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 (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.

R
library(vcd)
ornith=read.csv(“forelimb_tern.csv”)
attach(ornith)
colors <- c(“black”,”red”,”green”,”blue”)
pch <- substr(levels(taxon), 1, 1)
pdf(“test.pdf”)
ternaryplot(
ornith[,2:4],
pch = as.character(taxon),
col = colors[as.numeric(taxon)],
main = “Ornithischian Limb Bone Proportions”
)
dev.off()