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Post by sam1 on Oct 22, 2019 16:20:30 GMT 5
Well then..this does not look favorable at all to megalodon even in terms of jaw damage output alone. Further, a 14.8m megalodon would appear a lot smaller than a 15.5m livyatan. Actually, a ~ 17m megalodon would be needed to roughly match a 15.5m livyatan, due to the fact that TL measurement principle is different for cetaceans and sharks(the end point of a body vs the tip of the caudal fin) I'm doing some illustrations, will finish them when I find the time. |
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Post by Grey on Oct 22, 2019 17:54:47 GMT 5
This is interesting but I won't put too much faith in this comparison. There are other ways to calculate the average size of megalodon and there is no indication whatsoever that the Livyatan holotype represents what a 14.8 m meg represents for its own kin. The actual shape and structure of the jaws is only based on assumptions.
This is certainly interesting, but nothing can be concluded from this.
Visual perception is deceptive, as a comparison with a scaled up image of the Calvert Marine Museum meg jaws (290 cm UJP, with 127 mm UA teeth) showed défavorably this time for the whale.
Not saying this is not plausible but certainly not conclusive.
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Post by Life on Oct 22, 2019 21:07:28 GMT 5
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Post by theropod on Oct 22, 2019 21:34:16 GMT 5
The average size is only for adult sharks. Sharks larger than 11.6 m according to grey’s estimates. The mean size of the whole sample is 11.1 m according to the same figures. The average size of the sample of white sharks reported by McClain et al. is 3.81 m, Caillet et al. reported average size at maturity (for both sexes) at 3.66-4.27 m, the mean of that range is just shy of 4 m, about 4% larger than the mean for the entire sample, that’s what I went with.
I think I have already addressed the problems with that comparison. Namely, the pronounced forced perspective in the photos. The Livyatan skull is around 3 m behind the person, whereas the megalodon jaws are about 2 m in front. Of course that makes the former look smaller, and the latter larger, than they really are.
As you will recall, I have already made a comparison with the same set of jaws, but scaled to the appropriate size, using the figure Grey estimates for the Yorktown dentition’s jaw (370 dUJP).  This is the distribution of crown widths expressed in ratios to the respective crown widths in the Yorktown dentition:  This is a sample of over 500 sharks, over 200 of which are adults if we assume the same ratio between the sample average and the mean size at maturity that is found in the great white (as of my knowledge, the most reasonable assumption we can make, although I am open to hearing alternatives. Using only the "adult" part of the population gives the average adult size at 86.5% the size of the Yorktown dentition. This method is actually a bit on the liberal side, as of course there would be individuals that actually have matured earlier or later than the mean size at maturity, and by using this size interval we are hence including some larger specimens and excluding some smaller ones. This skews the result upwards (the mean of {2,2,3,3,4,5} is higher than that of {1,2,3,3,4,5}), but I propose we go with this figure until someone comes up with a better one, since we lack any morphological or histological means to independently classify specimens as mature or immature. The new comparison is simply reflecting what happens if we scale the jaws to that size with respect to the Yorktown dentition. |
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Post by theropod on Oct 23, 2019 1:41:46 GMT 5
That depends a lot on the estimate, and how robust it is. The 15.4 m Livyatan in my reconstruction based on Brygmophyseter for example is measured to the posterior edge of the tail fluke, not the notch, to make them more comparable. Of course a whole range of estimates is possible for that specimen, it could just as well be 15.5 m measured to the notch in the fluke as to the posterior edge. But that thing in my estimate would still be almost as heavy as a 17 m megalodon, so I agree. A 14.8 m megalodon would likely not be appreciably larger than the lower estimate for Livyatan. This one is 14.9 m:  Though this is actually a depiction of a megalodon the size of the Yorktown specimen, depicted with both some positive allometry in bulk and jaw size, so the average scaled down from a higher estimate for that specimen would be slightly more slender and have about 13% smaller jaws. So I tend to think the average adult size for megalodon based on isolated tooth specimens is quite unlikely to be higher than the size of the Livyatan holotype. I think I’ve tested for every possibility of that scenario now, namely 1) using the upper estimate for megalodon, 2) using the lower estimate for Livyatan, 3) using an estimate of average size that is based on a very robust sample size, robust method (as far as isolated teeth go anyway) and more likely to be over- than underestimating it. But if someone can point out further ways to improve this calculation, I’d obviously be very interested in hearing them. |
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Post by sam1 on Oct 23, 2019 1:55:29 GMT 5
..except that the very comparison you're referring to is nothing resembling any objectivity. The perspective in megalodon jaw shot shows human standing a good feet behind, whereas the livyatan jaw is having a man standing in front of it! It makes for a ridiculously skewed comparison. I dare you to show us a properly scaled, equal perspective comparison. |
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Post by sam1 on Oct 23, 2019 2:01:23 GMT 5
That depends a lot on the estimate, and how robust it is. The 15.4 m Livyatan in my reconstruction based on Brygmophyseter for example is measured to the posterior edge of the tail fluke, not the notch, to make them more comparable. Of course a whole range of estimates is possible for that specimen, it could just as well be 15.5 m measured to the notch in the fluke as to the posterior edge. But that thing in my estimate would still be almost as heavy as a 17 m megalodon, so I agree. A 14.8 m megalodon would likely not be appreciably larger than the lower estimate for Livyatan. This one is 14.9 m: Though this is actually a depiction of a megalodon the size of the Yorktown specimen, depicted with both some positive allometry in bulk and jaw size, so the average scaled down from a higher estimate for that specimen would be slightly more slender and have about 13% smaller jaws. So I tend to think the average adult size for megalodon based on isolated tooth specimens is quite unlikely to be higher than the size of the Livyatan holotype. I think I’ve tested for every possibility of that scenario now, namely 1) using the upper estimate for megalodon, 2) using the lower estimate for Livyatan, 3) using an estimate of average size that is based on a very robust sample size, robust method (as far as isolated teeth go anyway) and more likely to be over- than underestimating it. But if someone can point out further ways to improve this calculation, I’d obviously be very interested in hearing them. That shark's jaws outline is way too large though. |
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Post by theropod on Oct 23, 2019 2:06:17 GMT 5
No need to point that out, didn’t I just explicitly write that? It’s based on allometry seen in white sharks (Mollet at al. dataset). But based on that allometry, the Yorktown meg itself would be 14.9 m long. So obviously the average size would be smaller in that case. If the Yorktown meg is 17 m +, and the average is ~14.8 m, then the jaws must be proportionately smaller.
Also, of course the line I marked on the picture represents the entire jaw perimeter, a large part of that wouldn’t be visible in life (in fact only ~60% of that is bearing teeth according to the estimate that gave this perimeter).
But yes, the jaw size depicted and compared there isn’t that of an average megalodon, it’s that of a Yorktown-sized megalodon, I just thought doing a new comparison for that was overkill.
Obviously that doesn’t mean some megs weren’t way bigger, with way bigger jaws. For example the mechanical jaws from "sharkzilla", based on the tooth found associated with the killed cetothere, which I’ve seen used in comparisons here before, would obviously belong to a near-max-sized individual, even though the size estimate back then was deceptively conservative on account of using tooth height methodology.
But then, we don’t know anything about how large larger Livyatan might have grown, so we should cut the speculation and not compare it to such specimens that are obviously exceptionally large.
This has been a problem on this thread from the beginning as far as I can tell. Scaling the size of a set of megalodon jaws is not so trivial, especially with the varying proportions they are reconstructed as, which affect all straight-line measurements you could try to scale them to. You need to measure a curved line, and account in some way for the camera angle if there is one. That’s probably why there is this overreliance on scaling based on the height of people in the photos, which causes the forced perspective.
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Post by Life on Oct 23, 2019 2:36:16 GMT 5
The average size is only for adult sharks. Sharks larger than 11.6 m according to grey’s estimates. The mean size of the whole sample is 11.1 m according to the same figures. The average size of the sample of white sharks reported by McClain et al. is 3.81 m, Caillet et al. reported average size at maturity (for both sexes) at 3.66-4.27 m, the mean of that range is just shy of 4 m, about 4% larger than the mean for the entire sample, that’s what I went with.
I think I have already addressed the problems with that comparison. Namely, the pronounced forced perspective in the photos. The Livyatan skull is around 3 m behind the person, whereas the megalodon jaws are about 2 m in front. Of course that makes the former look smaller, and the latter larger, than they really are.
As you will recall, I have already made a comparison with the same set of jaws, but scaled to the appropriate size, using the figure Grey estimates for the Yorktown dentition’s jaw (370 dUJP). This is the distribution of crown widths expressed in ratios to the respective crown widths in the Yorktown dentition: This is a sample of over 500 sharks, over 200 of which are adults if we assume the same ratio between the sample average and the mean size at maturity that is found in the great white (as of my knowledge, the most reasonable assumption we can make, although I am open to hearing alternatives. Using only the "adult" part of the population gives the average adult size at 86.5% the size of the Yorktown dentition. This method is actually a bit on the liberal side, as of course there would be individuals that actually have matured earlier or later than the mean size at maturity, and by using this size interval we are hence including some larger specimens and excluding some smaller ones. This skews the result upwards (the mean of {2,2,3,3,4,5} is higher than that of {1,2,3,3,4,5}), but I propose we go with this figure until someone comes up with a better one, since we lack any morphological or histological means to independently classify specimens as mature or immature. The new comparison is simply reflecting what happens if we scale the jaws to that size with respect to the Yorktown dentition. I am not sure what a comparison like that is intended to prove. This comes down to the 'opening aspect' of the Megalodon's jaw under consideration, as well as the size of Megalodon in question. Jaw opening to an extent  Jaw opening even further  Jaw opening to full extent
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Post by theropod on Oct 23, 2019 2:43:01 GMT 5
Life: What most comparisons are intended to "prove", their relative size.
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Post by Life on Oct 23, 2019 3:16:59 GMT 5
Life: What most comparisons are intended to "prove", their relative size. Sure. 1. You are comparing Megalodon's jaw structure (frontal view) to Livyatan's skull structure (side view). How is this a fair comparison? Megalodon's jaw structure [in question] depict a limited opening aspect - the shark could it open its jaw to noticeably greater extent if it wanted to (flexibility provided by cartilage) 2. You are comparing Megalodon's statistical average to the Livyatan holotype which seemingly fall in the upper echelon of the size range of the species. How is this a fair comparison? Some would want to compare largest of Megalodon to the Livyatan holotype instead. --- You should consider providing comparisons which factor-in different angles, sizes and perspectives - biomechanical considerations in particular. Difficult task though, due to lack of quality work in this respect. |
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Post by theropod on Oct 23, 2019 3:26:38 GMT 5
1) This is a comparison of both of them in their most commonly shown view (lateral for the whale, anterior or posterior, in this case the latter, for the shark), and the one that is likely most informative, using a picture you yourself where the one to provide. And of course a view that I have the data to scale properly. If I compared both in lateral view, the shark jaws would of course look smaller than they do here.
As I wrote my comparison was to illustrate relative size, not gape angle. The whale jaws aren't opened at all…
2) I am comparing the average adult (a probably liberal estimate of average adult size at that) to the only known specimen of the whale. What is your evidence that the holotype fell in the "upper echelon" of size for its species?
Sizes of animal populations are usually normally distributed (this is due to size depending on a superposition of a number of independent genetic and environmental factors, which results in a bell curve since the coincidence of an intermediate number of these factors is the most likely). That makes sizes around the average size the most common and therefore probable for a randomly sampled individual, with the probability decreasing the further from the average we get (the size distribution for megalodon shown above provides a rough example). Meaning a single individual is more likely to be average than particularly large or small.
Why would we want to compare such a specimen to a specimen that is large, as we know because we have a large sample of its species clearly demonstrating this?
And yes, I should certainly provide comparisons showing different sizes and angles, and I am planning to do so. But obviously, every comparison needs to be based on reliable data, which first have to be available in order to be able to make one.
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Post by theropod on Oct 23, 2019 4:26:13 GMT 5
I’ll give you an example. The meg dataset has 544 entries. I’ll generate a random number (using sample(1:544,1) ) between 1 and 544, pull that entry from the dataset, and see whether that falls closer to the average size (0.65) or the max size (1.25) of the sample. Here we go: > megdata$rYT[sample(1:544, 1)]
[1] 0.72812let’s repeat that a couple of times, let’s say with 10 random numbers: > megdata$rYT[sample(1:544, 10)]
[1] 0.4872710 0.3355408 0.6711666 0.3353687 0.8023485 NA 0.6170344
[8] 0.4051667 0.6102383 0.5429377
And again: > megdata$rYT[sample(1:544, 10)]
[1] 0.9045896 0.8695549 0.4153598 0.8837984 0.3754687 0.9802679 0.9935181
[8] 0.8684521 0.3870673 0.7493380
Or let’s try repeating that only on megalodon larger than average size at maturity, i.e. larger than 0.677, which are 223 specimens (of course technically just half a normal distribution, but there are still more individuals near the bottom of that size range, which is relatively closer to the mean, than near the top): The average in this case is 0.865, maximum still 1.25, so lets see whether our chance sampling turns up with the former or the latter: megdata$rYT[megdata$rYT>=0.6767964]->adultmegs
> adultmegs[!is.na(adultmegs)==T]->adultmegs
> adultmegs[sample(1:223, 10)]
[1] 1.1293910 0.6814581 0.9497792 0.8824853 0.7240493 0.9116998 0.8696101
[8] 0.8733678 0.7845937 0.9109272
> adultmegs[sample(1:223, 10)]
[1] 0.8023485 0.6800272 0.8147615 0.8696101 0.9882189 1.0429310 0.7781468
[8] 0.8020371 0.8912165 0.8885613
See my point? not one of these individuals is even close to maximum size. If you pick a random individual, it is way more likely to pick one close to the average. The Livyatan holotype represents such a pick. We can probably be confident that it is not a juvenile, but that’s about it, especially considering its tooth morphology, which still shows open pulp cavities characteristic of young sperm whales. Adult sperm whales also vary vastly in terms of size. Average for bulls of Physeter is about 14 m, but large bulls commonly reach 18 m, and sizes of over 20 m (possibly to 24 m) are also sometimes reached. If you pick a random Physeter bull however, you will likely get a 14 m one, not a 20 m one. Same for megalodon. And same for Livyatan.
This considered, do you see why we should compare the Livyatan holotype to an average adult megalodon, and not a large one? We have one individual, and having no choice but to make a hypothesis where that individual falls on the size distribution curve of its species, the most parsimonious hypothesis is to assume it falls close to the mean, because the probability to find such a specimen is highest.
(This whole exercise is of course only to illustrate the principle, it has no real scientific relevance, since all the actual evidence (notably the size distribution curve) that may have been needed has already been shown.) |
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Post by Life on Oct 23, 2019 5:33:57 GMT 5
I’ll give you an example. The meg dataset has 544 entries. I’ll generate a random number (using sample(1:544,1) ) between 1 and 544, pull that entry from the dataset, and see whether that falls closer to the average size (0.65) or the max size (1.25) of the sample. Here we go: > megdata$rYT[sample(1:544, 1)]
[1] 0.72812let’s repeat that a couple of times, let’s say with 10 random numbers: > megdata$rYT[sample(1:544, 10)]
[1] 0.4872710 0.3355408 0.6711666 0.3353687 0.8023485 NA 0.6170344
[8] 0.4051667 0.6102383 0.5429377
And again: > megdata$rYT[sample(1:544, 10)]
[1] 0.9045896 0.8695549 0.4153598 0.8837984 0.3754687 0.9802679 0.9935181
[8] 0.8684521 0.3870673 0.7493380
Or let’s try repeating that only on megalodon larger than average size at maturity, i.e. larger than 0.677, which are 223 specimens (of course technically just half a normal distribution, but there are still more individuals near the bottom of that size range, which is relatively closer to the mean, than near the top): The average in this case is 0.865, maximum still 1.25, so lets see whether our chance sampling turns up with the former or the latter: megdata$rYT[megdata$rYT>=0.6767964]->adultmegs
> adultmegs[!is.na(adultmegs)==T]->adultmegs
> adultmegs[sample(1:223, 10)]
[1] 1.1293910 0.6814581 0.9497792 0.8824853 0.7240493 0.9116998 0.8696101
[8] 0.8733678 0.7845937 0.9109272
> adultmegs[sample(1:223, 10)]
[1] 0.8023485 0.6800272 0.8147615 0.8696101 0.9882189 1.0429310 0.7781468
[8] 0.8020371 0.8912165 0.8885613
See my point? not one of these individuals is even close to maximum size. If you pick a random individual, it is way more likely to pick one close to the average. The Livyatan holotype represents such a pick. We can probably be confident that it is not a juvenile, but that’s about it, especially considering its tooth morphology, which still shows open pulp cavities characteristic of young sperm whales. Adult sperm whales also vary vastly in terms of size. Average for bulls of Physeter is about 14 m, but large bulls commonly reach 18 m, and sizes of over 20 m (possibly to 24 m) are also sometimes reached. If you pick a random Physeter bull however, you will likely get a 14 m one, not a 20 m one. Same for megalodon. And same for Livyatan. This considered, do you see why we should compare the Livyatan holotype to an average adult megalodon, and not a large one? We have one individual, and having no choice but to make a hypothesis where that individual falls on the size distribution curve of its species, the most parsimonious hypothesis is to assume it falls close to the mean, because the probability to find such a specimen is highest.
(This whole exercise is of course only to illustrate the principle, it has no real scientific relevance, since all the actual evidence (notably the size distribution curve) that may have been needed has already been shown.) 1. Large Megalodon would be far lower in number than juvenile Megalodon whose teeth are easily accessible from formerly shallow water environments or supposedly nursery locations. 2. As for Livyatan holotype falling in the upper echelon of size range of Livyatan-types, following study is very telling: "The large size of BAR-2601 and MML 882, together with the presence of an occlusion surface, indicating the presence of functional teeth in both the maxilla and the mandible, and teeth with massive, robust roots, support an attribution of these specimens to stem physeteroids (Kazár, 2002; Reumer et al., 2017). From the same locality and bed were BAR-2601 and MML 882 come, Gondar (1975) described the basal physeteroid Preaulophyseter gualichensis. This taxon differs from BAR-2601 and MML 882 in the absence of longitudinal ridges and grooves, and smaller size, among several other features.
The large size and robustness of specimens BAR-2601 and MML 882 suggest their inclusion within “macroraptorial sperm whales” (sensu Lambert et al., 2016). Among macroraptorial sperm whales, BAR-2601 and MML 882 are notably large. In fact, in most taxa, the maximum mesiodistal diameter of teeth barely exceeds 50 mm in size (32 mm in Acrophyseter deinodon, 34 mm in A. robustus, <56 mm in Zygophyseter varolai, < 40mm in Brygmophyseter shigensis; Varola et al., 1988; Hirota & Barnes, 1994; Bianucci & Landini, 2006; Lambert et al., 2016). Further, in spite of the fact that BAR-2601 and MML 882 fall within the size range of Albicetus, they clearly differ from the latter in having suboval cross-section, instead of subrectangular (Boersma & Pyenson, 2015).
On the other hand, specimens BAR-2601 and MML 882 approach in size, robustness, and cross-section Livyatan melvillei which is the cetacean with the largest known dentition, having disproportionately large teeth that are invariably larger than 80 mm in minimum mesiodistal diameter (Lambert et al., 2010). The combination of characters of specimens BAR-2601 and MML 882 is congruent with L. melvillei. However, the teeth of Livyatan have a maximum diameter between 100 and 120 mm, the apical tooth having 81 mm (Lambert et al., 2010, 2016), being larger than specimens here described. Because of this, and that only isolated teeth are available, we refrain from referring BAR-2601 and MML 882 to the species level, and we choose for an open taxonomic nomenclature, referring them as aff. Livyatan sp." - Piazza et al (2018) Citation: Piazza, David & Agnolin, Federico & Lucero, Sergio. (2018). First record of a macroraptorial sperm whale (Cetacea, Physeteroidea) from the Miocene of Argentina. REVISTA BRASILEIRA DE PALEONTOLOGIA. 21. 276-280. 10.4072/rbp.2018.3.09. |
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Post by theropod on Oct 23, 2019 6:23:50 GMT 5
I have already adressed that as well, see here: theworldofanimals.proboards.com/post/43733theworldofanimals.proboards.com/post/43747All the isolated teeth are within the size range of teeth of the Livyatan holotype. Yes, aome are slightly larger or smaller than the mean, as is to be expected since the size of the teeth varies along the tooth row, just like in megalodon, but the differences are quite insignificant. This only reinforces that the holotype is a normal-sized individual. Unsurprising, since these teeth are referred to Livyatan primarily on the basis of their similar size. This is no more evidence that the Livyatan holotype was a large individual than comparing a random megalodon tooth to an anterior without considering the former's position might be different. |
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