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46 ReferencesHurlburt, G. R., R. C. Ridgely, and L. M. Witmer. In press. Relative size of brain and cerebrum in Tyrannosaurus rex: an analysis using brain-endocast quantitative relationships in extant alligators; pp. 134-154 in J. M. Parrish, M. Henderson, P. J. Currie, and E. Koppelhus (eds.), Origin, Systematics, and Paleobiology of the Tyrannosauridae. Northern Illinois University Press.
Authors and Editors
Abstract
Brain and cerebrum mass are estimated from endocasts of three tyrannosaurid taxa (Tyrannosaurus rex, Gorgosaurus, and Nanotyrannus) using morphological and quantitative brain-endocast relations in a size series of sexually mature alligators (Alligator mississippiensis). The alligator size series (N = 12) ranged from the smallest sexually mature size to the larg- est size commonly encountered. Alligator brain mass (MBr) increased regularly with increasing body mass, while the ratio of brain mass to endocast volume (MBr:EV) declined regularly from 67 percent to 32 percent. The ratio of cerebrum mass to cerebrocast was 38 percent in the largest alligators and regularly exceeded the MBr:EV ratio by 5.6 percent. For estimates from endocasts of non-avian dinosaurs of unknown sex, a MBr:EV ratio of 37 percent was used, the mean of the ratio of the largest male and female alligators. A corresponding 42 percent ratio was used for the cerebrum-cerebrocast ratio.
Relative brain size was measured as Encephalization Quotients (EQs) based on brain-body relations in extant non-avian reptiles (REQs) and birds (BEQs). Tyrannosaurus rex has the relatively largest brain of all adult non-avian dinosaurs, excepting certain small maniraptoriforms (Troodon, Bambiraptor, and Ornithomimus), which are well within the extant bird relative brain size range. The relative brain size of T. rex is within the range of extant non-avian reptiles and, at most, 2 standard deviations (SDs) above the mean of non-avian reptile log REQs, which are normally distributed. Gorgosaurus REQs overlapped the lower end of the T. rex. Log BEQs of all
theropods, excepting small maniraptori- forms, were well below the range of extant birds. Nanotyrannus log REQs were anomalously high for an adult, but the difference between Nanotyrannus log REQs and T. rex values paralleled the difference between log REQs of the smallest subadult and largest alligators. Nanotyrannus cerebrum:brain ratios were also consistent with those of an older
juve nile or youngest subadult. Cerebrocast:endocast ratios of the three T. rex endocasts ranged from 41.1 to 43.5 percent, and cerebrum mass:brain mass (MCb:MBr) ratios range from 47.5 to 49.53 percent, more than the lowest ratios for extant birds (44.6 percent) but very close to ratios (45.9–47.9 percent) typical of the smallest sexually mature alligators. In Carcharodontosaurus saharicus, these ratios were 37.1 percent and 42.1mpercent, respectively, the latter essentially identical to actual MCb:MBr ratios (40.76–42.91 percent) of the two largest alligators. Although the relative brain size of Carcharodontosaurus (SGM-Din 1), was approximately
two thirds that of T. rex, the MCb:MBr ratio of the former was only 5.5–7.5
percent less than that of T. rex.
134
6.1. Left lateral view of endo-
cranial cast of wild Alligator
mississippiensis. Skull length
34.3cm, estimated body
length, 2.6m. Scale bar equals
1cm.
©2013 by Indiana University Press. All rights reserved.
135
6
Relative Size of Brain and Cerebrum in
Tyrannosaurid Dinosaurs: An Analysis
Using Brain-Endocast Quantitative
Relationships in Extant Alligators
Grant R. Hurlburt, Ryan C. Ridgely, and Lawrence M. Witmer
Brain and cerebrum mass are estimated from endocasts of three tyran-
nosaurid taxa (Tyrannosaurus rex, Gorgosaurus, and Nanotyrannus) using
morphological and quantitative brain-endocast relations in a size series
of sexually mature alligators (Alligator mississippiensis). The alligator size
series (N = ) ranged from the smallest sexually mature size to the larg-
est size commonly encountered. Alligator brain mass (MBr) increased
regularly with increasing body mass, while the ratio of brain mass to
endocast volume (MBr:EV) declined regularly from percent to
percent. The ratio of cerebrum mass to cerebrocast was percent in the
largest alligators and regularly exceeded the MBr:EV ratio by . percent.
For estimates from endocasts of non-avian dinosaurs of unknown sex, a
MBr:EV ratio of percent was used, the mean of the ratio of the largest
male and female alligators. A corresponding percent ratio was used for
the cerebrum-cerebrocast ratio.
Relative brain size was measured as Encephalization Quotients
(EQs) based on brain-body relations in extant non-avian reptiles (REQs)
and birds (BEQs). Tyrannosaurus rex has the relatively largest brain of
all adult non-avian dinosaurs, excepting certain small maniraptoriforms
(Troodon, Bambiraptor, and Ornithomimus), which are well within the
extant bird relative brain size range. The relative brain size of T.rex is
within the range of extant non-avian reptiles and, at most, standard
deviations (SDs) above the mean of non-avian reptile log REQs, which
are normally distributed. Gorgosaurus REQs overlapped the lower end
of the T.rex. Log BEQs of all theropods, excepting small maniraptori-
forms, were well below the range of extant birds. Nanotyrannus log REQs
were anomalously high for an adult, but the difference between Nano-
tyrannus log REQs and T.rex values paralleled the difference between
log REQs of the smallest subadult and largest alligators. Nanotyrannus
cerebrum:brain ratios were also consistent with those of an older juve-
nile or youngest subadult. Cerebrocast:endocast ratios of the three T.rex
endocasts ranged from . to . percent, and cerebrum mass:brain
mass (MCb:MBr) ratios range from . to . percent, more than
the lowest ratios for extant birds (. percent) but very close to ratios
(.–. percent) typical of the smallest sexually mature alligators. In
Abstract
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Hurlburt, Ridgely, and Witmer
136
Carcharodontosaurus saharicus, these ratios were . percent and .
percent, respectively, the latter essentially identical to actual MCb:MBr
ratios (.–. percent) of the two largest alligators. Although the rela-
tive brain size of Carcharodontosaurus (SGM-Din ), was approximately
two thirds that of T.rex, the MCb:MBr ratio of the former was only .–.
percent less than that of T.rex.
Endocasts (endocranial casts) are natural or articial casts made from
the endocranial (or brain or cranial) cavity of vertebrates, or they exist as
virtual endocasts produced by laser or X-ray computed tomography (
scans). The external morphology of an endocast corresponds to the ex-
ternal surface of the dura mater, of which the surface topography reects
contained sinuses and underlying blood vessels.
Excepting species in which the brain lled the cranial cavity, the
endocasts of non-avian dinosaurs strongly resemble those of crocodil-
ians in general proportions and specic anatomical features. Among
non-avian dinosaurs, the brain apparently lled the cranial cavity in the
following taxa: pachycephalosaurs, small theropods, Archaeopteryx, and
the hypsilophodont Leaellynasaura (Russell ; Hopson ; Nicholls
and Russell ; Rich and Vickers-Rich ; Currie and Zhao ;
Osmólska ; Evans ). This is inferred because the skull surface,
and thus the corresponding endocast, reproduces the contours of the
gross brain divisions (cerebrum, midbrain, cerebellum) and, in some
cases, the blood vessels of the brain surface, as in extant birds (Iwaniuk
and Nelson ), pterosaurs (Hopson ; Witmer et al. ), and
most mammals (Hurlburt , and references cited therein). In most
other dinosaurs, the endocranial surface does not bear impressions of
brain divisions or the cerebral (vs. dural) blood vessels, indicating that the
brain either did not ll the endocranial cavity or, at most, contacted the
endocranial surface at the lateral poles of the cerebrum, as in hadrosaurs
(Evans ). These endocasts resemble those of extant crocodilians,
in which the brain does not ll the cranial cavity (Hopson ). In the
largest alligators, the only brain parts that contact the endocranial walls
are the lateral poles of the cerebrum (Hurlburt, unpublished results).
This resemblance makes endocasts of crocodilians excellent models for
the brain-endocast relationship in most dinosaurs.
Brain-Endocast Relations in Extant Non-avian Reptiles
Brain volume traditionally has been estimated for non-avian reptiles using
a brain-mass:endocast volume ratio (MBr:EV) of .; that is, the brain
occupies percent of the brain cavity. This ratio is based on an observa-
tion of the Sphenodon brain (Dendy ) and the MBr:EV ratio in one
Iguana specimen (Jerison ). Although a very rough approximation
(and one re-evaluated here), it provided a productive starting point (Hop-
son , ). Larsson et al. () made an important contribution in
Introduction
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Size of Brain and Cerebrum in Tyrannosaurids
137
analyzing relative size of the brain and cerebrum in several theropods
and comparing them to non-avian reptiles and birds. Their approach
made use of laser-scan data and analyzed brain and cerebrum size in a
phylogenetic context. They tested, for the rst time, the hypothesis of
increasing size of the cerebrum relative to the rest of the brain in a phy-
logenetic context and also pioneered the study of brain division scaling
in extinct taxa.
Relative Brain Size and Encephalization Quotients
Brain and body mass are highly correlated, as exemplied by the high
correlation coefcients of equations in this paper. Relative brain size is
the size of the brain compared to the size of the body, usually measured
as body mass. It has been used to infer cognitive capacity and thermo-
regulatory mode in extinct vertebrates (Jerison ; Hopson , )
and associated with complex cognitive behavior in birds and mammals
(Lefebvre et al. ; Marino ). Because the specic gravity of the
brain is approximately unity (Jerison ; Hurlburt ), brain size can
be expressed as mass or volume. A commonly used measure of relative
brain size is the Encephalization Quotient (; Jerison ), which
is the ratio of brain mass to a predicted brain mass, obtained from the
brain-body equation of a reference group, such as non-avian reptiles or
birds (Jerison ). Jerison () was the rst to state that dinosaurs had
brains of the size expected for non-avian reptiles of their body mass. He
supported this statement with graphical illustrations of brain-body rela-
tions in reptiles and dinosaurs, although four of his ten dinosaurs actually
had LVEQs (Lower Vertebrate EQs; discussed below) less than those of
the least encephalized reptile (Hurlburt ). His EQs were based on
two equations, both with a slope (b) of ., and with intercepts (a) of
. and . for “lower” and “higher” vertebrates, respectively (Jerison
). He tted the . slope “by eye” to the brain-body point scatter be-
cause it is the coefcient relating volume to surface area. He considered
it a “theoretical” slope, but it is more properly termed a “hypothetical”
slope. Hurlburt () developed Reptile EQs (REQs), and Bird EQs
(BEQs) using species-based brain-body equations. The reduced major
axis regression () brain-body equation for non-avian reptiles by spe-
cies (N = ) is
log MBr = −. + (. × log MBd), ()
where MBd is body mass, r = ., and the percent condence limits
() of b are . and .. The brain-body equation for birds
by species (N =) is
log MBr = −. + (. × log MBd), ()
where r = . and the percent of b are . and .. These
equations were based on much larger and more taxonomically compre-
hensive samples than those of Jerison (). The percent condence
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Hurlburt, Ridgely, and Witmer
138
limits ( percent ) of both equations exclude ., constituting clear
evidence that the . slope is inappropriate and falsifying Jerison’s hy-
pothesis. Moreover, the categories of birds (the monophyletic Aves) and
the grade of non-avian reptiles are more appropriate than the categories
of “lower vertebrates” (sh, amphibians, and reptiles) and “higher” ver-
tebrates (birds and mammals) used by Jerison (). The bird slope is
steeper than the reptile slope but within the percent of the reptile
slope. The bird intercept is approximately times that of the non-avian
reptile slope (Hurlburt ).
The corresponding formulae (based on species-level equations)
are
= MBr/(. × MBd.) ()
and
= MBr/(. × MBd.), ()
where antilog
10
−. = .; antilog
10
−. = .. The equa-
tion is appropriate for data with unequal variation in x and y variables, as
is typical of brain and body data (Sokal and Rohlf ). From this point
on, the term “non-avian reptiles” refers to extant non-avian reptiles.
The purposes of this study are ()to determine three regression equa-
tions relating (a) log endocranial volume (), (b) log brain mass (MBd),
and (c) to (snout to tail-tip length) in a size series of alligators;
()to determine ratios of brain-mass:endocast-volume (MBr:EV) and
cerebrum mass:cerebrocast-volume (MCb:CbcV) in a size series of al-
ligators; ()to determine and log ranges of reptiles and and
log ranges of birds; ()to estimate endocranial and cerebrocast vol-
ume from actual or virtual endocasts of several large theropod dinosaurs
and to estimate MBr and MCb from dinosaur endocasts using MBr:EV
and MCb:CbcV ratios in alligators; ()to compare relative brain size of
dinosaurs with that of reptiles and birds, using REQs and BEQs; ()to
calculate ratios of cerebrum to total brain size in dinosaurs and compare
these ratios to those of reptiles and birds; ()to discuss methods of analyz-
ing brain size, including methods of obtaining volumes from dinosaur
endocasts; and ()to test hypotheses regarding evolution of brain size.
The fossil specimens consisted of three taxa of the Late Cretaceous tyran-
nosaurids Tyrannosaurus rex ( , , ),
Gorgosaurus libratus ( ), and “Nanotyrannus lancensis” (
), as well as two allosauroids, the late Jurassic allosaurid Allosaurus
( ) and the late Cretaceous carcharodontosaurid Carcharodon-
tosaurus (SGM-Din ). In addition, EQs were calculated from endocast
data for Archaeopteryx ( ) and three small theropods: Bambi-
raptor ( ), Ornithomimus ( ), and Troodon (
.. and ..). To provide a context for the theropod data,
we also provide data for other dinosaur taxa. The relations of brain to
Methods and
Materials
Institutional Abbre-
viations AMNH, American
Museum of Natural History,
New York; BMNH, The Natural
History Museum, London; CM,
Carnegie Museum of Natural
History; CMNH, Cleveland
Museum of Natural History,
Cleveland; FMNH, Field
Museum of Natural History,
Chicago; NMC, National
Museums of Canada, Ottawa;
KUVP, Kansas University Natu-
ral History Museum, Lawrence;
ROM, Royal Ontario Museum,
Toronto; RTMP, Royal Tyrrell
Museum of Paleontology,
Drumheller, Alberta; SGM,
Ministere de l’Energie et des
Mines, Rabat, Morocco; UUVP,
University of Utah, Salt Lake
City.
©2013 by Indiana University Press. All rights reserved.
Size of Brain and Cerebrum in Tyrannosaurids
139
endocast and of cerebrum to cerebrocast were determined from a size
series of sexually mature alligators (Alligator mississippiensis), of which
half were wild and half were pen-raised domestic animals.
Volumetric Relations between Brain and Endocast and between
Cerebrum and Cerebrocast in Alligator mississippiensis
In the alligator sample, MBd ranged from . to .kg, ranged
from . to .m, and MBr ranged from . to .g (Hurlburt and
Waldorf ). Although alligators have been known to reach slightly
exceeding m, generally there is little growth after .m in males
and .m in females. Alligators can be sexually mature at .cm
(Woodward et al. ). Thus, the sample ranged from the smallest sexu-
ally mature individual – that is, the smallest subadult – to the largest com-
monly encountered size. It thus constitutes a useful comparison sample
for studying relations between relative brain size and ontogenetic age in
extinct, non-avian archosaurs.
Brains were removed immediately postmortem in the alligators and
weighed within – minutes, following removal of the olfactory tracts.
Brain weight included pia mater but excluded the pituitary gland, dura
mater, arachnoid, grossly visible blood vessels, and any dried blood, which
occurred between the meninges in some specimens. Brains were dis-
sected into gross divisions (cerebrum, cerebellum, optic lobes [=tectum],
and brain stem, including diencephalons), which were then weighed.
The rst three divisions were cut off from the brain stem in a horizon-
tal plane. Divisions were xed in percent formalin. The skulls were
cleaned, and endocasts were made by applying successive layers of latex
to the skull and calvarium. Because the specic gravity of brain tissue ap-
proximates unity (one), brain volume and mass are used interchangeably.
Volumes of alligator endocasts were determined by suspending endocasts
from an electronic balance, once in air and once immersed in water. The
difference in the two masses equals the mass (g) of water displaced by the
volume of the cast. Because the specic gravity of water is one, this mass
equaled the volume in milliliters (Alexander ).
Limits and landmarks on alligator and dinosaur endocasts were cho-
sen to correspond to the brain portion of the endocast. The limits were
anteriorly, the point where the cerebrum narrows to meet the olfactory
tract, and posteriorly, the stump of the hypoglossal nerve (XII). Endocast
portions beyond these limits were removed, as were foramen llings
corresponding to nerves and blood vessels. Cerebrocast volumes were
determined by suspending the cast with the water line at the posterior
cerebrocast boundary line and again subtracting the wet mass from the
dry mass.
In alligators, the cerebrocast boundary line was somewhat oblique,
from rostrodorsal to caudoventral (Fig. .). The line always fell just
at the posterior contact of the cast of the infundibulum connecting to
the pituitary. The cerebrocast (endocast portion corresponding to the
Other Terminology and
Abbreviations 95 percent
CL, 95 percent confidence
limits; BEQ, Bird Encepha-
lization Quotient based on
species-level equations; CbcV,
cerebrocast volume (ml);
cerebrocast, endocast portion
corresponding to cerebrum;
DGI, Double Graphic Integra-
tion; EV, endocast volume
(ml); HVEQ, Higher Vertebrate
Encephalization Quotient; log,
log
10
; LVEQ, Lower Vertebrate
Encephalization Quotient;
MBd, body mass (g); MBr,
brain mass (g); MCb, cere-
brum mass (g); REQ, Reptile
Encephalization Quotient
based on species-level equa-
tions; RMA, reduced major
axis (regression equation); SD,
standard deviation; TL, total
length measured from snout
to tail tip.
©2013 by Indiana University Press. All rights reserved.
Hurlburt, Ridgely, and Witmer
140
forebrain) includes the cerebrum and also unavoidably includes the por-
tions corresponding to the diencephalon, optic chiasma, and optic tracts
because the cerebrum lies dorsal and lateral to these brain components.
Alligator cerebrum-cerebrocast ratios are the ratio of the cerebrum alone
to the cerebrocast.
The MBr:EV ratio was determined for alligators, and least squares
regression equations were calculated with and MBr as dependent
variables and as the independent variable. Reptile Encephalization
Quotients of a sample including four additional specimens (total N=)
were calculated to describe the ontogenetic pattern relative to . These
four were included to increase sample size although cerebrum data were
unavailable for these specimens. Total length was used because some al-
ligators were pen-raised and heavier for their length than wild alligators.
Relative Brain Size in Extant Non-avian Reptiles and Birds
Both non-avian reptile log REQs and bird log BEQs were normally
distributed, unlike either non-avian reptile REQs or bird BEQs (all loga-
rithms are log
10
in this paper). Accordingly, dinosaur log REQs and log
BEQs were compared to ranges of these parameters in non-avian reptiles
and birds and analyzed in terms of z-scores ( units) as appropriate (So-
kal and Rohlf ). Additionally, the relationship between log REQs and
in alligators was calculated (Hurlburt, unpublished data) to describe
the ontogeny of in a modern group.
Estimating Body Mass, Brain Mass, and Relative
Brain and Cerebrum Size in Dinosaurs
Except for those of Nanotyrannus and Bambiraptor, dinosaur body mass
(MBd) estimates were taken from the literature. In most cases, two esti-
mates were used to cover a range of reasonable possible masses because
no robust mechanism for MBd estimation has been universally accepted
for extinct vertebrates (Hurlburt, , ). The MBd of Nanotyrannus
lancensis ( ) was calculated from estimated femoral circum-
ference. Femoral length was calculated from premaxilla-quadrate skull
length (mm; Gilmore ) using Currie’s () least squares regres-
sion equations for tyrannosaurids (N = , r = .) and tyrannosaurines
(N = , r = .), giving femoral lengths of . and .mm,
respectively. Femoral circumference was estimated from femoral length,
using the “All Theropods” regression equation (n = , r = .)
of Christiansen (), giving femoral circumferences of . and
.mm, respectively. Body mass was calculated using the equation
W = . Cf ., ()
where W is mass (g), and Cf is minimum femur circumference (mm)
(Anderson et al. ). Adult MBd of Bambiraptor was calculated from Cf
of an adult femur cast provided by David Burnham, and of Ornithomimus
©2013 by Indiana University Press. All rights reserved.
Size of Brain and Cerebrum in Tyrannosaurids
141
from Cf of , an adult femur. Volumes of dinosaur endocasts and
cerebrocasts were taken by one of three methods: ()Double Graphic
Integration (; see Jerison ; Hurlburt ) of illustrations of en-
docasts of Carcharodontosaurus saharicus (SGM-Din ; see Larsson )
and of Tyrannosaurus rex ( ; see Hopson ), () volume
calculation from virtual endocasts produced from three dimensional
scans of the four tyrannosaurids, and () water displacement by the
wet-dry method, as described above, of an endocast of Allosaurus fragilis
( ). Volumes derived from scans were generated using Amira
.. visualization software.
The posterior limit of the cerebrocast in dinosaurs was dened as a
vertical line in the transverse plane just posterior to the bulge correspond-
ing to the cerebrum. This line was usually just rostral to the rostral limit of
the base of the cast of the trochlear nerve (IV) where apparent. Dinosaur
MBr and MCb were obtained by applying the MBr:EV and MCb:CbcV
ratios of the largest alligators and also by application of the widely used
percent ratio. The percent ratio was used both for comparison to results
of other studies and because it is the ratio of alligators halfway between
the youngest and oldest sexually mature specimens. In addition, MBr
and MCb values for Nanotyrannus were also obtained using MBr:EV
and MCb:CbcV ratios typical of the youngest subadult alligators, owing
to the hypothesis that it is a juvenile, as indicated by suture contacts, and
as bone grain indicates juvenile status for Nanotyrannus (Carr ). No
ratios are known for juvenile alligators. Calculated dinosaur log EQs were
compared to ranges of log REQs of non-avian reptile species (N = )
and of log BEQs of bird species (N = ). Encephalization Quotients
for other dinosaur species, including small theropods, were also used
to provide a context for analysis of large theropods. Encephalization
Quotients for small theropods and Archaeopteryx were calculated from
endocast and MBd data in Russell (; see Nicholls and Russell ),
Hopson (), Currie and Zhao (), Hurlburt (), Elzanowski
(), Burnham (), and Dominguez Alonso et al. () or as de-
scribed in Methods. Encephalization Quotients were calculated for other
dinosaurs (stegosaurs, ankylosaurs, ceratopsians, and sauropods), applying
MBr:EV and MCb:CbcV ratios in alligators to . These data are from
Hurlburt () with two exceptions. The of Stegosaurus (.ml)
was obtained by of the endocast of gured in Galton ().
The of Iguanodon was obtained by of the brain cavity of
R, an isolated endocranium (Andrews ; Norman ), after
excluding an area corresponding to an extensive sinus complex (Norman
and Weishampel ).
Brain:Endocast and Cerebrocast:Cerebrum
Ratios in Alligator mississippiensis
The MBr:EV (brain mass to endocast volume) ratio decreased from
percent in the smallest to percent in the largest alligators. Among the
Results and
Discussion
©2013 by Indiana University Press. All rights reserved.
Hurlburt, Ridgely, and Witmer
142
three largest males, the range was –mm, the MBr range was
.–.g, and the MBr:EV ratio range was .–. percent with a
mean of . percent. The largest female ( .cm, MBr g) had an
MBr:EV ratio of . percent. Alligator REQs regularly declined from
. (log value = .) in the smallest alligator ( = mm) to .
(log value =−.) in the largest alligator ( = mm), in a mixed
sample of wild and domestic alligators (N = ; see Fig. .). The associ-
ated least squares regression equation, = . + (−. × log ),
had percent of (−.–.) enclosing the slope (b = −.) of
the smaller sample (N = ).
Endocast volume increases faster than MBr relative to . In the
least squares regression equation relating log (ml) to log (mm),
the slope (b = .; percent ., .; r = . ) is statistically
signicantly larger than the slope of the equation relating log MBr (g)
to (mm), where b = . ( percent ., .; r = .), al-
though both variables increase with increasing body size (Hurlburt and
Waldorf ). To take into account the pronounced sexual dimorphism
of alligators, in which the greatest male size markedly exceeds that of
females, MBr estimates from in mature dinosaurs and crocodilians
should apply the largest male ratio ( percent) for undoubted males, the
male-female mean ( percent) when specimen sex is unknown, and the
largest female ratio ( percent) for undoubted females when sexual di-
morphism is known. The mean cerebrum:cerebrocast ratio of the largest
males and females of percent was applied to estimate cerebrum mass
from dinosaur cerebrocasts.
Relative Brain Size in Extant Non-avian Reptiles and Birds
Reptile Encephalization Quotients of the non-avian reptile species
ranged from . to .; the BEQs of extant avian species ranged
from . to .. Figure . shows polygons that surround the non-
avian reptile and bird brain-body data on which the equations are
based. Figure . shows the same polygons and unlabeled dinosaur
brain-body data with the slopes for the Lower Vertebrate and Higher
Vertebrate ( and ) equations. The slope, empirically
6.2. Reptile Encephalization
Quotients (REQs) of alligators
and log TL (total length) of
Alligator missippiensis. Least
squares regression equation:
REQ = 8.56 + (−2.22 × log TL;
r = 0.907).
©2013 by Indiana University Press. All rights reserved.
Size of Brain and Cerebrum in Tyrannosaurids
143
6.3. Log brain (MBr) and body
mass (MBd) of dinosaurs, plot-
ted with slopes of brain-body
equations of non-avian reptile
species (lower slope) and bird
species (upper slope). Polygons
surrounded brain-body point
scatters of non-avian reptiles
(N = 62) and birds (N = 174),
as indicated. Legend: filled
triangles, tyrannosaurids; filled
diamonds, other theropods;
hollow circles, other dinosaurs.
Abbreviations: Al, Allosaurus;
Arch, Archaeopteryx, BAd,
Bambiraptor, estimated adult
values; BJ, Bambiraptor,
juvenile; G, Gorgosaurus; N,
Nanotyrannus; Orn, Ornitho-
mimus; Trx, Tyrannosaurus rex;
Tro, Troodon.
6.4. Comparison of slopes of
Lower Vertebrate Encephaliza-
tion Quotient (LVEQ), Higher
Vertebrate Encephalization
Quotient (HVEQ), Reptile
Encephalization Quotient
(REQ), and Bird Encephaliza-
tion Quotient (BEQ) equations.
Polygons and dinosaur data
as in Figure 6.3. Jerison
(1973) chose the 0.67 slope
of both the LVEQ and HVEQ
because it is the coefficient
of the volume to surface area
relationship and fitted the
intercepts (0.007 and 0.07)
“by eye” to the Lower and
Upper Vertebrate brain-body
point scatters. The LVEQ slope
passes above most dinosaur
data points, and four of
Jerison’s ten dinosaur genera
had LVEQs less than those of
the least-encephalized reptiles.
The REQ slope passes through
the middle of the dinosaur
distribution. Both the REQ
and BEQ equations were em-
pirically derived. Lower Verte-
brates: fish, amphibians, and
reptiles; Higher Vertebrates:
birds and mammals.
derived from reptile brain-body data, passes through the middle of the
dinosaur brain-body distribution, whereas the slope (dashed), passes
above most dinosaur brain-body points, and results in lower LVEQs
for several dinosaurs than for the least-encephalized reptiles (Hurlburt
). Neither non-avian reptile REQs nor bird BEQs were normally
distributed (Hurlburt ), but both non-avian reptile log REQs (range:
−.–.) and bird log BEQs (range: −.–.) were normally
distributed. Accordingly, dinosaur log EQs were compared to statistics of
distribution (mean and ) of reptile log REQs and bird log BEQs. The
reptile log distribution has mean −. and .; the mean
+ SDs is −. and ., respectively. The bird log BEQs distribution
has mean . and .; the mean ± SDs is −. and .,
respectively (see Tables . and .; Figs. . and .).
©2013 by Indiana University Press. All rights reserved.
Hurlburt, Ridgely, and Witmer
144
0
4
8
12
16
20
24
28
32
36
40
44
48
52
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
Dinosaur & bird log BEQs
Number of Species
Ara
2 spp
.
Arch
A
OrnithomimusA
Troodon
Bambiraptor(Ad)
Bambiraptor
(Juv)
Struthio
Arch B
OrnithomimusB
Nan (2/4)
6.5. Log
10
REQs of dinosaurs
and 62 non-avian reptile
species. Vertical dashed lines
indicate non-avian reptile
mean log REQ and mean ± 2
SDs. Non-avian reptile log REQ
range, −0.318–0.237; mean,
−0.0087; SD, 0.1968; mean ±
2 SDs, −0.403– 0.385. Open
bars, reptiles; cross-hatched
bars, dinosaurs; filled bars,
reptile and dinosaur bars of
equal height. Abbreviations:
A and B indicate two MBd
estimates (two MBrs for
Arch.); Ad, adult; Carch,
Carcharodontosaurus, Gorg,
Gorgosaurus; Juv, juvenile;
Nan, Nanotyrannus; Trx 2081
& 5117, Tyrannosaurus rex
FMNH PR 2081 and AMNH
5117. Other abbreviations as
in Figure 6.3.
6.6. Log
10
BEQs of Archaeop-
teyx, dinosaurs, and 174 bird
species. Bird log BEQ range,
−0.447– 0.475; mean, 0.0002;
SD, 0.1815; mean ± 2 SDs,
−0.363–0.363. Extant bird
species are underlined. Open
bars, birds; cross-hatched bars,
dinosaurs; filled bars, bird and
dinosaur bars of same height.
Dashed lines and abbreviations
as in Figure 6.4.
Body Mass, Endocast Volume, Brain Mass,
and Cerebrum Mass in Dinosaurs
Tyrannosaurus is assigned a MBd range of –kg, from Holtz
() and Henderson (; modied from kg), respectively, un-
less other estimates for individual specimens were available. This MBd
range encloses the estimates of kg for T.rex by Christiansen (),
©2013 by Indiana University Press. All rights reserved.
Size of Brain and Cerebrum in Tyrannosaurids
145
of .kg by Seebacher (), and estimates by all researchers cited by
Seebacher (), except Anderson et al. (). The estimate by Ander-
son et al. () was more than . SDs below the mean of estimates by
six researchers using various methods, more than twice the next greatest
deviation (analysis of data in Seebacher ). The large
specimen of T.rex had an estimated ontogenetic age of . years (Erick-
son et al. ). The Gorgosaurus MBd estimate ( kg) is calculated
from Cf (mm) of .. by Erickson et al. (), who suggests
it is likely an underestimate (Erickson, pers. comm., ). Estimates for
individual T. rex specimens of kg for and kg for
kg are from Erickson et al. () and Erickson (pers. comm.,
May ) and are based on the equation of Anderson et al. (). Given
the discrepancy between the results of Anderson et al. () and those
of other researchers for T.rex, these are probable underestimates but
permit comparisons to the other T.rex specimens. Anderson et al. ()
produced their equation for bipedal dinosaurs by tting a regression line
with a slope of . to the MBd: Cf data point for a model and femur
of Troodon. Their T.rex and Allosaurus MBd estimates were two thirds
of Colbert’s () estimates from scale models, and their Anatosaurus
MBd estimate exceeded the estimate from Colbert’s () model. The
. slope was the exponent of an equation predicting MBd from the sum
of femur and humerus circumferences of mammal species, of which
massed under kg and only two exceeded kg (Anderson et
al. ). This exponent may notably underestimate MBd in large ter-
restrial amniotes (>kg) because leg bones of the smaller amniotes
have smaller duty factors (Alexander et al. ) and experience greater
compressive forces during locomotion (Hurlburt ). The method may
be more accurate for smaller theropods near the mass of Troodon (kg),
such as Bambiraptor and Nanotyrannus.
Body mass estimates for Allosaurus of and kg were obtained
from Colbert () and Anderson et al. (), respectively. Body masses
of and kg were used for Carcharodontosaurus, assuming its
MBd to be in the same range as T.rex, following Larsson et al. ().
Table . lists endocast volumes for theropods. The endocast
volume (ml) estimate for is about percent of the
presumably more accurate estimate (.ml) and is not used in
the following analyses of T.rex. The over-estimate of endocast volume
by the method is likely due to erroneous inclusion of volumes of
the concave regions dorsal to the brainstem and lateral to the optic lobes
and cerebellum, but it is accurate when the subject analyzed is convex
(Hurlburt ). The produced by Larsson et al. () for
appears to be an underestimate caused by methodological limitations and
is not used in the following analyses. Higher values were obtained in this
study for the Allosaurus than by Larsson et al. (), although both
used water displacement. The estimates calculated in this study are used
here because there was more control, but EQs resulting from both sets
of estimates are similar. Double Graphic Integration produced higher
©2013 by Indiana University Press. All rights reserved.
Hurlburt, Ridgely, and Witmer
146
Table 6.1. Body mass, endocast volumes, associated brain volumes, REQs and log REQs of large alligators (ROM R8328 and
R8333) and large theropod dinosaurs
Specimen Meth EV (ml) MBr 37%
(ml)
MBr 50%
(ml)
MBd
(t)
REQ
37%
REQ
50%
log REQ
37%
log REQ
50%
T 5117 (4.3) CT 313.64 116.05 156.8 4.312 1.604 2.168 0.205 0.336
T 5117 (7) CT 313.64 116.05 156.8 7.00 1.227 1.659 0.089 0.220
T 5029 (5) CT 381.76 141.25 190.9 5.00 1.799 2.432 0.255 0.386
T 5029 (7) CT 381.76 141.25 190.9 7.00 1.494 2.019 0.174 0.305
T 2081 (5.65) CT 414.19 153.25 207.1 5.654 1.824 2.465 0.261 0.392
T 2081 (7) CT 414.19 153.25 207.1 7.00 1.621 2.190 0.210 0.340
T 5029 (5) DGI 404.0 149.48 202.0 5.00 1.904 2.573 0.280 0.410
G 1247 CT 128.93 47.70 64.47 1.11 1.400 1.892 0.146 0.277
N 7541 (0.24) CT 111.18 41.14 55.59 0.24 2.812 3.800 0.449 0.580
N 7541 (0.28) CT 111.18 41.14 55.59 0.28 2.597 3.510 0.414 0.545
N 7541 (0.24) CT 111.18 67% = 74.491 0.24 67% = 5.092 67% = 0.707
N 7541 (0.28) CT 111.18 67% = 74.491 0.28 67% = 4.703 67% = 0.672
C Din 1 (5) DGI 263.68 97.56 131.8 5.00 1.243 1.680 0.094 0.225
C Din 1 (7) DGI 263.68 97.56 131.8 7.00 1.032 1.394 0.014 0.144
C Din 1 (5) Lsr 224 82.88 112 5.00 1.056 1.427 0.024 0.154
A 294 (1.4) WaH 187.9 69.52 93.95 1.40 1.791 2.420 0.253 0.384
A 294 (2.3) WaH 187.9 69.52 93.95 2.30 1.361 1.839 0.134 0.265
A 294 (1.4) WaL 169.0 62.53 84.5 1.40 1.610 2.176 0.207 0.338
ROM R8328 WaH 27.34 10.50 — 0.238 0.721 — 0.060 —
ROM R8333 WaH 32.94 10.51 — 0.277 0.663 — 0.055 —
Note: REQ = MBr/(0.0155 × MBd
0.553
), both MBr and MBd in grams. Non-avian reptile REQ range: 0.402–2.404. Nonavian reptile log
REQ mean ± 2 SDs, −0.403–0.385. MBr, brain mass estimated from EV using alligator MBR:EV ratios. 37% or 50% indicates ratio used,
but 67% used for Nanotyrannus (italicized in table). Two MBd estimates for most species (see Methods). Numbers in parentheses after
specimens indicate MBd. Abbreviations: A 294, Allosaurus UUVP 294; ROM R8328 and R8333, data for ROM alligator specimens; C Din
1, Carcharodontosaurus saharicus SGM Din-1; CT, computed tomography scans; DGI, Double Graphic Integration; EV, endocast volume; G
1247, Gorgosaurus ROM 1247; Lsr, laser scan (Larsson et al. 2000); MBd, body mass; MBr, brain mass; Meth, method by which volumes
were obtained from endocasts; MBd, body mass in metric tons; MBr, brain mass (% indicates ratio); N 7541, Nanotyrannus lancensis
CMNH 7541; REQ, Reptile Encephalization Quotient; T 5117, Tyrannosaurus rex AMNH 5117; T 5029, T.rex AMNH 5029; T 2081, T.rex
FMNH PR 2081; WaH, volumes by water displacement by Hurlburt; WaL, volumes by water displacement by Larsson.
values than the laser scan for Carcharodontosaurus and are perhaps less
accurate for reasons given above, but EQs again are similar between
values from laser scan and methods.
Dinosaur MBr was estimated by the mean of the MBr:EV ratio of
the largest males and female alligators ( percent) because the sexes of
individual dinosaur specimens is unknown. Similarly, dinosaur cerebrum
mass was obtained by applying the mean ratio of the largest males and
females ( percent). The possibility that some dinosaur specimens were
not full adults is dealt with by application of the percent MBr:EV ra-
tio. All dinosaurs were treated as adults, including Allosaurus ,
which J.Madsen (pers. comm., June ) considered to be an adult de-
spite Rogers () regarding it as a subadult. Brain mass was considered
to equal in small theropods and Archaeopteryx.
Table . provides estimates of body mass (MBd), endocast volume
(), estimated brain mass (MBr), and methods by which was ob-
tained. Figure . plots brain body data of large theropods, small the-
ropods and other dinosaurs (stegosaurs, ankylosaurs, ceratopsians, and
©2013 by Indiana University Press. All rights reserved.
Size of Brain and Cerebrum in Tyrannosaurids
147
Table 6.2. BEQs and log BEQs of theropod dinosaurs
Specimen Meth EV
(ml)
MBd (t) BEQ
(37%)
BEQ
(50%)
log BEQ
(37%)
log BEQ
(50%)
T 5117 (4.3) CT 313.64 4.312 0.121 0.163 −0.918 −0.787
T 5117 (7) CT 313.64 7.00 0.091 0.123 −1.042 −0.911
T 2081 (5.65) CT 414.19 5.654 0.136 0.184 −0.867 −0.736
T 2081 (7) CT 414.19 7.00 0.120 0.162 −0.921 −0.791
T 5029 (5) CT 381.76 5.00 0.135 0.182 −0.871 −0.740
T 5029 (7) CT 381.76 7.00 0.110 0.149 −0.957 −0.826
T 5029 (5) DGI 404.0 5.00 0.143 0.193 −0.846 −0.715
T 5029 (7) DGI 404.0 7.00 0.117 0.158 −0.932 −0.801
G 1247 CT 128.93 1.11 0.111 0.150 −0.955 −0.824
N 7541 (0.24) CT 118.18 0.24 0.236 0.318 −0.628 −0.497
N 7541 (0.28) CT 118.18 0.28 0.216 0.292 −0.665 −0.534
N 7541 (0.24) CT 118.18 0.24 67% = 0.427 67% = −0.370
N7541 (0.28) CT 118.18 0.28 67% = 0.392 67% = −0.407
A 294 (1.4) WaH 187.9 1.40 0.141 0.190 −0.852 −0.722
A 294 (2.3) CT “ 2.30 0.105 0.142 −0.979 −0.849
C Din 1 (5) DGI 263.68 5.00 0.093 0.126 −1.031 −0.901
C Din 1 (7) DGI “ 7.00 0.076 0.103 −1.118 −0.987
ROM R8328 WaH 10.50 0.238 0.060 — −1.219 —
ROM R8333 WaH 10.51 0.277 0.055 — −1.258 —
Note: BEQ = MBr/(0.117 × MBd
0.590
); both MBr and MBd in grams. Encephalization Quotients are estimated from MBd and estimated MBr
in Table 6.1. Note smallest subadult ratio (67%) used for Nanotyrannus in 50% column (italicized in table). Bird BEQ range: 0.357–2.986.
Bird log BEQ mean ± 2 SDs, −0.363–0.363. Abbreviations: BEQ, Bird Encephalization Quotient. Other abbreviations as in Table 6.1.
Species MBd (g) EV (ml) REQ BEQ log REQ log BEQ
Ornithomimus A 175000 87.9 7.145 0.606 0.854 −0.218
Ornithomimus B 125000 87.9 8.606 0.739 0.935 −0.132
Troodon 45000 41.0 7.067 0.630 0.849 −0.201
Bambiraptor Juv 2240 14.00 12.680 1.263 1.103 0.101
Bambiraptor Ad 6581.96 14.0 6.986 0.669 0.844 −0.175
Archaeopteryx A 468 1.60 3.445 0.363 0.537 −0.440
Archaeopteryx B 468 1.76 3.789 0.400 0.579 −0.398
Note: Endocast data from Archaeopteryx (BMNH 37001), Bambiraptor (KUVP 129737), Ornithomi-
mus (NMC 12228), and Troodon (RTMP 86.36.457 and RTMP 79.8.1). Data from Hurlburt (1996),
except for Bambiraptor and Archaeopteryx (see text). MBr = EV since the brain filled the cranial
cavity. Abbreviations: Ad, adult; Juv, juvenile. Other abbreviations as in Tables 6.1 and 6.2.
Table 6.3. Body mass,
endocast volume, EQs and
log EQs for three Late Creta-
ceous small theropods and
Archaeopteryx
sauropods) with slopes and polygons that surround brain-body data of
reptile (N = ) and bird (N = ) species.
Relative Brain Size in Dinosaurs
Tables . and . provide REQs, BEQs, log REQs, and log BEQs for all
large theropods analyzed, and Table . gives data for three Late Creta-
ceous small theropods and Archaeopteryx. Figures . and . are histo-
grams of log REQs and log BEQs of large theropods, small theropods, and
other dinosaurs. Encephalization Quotients based on percent MBr:EV
ratios are more consistent with the analytical method, but EQs from
©2013 by Indiana University Press. All rights reserved.
Hurlburt, Ridgely, and Witmer
148
percent ratios are provided for reasons given above. Comparisons among
species are made using raw (i.e., not log-transformed) data, which are
more easily comprehended; comparisons to reptile and bird distributions
are made with log EQs, which are normally distributed, unlike raw EQs.
Tyrannosaurus rex
has the largest relative brain size
of any dinosaur, other than some small theropods. Reptile Encephaliza-
tion Quotients of T.rex range from. to . ( percent ratio) and .
to . ( percent ratio). The highest T.rex log ( percent ratio)
is no more than SDs above the mean of reptile REQs, with one excep-
tion, from a percent MBr:EV ratio for , an unlikely
ratio because this is the ontogenetically oldest and most mature T.rex
in the sample (Table .; Fig. .). A high log from a percent
MBr:EV ratio for the value is discounted because probably
overestimates total . Log BEQs of T.rex are almost SDs below the
mean bird log and well below the lowest bird log (−.; see
Table . and Fig. .). It appears that the body size sequence of T.rex
specimens increases through , , and ,
and the pattern of increasing with body size is typical of alligators,
as is continuing increase in body size with ontogenetic age (Table .).
Gorgosaurus ( ) is less encephalized than T.rex, and only the
(.) derived from a percent MBr:EV ratio reaches the lower end
( percent ratio) of the range of T.rex (Table .; Fig. .), while
a percent MBr:EV ratio produces an of .. is clearly
a subadult (Carr ). If Gorgosaurus and T.rex follow a similar growth
trajectory, these REQs are lower than would be expected of a subadult
T.rex because ontogenetically younger alligators have larger relative brain
sizes than adults.
Reptile Encephalization Quotients of Nanotyrannus (e.g., .–
. for a percent MBr:EV ratio) clearly exceed the range of
Tyrannosaurus rex, even for a percent MBR:EV ratio for T.rex (Table
.). Log REQs ( percent ratio: .–.) are more than SDs
above the reptile log mean (mean + SDs = −.–.). Larger
MBR:EV ratios produce even higher REQs for Nanotyrannus (Table
.). Expressed as SDs of reptile log REQs (z-scores), Nanotyrannus log
REQs are . SDs above T.rex values whether comparing percent
or percent MBr:EV ratios and are as much as . SDs above the rep-
tile log mean (Sokal and Rohlf ). When calculated from a
percent MBr:EV ratio, Nanotyrannus log REQs are .–. SDs above
the reptile mean and about .–. SDs above the highest T.rex values
(z-scores = . for percent ratio, . for percent ratio; see Table
.). If Nanotyrannus is a juvenile or young subadult of T.rex or a simi-
lar tyrannosaurid, the difference between its log REQs and those of an
adult tyrannosaurid such as T.rex approximates the difference (. SDs)
between log REQs of the smallest subadult and largest adult alligators
in the comparison sample (Tables ., .; Figs. ., .). Nanotyrannus
log REQs are consistent with those of a young subadult or older juvenile
©2013 by Indiana University Press. All rights reserved.
Size of Brain and Cerebrum in Tyrannosaurids
149
tyrannosaurid. Conversely, even the smallest Nanotyrannus MBr estimate
produces REQs much larger than those of any adult dinosaur whose
brain does not ll the cranial cavity; we consider this to be unlikely and
therefore inconsistent with adult ontogenetic status. Nanotyrannus log
BEQs are more than SDs below the bird log mean, even with the
large percent MBR:EV ratio (Table .; Fig. .).
Data for the two allosau-
roids indicate that Carcharodontosaurus had an range of .–.,
less than that of Allosaurus (.–.) and about two thirds
that of Tyrannosaurus rex (Table .; Figs. ., .). Neither dinosaur
enters the bird range (Table .; Fig. .). However, the spread of Al-
losaurus MBd estimates is wide, and REQs from the larger MBd estimate
approximate those of Carcharodontosaurus.
Archaeopteryx Brain mass
ranged from . to . ml, exceeding an estimate of . ml from of
the gure of Archaeopteryx in Bühler (; also see Hurlburt ). Body
mass was g (Elzanowski ). The log range (.–.) is
more than . but slightly less than SDs above the mean reptile log ,
and its brain-body points overlapped the lower edge of the bird brain-body
polygon (Figs. ., .). The log BEQs of Archaeopteryx (−.–−.)
are within the bird log range, overlapping values for Struthio (Figs.
., .), although slightly more than SDs below the bird log range.
These results falsify the hypothesis that Archaeopteryx lies between the
reptile and bird relative brain-body distributions (Larsson et al. ).
Cerebrocast:Endocast Volume and Cerebrum:Brain
Mass Ratios in Theropod Dinosaurs
Larsson et al. () suggested that relative cerebrum size increased in
coelurosaurian dinosaurs, the lineage leading to and including birds,
relative to allosauroids, a lineage including Carcharodontosaurus, a large
theropod approximately equal in MBd to Tyrannosaurus rex. They com-
pared the ratio of cerebrocast to , considering it equivalent to the
MCb:MBr ratio. To test this hypothesis, we computed the same ratios
using MCb estimates from applying the alligator MCb:CbcV ratio to
scans of dinosaur endocasts. We also combine the result of a laser
scan for with of the cerebrocast of Carcharodontosaurus because
is fairly accurate for convex solids but less so for entire endocasts, as
discussed above.
Cerebrocast volume:endocast volume ratios from scans of the
three Tyrannosaurus rex and Gorgosaurus specimens ranged from .
to . percent, and MCb:MBr ratios ranged from . to . percent
(Tables . and .). While MCb:MBr ratios estimated for T.rex enter the
lower end of ratios typical of birds, they are very close to ratios (.–.
percent) typical of the smallest sexually mature alligators (Table .).
©2013 by Indiana University Press. All rights reserved.
Hurlburt, Ridgely, and Witmer
150
Table 6.4. Endocast (EV) and cerebrocast (CbcV) volumes, associated brain and cerebrum mass (MCb), and associated CbcV:EV
and MCb:MBr ratios of large alligators and theropod dinosaurs
Specimen Meth Brain part of
EV (ml)
CbcV (ml) EV less CbcV
(ml)
MBr = 37%
EV (ml)
MCb = 42%
CbcV (ml)
CbcV: EV
Ratio (%)
MBr: MCb
Ratio (ml)
T 5117 CT 313.64 131.4 182.3 116.05 55.17 41.88 47.54
T 2081 CT 414.19 170.2 244.0 153.25 71.48 41.09 46.65
T 5029 CT 381.76 165.9 215.8 141.25 69.69 43.47 49.34
T 5029 DGI 404.0 147.8 256.2 149.48 62.07 36.58 41.53
T 5029 Lsr 343 111.8 231.2 126.91 46.96 32.59 37.00
G 1247 CT 128.93 56.0 72.9 47.70 23.52 43.43 49.30
N 7541 (Ad) CT 111.18 64.73 46.45 41.14 27.19 58.22 66.09
N 7541 (Sub) CT 111.18 64.73 46.45 74.49 46.61 58.22 62.57
C Din 1 DGI 263.68 83.1 180.6 97.56 34.90 31.51 35.77
C Din 1 Lsr,DGI 224 83.1 140.9 82.88 34.90 37.10 42.11
C Din 1 Lsr 224 53.7 170.3 — — 23.97 24.00
A 294 WaH 187.9 101.7 86.2 69.52 42.71 54.12 61.44
A 294 WaL 169.0 46.7 122.3 — — 27.63 27.63
ROM R8328 4 WaH 27.34 10.9 6.2 10.50 4.28 39.87 40.76
ROM R8333 WaH 32.94 11.3 6.0 10.51 4.51 34.15 42.91
Note: Theropod dinosaur volumes were calculated using MBr:EV (37%) and MCb:CbcV (42%) ratios of largest adult alligators. Nanotyran-
nus (N 7541) EV and CbcV were estimated using ratios from smallest subadult alligators, which were MBr:EV, 67%, and MCb:CbcV, 72%.
Both Larsson et al. (2000) and the present study obtained Allosaurus volumes by water displacement. For Carcharodontosaurus, one CbcV:
EV and one MCb:MBr ratio were obtained by combining CbcV from DGI with EV from a laser scan (Larsson et al. 2000). Abbreviations:
Ad, adult; CbcV, cerebrocast volume; Sub, sub-adult. Other abbreviations as in Tables 6.1 and 6.2.
Specimen Meth CbcV:EV Ratio (%) MCb:MbrRatio (%)
T. rex (N = 3) CT scans 41.1–43.5 46.6–49.3
G 1247 43.3 49.3
N 7541 (Ad) 58.2 66.1
C Din 1 (5) DGI 31.5 35.8
C Din 1 (7) Lsr-DGI 37.1 42.1
A 294 54.1 61.4
Two smallest alligators 37.9–43.8 44.8–47.9
Two largest alligators 34.2–39.9 40.8–42.9
Reptiles: Mn ratio = 33.52.
Actual range in column 3
23.57–43.56
Reptiles: Mn ratio ± 2 SDs 25.6–41.5
Ameiva
and largest alligator Alligator
31.4, 40.8
Birds: Mn ratio = 63.7.
Actual range in column 3
44.6–82.3
Birds: Mn ratio ± 2 SDs 47.4–80.0
Note: MCb:MBr ratios were calculated from cast volumes for all fossil specimens. Only MCb:MBr
ratios are provided for extant species other than alligators. For the two smallest alligators, TL =
1613 mm and 1985 mm; for the two largest alligators, TL = 3759 mm and 3810 mm. Abbrevia-
tions: Mn, mean; Rep, Reptile; TL, snout to tail tip length. Other abbreviations as in Tables 6.1 and
6.2.
Table 6.5. Cerebrocast:
endocast volume (CbcV:EV)
and cerebrum:brain mass
(MCb:MBr) ratios of dinosaurs,
alligators, nonavian reptiles,
and birds. Ameiva data from
Platel (1979).
©2013 by Indiana University Press. All rights reserved.
Size of Brain and Cerebrum in Tyrannosaurids
151
Because it cannot be determined whether a larger MCb:MBr ratio arises
from a larger MCb or a decline in one or more of the other brain divi-
sions, this result can be taken to indicate an avian-like condition, but
tyrannosaurid MCb:MBr ratios are high. These ratios do not reect the
signicant difference in brain size relative to body size between T.rex and
birds, and thus that bird cerebrum size is relatively larger than in T.rex.
The same applies to differences in relative cerebrum size between Car-
charodontosaurus and T.rex. Ratios are useful in comparisons between
related taxa of similar relative brain size.
Nanotyrannus has a CbcV:EV ratio of . percent. Its MCb:MBr
ratios are . percent, using adult brain:endocast ratios, and . per-
cent, using youngest subadult brain:cast ratios (Tables ., .). These
CbcV:EV and MCb:MBr ratios are percent or more higher than for
other tyrannosaurids and than for alligators and other reptiles (Tables
. and .). While these ratios resemble those of the Allosaurus endo-
cast, the endocasts are dissimilar in appearance, whereas the Nanotyran-
nus endocast resembles those of other tyrannosaurids. Because higher
MCb:MBr ratios are typical of ontogenetically younger alligators, these
data support the hypothesis that Nanotyrannus is a young subadult or
juvenile, as do data.
Larsson et al. () proposed that cerebral volume is percent
greater in T.rex than in Carcharodontosaurus, accounting in part for the
larger relative brain size of T.rex. Cerebrum mass:brain mass ratios of
Carcharodontosaurus are as high as . percent when combining laser-
scanned and of CbcV, comfortably in the upper reptile range and
only – percent less than those of T.rex. This rejects the hypothesis that
cerebral volume is percent greater in T.rex than in Carcharodonto-
saurus (Larsson et al. ). A quite high MCb:MBr ratio (. percent)
was obtained for Allosaurus. This may be due to experimental error or to
relative size differences of other brain components.
The purpose of this study was assessment of the relative brain and rela-
tive cerebrum size of tyrannosaurid dinosaurs (Tyrannosaurus rex, Gor-
gosaurus, and Nanotyrannus) and comparison of these data to results for
allosauroid dinosaurs (Allosaurus and Carcharodontosaurus). To measure
relative brain size, EQs (Encephalization Quotients) were calculated
using brain-body data for extant non-avian reptile species (N = ) and
extant bird species (N = ). We compared dinosaur log EQs to the
ranges of reptile log REQs and bird log BEQs because these samples
were normally distributed, unlike either reptile REQs or bird BEQs. To
estimate brain mass (MBr) from dinosaur endocast volume (), the
MBr:EV ratio was determined in a size series, ranging from the smallest
sexually mature to the largest commonly encountered size, of Alligator
mississippiensis, an examplar of the extant archosaurian clade Croco-
dylia. The mean of MBr:EV ratios of the largest male and female was
percent, and the ratio was percent in the smallest sexually mature
Summary
©2013 by Indiana University Press. All rights reserved.
Hurlburt, Ridgely, and Witmer
152
alligators. Dinosaur MBr and MCb (cerebrum mass) were estimated
from virtual endocasts produced from scans and also from laser scans
and double graphic integration. Brain mass was estimated from in
dinosaurs using the adult ratio and in Nanotyrannus, a possible juvenile,
also using the youngest subadult ratio. Estimates were also made using
the traditional percent MBr:EV ratio, for comparison to previous stud-
ies and because this is the MBr:EV ratio in midrange subadult alligators,
appropriate for the Gorgosaurus specimen. Relative brain sizes of small
theropods and a wide sample of other dinosaurs were also determined to
provide a context for evaluation of these large theropods. The cerebrum
mass:brain mass (MCb:MBr) range was compared among dinosaurs and
between dinosaurs and each of reptiles and birds.
This is the rst study to use empirically based brain:endocast (MBr:EV)
and cerebrum:cerebrocast (MCb:CbcV) ratios, derived from extant al-
ligators, to estimate dinosaur relative brain and relative cerebrum size.
It is also the rst to measure dinosaur relative brain size by Reptile En-
cephalization Quotients (REQs) and Bird Encephalization Quotients
(BEQs). Both MBr and increase with body size in alligators, but
the MBr rate is signicantly less, so that the MBr:EV ratio in alliga-
tors declines with increasing body size, as does . Other than small
theropods, which are well within the relative brain size range of extant
birds, Tyrannosaurus rex has the largest relative brain size of any dinosaur
but is within the relative brain size of extant reptiles and within SDs
of the mean of reptile log REQs. It is well below the relative brain size
range of extant birds. Gorgosaurus plots at the lower end of log REQs of
T.rex. The log REQs of Nanotyrannus lancensis are anomalously high
for an adult but consistent with a juvenile or very young subadult age.
The difference between its log REQs and those of an adult T.rex paral-
leled the difference between the youngest subadult and the oldest adult
alligators of the comparison sample, when measured as log reptile
units. Nanotyrannus MCb:MBr ratios were also consistent with an
older juvenile or young subadult ontogenetic age. Carcharodontosaurus
has an about two thirds that of T.rex and showed no increase in
relative brain size compared to the late Jurassic Allosaurus, supporting a
hypothesis of a trend of larger relative brain size in coelurosaurian com-
pared to allosauroid dinosaurs. All three late Cretaceous small theropods
(Bambiraptor, Troodon, and Ornithomimus) plotted well within in the
bird log range and well above the reptile log range. The relative
brain size range of Archaeopteryx overlapped the lower edge of the bird
log range and exceeded the reptile range. Both tyrannosaurids
and allosauroids had cerebrum mass:brain mass (MCb:MBr) ratios in
the high end of the reptile range, and T.rex entered the low end of the
bird MCb:MBr range. These values were also similar to those of subadult
alligators. The MCb:MBr ratio of Carcharodontosaurus was less than
Conclusion
©2013 by Indiana University Press. All rights reserved.
Size of Brain and Cerebrum in Tyrannosaurids
153
percent below that of T.rex, falsifying a hypothesis that a larger cerebrum
accounted for the larger brain of T.rex.
We thank R. Elsey of the Rockefeller Wildlife Refuge in Louisiana, Allan
Woodward of the Florida Fish and Wildlife Conservation Commission,
and Bubba Stratton, an independent alligator control agent in Florida,
for facilitating acquisition of alligators.
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