Note: This is a guest post from paleontologist and ODP contributor Randy Irmis, of the Utah Museum of Natural History.
As our fearless project leaders have stressed many times, we’re not just gathering this mountain of data for fun – we are doing it to answer major questions about the evolution of ornithischian dinosaurs. Such a great dataset can be used many ways, and we hope that other folks will do their own analyses. However, the big questions the ODP team is hoping to answer are largely related to the evolution of locomotion. One of the ways to attack this problem is to look at disparity.
Disparity vs. Diversity
Before we talk about how to investigate disparity, it’s important to discuss the meaning of this concept. Many people – including many professional scientists – confuse disparity and diversity, using the terms interchangeably, even though they are distinct concepts. In simplest terms, diversity is how many things there are, whereas disparity is how different things are. Thus, when folks talk about “morphological diversity”, what they really mean is “morphological disparity.” Take for example two sets of species of ornithischian dinosaurs. Set A includes Triceratops, Stegosaurus, and Ankylosaurus, and Set B includes Parasaurolophus, Edmontosaurus, and Lambeosaurus. These two sets have equal diversity, because they both include three species. In contrast, Set A has a higher disparity than Set B. This is because A includes three drastically different body forms, whereas B are all hadrosaurs (duck-billed dinosaurs) with the same basic body type.
One can make a qualitative comparison of disparity like the one I just described above, but this can easily become problematic when comparing taxa that differ in subtle or different ways. Thus, studies of disparity generally seek to quantify disparity in some way. The added advantage of this approach is that we can apply statistical methods to test the significance of observed differences in the data. Because most of life are complex organisms, it can often be difficult to entirely quantify in all forms the disparity between two sets of species (or other taxa). Thus, most studies choose to focus on one or more aspects of disparity. In our case, we are interested in the limbs of ornithischian dinosaurs – so the ODP will specifically be focusing on the limb disparity of ornithischian dinosaurs.
One of the most common ways to quantify disparity is by some measure of shape and size. This can be done with traditional morphometric linear measurements like those gathered for the ODP, or by more sophisticated methods such as geometric morphometrics. The simplest way to quantify disparity is using bivariate plots, with one variable on the x axis and one variable on the y axis. You can see such a plot in the accompanying figure, where I’ve used actual data from the ODP database. A necessary concept to understand is that of “morphospace”; that is, the theoretical space that includes all possible measurements. When we’re dealing with two variables, such as this bivariate plot, morphospace is often called the “cartesian plane.” In any morphospace, whether you’re dealing with two or two hundred variables, disparity is simply a measure of the distance in space between different individual or groups of data points.
In this figure, I’ve graphed humerus length vs. femur length for a specimen of Lesothosaurus, Edmontonia, and Tenontosaurus. You can see that there is a greater distance between Lesothosaurus and Tenontosaurus than there is between Tenontosaurus and Edmontonia. This means that there is a greater disparity in these measurements between Lesothosaurus and Tenontosaurus, than between Tenontosaurus and Edmontonia. In the case I’ve just shown you, size accounts for most of the disparity. Tenontosaurus and Edmontonia group closely mainly because they are so much larger than Lesothosaurus. There are many different methods for removing size from morphometric data so that we can just examine shape disparity. In this example, we’ve just looked at two variables and three data points. We could instead plot many hadrosaur and many ankylosaur data points, to get a better idea of the variance within each group before comparing between the two groups. Similarly, we can use multivariate statistical methods to examine the disparity of many different variables (in our case linear measurements) at once.
Disparity and the ODP
Now that we have a basic understanding of disparity, what do we do with it, and why should we care? There are many questions we are hoping to ask with this data. For example, were certain clades of ornithischian dinosaurs conservative in terms of limb shape whereas others had more variance? This requires investigating disparity within different clades. In contrast, we can ask whether disparity in limb shape between clades correlates with phylogeny or not. That is, do you always have less disparity between two closely related clades, and high disparity between two distantly related clades? One particularly cool question that we can use disparity to address is whether variance in limb shape changed through time within a clade. So, one might want to know if ornithischians increased, decreased, or stayed stable in limb disparity through the Mesozoic. To answer this question, we have to separate our data into different time slices (e.g., Late Triassic, Early Jurassic, Middle Jurassic, etc) and measure disparity separately for each time slice of data.
Another potentially informative comparison might be how the disparity between forelimb and hindlimb changed within and among groups, and through time. For example, marginocephalians (pachycelphalosaurs and ceratopsians) include both bipedal and quadrupedal animals, whereas the Thyreophora (stegosaurs and ankylosaurs) were predominantly quadrupedal. In quadrupedal groups, one might expect lower disparity between fore- and hindlimb measurements than in bipedal groups, where the forelimbs are distinctly shorter than hindlimbs. To conduct such an analysis, one takes advantage of the fact that there are equivalent bones in the forelimb and hindlimb. That is we can compare disparity between the humerus and femur, ulna and tibia, radius and fibula, metacarpals and metatarsals, etc.
All of these comparisons of disparity help us address macroevolutionary questions about diversification, adaptive radiations, changes in locomotion, etc. One might predict that if a group undergoes a diversification event, it might show greater variance in body shape, etc., and we can test this by looking at disparity. Similarly, one might predict that an adaptive radiation related to the evolution of quadrupedality should show a change in limb disparity. We hope to answer many of these questions by analyzing limb disparity using the ODP dataset. And we wouldn’t be able to do it without everyone’s help in gathering the data!
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.
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.