Advertisement
Research Article

A Computational Analysis of Limb and Body Dimensions in Tyrannosaurus rex with Implications for Locomotion, Ontogeny, and Growth

  • John R. Hutchinson mail,

    jrhutch@rvc.ac.uk

    Affiliation: Structure and Motion Laboratory, Department of Veterinary Basic Sciences, The Royal Veterinary College, Hatfield, Hertfordshire, United Kingdom

    X
  • Karl T. Bates,

    Affiliation: Department of Musculoskeletal Biology, Institute of Aging and Chronic Disease, University of Liverpool, Liverpool, United Kingdom

    X
  • Julia Molnar,

    Affiliation: Structure and Motion Laboratory, Department of Veterinary Basic Sciences, The Royal Veterinary College, Hatfield, Hertfordshire, United Kingdom

    X
  • Vivian Allen,

    Affiliation: Structure and Motion Laboratory, Department of Veterinary Basic Sciences, The Royal Veterinary College, Hatfield, Hertfordshire, United Kingdom

    X
  • Peter J. Makovicky

    Affiliation: Department of Geology, Field Museum of Natural History, Chicago, Illinois, United States of America

    X
  • Published: October 12, 2011
  • DOI: 10.1371/journal.pone.0026037
  • Published in PLOS ONE

Reader Comments (6)

Post a new comment on this article

Tyrannosaurus body mass is slightly overestimated but its mucle is greatly underestimated!

Posted by Celestist on 08 Dec 2011 at 20:01 GMT

Henderson and Eric Snively in their paper “Tyrannosaurus en pointe: Allometry Minimized Rotational Inertia of Large Carnivorous Dinosaurs” calculated the body mass of large Tyrannosaurus Rex FMNH PR 2081 (SUE) to be about 10220kg, their torso is about same size as Hutchinson’s estimate, with higher skull and torso density (averaging 89%) but emaciated limbs segments.

Notice, before Frank Anderson’s long bone circumference (1985) method become popular (partly not because of its accuracy, but because it is very expedient) , Alexander estimated the smaller AMNH 5027 had a life body mass of 7400kg, the larger FMNH PR 2081, by simple linear scaling (1.12^3) should be between 10400kg, even account for large air sac and empty abdominal cavity, the body mass will still be at least 9000+kg

Also, just from virtue estimate, FMNH PR 2081, even with enlarge air sac, can’t be less than 120% the mass of the largest individual of deinosuchus*(~12meter, David, Langston, unpublished material) base on scaling wild American alligators (7800-8400kg).

Hutchinson minimum estimate of SUE’s torso is indeed too big, from the size of the ribs and vertebrate given in “Osteology of Tyrannosaurus Rex: Insights from a nearly complete skeleton and high-resolution computed tomographic analysis of the skull”, FMNH PR 2081 had torso more likely about 4000kg (with empty abdominal cavity and enlarged air sac), but Hutchinson’s limb and tail is “true” minimum estimates, so it is incorrect to compare the minimum limb and tail with the maximum size torso.

More likely, SUE’s body mass should be
Head 450kg (part of Hutchinson’s head is mixed with the neck)
Neck 520kg (average)
Body 4000kg (average)
Thigh 2150kg (average, there is no problem with this one, MOR 555’s max thigh estimate fit SUE well)
Shank 620kg (average)
Tail 1990kg (average)
Forelimb 20kg (average)
Total: 9750kg (average)
Notice, after decreased the inflated torso, SUE’s center of gravity is reverted back to “normal” by the now larger limbs and tail.

George Paul estimate a 13.6 meter tyrannosaurus to be 12 tons, but he revised his estimate with no reason, other than subjective influenced by the highly unreliable Long circumference method.
Notice that center of mass is different in dinosaur; the 25.7+ meter long Diplodocus carnegiei had a femur about the same diameter as SUE, the Diplodocus femur is longer (154cm) but the muscle is much less than SUE’s thigh(593*2 or 740*2 kg compare to SUE’s min of 1287 or 2150kg, or 2670kg), (reference on Diplodocus leg mass, Henderson, 1997, 2006), supporting 78% of its total body mass, assume Diplodocus carnegiei body mass estimate ranges from 12000-20000kg (Anderson, Christiansen, Per, Frank Seebacher) SUE’s femur should be able to support 78% of Diplodocus Carnegiei type specimen’s mass, which is 9360kg to 15600kg, the last estimate is exaggerated, but body mass of 9910kg is reasonable within this limit.


Extensor muscle among (tail extensor I used maximum estimate, after pictorial comparison as well as text review of Philip Currie’s work, the total muscle CFL should be 52% of total flesh mass of the tail, and after accounted other muscle , two side combine total of 1122 is reasonable)

FMNH PR 2081 (95%*(((2150+561(2/.95))*54%))+(34%*2150)))+(95%*620*(47%))=2680.11*106%(musle density) =2840.9kg, this about (2840.9/ 9750+160) = 28.65%
My estimate of the three tyrannosaurus Rex (Jane is excluded for being a nanotyrannus.)

SUE has 28.65% extensor
MOR had 26.5%
Stan had 27.23%
CM had 27.23%
SUE has larger extensor relative to its body, not smaller as suggest by Hutchinson.

SUE my average 9910kg Hutchinson’s average 13996kg
Stan my average 8140.5kg Hutchinson’s average 8385kg
CM my average 8787.5kg Hutchinson’s average 9081kg
MOR my average 8253.5kg Hutchinson’s 8272kg

Notice that my Stan is smaller than MOR 555, which is reasonable, because Stan has smaller SVL than MOR 555, and after I corrected the compressed rib cage of MOR, it turns out to be a bit bigger than Stan, not surprising since MOR 555 has femur circumference marginally larger than average left+right of the giganotosaurus MUCPv-CH1.

SUE had 19th pre-sacral vertebrate diameter about 27 cm, and the 23th pre-sacral vertebrate’s diameter about 29-30cm
In comparison MOR has 19th pre-sacral vertebrate diameter is only 19 cm, CM has 19th pre-sacral vertebrate diameter of about 23 cm, and 23th pre-sacral vertebrate is about 27cm.
So from vertebrate size, SUE should be 10% to 17% heavier than CM, and CM should be about 20% larger than MOR*

George Paul said that Tyrannosaurus rex body mass should not be 50% larger than average, but this makes no sense, modern polar bear in difference region of Canada, had adult mass range from 200-800kg, dependent on sex, age and location, Siberian male tiger has body mass range from 160-270kg.

Furthermore, the four tyrannosauruses are separated geographically and chronically, so each of them can be even treated as a separate subspecies. Plus SUE is older than the others.
SUE‘s femur is 2% longer than Stan, but circumference and distal end is more than 15% wider, so overall size of SUE should be much larger than Stan.

*notice giganotosaurus has a dorsal vertebrate of only 15 cm diameter, even less than the diameter of tyrannosaurus cervical vertebrate, so giganotosaurus base vertebrate scaling should be much lightly build than T-rex, thus smaller in term of mass, and its metatarsus both on Acrocanthosaurus NCSM 14345 and mapusaurus should be about 17cm shorter than CM 9380 tyrannosaurus specimen, this is more than enough to cancel out the 13 cm longer femur(giga’s femur is far less robust, the femur distal diameter of giganotosaurus is 10 cm shorter than CM 9380) femur, and that tibia is 8 cm shorter than CM, so giganotosaurus is both shorter overall and less massive than T-rex, so it should be consider smaller than T-rex, MUCPv-95 is highly unreliable, and even if it is put into the equation, being equally complete by bone count, the huge tyrannosaurus rex UCMP 137538 (17+% longer than SUE, 25-33% wider, base length diameter pedal IV-II)should also be consider with equal validity, which will total out-weight and out-lengthMUCPv-95

*deinosuchus has extremely weak femur, using Farlow (2005)’s alligator limb circumference method, a 12 meter deinosuchus will be at most 3500kg ( a smaller Specimen with SKL of 1475mm, HL of 1370, TL 9.6M, weight 1794kg, larger specimen=(12.0/9.6)^3.25)
*a mugger crocodile with SVL of 1.3 meter can weight as less of 40kg, assume the largest deinosuchus has a SVL 5.71meter (Paul Sereno, 2001, SVL of 12 meter long sarcosuchus) , produce approximately 3400-3800kg. Which fit well with the limb method, notice the interesting tendency of accepting always the largest estimate for crocodile such as deinosuchus and sarcosuchus, and exaggerate the estimate further to 10 short tons (9100kg) in popular media, but reject larger estimate of theropod, which ironically be default should be much bigger than crocs.

No competing interests declared.

RE: Tyrannosaurus body mass is slightly overestimated but its mucle is greatly underestimated!

jrhutch replied to Celestist on 09 Dec 2011 at 16:20 GMT

Your comments are intriguing but too little information is provided to evaluate them scientifically. Our analysis was about bounding the range of possible morphologies of Tyrannosaurus bodies and using those to characterize possible growth changes and their biological consequences. We made the point in our paper, as we have made in numerous prior analyses, that focusing on one answer is naive because too much is unknown for even these seemingly familiar fossil organisms.

We have a few specific responses to your many points above, but generally find the argument too unstructured and unclear for a detailed response. We urge you to develop this more explicitly. A lot of implict assumptions are being made and not questioned. It is not clear how your muscle mass estimates were done and how sensitive they are to your assumptions.

We question the relevance of crocodylomorph scaling equations for dinosaurs.

Nanotyrannus remains of controversial taxonomic validity, and the Jane specimen's referral to that is a separate issue that is questionable as well.

However your points about size variability in extant populations and across geological time are trenchant critiques of Paul's rebuttal; we agree. You also make some good points about differences in skeletal dimensions in the adult Tyrannosaurus specimens we modelled.

No competing interests declared.

RE: Tyrannosaurus body mass is slightly overestimated but its mucle is greatly underestimated!

cabrochu replied to Celestist on 20 Jan 2012 at 14:45 GMT

I am curious as to how torso mass estimates were derived for FMNH PR2081 ("Sue") based on measurements in the monograph describing it. Nearly all of the bones forming the torso - ribs, vertebrae, gastralia - are distorted to some extent, and many are incomplete.

If the estimate is based on images of the mounted skeleton - as I pointed out in a different comment, the torso *as mounted* is a compromise between having it look like a "normal" torso, facilitating removability of the bones for study and maintenance, and correct anatomical articulation. It was impossible to maximize all three because of the distortion issues, and the gastralia aren't even on them mount - so I would urge extreme caution when using the mounted skeleton to estimate volume.

This isn't intended to cast doubt on the arguments made in your comment - only to learn more about how the volume/mass estimates were generated for that particular specimen.

Christopher A. Brochu

No competing interests declared.

RE: Tyrannosaurus body mass is slightly overestimated but its mucle is greatly underestimated!

Celestist replied to Celestist on 09 Feb 2012 at 22:31 GMT

I actually I am base on your initial measurement or the "average mass". except that I modified the tail and the torso a little. most is base on the average of your max and min estimate, except when the max estimate see too extreme (example, SUE's tail), I will (2*min + max)/3, very crude estimate.

I curious that why you list the "max" and "min" but did not the value that you consider to be "fit" as kate and Philiph L did for the BMNH replica of BHI 3033

I listed crocodylomorph scaling just to point out that what seeming "concrete" estimate such as Deinosuchus CM 960 12meter 8000kg can be also senstive, at least more senstive than T-rex, which actually is far more complete.

base deinosuchus on different specie of modern crocodylomorph can also result in a significent range of change, any way CM 960's dorsal vetebrate 16th is only 140mm long, I high specluate that it is above 11 meter even if measure alone the vetebrate countour. more like 10 meter between two points.

I known several literature works like accept the point that the largest deinoscuhus is mush heavier than MOR 555 as a simple given, but actually them about the same mass or The T-rex is a bit heavier.

No competing interests declared.