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Post by Grey on Feb 22, 2014 22:09:43 GMT 5
But how do you know the size of the tooth in the picture I posted ? I'm not even sure the author measured it himself at this time...
You think to be able to present a solid equivalent to Shimada's based on JP rather than CH ? If you do so, I'd suggest you to present it to some fossils sharks authorities...
Of course, once the skeleton in Peru is studied, we'll know much better Meg proportions and will be able to tweak a bit the available methods or make a new one.
That's the problem I have with the toothrow length, I'm not sure the initial formula, based on the great white datas, effectively accounts the differences in Meg dentition.
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Post by theropod on Feb 22, 2014 22:20:29 GMT 5
I already wrote that, I scaled the picture on screen until the hand was about the size of my own. Then I just measured it with a ruler. That is of course a rough figure (just like those comparisons using humans as scale bars), my point was just to verify whether it really was so gigantic. Since the results, using liberal assumptions, are between 14.6-17.2m, I’m not agreed that it is. That is a large specimen, but I know what you refer to when you state "gigantic", as I also know we have a different understanding of what a large megalodon is.
Not an equivalent, an alternative that eliminates a source of error.
The whole point about toothrow lenght (or jaw perimeter) is that it will not be subject to inaccuracy due to those differences in the dentition. As long as the toothrow and TL scaling relationship is constant (i.e. unless one has a proportionally smaller or larger mouth, which is not indicated by anything or anyone), this works well. On the other hand, if a method bases on tooth height, it’s affected by whether both have teeth the same relative height (some species have taller crowns), and by how the tooth height changes along the dentition. Tooth width is better, but it is still affected by differences in the width of individual teeth. The sum of all tooth widths however puts strong constrains on the size of the jaw, and on that of the whole animal.
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Post by Grey on Feb 22, 2014 22:46:16 GMT 5
I've myself too measured the tooth while scaling the hand to mine, but that's really heavily unreliable as even less than 1 cm of difference can have great impact on the result. Hands proportions vary greatly, I'm tall, robustly built but my hands are fairly small and gracile for my size. That's why I've not reported anything from this here. I wanted initially to get an estimate of CH on that tooth.
Regarding the toothrow estimates, the main problem remains that we ignore which tooth spacing to include in the calculation, making the results we've got insecuring to me.
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Post by theropod on Feb 22, 2014 22:50:21 GMT 5
As I wrote, I’ve got big hands. I was making a ballpark estimate using liberal assumptions (the biggest tooth spacing, the posteriormost conceivable tooth position...). Shimada’s method wouldn’t do any better here, especially since the tooth is incomplete. Of course exact measurements would be appreciated, but based on what’s available I’m not agreed with your feeling that it’s particularly big.
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Post by Grey on Feb 22, 2014 22:58:43 GMT 5
In any case it's not small, particularly if we argue that Megalodons above 15 m are considered "large". I'd prefer exact measurements than assumptions liberal or not. The tooth is not complete but it is possible to reconstruct it its original shape, like done for the tooth found with the associated vertebra in Denmark. I'm still skeptical in the ability to fairly estimate using toothrow proportions as we may lack some factors regarding that method.
Since you have a ruler, maybe you can in the same way try to predict the CH of that tooth.
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Post by theropod on Feb 22, 2014 23:54:18 GMT 5
I’m not saying it’s small. I thinkm it’s an average to large adult, but not that exceptional. What factors do you think we are missing? Intraspecific variation of course affects the extrapolation, but it also affects the estimates in all other methods. Interdental spacing is a problem, but we can at least constrain how large it should have been. In great white shark jaws, it seems to be no more than 15% (some specimens showing none at all).
Do you have an image of a L5 or L4 in a decent resolution?
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Post by Grey on Feb 23, 2014 0:01:49 GMT 5
No image of a confirmed L4 or L5 but I really think the diagramm is well enough for this. And even whitout, it is possible IMO to draw the shape of the tooth based on the base of the crown, curved on one side and rather straight on the other. The goal is not to make a L4 or L5 but to make the most exactly possible original tooth.
The actual size is a matter of exactitude in the measurements of that tooth, the perspective potentially complicates this. "Seems to be no more than 15 %", that's the problem, "seems" only, we do not have any data there.
Have you consulted the paper by Mike Siversson where he estimates size in Cardabiodon and Cretoxyrhina ? I'm going to check it, it seems to me he uses extensively the method.
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Post by theropod on Feb 23, 2014 3:06:33 GMT 5
You mean the description of Cardabiodon venator? Siverson, M. and Lindgren, J. 2005. Late Cretaceous sharks Cretoxyrhina and Cardabiodon from Montana, USA. Acta Palaeontologica Polonica 50 (2): 301–314.? No, I haven’t read it properly so far. But I know that another paper? Siversson coauthored uses the regressions from Lowry et al. 2009. A detail I had previously overlooked is that the paper in question used 1mm of distance between individual teeth, resulting in a lower jaw toothrow lenght of 746mm for the C. ricki specimen. There were 4 anterior and 12 lateroposterior teeth, i.e. 16 tooth width + 15×1mm=>2% of spacing. 15% are an upper bound, and you find this reflected in the estimates. I’ve got better material than that diagram, you once posted photos of the complete dentitions (Hubbell’s and Uyeno et al.’s). Unfortunately it’s not that easy. If you want a rigorous reconstruction of a piece missing a considerable part, that’s not as easy as just drawing two straight lines from the point were it’s broken. The proportions of the teeth are not the same. They are all roughly triangular, but some are proportionally shorter, others taller, and the edges are not straight but curved, to a varying degree. I’ve already attempted a restoration, by superimposing the laterals from the photographs on them, but none of them fitted well (actually L1 was still the best and the rest were all really bad). I think it’s pointless to try using this for a size estimate, especially since we have got a better method, at hand, that’s easier to apply in this case. Sure, exact measurements do matter. But in the absence of those, imprecise measurements are a whole lot better than feelings.
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Post by Grey on Feb 23, 2014 6:35:30 GMT 5
I thought the photos of Hubbell's was too distant to allow to easily distinguish the shape of the teeth. I've not posted the dentition of Uyeno et al., it was another dentition reportedly found in the Yorktown formation. Yes in that paper Siversson makes also a revision of the size estimate of Shimada of a Cretoxyrhina specimen. it is interesting to note that Siversson used Carcharodon formula from Lowry to estimate Cardabiodon which shows a dentition vastly different than Carcharodon (and Carcharocles) with smaller and more numerous teeth. I trust you in that the actual tooth spacing is 2 % but even so, keep in mind then that Siversson several times reported the max size he got with that method for Megalodon was almost 20 m TL. That's what I explain by "we may ignore some data in the calculation for Meg". You need 15 %, with the widest Meg tooth we know, to get something very similar to Siversson estimates whereas with 2 % (that are perhaps only to be applied on the lower jaw) he apparently gets a size near 20 m, and with no certainty of the identity of the tooth he used. There's something we ignore yet or that we've overlooked in the whole calculation. Another poin, I still have a hard time with the calculation using the formula of Lowry. Note that for a reason I ignore this Megalodon dentition uses a smaller intermediate tooth...
The upper anterior of Megalodon are roughly twice the width of the white shark upper, but the whole dentition of Meg is clearly more than twice the size of the great white dentition. That's why I'd expect to get a size estimate a deal larger than the size estimate based on tooth width from an upper using toothrow lenght method in Meg. Unless of course we're agreeing Megalodon had a disproportionate mouth which is still possible but in the realm of the speculation. In a simplistic but direct approach, using the length of these dentitions, if we agree the great white dentition represents a 6 m shark, the Meg dentition represents something about 14.4 m, and that's couting that smaller intermediate tooth. I provided a similar example earlier. Regarding the tooth in the pic, the only way is to examine it directly, which is not possible directly, but based on what the picture shows, my bet is on L4, L5 at worst. The first lateral shows a more symetrical shape with no curve, and a massive crown. Anyway that's pointless to discuss it. Perhaps Pimiento will get this one included in her paper...
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Post by theropod on Feb 23, 2014 16:19:13 GMT 5
I thought the photos of Hubbell's was too distant to allow to easily distinguish the shape of the teeth. I've not posted the dentition of Uyeno et al., it was another dentition reportedly found in the Yorktown formation. Thanks, I must have gotten that wrong. 4 anterior and 6 lateral teeth in the lower jaw is fewer, not more teeth than in Carcharocles and Carcharodon. Perhaps Siversson also used this formula for his other estimates. He seemingly likes being vague about his methods, but his estimates fit those you get for the largest teeth using Lowry et al. Also, I highly doubt any Megalodon expert would not be aware of those teeth. It’s likely his estimates for the upper end of Megalodon’s size range base on Hubbell’s specimen. I remember in his talk he estimated the biggest specimens as 18-19m and yet also used the term "approaching 20m". that does not have to mean he really got an estimate that was 20m. siversson seems to like very rough size figures. Note that I don’t say that ~15% is not possible, but it is certainly not conservative. 2% are also possible, or indeed anything between 0% and 15%. That’s a normal scope of variation, you’ll find even greater fluctuations if you use single teeth. If anything, one would expect the spacing in the lower-jaw dentition to be greater (greater use for anchoring than for slashing), but we can do the same with the lower jaw if you want. I’ll attach you a spreadsheet. Hope it works. You wrote that before, but that’s a fallacy. If you use the toothrow lenght, you first extrapolate it based on the proportions of megalodon, not those of the great white shark. I.e. that C. megalodon has relatively smaller upper anteriors is accounted for, as is that it has relatively larger posteriors. C. megalodon’s dental proportions are not the same, which this method is the only one to account for. As I explained earlier, that’s the very reason I favour this method. The problem you are talking about is much worse when using tooth heights (the biggest tooth in the dentition is proportionally just some 6% wider in the great white than in C. megalodon, but the longest is 28% longer and the shortest just 60% the lenght) than when using tooth widths. What is wrong about simply using the formulas from Lowry et al.? You have previously reminded me regularly that such "direct sizing" was far too simplistic, especially if it’s guess-based. The crown looks quite massive actually, judging by the shape of the edges both L4 and L5 have crowns that are too short.
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Post by Life on Feb 23, 2014 16:37:56 GMT 5
A large tooth found by a scuba diver. Using the 1 dollar bill, I've measured to tooth to be 14.2 cm wide, 17.7 cm in vertical height, with a crown height about 13.5 cm (keepig in mind the tip of the crown which seems incomplete). I was not able to measure the slant and I'm not sure of its position. I someone wants to verify the measurements. Looks like A3.
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Post by theropod on Feb 23, 2014 18:18:37 GMT 5
Sometimes A3s seem to be very robust and wide, but the majority seem to fit well.
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Post by Grey on Feb 23, 2014 22:05:59 GMT 5
You welcome, with all the posts in that thread that's easily confusing. I have overlooked that but that's really strange as in his talks, he makes a clear statement that Cardabiodon is remarkable because of its small teeth (which led to underestimates initially) in high number. Just looking at the count of the lower jaw here compared with an Isurus. Perhaps that's you who have overlooked something ! The main feature of Cardabiodon is its smaller but numerous teeth. No I don't think Siversson is that vague. He precisely says in his talk on YT the largest number he got was "about 19 m", this after showing a tooth he estimates coming from a 18 m shark. After this he says "close to 20 m" showing a scale comparison of Meg. In all his talks and interviews as well as in the mails he sent me he says 19 m or almost 20 m. This either means he found something at around 19 m or a bit higher approaching 20 m. There's less than one metre of margin from what we can deduce. That's not a rough figure. His estimates fit roughly the largest we get if he effectively used 15 % of tooth spacing, which we don't know and seems to not be the case as he seemingly used about 2 % for Cardabiodon in his paper. Megalodons experts are not all necessarily aware of the teeth in private collection and even so of their actual measurement. Chuck Ciampaglio once said me "he thought Gordon Hubbell has a very large tooth exceeding 7 inches", Brett Kent is aware of a Chilean tooth he suspects bigger than any other he has seen (and he spent time to Hubbell's collection) whereas no other scientist talked about that specimen. Unless they've approached and measured. Nothing says Siversson knows the measurement of Hubbell tooth even if it's possible. But did he got 19 m or more based on that tooth ? And with which percentage used in Lowry formula ? We don't know yet. Now here's an interesting point, in his talk he has precisely estimated the owner of that tooth (I think you had measured that tooth months ago) at 18 m. Using that width and measurement and comparing with others large teeth like Hubbell's, we could get something interesting. For sure. I just wonder what is the spacing Siversson used in his calculation. Also, knowing he directly measured actual sharks jaws I expect from him to have a proper idea of the most accurate percentage to use. I don't know if in the lower jaw it has to be greater, but 2 % isn't huge. If using less great than 2 % in the upper he still has found a size of about 19 m, that means there's something we ignore in the whole calculation. I've understood how it works, I meant that there's something I don't get because of the proportions of Megalodon teeth. Also, thanks for the doc, but 3365.426506 mm for C. carcharias upper jaws and 1997.5 mm in Isurus upper ? I've got this, what I recall is the contradiction between the respective size of the toothrows and the respective results. I'd expect a size a bit larger than using solely tooth width because of these differences in Meg dentition. I had sent you a comparison where Kent posted for example a scale where he estimated Parotodus through tooth width method and jaws perimeter method, jaws perimeter yeilding a sensibly larger size. I've just made that direct sizing based on toothrow to explain my question, not to make an actual estimate. I really appreciate Lowry et al. I only state that we ignore some factors used by Mike Siversson in the case of C. megalodon and I try to find this. Not agreed because of the curved side which partially reduce the volume of the crown on one side, like in L4 and L5, the more frontal laterals are more symetrical, the widest tooth is among these. But that's endless and not really the most interesting part at now since we don't have any mean to verify this. Thanks again for the graph.
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Post by Grey on Feb 23, 2014 22:24:32 GMT 5
A large tooth found by a scuba diver. Using the 1 dollar bill, I've measured to tooth to be 14.2 cm wide, 17.7 cm in vertical height, with a crown height about 13.5 cm (keepig in mind the tip of the crown which seems incomplete). I was not able to measure the slant and I'm not sure of its position. I someone wants to verify the measurements. Looks like A3. If that's the case and if the measurements by Theropod are accurate, by any method it seems to suggest a gigantic Megalodon at about 21.6 m TL through Shimada's formula. By comparison with the Yorktown set proportions, that would mean the A1 in the dentition was 161.7 mm wide and 150.35 mm wide using Hubbell's set. That tooth factually comes from a very very large shark. Found by a scuba diver...
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Post by Life on Feb 23, 2014 22:49:58 GMT 5
Sometimes A3s seem to be very robust and wide, but the majority seem to fit well. A3 in Megalodon are massive, not sometimes. The tooth in question matches A3 structure. Root structure alone indicates Anterior position and blade is not bended like in lateral teeth. If that's the case and if the measurements by Theropod are accurate, by any method it seems to suggest a gigantic Megalodon at about 21.6 m TL through Shimada's formula. By comparison with the Yorktown set proportions, that would mean the A1 in the dentition was 161.7 mm wide and 150.35 mm wide using Hubbell's set. That tooth factually comes from a very very large shark. Found by a scuba diver... When I saw this tooth, my gut told me that this one massive beast.
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