Measuring brachiosaur mass using minimal convex hulls

June 6, 2012

I don’t have time to write about this properly, but a few people have asked me about the new Sellers et al. (2012) paper on measuring the masses of extinct animals — in particular, the Berlin Giraffatitan — by having a CAD program generate minimal complex hulls around various body regions. Rather than write something new about it, I’m going to publish the comments that I sent Ed Yong for his Discover piece on the new technique:

Hi, Ed, good to hear from you. Yes, it’s a good paper: a useful new technique that has some useful properties, most importantly that it requires no irreproducible judgements on the part of the person using it, and that it’s ground-truthed on solid data from extant animals.

It’s a reassuring sanity-check to find that my (2009) mass estimate falls well within their method’s 95% confidence interval, and is in fact within 0.6% of their best estimate.

There are a couple of problems with this study, which I hope will be addressed in followups. The authors are honest enough to touch on all of these problems themselves, though! They are:

1. All the extant animals used to determine the fudge factor are mammals, which means they are not necessarily completely relevant to dinosaurs. In particular I would very much like to have seen regression lines and correlation coefficients for this method for birds and crocodilians, both of which are much more closely related to Giraffatitan.

2. Much depends on the reconstruction of the torso, particular the position of the ribs, which is very difficult to do well and confidently with dinosaurs. In my volumetric analysis (Taylor 2009:803) I found that the torso accounts for 70% of total body volume in Giraffatitan, so rib orientation will make a big difference to overall mass. Sauropod ribs that are well preserved and undistorted along their whole length are extremely rare.

3. Use of a single density value for the whole animal, while appropriate for mammals, really isn’t for brachiosaurs, in which the very long neck likely had a density no more than half that of the legs. I’m not sure what can be done about this, though, since any attempt to correct for density variation involves subjective guesswork. Then again, so do all guesses at overall body density in dinosaurs.

Issue 1 bothers me most, because the convex hulls of limb segments in mammals will be proportionally much larger than in sauropods, due to the complex shapes of mammalian long-bone ends. I worry that using mammals as a baseline will underestimate sauropod leg mass.

Still, even with these caveats, it’s a good exposition of an important new method which I expect to see widely adopted.

Hope that’s helpful.

In short: good work, widely applicable, and probably the best mass-estimation technique we now have available for complete and near-complete skeletons. It would be good to see it applied to (say) the Yale, AMNH and CM apatosaurs.

Composite illustration from Sellers et al.’s press release. Top left: bear skeleton from the Oxford University Natural History Museum, presumably Ursus maritimus: original skeleton, derived point cloud and convex hulls (also used as Sellers et al. 2012:fig. 1). Top right: shedloads of awesome. Bottom: complex hulls around body segments of Giraffatitan.


Sellers, W. I., J. Hepworth-Bell, P. L. Falkingham, K. T. Bates, C. A. Brassey, V. M. Egerton and P. L. Manning. 2012. Minimum convex hull mass estimations of complete mounted skeletons. Biology Letters, online ahead of print. doi:10.1098/rsbl.2012.0263

Taylor, Michael P. 2009a. A re-evaluation of Brachiosaurus altithorax Riggs 1903 (Dinosauria, Sauropoda) and its generic separation from Giraffatitan brancai (Janensch 1914). Journal of Vertebrate Paleontology 29(3):787-806.

19 Responses to “Measuring brachiosaur mass using minimal convex hulls”

  1. I think the paper’s biggest issue aside from 1. is that it conflates volume and mass. Given the word limit that’s practically impossible to fix, though.

    So what the authors present is a very good way of calculating the volume of a mammal, which means that because mammalian densities are so uniform we can simply calculate the mass from it.

    For less uniform mass distributions and overall densities, a more detailed approach could be adopted.

    Still, an excellent and brilliant approach :)

  2. Mike Taylor Says:

    Yes; I give the authors extra credit for using some of their precious wordcount to actively draw attention to deficiencies in the current version of the method. (Though I’d give them even more credit if they’d send the paper to a venue with a less ridiculous length limit.)

  3. Mike Taylor Says:

    Meanwhile, I see something that disturbs me in the publicity image: while the convex hulls around the bear treat the neck as a single object, those around the brachiosaur seem to have split the neck rather arbitrarily into five segments. Hmm. So we’re not really comparing like with like; and, worse, not explaining the approach.

    All the methods section says is: “The model was subsequently divided into functional segments: hind and fore feet, metatarsus and metacarpus, shank and forearm, thigh and arm, tail, torso (which included the attached scapulae), neck and head.”

  4. Publish or perish is getting absurdly extreme in the UK right now; nobody wants to publish “lower” than absolutely necessary!

    Added to that some (but not these) UK and US authors have just rediscovered the “do-not-cite-non-English researchers” theme. To the point where exactly parallel research on two sister groups of animals does not cite the papers on the other group. OUCH!

    It feels a bit like full-time researchers in the UK are getting desperate in their fight for funding.

  5. Mike Taylor Says:

    What do you mean by “publish lower”? Biology Letters’ impact factor of 3.651 is 20% lower than PLoS ONE’s 4.411, so on that basis putting this in the no-length-limits venue would have been a more prestigious move. And it would have been open access.

  6. A lot of stuffy old farts regard PLoS ONE as a dump.

  7. Mike Taylor Says:

    No doubt some do — but not Bill Sellers. I know this partly from having talked to him about it on the bus to the airport after the Bonn sauropod conference, but also from a publication record including and

  8. not Bill – but who might be judging Bill and his co-authors?

  9. Good catch with the neck segmentation Mike – I’m also concerned with how slab-sided the Berlin brachiosaur mount is – this method has been talked up as being “superior to artistic reconstructions”, but all it’s really doing is shifting the reconstruction burden to people who build mounts (who must fight against gravity and are often not anatomical specialists).

    So while I think this technique has promise, but it needs to be treated as a beta release at this point IMO.

  10. Mike Taylor Says:

    This method has been talked up as being “superior to artistic reconstructions”, but all it’s really doing is shifting the reconstruction burden to people who build mounts.

    I don’t think that’s quite right. Other volumetric approaches are also dependent on the artistic/anatomical judgement of mounted skeletons, but then add another layer of interpretation on top of that. The Sellers method doesn’t eliminate subjectivity, but it makes a real reduction.

  11. I have to largely disagree with you on this one Mike – while I can’t speak for other skeletal “drawing-ers”, I can say that mounted skeletons (or rather the position a mount is in) plays no role what so ever in my reconstructions, and I have a hard time believing they do in others who are doing even a minimally competent job.

    A mount and a skeletal reconstruction both start with the bones, and while a mount is less liable to commit accidents of scaling or foreshortening (although not always when combining multiple specimens…which is often not labeled on mounts) it introduces significant new sources of error as it has to fight the realities of metal frames and gravity. Having put up over two dozen dinosaurs I feel semi-qualified to say that the mounts are among the more accurate in the world, and are all inferior in terms of anatomical precision compared to the skeletal reconstructions I’ve done of the same species (often the same specimens).

    I’m not saying there isn’t merit to the idea, it’s just that there’s no magic to mounts. Worse, the fact that attitudes are already being expressed that “they strip away one layer of subjectivity” suggests to me that people are deceiving themselves about the role that subjectivity and just plain old practical problems (weight of the bones, strength of the frame material, patience of the welder, etc.,) play in a mount, even one created under the guidance of modern paleontologists.

    The method is likely to yield much better results if the bones are scanned separately and placed back together accurately in virtual space prior to applying the mathematical volumes. Of course some will respond that this just begs the question of “who determines what is the right position?”, but that’s exactly my point:

    There are no short cuts to getting the anatomy right. Neither an existing mount nor an existing skeletal is correct or better simply because of the technique or because you don’t know who was doing the interpretation. Each must rise and fall based on the individual details, and using a mount does not make that significantly easier or less subject to error.

    That said, assuming that one has an accurate virtual skeleton then this technique looks quite promising, assuming the dry mass fraction of bone volume to body mass holds up with non-mammals (or if it can be adjusted for archosaurs).

  12. Mike Taylor Says:

    Sorry, didn’t mean to imply that skeletal mounts are necessarily more accurate that drawn skeletal reconstructions — only that of the various methods based on a physically mounted skeleton, the Sellers method that does not involve further interpretation is in that respect better than methods that try to guess how much flesh to put onto the mount — e.g. the truly horrible estimation of Gunga et al. (1995) which IIRC came up with about 75 tonnes.

  13. Ahh, gotcha. I agree that compared to other mount-based methods this is superior (again assuming we can document the same fractional numbers for archosaurs). My issue is that in the press people are comparing it directly to volumetric estimates made from sculptures and/or mathematical models based on skeletals – and which of those three work best is probably going to largely depend on the quality of the reconstructions (mount or otherwise) being used.

  14. Asier Says:

    I´m totally agree with Scott, when he say “The method is likely to yield much better results if the bones are scanned separately and placed back together accurately in virtual space prior to applying the mathematical volumes.

    This method should be precise if the skeleton mounts were accurate, but most of them there aren´t at all… even with extant animals. For example, elephant skeletons in general are really bad mounted with scapulas really low in the chest (in the flesh are the highest point) and with the ribs too vertical, in fact in alive elephant the belly is a bit wider than the pelvis but in mounted skeleton the thorax is often considerably narrower… fossil ribs or the ribs from dead animal are more straight than in the flesh, so probably the mounted Giraffatitan skeleton would had had more wider belly when it was alive.

    By the image I think that a lot of soft tissues, muscles and skin is missing in the 3d Giraffatitan.

    Anyway, welcome to the new methods and new ideas!!!

  15. Asier, that’s the idea: the flesh is not reconstructed as is likely was, but only as a minimum convex hull (Mike, Freudian in the title or did you mis-read the paper’s title?). Then, a correction is added, by multiplying the resulting volume with a factor that was determined from living animals.

    And yes, digital mounts from individual HR scans of bones are best.
    Now who the heck was the guy who was doing that shit with Kentrosaurus and Plateosaurus????? ;)

  16. Mike Taylor Says:

    Yeesh! Good catch on the dumb typo in the title — now fixed. Thanks.

  17. Zhen Says:

    Mike, slightly off topic, but is this research using the same method that they previously used to measure the weight of Tyrannosaurus?

    It sounds similar, but I’m not sure if its the same method.

  18. Mike Taylor Says:

    Similar, yes; not the same, no.

  19. Zhen, the difference is that the Sue work made assumptions about the soft tissues’ volume, whereas the new technique simply assumed that the proportion of soft tissues to the calculated volume that is strictly limited to the volume defined by the skeleton is the same in all animals.

    Now, that assumptions seems to be true for mammals, and I still have my doubts if we can simply extrapolate to archosaurs, but is certainly significantly different from making explicit assumptions about the shape and volume of soft tissues of a specific animal.

    On the other hand, I do think that volumetric modelling using as a guide works such as Allen et al. 2009 is a valid approach – given the uncertainties of applicability of the Sellers et al. method to archosaurs maybe even a superior method right now.

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