Archive for the ‘Data Exploration’ Category

Some (finalish) results!

May 17, 2013 9 comments

Matt and I have been meeting weekly for the past three weeks to have ODP work days–just to crank through analyses, etc. Mostly, it’s a matter of sitting down and forcing each other to do stuff. Matt’s posting soon, but in the meantime I thought I’d throw out some “final” results. These are regressions on phylogenetically independent contrasts (PICs), with analyses considering the whole sample, unequivocal quadrupeds (following Maidment and Barrett’s assignments), and unequivocal bipeds (following Maidment and Barrett, again).

A few quick notes (all of which are going into the main article text at some point)…PICs were calculated in the PDAP package of Mesquite. Limb lengths were log-transformed prior to analyses (which helped to move things towards normality a little bit, but not entirely). Branch lengths were initially set to divergence times, but we found that these violated the assumptions of PICs, and thus some transforms were used (to be outlined in the manuscript as well as a future post, once we’ve pulled that text together).

Below, I’m including the preliminary results text for this part of the analysis, the associated table, and table caption. Enjoy! And feel free to throw in some comments if you have any.

Intra- and interlimb scaling
Analyses including all taxa as well as analyses considering only unequivocal quadrupeds showed similar scaling patterns. Forelimb length scaled with strong positive allometry relative to hind limb length, whereas the distal hind limb elements (tibia and metatarsal III) collectively scaled with strong negative allometry relative to femur length. The distal forelimb (radius and metacarpal III) scaled isometrically relative to the humerus; however, we note that the lower confidence interval for the entire sample only barely excludes positive allometry. We thus speculate that a larger sample may ultimately demonstrate positive allometry.
When considering only unequivocal bipeds, none of the slopes differed from isometry. However, we note that this subset of taxa also had some of the smallest sample sizes considered here, and a larger sample might uncover allometric scaling patterns.

Table. Results of RMA (reduced major axis) regressions of PICs (phylognetically-independent contrasts) for logged limb segment lengths in ornithischian dinosaurs. In the “Allometry” column, “0” indicates a slope indistinguishable from isometry, “+” indicates a slope consistent with positive allometry, and “-” indicates a slope consistent with negative allometry. The numbers in parentheses in the “Slope” indicate the 95 percent confidence interval for the slope.










Distal Forelimb


1.139 (0.996–1.301)





Distal Hind Limb

0.812 (0.715–0.921)







1.301 (1.198–1.413)



Quadruped Only


Distal Forelimb


1.138 (0.929–1.393)



Quadruped Only


Distal Hind Limb

0.742 (0.581–0.949)



Quadruped Only




1.237 (1.027–1.489)



Biped only


Distal Forelimb


0.829 (0.588–1.17)



Biped only


Distal Hind Limb


0.903 (0.739–1.105)



Biped only




1.009 (0.543–1.876)



Regressions for PICs including the entire sample. The blue line indicates isometry.

Regressions for PICs including the entire sample. The blue line indicates isometry.




Presentation Draft – Early Results

October 12, 2012 4 comments

On Saturday, I’ll be giving a short presentation about (very) preliminary results from the ODP, for the 1st Annual Southwest Regional Joint DVM&DCB (Division of Vertebrate Morphology and Division of Comparative Biology) meeting of SICB (Society of Integrative and Comparative Biology). This conference is a one-day event held on the campus of Cal State San Bernardino, and targets functional morphologists and their kin (including paleontologists).

The presentation is entitled “Morphological disparity, locomotion and limb proportions in ornithischian dinosaurs,” and it’s set up as a 5 minute talk. One of the cool things about DVM is the option of a 5 minute format – perfect for work that is in its nascent stages or “crazy” ideas that you just want to throw out there. Given the very preliminary nature of the analysis (and the fact that I’m co-author on three posters at the Society of Vertebrate Paleontology meetings next week), I jumped at the chance for this format. Plus, the talk was a good opportunity to kick my butt in gear and do some real analysis.

I don’t have a lot of time at this second to detail every aspect of the methods, but here is a sketch:

  • Data were trimmed down to one entry per taxon, choosing the largest and most complete specimen possible. In a handful of cases, missing data were interpolated via regression (to estimate tibia length from fibula length) or other specimens of the same taxon.
  • Taxa were binned into five time categories, each spanning roughly 34 million years. Any finer bins, and there just weren’t enough taxa.
  • I ran principal coordinates analyses on the data, for forelimb, hindlimb, and all limbs together. Within each temporal bin from the results, I calculated the sum of variance and nth root of variance. This gives a measure of morphological disparity in each bin – high variance, high disparity. The analyses were run with the raw data, as well as data that were standardized within each taxon by the geometric mean. This was to attempt to remove the effects of body size.
  • I plotted the data in each bin. In order to compare the raw results vs. geometric mean results, I normalized the data to the largest value in each category.
  • A few notes of caution – I did not perform any statistical tests on the data (bootstrapping, confidence intervals, etc.). So, the results should not be considered to have particular statistical significance at any level. Also, no attempt was made to accommodate for sampling effects or phylogeny. Caveat emptor.
  • In any case, there are some cool results. Looking at hind limbs, there is a big jump in disparity after the first 60 million years (or so) of evolution – not unexpected, given the explosion of forms in the mid-Jurassic. What was more interesting was the fact that the disparity stayed constant when looking at raw values, but when values were corrected for size using a geometric mean, there was a big drop in disparity during the last 60 million years or so. On first consideration, this suggests to me that body size is driving some of the disparity values. Body size stayed big after the Middle Jurassic, but overall morphological disparity (in what those large body forms looked like) decreased. I wonder if some of this is due to the extinction of stegosaurs (with their bizarro limbs) at the end of the Jurassic / early Cretaceous. Forelimb disparity (when correcting with a geometric mean) by contrast takes a big jump in the late Cretaceous – I wonder if this is due to hadrosaurs, with their conventional hind limbs but really, really weird forelimbs. Food for thought.

Tonight I put together a first draft of the slides for my presentation. Supporting data are here, and a PDF of the slides is here. I’m going to do some more editing tomorrow, so any suggestions are welcome. Keep in mind that the slides are pretty rough right now, so forgive any ugliness there. Also, remember that I’m dealing with a 5 minute format, so there’s only so much more I can add (and I think I’ll have to trim some stuff – we’ll see how much time is in the mix after I run through it once out loud).

The final version, after presentation on Saturday, will be archived at figshare.

On continua and categories in paleoecology. . .or, an example application of ODP data

July 14, 2011 9 comments

Today we’re delighted to have a guest post from Dr. Chris Noto, a new assistant professor at University of Wisconsin-Parkside, and an old friend of mine from our graduate school days together at Stony Brook University. Chris has had a long-running interest in dinosaur paleoecology, and thus it only seemed natural for him to apply these interests to the ODP data. Enjoy!

Chris Noto

Chris Noto, at home in the field

In describing the ecology of an organism our first inclination may be to simply go observe it in its day-to-day existence. Therefore, at its core, ecology is primarily a science of the living and this is reflected in the methods and theories one finds in the literature. Over the past couple decades there has been a growing interest in the relationship between organismal morphology and ecology, which is now often referred to as “ecomorphology”(Losos 1990; Ben-Moshe et al. 2001; Aguirre et al. 2002; Zeffer et al. 2003; Sacco and Van Valkenburgh 2004). This has opened entire new areas of research into the covariation between organisms and their environment, which is also the basic foundation for understanding evolutionary change over longer spans of time.

Some paleontologists have applied ecomorphological principles to reconstructing the paleoecology of certain extinct groups, including carnivorans (Palmqvist et al. 1999), birds (Hertel 1995), and especially ungulates (Solounias and Semprebon 2002; Meehan and Martin 2003; DeGusta and Vrba 2005; Klein et al. 2010). Changes in the types and/or proportions of ecomorphs in a fossil community have also been used as evidence of environmental and evolutionary responses to climate change(Van Valkenburgh 1995; Meehan and Martin 2003; Badgley et al. 2008; Noto and Grossman 2010). You will note though that a lot of this research relies on comparison to living analogs related to the fossil groups in question. How do we explore the paleoecology of groups that completely lack extant analogs?

If there’s one thing we’ve learned through all this research, it’s the fact that:

  1. Certain morphological adaptations occur regardless of species (convergence) because of specific habitat constraints, and
  2. Morphological differences between species will occur due to diverging ecologies, even if we don’t know exactly what ecological functions those morphological differences actually represent.

But, we won’t know those differences exist until we look for them. Paleoecology is first and foremost comparative: we take our fossils and compare them to other related taxa and living forms to better understand their place in the original community. Often we assign categories to taxa, such as “carnivore”, “biped”, etc.; however, differences between species are often better described by a continuum than a set of categories(Carrano 1999). The morphology of an organism reflects the amount of time it spends doing certain activities or performing certain functions. For example, a sloth can swim on occasion even if it is not particularly well adapted for it. Dinosaur paleoecology is finally moving in the direction of our mammalian colleagues by using quantitative measures of morphology (which allow for continua) instead of assigning discreet categories.

The ODP is one of the first large-scale projects to bring together the kind of dataset necessary to study dinosaur ecomorphology. In a recent paper I published looking at differences between dinosaur fossil communities (Noto and Grossman 2010), I was forced to use categories in assigning ecomorphs, which artificially restricted the analysis by forcing me to choose a category when uncertainty existed. In this case it was whether certain non-hadrosaur ornithopods were bipedal or quadrupedal. With ODP data, it is now possible to take a more quantitative (and nuanced) approach to this question.

To explore possible trends in ornithischians, I used humerus length and mediolateral width measurements to calculate Mike Taylor’s Gracility Index (GI; Taylor 2009) using only the largest individual from each species. These data were log transformed and plotted against the log of humerus length (to help minimize the effects of size and codependency). The resulting plot clearly separates the taxa, with more bipedal taxa having relatively gracile humeri and quadrupedal groups have more robust humeri. There are two ways to use this graph. First, we can look at the distribution of taxa from each group and see whether they fit more towards a bipedal or quadrupedal type; those intermediate to the extremes are referred to as facultative. These are my own divisions based on where I see breaks in the data. Basal ceratopsians, for example, occur mainly towards the bipedal or facultative ends of the spectrum, while derived Neoceratopsians are firmly on the quadrupedal end of things. Another way to look at the plot is how robust we may expect the humerus to be for a taxon of a given size. The dashed line is drawn across the middle of the plot. For a given humerus length we can compare GI between taxa. For example, Iguanodon has a more robust humerus (lower GI) than most ornithopods in the dataset. Furthermore, we can spot outliers, which may point to either extreme specialization or faulty data. The theropod Mononykus has an extremely robust humerus, approaching the level of Triceratops, which is related to its specialized digging forelimb. On the other hand, Cerasinops appears to have the most robust humerus of all, however as Mike pointed out to me, the original paper describes the humerus as extremely gracile and gives no width measurement. So where did the width measurement come from? This particular data point is worth another look.

Ecomorphology Plot

Humeral robustness as a function of humeral length. Select taxa labeled in gray. Cera.=Cerasinops, Gypo.=”Gyposaurus”, Herr.=Herrerasaurus, Igua.=Iguanodon, Mono.=Mononykus, Post.=Postosuchus, Psit.=Psittacosaurus, Scut.=Scutellosaurus, Stego.=Stegosaurus, Thec.=Thecodontosaurus, Tric.=Triceratops.

As you can see, the distribution of humeral morphologies indicates a gradual continuum of locomotor strategies from fully bipedal to full quadrupedal. Quantitative data such as this could then be fed into a paleoecological analysis instead of categories, allowing for more refined analysis of ecological differences and similarities among paleocommunities over space and time. While evolutionary trends are certainly important, we must not forget the ecological context of the morphological patterns we are studying.


Aguirre LF, Herrel A, van Damme R et al. (2002) Ecomorphological analysis of trophic niche partitioning in a tropical savannah bat community. Proceedings of the Royal Society of London Series B-Biological Sciences 269:1271-1278

Badgley C, Barry JC, Morgan ME et al. (2008) Ecological changes in Miocene mammalian record show impact of prolonged climatic forcing. Proc Natl Acad Sci U S A 105:12145-12149

Ben-Moshe A, Dayan T, Simberloff D (2001) Convergence in morphological patterns and community organization between Old and New World rodent guilds. Am Nat 158:484-495

Carrano MT (1999) What, if anything, is a cursor? Categories versus continua for determining locomotor habit in mammals and dinosaurs. J Zool 247:29-42

DeGusta D, Vrba E (2005) Methods for inferring paleohabitats from discrete traits of the bovid postcranial skeleton. J Archaeol Sci 32:1115-1123

Hertel F (1995) Ecomorphological indicators of feeding behavior in recent and fossil raptors. Auk 112:890-903

Klein RG, Franciscus RG, Steele TE (2010) Morphometric identification of bovid metapodials to genus and implications for taxon-free habitat reconstruction. J Archaeol Sci 37:389-401

Losos JB (1990) Ecomorphology, performance capability, and scaling of West Indian Anolis lizards: an evolutionary analysis. Ecol Monogr 60:369-388

Meehan TJ, Martin LD (2003) Extinction and re-evolution of similar adaptive types (ecomorphs) in Cenozoic North American ungulates and carnivores reflect van der Hammen’s cycles. Naturwissenschaften 90:131-135

Noto CR, Grossman A (2010) Broad-scale patterns of Late Jurassic dinosaur paleoecology. PLoS ONE 5:e12553

Palmqvist P, Arribas A, Martinez-Navarro B (1999) Ecomorphological study of large canids from the lower Pleistocene of southeastern Spain. Lethaia 32:75-88

Sacco T, Van Valkenburgh B (2004) Ecomorphological indicators of feeding behaviour in the bears (Carnivora : Ursidae). J Zool 263:41-54

Solounias N, Semprebon G (2002) Advances in the reconstruction of ungulate ecomorphology with application to early fossil equids. Am Mus Novit:1-49

Taylor M (2009) A re-evaluation of Brachiosaurus altithorax Riggs 1903 (Dinosauria, Sauropoda) and its generic separation from Giraffatitan brancai (Janensch 1914). J Vert Paleontol 29:787-806

Van Valkenburgh B (1995) Tracking ecology over geological time – evolution within guilds of vertebrates. Trends Ecol Evol 10:71-76

Zeffer A, Johansson LC, Marmebro A (2003) Functional correlation between habitat use and leg morphology in birds (Aves). Biol J Linn Soc 79:461-484

Forelimb Proportions, Ternary Style

November 16, 2010 11 comments

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”

Categories: Data Exploration

By Popular Demand. . .

March 10, 2010 11 comments

Femur:Tibia Ratio in Marginocephalians, and Relevant Outgroups

As a follow-up to our last post on thyreophorans, here are marginocephalians (ceratopsians and pachycephalosaurs) with some of their outgroups. Moving or removing the uncertainly-placed Stenopelix has little effect on character reconstruction.

Categories: Data Exploration

Data Are Pretty

March 9, 2010 18 comments

Now that we’ve gotten a reasonable phylogeny hammered out, it’s time to start putting it to use! Just for fun, I used the (open source and free to download) program Mesquite to plot the femur:tibia ratio (as John Dziak had talked about not so long ago) as it changed from basal ornithischians up through Thyreophora, the clade including ankylosaurs and stegosaurs. The cladogram shown here only illustrates taxa for which we know the ratio, and species with multiple individuals had their data averaged.

Femur:Tibia Ratio

Femur:Tibia Ratio, With a Focus on Thyreophora. Larger values equal relatively long femora.

Note that everything up through and including Scutellosaurus is presumed to be bipedal; after that, they’re quadrupedal. There’s a rather major change! Rather than the tibia being longer than or approximately equal in length to the femur, the femur ends up much longer than the tibia (and Stegosaurus is just insane in this respect)! Now the interpretation of this isn’t as easy as you might think. Is it due to being quadrupedal? Or is it due to being a big animal? The bipedal guys are all small, and the quadrupedal guys are all relatively large, so it’s tough to separate these two factors. Either way, we can say something interesting about locomotor evolution! And, note that the branches between nodes are reconstructed, with a reasonably wide error bar. So, please don’t consider them absolute truth.

And while I’m thinking of it. . .why didn’t theropods ever go quadrupedal? Some of them are as big as the largest quadrupedal ornithischians! Quadrupedal vs. bipedal locomotion can’t strictly be a size thing, then. Is there something about being a carnivorous dinosaur that discourages quadrupedalism? Perhaps the use of the forearms for prey acquisition? This is something we’ll want to touch on in the paper.

P.S.: The latest version of the combined spreadsheet is available here (Excel spreadsheet).

Categories: Data Exploration

Mid-December Update

December 13, 2009 Leave a comment

We’re long overdue for an update post. Many of our regular contributors, and a few new ones, have kept the data rolling in. Now, we’ve got over 1,400 verified entries! Thank you to everyone who has helped out with this effort. We’ve got another month and a half of data collection (according to the current schedule), so it’s not too late to get in on the action.

I’d like to give special recognition to ODP contributor Rob Taylor, who has done some fantastic work in cross-checking bibliographic entries with the various verification and public data lists. It’s a tedious task, but very important for ensuring that we have the best database possible. Thank you, Rob!

Finally, let’s do a little data exploration. Although stegosaurs have a rather crummy fossil record when it comes to delicate bits like hands and feet (or at least a crummy publication record), for some reason their ontogenetic series are crazy good. And, people who work on ontogeny of stegosaurs actually publish raw measurements! This means we can do some pretty cool meta-analyses of their data.

Femur Length vs. Tibia Length in Stegosaurus

I pulled out all of the data that are referable to Stegosaurus (or plausibly referable to Stegosaurus), and found specimens with humerus, ulna, femur, and tibia measurements. The specimens range from the really big (femur length 1,300 mm) to the rather small (femur length ~300 mm). At right is a log plot showing hind limb proportions for those individuals with both femora and tibiae preserved. We can make a comparable plot for humerus vs. ulna (not shown), and also run regressions on the data.

Interestingly, femur length and tibia length scale isometrically–their proportions are similar, regardless of body size (RMA slope=1.0057, 95 percent confidence interval 0.9049 – 1.07, N=15). By contrast, the ulna scales with positive allometry relative to the humerus–it gets relatively longer as body size increases (RMA slope=1.16, 95 percent confidence interval 1.087 – 1.317, N=15). Perhaps this is due to the olecranon process being bigger in bigger animals? We can’t really tell from the data. Finally, it looks like the humerus scales with negative allometry relative to the femur, although the confidence interval just barely includes isometry (RMA slope=0.964, 95 percent confidence interval 0.9081 – 1.004, N=14). [Note: If you’re not familiar with terms like allometry and isometry, check out this post for an explanation. And, all of the slopes presented above are for log-transformed data] It would be lots of fun to compare the stegosaur data with other ornithischians, but unfortunately the published data are just too sparse right now.

Stegosaurus, from Marsh's 1896 Dinosaurs of North America


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