How slender were the humeri of Giraffatitan?

May 23, 2014

Continuing with what seems to have turned out to be Brachiosaur Humerus Week here on SV-POW! (part 1, part 2, part 3), let’s consider the oft-stated idea that brachiosaurs have the most slender humeri of any sauropod. For example, Taylor (2009:796) wrote that:

Discarding a single outlier, the ratio of proximodistal length to minimum transverse width (Gracility Index or GI) in humeri of B. brancai [i.e. Giraffatitan] varies between 7.86 for the right humerus HMN F2 and 9.19 for the left humerus HMN J12, with the type specimen’s right humerus scoring 8.69, slightly more gracile than the middle of the range […] For the B. altithorax type specimen, the GI is 8.50, based on the length of 204 cm and the minimum transverse width of 24 cm reported by Riggs (1904:241). However, the B. altithorax humerus looks rather less gracile to the naked eye than that of B. brancai, and careful measurement from Riggs’s plate LXXIV yields a GI of 7.12, indicating that the true value of the minimum transverse width is closer to 28.5 cm. As noted by Riggs (1903:300-301), the surface of the distal end of this humerus has flaked away in the process of weathering. Careful comparison of the humeral proportions with those of other sauropods (Taylor and Wedel, in prep.) indicates that the missing portion of this bone would have extended approximately a further 12 cm, extending the total length to 216 cm and so increasing the GI to 7.53 – still less gracile than any B. brancai humerus except the outlier, but more gracile than any other sauropod species except Lusotitan atalaiensis (8.91), and much more gracile than the humerus of any non-brachiosaurid sauropod (e.g., Diplodocus Marsh, 1878 sp., 6.76; Malawisaurus dixeyi Jacobs, Winkler, Downs and Gomani, 1993, 6.20; Mamenchisaurus constructus Young, 1958, 5.54; Camarasaurus supremus Cope, 1877, 5.12; Opisthocoelicaudia skarzynskii Borsuk-Bialynicka, 1977, 5.00 – see Taylor and Wedel, in prep.)

Implicit in this (though not spelled out, I admit) is that the humeri of brachiosaurs are slender proportional to their femora. So let’s take a look at the humerus and femur of Giraffatitan, as illustrated in Janensch’s beautiful 1961 monograph of the limbs and girdles of Tendaguru sauropods:

Janensch1961-tendaguru-limbs--plates-AJ--giraffatitan-limb-bones

The first thing you’ll notice is that the humerus is way longer than the femur. That’s because Janensch’s Beilage A illustrates the right humerus of SII (now properly known as MB R.2181) while his Beilage J illustrates the right femur of the rather smaller referred individual St 291. He did this because the right femur of SII was never recovered and the left femur was broken, missing a section in the middle that had to be reconstructed in plaster.

(What’s a Beilage? It’s a German word that seems to literally mean something like “supplement”, but in Janensch’s paper it means a plate (full-page illustration) that occurs in the main body of the text, as opposed to the more traditional plates that come at the end, and which are numbered from XV to XXIII.)

How long would the intact SII femur have been? Janensch (1950b:99) wrote “Since the shaft of the right femur is missing for the most part, it was restored to a length of 196 cm, calculated from other finds” (translation by Gerhard Maier). Janensch confused the left and right femora here, but assuming his length estimate is good, we can upscale his illustration of St 291 so that it’s to SII scale, and matches the humerus. Here’s how that looks:

Janensch1961-tendaguru-limbs--plates-AJ--giraffatitan-limb-bones-scaled

Much more reasonable! The humerus is still a little longer, as we’d expect, but not disturbingly so.

Measuring from this image, the midshaft widths of the femur and humerus are 315 and 207 pixels respectively, corresponding to absolute transverse widths of 353 and 232 mm — so the femur is broader by a factor of 1.52. That’s why I expressed surprise on learning that Benson et al (2014) gave Giraffatitan a CF:CH ratio (circumference of femur to circumference of humerus) of only 1.12.

Anyone who would like to see every published view of the humeri and femora of these beasts is referred to Taylor (2009:fig. 5). In fact, here it is — go crazy.

Taylor (2009: figure 5). Right limb bones of Brachiosaurus altithorax and Brachiosaurus brancai, equally scaled. A-C, humerus of B. altithorax holotype FMNH P 25107; D-F, femur of same; G-K, humerus of B. brancai lectotype HMN SII; L-P, femur of B. brancai referred specimen HMN St 291, scaled to size of restored femur of HMN SII as estimated by Janensch (1950b:99). A, D, G, L, proximal; B, E, H, M, anterior; C, K, P, posterior; J, O, medial; F, I, N, distal. A, B, D, E modified from Riggs (1904:pl. LXXIV); C modified from Riggs (1904:fig. 1); F modified from Riggs (1903:fig. 7); G-K modified from Janensch (1961:Beilage A); L-P modified from Janensch (1961:Beilage J). Scale bar equals 50 cm.

Taylor (2009: figure 5). Right limb bones of Brachiosaurus altithorax and Brachiosaurus brancai, equally scaled. AC, humerus of B. altithorax holotype FMNH P 25107; DF, femur of same; GK, humerus of B. brancai paralectotype HMN SII; LP, femur of B. brancai referred specimen HMN St 291, scaled to size of restored femur of HMN SII as estimated by Janensch (1950b:99). A, D, G, L, proximal; B, E, H, M, anterior; C, K, P, posterior; J, O, medial; F, I, N, distal. A, B, D, E modified from Riggs (1904:pl. LXXIV); C modified from Riggs (1904:fig. 1); F modified from Riggs (1903:fig. 7); GK modified from Janensch (1961:Beilage A); LP modified from Janensch (1961:Beilage J). Scale bar equals 50 cm.

Notice that the femur of Giraffatitan, while transversely pretty broad, is freakishly narrow anteroposteriorly. The same is true of the femur of Brachiosaurus, although it’s never been shown in a published paper — I observed it in the mounted casts in Chicago.

Weird.

Calculations

So let’s take a wild stab at recalculating the mass of Giraffatitan using the Benson et al. formula. First, measuring the midshaft transverse:anteroposterior widths of the long bones gives eccentricity ratios of 2.39 for the femur and 1.54 for the humerus (I am not including the anterior prejection of the deltopectoral crest in the anteroposterior width of the humerus) . Dividing the absolute transverse widths above by these ratios gives us anteroposterior widths of 148 for the femur and 150 mm for the humerus. So they are almost exactly the same in this dimension.

If we simplify by treating these bones as elliptical in cross section, we can  approximate their midshaft circumference. It turns out that the formula for the circumference is incredibly complicated and involves summing an infinite series:

0a1f9b3824382486507885622ddcf283

But since we’re hand-waving so much anyway, we can use the approximation C = 2π sqrt((a²+b²)/2). where a and b are the major and minor radii (not diameters). For the femur, these measurements are 176 and 74 mm, so C = 848 mm; and for the humerus, 116 and 75 mm yields 614 mm. (This compares with FC=730 and HC=654 in the data-set of Benson et al., so we have found the femur to be bigger and the humerus smaller than they did.)

So the CF:CH ratio is 1.38 — rather a lot more than the 1.12 reported by Benson et al.  (Of course, if they measured the actual bones rather than messing about with illustrations, then their numbers are better than mine!)

And so to the mass formula, which Campione and Evans (2012) gave as their equation 2:

log BM = 2.754 log (CH+CF) − 1.097

Which I understand to use base-10 logs, circumferences measured in millimeters, and yield a mass in grams, though Campione and Evans are shockingly cavalier about this. CH+CF is 1462; log(1462) = 3.165. That gives us a log BM of 7.619, so BM = 41,616,453 g = 41,616 kg.

Comparison with Benson et al. (2014)

Midshaft measurements and estimates for SII long bones (all measurements in mm)
SV-POW! Benson et al.
Femur Humerus Femur Humerus
Transverse diameter 353 232 240
Transverse radius 176 116 120
Anteroposterior diameter 148 150 146
Anteroposterior radius 74 75 73
Circumference 848 614 730 654
Total circumference 1462 1384
Mass estimate (kg) 41,616 34,000

My new mass estimate of 41,616 kg is is a lot more than the 34,000 kg found by Benson et al. This seems to be mostly attributable to the much broader femur in my measurement: by contrast, the humerus measurements are very similar (varying by about 3% for both diameters). That leaves me wondering whether Benson et al. just looked at a different femur — or perhaps used St 291 without scaling it to SII size. Hopefully one of the authors will pass by and comment.

More to come on this mass estimate real soon!

References

 

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19 Responses to “How slender were the humeri of Giraffatitan?”

  1. Matt Wedel Says:

    One of your references needs updating. I think that last one should be:

    Taylor and Wedel, in prep. Well, seriously, dude, that manuscript is so straightforward and you’ve just written most of the discussion in this post series. Why don’t we just decide that we’re going to take one week–just not next week–and knock it out? Whatever we have at the end of the week goes up as a PeerJ preprint. That ought to keep our feet to the fire.

  2. Allen Hazen Says:

    Leg-bone circumference works as a predictor of body mass because it is a reasonable proxy for structural strength of the leg column. Not being a civil engineer, I can’t say anything definite here, but I would think that an elliptical cross section would not be as strong as a circular cross section of the same circumference. (Imaginary experiment: take the cardboard centres from two rolls of paper towels. Leave one round, carefully press the other until it assumes an elliptical cross section. Use both as columns to support a pile of encyclopedia volumes. Which buckles first?)

    So, since the humerus is wide but “freakishly” thin front-to-back, would its circumference perhaps give a misleadingly high body mass estimate, given that the formula is derived from taxa with humeri of more nearly circular cross section?

    (And no, I have no idea whatever how the effect of this would compare quantitatively with all the OTHER sources of uncertainty in body mass estimation!)

  3. Mike Taylor Says:

    Matt, on the humerus paper: I currently have twelve other papers in the queue to do before that one. But I will add it to the list. Meanwhile, don’t forget that paper’s sibling, Wedel and Taylor on North American brachiosaur cervicals, which has dormant for about the same length of time.

    Allen, I think that in your thought experiment the circular and elliptical tubes would be equally strong when it comes to supporting encyclopaedias — i.e. in longitudinal compression. The real issue is bending. The elliptical tube is stronger against bending parallel to its major axis, and weaker against bending parallel to its minor access.

    What does this tell us about the forces acting on brachiosaur femora in life? That the were subject to more mediolateral force than anteroposterior? That is odd for limbs that were swung back and forth in locomotion. I don’t know what to make of it. (And by the way, nearly all sauropod femora are broader than they are anteroposteriorly thick — brachiosaurs just take it to extremes.)

  4. Mark Robinson Says:

    Mike, I believe that you’re right about the cross-sectional area of a columnar structure being relevant to its ability to bear a static load, but that the shape is more important for withstanding non-vertical forces. I don’t know whether either is necessarily better than the other for calculating the masses of animals but Campione and Evans (2012) seem to show that circumference is a good proxy.

    As for why sauropod femora are thicker laterally than anteroposteriorly, I wonder if it’s to do with their ability to counteract any “wobble” as they transfer weight to a foot during locomotion? They have large muscles designed to swing their limbs forwards and backwards with which they can probably also make small adjustments to resist any instability anteroposteriorly. However, I imagine that they have less muscle power available to deal with any lateral wobbliness so perhaps this is compensated for by having transversely wider femora?

    Further hand-waving leads me to think that this (transversely wider femora) might be more noticeable in sauropods with a narrower stance (potentially less-stable laterally) and, if so, that there might also be a difference between humeri and femora with sauropods whose forelimb stance is wider than that of their hindlimbs.

    How do titanosaur femora compare?

  5. Matt Wedel Says:

    In each step cycle, all of the weight from the back half of the body had to be borne on a single femur, which was loaded eccentrically. I’ll bet that’s the driver for sauropod femora being wide in cross-section.

    I wonder at what size that kicks in at? I’ve never looked closely enough at elephant femora to tell if they’ve started down the same path. Where’s John of the Freezers when you need him?

    Also, here’s a project for some enterprising youngster: survey femoral cross-sectional eccentricity in sauropodomorphs and see if it correlates to body mass, as estimated both volumetrically and by limb bone allometry. If anyone has done that, I don’t think I’ve seen it. Wilson and Carrano discussed femoral eccentricity a bit, but I don’t know of any attempt at a broad survey.

  6. Mike Taylor Says:

    In each step cycle, all of the weight from the back half of the body had to be borne on a single femur

    That is true: but during that phase of the step cycle, the femur in question is driving the body forward, and so bearing the most powerful anteroposterior bending force that it has to withstand. So to me that seems like it would if anything require the opposite kind of eccentricity: femur cross-sectional area longer anteroposteriorly than transversely.

    Also: it’s equally true that in another part of the step cycle, a single humerus has to bear all the weight of the front half of the body — so why isn’t the humerus similarly eccentric?

    And finally: why would brachiosaur femora be so much more eccentric than, say, those of apatosaurs? (I don’t offhand know what the situation is with big titanosaurs — does anyone?)

    All in all, I think there’s more going on here — something that we’ve not understood.

    Someone ought to model the locomotion forces properly instead of just waving their hands like we are.


  7. It might be naive, but it seems to me that even when restricting to the static balance of forces, one should expect such bones to be eccentric. Indeed, when one looks at the flying buttresses of a cathedral one is not surprised to see that they can be quite thin in the “anteroposterior” direction, but are always wide in the “mediolateral” direction. On the contrary, inner pillars are usually round.

    So, might the eccentricity of bones (and the eccentricity variation between different bones) be explained by (or could be used to predict) the way they are placed: supporting weight vertically as a pillar, or supporting it more laterally as a flying butress?

  8. Mark Robinson Says:

    Regarding the greater eccentricity of brachiosaur femora, are their humeri generally less eccentric than, say, those of diplodocids? Also, what percentage of (static) mass is borne by a brachiosaur’s hindlimbs versus its forelimbs, and how does that compare with other sauropods?

  9. Matt Wedel Says:

    And finally: why would brachiosaur femora be so much more eccentric than, say, those of apatosaurs?

    Are they actually that much more eccentric? I know that Amphicoelias is the oddball for having a circular femur cross-section–although I’ve heard that some specimens of Diplodocus have round femora as well–which suggests that the default for diplodocids is to have femora that are at least somewhat elliptical in cross-section.

    But your larger point, about actually knowing stuff instead of just hand-waving, is well taken. Hopefully if we say enough dumb stuff, Matt Bonnan or Heinrich Mallison will show up to correct us.

  10. Mike Taylor Says:

    And finally: why would brachiosaur femora be so much more eccentric than, say, those of apatosaurs?

    Are they actually that much more eccentric?

    Yeah, I think so. I know femoral eccentricity is widespread in sauropods, but seriously, look at the Giraffatitan figure up there, it’s crazy.

    Femoral eccentricity is one of the characters in most sauropod cladistics matrices: for example, in Harris (2006), which has been the basis of my own lightly modified analyses (Taylor and Naish 2007, Taylor 2009, Taylor et al. 2011), it’s character 284, “Ratio of mediolateral:craniocaudal diameter of femur at midshaft”, with scores 0 (‘=1.85’). As you can see, Giraffatitan is right off the scale. (And so is Brachiosaurus, thought I think not quite so extreme.)

    Hopefully if we say enough dumb stuff, Matt Bonnan or Heinrich Mallison will show up to correct us.

    That’s the plan. Though given that failure of that strategy so far, we may have to up the Dumb Factor.

  11. Adam Says:

    Hi Guys

    I can’t add much to the discussion on the biomechanical benefits of a transversely eccentric femoral shaft but note that it seems to be correlated with graviportalism. Matt asks the pertinent question, at what size does this kick in? Elephants, from memory, do have quite eccentric femur as does the extinct marsupial Diprotodon (which was ‘only’ white rhino to hippo sized). I could add that at first glance the cross section of Antetonitrus femur is also very eccentric but a look at the femur in distal or proximal view indicates that there is a large amount of plastic deformation (its squished) even though the shaft looks well-preserved and crack-free. I sometimes wonder if the crazy eccentricity of really big sauropods has been exagerated by post-depositional forces in almost all cases. – can’t always take fossils at face value.

  12. Nima Says:

    41,616 kg? So Giraffatitan is heavy again :)

    Then again, cases of the effect of femoral eccentricity on mass may not always be easy to predict.

    This is why I always liked the model-dunking method, instead of the complicated equations method. Visually you can draw your own conclusions about the reliability of the model used, rather than having to pick apart complex maths and proofs. It may be entirely possible that the maths could differ significantly with different species (muscle mass ratios, pneumaticity, etc. all are factors.)

    I suspect pneumaticity could reduce the weight well below 41 tons. But perhaps our image of what Giraffatitan looked like has been too skewed by Greg Paul’s starving skeletals.

  13. Ian Corfe Says:

    Nice analysis. A couple of notes, questions and thoughts:

    – Is the HMN St 291 femur the same as the ‘Ni’ locality one used in the Giraffatitan mount (right femur)? As far as I can see Campione & Evans 2012 used only the mounted specimen for both humerus and femur circumferences, using actual circumference measurements not extrapolating from length/breadth dimensions, and the same data was used in Benson et al 2014.

    – You note the left femur of SII is broken and missing the middle section, and reconstructed with plaster. Is this likely to have also underestimated the true circumference if this was the femur measured rather than the right side femur from another individual?

    – Although your Giraffatitan linear humerus measurements are very similar to those of Campione & Evans 2012/Benson et al 2014, the circumference you calculated is a bit further (around 7%) from that measured by the authors, and it is that that feeds into the mass estimation.

    – Benson et al 2014 note their method for estimating circumference from linear measurements (though only used for Brachiosaurus, not Giraffatitan) as follows:

    “To estimate femoral circumferences from observed diameters, we parsed our data into a set of 29 groups, including paraphyletic grades (denoted ‘basal’). These were intended to represent approximate ‘body plan’ groupings that should have similar relationships between humeral and femoral shaft diameters and their circumferences, a hypothesis that was tested using regression.

    For each of the femur and humerus, each group contained some taxa for which the minimum shaft circumference and both its anteroposterior and mediolateral diameters were known, some taxa for which only a subset of these measurements were known, and some taxa for which none of these were known (for example, if the bone was not preserved in a specimen of that taxon). We estimated femoral circumferences for taxa in which at least one diameter was known by taking the following steps:
    (1) We estimated the ordinary least squares regression equation of anteroposterior shaft diameter on mediolateral shaft diameter, and mediolateral shaft diameter on anteroposterior shaft diameter for each group in which both measurements were known in at least three taxa.
    (2) For groups in which a significant (p < 0.05) regression relationship existed between the diameters, we used those relationships to predict the second diameter measurement for taxa in which only one diameter measurement was known. In general, bipedal groups with sufficient sample sizes had well-constrained relationships between the diameters of their mass-supporting stylopodials, but the relationship was weaker in some quadrupedal groups, especially Ceratopsidae, Hadrosauroidea and Sauropoda, suggesting they exhibit more variable eccentricity (Table S1).
    (3) We used equation [4] below to convert pairs of diameters (dml = mediolateral diameter; dap = anteroposterior diameter) into circumferences, assuming that the bone shaft has an oval cross-section (circumferenceoval):

    [4] circumferenceoval = pi * ((3 * (dml + dap)) – (((3 * dml + dap)*(dml + 3 * dap))0.5))

    (4) Measured shaft circumference was regressed through the origin on circumferenceoval for each group. All R2 values exceeded 0.985 and the slopes of the regression lines (ranging from 0.92–1.10) were used as correction factors to translate circumferenceoval into an estimate of the true shaft circumference for taxa in which a measured shaft circumference was not known. Some groups had too little data to estimate a correction factor. Thus, the factor for Dromaeosauridae was used for Avialae and Alvarezsauroidea, the factor for Titanosauriformes was used for Macronaria, the factor for Eusauropoda was used for Sauropoda, the factor for basal Ornithischia was used for Pachycephalosauria, and the median factor for all groups was used for Therizinosauria."

    So for the Brachiosaurus humerus where no circumference or ant-post diameter was measured, the ant-post diameter was predicted using the regression of all 'basal Titanosauriformes'. The circumference was then calculated from the oval formula, and then a correction factor added based on the regression of measured circumference vs circumference oval for 'basal Titanosaurifomes'.

    As far as I can see, this is likely to overestimate the ant-post diameter (based on the slenderness of brachiosaurid humeri), and thus the humerus circumference of Brachiosaurus. That probably means the femur:humerus ratio of Brachiosaurus may be underestimated because of an overestimated humerus circumference (though the humerus circumference isn't reported in Benson et al 2014 data), while that for Giraffatitan may be also underestimated, but due to a smaller than expected femur circumference from either a reconstructed femur or small sized femur from a different individual to the humerus.

    Looking forwards to the next post!

  14. Ian Corfe Says:

    Oh yes, and in terms of mass, this probably means the Brachiosaurus mass is overestimated and the Giraffatitan mass underestimated, using this method. So they were probably closer in mass as you previously pointed out! (Though that doesn’t help determine if brachiosaur mass is in general overestimated by the method, just points out specific potential problems with those mounts/specimens)…


  15. […] Since we’re currently in a sequence of Brachiosaurus-themed posts [part 1, part 2, part 3, part 4, part 5, part 6], this seems like a good time to fix that. So here is my response, fresh from […]


  16. […] our Brachiosaurus series [part 1, part 2, part 3, part 4, part 5, part 6, part 7], here is another historically important photo scanned from the Glut […]

  17. Ian Corfe Says:

    Following up from the above to figure out the estimated Brachiosaurus humerus circumference:

    Working backwards through the equations to figure the estimated humerus circumference of Brachiosaurus gives a figure of 688mm. So Brachiosaurus had an (estimated) humerus 688mm circumference, femur 940mm, giving a ratio of 1.37:1 and total C(h+f) 1628mm for a mass of 56000kg. Giraffatitan measured and estimated by Benson et al 2014 measurements is humerus 654 (about 5% smaller than Brachiosaurus), femur 730 (22% smaller), ratio 1.12:1, total C(h+f) 1384 (15% smaller) for a mass of 34,000kg (39% less mass). The measurements and estimates by Mike are above.

    If Benson et al 2014 and Campione & Evans 2012 used the smaller femur of the Berlin Giraffatitan mount, from a different, smaller individual, for their measurements, then that could possibly explain the discrepancy (as Mike and I both suggest earlier). Assuming the same 1.37:1 ratio between femur and humerus for Giraffatitan as for Brachiosaurus (and so both humerus and femur about 5% smaller than in Brachiosaurus), we get:

    Giraffatitan humerus = 654mm, femur = 893 (which is 5% larger than Mike’s estimate from the 2 diameters), total C(h+f) 1547 (6% larger than Mike’s estimate), for a mass of 48625kg (13% less mass than Brachiosaurus, but 17% greater than Mike’s Giraffatitan estimate and 43% greater than the Benson et al 2014 estimate).

    As noted above though, this may be the wrong femur:humerus ratio if that of Brachiosaurus is underestimated by overestimating the humerus circumference…

  18. Mike Taylor Says:

    I hope the message people are taking away from this is not “Brachiosaurus weighed 56000 kg”, but “Be very wary of mass estimates extrapolated from a single measurement of a single bone”!


  19. […] As promised, some thoughts on the various new brachiosaur mass estimates in recent papers and blog-posts. […]


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