No, David Attenborough, you can’t tell how heavy a dinosaur was from the circumference of its femur

January 12, 2016

I was a bit disappointed to hear David Attenborough on BBC Radio 4 this morning, while trailing a forthcoming documentary, telling the interviewing that you can determine the mass of an extinct animal by measuring the circumference of its femur.

We all know what he was alluding to, of course: the idea first published by Anderson et al. (1985) that if you measure the life masses of lots of animals, then measuring their long-bone circumferences when they’ve died, you can plot the two measurements against each other, find a best-fit line, and extrapolate it to estimate the masses of dinosaurs based on their limb-bone measurements.


This approach has been extensively refined since 1985, most recently by Benson et al. (2014). but the principle is the same.

But the thing is, as Anderson et al. and other authors have made clear, the error-bars on this method are substantial. It’s not super-clear in the image above (Fig 1. from the Anderson et al. paper) because log-10 scales are used, but the 95% confidence interval is about 42 pixels tall, compared with 220 pixels for an order of magnitude (i.e. an increment of 1.0 on the log-10 scale). That means the interval is 42/220 = 0.2 of an order of magnitude. That’s a factor 10 ^ 0.2 = 1.58. In other words you could have two animals with equally robust femora, one of them nearly 60% heavier than the other, and they would both fall within the 95% confidence interval.

I’m surprised that someone as experienced and knowledgeable as Attenborough would perpetuate the idea that you can measure mass with any precision in this way (even more so when using only a femur, rather than the femur+humerus combo of Anderson et al.)

More: when the presenter told him that not all scientists buy the idea that the new titanosaur is the biggest known, he said that came as a surprise. Again, it’s disappointing that the documentary researchers didn’t make Attenborough aware of, for example, Paul Barrett’s cautionary comments or Matt Wedel’s carefully argued dissent. Ten minutes of simple research would have found this post — for example, it’s Google’s fourth hit for “how big is the new argentinian titanosaur”. I can only hope that the actual documentary, which screens on Sunday 24 January, doesn’t present the new titanosaur’s mass as a known and agreed number.

(To be clear, I am not blaming Attenborough for any of this. He is a presenter, not a palaeontologist, and should have been properly prepped by the researchers for the programme he’s fronting. He is also what can only be described as 89, so should be forgiven if he’s not quite as quick on his feet when confronted with an interviewer as he used to be.)

Update 1 (the next day)

Thanks to Victoria Arbour for pointing out an important reference that I missed: it was Campione and Evans (2012) who expanding Anderson et al.’s dataset and came up with the revised equation which Benson et al. used.

Update 2 (same day as #1)

It seems most commenters are inclined to go with Attenborough on this. That’s a surprise to me — I wonder whether he’s getting a free pass because of who he is. All I can say is that as I listened to the segment it struck me as really misleading. You can listen to it for yourself here if you’re in the UK; otherwise you’ll have to make do with this transcript:

“It’s surprising how much information you can get from just one bone. I mean for example that thigh bone, eight feet or so long, if you measure the circumference of that, you will be able to say how much weight that could have carried, because you know what the strength of bone is. So the estimate of weight is really pretty accurate and the thought is that this is something around over seventy tonnes in weight.”

(Note also that the Anderson et al./Campione and Evans method has absolutely nothing to do with the strength of bone.)

Also of interest was this segment that followed immediately:

How long it was depends on whether you think it held its neck out horizontally or vertically. If it held it out horizontally, well then it would be about half as big again as the Diplodocus, which is the dinosaur that’s in the hall of the Natural History Museum. It would be absolutely huge.

Interviewer: And how tall, if we do all the dimensions?

Ah well that is again the question of how it holds its neck, and it could have certainly reached up about to the size of a four or five storey building.

Needless to say, the matter of neck posture is very relevant to our interests. I don’t want to read too much into a couple of throwaway comments, but the implication does seem to be that this is an issue that the documentary might spend some time on. We’ll see what happens.


22 Responses to “No, David Attenborough, you can’t tell how heavy a dinosaur was from the circumference of its femur”

  1. Stephen Gunnell Says:

    Mike, I’m not seeing your point here. From my PoV as a non palaeontologist you seem to have successfully argued that you CAN tell weight from femur circumference. Complaining about a 60% error range just looks like nitpicking.

  2. Mike Taylor Says:

    You think 60% is nitpicking?

    I weight 100 kg. Assuming my mass is within the 95% confidence interval, the same femur could mean that I weighed 160 kg or 62 kg. I think that is a pretty big deal.

  3. Thomas Holtz Says:

    To clarify, you CAN tell how massive a dinosaur was from the circumference of its femur. You simply can’t tell it precisely.

  4. Mike Taylor Says:


    Although the same would be true of a pedal phalanx — just that there is even more uncertainty. And none at all was conveyed on the radio this morning.

  5. Michael Richmond Says:

    Perhaps this is one of those uncomfortable situations in which the person being interviewed finds himself in a no-win situation.

    Q: The authors of the paper state that the mass of the Calvinoceratops was 4 tons. How did they do that?

    A: It was a wild guess.

    No, that doesn’t work. But neither, in many cases, does this:

    Q: he authors of the paper state that the mass of the Calvinoceratops was 4 tons. How did they do that?

    A: Well, first, we looked at a large set of animals living in the world today, ranging in size from tiny mice and shrews to the largest rhinos and elephants. We can measure the masses of these animals accurately, of course. Now, if we dissect these animals and measure certain properties of bones in the arms and legs, we can find a relationship between the sizes of the bones and the masses of the animals. The relationship has quite a bit of scatter, with a —

    Q: Sorry, that’s all the time we have today. Thank you very much, Professor.

    Given the constraint of providing an answer within the desired 15 seconds, and avoiding any words that would give listeners math anxiety, it’s easy to fall into the habit of making statements that sound much more definitive than one actually knows them to be.

    The fact that Attenborough used the words “femur” and “circumference” is a point in his favor: the interested reader has enough information look up the real story.

    I understand your frustration — I certainly have made my own cutting remarks after hearing interviews with fellow scientists — but it’s a tough business, and I’m willing to cut Attenborough some slack.

  6. Mike Taylor Says:

    Actually, your hypothetical answer is pretty darned good. I’d have been more than happy to have heard that this morning; and I’d love to hear explanations on that level when people are interviewed on aspects of science that I don’t know about.

    The thing is, after 64 years in the science-broadcasting business he is literally the most experienced person ever in this field. I’d have hoped that if anyone could do it right, he could.

    But as I say, my quarrel really is not with Attenborough, but with the documentary production team that apparently have him only a grossly over-simplified version of the truth.

  7. Andrew Stuck Says:

    If nothing else, shouldn’t the varying degrees of pneumaticity (I’m sure I misspelled that) throw off any measurement based on the femur alone? And then you get into varying body proportions…

  8. Mike Taylor Says:

    Well, yes, pneumaticity is one of many factors that affects body mass — but likely nowhere near the most important one. Athleticism is a big deal, and overall body shape, and seasonal fat-bearing, and simple individual variation.

  9. Matt Wedel Says:

    Given that Attenborough was explaining science that other people had done, the inherent limitations of the interview format, and the fact that a lot of work has been done to estimate the masses of dinosaurs from their limb bones (with vary degrees of emphasis on the necessarily wide error bars), I’m okay with it.

    I still have a healthy skepticism about whether this thing is actually any bigger than Argentinosaurus. I’ll feel a lot better once there’s a formally published description and mass estimate. Until then, it’s just science by press release. Here’s hoping someone delivers the goods, and soon.

  10. Thank you for the post! Speaking as a complete layperson, I love to hear more informed people’s take on pop science. I do know, after all, that constraints of time and accessibility mean an interview will inevitably contain some fuzzy science, but will generally have little idea how or where. So this is a great way to look behind the scenes, thank you!

  11. Campione and Evans published a paper in 2012 expanding Anderson et al.’s dataset and came up with a revised equation (the paper is “A universal scaling relationship between body mass and proximal limb bone dimensions in quadrupedal terrestrial tetrapods” and is open access, but I’m avoiding a link here in case that sends comments to spam). That’s the equation Benson et al. then used for their dinosaur body mass through time paper. When they estimated some dinosaur masses using the new equation, the error ranges are more like 20% in either direction – still not perfect, but I would say not too bad either.

  12. I was involved in the documentary, to a modest degree, but I am not aware what methods were used for the body mass estimation. The article says that 2 methods were used. Other than something involving femur circumference, I don’t know which. I do feel like this is an issue where it is impossible to satisfy everyone. Documentaries can’t often go over the uncertainty regarding every parameter they discuss, even the important ones. Like other commenters above say, there is just too little time and it quickly becomes a boring esoteric issue that mainly scientists would care about. I think the key thing is how the matter is handled in scientific publications, not documentaries, and I don’t think it’s Attenborough’s responsibility to suss out the science himself. As Matt notes above, there are just too many limitations to a documentary, or news story, to do this.

    I think very often scientists and others conflate coverage of documentaries/news stories and scientific publicationx. The standards are extremely different in both and long have been. Conflating them will inevitably lead to disappointment and can be misleading.

    I think the goals of the documentary were to celebrate (1) a discovery of some really well-preserved and huge titanosaurs, (2) the neat story behind the discovery and subsequent work, (3) fossils that are complete enough that science can begin to say something more confident about the lives of the animals, and (4) pretty pictures of amazing things to inspire awe in the public. None of this implies or requires 100% accuracy or delving into the intricacies.

    TLDR: W4TP

  13. Mike Taylor Says:

    Thanks, Victoria, for this important reference which I missed. I’ve added an update. BTW., feel free to include links in comments here: you’re known to the system as a non-spamming commenter, so your comments are unlikely to be held up; and even if they are, I usually get to moderating them through within an hour or two.

    Since the general feeling seems to be that what Attenborough said was OK, I’ve transcribed the actual words and linked to the audio so you can make up your own minds. All I can say is that as I heard it going out live, I found it terribly disappointing.

  14. Illiterate Scholar Says:

    Whatever the case, I hope you guys will talk more about this Titanosaur in the coming days. I’m so hyped. I’m skipping work in the morning to see the new mount on Friday.

    BTW, more pictures of the femur are now available online with David Attenborough next to it for reference.

  15. Mike Taylor Says:

    I certainly imagine we’ll write about once the paper’s out. Until then, well, we may have something to say about the documentary, but that would more likely be about the communication than the subject.

  16. Illiterate Scholar Says:

    Any idea when we’ll get the paper?

  17. Jordan Says:

    Hypothetical question: how small should the error bars be before we can say we “know” how big an animal was?

  18. Mike Taylor Says:

    Illiterate Scholar: sorry, no, I know nothing of the plans for the paper.

    Jordan, that is a good question, to which I don’t have a good answer. What are your thoughts? One useful thing to know would be this: given a complete human skeleton, how wide is the 95% confidence interval for the mass of the living person?

  19. Michael Richmond Says:

    It’s just a teeny little portion of the answer to Mike’s question, “How wide is the 95% confidence interval for the mass of the living person?”, but you can get some ideas by looking at

    Click to access sr11_014acc.pdf

    which provides median and 25-th and 75-th quartile values for weight of humans as a function of height (in the US, 1960-1962). You can break the numbers down by sex and age, too.

    Presumably one could do a better job with additional measurements of individual bones, but at least this is a start. For example, men between 45 and 54 years old, of height 69 inches, ranged (25th to 75th quartile) from 153 to 190 pounds. That’s a range of about +/- 11 percent.

    I’m sure one could have fun seeing if the range is larger or smaller for old people, or young people, or men, or women, etc.

  20. Andy Farke Says:

    Also important: there is no One True Body Mass for an individual. It’s highly variable by season, health, foraging success, etc. IIRC, the body masses used for most studies tied to skeletal parameters are single points representing mass at death. This of course does not invalidate the work–but I would be curious to see if the error bars are much less relevant when accounting for variation within a particular individual over time. Do skeletal dimensions correlate with max mass? min mass? average mass? mass at skeletal maturity?

    That would actually be a great project for someone else – how does body mass vary from day to day for a non-primate organism? And how does this relate to skeletal parameters? The former question has some research, but I don’t know of anything (off the top of my head) for the latter facet.

  21. Marco Says:

    Hello everyone!
    First I m not a big fan of mass est based on a sigle skeletal element (I Know the limits of this practice and the Huge error) but I m not here for this today…
    I m here for asking if is possible for Someone posting good photos of Futalognkosaurus dukei vertebrae…
    I Know this is a big off-topic but the blog is SvertebraePOW right?
    Thank you

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