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Analytical Software

March 10, 2010 10 comments

As the past two posts have attested, we are on the cusp of doing some actual, real-life analysis. If at all possible, I want to run the analyses using freely available, open source software. Fortunately, all of the major software packages for phylogenetically-informed, quantitative analaysis are free! Here are the ones I’m looking at:

  • For constructing trees and some simple analyses: Mesquite. (all of the tree plots you’ve seen have been done in this program)
  • For general statistical analysis: R, along with the smatr, ape and ggplot2 packages. I will make a serious effort to post all scripts that are used to generate graphics and analyses; I would encourage all of you to do the same.
  • For additional analysis of quantitative data in a phylogenetic context: COMPARE.
Categories: Basics, Miscellaneous

The Analyses Ahead

February 23, 2010 52 comments

Scutellosaurus, a presumably bipedal thyreophoran, unusual in a clade that was almost entirely quadrupedal

As we finish up combining the data, it’s time to start thinking about the specific analyses that we’re going to do. What are the specific questions we’re asking? What are the techniques that we need to address the questions? Some excellent discussions between ODPers have been happening in one of the recent posts, and I was hoping to continue that here. In particular, I wanted to refocus the discussion on the project’s essential questions, and consider the types of analyses that we can use to answer each question. I’m just thinking out loud here (this is open notebook science, after all), and invite suggestions and discussion in the comments section. In particular, I’m referencing the “big questions” outlined in one of our first posts.

Why did ornithischians evolve quadrupedality multiple times?
I think this one is going to have to simply rely upon our interpretation of the data. After all, we can perhaps answer “how,” but the “why” can’t really be answered in this setting. So, it’s something to consider in the “discussion” section of the paper. But, see the next question. . .

Was the evolution of quadrupedality consistently associated with an increase in body size?
Here, we’re basically looking at evolutionary trends. In other words, can we detect a trend in body size within various ornithischian lineages? The more I think about this, the less I’m convinced we can directly answer the question (if you disagree, and have a solution, pipe up in the comments, please). One problem is the difficulty in knowing whether or not certain taxa were truly quadrupedal. So, where do you make the cut-off for quadrupedal vs. bipedal vs. both? In many cases we just don’t know. There’s a danger in circular reasoning, too (the limb bones look like it’s quadrupedal, so we call it quadrupedal, and then use it as an example of a quadrupedal taxon for analysis of limb bones).

But, I think we can detect trends across Ornithischia as a whole, and within specific lineages. For instance, is there a trend for increasing body size across Ornithiscians? Is there a trend for increasing body size within Ornithopoda? Ceratopsia? Thyreophora? In fact, Matt Carrano found a consistent and statistically significant increase in body size within ornithischians (and indeed, within most dinosaurs) when considering femoral measurements (go here to download a free PDF of Carrano, 2006).  So, that makes this question a little less interesting (and indeed, less publishable, because it’s already been done). Do you think we should move it to the back burner? Or should we spin it in another way? Thoughts are welcome.

Did different groups of quadrupedal ornithischians arrive at this body form in similar ways, or did they have different strategies?
Here (as far as I know) is a genuinely novel question, and I think it’s the core of the ODP’s current phase. What we’re really saying (I think) is this: We know that thyreophorans, hadrosaurs, and ceratopsids independently evolved quadrupedal locomotion. Did each group have similar limb proportions, or were they different? I think this is where we’ll want to look at principal components analysis, at least as a starting point for data visualization. And, we’ll have to do that within a phylogenetic context. A recent paper by Liam Revell (2009) addressed how to do this (thanks to ODPer Randy Irmis for bringing up this paper; you can download it for free here – it’s well worth a read).

A second way to look at this question is to look for trends in certain structures – for instance, do the metacarpals tend to get elongated in each group (relative to the rest of the arm) as different clades became quadrupedal? Here, we might use a simple non-parametric correlation of the ratio with patristic distances (see the Carrano paper, again, and references therein, for a brief introduction to this method), to investigate that question within different lineages. Basically, patristic distance estimates the distance of a particular species from the base of the tree (by the number of branching points leading up to it). A taxon that split off early in a group’s evolution would have a low patristic distance, and vice versa for one that split off late in a group’s evolution. So, we might look at the correlation of metacarpal:arm length ratio to patristic distance for thyreophorans, hadrosaurs, and ceratopsians.

I think I’ll end here for now! Please add thoughts, suggestions, corrections, and anything else you think relevant in the comments. Next time, I’ll move on to the final issue, quantifying morphological disparity in ornithischian evolution.

References
Carrano, M. T. 2006. Body-size evolution in the Dinosauria. In M. T. Carrano , R. W. Blob, T. J. Gaudin & J. R. Wible (eds.), Amniote Paleobiology: Perspectives on the Evolution of Mammals, Birds, and Reptiles. University of Chicago Press, Chicago:225-268. Freely available here.
Revell, L. J. 2009. Size-correction and principal components for interspecific comparative studies. Evolution 63: 3258-3268. Freely available here.

Image at beginning of post by Pavel Riha, licensed under the Creative Commons Attribution ShareAlike 3.0 License.

Beware the Shifting Catalog Number

February 12, 2010 4 comments

Those who have contributed to the ODP over the last few months know that a single specimen might have measurements featured in 2, 3, 4, or more separate scientific papers. In order to keep data entry and verification as transparent as possible, we’ve included the presentation from each scientific paper as a separate entry. Now, though, it’s time to combine these separate entries into composite entries that can be analyzed as a single unit (see this post for how you can help).

But, we do face some real challenges in cobbling this information together. One major problem concerns different specimen numbers or museum abbreviations for the same specimen. For those who aren’t familiar with the museum world, every specimen in a museum gets a unique number. This helps us to keep track of the data with each specimen (not just measurements, but locality information, storage location, etc.). Rather than saying “that big T. rex skull on display in that big New York museum,” we just say “AMNH 5027″. This means that it’s specimen number 5027 at the American Museum of Natural History; there’s only one specimen with that number. Believe it or not, some people memorize such minutia (maybe you’re one of them). I know the specimen numbers for most of the well-known ceratopsian skulls (just mention the phrase “YPM 1822″, and Triceratops prorsus springs to mind), but still have a tough time remembering my wife’s birthday. Believe me, I catch grief for that one.

At any rate. . .in some cases, it’s pretty easy to figure out multiple presentations of the same specimen. AMNH FR5240 (American Museum of Natural History Fossil Reptile #5240) is pretty certainly the same as AMNH 5240. There are just a few extra letters (to distinguish 5240 in the fossil reptile collection from 5240 in the modern fish collection, for instance).

Sometimes things get complicated. For instance, museums change names. The old “Geological Survey of Canada” specimens eventually became “National Museum of Canada” specimens, which then morphed into “Canadian Museum of Nature” specimens when the institution changed its name. So, the Chasmosaurus skeleton that started out as GSC 2245 became NMC 2245 became CMN 2245. “CMN” seems to be the abbreviation of choice nowadays, and luckily the specimen numbers stayed the same. Sometimes historic abbreviations are carried on through sheer inertia. For instance, “USNM” stands for “United States National Museum.” Yet, it hasn’t been called that in decades – today we know it as the “National Museum of Natural History” (or just “The Smithsonian” to most of the general public). But, for various reasons (including overlap in abbreviations with all of the other countries’ national museums), “USNM” still stands. When different publications use different abbreviations, we still have to sort out what’s going on.

Proto

AMNH 6471. . .I mean, CM 9185. This file is licensed under the Creative Commons Attribution ShareAlike 3.0 License, modified from an original posted to the Wikimedia Commons by Kevmin.

Sometimes things get really complicated. Did you know that the Protoceratops skeleton listed as AMNH 6471 by Brown and Schlaikjer’s 1940 paper is now known as CM 9185? This happened when the specimen was sent from the American Museum of Natural History to the Carnegie Museum in Pittsburgh. The only reason I know of this is because Matt Carrano had noted this in one of his data entries, and also through a chance reading of a 1981 publication on dinosaurs of the Carnegie by Jack McIntosh.

And sometimes things get just flat-out twisted. Back in the day, the Royal Ontario Museum completely renumbered their fossil collection. What was once known as the Corythosaurus ROM 5505 is now ROM 845. The Lambeosaurus ROM 6474 is now called ROM 1218. Thankfully, some papers indicate the old and the new catalog numbers. But not always. There are measurements from old papers of certain specimens (e.g., ROM 5167 and ROM 5971, specimens of Edmontosaurus regalis and Prosaurolophus maximus, respectively) that just aren’t clear. So, we’ll either hope that someone out there reading this knows the current specimen number, or we’ll have to contact a curator at the museum to find out. (feel free to chime in in the comments, if you know the answer)

These sorts of things are hugely important for the utility of our dataset, and we’re depending on each other to get these details ironed out. That’s the real strength of an open project like the ODP – anyone can contribute!

Categories: Basics, Key Concepts

Don’t Despair! Using Our Data to Investigate Disparity

December 16, 2009 9 comments

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.

Quantifying Disparity

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!

Categories: Basics

Developing a measurement protocol, part 1

September 16, 2009 13 comments

By now, those of you who have been entering data from the literature — and maybe even more those who have been measuring bones themselves — will have noticed that it’s not quite as straightforward as it sounds.  Some bones are crushed, distorted, broken, reconstructed, lost in soft peat for three months and recycled as firelighters.  And what exactly is the “length” of a curved bone like the femur of many ornithopods?  And where exactly is the “midshaft” that’s measured for the midshaft diameter?  And so on.

We want to develop an explicit protocol for what bones are worth including, what measurements need taking and how they should be taken.  But to do that, we’ll need your help.  We want to know what issues you’ve come up against as you’ve worked on ODP data, so we can figure out standard answers.  Post your questions as comments to this article: we’ll discuss them in the comments, and when we feel we have consensus, we’ll start to assemble a protocol document.

Our general feeling is that yes, there will be minor errors and distortions in the data, but there is no reason to suspect systematic bias and therefore not much to worry about (and not much we can do about it). Hopefully the database that we’re putting together will live forever and in the future people will revisit these specimens and submit “cleaned up” measurements in cases where that’s warranted. But that doesn’t mean we can’t be doing useful stuff in the meantime. It also doesn’t mean that we shouldn’t acknowledge these problems and fix them wherever possible.

So: (a) yes, crushing, distortion, reconstruction, measurement conventions, etc. are all valid concerns; (b) we will strive to overcome them to the extent possible, both immediately for the first paper and ultimately for the evolving database; but (c) these problems plague any large quantitative study of morphology — the only difference with the ODP is that those problems are out in the open; and (d) we don’t anticipate systematic bias and don’t think these problems are serious enough to prevent us from doing useful work right now.

Right then: questions, please!

Brachiosaurus altithorax holotype FMNH P25107, last three presacral vertebrae in right lateral view.  Sorry, I can't break the habit.

Brachiosaurus altithorax holotype FMNH P25107, last three presacral vertebrae in right lateral view. Sorry, I can't break the habit.

Categories: Basics, Tutorials

Introducing the Open Dinosaur Project

September 8, 2009 15 comments

Hello, and thanks for dropping by at the Open Dinosaur Project.  This blog is part of a wider project, in which we hope — with your help — to make some science.  We want to put together a paper on the multiple independent transitions from bipedality to quadrupedality in ornithischians, and we want to involve everyone who’s interested in helping out.  We’ll get to the details later, but the basic idea is to amass a huge database of measurements of the limb bones of ornithischian dinosaurs, to which we can apply various statistical techniques.  Hopefully we’ll figure out how these transitions happened — for example, whether ceratopsians, thyreophorans and ornithopods all made it in the same way or differently.

Who are “we”, I hear you ask.  The core ODP team is Andy Farke (curator at the Raymond M. Alf Museum of Paleontology, Claremont, California), Matt Wedel (Western University of Health Sciences, Pomona, California) and Mike Taylor (University College London).  We’re all researching and publishing scientists, specialising in dinosaurs — although up until now Matt and Mike have concentrated on sauropods.

As for who you are: if you care about dinosaurs, and want to make some science, then you can be involved.  It doesn’t matter whether you’re a seasoned professional palaeontologist, a high-school kid or a retired used-car salesman: so long as you can conduct yourself like a professional, you’re welcome here.

And now, for the gory details. . .

Once Again, The Research
We will create a comprehensive database of skeletal measurements for ornithischian dinosaurs, with the goal of investigating the evolution of locomotion and limb proportions in this group.

Why Ornithischians?
In terms of locomotion, ornithischians–the group of dinosaurs including stegosaurs, ankylosaurs, iguanodonts, horned dinosaurs, “duck-billed” dinosaurs, and more–are ridiculously diverse. From a bipedal ancestor, ornithischians evolved quadrupedality at least three times–in thyreophorans (ankylosaurs+stegosaurs), ornithopods (iguanodonts, duck bills, and relatives), and ceratopsians (the horned dinosaurs). This is an intriguing transition, but one that has received almost no study.

The Big Questions
A number of questions are driving the project. Some of them may be answered immediately. Some may be answered later. Some may turn out to be unanswerable in the present study. This is all part of how science works! From the very start, we want to keep the spirit of inquiry open and freely accessible for everyone.

  • Why did ornithischians evolve quadrupedality multiple times? Was it consistently associated with an increase in body size?
  • Did different groups of quadrupedal ornithischians arrive at this body form in similar ways, or did they have different strategies?
  • How diverse was the body plan of ornithischian dinosaurs?
  • Did different clades of ornithischians scale the relative proportions of their limb bones in different ways?

Constructing the Database
A huge, virtually untapped resource of skeletal measurements resides in the published scientific literature. In order to put these measurements to good use, it is necessary to place the data into a form that can be analyzed mathematically. Essentially, we aim to construct a giant spreadsheet with as many measurements for ornithischian dinosaur limb bones as possible. For simplicity, we will focus on bone lengths and diameters along the shaft. From the forelimb, we will look at the scapula, coracoid, sternal plates, humerus, radius, ulna, and manus (“hand”). Within the hind limb, we will look at the femur, tibia, fibula, and pes (“foot”).

In the old days, this would require a lot of time in the library stacks. Some aspects of the project may still require this. But, a number of scientific papers are now freely available to the general public! So, anyone with an internet connection can help out.

Who Can Participate?
Anyone! We do not care about your age, education, previous paleontological experience, or geographic location. You don’t have to be a professional paleontologist – just a person who is willing to act professionally in the accurate and ethical collection, analysis, and interpretation of real scientific data.

What Can I Do?
It’s simple! Just locate the necessary scientific papers, and start entering data into our spreadsheet. If you have access to real specimens, you may enter these data.

What Do I Get Out of This?
Two things – 1) the thrill of participating in real scientific research; and 2) an opportunity for authorship on a scientific paper. Yes, you read that correctly. All contributors to the database are given the option of joining us as authors for the final published paper. If you opt out of authorship, you will still be listed in the acknowledgments (unless you request otherwise).

How Do I Sign Up?
Simply drop an email to project head Andy Farke – andrew.farke@gmail.com – with your name and preferred email address. If you have an institutional affiliation, please include that also. . .but remember that a formal academic affiliation is not required!

Help! I’m Lost!
Never fear. . .we’re going to publish a series of tutorials in the next few days outlining how to search for scientific literature, what measurements to look for, and other important introductory pieces for those new at the research game.

Categories: Basics
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