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Post by theropod on Jan 6, 2014 16:17:19 GMT 5
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Post by Grey on Jan 6, 2014 18:19:30 GMT 5
The same regression, with slightly more precise parameters (the previous ones seem to have been rounded). He wrote it based on a dataset from Hubbel 1996. Its not the same picture since it shows the estimated size of Carcharocles. Can you post it, even if this is not conclusive, that's good to have all the material. Or ask Kent if you prefer. From the research programm of Pimiento : ufdc.ufl.edu/UFE0041399/00001/pdf Certainly not a guess, he always uses the same figures in his talks and explained me that he used jaws perimeter. I got too 9.45 m, but that's without any interdental spacing, so quite below the predictions of Siversson. It also gives an underestimate with Hubbell's white shark. Absolutely, it figures in Mollet's list with all the measurements. Largest white shark caught off California : elasmollet.org/Cc/Cc_list.htmlBoneclones has a cast of these jaws and directly refers to Hubbell's original set. But I'm not surprised that without interdental spacing accounted, this gives such an underestimate. Using the same added percentage (25 %) to Hubbell's great white to Hubbell's meg set, the TL is now 11.79 m. Certainly, counting only the interdental spacing. Makos are probably not a good model but let's try with anything available and at least (far) related... We just need to know which was the interdental spacing in meg (does someone knows ?). Or we need to know the most likely living model regarding this spacing (does Siversson has an idea ?). The best I know are the teeth marks on the arge Pliocene balaenopterids, by a shark estimated in at 4-7 m (Gottfried's method), with distance between marks about 6 cm. |
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Post by Grey on Jan 6, 2014 18:21:16 GMT 5
Yes that's what I suspect too. White sharks are a pain in the ass. In one interview, Hubbell's said that this is especially great whites that are difficult to estimate from their dentition. Hence, Siversson basis on others lamnids ? I don't have access to page 95 of Klimley's book. |
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Post by theropod on Jan 6, 2014 19:35:35 GMT 5
GreySorry, here you go: 1.196(TWcm)+0.706
R²=0.656He seems to consider this a valid method, but pointed out the problems inherent to calculations for giant taxa based on samples of so much smaller ones. I'll send you a picture of page 95 in that book then. I think that was the regression Kent used (Mollet et al. 1996), however it somehow won't work for me. The teeth marks won't help us much (we have the same data for great whites too, there are too many variables such as all the tooth widths and spacings and so on...). Largest white shark caught off California. Measured length was 18 feet 1/2 inch (5.50 m). Thanks to Mike Shaw, SeaWorld (pers.comm.) Taxidermied specimen was on display at SeaWorld and jaw was later acquired by Gordon Hubbell. Total weight 4,150lbs (1514 kg) (page58 "The Sea World Book Of Sharks" by Eve Bunting). Liver mass 272 kg (600 lbs, 14.46 %); heart mass 4.5 kg (10 lbs, 0.24 %); girth 3.1 m (10' 2", 56% of TL). Shark was harpooned by fisherman Weeren near West end of Catalina Island on June 13, 1976 (14.8 km from shore of Catalina Island, 27.8 km from California coast). Accoroding to Le Boeuf et al. (1982) the stomach contents were nearly digested and could not be identified. The bulk of the material suggested a large animal, probably a marine mammal. Klimley (1985, Fig. 7) reported that the stomach contents of this fish were identified as elephant seal (Mirounge angustirostris) and that the estimated mass was 680 kg. However, these data apply to a different white shark caught on 7 Sep 1975 with TL ~5 m, namely #6 in Table 1 in Le Boeuf et al (1982) for which the stomach content were identified as elephant seal and it was estimated that the elephant seal probably measured 3 m TL and weighed 450 to 680 kg. Thanks to Andrew Sprott who later located an UPI photo with caption in the Fresno Bee dated 17 June, 1976. From Bone Clone Website: "The original jaw was prepared by Dr. Gordon Hubbell, a leading researcher in sharks. The original specimen was brought to Sea World in San Diego and was caught off the Southern California coast. The jaw contains a total of 230 teeth (5 rows of 46)." TL is reported to be 19' 6" (5.94 m) which is a likely overestimate. According to Ralph Collier (email to Andrew Sprott) this shark was measured by Shelly Applegate and Ralph to be TL = 19' 3.5" (5.88 m) and mass 4,680lbs (2123 kg). These appear to be overestimates also. The combined tooth widths are 747mm, which would yield 4444mm TL, so the jaw perimeter would have to be almost 24% greater to achieve our 5.5m size (10^1.007*LOG(5500)-0.8/747). We should check that with some other specimens. Lamna and perhaps Alopias (correcting for the hypertrophied fin lobe of course) would be interesting models. The problem is that they are even smaller compared to Carcharocles. I think the great white is still the best model due to its similarities in tooth shape, macrophagous ecology and its relatively large size, but there probably is some error in our calculations so far.
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Post by Grey on Jan 6, 2014 20:41:22 GMT 5
Thanks man. Can you send me the graph privately if possible ?
24%...yes I said almost 25% as the translation in metric of 18 feet 2 inches is 5.53 m...
Yes, using others great whites seems the most tenable. It still seems at looking Mollet's morphometrics that jaws perimeter is more stable than tooth width alone in great white so...
Alopias and Lamna are way smaller than Carcharodon indeed. However, Siversson used both of them for megalodon. I wonder if, despite the size disparity, scaling a small Isurus or Lamna to a Carcharodon size woud really induce such a vast potential error. I'd like that Siversson responds me but paleontoogists are not all that available...
I don't know if in our calcuation there is such an error regarding that great white specimen as I've verified it several times. Counting only the tooth row definitely induces some underestimate, in that case for the least. We should try on others great whites indeed.
Or perhaps meg had no interdental spacing at all and was smaller by a margin than we think ? But sounds unlikely to me given the various hints and that even somewhat conservative methods give higher results. I wonder too if Brett did not forget some factor while explaining that method.
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Post by theropod on Jan 6, 2014 21:29:02 GMT 5
Yes, the jaw perimeter is probably still the best we can use so far.
Carcharodon already induces a huge potential error, so I presume smaller taxa will be a bit worse, but not massively. Also, with an R² of 0.90-0.99 the toothrow-lenght regressions appear to be way more reliable than the tooth with with a correlation of 0.65...
I've forwarded you my latest informations. It seems the tooth spacing is simply quite variable. so our "underestimates" are possible, but larger estimates are possible too.
ItÂ’d be good to have a few more specimens for which both tooth measurements and and TL are known to compare it too, from that we could deduce the typical degree by which mere tooth measurements underestimate it.
edit: The text says 18ft 1/2in, which translates to 5.4991m
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Post by Grey on Jan 6, 2014 21:55:18 GMT 5
Maths...If I'm not a paleontologist today it's partly because of that. Thanks for confirming this. Indeed, toothrow appears more reliable than measurement on isolated teeth.
However, his referral to sabertooth cats and the fact that a small part appears more reliable at estimate total lenght than a larger part is interesting.
But anyway we cannot verify this on the megatoothed sharks at now so...
The way I see things is that Brett suggests any possibility between 13.9 m and 21 m TL for a 14 cm wide UA, using the graph from Mollet about the great white.
But Siversson, with an UA I guess of similar size (I don't know if he used the 15 cm wide UA owned by Hubbell), suggests something more precise apparently a bit over 19 m.
And that's what interest me, how Siversson (who's also a world leading authority in fossils lamniforms) arrived to this figure ? Even though he has not published this (that would solve all this discussion), he regularly uses that figure in his talks and so as the latest estimate.
But I have the feeling he's been bored to respond me. He's a nice guy but less available on the net, or perhaps finding my way to formulate questions not that interesting (epic second degré in the line). If you want to contact Mike about this on occasion don't hesitate.
I'm positive to check others great whites measurements to see how this variation occurs, even though this is already indicated in Brett's graph. And I'm not sure if it'd be possible to get just as detailled datas about great white sets than the boneclones paper.
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Post by theropod on Jan 7, 2014 0:26:42 GMT 5
Concerning that part, I presume this is an exception, but it should show us that we shouldn't take this for granted.
Did Siversson give a confidence interval anywhere?
looking forward to what youÂ’ll find regarding the great whites.
Kent responded me that he prefers the figure we got based on the great white regression and the problem with Isurus and the 25% spacing is the different functional morphology, since cutting teeth need to be more tightly spaced. So it seems mako sharks aren't a suitable model. I'll forward you the message.
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Post by Grey on Jan 7, 2014 0:44:56 GMT 5
Thanks for the mail and I'm agreed with Brett. We need others GW sets, but I'd think that something like 16-17 % is just somewhat pausible. It woud be good to have a scientific reference about the interdental spacing in Carcharodon.
No, Siversson did not give me this but check your PM...
Indeed, Mako, because of its teeth totally different, does not appear to be that reliable.
In fact, if we had today a shark with teeth owning exactly the same shape as meg, that would be much easier. That's the differences and variations in GW jaws and teeth morphometric which prevent to be certain at all of this.
By the way, I think about this : the potential underestimates using the great white teeth are perhaps related to the fact Carcharodon teeth are mostly quite narrower, less wide, than the very heart-shaped UA in megalodon ?
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Post by theropod on Jan 7, 2014 2:22:45 GMT 5
Thank, you for the message, thatÂ’s interesting. So Siversson didn't actually use the circumference but the widths of the dentulous part of the jaws.
The problem here is that it heavily depends on whether the jaw reconstruction is correct, while the toothrow lenght or jaw perimeter is less dependant on shape (long and narrow or short and wide?).
It appears among extant sharks Carcharodon is still one of the best available analogies for Carcharocles, since at least they both share somewhat broad, triangular and serrated cutting teeth and the great white is the closest we come in terms of ecology.
I donÂ’t think I understand what you mean regarding the difference in tooth shape.
Of course they are not the same (that would be quite strange considering C. megalodon is about 20 times larger) but why does this affect the result of the method? Also, we donÂ’t really know the size of Carcharocles, what indicates it may be an underestimate is that it underestimated a specimen of Carcharodon.
I think we should treat all the figures with appropriate caution, but the figure based on the Carcharodon regression can be treated as a lower bound.
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Post by Grey on Jan 7, 2014 2:43:59 GMT 5
He gets the dentulous part, than the circumference, then the total size. But we do not have the details. I think Siversson, given the jaw width he gives, attributes to meg a jaw "long and narrow" like Isurus or Carcharodon. The question is, what is the basis of his assumption ? Still yes, it is undisputable that Carcharodon is the best model from several views. My point is that great white teeth appear quite narrower than meg's in some case. Also, the third UA in great white is noticeably smaller than the others Upper and Lateral. This may give a total toothrow smaller than in meg which has quite wide teeth and not having that third upper that small like in Carcharodon. So I wonder how it influence the total size of the beast. Compare :   You can see if we compare both dentition in size, th UA in Carcharodon are wider than meg. But meg's row is still longer in lenght (the respective spacing between each tooth seems equal and even wider too in the great white set). In short, the dentition of meg seems a bit larger. Hence the "smaller" sizes estimates we've got so far with Carcharodon ? Carcharodon produces reasonnable but conservative estimates for meg in the absence of knowledge about the interdental spacing in the latter ? Ony asking, don't forget I can be lost while discussing maths and numbers  |
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Post by theropod on Jan 7, 2014 22:42:40 GMT 5
Yes, relation to the underestimate for this Carcharodon makes much more sense. However this regression was made for great whites, and seems to be quite reliable for it.
I would consider it more likely this underestimate is linked to variation in interdental spacing, this one probably tending towards the upper end of the scope (ie. this one likely has pretty big tooth spacing, considering the figures we came up with, meaning just added tooth widts will underestimate it more greatly than usual for the species).
Either way whether and how different the relationship between jaw size and TL is in otodontids is anyones guess, but we currently have no reason to presume it is greatly different in either direction (keep in mind that doesnÂ’t mean it wouldnÂ’t likely be different, but we simila donÂ’t know how and whether from any evidence).
What seems quite clear tough is that at comparable jaw size and likely overall size too Carcharodon has the longer teeth, since they are more elongate.
Cool pictures btw!
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Post by Grey on Jan 7, 2014 23:37:25 GMT 5
Thanks, I've not made the scale intentionally actually.
It makes sense for this Carcharodon indeed (Hubbell's set) but the set in the pic above is not from the same great white, it is precised the shark was 5.2 m TL, this is not a set from the 5.5 m specimen. At least I don't think.
It still seems to me the toothrow of megalodon is longer even if placing the respective UA teeth at parity width in both species.
Would be interesting to see more precise comparative size scales of these sets to see this.
But I have the impress that this indicates great white, though being clearly the best analogous to megalodon to use as model, yeilds somewhat conservative, but tenable, TL estimates for meg using jaws perimeter, at least based on Brett's graph (talking ony about the mean estimate).
How Siversson came up with about 19 m TL (precisely) is what I'd like to know.
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Post by theropod on Jan 8, 2014 0:45:52 GMT 5
That may well be (longer toothrow at parity UA width), since the anterior teeth in Carcharodon appear to be proportionally larger. However, why should this produce conservative estimates for megalodon based on jaw perimeter?
Perhaps based on the UA width (we can probably counteract this by simply using the largest tooth in the dentition instead), but for the jaw perimeter or toothrow lenght it shouldnÂ’t matter, unless for some reason having proportionally wider lateral teeth means having a proportionally smaller mouth.
Siversson uses the width at the posterior teeth, not directly jaw circumference (which would be much bigger of course), based on comparison to extant sharks (though IÂ’m pretty sceptical regarding the use of Mako shark jaws as a template). The question is: How does he scale the whole thing to Megalodon-size? Is he using direct sizing, as with Cardabiodon or yet another regression we donÂ’t know about (and if, how reliable is it?).
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Post by Grey on Jan 8, 2014 1:23:04 GMT 5
Well, Carcharocles is not only a scaled up version of Carcharodon. It depends if was simply 2.5-3 times larger at with a larger toothrow/mouth or with the same proportions with a slighty larger TL.
This appears conservative to me while using directly Hubbell's tooth set.
Hmm, Siversson determines the transverse width at the posterior teeth in the mal I've given you, but he only explained how he calculated the dimensions of the jaws.
In his talk, he said he used jaws circumference.
That's the question indeed. What's the detais of his works. But he seems quite affirmative as he uses that estimate in all his talks.
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