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juvenile P. engelhardti by theropod1 juvenile P. engelhardti :icontheropod1:theropod1 25 2 Plateosaurus engelhardti by theropod1 Plateosaurus engelhardti :icontheropod1:theropod1 12 1 Allosaurus sp. by theropod1 Allosaurus sp. :icontheropod1:theropod1 39 13 Ceratosaurus nasicornis by theropod1 Ceratosaurus nasicornis :icontheropod1:theropod1 28 5 Majungasaurus by theropod1 Majungasaurus :icontheropod1:theropod1 18 7 The whale and the shark by theropod1 The whale and the shark :icontheropod1:theropod1 62 66 Livyatan melvillei by theropod1 Livyatan melvillei :icontheropod1:theropod1 36 33 Baryonyx walkeri by theropod1 Baryonyx walkeri :icontheropod1:theropod1 13 10 Suchomimus tenerensis by theropod1 Suchomimus tenerensis :icontheropod1:theropod1 12 3 another Carnotaurus by theropod1 another Carnotaurus :icontheropod1:theropod1 11 0 Kulindadromeus in color by theropod1 Kulindadromeus in color :icontheropod1:theropod1 11 9 Kulindadromeus zabaikalicus by theropod1 Kulindadromeus zabaikalicus :icontheropod1:theropod1 16 1 Spinosaurus aegyptiacus: new reconstruction by theropod1 Spinosaurus aegyptiacus: new reconstruction :icontheropod1:theropod1 32 36 A deep-bodied arm reptile by theropod1 A deep-bodied arm reptile :icontheropod1:theropod1 13 8 American Beast by theropod1 American Beast :icontheropod1:theropod1 22 21 Batrachotomus kupferzellensis  by theropod1 Batrachotomus kupferzellensis :icontheropod1:theropod1 5 9

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[Bg] Throughout the years, there have been various attempts to reconstruct the extinct giant shark, Carcharocles (Otodus) megalodon. Most of these have based on its modern relative and closest living analogue, the great white shark Carcharodon carcharias.
That is the first thing important to note here, because all the following is exclusively based on the white shark. Of course the very real possibility remains that C. megalodon looked nothing like envisioned here, but that is useless as long as there are no data to aid in coming up with a more likely reconstruction. Most people seem to be quite fine with using the white shark as an analogue, as am I, and it’s primarily those people that this is targeted at.

There is a common trend of portraying C. megalodon as a sort of overgrown great white shark on steroids. As those who have read certain previous posts of mine already know, this is partly based on real data, and partly on conjecture, but so far it has not been possible to largely eliminate that element of conjecture because of the lack of quantitative methodology used in reconstruction.

The real data are two-fold:
> Firstly, the fossil teeth of C. megalodon are thicker and (relative to their height) wider than those of white sharks, at least the larger anterior and anterolateral ones. At a similar overall size (width, length or circumference) of the jaws, the anterior teeth of megalodon would hence be shorter and stouter, i.e. more robust. Most likely, this is an effect of both the gigantic size and the effects of scaling (i.e. allometry), it’s phylogenetic heritage (other otodontid teeth are also very thick labiolingually), and its behaviour (dealing with, in absolute terms, very large prey items). However the effect this might have on jaw morphology is difficult, of not impossible, to estimate.
> Secondly, the allometric scaling of body mass in extant white sharks suggests that larger sharks tend to be more robust than smaller ones, which can be extrapolated, albeit with questionable relevance, to the size of megalodon. There have been six published regression equations for deducing white shark mass from total length (Fig. 1), which provide the data I am relying on here.
Megmass - by theropod1

Fig. 1: Length-weight relationships of C. carcharias according to various published sources (See references).
These data indeed support that larger sharks should (most likely) be more robust. Which is about where the considerations typically end. But is there a way to approach this question with a bit more rigor than just taking an arbitrary great white shark and bulking it up by an arbitrary amount? It turns out that yes, there is.

[M&M] First, let’s establish what sizes will be used. Changing these slightly will not have major effects, as you are going to see. But for the sake of comparison, I am going to be using a 5m great white shark (good-sized, but still a relatively common size for the species, which is always advantageous) and a 16.8m megalodon (a size suggested in a recent SVP abstract (Perez et al. 2018, SVP abstract volume p. 196) for a specimen with a complete, associated dentition, and also a size I have shown previously). This is not supposed to be a comment on megalodon maximum or average sizes, but on its morphology, so I’ll leave it at that.

The equations suggest that the 16.8m megalodon (46,112-56,797kg) would be between 0 and 23% heavier than an isometrically scaled great white shark of (1,083-1,294kg at 5m). Using the average of all 6, the megalodon is 13.6% heavier than the great white at the same length. Since length is fixed, we can attribute this entire increase in robusticity to the body cross-section, the function of width and depth. Assuming the increase is the same in both dimensions, we get the percentage of increase by taking the cube root, giving us 6.6%. So in other words, we should be drawing megalodon 6.6% wider and deeper-bodied than a great white shark. That’s as much as I’ve written previously. Now, the debatable part is obviously going to be what great white that should be, because most pictures of great whites, especially nice ones in orthogonal views without deformation or distortion, have no weight measurements attached to them.

So to solve this problem, I constructed a digital 3d model of a great white shark in Blender using lateral and top-view pictures of great whites and reference drawings (e.g. ¹) as a basis. I modeled the trunk, pectoral, first dorsal and tail fins separately and then unified them using a boolean modifier. The other fins were omitted from the model to avoid it becoming overly complex and computationally demanding, as they would add very little mass anyway. Then I adjusted its width and depth (isometrically) to make it fit the predicted body masses.

[RESULTS] The resulting reconstruction (Fig. 2) suggests a robust, but streamlined body shape, even for the maximum model scaled to 56.8t.
The bulk increase necessary in terms of scaling of the body cross-section is not extreme. Even the maximum model, based on Gottfried et al.’s results, is still well-within the range of variation seen in extant great whites. The great white reconstruction also lends weight to the drawn representations of white sharks as commonly found in reference books (e.g. Compagno 1984) being good representations of the statistically typical proportions of the species as a whole.
Megcomp by theropod1
Fig. 2: Surface model of C. carcharias and C. megalodon (16.8m) scaled to match predicted volume. Specific gravity is assumed as 1.0. Green model reflects the mass predicted by the allometric equation in Gottfried et al. 1996, which suggests the highest body mass at almost 57t.  Blue and red models reflect the mean of masses predicted by 6 regression equations (see references). Scalebars: 1m each. Grid: 2m per cell. Human diver: ~1.8m standing height.


[D&C]One caveat to this is that I did not model the buccal cavity of the shark, as I did not have a reference for it. With the mouth closed, I assumed it would not greatly decrease the volume of the shark for given external dimensions as long as the mouth was closed, as modeled here. If indeed it does, then this might result in an underestimation of the external dimensions of a shark of a given body mass, although I don’t think this is likely. Should you have information to the contrary, please let me know.

There have been well-founded suggestions that megalodon would have had a proportionately larger tail fin to maintain high speeds and activity levels at its large size, and I agree with this, as it is consistent with a possible higher vertebral count and with the scaling effects at its large body size. This would largely have a negligible impact on mass. In the great white model at 1.2t, the tail fin masses less than 30kg. Even doubling the fin size would not greatly increase the size of the model. In the above representation, the fins are scaled up in width and height along with the body largely for practical reasons and because there is no way to precisely estimate their proper size.
Most likely, the tail fin would be somewhat larger in life than it is portrayed here, which is what I am going to use for the drawn reconstruction I plan to follow this up with.

So with that out of the way how does this leave extremely bulky megalodon reconstructions, such as these?

Well, as with great whites, there would have been a large level of variation. These estimates represent the mean. This is, for obvious reasons the most sensible representation for the species. This does not mean that there couldn’t have been some megalodon individuals that were in fact as bulky as portrayed, just like there are some great white sharks that are ridiculously bulky compared to the normal body shape of the species.
It’s just that they get far too much representation, and are ironically often considered to be the most reliable reconstructions. On the other hand, it’s also entirely plausible for some megalodons to not be bulkier than normal great whites at all. One of the aforementioned equations, McClain et al., in fact did not find allometry in their dataset at all.

Bottom line: The most accurate and rigorous data suggest megalodon should be portrayed on average ~7% deeper and wider-bodied than a typical great white shark. The above model (blue reconstruction, Fig. 2) illustrates the resulting body shape. Various scaling equations found slightly different values varying from 0 (i.e. isometry) to 11%, but it does not seem like such differences would have a massive impact on how bulky the animal would look, at least not sufficiently to lend support to the many extremely robust reconstructions out there. These appear to not be supported by any quantitative data and should be considered representations of unusually heavyset, pregnant and or full-stomached individuals, not a typically robust, large megalodon.

References:
Casey, John G.; Pratt, Harold L. 1985. Distribution of the White Shark, Carcharodon carcharias, in the Western North Atlantic. Memoirs of the Southern California Academy of Sciences, 9 (Biology of the White Shark, a Symposium) pp. 2-14.
Compagno, L.J. 1984. Sharks of the world: an annotated and illustrated catalogue of shark species known to date. FAO Fisheries Synopsis Volume 4 (No. 125).
Gottfried, Michael D.; Compagno, Leonard J.V.; Bowman, S. Curtis. 1996. Size and Skeletal Anatomy of the Giant “Megatooth” Shark Carcharodon megalodon. In: Klimley, Peter A.; Ainley, David G.: Great White Sharks: the biology of Carcharodon carcharias. San Diego, pp. 55-66.
Kohler, Nancy E.; Casey, John G.; Turner, Patricia A. 1995. Length-Length and Length-Weight Relationships for 13 Shark Species from the Western North Atlantic. Fishery Bulletin, 93 pp. 412-418.
McClain, Craig R.; Balk, Meghan A.; Benfield, Mark C.; Branch, Trevor A.; Chen, Catherine; Cosgrove, James; Dove, Alistair D.M.; Gaskins, Lindsay C.; Helm, Rebecca R.; Hochberg, Frederick G.; Lee, Frank B.; Marshall, Andrea; McMurray, Steven E.; Schanche, Caroline; Stone, Shane N.; Thaler, Andrew D. 2015. Sizing ocean giants: patterns of intraspecific size variation in marine megafauna. PeerJ, 3 (715) pp. 1-69.
Mollet, Henry F.; Cailliet, Gregor M. 1996. Using Allometry to Predict Body Mass from Linear Measurements of the White Shark. In: Klimley, Peter A.; Ainley, David G.: Great White Sharks: the biology of Carcharodon carcharias. San Diego, pp. 81-89.
Tricas, Timothy C.; McCosker, John E. 1984. Predatory Behaviour of the White Shark (Carcharodon carcharias) with notes on its biology. Proceedings of the California Academy of Sciences, 43 (14) pp. 221-234.

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:iconthaanonymousperson:
ThaAnonymousPerson Featured By Owner Oct 1, 2017
Are you from Carnivora
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:icontheropod1:
theropod1 Featured By Owner Nov 24, 2017  Student Traditional Artist
yes
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:icondinopithecus:
Dinopithecus Featured By Owner Edited Mar 19, 2017
This may be quite a really, really stupid question, but I've been wondering about it.

Let's say a cat or bear grappled onto the neck of an equal-sized predatory theropod (of what clade (carnosaurs, tyrannosaurids, megalosaurids, etc.) you decide). Would the latter's cervical flexibility and cranial flexibility from the atlas be sufficient for it to turn its head/neck to the side and bite down on the carnivoran's forelimb (theropod necks were particularly flexible, right?)? Would some with powerful necks have the power and flexibility to free themselves through vigorous shaking?

I'm so sorry. Spending >4 years debating on animal vs. animal forums can make you think a little hard about this stuff.
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:icontheropod1:
theropod1 Featured By Owner Mar 23, 2017  Student Traditional Artist
First of all, depends on the theropod in question, they aren't that similar across the ranks in that regard. Some had more flexible necks than others. And of course it depends on what angle the opponent would be relative to the theropod.

So rather than giving you an overgeneralized answer to that question, here’s a very helpful visualisation from Snively et al. 2013:
palaeo-electronica.org/content…

Shown (3) is the maximum lateral range of motion of the head and neck of Allosaurus.
A couple of things to note: Of course Allosaurus is considered one of the large theropods with a rather high degree of cervical flexibility. I don’t know much about Megalosaurs in this regard. A derived tyrannosauroid would almost certainly be less flexible, but of course it would also have a shorter neck to make up for that, which would make grappling it even more difficult.
As you see the individual joints, including the craniocervical articulation, aren’t all that flexible, but if you add up the angles over several you end up able to flex that neck quite a bit rather quickly. So it’s very important to take into consideration where that hypothetical grappling animal has its hold on the neck, and how much of its length is still free to move. That’s of course also relevant because grappling more anteriorly would give the grappler much better leverage and make escaling its grasp much more difficult.
So perhaps theropod flexibility was sufficient for what you describe, perhaps not, depending on where the attacker is standing compared to the theropod and what theropod we are talking about.

As for shaking vigorously, there are certainly theropods I could see doing that, though of course the neck is a vulnerable region and doing so would be risky. But again, depending on the attacker I suppose it could work in some cases.
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:icondinopithecus:
Dinopithecus Featured By Owner Mar 24, 2017
"As you see the individual joints, including the craniocervical articulation, aren’t all that flexible"

Yeah, I find that puzzling. I read that the large articular surfaces of theropod zygapophyses promoted neck flexibility; I imagined it would be by making the individual joints flexible. The opisthocoelus morphology of carnosaur cervicals should also have helped with this. Lastly, Snively's reconstruction doesn't look like the cranium is flexed all that much from the atlas, but theropods had more or less spherical occipital condyles, allowing for great mobility at the joint.

Did these things just really not help that much to make the individual joints flexible in absolute terms?
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:icontheropod1:
theropod1 Featured By Owner Mar 25, 2017  Student Traditional Artist
I didn’t mean to say Allosaurus’ neck wasn’t flexible. For a cervical skeleton, it’s in all likelyhood very flexible. But individually, intervertebral joints or the craniocervical joint still don’t have huge ranges of movements.
They never do, probably those in Allosaurus already have a comparatively large range of movement (as you correctly point out, they are in fact adapted for that), but individual vertebrae simply don’t move all that much. It’s the summation of many small rotations that ends up making the neck flexible.
What I meant to say by that: it really matters how much neck there is to make that turn you were referring to, because it can’t just bend 90° in a single spot.

Simply put, the measure of what’s flexible for an intervertebral joint isn’t the same as that for a jaw joint, or knee joint etc., because they don’t have to be and vertebrae are loaded in a very different way from jaw or limb bones. They need those support structures, like zygapophyses, cervical ribs and neural spines to provide adequate support to the spine without excessive muscular effort despite its mostly horizontal posture. Allosaurus does have a comparatively flexible neck. Part of the reason why is that its skull likely wasn’t very heavy compared to some other theropod skulls, meaning it needed less rigid support. But still individual vertebral joints will generally not be as flexible as some other joints in the body, and this is why.
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:icondinopithecus:
Dinopithecus Featured By Owner Edited Sep 24, 2016
Hey theropod.

You might be aware of what I asked you on WoA* (i.e. seeing if my argument on theropod agility on Carnivora was sound). If I was asking for too much, then I apologize.

I just have one question for you now regarding the topic. Since theropod legs were pretty much at the center of mass, theropods would have produced little torque compared to quadrupedal animals. Did they have a way of solving this problem?

Thanks. :) (Smile) 

*Or if you're not, well, you could still check out hippo vs. Carnotaurus on Carnivora to at least see what I'm talking about.
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:icontheropod1:
theropod1 Featured By Owner Sep 27, 2016  Student Traditional Artist
Just because it would be a shame to leave this unanswered, even though this is pretty much just what I wrote on WoA:
I think their way of solving that problem was simply by producing more force.
Quadrupeds have better leverage because they have two leg pairs, but most theropods have humungous musculature powering their hindlegs, i.e. more force to make up for that. Whether they could produce just as much torque I don’t know, but even if not, how fast a quadruped can turn may be limited for other reasons than the sheer ratio between torque and RI.
The rotational inertia would likely be somewhat greater due to their more elongated body shape than the typical quadruped, but that’s certainly highly dependant on the theropod and quadruped in question (theropods do have more or less effective means to lighten the ends of their bodies).
This is partly offset by what we already discussed; potentially quicker capacity of excerting torque because of shorter moment arm, and flexing of the body (also more effective in some theropods than in others) while turning in order to reduce RI. I’ve got no quantification of this, but I doubt this is enough to offset their long body shapes and make them able to turn on the spot just as well as a same-sized quadruped. However as I wrote
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:icondinopithecus:
Dinopithecus Featured By Owner Edited Dec 6, 2016
About that topic (or really to deviate from it):

Remember how you said elephants are kind of a (rough, at least) sauropod analogue when it comes to dealing with predators (they're neither behaviorally nor anatomically adapted for dealing with predators as massive as they are)? Well, another person I asked on Carnivora agrees that their body plan takes advantage of being so large.

Do you know of any ways this might hold true? That is, what about their anatomy makes them so reliant on size? Having tusks makes it kind of hard to believe (although, I recently read a publication saying that elephant tusks have a rather low tensile strength and are susceptible to fracture, for whatever it's worth).
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