributed(leptokurtotic)residualsonanarithmeticscale

(Bates et al ., 2009; Bert ram & Biewener, 199 0; Engelman, 2023a)

with extremely long ‘tails’ to the resulting distribution. This in

turn results in largeerror barsand substantialuncertaintyin body

size estimates, often beyond what is morphologically plausible.

Phylogeneticcomparativeleastsquaresandvolumetricestimation

methods provide possible mitigation measures, although in both

cases reducederror rangecomesata trade-offwith predictionac-

curacy(Campione,2017; Campione & Evans,2012).Whilethis un-

certa inty is unavoid able, it shoul d be accounted fo r when making

biologicalinferencesaboutpalaeoecology.Allmathematicalmodels

haveassumptionsandlimitations,thevalidityofwhichshouldideally

becarefullyconsideredwhenselectingproxiesfromwhich toesti-

matebodysizeand/orforminextincttaxa.

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4.2 | Incomplete specimens

In most c ases, the bod y size and/or form of ext inct animal s must

beestimatedfromextantproxiesduetothelackofcompletefossil

specimens. At a basic level, it is impossible to confidently and ac-

curatelypredictthebody sizeorformofanextinctorganismwith-

outcompletespecimensasresearchershavenowayofknowingthe

sizeorshapeofmissingelementswithoutrelyingoninferencefrom

proxytaxa.Thisissueaffectseachofthefourcasestudiesdiscussed

here, noneof whichareknownfromcompletespecimens(Bendix-

Almgreen, 1966 ; Bianu cci et al., 2023; Engelman, 2022b; Sternes

et al., 2024; Figure 2). In deed, the fr agmentar y nature of rem ains

used to reco nstruct t he body size and for m of many extinc t taxa

cansubstantiallyincreaseerror.Fragmentaryremainsareoftenfirst

used to estimate the size of some larger or complete morphologi-

calstructure (e.g.,skull),which isinturnused toapproximatetotal

lengt h. These casc ading assumpti ons result in the pr opagation of

errorateachstageofreconstruction(Molnar&Vasconcellos,2016),

furthercomplicatingdownstreamecological,evolutionaryand bio-

mechanical interpretations.

A lack of anato mically comple te specimens also i ncreases the

likelihoodofexistingremainsbeing misinterpretedasbelongingto

different species and/or parts of the body. Errors in body size and

formestimationresultingfromanatomicalmisinterpretationormis-

diagnosis c an be seen in Helicoprion,wheretheconsensusposition

ofthetoothwhorl on thebodyhaschanged on multiple occasions

(Bendix-Almgreen,196 6; Karpinsky,1899).Similarly,extrememod-

ifications in the available vertebrae of Perucetus relative to other

basilosauridspreventapreciseidentificationoftheirpositionwithin

thevertebralcolumn,whichaddsconsiderableuncertaintytobody

size estimations. For Dunkleosteus,lengthsof5–10 mwereat least

partlybasedonaprioriassumptionsofthistaxonexhibitingagreatly

shortenedtrunkarmourcomparedtootherarthrodires,whichwere

nevervalidatedandindeedsubsequentobservationsshoweditwas

likelyincorrect(Engelman,2024).Unfortunately,thelimitationsas-

sociatedwithincompletefossilspecimensaredifficulttoovercome

without new palaeontological evidence. Yet, this issue highlights

that bod y size and/or form estimat es are intrinsic ally uncert ain if

lacking adequatefossil material.Whereverpossible,studies should

take this into consideration and acknowledge the potential for new

palaeontologicalinterpretationsofthefossilspecimensuponwhich

estimations are based.

4.3 | Intraspecific variation

Another important consideration whenselec tingproxies for esti-

mating bodysizeandforminextincttaxais intraspecificvariation.

Ontogeny and sexual dimorphism exert substantial influence on

bothbodysizeandshape (Honeet al., 2016; Mallon, 2017; Motani

et al., 2018; Paiva et al., 2022; Sanchez-Villagra, 2010), and this

needs to be t aken into account w hen reconstr ucting ext inct spe-

cies.Somestudiesuseregressionequationsderivedfromallometric

patternswithinasinglespeciestoproducetheirsizeestimates(e.g.,

Crocodylus porosus and Gavialis gangeticus in Sereno et al., 2001;

Physeter macrocephalus in Lambert et al., 2010; and Carcharodon

carchariasinGottfried etal., 1996), and thisraisesconcerns about

conflating intraspecific patterns of allometry across the growth

curve ofasinglespecieswith true patternsof interspecific allom-

etry in mature individuals (Paiva et al., 2022). Several s tudies on

extinctmegafaunahavenotedthatevenverylargeindividuals‘still

appear to be growingat thetimeofdeath’based on suturalfusion

and bone microstr ucture (Buchy et al., 2003; Evans et al., 2014;

Honeetal.,2016;Lomaxetal.,2024),yetinmanycasesstillappear

tobesexuallymature(Ericksonetal.,2007;Lee&Werning,2008).

This has sometimes led to speculation thattheseorganisms could

reach stilllarger sizesunsampledbythe fossilrecord, butanalter-

nateneeds to beconsideredthat thispatternisaresult of paedo-

morpho sis or peramor phic hypermo rphosis – i.e., de laying sutura l

closure and prolonging features allowing rapid growth well into

adulthood,withgrowthslowingbutnotceasinguponsexualmatu-

rity (Le e & Werning, 2008) a nd cessation on ly occurring wi th se-

nescence –which has been proposed as the mechanism bywhich

theseanimalsachievedsuchspectacularsizesinthefirstplace(Lee

&Werning, 20 08; Lomaxet al., 2018). A goodexampleofthis are

Pliosauridae,whichrarelyexhibitneurocentralfusionevenasadults

(Araújo & Smith, 2023;Knutsen et al., 2012; McHenry,2009) – a

feature ot herwise commo nly used as an indic ator of osteologic al

maturit y in reptiles . This suggest s that some of th ese supposed ly

somaticallyimmatureindividualscouldbeclosetotypicaladultsize

andthattraditionalmarkersofsomaticmaturitymaybelessinform-

ativeformegafauna(Honeetal.,2016).

Where shape estimates come from a small number of re-

mains (e.g., Helicoprion, O. megalodon and Perucetus), life stage

and sex ca nnot be include d as confounding va riables in regr es-

sion and volu metric mod els. It is prac tically im possible to kn ow

the full size r ange of an extin ct species (Ma llon & Hone, 2024;

Sanchez-Villagra, 2010), and we rarelyhave an adequate under-

standingof sexualdimorphisminthesetaxa. Thus,thefewfossil

samplesthatdoexistaresimplytreatedasstandardfortheirspe-

cies or population. Even in therare cases that isolated fossilre-

mainscanbedistinguishedaseitheradultorjuvenile,phenomena

such as pathologic gigantism (e.g., Carboniferous cephalopods,

Manger et al., 1999)andinsulardwarfism(e.g.,Palaeoloxodon and

Europasaurus,Herridge&Lister,2012; Sander et al., 2006) make

this assumption questionable. Similarly, it must be questioned

whether treating the maximum sizes reached by presumably

exceptional individuals as representative of the species in pa-

laeoeco logical stu dies is as inform ative as using the m ore mod-

est averageadult size (Mallon & Hone,2024:p. 8). For example,

MallonandHone(2024)speculatedthatahypothetical15-mand

15-t‘worldrecord’Tyrannosaurus rexwoul db esoslowandrequire

somuchfoodthatitwouldhavetorelyonscavengingorshiftprey

focustosympatrictitanosaurs–neitherofwhichwouldberealis-

ticbehaviourforthespecies.Issuesofontogenyandintraspecific

variationwillcontinuetobeanissueregardlessoftheproxytaxon

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usedbutshouldaccountedforwhenconsideringwhichindividuals

ofthisproxyaretobeusedforsizeandformreconstructions,par-

ticularly where volumetric approaches are used. Ideally, studies

shouldconductroutinesensitivitytestsconsideringmultiplemod-

elsthat accountfor variation in bothontogeneticstageandsex.

Mostimporta nt ly,re searcherssh ouldnotassum et hatsizeorform

reconstructions made froma handful of incomplete remains are

representative of the fullrangeofmorphology seenin an extant

species,orthattheseremainsrepresentthe‘average’morphology.

4.4 | Phylogenetic placement

Whenselecting proxiesforestimating bodysize in extincttaxa,

consideration of the phylogenetic placementof both proxy and

extin ct focal taxo n is vital. Wher e proxies are sele cted on the

basis of phylogenetic similarit y, it is imperative that the phyloge-

neticplacementofbothtaxaiswellresolved,whichisfrequently

notthecase.Issues ofphylogenetic uncertainty are systemic in

palaeobiology(Marjanović&Laurin, 20 07; Reeder et al., 2015).

ThisisexemplifiedbyO. megalodon, where C. carcharias has gen-

erallybeenconsideredthebestmodernproxydespitetheuncer-

tain placement of O. megalodonwithinlamniformsharks(Sternes

et al., 2023, 2024).Atbest, thisphylogeneticuncertaintyraises

doubts aboutthevalidityofspecific proxytaxa and may distort

theresultsofphylogeneticcomparativeanalyseswhicharethem-

selves us ed to estimate bod y size in some studies ( Diniz-Filho

&Nabout, 2009; Paiva et al., 2022;Symonds &Elgar,2013). In

extremecases,phylogeneticuncertaintycouldcloudourunder-

st andin gofhom ologybet wee nt heanato micalun itsth atareused

to predict body size and form, making it impossible to clarif y the

validity of proposed proxies. Of course, proxies are not always

selectedonthebasisofphylogeny.Studiesmayalternativelyseek

tousetaxaassumedtobeconvergentinecologicalhabitsorbody

form(Engelman,2023b; Ferrón et al., 2 017).However,thistoois

problem atic given that th ere is no guarant ee that phylogene ti-

callydisparategroupsshoulddisplaysimilarscalingrelationships

betweenanatomicalfeatures,regardlessoftheperceiveddegree

of morphological convergence. For this reason, we favour the

consideration of phylogeny when selecting appropriate proxy

ta xab uts t res sth atforsuc han app roac ht obe val idrequ ire swe ll-

resolvedphylogeneticplacementofboththeproxyandthestudy

taxon. Ultimately,estimatesofbody sizeand form made in this

way must alw ays be treated wit h caution given t hat perceived

phylogenetic relationships between these taxa are intrinsically

hypotheticalinnatureandsubjecttorevisionupontheinclusion

of new data.

4.5 | Social pressures

While most spurious size/form estimates are likely driven by

some combinationof the factors outlined above (and a general

unawareness of biostatistical best practices), social pressures

and the nature ofresearch academia also have the potential to

influen ce reconstru ctions of body s ize/form in extin ct animals.

Studiesreportingspectacularsizesfororganismsareoftenwidely

readand publicised,which can significantly elevatethework of

early-career researchers and translatetosignificant opportuni-

ties for fu nding and pub lic interest . Some exti nct specie s have

gainedconsiderablemediaattentionasadirectresultoftheirun-

usualsizerelativetomodernanimals(Ferreiraetal.,2024;Head

et al., 2009, 2013; Molnar, 2004; Rinderknecht&Blanco, 2008;

Wroe et al., 2004)andmightotherwise have failedtoappear in

hi g h impactjou r n a l s orrece i v ewidesp r e a d p u blica t t e n t i o nift h e y

weresmaller.Atthesametime,whilejournalsareofteneagerto

publish on studies suggesting spectacular sizes, more modest,

revised estimates arelesslikely to be considered publishableas

theyareunlikelytogarnerbroaderinterest.Therealsoseemsto

beatendencyofhumannaturetooverestimatethesizeofmega-

faunaunless quantitativelymeasured.This iswell-demonstrated

byseveral studieson extant megafaunanoting that even expe-

rienced field biologists tend to overestimate the size of their

subjects(Greer,1974; Molnar, 2004; Randall, 1973; Wood, 1976 ;

Woodward et al., 1995 ).Otherpalaeontologistshavemadesimi-

larobservations.AsnotedbyGrilloandDelcourt(2017:p.83)in

th eirstu dyofa belisau ridthe rop ods,‘th efa c tth atmostpub lished

BL[bodylength;=totallengths]areoverestimatesreinforcesa

statementmadebyTherrienandHenderson(2007)thatthelack

ofcompleteskeletalremainsinlargetheropodsgivesfreecourse

to imagination, that allow researchers to present new specimens

as‘thelargest’,‘theheaviest’,orotherkindofsimilaradjectives’.

Similarly,Fuchsetal.(2020: p. 42) noted previous estimates of

sizeandformintheirstudyorganism(Enchoteuthis)seemedtobe

basedonthe‘hope’(wordingtheirs)ofamorespectacularanimal

ratherthananyfossilevidence.Whileitisunlikelythatthesefac-

tors are ac ting in all or even most cases of controversial size/form

estimates, the current landscape of academia does potentially

encourageoverlygeneroussizeestimates.Consequently,inour

attempt tocoverallpotential influencesonbodysize/formesti-

mates,wewouldberemisstonotmentionthesesocialpressures

as a potential bias.

Several factorsmayalso make researchers reluctanttopublish

modestsizeestimatesofextincttaxa.Researchersmaybereluctant

todownsizespectacularcharismaticmegafaunaforfear thatit will

reduce publicinterestintheir research areaor burn bridges in the

academiccommunity,whichcouldhavedownstreamconsequences

forcollaborations,fundingacquisition oreventheoutcomeofpeer

review. They may a lso fear museu ms may restri ct access to spe c-

imens or otherwise respond poorly to research downsizing their

flagshiptaxon. Furthermore, onemust be aware of backlash from

theever-growingfancommunitiesofprehistoricorganisms(suchas

Dunkleosteus, O. megalodonandtheropoddinosaurs)ontheinter net,

whomayfeelstronglyabout the perceivedappearance oftheir fa-

vourite organisms. None of these concernsare hypotheticals, and

all have happened at one point or another to many palaeobiologists

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GAYFO RD et al .

who study well-known, iconic fossil taxa, including some of those

mentionedinthepresentstudy.Allstudiesshouldbejudgedontheir

scientificmerit throughdebateanddiscourse, through whichpro-

gressiveimprovementstoourunderstandingofextinctanimalscan

be gained.

5 | CONCLUSIONS

All body size and shape estimates of extinct species rely to some

extentonextinctorextantproxies.Theseestimatescanprovideim-

portant ecological and evolutionaryinformationand will continue

todosointhefuture.However,severalimportantlimitationsmust

beconsideredwhenusingsuchanapproach.Theutilityandvalidity

ofa given proxy depends notonly on perceived morphologicalor

phylogen etic relation ships but also o n the qualit y and quantit y of

thefossilrecord, palaeontologists' interpretationoftheirexamined

material, our understanding of ontogeny and sexual dimorphism,

and the degree of phylogenetic uncertainty involved. At a more

fundamental level,thechosenproxyspecies may influencetheva-

lidityofthemathematicalmodellingapproacheschosen.Weargue

that tak ing precaut ionary me asures to addr ess these fa ctors is of

paramo unt importa nce when determi ning which prox y taxa upon

which size and form reconstructions of extinct taxa will be based

andshouldbetreatedasnecessar y.Manyoftheseuncertaintiesare

unavoidablewhendealingwithfragmentaryextincttaxa.However,

whereverpossible,studiesshouldexplicitlyreferencetheselimita-

tions, improving therobustness of theecological and evolutionary

inferences that can be drawn.

AUTHOR CONTRIBUTIONS

Joel H. Gayford: C onceptualizat ion (lead); writi ng – original draf t

(lead); writing – review and editing (lead). Russell K. Engelman:

Conceptualization (supporting); writing – original draft (support-

ing); wri ting – review and edi ting (support ing). Phillip C. Sternes:

Conceptualization(supporting);writing–originaldraft(supporting);

writing–reviewandediting(supporting).Wayne M. Itano:Wr iting–

originaldraft(supporting);writing–reviewandediting(supporting).

Mohamad Bazzi:Writing–originaldraft(supporting);writing–re-

viewandediting(supporting).Alberto Collareta:Writing– original

draft(supporting);writing–reviewandediting(supporting).Rodolfo

Salas- Gismondi:Writing–originaldraft(supporting);writing–re-

view and editing (supporting). Kenshu Shimada:Conceptualization

(supporting);writing– original draft (supporting); writing – review

andediting(supporting).

ACKNOWLEDGEMENTS

Theauthors wish to thank the following people for discussionson

thebody size inextinct vertebrates:RKE:J.Cisneros,H.G. Ferrón,

N.Gardner,M.Greif,M.B.Habib,R.Hawley,C.Hays,A.L.S.Paiva,J.

PardoandR.Shell;AC:E.Amson,O.LambertandG.Bianucci.The

authorsalsowish to thankthetwo anonymous reviewers for their

commentsthatgreatlyimprovedthequalityofthismanuscript.

FUNDING INFORMATION

TheresearchofACissupportedbyagrantfromtheItalianMinistero

dell'UniversitàedellaRicerca(PRINProject2022MAM9ZB).

CONFLICT OF INTEREST STATEMENT

Theauthorsdeclarethattheresearchwasconductedintheabsence

ofanycommercialorfinancialrelationshipsthatcouldbeconstrued

as a potential conflict of interest.

DATA AVA ILAB ILITY STATE MEN T

Nodatasetsweregeneratedorusedinthisstudy.

ORCID

Joel H. Gay ford https://orcid.org/0000-0002-0839-3940

Russell K. Engelman https://orcid.org/0000-0002-9988-7427

Phillip C. Sternes https://orcid.org/0000-0001-7223-3725

Wayne M. Itano https://orcid.org/0000-0002-9709-2436

Mohamad Bazzi https://orcid.org/0000-0002-9495-0781

Kenshu Shimada https://orcid.org/0000-0001-7836-809X

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