Sunday, September 7, 2014

On this occasion of receiving a new giant dinosaur: thinking about dinosaur size estimates

Dinosaur size is something that seems to reduce even otherwise sensible folks to fanboys or fangirls. One of the points that is inevitably addressed in a popular article on a new dinosaur (along with the de rigueur reference to Tyrannosaurus rex) is how big it was. Maybe it was the size of a dog, or a horse, or an elephant. They keep standard elephants in various cities for comparative purposes, just like the old prototype meters. (If a dinosaur is between the size of a dog and about half an elephant, it doesn't get press unless it's got some kind of schtick.) A classic of children's books is "the length of [x number of] school buses". One that seems largely retired is "could look into a [x]-story window". If you are familiar with the nuts and bolts of Wikipedia, and ever go spelunking under the "history" tab of dinosaur articles, you'll find that one of the most common sequences of edits is someone wedging an extra meter or five tons into a size estimate, followed by someone reverting them. You might think that these measurements are pretty darn solid and reliable, for all the passion they inspire. Well...

"Faster than a beer-league softball player! More powerful than the disapproval of your peer group! Longer than the average school bus! Able to look into second-story windows without straining itself!"

"We're all individuals!"

The perils of dinosaur size estimates are fairly simple to enumerate. Let's begin with the subjects being observed. Most dinosaurs are known from the remains of a single individual. In virtually all cases, that individual's skeleton is incomplete, so some improvisation with (hopefully) related animals is required if you want to fill in the gaps. Say you've got a best-case scenario, where the skeleton is basically complete and articulated. You are now equipped to make intelligent statements about the size individual. There are a number of important parameters that you can't take into account:
  • How has crushing and deformation distorted the specimen?
  • How old was the individual?
  • What sex was the individual, and is that important for dimensions?
  • Was this individual normally proportioned? Was it unusually large or small? Did it have any conditions that affected its size?
  • Did it belong to a species that had different sizes in different geographic areas?
  • Did its species change size over the time it existed?
  • Did its species have significant nonbony tissues or other non-fossilized characteristics that affected its size? For example, was there a lot of cartilage? Were there thick intervertebral discs? Did it have a lot of air sacs that would have made it lighter? How about its muscles and fat deposits? How much weight would feathers add?
If, like most cases, you only get part of the skeleton or just a few bones, things just get worse.

If you have multiple individuals, many of these problems still hold, but you can at least start to address some of them. For example, typical proportions will start to come into focus, and alterations from crushing and deformation will be more obvious.

Making measurements

Let's say you've somehow stumbled onto a find that would make even the coldest-hearted paleontologist weep. You've got 500 complete, articulated skeletons of Tyrannosaurus rex in a small area, and you know they all died at the same time because each one is holding a ticket, fashioned from an ankylosaur scute, with the same date on it. Aside from the fact that everyone at the next Society of Vertebrate Paleontology meeting will either want to be your best friend or kill you out of jealousy, you now have a sample size that will allow you to do some interesting things statistically (as long as you remember that the answers apply to the tyrannosaurs of this time and place). Inevitably, someone is going to want to know the biggest/smallest/average. What is the best way to answer this?

Measuring a whole Tyrannosaurus is an interesting conceptual problem. If you want to get the length, you quickly run into the realization that you are dealing with something that is not a straight line. How do you take into account the natural curves of the body? In various reptiles and amphibians, a length known as "snout to vent" is often used, from the tip of the snout to the opening of the versatile cloaca; the idea is to exclude the tail, which is variable and often lost and regrown. Dinosaurs are not as convenient; the problem is not so much the tail but the neck and anterior torso, which are often strongly curved (see for example hadrosaurs and stegosaurs). Going along the curve of certain dinosaurs will lead to greater lengths than the animal's "effective" length (which is affected by choices in reconstruction). Despite this rather obvious issue, it is rare that anyone explains how exactly they measured when they tell you that, say, their new pachycephalosaurid Curleyia howardi was 2.5 meters long. Is that along the curve, which is reasonably simple albeit anatomically impossible to actually attain, or something else? If you want to get the mass, well, you have your choice of formulas for estimation, all of which have their strong points, biases, and flaws (and there's certainly no harm in using multiple methods). The important thing, again, is to say how you did it.

Height is not a particularly useful dimension for dinosaurs, and has receded into the same place where they keep the dinosaurs with the "tailed scaly human" posture. Dinosaurs were hindlimb dominant, so shoulder height isn't relevant for most. The hindlimbs of most were permanently flexed, so you run into the "straight line" problem again if you try to get at hip height. Head height runs into a multitude of problems, from which part of the head is considered the benchmark, to the posture of the limbs and neck, to the fact that many dinosaurs had low heads but big bodies (armored dinosaurs especially). Oddly, the more you get into the question of overall linear dimensions, the more it seems like dinosaurs didn't "want" to be measured, at least not with any simple straight lines.


Say you've done a great job estimating size. You send your estimates off into the world. Immediately they become used as monolithic figures for the entire species, over its entire time of existence, over its entire geographic range, for both sexes and all individuals, as if every individual of that species or genus came standard-issue and produced to exacting manufacturing standards, like a plastic toy. Then your numbers will be abandoned once someone comes up with a more pleasing (read: larger) estimate.

In the end

There's nothing intrinsically wrong with being fascinated with how massive or long a given dinosaur was. The tricks are to recognize the very real limitations of our knowledge of dinosaur size, to clearly explain what you're doing if you're in the business of making estimates, and to avoid getting caught up in the whole thing. Taking it too seriously just ruins things. When people start arguing about this dinosaur being 14 or 15 or 16.75 m long, compared to that dinosaur at 13 or 16.3 m long, vis-à-vis an isolated jaw in a museum collection that can be extrapolated to an 18.9 m critter under certain conditions, there's not a darn thing that can be done except to leave quietly. This is not to pick on news-media-dinosaur-of-the-past-week Dreadnoughtus or news-media-dinosaur-of-this-week Spinosaurus. They just happened to be there, that's all. In general, these principles also apply to other forms of ancient life; it's just easy to point to dinosaurs because size has for so long been one of their calling cards.

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