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()

Relevant References for the ODP

Olde Timey Restoration of Scelidosaurus, after Marsh

In response to a recent query on this blog, ODPer Christian Foth contributed a list of papers potentially relevant to the ODP, specifically limb posture and evolution in ornithischian dinosaurs. It’s important to recognize work that others did before and see how it relates to ours. Furthermore, a good reference list is essential for the upcoming manuscript.

What can you do?

If you think of another paper that might be added to the list (within reason, of course), drop a line in the comments section. If you are interested in providing a summary of a certain paper as a guest blog post (either here or at your own blog), that would be great, too. As always, one need not be a Ph.D’ed scientist to apply! We’re just looking for a short summary.

For my part, I added the Middleton and Gatesy reference – although it deals with theropods, I think some of the background info and analytical methods are quite relevant. Hmm. . .that might be a good one to blog about.

Reference List in Progress

Alexander R. 1985. Mechanics of posture and gait of some large dinosaurs. Zoological Journal of the Linnean Society 83: 1-25.
Bakker RT. 1968. The superiority of dinosaurs. Discovery 3 (2): 11-22.
Biewener (1983). Allometry of quadrupedal locomotion: the scaling of duty factor, bone curvature and limb orientation to body size. J. Exp. Biol. 105: 147-171.
Bonnan MF & P Senter. 2007. Were the basal sauropodomorph dinosaurs Plateosaurus and Massospondylus habitual quadropeds. Special Papers in Palaeontology 77: 139–155
Bonnan, MF, & AM Yates. 2007. A new description of the forelimb of the basal sauropodomorph Melanorosaurus: implications for the evolution of pronation, manus shape and quadrupedalism in sauropod dinosaurs. pp. 157-168 in: Paul M. Barrett and David J. Batten (eds.), Special Papers in Palaeontology 77: Evolution and Palaeobiology of Early Sauropodomorph Dinosaurs. The Palaeontological Association, U.K.
Bultynck P (1992) An assessment of posture and gait in Iguanodon bernissartensis Boulenger, 1881. Bulletin de l’Institut Royal des Sciences Naturelles de Belgique: Sciences de la Terre 63: 5-11.
Carrano MT. 2000. Homoplasy and the evolution of dinosaur locomotion. Paleobiology 26 (3): 489-512.
Carrano MT (2001) Implications of limb bone scaling, curvature and eccentricity in mammals and non-avian dinosaurs. Journal of Zoology 254: 41-55.
Dilkes DW. 2000. Appendicular myology of the hadrosaurian dinosaur Maiasaura peeblesorum from the Late Cretaceous (Campanian) of Montana. Transactions of the Royal Society of Edinburgh, Earth Sciences 90: 87-125.
Dilkes DW. 2001. An ontogenetic perspective on locomotion in the Late Cretaceous dinosaur Maiasaura peeblesorum (Ornithischia: Hadrosauridae). Canadian Journal of Earth Sciences 38: 1205-1227.
Dodson, P & JO Farlow. 1997. The forelimb carriage of ceratopsid dinosaurs. DinoFest International Proceedings 393-398.
Galton PM. 1970. The posture of hadrosaurian dinosaurs. Journal of Paleontology 44 (3): 464-473.
Garstka WR & DA Burnham. 1997. Posture and stance of Triceratops. Evidence of digitigrade manus and cantilever vertebral column. DinoFest International Proceedings 385-391.
Heinrich DE, Bruff CB & DB Weishampel. 1993. Femoral ontogeny and locomotor biomechanics of Dryosaurus lettowvorbecki (Dinosauria, Iguanodontia). Zoological Journal of the Linnean Society 108: 179-196.
Hutchinson JR. 2004. Biomechanical modeling and sensitivity analysis of bipedal running ability. I. Extant taxa. Journal of Morphology 262: 421-440.
Johnson RE, Ostrom JH (1995) The forelimb of Torosaurus and an analysis of the posture and gait of ceratopsian dinosaurs. In: Thomason JJ, editor. Functional Morphology in Vertebrate Paleontology. New York: Cambridge University Press. pp. 205-218.
Kilbourne BM & PJ Makovicky. 2010. Limb bone allometry during postnatal ontogeny in non-avian dinosaurs. Journal of Anatomy 217: 135-152.
Kubo T & MJ Benton. 2007. Evolution of hindlimb posture in archosaurs: limb streeses in extinct vertebrates. Palaeontology 50 (6): 1519-1529.
Lee DV & SG Meek 2005. Directionally compliant legs influence the intrinsic pitch behaviour of a trotting quadroped. Proceedings of the Royal Society B 272(1563): 567–572.
Mallinson. 2010. CAD assessment of the posture and range of motion of Kentrosaurus aethiopicus Hennig 1915. Swiss J Geosci 103: 211-233.
McMahon, T (1975) Allometry and biomechanics: Limb bones in adult Ungulates. Am. Nat. 109:547-563.
Middleton KM & S Gatesy. 2000. Theropod forelimb design and evolution. Z J Linn Soc 128: 149-187
Organ CL. 2006. Biomechnics of ossified tendons in ornithopod dinosaurs. Paleobiology 31 (4): 652-665.
Papantoniou V, Avlakiotis P & R Alexander. 1999. Control of a robit dinosaur. Phil.Trans. R. Soc. Lond. B 354: 863-868.
Paul GS & P Christiansen. 2000. Forelimb posture in neoceratopsian dinosaurs: implications for gait and locomotion. Paleobiology, 26 (3): 450–465.
Romer AS. 1923. The ilium in dinosaurs and birds. Bulletin American Museum of Natural Histroy 48: 141-145.
Raichlen DA. 2006. Effects of limb mass distribution on mechanical power outputs during quadrupedalism. The Journal of Experimental Biology 209: 633-644
Romer AS. 1927. The pelvic musculature of ornithischian dinosaurs. Acta Zoologica 8: 225-275.
Sellers WI & PL Manning. 2007. Estimating dinosaur maximum running speeds using evolutionary robotics. Proceedings of Royal Society B 274: 2711-2716.
Senter P. 2007. Analysis of forelimb function in basal ceratopsians. Journal of Zoology 273: 305-314.
Sternberg CM. 1965. New restoration of hadrosaurian dinosaur. National Museum of Canada, Natural History Papers 1-5.
Taylor CR. 1978. Why change gaits? Recruitment of muscles and muscle fibers as a function of speed and gait. American Zoologist 18: 153.161.
Tereshchenko VS. 1994. A reconstruction of the erect posture of Protoceratops. Paleontological Journal 28 (1): 104-119.
Tereshchenko VS. 1996. A reconstruction of the locomotion of Protoceratops. Paleontological Journal 30 (2): 232-245.
Tereshchenko VS. 2008. Adaptive features of protoceratopoids (Ornithischia: Neoceratposia). Paleontological Journal 42 (3): 273-286.
Thompson S & R Holmes. Forelimb stance and step cycle in Chasmosaurus irvenenesis (Dinosauria: Neoceratopsia). Palaeontologica Electronica 10 (1): 5A.
Thulborn RA. 1982. Speeds and gaits of dinosaurs. Palaeogeography, Palaeoclimatology, Palaeoecology, 38: 227-256.
Thulborn RA. 1984. Preferred gaits of bipedal dinosaurs. Alcheringa 8 (3): 243-252.
Yates, Adam M., Matthew F. Bonnan, Johann Neveling, A. Chinsamy and Marc G. Blackbeard. 2009. A new transitional sauropodomorph dinosaur from the Early Jurassic of South Africa and the evolution of sauropod feeding and quadrupedalism. Proceedings of the Royal Society B, published online. doi:10.1098/rspb.2009.1440

 

• Alexander R. 1985. Meachanics of posture and gait of some large dinosaurs. Zoological Journal of the Linnean Society 83: 1-25.

• Bakker RT. 1968. The superiority of dinosaurs. Discovery 3 (2): 11-22.

• Bonnan MF & P Senter. 2007. Were the basal sauropodomorph dinosaurs Plateosaurus and Massospondylus habitual quadropeds. Special Papers in Palaeontology 77: 139–155

• Carrano MT. 2000. Homoplasy and the evolution of dinosaur locomotion. Paleobiology 26 (3): 489-512.

• Dilkes DW. 2000. Apendicular myology of the hadrosaurian dinosaur Maiasaura peeblesorum from the Late Cretaceous (Campanian) of Montana. Transactions of the Royal Society of Edinburgh, Earth Sciences 90: 87-125.

• Dilkes DW. 2001. An ontogenetic perspective on locomotion in the Late Cretaceous dinosaur Maiasaura peeblesorum (Ornithischia: Hadrosauridae). Canadian Journal of Earth Sciences 38: 1205-1227.

• Dodson, P & JO Farlow. 1997. The forelimb carriage of ceratopsid dinosaurs. DinoFest International Proceedings 393-398.

• Galton PM. 1970. The posture of hadrosaurian dinosaurs. Journal of Paleontology 44 (3): 464-473.

• Garstka WR & DA Burnham. 1997. Psoture and stance of Triceratops. Evidence of digitigrade manus and cantilever vertebral column. DinoFest International Proceedings 385-391.

• Heinrich DE, Bruff CB & DB Weishampel. 1993. Femoral ontogeny and locomotor biomechanics of Dryosaurus lettowvorbecki (Dinosauria, Iguanodontia). Zoological Journal of the Linnean Society 108: 179-196.

• Hutchinson JR. 2004. Biomechanical modeling and sensitivity analysis of bipedal running ability. I. Extant taxa. Journal of Morphology 262: 421-440.

• Kilbourne BM & PJ Maklovicky. 2010. Limb bone allometry during postnatal ontogeny in non-avian dinosaurs. Journal of Anatomy 217: 135-152.

• Kubo T & MJ Benton. 2007. Evolution of hindlimb posture in archosaurs: limb streeses in extinct vertebrates. Palaeontology 50 (6): 1519-1529.

• Lee DV & SG Meek 2005. Directionally compliant legs influence the intrinsic pitch behaviour of a trotting quadroped. Proceedings of the Royal Society B 272(1563): 567–572.

• Mallinson. 2010. CAD assessment of the posture and range of motion of Kentrosaurus aethiopicus Hennig 1915. Swiss J Geosci 103: 211-233.

• Organ CL. 2006. Biomechnics of ossified tendons in ornithopod dinosaurs. Paleobiology 31 (4): 652-665.

• Papantoniou V, Avlakiotis P & R Alexander. 1999. Control of a robit dinosaur. Phil.Trans. R. Soc. Lond. B 354: 863-868.

• Paul GS & P Christiansen. 2000. Forelimb posture in neoceratopsian dinosaurs: implications for gait and locomotion. Paleobiology, 26 (3): 450–465.

• Romer AS. 1923. The ilium in dinosaurs and birds. Bulletin American Museum of Natural Histroy 48: 141-145.

• Raichlen DA. 2006. Effects of limb mass distribution on mechanical power outputs during quadrupedalism. The Journal of Experimental Biology 209: 633-644

• Romer AS. 1927. The pelvic musculature of ornithischian dinosaurs. Acta Zoologica 8: 225-275.

• Sellers WI & PL Manning. 2007. Estimating dinosaur maximum running speeds using evolutionary robotics. Proceedings of Royal Society B 274: 2711-2716.

• Senter P. 2007. Analysis of forelimb function in basal ceratopsians. Journal of Zoology 273: 305-314.

• Sternberg CM. 1965. New restoration of hadrosaurian dinosaur. National Museum of Canada, Natural History Papers 1-5.

• Taylor CR. 1978. Why change gaits? Recruitment of muscles and muscle fibers as a function of speed and gait. American Zoologist 18: 153.161.

• Tereshchenko VS. 1994. A reconstruction of the erect posture of Protoceratops. Paleontological Journal 28 (1): 104-119.

• Tereshchenko VS. 1996. A reconstruction of the locomotion of Protoceratops. Paleontological Journal 30 (2): 232-245.

• Tereshchenko VS. 2008. Adaptive features of protoceratopoids (Ornithischia: Neoceratposia). Paleontological Journal 42 (3): 273-286.

• Thompson S & R Holmes. Forelimb stance and step cycle in Chasmosaurus irvenenesis (Dinosauria: Neoceratopsia). Palaeontologica Electronica 10 (1): 5A.

• Thulborn RA. 1982. Speeds and gaits of dinosaurs. Palaeogeography, Palaeoclimatology, Palaeoecology, 38: 227-256.

• Thulborn RA. 1984. Preferred gaits of bipedal dinosaurs. Alcheringa 8 (3): 243-252.

The Data Set (as it sits now)

The ODP has accumulated a whole lot of data, and now we have to make some sense out of it. The first step was to pare it down from the original monstrous mass. Based on a very lively discussion (see this post and links therein), the data are pretty much trimmed. In addition to posting a link to those data (in response to this query by Hiro), I wanted to explain some of what I’ve done with the data.

The file, freely available as an Excel workbook, contains several spreadsheets. These are explained below, by spreadsheet:

• To Analyze: Includes all of the data, minus highly incomplete or juvenile specimens. As you may recall, juveniles were rates as those listed as such in the literature, or individuals which were less than 2/3 the size of the largest individual for a species.
• Deletion Candidates: The home for the highly incomplete or juvenile specimens mentioned above. We don’t want to throw them away, after all.
• Fore Hind1 & ForeHind 2: Worksheets where I was just playing around with various ways of looking at the combined data.
• Ratios: A whole bunch of ratios between various limb elements; it’s worth exploring. This will require a more detailed post in the not-so-distant future, to explain many of these.

You’ll probably notice the abbreviation “IM”. This refers to an intermembral index – basically, the ratio between forelimb and hind limb length. There are several ways to calculate it. These include:

• IM1(U)=(Humerus+Ulna)/(Femur+Tibia)
• IM2(U)=(Humerus+Ulna+MCIII)/(Femur+Tibia+MTIII)
• IM1(R)=(Humerus+Radius)/(Femur+Tibia)
• IM2(R)=(Humerus+Radius+MCIII)/(Femur+Tibia+MTIII)

There are several other possible ways to calculate this, but they often aren’t practical in terms of missing data (many more tibiae are known than fibulae). I would suggest that intermembral indices calculated with the radius are most desirable, for two reasons. First, the radius is a widely preserved and measured bone. Second, you don’t have to deal with the olecranon process, which exaggerates the functional length of the ulna in some animals.

There you have it! Comments?

Return of the ODP!

Mantellisaurus, a big ornithopod

It’s bAAAAaaaack!

The hiatus has been a long one (far longer than expected), but now it’s time to get the show on the road again. Life has been busy for everyone, but it’s time to make some time for the ODP. Basically, Wedel was over the other night and reminded me I should do a blog post. There’s so much to see, so much to do, so much to talk about! Here’s some highlights:

• The dataset is pretty much all together; we just have to finish analyzing the darned thing. Stay tuned for more.
• I (Andy) had a fun time at SVP in Pittsburgh, and got to meet a number of ODP volunteers there. Awesomeness!
• Casey Holliday and colleagues published an interesting article on articular cartilage in dinosaur limb bones, suggesting that limb lengths may have been up to 10 percent longer than we see just from the bones. Read the paper for free at PLoS ONE – anyone interested in doing a guest post on it, perhaps?
• We should probably start putting together a reference list of papers related to the mission of the ODP: analyzing limb proportions in ornithischian dinosaurs. I’ll probably start a thread for that, too.

As added incentive, I made the ODP one of my personal goals for the Paleo Project Challenge. If you haven’t checked out the challenge yet, please do so. The main premise: make a plan to complete a project, or else face public humiliation. Let’s see if it works. . .

That’s all for now!

Image credit: By Steveoc 86, from Wikimedia Commons.