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A quick word or two regarding the size of everyone’s favourite extinct shark, Carcharocles (also known as Megaselachus, also known as Otodus, also known as Carcharodon–That might be a record for the largest number of genus names in use for a single species in the last two decades’ literature) megalodon.
As we have learned to expect from something really large and with such scrappy remains (isolated teeth, with vertebrae or more complete dentitions being known in a small number of poorly- to undocumented cases), people greatly enjoy speculating about its size. Only in this case, people advising the use of conservative methods are often just drowned out (and trolled and bashed into submission) by the internet movement that understandably enjoys the thought of a species of 60ft shark that killed everything in its path with a single bite, aided by the fact that too many of those people mistake scientistsfic’ enthusiasm (or pretty much any statement they can find anywhere,never mind that it’s often some discovery channel documentary they are using as a source) for some sort of endorsement of their sensationalism.
Scientists have also made enthusiastic statements about 1.7m sauropod footprints, its funny there aren’t thousands of people all over the internet celebrating that.

That isn’t to say that speculating is wrong–we wouldn’t get anywhere without it. And certainly even liberal methodologies deserve their place (in EVERY taxon).
But that doesn’t mean they are the only ones deserving of that, and it doesn’t mean we that place is necessarily as the most commonly cited and reproduced estimation, neither does it mean the only way to get an estimate that doesn’t get labeled as "too low" should be by searching out the individual Great White Shark with the largest body length and proportionately smallest teeth to estimate length, then using the predictive equation for body mass on that which yields the highest results, to come up with such extreme but undeniably popular estimates as the 20m+ and 100t+ figures you can read everywhere.
There is a fundamental difference between nitpicking such a figure to represent this animal’s body size in general, and publishing it as a hypothetical (and, as noted by the authors, unreliable) estimate, as was done by the scientific study that people generally cite when its about its size (see below).

That gets even more comical when it gets to discussing how C. megalodon compares to other giant predators. I can’t help but be amused by their confidence in such biased comparisons when representing C. megalodon as an 18-20m critter even though those are the sizes of a handful of individuals in thousands. To jump ahead a bit, there appears to be quite some sensationalism in claims that it is the biggest predator of all time.
Leaving aside the implication of certainty that is expressed in this statement despite the incompleteness of the fossil record (and its fossil record in particular, with most animals people don’t make confident size estimates from teeth), there is a plain and simple lack of data supporting such claims. Certainly it is among the top 2 or 3 contenders, being comparable in size to its contemporary Livyatan melvillei, to the point where it is warranted to not make any statement about which is larger considering the lack of sufficiently complete fossils, and the lack of a sufficiently large sample of the latter’s population.

I don’t have a problem with the thought that 20m megatooth sharks existed, just like how 1t polar bears exist(ed), but this estimate is useless for all (scientific) intends and purposes because it does not base on solid data, and because it doesn’t relate to a normal individual at all (you know, the kind of megalodon that made all those bite marks, the kind you’d expect and fear to swim into if you were a miocene mysticete, in short, the kind that made up the bulk of the adult population of this species).
Those figures represent hypothetical freak specimens, based on more or less reliable hints, and back when this estimate was published it was conceived as such–deliberately basing on the largest (unreliable, and noted as such by Gottfried and colleagues) and most unusually proportioned report of a great white that was available.

Carcharocles Megalodon-backgroundless by theropod1

Life reconstruction, based on the anatomy of the extant great white shark (adapted from Compagno 1984) and accounting for allometric increase in robusticity as per the data outlined below.

So for a less biased picture, conservative methods are in order, especially when the whole matter has to be based on a handful of teeth.
Keep in mind the actual meaning of "conservative"; not "the lowest", although it often gets used in that sense, even by myself. Yet in principle I am not an advocate of automatically considering the lowest estimate the most conservative.
In fact, it is not unusual for the lowest estimates to be liberal, when, for example, someone made extra assumptions in order to produce a minimum estimate, under the mistaken impression that it would make it more parsimonious (yet being too small isn’t really any better than being too large).
So here, what I mean is the most parsimonious method, the one that keeps biased (e.g. aimed at producing an extreme estimate in either direction) or poorly  assumptions, the one avoiding to sum up such biases and instead leaving them to cancel out each other if they can not be avoided. In short, the best and most objective estimate. Unfortunately that use of the term will probably not gain popular acceptance, so lets get back on topic.

So is there a way of making this more objective and exercising some caution in this sense? Yes, I think there is.

Firstly, the most important size metric of a species isn’t the size of the biggest thing you can find some tiny fragment of (btw teeth in general are actually tiny fragments, and scientists don’t bother estimating body size from them in many cases). It’s the species average size that’s most important, most objective, and least error-prone, so that’s what I’m most interested in here.
The background is that Pimiento & Balk 2015 actually estimated it fairly recently, and came up with an average of ~10m for 544 individuals of all ages.
But this still isn’t a very good means of comparison; depending on an animal’s reproductive strategy, the number of immature specimens in such a sample can vary, and accordingly species whose social and ecological adult stage is larger can end up smaller (or vice versa). To account for that, one can take the mean size of a subsample, namely all those that are above the mean size at maturity.
Gottfried et al. 1996 estimated mean sizes at maturity for both females and males based on the Great White shark, and the average is 11.9m, which is broadly consistent, if not a bit higher, than what would be indicated by the relative size at maturity of C. carcharias (cf. Cailliet et al. 1985, Casey & Pratt 1985, McClain et al. 2015). In Pimiento & Balk’s sample, the average of individuals estimated to be this long or longer is ~14m.

Now, assume we want to know the size of a large megalodon. Not crazy-freaky-outlier-large, but large. One such specimen is known from Denmark, and consists of a huge tooth associated with a number of vertebrae, which means that this specimen is, unlike most megatooth sharks, not a tooth lost by some individual at a random moment of its life, but an actual fossil "skeleton" if that word is appropriate.
Unfortunately there’s no telling whether any of the vertebrae are the largest in the collumn, and there is also vague indication of C. megalodon’s vertebrae being proportioned differently from those of C. carcharodon. So we’re still stuck with a tooth, but at least we have a more substantial specimen that this tooth once belonged to.
The piece of eviscerating awesome in question is 12.6cm wide and 15.8cm tall, with a 11.9cm tall crown. Based on its massive built, slight tilt and size, it is likely to be one of the first three laterals, which include what is often the widest tooth in the dentition.

There are multiple ways of estimating the size from these measurements. One that is currently very popular is based on individual regressions estimating total length from tooth-crown height in Great White sharks (Shimada 2001, cited in Pimiento et al. 2010).
Using these regressions for the first three lateral teeth, the mean estimate is 16.8m.
Another method, and one which I personally prefer because it solves a number of the problems associated with using a significantly smaller relative as the sole analogue, is first extrapolating the length of the entire tooth row from the width of the tooth, and then using a regression designed for estimating total length from the length of the tooth row (Lowry et al. 2009, see also Newbrey et al. 2013/in press, and this list of measurements of two cast megalodon dentitions→. That way differences in proportions within the dentition are reduced to the impact of individual, not interspecific, variation, and the resulting estimate assumes them to follow the same trend in terms of relative jaw size.
Even though the literature seemingly suggests significantly less, I went with an interdental spacing of ~15% in addition to the summed tooth widths, because it corresponds to what one can roughly measure in the most widely spaced pictures of great white shark jaws and it is only fair towards the tested hypothesis to use the most optimistic reasonable regression).
Coincidentally this gives us the same mean size estimate for the three positions, 16.8m. Quite funny actually.

It is an intriguing side note (even though it’s just a coincidence, it pretty much rules out the whole "these figures are different from the official ones" side of criticism, because they aren’t) that this size estimate also coincides with the highest one estimated by Gottfried et al. 1996 that was deemed reliable, as well as with the biggest specimen from the nursery described by Pimiento et al. (2010). This was hence the highest proper size estimate in the literature for almost two decades. Even now, only less than 3% of all megalodon specimens in Pimiento & Balk’s dataset provide a record of the species reaching or exceeding this size, and at most by about 7%, so I find it quite save to assume that this can be considered representative of a very large megalodon.

Length estimates are of course only half of the equation. The most determining factor (though unfortunately highly prone to fluctuations) of the animal’s biology is its body mass. And sure enough, estimating body mass from total length in extant sharks has received almost unparalleled attention as far as size estimates go.
The following is a graph showing 6  [!] different regression equations between total length and body mass for the extant white shark, C. carcharias. In order to avoid biases I’ve applied all of them and marked the mean, maximum and minimum estimates:
Megmass - by theropod1
As apparent from the exponents, most of these studies found positively allometric growth in terms of body mass, i.e. larger sharks get bulkier. That is also what my reconstruction bases on (unimaginative as you may call it, since it’s the boring bulked-up great white you always see when it’s about meg). I’m certainly open to other possibilities, it’s just that I have not yet seen any convincing arguments to suggest they are more likely than this (e.g. very elongated or compact sharks).

So as you can see, the average adult megalodon is predicted to be ~29t in mass, no more than 32t and no less than 26t, and the large specimen from Denmark is expected to be ~52t (between a minimum of 46t and a maximum of 57t). The average of the entire population would be ~10t, similar to a very large bull orca (which is impressive enough considering that that average corresponds to what is probably a large sub-adult).
And yes, there are some megalodons that realistically reached or exceeded the 18m-mark (at which length they’d be expected to weigh in at ~64t), and some exceptional fossils could indicate lengths of ~20m (and probably ~89t). But their overall relevance is in no proportion to their size. Consider this; of the 544 teeth in Pimiento & Balk’s sample, none produced an estimate higher than 17.9m, so individuals significantly above that size are obviously too rare for much of a demographic impact.

Most fossil organisms are represented by small samples, and it is likely that they are centered around the average and that "maximum size" remains unknown in virtually all of them. That’s because the likelihood of finding exceptionally large (or small) individuals is typically lower than finding normal-sized ones, and the small number of individuals known for most of them is not in favour of finding such exceptions.
So please guys, when you talk about this animal’s size, be a bit more precise, differentiate, and don’t mix average, large, small and maximum-sized specimens up all the time, because it tends to lead to conclusions that are entirely unwarranted.
C. megalodon
is not an 18m shark, nor for that matter is there any species of 18m sharks. Only a species (possibly two if one includes Rhincodon) that occasionally gets that big. There is no species of 1t bear either, and sperm whales aren’t 24m long and don’t weigh 130t, occasional outsized specimens notwithstanding.

PS: I do realize this looks like a rant, and honestly, it is. I’m sure we all have issues that annoy us, some more than others. That doesn’t mean I am not appropriately impressed by C. megalodon or anything like that, just that I think some people are overdoing it in that regard.

    Bendix-Almgreen, Svend E. (1983): Carcharodon megalodon from the Upper Miocene of Denmark, with comments on elasmobranch tooth enameloid: coronoïn. Bulletin of the geological Society of Denmark, 32 pp. 1-32.
   Cailliet, Gregor M.; Natanson, Lisa J.; Welden, Bruce A.; Ebert, David A. (1985) Preliminary studies on the Age and Growth of the White Shark, Carcharodon carcharias, Using Vertebral Bands. Memoirs of the Southern California Academy of Sciences, 9 (Biology of the White Shark, a Symposium.) pp. 49-60.
   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, Leonard J.V. (1984): Sharks of the World. An Annotated and Illustrated Catalogue of Shark Species Known to Date. Part 1 – Hexanchiformes to Lamniformes. FAO Fisheries Synopsis, 125 (4) pp. 1-249.
    Kallal, Robert J.; Godfrey, Stephen J.; Ortner, D. J. (2010): Bone Reactions on a Pliocene Cetacean Rib Indicate Short-Term Survival of Predation Event. International Journal of Osteoarchaeology, 22 (3), pp. 253-260.
    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.
Lowry, Dayv; Castro, Andrey L. F. de; Mara, Kyle; Whitenack, Lisa B.; Delius, Bryan; Burgess, George H.; Motta, Philip: (2009): Determining shark size from forensic analysis of bite damage. Marine Biology, 156 pp. 2483-2492.
    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.
    Newbrey, Michael G.; Siverson, Mikael; Cook, Todd D.; Fotheringham, Allison M.; Sanchez, Rebecca L. (2013, in press): Vertebral morphology, dentition, age, growth, and ecology of the large lamniform shark Cardabiodon ricki. Acta Palaeontologica Polonica, in press, pp. 1-65.
    Pimiento, Catalina; Balk, Meghan A. (2015): Body-size trends of the extinct giant shark Carcharocles megalodon: a deep-time perspective on marine apex predators. Paleobiology, 41 (3), pp. 479-490.
    Pimiento, Catalina; Ehret, Dana J.; MacFadden, Bruce J.; Hubbell, Gordon (2010): Ancient Nursery Area for the Extinct Giant Shark Megalodon from the Miocene of Panama. PLoS ONE, 5 (5), pp. 1-9.
    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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Dinopithecus Featured By Owner Edited Feb 16, 2017
And I don't stop coming with the questions...

I wanted to ask you something: are the capacities for forelimb pronation and supination really necessary for theropods to 'grapple' as per cats, bears, or mustelids? When LionClaws was relatively active on Carnivora recently, he stated his belief that the inability for theropod forelimbs to pronate or supinate made them less suited for grappling. Is this really true? I used to think that as bipeds that don't need to pronate or supinate for locomotion and with hands fixed in a position that allows for grasping (i.e. the palms face inward) that it wouldn't really matter.
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.
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
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).
theropod1 Featured By Owner Dec 9, 2016  Student Traditional Artist
I’m not sure what you mean by "their body plan takes advantage of being so large". Every large animal takes advantage from that large size, otherwise it wouldn’t have become large in the first place. And every body plan depends on its owner being the size at which it evolved to function properly.

Surely an elephant tusk could fatally injure an elephant-sized animal given the right circumstances.
The point is that there are body plans, weapons, and importantly, behavioural adaptions that would be better suited to do so.
If I recall correctly I touched on this the last time I discussed this: despite their undeniable intelligence, they still never, in their entire evolutionary history, have had to deal with predators that were anywhere close to their own size, and it seems unlikely an elephant that had to do this suddenly would be up to the challence simply on the basis of using the appropriate behavioural response.
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kirkseven Featured By Owner Edited Aug 20, 2016
Remember the 11-11.2 meter figure for the avrage T.Rex? By Larson
Could we factor in specimens like AMNH 5027 and MOR 008 who didn't
Have Femurs could these avrage figure size be Larger?

☆mind you scott hartman said we dont have a statistically valid sample
To create an average, but it's fun to speculate.
theropod1 Featured By Owner Aug 21, 2016  Student Traditional Artist
It could. However note that MOR 008 seems to plausibly fall within the 11-11.2m range itself, at least based on its more accurately restored skull length of 1.34m.

The question is how to get an unbiased sample, especially if we have got individual subsamples that differ markedly from each other.

The statistical significance is not high either way, but the figures could at least be indicative if we can objectively sample and estimate as many specimens as possible (in fact there are probably even enough T. rex specimens to get fairly significant results, well over 50 in total, but we lack data on many of them and will probably not get them any time soon).
That way at least 15 or 20 specimens will give us a much better idea of the normal size of the species than one, so lack of statistical significance is no reason not to at least do the best we can.
kirkseven Featured By Owner Edited Aug 21, 2016
About MOR 008 it does appear to look similar to
AMNH 5027 which could suggest something longer
Than sue. (I'm not sure if it would be heavier)

And blazes image seems to suggest that the corrected
Version of the skull is 140cm going by pixel count.
theropod1 Featured By Owner Aug 27, 2016  Student Traditional Artist
That depends on how you measure it. I had forgotten Blaze assumed the measurement to be Pmx-qj, so yeah, if it was, it is fairly large (134cm in MOR 008 vs 141cm in sue), but honestly the 1.5m skull length figure could be referring to any measurement of the skull, not necessarily the smallest.
About AMNH 5027: I wouldn’t go by the looks (I really don’t trust the restored skull shape to be so precise as to exactly distinguish which specimens it resembles most), but a proportionately smaller skull than sue is certainly plausible. On the other hand I doubt that’s going to affect the average size much, since we have to equally consider proportionately longer legs than in sue, so skulls of smaller individuals may be giving conservative estimates, but in exchange the femora are giving upper estimates when scaling both based on sue. But yeah, that’s a valid point.
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Valia2305 Featured By Owner Aug 9, 2016  Hobbyist Artist
I love your reconstructions and mainly paleoart!!! Here's a watch and a bunch of favorites from me!!!!! :happybounce:
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