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Research

Cite this article: Bates KT, Falkingham PL,

Macaulay S, Brassey C, Maidment SCR. 2015

Downsizing a giant: re-evaluating

Dreadnoughtus body mass. Biol. Lett. 11:

20150215.

http://dx.doi.org/10.1098/rsbl.2015.0215

Received: 18 March 2015

Accepted: 18 May 2015

Subject Areas:

biomechanics, evolution, palaeontology

Keywords:

Dreadnoughtus, body mass, modelling,

scaling equations

Author for correspondence:

Karl T. Bates

e-mail: k.t.bates@liverpool.ac.uk

Electronic supplementary material is available

at http://dx.doi.org/10.1098/rsbl.2015.0215 or

via http://rsbl.royalsocietypublishing.org.

Palaeontology

Downsizing a giant: re-evaluating

Dreadnoughtus body mass

Karl T. Bates1, Peter L. Falkingham2, Sophie Macaulay1, Charlotte Brassey3

and Susannah C. R. Maidment4

1

Department of Musculoskeletal Biology, University of Liverpool, Duncan Building, Daulby Street,

Liverpool L69 3GE, UK

2

School of Natural Sciences and Psychology, Liverpool John Moores University, James Parsons Building,

Bryon Street, Liverpool L3 3AF, UK

3

Faculty of Life Sciences, University of Manchester, Manchester M13 9PL, UK

4

Department of Earth Science and Engineering, Imperial College, South Kensington, London SW7 2AZ, UK

PLF, 0000-0003-1856-8377

Estimates of body mass often represent the founding assumption on which bio-

mechanical and macroevolutionary hypotheses are based. Recently, a scaling

equation was applied to a newly discovered titanosaurian sauropod dinosaur

(Dreadnoughtus), yielding a 59 300 kg body mass estimate for this animal.

Herein, we use a modelling approach to examine the plausibility of this mass

estimate for Dreadnoughtus. We find that 59 300 kg for Dreadnoughtus is

highly implausible and demonstrate that masses above 40 000 kg require

high body densities and expansions of soft tissue volume outside the skeleton

several times greater than found in living quadrupedal mammals. Similar

results from a small sample of other archosaurs suggests that lower-end mass

estimates derived from scaling equations are most plausible for Dreadnoughtus,

based on existing volumetric and density data from extant animals. Although

volumetric models appear to more tightly constrain dinosaur body mass, there

remainsa clear need tofurther supportthese models with more exhaustive data

from living animals. The relative and absolute discrepancies in mass pre-

dictions between volumetric models and scaling equations also indicate a

need to systematically compare predictions across a wide size and taxonomic

range to better inform studies of dinosaur body size.

1. Introduction

Sauropod dinosaurs include the largest terrestrial animals to have ever evolved,

and mass properties are regarded as a crucial component of their functional,

behavioural and evolutionary dynamics [1]. Recently, Lacovara et al. [2] descri-

bed a gigantic, near-complete titanosaurian sauropod, Dreadnoughtus schrani,

from Argentina. These authors used a scaling relationship between long bone

(femoral plus humeral) circumference and body mass [3] to derive a mass esti-

mate of 59 300 kg for the holotype of Dreadnoughtus. This scaling equation is

well supported statistically in living tetrapods and to date has been used to esti-

mate the body mass of extinct taxa to facilitate studies of physiology and growth

(e.g. [4]) and macroevolutionarydynamics [1]. However, the mass estimate seems

high given that in overall skeletal proportions Dreadnoughtus only marginally

exceeds those of near-complete specimens of other sauropods (e.g. Apatosaurus

and Giraffatitan) whose masses have been estimated at 25 –35 000 kg by various

methods (e.g. [3,5]). In this paper, we use a digital three-dimensional skeletal

model and volumetric reconstructions to directly examine the plausibility of the

&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

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59 300 kg mass estimate for Dreadnoughtus,andsubsequently

comment upon the use of scaling equations to estimate dinosaur

body mass.

2. Material and methods

A digital model of the Dreadnoughtus skeleton from Lacovara et al.

[2] was used as a basis for a three-dimensional volumetric model

(figure 1). For comparative purposes, we also modelled six

extant taxa (three birds, two crocodilians and one lizard) and

two other large sauropods using identical methods: Giraffatitan

brancai, based on a laser scan of MB (Museum fu

¨r Naturkunde,

Berlin, Germany) SII from our previous study [5], and Apatosaurus

louisae, based on a new three-dimensional model of CM (Carnegie

Museum, USA) 3018 generated using photogrammetry [6]. Each

three-dimensionalskeletal model was posed in a standard ‘neutral’

posture, with the tail and neck extending horizontally and the

limbs in a fully extended, vertical position (figure 1). Models

were then divided into the following body segments: head, neck,

‘trunk’ (thorax and limb girdles), tail, thigh, shank, foot, humerus,

forearm and hand.

The holotype of Dreadnoughtus is missing most of the cervical

vertebrae, as well the manus, skull and distal tip of the tail. Our

convex hulling approach [5] to volumetric reconstruction involves

tight-fitting three-dimensional convex polygons to each body seg-

ment. As the extent of an object’s convex hull is dictated solely by

its geometric extremes, we were able to minimize the amount of

skeletal reconstruction in our model (electronic supplementary

material, figure S1). For the hand and skull, we used photo-

grammetric models of these elements from Rapetosaurus (FMNH

PR 2209), another titanosaur, and re-scaled them using the recon-

struction in Lacovara et al. (fig. 2 in [2]). To allow convex hulling to

connect the ‘trunk’ and neck segments, we duplicated the ninth

cervical vertebra preserved in the specimen and placed its pos-

terior surface above the most anterior point of pectoral girdle at

a height consistent with the position of the preserved dorsal ver-

tebrae. An additional 10% was added to the distal tail using the

reconstruction of Lacovara et al. [2] as a guide (electronic sup-

plementary material, figure S1). In the electronic supplementary

material, we provide extensive sensitivity tests of our skeletal

(a)

(b)

(d)

(c)

Figure 1. Dreadnoughtus three-dimensional skeletal model and the (a) convex hull, (b) plus 21%, (c) maximal and (d) scaling equation mass volumetric recon-

structions in lateral, oblique and aerial views. Black structures are respiratory volumes. (Online version in colour.)

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reconstruction procedure (electronic supplementary material,

figures S1– S8).

The minimum convex hull volume for each skeletal body seg-

ment was calculated using the MATLAB (www.mathworks.com)

qhull command [5,8]. The total minimum convex hull volume pro-

vides the minimum volume estimate for each animal, and a

baseline for our sensitivity analysis in which we generated three

further models. In the first model, the minimal convex hulls were geo-

metrically expanded by 21%, following a previous study in which

live body mass was estimated to have been on average 21% greater

than that calculated from minimum convex hulls for a range of

extant mammals [5]. We subsequently generated a ‘maximal mass

model’ in which the volume of the trunk segment was increased by

50% and those of all other segments by 100%. Finally, we expanded

the minimum convex hull model of Dreadnoughtus by the amount

required to match the total body masses predicted by the scaling

equation of [3]. For the sauropod models, body segments were

given an initial density of 1000 kg m

23

.Zero-densityrespiratory

structures in the head, neck and ‘trunk’ segments were reconstructed

and the volumes of these structures subtracted from their overall seg-

ment volume, as in previous volumetric studies of dinosaurs [7,9,10].

Homogeneous body densities were used for the extant taxa, based on

published values for crocodiles and chickens [10].

3. Results

The convex hull volume reconstruction of Dreadnoughtus

results in a total body volume of 26.910 m

3

(figure 1aand

table 1). Expanding this minimum convex hull volume by

21% raises the whole-body volume to 32.534 m

3

(figure 1b),

while the volume of our maximal model is 43.016 m

3

(figure 1c). Deducting the volume of our reconstructed

Table 1. Mass property data for convex hull reconstructions of Dreadnoughtus,Apatosaurus and Giraffatitan, and summary of whole-body mass data from

different model iterations.

Dreadnoughtus Apatosaurus Giraffatitan

convex hull

volume

(m

3

)

density

(kg m

23

)

mass

(kg)

volume

(m

3

)

density

(kg m

23

)

mass

(kg)

volume

(m

3

)

density

(kg m

23

)

mass

(kg)

body segments

head 0.033 1000 33.49 0.02 1000 23.46 0.06 1000 59.45

neck 3.110 1000 3109.99 2.62 1000 2615.16 2.46 1000 2461.00

trunk 20.382 1000 20 381.96 20.12 1000 20 187.65 19.85 1000 19 850.92

tail 1.011 1000 1011.35 1.86 1000 1861.20 0.78 1000 774.76

humerus 0.186 1000 186.08 0.23 1000 232.34 0.30 1000 298.78

forearm 0.097 1000 97.36 0.10 1000 103.01 0.16 1000 160.67

hand 0.024 1000 24.11 0.03 1000 25.96 0.09 1000 85.98

humerus 0.186 1000 186.08 0.28 1000 275.31 0.30 1000 298.78

forearm 0.097 1000 97.36 0.10 1000 103.01 0.16 1000 160.67

hand 0.024 1000 24.11 0.03 1000 25.96 0.09 1000 85.98

thigh 0.246 1000 246.13 0.35 1000 351.27 0.29 1000 294.19

shank 0.110 1000 109.86 0.21 1000 208.57 0.19 1000 193.06

foot 0.042 1000 41.91 0.08 1000 84.62 0.04 1000 35.69

thigh 0.246 1000 246.13 0.35 1000 351.27 0.29 1000 294.19

shank 0.110 1000 109.86 0.21 1000 208.57 0.19 1000 193.06

foot 0.042 1000 41.91 0.08 1000 84.62 0.04 1000 35.69

axial total 25.50 1000 24 536.80 24.62 1000 24 687.47 23.15 1000 23 146.13

hind limb total 0.796 1000 795.80 1.289 1000 1288.92 1.046 1000 1045.88

fore limb total 0.614 1000 615.09 0.722 1000 722.62 1.092 1000 1090.87

whole body 26.91 1000 25 947.68 26.63 1000 26 699.01 25.28 1000 25 282.88

respiratory structures

head 0.003 1000 3.43 0.001 1000 0.99 0.0036 1000 3.60

neck 4.30 1000 4303.67 4.60 1000 4602.86 5.00 1000 5000.39

trunk 0.49 1000 486.48 0.29 1000 291.95 0.33 1000 332.54

model iteration

minimum

convex hull

26.91 821.9 22 117.98 26.63 818.8 21 803.21 25.284 788.8 19 946.35

plus 21% model 32.53 852.7 27 741.68 32.26 850.5 27 363.56 30.54 825.2 25 204.65

maximal model 43.02 888.6 38 224.57 43.08 886.4 38 187.23 40.40 867.9 35 060.42

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respiratory structures from each of these models yields total

body masses of 22 117, 27 741 and 38 225 kg for the three

model iterations. These data and data from equivalent

models of Apatosaurus and Giraffatitan (figure 2a,b)areshown

in table 1, while the data from extant taxa are tabulated in the

electronic supplementary material (tables S1– S6, and figures

S8 and S9). Convex hull volumes are available in the electronic

supplementary material.

4. Discussion and conclusion

The mass of Dreadnoughtus was estimated at 59 300 kg using

the raw bivariate predictive equation of Campione & Evans

[3]. The masses of our three volumetric reconstructions

of Dreadnoughtus (figure 1a–cand table 1) are equivalent to

37, 47 and 64% of the 59 300 kg scaling equation mass.

The ‘average per cent prediction error’ from the bi-variate

equation gives a minimum mass of 44 095 kg (5780 kg or 15%

higher than our ‘maximal’ model) and a maximum mass of

74 487 kg (36 262 kg or 95% higher than our ‘maximal’

model). The ‘95% prediction interval’ from the equation

yields a range of 32 000– 109 000 kg for Dreadnoughtus, which

overlaps with model estimates (figure 2).

Convex hulling provides a close, objective approximation of

the body volume defined by a skeleton alone [5,8]. A volume

2.38 times larger than that of our convex hull model is required

for Dreadnoughtus to achieve the mean or ‘best-estimate’ scaling

equation mass of 59 300 kg, using our estimates for the size of

respiratory structures (figure 1d). This represents an expansion

more than 6.5 times greater than the average value found in a

sample of quadrupedal mammals spanning major taxonomic

groups [5]. This 2.38 times expanded model (figure 1d)hasa

bulk density of 925 kg m

23

, which is higher than any presen-

tly published estimate for sauropods (range 791– 900 kg m

3

;

electronic supplementary material, table S7). If lower-end

estimates of 800 kg m

23

for sauropod density [7] are correct,

then achieving a body mass of 59 300 kg for Dreadnoughtus

would require body and respiratory volumes of 74.125 m

3

and 14.825 m

3

, respectively, the latter representing a 310%

expansion of our respiratory volumes (figure 1). Filling the

entire ribcage with a zero-density respiratory structure (elec-

tronic supplementary material, figure S7), which is obviously

highly implausible, only produces a 212% increase in respirat-

ory volume. It is clear from our model that bulk densities as

low or approaching 800 kg m

3

cannot be reconciled with a

total body mass of 59 300 kg given the skeletal proportions of

Dreadnoughtus and the space available within the ribcage for

low-density respiratory structures.

Comparison of mass predictions from volumetric recon-

structions of near-complete skeletons of Apatosaurus and

Giraffatitan (figure 2) to the mean scaling equation masses, pro-

duces a qualitatively similar result: scaling equation mass

predictions exceed those of our maximal models (figure 2c,d).

The disparity between the two approaches increases further if

the whole-body densities of these models are set to lower-end

20 000

40 000

60 000

120 000

80 000

100 000

body mass (kg)

Apatosaurus DreadnoughtusGiraffatitanApatosaurus DreadnoughtusGiraffatitan

95PI

PPE

95PI

PPE

95PI

PPE

95PI

PPE

95PI

scaling equation convex hull model plus 21% model maximal model

PPE

95PI

PPE

(a)(b)

(d)(c)

Figure 2. Comparison of skeletal proportions and convex hull volumes for Apatosaurus (top), Dreadnoughtus (middle) and Giraffatitan (bottom) in (a) dorsal and

(b) lateral views. Comparison of mass predictions from the models in this study to masses derived from the scaling equation [2], with (c) model mass and density

calculated using reconstructed zero-density respiratory structures, and (d) density artificially set to 800 kg m

23

[7]. The positive error bar on our maximal models

represents the mass predicted by expanding convex hull volumes by the highest exponent (1.91) for mammals [5] and archosaurs to date. The ‘PPE’ error bars on

scaling equation outputs represent the average ‘per cent prediction error’, whereas ‘95PI’ error bars represent the ‘95% prediction interval’.

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estimates for sauropods (800 kg m

23

[7]) rather than predicting

density by inclusion of respiratory structures. In the case of

both Apatosaurus and Giraffatitan, there is clear overlap between

the lowest scaling equation estimates and our maximal models,

although as with Dreadnoughtus there remains no overlap

between the lowest scaling equation masses and those derived

from the upper bounds of the mammalian convex hull

expansion exponent (figure 2).

Convex hull volumes for extant taxa produced here

required scaling exponents of between 1.18 and 1.91 (electronic

supplementary material, tables S1– S6, and figures S8 and S9)

to reach actual measured body masses, with three animals

(American alligator 1.69; guineafowl 1.91; leghorn chicken

1.87) requiring exponents greater than that applied in our

‘maximal’ models (figure 1). However, increasing convex

hull volume by 2.38, as required for our reconstruction of

Dreadnoughtus to reach the mean scaling equation mass, results

in substantial mass overestimates for all modelled extant

taxa (23– 102% overestimates; see electronic supplementary

material, tables S1–S6).

Our analysis emphasizes a number of important points that

should be considered in future studies. Firstly, it is vital

that uncertainties and likely error magnitudes are explicitly

acknowledged in mass estimates derived from all methods,

including scaling equations. Our analysis also reveals that the

higher range estimates predicted by bivariate scaling equations

[3] appear to be highly incompatible with volumetric models

that are based directly on currently available volume and den-

sity data from living vertebrates ([5]; electronic supplementary

material, tables S1–S6). Indeed, in the case of Dreadnoughtus,

the mean, and perhaps even some lower-end, scaling equa-

tion estimates appear to be implausible based on current

data (figures 1 and 2). The high scaling equation mass for

Dreadnoughtus also appears to result in a discrepancy in relative

mass predictions between the modelled sauropods; our convex

hull volumes (which providea close approximation of the body

volume defined by the preserved skeleton) of Apatosaurus

and Giraffatitan represent 0.9 and 0.985 that of Dreadnoughtus,

which appears congruent with the overlap in gross linear

body proportions (electronic supplementary material,

figure S11). By contrast, mean scaling equation mass predic-

tions for Apatosaurus and Giraffatitan are 0.57 and 0.70 that of

Dreadnoughtus (figure 2). While differences in skeletal : extra-

skeletal dimensions should be expected [3], even in relatively

closely related taxa (electronic supplementary material, tables

S1–S6) it seems unlikely that differences in skeletal proportions

of these three sauropods (figure 2; electronic supplemen-

tary material, figure S11) are sufficient to account for the

20–25 000 kg difference in body mass predicted by the scaling

equation. Thus, even physiological and macroevolutionary

studies that use relative mass values or distribute taxa into dis-

crete mass ‘categories’ based on scaling equation estimates

should take the maximum range of values or error inherent

in these equations into account.

Recently, a similar pattern of divergence between volu-

metric and linear-based mass estimates was found for an

exceptionally complete Stegosaurus skeleton [8]. The authors

attributed this discrepancy to the ontogenetic status of the

individual. Certain skeletal features may indicate that the

Dreadnoughtus holotype was still growing at the time of

death [2]. As an organism’s body proportions change with

age, the application of a scaling equation derived from

modern adult skeletons to the limb bones of a sub- or

young adult may be erroneous. At least some of the inconsis-

tency we find here between mass estimation techniques may

therefore be due to the ontogenetic stage of the specimen.

Given the absence of confirmed ‘adult’ skeletal material for

Dreadnoughtus however, it would be challenging to account

for this phenomenon.

Estimating the mass of extinct animals is challenging [3,5,

8–10]. By directly using the determinates of mass (volume

and density) and maximizing skeletal evidence, volumetric

approaches allow inherent uncertainties in mass predictions to

be explicitlyassessed (figures 1 and 2) and plausiblelimits estab-

lished based on data and models of extant taxa. Our analysis

reveals the importanceof extending current analyses of dinosaur

body mass i n two ways; first and fo remost by addition of further

volumetric and density data on living taxa in order to more

tightly constrain maximum plausible values for extinct animals.

Second, a systematic comparison of dinosaur mass predictions

from modelling and scaling equations, across a wide taxonomic

and size range, is needed to identify and explain discrepancies

between the two approaches (figure 2). Such a study would

not only lead to more informed estimates of dinosaur body

mass, but could also shed light on musculoskeletal adaptations

for large body size in different dinosaur lineages.

Data accessibility. Convex hull models are downloadable from Dryad

(http://dx.doi.org/10.5061/dryad.t5606).

Authors’ contributions. K.T.B., S.C.R.M., C.A.B. and P.L.F. designed the

experiments; K.T.B., S.M. and P.L.F. collected the data; K.T.B.,

C.A.B, S.C.R.M. and S.M. analysed the data; all authors contributed

to the manuscript.

Competing interests. The authors declare that they have no competing

interests.

Funding. K.T.B. and S.M. acknowledge funding from the Adapting to

the Challenges of a Changing Environment (ACCE) NERC doctoral

training partnership.

Acknowledgements. Nicola

´s Campione and two other anonymous

reviewers are thanked for their comments, which greatly improved

the paper.

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