Home > Data Exploration > Forelimb Proportions, Ternary Style

Forelimb Proportions, Ternary Style

An important part of our manuscript will simply be a description of limb proportions in ornithischian dinosaurs. For this, ternary plots really have no parallel. These graphs simultaneously plot three variables in two dimensions on an equilateral triangle. And wouldn’t you know it – we can consider each dinosaur limb to have three major bones! In the case of the forelimb, these are the humerus, radius, and metacarpal III (see this post for an explanation of why we would look at the radius rather than the ulna).

In the figure below, I’ve generated a quick and dirty ternary plot for ornithischian dinosaur forelimb proportions. You’ll note that ornithischians occupy a very small chunk of morphospace! Hadrosaurs (and one or two non-hadrosaurid ornithopods; likely ones very close phylogenetically, such as Tethyshadros) have their own special brand of metacarpal lengths (this has been discussed before). It’s an absolute shame that stegosaurs and pachycephalosaurs simply aren’t represented!

Comments or thoughts are very welcome – and if you want to generate other versions of the plot, all data are freely available (see below). In fact, we encourage you to play with the data. Drop a note in the comments if there’s an image you’d like to post here, too!

Ornithischian Limb Proportions

Ornithischian Limb Proportions (A=ankylosaurs; C=ceratopsians; H=hadrosaurs; O=non-hadrosaur ornithopods)

What Species Are Included?

  • Any species for which the three major bones of the forelimb (humerus, radius, and MC III) were known. For taxa with multiple individuals, only the largest was used. Known juveniles are excluded, to my knowledge.

How Was It Plotted?

  • The following text provides the sequence of commands that I typed into the terminal, to produce the plot. I created this plot using R 2.10.1, running on Ubuntu 10.04. The file “forelimb_tern.csv” can be downloaded here. It is taken from the “Fore Hind 1″ tab in the spreadsheet posted the other day.
  • These commands read the data file, plot a ternary plot, and export said plot to a PDF. [Important: Your web browser may "cleverly" reformat the quote marks into 'smart quotes'; so, reformat back before pasting into your terminal]
  • After I had the PDF, I manipulated it in GIMP and Inkscape, in order to produce the graphic seen above.
  • This is surely the most inelegant way to accomplish the task; I received some odd errors when trying to add a legend, and never figured out how to plot just the portion of the graph with the data. If anyone figures this out, I’d love to hear it! We will almost certainly produce a nicer version of this plot for the final manuscript.

colors <- c(“black”,”red”,”green”,”blue”)
pch <- substr(levels(taxon), 1, 1)
pch = as.character(taxon),
col = colors[as.numeric(taxon)],
main = “Ornithischian Limb Bone Proportions”

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Categories: Data Exploration
  1. Tracy Ford
    November 16, 2010 at 6:14 am

    What about the lenght of the phalanges and shape of the unguals? That would help indicate if it walked on its fore limbs or not.

  2. Andy Farke
    November 16, 2010 at 6:53 am

    Good point, Tracy. As you’ll note in one of our early posts, we can look at phalangeal length pretty easily. Ungual shape is tougher to get at, of course, with our data set. Footprints are probably the best indicator for biped vs. quadruped, in the end.

  3. Chris Noto
    November 16, 2010 at 3:24 pm

    I’m going to start playing around with the data again, but in the meantime I found two sites with free programs that make ternary plots. I know they’re not open-source, but I thought I’d share anyways, especially for those of us who haven’t learned R yet.

    Windows: http://www.prosim.net/en/newsletter/en_2005.02.12_pdt.html

    Mac: http://mac.softpedia.com/get/Math-Scientific/DeltaPlot.shtml

  4. Chris Noto
    November 16, 2010 at 4:21 pm

    While I’m playing with the new data I thought I’d post links to two free ternary plot programs. I know they’re not open source but they are free to use for those of us who haven’t yet learned R.

    Windows: http://www.prosim.net/en/newsletter/en_2005.02.12_pdt.html

    Mac: http://mac.softpedia.com/get/Math-Scientific/DeltaPlot.shtml

  5. Rob Taylor
    November 18, 2010 at 5:29 pm

    In reference to stegosaurs not being represented, is there a reason that USNM 4937 was excluded from the ternary plot, or possibly it was just an oversight? I noted that a combined entry for this specimen remains on the ‘To Analyze’ worksheet and includes length measurements for the humerus, radius and MCIII.

  6. Rob Taylor
    November 18, 2010 at 6:08 pm

    Note that if we did include our stegosaurian candidate (and assuming I did the math right), I think it would fall within the same morphospace as the non-hadrosaurian ornithopods. It looks to have forelimb proportions that are almost identical to those of Tenontosaurus tilletti specimen OU 11, which I believe is plotted.

  7. Andy Farke
    November 18, 2010 at 6:16 pm

    Rob Taylor :

    In reference to stegosaurs not being represented, is there a reason that USNM 4937 was excluded from the ternary plot, or possibly it was just an oversight? I noted that a combined entry for this specimen remains on the ‘To Analyze’ worksheet and includes length measurements for the humerus, radius and MCIII.

    Must have been an oversight – I must have used an overly pruned version of the spreadsheet that only included specimens with both complete forelimb and hindlimb measurements.

  8. emanuel tschopp
    November 19, 2010 at 8:37 am

    SMA 0092 (Stegosaurus or Hesperosaurus mjosi) has a complete right foreleg. Is there a reason why you only took the left one? I guess for the ratios it wouldn’t make a difference as long as we don’t compare left and right bones as if they were from the same side, right?

  9. Chris Noto
    November 23, 2010 at 9:41 pm

    As for making ternary plots, SigmaPlot can also produce them and is quite flexible in terms of presentation (letters instead of points, etc.). I have a copy of SigmaPlot on my computer and would be happy to make more plots, especially if there are difficulties getting them to come out just right in R.

  10. William Miller
    November 25, 2010 at 3:48 am

    I’m surprised by how closely the ceratopsians are clustered together, considering that there are very different body plans in there — I would have expected Psittacosaurus to fall out very differently from Styracosaurus or Centrosaurus.

  1. May 25, 2011 at 11:42 pm

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