I have several small ordered sequences of data, each of about five to ten elements. For each of them, I want to calculate a metric which captures how much they vary along the sequence. I don’t want standard deviation, or anything like it, because that would consider the sequences 1 5 2 7 4 and 1 2 4 5 7 equally variable, whereas for my purposes the first of these is much more variable.

Here is a matric that I think does what I want, and will allow me to compare different sequences for variability-along-the-sequence.

For the n-1 pairs along the sequence of n elements, I take the difference (absolute value, so always positive) between elements i and i+1. Then I average all those differences. Then I divide the result by the average of the values themselves, to normalise for magnitude.

Some example calculations:

  • For the sequence 1 5 2 7 4, the differences are 4 3 5 3, for a total of 15 and an average of 3.75. The average of the values is 1+5+2+7+4 = 19/5 = 3.8, which gives me a metric of 3.75/3.8 = 0.987.
  • For the sequence 1 2 4 5 7, the differences are 1 2 1 2, for a total of 6 and an average of 1.5. The average of the values is again 3.8, which gives me a metric of 1.5/3.8 = 0.395.
  • So the first sequence is 0.987/0.395 = 2.5 times as sequentially variable as the second sequence.
  • And for the sequence 10 20 40 50 70 (which is the same as the previous one, but all values ten times greater), the differences are 10 20 10 20, for a total of 60 and an average of 15. The average of the values is 38, which gives me a metric of 15/38 = 0.395, the same as before — which is as it should be.

And now, my question! Does this metric, or something similar, already exist? If so, what is it called? Or if I should be using something else instead, what is it?

(It happens that my sequences are the aspect ratios of the cotyles of consecutive vertebrae, but that’s not important: whatever metric we land on should work for any sequences.)

Taylor 2015: Figure 8. Cervical vertebrae 4 (left) and 6 (right) of Giraffatitan brancai lectotype MB.R.2180 (previously HMN SI), in posterior view. Note the dramatically different aspect ratios of their cotyles, indicating that extensive and unpredictable crushing has taken place. Photographs by author.

Back in 2017, I showed the world 83.33% of my collection of sauropod-themed mugs. Time passes, and I have lost some of them and gained some more. The tally now stands at eight, and here they are:

My missing Brontomerus mug never did turn up. In the mean time, I have also lost or maybe broken the Sauroposeidon mug, the old black-and-white Archbishop mug, and the single-view Xenoposeidon mug. The dissertation mug still survives, but has faded into total illegibility, so I don’t count it any more.

On the more positive side, the sexual selection mug — second from the right in the old photo, and bottom left in the new one — survives, in fact the only one to have done so. All the others are new acquisitions. Let’s take a look:

Back row, left to right:

  1. The new, improved Archbishop dorsals A and B mug. Unlike the original, this is in glorious colour, and rearranges the elements to show anterior view on the front, and left and right lateral on the sides.
  2. The new, improved Xenoposeidon mug. It’s laid out the same way with the anterior view on the front and left and right lateral views on the sides.
  3. One that Fiona made for my birthday, showing one of the publicity photos from the original Xenoposeidon description: the one of which a newspaper columnist wrote “I wish my husband looked at me the way he looks at this bone”.
  4. A mug made by Mark Witton, which I saw at TetZooCon 2019 and made him an offer for. It shows his own Diplodocus artwork, an update of an earlier piece that he did for Matt, Darren and me to publicise our 2009 paper on sauropod neck posture. (Details here.)

Front row, left to right:

  1. The sole survivor, showing the introductory here’s-what-sauropod-necks-are-like illustration from our 2011 paper on why those necks were not sexually selected.
  2. The sauropod neck gallery used as Figure 3 in my and Matt’s 2013 PeerJ paper “why giraffes have short necks”.
  3. One of the world’s few caudal pneumaticity mugs, using all the illustrations from Matt’s and my 2013 paper, and inspired by the freakily consistent colour palette of those illustrations.
  4. This one needs a bit of explaining. See below.

For reasons that no-one — least of all he — understands, my youngest son bought a pair of Dawn French mugs as a birthday or Christmas present for Fiona. (No-one in our family is particularly a fan, it was one of those random things.) Since then, he has given her five or six more identical mugs.

Because I do not like these, I insist that they hang on one mug tree, and the sauropod mugs on another. It was to break down this mug apartheid that our eldest made for us this final mug, which shows both Dawn French and a reconstruction of the Xenoposeidon vertebra (from my 2018 paper). Where does it live? Usually, it sits on the shelf between the two mug trees.

So this is how things stand. (I drink a lot of tea, so these mugs all see plenty of action.) I really should make myself a new Brontomerus mug, and perhaps a pneumatic variation one.

Here’s Easty dirty, with a dull-looking shell and a pretty serious ‘tub ring’ of hard-water stains around the crown of her carapace. This shot is a few years old, but she looks about the same now when she’s filthy. But here’s how she cleans up:

On Saturday I gave her a good soak in some warm distilled water and scrubbed her shell with a toothbrush. She shined up beautifully. I should have tried shooting a video, because the keratinous scutes on her shell are a bit translucent, and when full sunlight hits them they take on a depth and luster that I had not previously appreciated (heh).

I shot some reference images in the cardinal directions. If you need dorsal, lateral, or ventral views of an adult female Three-toed box turtle, Terrapene carolina triunguis, it’s your lucky day.

The lateral view is interesting, because you can clearly see the joint between the two halves of her plastron, both of which can raise like drawbridges to completely seal her behind an impenetrable wall of bone and keratin. You can also tell that her posterior plastron is gently convex, which is a female trait. As in many other turtles, male box turtles tend to have at least a gently concave posterior plastron, to help them stay on top of the females during mating.

And a ventral view, giving a good look at her plastron. Note her tiny, tiny tail, with the swelling for the vent just visible in the shadow of the plastron, about even with the edge of the carapace — that’s another female trait, whereas males have longer tails and a more distal vent for mating. You can also see yellow lines cutting across some of the scutes of her plastron — those are the outlines of her plastral bones showing through the overlying keratin. As in carapace, the keratinous scutes overlap the edges of the bones to form a sort of biological plywood. A lot of the growth lines have been worn off of her plastron, which is totally normal, but for the most part you can tell where the growth centers were originally located.

I also gave baby turtle a proper bath, with supervision. Baby box turtles can swim just fine, but if the water is inconveniently deep they can sometimes get flipped over on their backs, be unable to right themselves, and drown. She really did not like not having something to haul out on, so I put in the black jar lid you see in the photo. This particular pic is overexposed, which was a happy accident, because now you can see that the apparently dark and featureless areas of her shell and head are in fact very intricately patterned (compare to her dry photo at the top of this post). I’m really looking forward to seeing how her colors come in over the next few years.

And here’s her plastron. Baby turtle is a different subspecies from Easty — she’s a true Eastern box turtle, Terrapene carolina carolina — so she should have stronger patterns on both her carapace and her plastron when she gets bigger. Her head my also be more vibrantly colored, although Easty is no slouch in that department.

I put the two of them next to each other for a very closely-supervised comparison shot. I had been worried that Easty might have a go at baby turtle, but actually the opposite was true. The wee monster frankly terrorized Easty by nipping at her toes –and this was after eating two small slugs from the back yard — so I brought that experiment to a swift end, and got nipped on the finger for my trouble. I happened to be filming when baby turtle nipped Easty’s toe and my finger, and I will try to get those videos cleaned up and posted soon. Watch this space.

Click to embiggen. Trust me on this.

What I think of as our phylogenetically-extended nuclear family grew by one this week: we got a baby box turtle. We got her from a local hobbyist, who hatched her last summer. We haven’t named her yet, so for now she’s just Baby Tiny Turtle. Unlike Easty, who is the three-toed subspecies, Terrapene carolina triunguis, baby turtle is an Eastern box turtle sensu stricto, Terrapene carolina carolina, so she might end up being quite colorful (f’rinstance). She already has pretty complex patterns of lines and spots on the sides and top of her head and on her beak, but she’s so small that you can’t really see them unless you take a photo and zoom in.

(Aside: how do we know she’s a she and not a he? Personally I’d be lost, but the guy who hatched her says that at this age he can sex the babies correctly about 80% of the time, based on the position of the cloaca — it’s farther from the base of the tail in males. If she turns out to be a he, we’ll love him just the same, we’ll just keep him away from Easty.)

Speaking of her size, here’s an obligatory random-objects-for-scale photo. Baby turtle was closer in size to that US quarter when she hatched. You can tell that she’s grown a bit already because each scute on her shell has a outer rim of smooth new keratin. It’s a bit bittersweet, because I want her to grow big and strong and healthy, but I will miss the tiny turtle days when she is bigger. 

If you just want to die of cuteness, watch this video of her trying to eat some banana. She got it all down eventually, but with a little more adventure than either of us expected. If you turn up the volume, you can hear me talking her through it. That was entirely for my benefit, because I’m a big ole softy who talks to animals a lot, and she got through just fine on her own.

Full bulletins as events warrant.

The early armored fish Bothriolepis, which Yara Haridy affectionately refers to as a “beetle mermaid”. Art by Brian Engh, dontmesswithdinosaurs.com.

If I had to sum up my main research program over the past 20+ years, it would be, “Why pneumatic bone?” Or as I typically put it in my talks, most bone has marrow inside, so if you find bone with air inside, someone has some explaining to do (f’rinstance).

One of the reasons I like hanging out with Yara Haridy is that she is interested in an even more fundamental question: “Why bone?” And also “How bone?” And she has a paper out today that gives us new insights into the form and function of bone cells — osteocytes — in some of the earliest vertebrates that had them (Haridy et al. 2021; if you’re in TL;DR mode, here’s the link). 

Bones have multiple functions in vertebrate bodies: they’re a mechanical framework for our muscles, and a mineral reservoir, and form armor in many taxa, and are involved in hormone regulation, and doubtless other things that we are still discovering, even now. To fulfill those functions, bone tissue has to be formed in the first place, it has to be maintained, and it has to be able to be reshaped as an individual grows. Derived extant vertebrates, including humans, have an impressive array of cellular machinery to make all those things happen. Central to most of those operations are osteocytes, the cells inside living bone, which maintain intimate connections to extracellular bone tissue and to other osteocytes via fine, tentacle-like processes.

Individual osteocytes look something like the Flying Spaghetti Monster. The central portion of the FSM, with the meatballs, is the osteocyte body, and the noodly appendages are the processes.

Now imagine that you cloned the FSM many, many times, and the resulting array of FSMs stayed in physical contact with each other via their noodly appendates, forming a network.

Then imagine that you entombed all of the cloned FSMs in concrete. This is more or less what cellular bone — the kind you find in humans, dinosaurs, and even some jawless fish — looks like on the microscopic scale: osteocytes (the FSMs) and their processes (the noodly appendages) embedded in space-filling stuff (the bone matrix). Some critters, including teleost fish, have acellular bone, but I don’t have time for those unbelievers today.

When an animal dies and decomposes, the osteocytes and their processes decay away, leaving behind the spaces that they used to occupy. The big spaces that hold osteocytes are called lacunae, and the little tunnels that hold the osteocyte processes (noodly appendages, in this metaphor) are canaliculi. Collectively, the lacunae and canaliculi form the lacunocanalicular network or LCN.

Those spaces can then be filled by matrix — not extracellular bone matrix, but future rock matrix, like mud and clay. In point of fact, not all of the spaces are filled with matrix. Even in their 420-million-year-old fish, Yara and colleagues found some osteocyte lacunae that had not been filled with matrix, and were filled by air instead. Whether the lacunocanalicular network is filled with matrix or air, its preservation in fossil bone has turned out to be a boon for paleontologists, because we can ‘see’ the sizes and shapes of osteocytes, and their level of connectivity, by studying the lacunae and canaliculi they left behind. 

Histological thin section of bone in the osteostracan Tremataspis mammillata (MB.f.TS.463), imaged with transmitting light microscopy showing osteocyte lacunae (osl) and canaliculi (ca); scale bar, 100 microns. Haridy et al. (2021: fig 2A).

Traditionally osteocyte lacunae and canaliculi in fossil bone have been imaged by taking thin sections of the specimens and looking at them under microscopes.

Synchrotron tomography of bone of Bothriolepis trautscholdi (MB.f.9188a) with the vasculature and osteocytes segmented; scale bar, 0.4 mm. (D) Close-up of tomography in (C) showing the resolution of the osteocyte lacunae volumes; scale bar, 10 microns. bs, bone sample; vs, vasculature channels. Modified from Haridy et al. (2021: fig. 2C-D).

If you’re fancy, you can also do synchrotron tomography, which is fine enough to show osteocyte lacunae — the colored blobs in the image on the right, above.

Those methods have their limitations. Light microscopy will reveal both lacunae and canaliculi in 2D, but it’s hard to get a 3D understanding of the lacunocanalicular network that way (at least in fossils; in modern samples it can be done with confocal miscoscopy). Synchrotron tomography can resolve lacunae in 3D, but not canaliculi, sort of like a map that shows only cities but not the highways that connect them.

Enter FIB-SEM: focused ion beam scanning electron microscopy. An ion gun blasts the specimen with a beam of gallium ions, which vaporizes a slice of the specimen that is less than 1 micron thick, and an SEM images the freshly exposed face. If you do this over and over again, you can build up a 3D model of the stuff that once occupied the volume that got zapped. 

FIB-SEM tomography imaging and processing of the fossil jawless vertebrate Tremataspis mammillata (MB.f.9025). (A and B) FIB-SEM setup showing the FIB in relation to the SEM both aimed at the region of interest. (C) Bone surface with an excavate area made by the FIB. (D) Internal wall of the excavated area lined with small black dots that are the fossil osteocyte lacunae. (E) Single osteocyte lacuna from the surface that is scanned; the single SEM image shows the lacunae and canaliculi in black and the mineralized bone in gray; scale bar, 5 microns. (F and G) An image stack is obtained, and 3D made of fossil LCN can be made. Haridy et al. (2021: fig 3).

FIB-SEM is fine enough to resolve both osteocyte lacunae and canaliculi — the lacunocanalicular network or LCN — in three dimensions, in fossil specimens where confocal light microscopy doesn’t always work very well. And the resolution is pretty insane. The rough edges on the 3D models of the LCN aren’t sampling artifacts, they’re accurately reflecting the real morphology of the walls of the lacunae and canaliculi as they were preserved in the fossil bone.

But wait — that’s not all! Not only can FIB-SEM show us osteocyte lacunae and canaliculi in incredible detail in three dimensions, it can also help us figure out at least some of what osteocytes were doing. Together, osteocytes and their processes can sense mechanical strain in bone, trigger bone remodeling, and resorb and lay down bone from the walls of the lacunae and canaliculi. That last process starts with osteocytic osteolysis — the resorption of bone matrix (= osteolysis) from the lacunae and canaliculi by the osteocytes themselves (as opposed to the more familiar destruction of bone at a larger spatial scale by osteoclasts), which is typically followed by the replacement of new matrix where the old bone used to be. Lots of extant vertebrates do osteocytic osteolysis, especially those that have a high demand for calcium and phosphorus in physiologically challenging times. Examples including migrating salmon, lactating mice, and lactating humans. But when did that capacity evolve — did the earliest osteocytes already have the ability to resorb and replace bone? As Yara said to me when she was telling me about her new paper, “We think we know how things work by looking at extant animals, but we’re looking at this highly pruned tree, and we can’t just assume that things worked the same way earlier in our evolutionary history.” 

Yara wanted to investigate when osteolytic osteolysis first evolved when she started her dissertation in 2018, but she didn’t know that FIB-SEM existed. Then she was visiting a neutron tomography facility in Berlin and she saw a poster on the wall about people using FIB-SEM to image corrosion in batteries on ultra-fine scales. She thought, “Wow, the corrosion pits in the batteries look like osteocytes!” The rest you probably figured out faster than it’s taking me to write this sentence: together with her collaborators, she got some samples of bone from the jawless fish Tremataspis and Bothriolepis and zapped them with the FIB-SEM.

Osteocytic osteolysis as a mechanism for early mineral metabolism. (A to C) Illustrations depicting the process of osteocytic osteolysis; the phases are stasis phase, dissolution phase, and redeposition phase, respectively. (D) Single SEM image from the FIB-SEM acquisition showing the air-filled osteocyte lacunae and canaliculi of T. mammillata. (E) Same SEM image as in (D) with contrast shifted to show the demineralized zone surrounding the lacunae. (F and G) 3D render of the stack of images from (D and E) T. mammillata (MB.f.9025). The 3D model shows several osteocytes and their canaliculi, with the red areas showing where the “areas of low density” were found. ald, area of low density; os, osteocyte. Scale bar, 5 microns.

And, wonder of wonders, some of the osteocyte lacunae in Tremataspis were surrounded by a halo of less-dense bone, which is evidence for osteocytic osteolysis. Now, Yara and colleagues can’t be sure whether the bone is less dense because it was being resorbed when the animal died — the actual lytic or bone-destructive phase — or because new bone was being laid down after the old bone had been resorbed; naturally the new bone is less dense as it being formed than it will be when it is complete. They also can’t be sure why the process was occurring in that one individual Tremataspis. Mice only do osteocytic osteolysis when they’re lactating, and salmon only do it when they’re migrating, so the presence of osteocytic osteolysis might indicate that the Tremataspis in question was doing something stressful related to its ecology or life history — both topics we know almost nothing about.

Yara and colleagues didn’t find any evidence of osteocytic osteolysis in their Bothriolepis sample, but this is one of those ‘absence of evidence is not evidence of absence’ things — you wouldn’t find evidence of osteocytic osteolysis in my skeleton either, despite a long ancestral history, because I’m skeletally healthy, not fasting or migrating, and not lactating. Possibly other Bothriolepis individuals that were going through a rough patch, metabolically speaking, would show osteocytic osteolysis. So far, as a species, we’ve only looked at the one sample, from the one individual.

I asked Yara what she wanted people to take away from her new paper. Her response:

  1. We have technology can image fossil bone cells at the same resolution that we can see modern bone cells.
  2. Bone metabolism was going on 420 million years ago, in the earliest osteocytes, the same way it happens in modern mammals, including humans. 

I expect that we will see a lot more FIB-SEM papers on fossils in years to come. That research program started today, with the publication of Haridy et al. (2021). I often sign off posts with “stay tuned”, and this time I really mean it.


Yara Haridy, Markus Osenberg, André Hilger, Ingo Manke, Donald Davesne, and Florian Witzmann. 2021. Bone metabolism and evolutionary origin of osteocytes: Novel application of FIB-SEM tomography. Science Advances 7(14): eabb9113. DOI: 10.1126/sciadv.abb9113.

Matt dropped me a line midweek about the catalogue of complete sauropod necks, with some interesting thoughts. He broke down the necks as listed across a basic phylogeny of sauropods, and counted the occurrences:

Simplified phylogeny of Sauropoda, showing counts of complete and near-complete necks. Captions: C, complete and described; U, complete but undescribed; –1, missing the atlas but otherwise complete; O, other near-complete necks; T, total.

Matt and I were both surprised to see that non-neosauropods are quite well represented, both inside and outside of Mamenchisauridae — although it’s a pity that two of those ten specimens are of Jobaria, for which we have next to zero information.

Diplodocoids are surprisingly poorly represented, with essentially just one each in Dicraeosauridae and Diplodocidae that are complete. And brachiosaurids are a black hole, with absolutely no representation — see the 2015 preprint for details on how unconvincing the neck of Giraffatitan is.

But camarasaurids are crushing it, probably just by being the most abundant sauropods of all time in terms of individual specimens in museums. (Of course when we say “camarasaurids”, we just mean Camarasaurus, which is the only named sauropod currently considered to belong to Camarasauridae unless you follow Mateus and Tschopp (2013) in considering Cathetosaurus to be generically distinct. But Matt and I both suspect that Camarasaurus is way over-lumped, so we’ll see how this pans out over the next decade or two.)

It’s surprising, though, that the second and third best represented sauropods in museums, Diplodocus and Apatosaurus, are both barely represented in terms of complete necks. And while it’s encouraging to see quite a few complete and nearly-complete necks among somphospondyls, including titanosaurs,it’s disappointing that about half of them are not yet described.


A couple of months ago, I asked for your help in compiling a list of all known complete sauropods necks. This has gone really well, and I want to thank everyone who chipped in, and all the various authors I have contacted for details as a result.

My next step is to take the raw data in the Google spreadsheet that I have been maintaining, and write it up as prose for the paper that I am shortly going to resubmit, having first done so back in 2015. And I thought it would make sense to draft that section here on SV-POW!, so I can get any further feedback before I finalize it for the manuscript.

Young and Zhao (1972:figure 3). Mamenchisaurus hochuanensis holotype CCG V 20401 as is occurred in the field.

So here goes: any additional comments at this stage will be welcome!

Unambiguously complete necks are known from published accounts of only a few sauropod specimens. In chronological order of description, the following specimens were found with their necks complete and articulated, and have been adequately described:

  • CM 11338, a referred specimen of Camarasaurus lentus described by Gilmore (1925). This is a juvenile specimen, and thus does not fully represent the adult morphology. (McIntosh et al. 1996:76 claim that this specimen is the holotype, but this is not correct: YPM 1910 is the holotype — see below.)
  • CM 3018, the holotype of Apatosaurus louisae, described by Gilmore (1936). The neck was separated from the torso but articulated from C1–C15, though the last three cervicals were badly crushed: see below for details.
  • CCG V 20401, the Mamenchisaurus hochuanensis holotype, described by Young and Zhao (1972). Each vertebra is broken in half at mid-length, with the posterior part of each adhering to the anterior part of the its successor; and all the vertebrae are badly crushed in an oblique plane.
  • ZDM T5402, a Shunosaurus lii referred specimen, described in Chinese by Zhang (1988), with English figure captions. Figure 22 depicts the atlas. Unlike the holotype T5401, this specimen is mature.
  • BYU 9047, the Cathetosaurus lewisi holotype, described by Jensen (1988). (Jensen incorrectly gives the specimen number as BYU 974.) This specimen was redescribed, and the species referred to Camarasaurus, by McIntosh et al. (1996). Although all 12 cervicals are present, “10–12, particularly 12, have suffered such severe damage that it is impossible to restore them” (McIntosh et al. 1996:76).
  • MACN-N 15, the holotype of Amargasaurus cazaui MACN-N 15, described by Salgado and Bonaparte (1991) who desribed “22 presacral vertebrae articulated with each other and attached to the skull and sacrum, relatively complete” (Salgado & Bonaparte 1991:335, translated.
  • ZDM 0083, the holotype of Mamenchisaurus youngi, described in Chinese by Ouyang and Ye (2002) with English figure captions. Figure 14 depicts the atlas and axis.
  • MUCPv-323, the holotype of Futalognkosaurus dukei, initially described by Calvo et al. 2007a and redescribed by Calvo et al. 2007b. The neck was found in two articulated sections which fit together without needing additional vertebrae in between (Jorge O. Calvo, pers. comm., 2021).
  • SSV12001, the holotype of Xinjiangtitan shanshanesis, described by Zhang et al. (2018). The original description of this specimen by Wu et al. 2013 included only the last two cervicals, which were the only ones that had been excavated at that time.

A few additional specimens are known to have complete and articulated necks, but have not yet been described:

  • USNM 13786, a referred subadult specimen of Camarasaurus lentus recently mounted at the Smithsonian. The specimen “was almost completely buried before the sinews had allowed the bones to separate” (letter from Earl Douglass to William J. Holland, 22 August 1918), and photographs kindly supplied by Andrew Moore show that the atlas was preserved.
  • MNBH TIG3, the holotype of Jobaria tiguidensis. Sereno et al. (1999:1343) assert that this species has 12 cervicals in all and say “One articulated neck was preserved in a fully dorsiflexed, C-shaped posture”. Sereno (pers. comm., 2021) confirms that the articulated neck is MNBH TIG3
  • SMA 002, referred to Camarasaurus sp. Tschopp et al. (2016), in a description of its feet, say that this specimen “lacks only the vomers, the splenial bones, the distal end of the tail, and one terminal phalanx of the right pes. The bones are preserved in three dimensions and in almost perfect articulation”.
  • MAU-Pv-LI-595, the “La Invernada” Titanosaur. Filippi et al. (2016) give a very brief account in an abstract. Filippi, pers. comm, 2021) says that the entire preserved specimen was articulated.
  • MAU-Pv-AC-01, an unnamed titanosaur mentioned in abstracts by Calvo et al. (1997) and Coria and Salgado (1999). The specimen was found in perfect articulation from skull down to the last caudal vertebrae (Rodolfo Coria, pers. comm., 2021).

The first cervical (the atlas) in sauropods is very different in form from the other vertebrae, and small and fragile. Consequently it is easily lost. Some further specimens have necks that are complete and articulated from C2 (the axis) backwards:

  • MB.R.4886, the holotype of Dicraeosaurus hansemanni, described by Janensch (1929), has a neck that complete and well preserved from C2 to C12 (the last cervical). Janensch referred to this as “specimen m” and writes “It was found articulated from the 19th caudal vertebra to the 9th cervical vertebra inclusive. The proximal part of the neck from the 8th cervical vertebra up to the axis was bent ventrally and lay at right angles to the distal part of the neck.” (Janensch 1929:41).
  • PMU 233, the holotype of Euhelopus zdanskyi, described by Wiman (1929) as “exemplar a” and redescribed by Wilson and Upchurch (2009).
  • ZDM T5401, the subadult holoype of Shunosaurus lii, described in Chinese by Zhang et al 1984. The quarry map (Zhang et al. 1984:figure 1) suggests that the atlas is missing.
  • MCT 1487-R, informally known as “DGM Series A”, described by Powell (2003). Gomani (2005:9) summarises as “12 cervical vertebrae, except the atlas, preserved in articulation with three proximal dorsal vertebrae”.
  • GCP-CV-4229, the holotype of Spinophorosaurus nigerensis, described by Remes et al. (2009). The specimen was found in very good condition and well articulated from C2 to C13, the last cervical. The atlas seems to be missing (Remes, pers. comm., 2021.

One other sauropod is complete from the first cervical, but probably not to the last:

  • MOZ-Pv1232, the holotype of Lavocatisaurus agrioensis, described by Canudo et al. (2018). This is complete from C1-C11. Canudo’s guess is that this is complete neck (Canudo, pers. comm, 2021), but the specimen doesn’t demand that conclusion and no known eusauropod has fewer than 12 cervicals.

Other sauropod specimens have necks that are complete and articulated from further back in the cervical sequence:

  • YPM 1910, Camarasaurus lentus, a mounted specimen described by Lull (1930). The neck is complete from C2 or C3, Lull was uncertain which.
  • SMA 0004, Kaatedocus siberi, described by Tschopp and Mateus (2012). Cervicals 3-14 are preserved.
  • AODF 888 (informally “Judy”), probably referrable to Diamantinasaurus, briefly described by Poropat et al. (2019). Preserved from C3 or maybe C4. “One posterior cervical (XIII or XIV) found several metres from articulated series, but appears to slot nicely into the gap between the articulated cervical series and the unprepared thoracic section, which might include at least one additional cervical (XIV or XV)” (Poropat, pers. comm. 2021).

Several necks are probably nearly complete, but it is not possible to knew due to their not being found in articulation:

  • CM 84, the holotype of Diplodocus carnegii, described by Hatcher (1901). C2–C15 are preserved, though not all in articulation; C11 may be an intrusion: see below for details.
  • ZDM T5701, the holotype of Omeisaurus tianfuensis, described by He et al. (1988). The neck was not articulated (He et al. 1988:figure 1), and was missing “two elements or so” (He et al. 1988:120).
  • QJGPM 1001, the holotype of Qijianglong guokr, described by Xing et al. (2015). On page 8, the authors say “The axis to the 11th cervical vertebra were fully articulated in the quarry. The atlas intercentrum and the 12th–17th cervical vertebrae were closely associated with the series.”
  • MNBH TIG9, a referred specimen of Jobaria tiguidensis. Wilson (2012:103) writes that this specimen “includes a partially articulated series of 19 vertebrae starting from the axis and extending through the mid-dorsal vertebrae.”
  • MNBH TIG6, another referred specimen of Jobaria tiguidensus, which has not been mentioned in the literature. Sereno (pers. comm., 2021) says that it is “a subadult partial skeleton with excellent neck” and that “the sequence was articulated from C2–11. Most of the ribs were attached as well.”

At the time of writing, the Paleobiology Database (https://paleobiodb.org/) lists more than 270 sauropod species. The nine unambigously complete and articulated necks therefore represent only one in 30 known sauropod species.

Note. The Jobaria tiguidensis individuals previously had specimen numbers beginning MNN, but the Musee National du Niger changed its name to Musée National Boubou Hama and the specimen numbers have changed with it.

It is said that, some time around 1590 AD, Galileo Galilei dropped two spheres of different masses from the Leaning Tower of Pisa[1], thereby demonstrating that they fell at the same rate. This was a big deal because it contradicted Aristotle’s theory of gravity, in which objects are supposed to fall at a speed proportional to their mass.

Aristotle lived from 384–322 BC, which means his observably incorrect theory had been scientific orthodoxy for more than 1,900 years before being overturned[2].

How did this happen? For nearly two millennia, every scientist had it in his power to hold a little stone in one hand and a rock in the other, drop them both, and see with his own eyes that they fell at the same speed. Aristotle’s theory was obviously wrong, yet that obviously wrong theory remained orthodox for eighty generations.

My take is that it happened because people — even scientists — have a strong tendency to trust respected predecessors, and not even to look to see whether their observations and theories are correct. I am guessing that in that 1,900 years, plenty of scientists did indeed do the stone-and-rock experiment, but discounted their own observations because they had too much respect for Aristotle.

But even truly great scientists can be wrong.

Now, here is the same story, told on a much much smaller scale.

Well into the 2010s, it was well known that in sauropods, caudal vertebrae past the first handful are pneumatized only in diplodocines and in saltasaurine titanosaurs. As a bright young sauropod researcher, for example, I knew this from the codings in important and respected phylogenetic analysis such as those of Wilson (2002) and Upchurch et al. (2004).

Until the day I visited the Museum für Naturkunde Berlin and actually, you know, looked at the big mounted Giraffatitan skeleton in the atrium. And this is what I saw:

That’s caudal vertebrae 24–26 in left lateral view, and you could not wish to see a nicer, clearer pneumatic feature than the double foramen in caudal 25.

That observation led directly to Matt’s and my 2013 paper on caudal pneumaticity in Giraffatitan and Apatosaurus (Wedel and Taylor 2013) and clued us into how much more common pneumatic hiatuses are then we’d realised. It also birthed the notion of “cryptic diverticula” — those whose traces are not directly recorded in the fossils, but whose presence can be inferred by traces on other vertebrae. And that led to our most recent paper on pneumatic variation in sauropods (Taylor and Wedel 2021) — from which you might recognise the photo above, since a cleaned-up version of it appears there as Figure 5.

The moral

Just because “everyone knows” something is true, it doesn’t necessarily mean that it actually is true. Verify. Use your own eyes. Even Aristotle can be wrong about gravity. Even Jeff Wilson and Paul Upchurch can be wrong about caudal pneumaticity in non-diplodocines. That shouldn’t in any way undermine the rightly excellent reputations they have built. But we sometimes need to look past reputations, however well earned, to see what’s right in front of us.

Go and look at fossils. Does what you see contradict what “everyone knows”? Good! You’ve discovered something!




1. There is some skepticism about whether Galileo’s experiment really took place, or was merely a thought experiment. But since the experiment was described by Galileo’s pupil Vincenzo Viviani in a biography written in 1654, I am inclined to trust the contemporary account ahead of the unfounded scepticism of moderns. Also, Viviani’s wording, translated as “Galileo showed this by repeated experiments made from the height of the Leaning Tower of Pisa in the presence of other professors and all the students” reads like a documentary account rather than a romanticization. And a thought experiment, with no observable result, would not have demonstrated anything.

2. Earlier experiments had similarly shown that Aristotle’s gravitational theory was wrong, including in the works of John Philoponus in the sixth century — but Aristotle’s orthodoxy nevertheless survived until Galileo.


“And in conclusion, this new fossil/analysis shows that Lineageomorpha was more [here fill in the blank]:

  • diverse
  • morphologically varied
  • widely distributed geographically
  • widely distributed stratigraphically

…than previously appreciated.” 

Yes, congratulations, you’ve correctly identified that time moves forward linearly and that information accumulates. New fossils that make a group less diverse, varied, or widely distributed–now that’s a real trick.

Okay, that was snarky to the point of being mean, and here I must clarify that (1) I haven’t been to a conference in more than a year, so hopefully no-one thinks I’m picking on them, which is good, because (2) I myself have ended talks this way, so I’m really sniping at Old Matt.

And, yeah, new fossils are nice. But for new fossils or new analyses to expand what we know is expected. It’s almost the null hypothesis for science communication–if something doesn’t expand what we know, why are we talking about it? So that find X or analysis Y takes our knowledge beyond what was “previously appreciated” is good, but it’s not a particularly interesting thing to say out loud, and it’s a really weak conclusion.

(Some cases where just being new is enough: being surprisingly new, big expansions [like hypothetically finding a tyrannosaur in Argentina], and new world records.)

Don’t be Old Matt. Find at least one thing to say about your topic that is more interesting or consequential than the utterly pedestrian observation that it added information that was not “previously appreciated”. The audience already suspected that before you began, or they wouldn’t be here.

I showed this post to Mike before I published it, and he said, “What first made you want to work on this project? That’s your punchline: the thing that was cool enough that you decided to invest months of effort into it.” Yes! Don’t just tell the audience that new information exists, tell them why it is awesome.


FIGURE 7.1. Pneumatic features in dorsal vertebrae of Barapasaurus (A–D), Camarasaurus (E–G), Diplodocus (H–J), and Saltasaurus (K–N). Anterior is to the left; different elements are not to scale. A, A posterior dorsal vertebra of Barapasaurus. The opening of the neural cavity is under the transverse process. B, A midsagittal section through a middorsal vertebra of Barapasaurus showing the neural cavity above the neural canal. C, A transverse section through the posterior dorsal shown in A (position 1). In this vertebra, the neural cavities on either side are separated by a narrow median septum and do not communicate with the neural canal. The centrum bears large, shallow fossae. D, A transverse section through the middorsal shown in B. The neural cavity opens to either side beneath the transverse processes. No bony structures separate the neural cavity from the neural canal. The fossae on the centrum are smaller and deeper than in the previous example. (A–D redrawn from Jain et al. 1979:pl. 101, 102.) E, An anterior dorsal vertebra of Camarasaurus. F, A transverse section through the centrum (E, position 1) showing the large camerae that occupy most of the volume of the centrum. G, a horizontal section (E, position 2). (E–G redrawn from Ostrom and McIntosh 1966:pl. 24.) H, A posterior dorsal vertebra of Diplodocus. (Modified from Gilmore 1932:fig. 2.) I, Transverse sections through the neural spines of other Diplodocus dorsals (similar to H, position 1). The neural spine has no body or central corpus of bone for most of its length. Instead it is composed of intersecting bony laminae. This form of construction is typical for the presacral neural spines of most sauropods outside the clade Somphospondyli. (Modified from Osborn 1899:fig. 4.) J, A horizontal section through a generalized Diplodocus dorsal (similar to H, position 2). This diagram is based on several broken elements and is not intended to represent a specific specimen. The large camerae in the midcentrum connect to several smaller chambers at either end. K, A transverse section through the top of the neural spine of an anterior dorsal vertebra of Saltasaurus (L, position 1). Compare the internal pneumatic chambers in the neural spine of Saltasaurus with the external fossae in the neural spine of Diplodocus shown in J. L, An anterior dorsal vertebra of Saltasaurus. M, A transverse section through the centrum (L, position 2). N, A horizontal section (L, position 3). In most members of the clade Somphospondyli the neural spines and centra are filled with small camellae. (K–N modified from Powell 1992:fig. 16.) [Figure from Wedel 2005.]

Here’s figure 1 from my 2005 book chapter. I tried to cram as much pneumatic sauropod vertebra morphology into one figure as I could. All of the diagrams are traced from pre-existing published images except the horizontal section of the Diplodocus dorsal in J, which is a sort of generalized cross-section that I based on broken centra of camerate vertebrae from several taxa (like the ones shown in this post). One thing that strikes me about this figure, and about most of the CT and other cross-sections that I’ve published or used over the years (example), is that they’re more or less bilaterally symmetrical. 

We’ve talked about asymmetrical vertebrae before, actually going back to the very first post in Xenoposeidon week, when this blog was only a month and a half old. But not as much as I thought. Given how much space asymmetry takes up in my brain, it’s actually weird how little we’ve discussed it.

The fourth sacral centrum of Haplocanthosaurus CM 879, in left and right lateral view (on the left and right, respectively). Note the distinct fossa under the sacral rib attachment on the right, which is absent on the left.

Also, virtually all of our previous coverage of asymmetry has focused on external pneumatic features, like the asymmetric fossae in this sacral of Haplocanthosaurus (featured here), in the tails of Giraffatitan and Apatosaurus (from Wedel and Taylor 2013b), and in the ever-popular holotype of Xenoposeidon. This is true not just on the blog but also in our most recent paper (Taylor and Wedel 2021), which grew out of this post.

Given that cross-sectional asymmetry has barely gotten a look in before now, here are three specimens that show it, presented in ascending levels of weirdness.

First up, a dorsal centrum of Haplocanthosaurus, CM 572. This tracing appeared in Text-fig 8 in my solo prosauropod paper (Wedel 2007), and the CT scout it was traced from is in Fig 6 in my saurischian air-sac paper (Wedel 2009). The section shown here is about 13cm tall dorsoventrally. The pneumatic fossa on the left is comparatively small, shallow, and lacks very distinct overhanging lips of bone. The fossa on the right is about twice as big, it has a more distinct bar of bone forming a ventral lip, and it is separated from the neural canal by a much thinner plate of bone. The fossa on the left is more similar to the condition in dorsal vertebrae of Barapasaurus or juvenile Apatosaurus, where as the one on the right shows a somewhat more extensive and derived degree of pneumatization. The median septum isn’t quite on the midline of the centrum, but it’s pretty stout, which seems to be a consistent feature in presacral vertebrae of Haplocanthosaurus.


Getting weirder. Here’s a section through the mid-centrum of C6 of CM 555, which is probably Brontosaurus parvus. That specific vert has gotten a lot of SV-POW! love over the years: it appears in several posts (like this one, this one, and this one), and in Fig 19 in our neural spine bifurcation paper (Wedel and Taylor 2013a). The section shown here is about 10cm tall, dorsoventrally. In cross-section, it has the classic I-beam configuration for camerate sauropod vertebrae, only the median septum is doing something odd — rather than attaching the midline of the bony floor of the centrum, it’s angled over to the side, to attach to what would normally be the ventral lip of the camera. I suspect that it got this way because the diverticulum on the right either got to the vertebra a little ahead of the one on the left, or just pneumatized the bone faster, because the median septum isn’t just bent, even the vertical bit is displaced to the left of the midline. I also suspect that this condition was able to be maintained because the median septa weren’t that mechanically important in a lot of these vertebrae. We use “I-beam” as a convenient shorthand to describe the shape, but in a metal I-beam the upright is as thick or thicker than the cross bits. In contrast, camerate centra of sauropod vertebrae could be more accurately described as a cylinders or boxes of bone with some holes in the sides. I think the extremely thin median septum is just a sort of developmental leftover from the process of pneumatization.

EDIT 3 days later: John Whitlock reminded me in the comments of Zurriaguz and Alvarez (2014), who looked at asymmetry in the lateral pneumatic foramina in cervical and dorsal vertebrae of titanosaurs, and found that consistent asymmetry along the cervical column was not unusual. They also explicitly hypothesized that the asymmetry was caused by diverticula on one side reaching the vertebrae earlier than diverticula on other other side. I believe they were the first to advance that idea in print (although I should probably take my own advice and scour the historical literature for any earlier instances), and needless to say, I think they’re absolutely correct.

Both of the previous images were traced from CTs, but the next one is traced from a photo of a specimen, OMNH 1882, that was broken transversely through the posterior centrum. To be honest, I’m not entirely certain what critter this vertebra is from. It is too long and the internal structure is too complex for it to be Camarasaurus. I think an apatosaurine identity is unlikely, too, given the proportional length of the surviving chunk of centrum, and the internal structure, which looks very different from CM 555 or any other apatosaur I’ve peered inside. Diplodocus and Brachiosaurus are also known from the Morrison quarries at Black Mesa, in the Oklahoma panhandle, which is where this specimen is from. Of those two, the swoopy ventral margin of the posterior centrum looks more Diplodocus-y than Brachiosaurus-y to me, and the specimen lacks the thick slab of bone that forms the ventral centrum in presacrals of Brachiosaurus and Giraffatitan (see Schwarz and Fritsch 2006: fig. 4, and this post). So on balance I think probably Diplodocus, but I could easily be wrong.

Incidentally, the photo is from 2003, before I knew much about how to properly photograph specimens. I really need to have another look at this specimen, for a lot of reasons.

Whatever taxon the vertebra is from, the internal structure is a wild scene. The median septum is off midline and bent, this time at the top rather than the bottom, the thick ventral rim of the lateral pneumatic foramen is hollow on the right but not on the left, and there are wacky chambers around the neural canal and one in the ventral floor of the centrum. 

I should point out that no-one has ever CT-scanned this specimen, and single slices can be misleading. Maybe the ventral rim of the lateral foramen is hollow just a little anterior or posterior to this slice. Possibly the median septum is more normally configured elsewhere in the centrum. But at least at the break point, this thing is crazy. 

What’s it all mean? Maybe the asymmetry isn’t noise, maybe it’s signal. We know that when bone and pneumatic epithelium get to play together, they tend to make weird stuff. Sometimes that weirdness gets constrained by functional demands, other times not so much. I think it’s very seductive to imagine sauropod vertebrae as these mechanically-optimized, perfect structures, but we have other evidence that that’s not always true (for example). Maybe as long as the articular surfaces, zygapophyses, epipophyses, neural spine tips, and cervical ribs — the mechanically-important bits — ended up in the right places, and the major laminae did a ‘good enough’ job of transmitting forces, the rest of each vertebra could just sorta do whatever. Maybe most of them end up looking more or less the same because of shared development, not because it was so very important that all the holes and flanges were in precisely the same places. That might explain why we occasionally get some really odd verts, like C11 of the Diplodocus carnegii holotype.

That’s all pretty hand-wavy and I haven’t yet thought of a way to test it, but someone probably will sooner or later. In the meantime, I think it’s valuable to just keep documenting the weirdness as we find it.