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Tyrannosaurus rex
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A prerequisite of isometric comparison is equal proportions between the two animals. Isometry is saying:
Mass unknown = ((length unknown/length known) + (depth unknown/depth known) + (width unknown/width known)) * mass known If the ratios within the parenthesis are each 1, then their sum, which is the scale factor, is isometric (3). Mathematically it can be written as follows: Scale factor = (length unknown/length known) + (depth unknown/depth known) + (width unknown/width known) If the animals have a difference in built, the sum of the of ratios will not be three, thus the relationship is not isometric. Therefore, T. rex and G. carolinii cannot be isometrically compared. As G. carolinii grows in length, it depth and width do not grow to the same degree. Therefore, the scale factor is less than 3. Using the femora, the math would be as follows: T. rex femur length/circumference: 1330 mm/590 mm; G. carolinii femur length/circumference: 1365 mm/520 mm Now I am not aware of any published diameters for G. carolinii, just the femoral circumference of 520 mm. We could split this into AP and LM diameters of a circle, but this extra step will not change the ratios we'd apply in the scaling equation. Therefore, we will just use femoral circumference as a surrogate for both depth and width. This would be accurate as long T. rex is not disproportionately wider in either the LM or AP directions. Scale factor G. carolinii/T. rex = (length G. carolinii/length T. rex) + (depth G. carolinii/depth T. rex) + (width G. carolinii/width T. rex) Scale factor G. carolinii/T. rex = (1365/1330) + (520/590) + (520/590) Scale factor G. carolinii/T. rex = 2.789 This is how regression scale factor are at the foundation derived. So if one wants to find the mass from length as the measure, the formula would be: Mass G. carolinii = (length G. carolinii/length T. rex)^2.789 * Mass T. rex Long story short, scaling a more robust animal up to longer but more gracile animal requires a scale factor less than 3. 
@tigerluver @Spalea
I do agree that Giganotosaurus and Tyrannosaurus do not scale to one another with the factor of 3 but that was not my point. My point was that assuming an identical build between the base of something and what you're scaling it up to, the scale factor was 3. Since Tyrannosaurus and Giganotosaurus are not identical in build (and therefore you cannot assume isometry between them), isometrically scaling them to one another does not necessarily fit within that and I think I agree with the comprehensive post on this. I just thought Spalea thought that with the identical result and base (ie: Giganotosaurus-form isometrically scaled to an identical Giganotosaurus-form 10% larger linearly), the scale factor would not have been 3. 
"fixed the anatomical inaccuracies"
I'm not sure if the one who makes the "corrections because they're inaccurate" are correct either, because we are dealing with fossils. Not living creatures. 
@tigerluver
Your demonstration is very interesting but I can to be not agree with it. If I'm focusing only on the t-rex's femur and giganatosaurus's femur, on their femurs volume ratio... Please just read... (Too painful to tape that on the keyboard)  *This image is copyright of its original author So we can see the femur volume is bigger for the t-rex. How can you deduce that the giganatosaurus's weigth would be equal to the (t-rex's weigth)^(number almost 3) ? Impossible. Quote:I'm not sure if the one who makes the "corrections because they're inaccurate" are correct either, because we are dealing with fossils. Not living creatures. Anything in particular you are referring to? I think I can be fairly certain that everything I had fixed was previously inaccurate and did have to be fixed. Let me know what you had in mind and I'll explain as best I can.
@tigerluver :
About 214: In fact I wanted to prove with the datas you given, that the t-rex's femur is more voluminous than the giganatosaurus's femur. So what ? A priori the t-rex's is the biggest animal of the two.
@Spalea, a scale factor of less than three means for length, G. carolinii has less volume than T. rex. Your analysis is repeating what the scale factor produced has already said. So if one wants to extrapolate a longer G. carolinii from a shorter T. rex, the scale factor takes into account the less volume per unit length and corrects for it. This was in support to your point that animals of different builds don’t scale isometrically.
(10-17-2020, 04:47 PM)DinoFan83 Wrote:Quote:I'm not sure if the one who makes the "corrections because they're inaccurate" are correct either, because we are dealing with fossils. Not living creatures. This. "Their model for Sue has the ribcage too wide; as they acknowledge themselves, "the torso of the mount is inflated in width due to a dorsal displacement of the transverse processes on the trunk vertebrae, which forced a dorsal displacement of the tubercular articulations and a lateral expansion of the rib cage as a whole." By my measurement it's about 1.8 meters as opposed to 1.6 meters in Scott Hartman's model, so it's about 13% too wide. -The dorsal ribs on the mount, instead of being angled backwards following Hartman, Larramendi, and Greg Paul's comment on the study, are strongly swept anteriorly, inflating the torso's volume. They're about 25% more anterior than the ribs in Hartman's, meaning the torso is 12.5% too voluminous with the rib articulation. -Following Scott Hartman's standards for soft tissue, the torso and the neck seem (to me at least) to have about 10% too much of it. The correction: Sue's torso mass is listed as 5,560 kilograms for the minimal model. Applying each correction will result in a decrease in its overall volume as will be discussed below. 10% more spinal curvature: Volume reduction of 10%, meaning the mass is decreased to 5004 kilograms. Deflating the ribcage 13%: Volume reduction of 13%, meaning the mass is reduced to 4428 kilograms. Sweeping back the ribs 25%: Volume reduction of 12.5%, meaning the mass is reduced to 3936 kilograms. 10% less soft tissue on the torso and neck: The neck model is listed as 504 kilograms, and with the torso at 3936 kilograms, this reduces their volumes to 458 and 3578 kilograms, respectively. Overall, correcting all of this, the minimal model is reduced by 2028 kilograms. Thus, with all these issues fixed, the minimal model for Sue of Hutchinson et al. ends up at 7472 kilograms, or 7.47 tonnes. Going by this, I would say that 7.47-8.4 tonnes is a good size range for Sue when considering both this and Hartman's model, with a mean of about 7.9 tonnes. Bear in mind that Scotty would have been about the same." Hutchinson did said the torso is inflated due to the distortion of the vertebrae. But I didn't remember the weight is downgraded (maybe except by Gregory S Paul and some others). Then, you came up with your own opinion with calculations that the Tyrannosaurus rexes are actually weigh less than 8 tonnes. How did you got charcharodontosaurids are much heavier than these tyrannosaurs? By your own calculations again? Can you give me your own depiction of how a Tyrannosaurus would compare with a Giganotosaurus and a Carcharodontosaurus, maybe a picture? I wanna see that. When I see weight estimations, I just don't pick several opinions of some people that aligned with my thoughts (that's what I see of most people). Because that would be bias. I will try to see both opinions from the people who make lower weight estimations and people who make higher weight estimations. And what I've found so far, the results are always gonna be different depending on the methods. Just like any experiments, with different methods you'll see different outcomes. But judging solely from the skeletons, I'll say both of them almost weigh the same although with some minor differences. That's my opinion. Quote:Hutchinson did said the torso is inflated due to the distortion of the vertebrae. But I didn't remember the weight is downgraded (maybe except by Gregory S Paul and some others). I'm not fully sure what you mean when you say this - do you want to know exactly how doing things like sweeping back the ribs and increasing spine curvature decreases torso volume, or do you want to know cases where the weight has been corrected downward by other researchers rigorously aside from Greg Paul's comment? If the latter, it's simply because no one has bothered to do so in the literature yet, instead choosing to do their own models of the skeletons. But if you meant something else, don't hesitate to let me know. Quote:Then, you came up with your own opinion with calculations that the Tyrannosaurus rexes are actually weigh less than 8 tonnes. How did you got charcharodontosaurids are much heavier than these tyrannosaurs? By your own calculations again? Both the tyrannosaurids and carcharodontosaurid models are weighed with the same overall method (volumetric) - be that water-dunk models, laser scan of a mounted skeleton corrected later on, or a computer model of a skeletal (graphic double integration). Any increase and decrease in the weights was simply due to changing things about some segments in the models (eg: fixing the density and the incomplete scapula in Greg Paul's Giganotosaurus, or changing things like the rib posture in Hutchinson's Tyrannosaurus). The weight increase for carcharodontosaurids is indeed based on my own calculations (as well as the work of some others like SpinoInWonderland), but everything here bases off the same method for mass estimation. This can be considered 100% apples to apples. Quote:Can you give me your own depiction of how a Tyrannosaurus would compare with a Giganotosaurus and a Carcharodontosaurus, maybe a picture? I wanna see that. I don't yet have the GIMP skills to correct Greg Paul's Giganotosaurus in regards to the scapula, which is my primary reference at this point. However, once I get the chance to do so I will. (10-18-2020, 07:48 AM)DinoFan83 Wrote:Quote:Hutchinson did said the torso is inflated due to the distortion of the vertebrae. But I didn't remember the weight is downgraded (maybe except by Gregory S Paul and some others). SpinoInWonderland... Hmm. I've seen him in those old forums in the past and he seems to be a fanboy of some sort. I don't think I'll take him seriously 100%. But till then, I think I'm still with my opinion that none of them are much obviously larger than the other (like how a brown bear is obviously much larger than a tiger or a lion) until people discovered more complete specimens. Quote:SpinoInWonderland... Hmm. I've seen him in those old forums in the past and he seems to be a fanboy of some sort. I don't think I'll take him seriously 100%. The key operative here being old forums. SpinoInWonderland is no longer any sort of a fanboy whatsoever; I know him personally and you may speak with him if you still doubt he isn't. Quote:But till then, I think I'm still with my opinion that none of them are much obviously larger than the other (like how a brown bear is obviously much larger than a tiger or a lion) until people discovered more specimens. That is why I always say that I only consider theropod A to be bigger than theropod B based on known specimens: because we'll never truly know who was bigger than whom until all giant theropods are as well sampled as Allosaurus or Tyrannosaurus for example. If we consider one poorly sampled theropod larger than another it needs to be based only on known specimens. (10-18-2020, 08:15 AM)DinoFan83 Wrote: The key operative here being old forums. SpinoInWonderland is no longer any sort of a fanboy whatsoever; I know him personally and you may speak with him if you still doubt he isn't. Hmm... Ok then. (10-18-2020, 08:15 AM)DinoFan83 Wrote: That is why I always say that I only consider theropod A to be bigger than theropod B based on known specimens: because we'll never truly know who was bigger than whom until all giant theropods are as well sampled as Allosaurus or Tyrannosaurus for example. If we consider one poorly sampled theropod larger than another it needs to be based only on known specimens. What are the largest complete skeletons of Giganotosaurus and Carcharodontosaurus so far? Quote:What are the largest complete skeletons of Giganotosaurus and Carcharodontosaurus so far? For Giganotosaurus, the largest complete skeleton is MUCPv-Ch1. No complete skeleton for Carcharodontosaurus has been found thus far; our only specimen still in existence (SGM-DIN 1) is a partial skull and nothing more.
This video shows a pack of tyrannosaurus chasing a triceratops. While the young t-rex were running after the prey without attacking it, they were driving it exactly where the adults were waiting it for.
It's a very plausible interpretation. But the adult t-rex are very passive, "exactly where"... Does that mean that the t-rex were able to communicate remotely during the hunt ? In this case they are rather evolved predators !
"A fossilized pair of Cretaceous dinos known as the "dueling dinosaurs" were preserved in incredible condition with evidence suggesting that the two may have been locked in a mortal struggle before their demise.
The impressive and dramatic fossil specimen still only partially uncovered from its surrounding sandstone includes a tyrannosaurus rex and a triceratops, and it will be going on display at the North Carolina Museum of Natural Sciences, The Charlotte Observer reported Tuesday. Injuries and tyrannosaur teeth found embedded in the triceratops' body suggest that the two were involved in a predator-prey scenario when they were preserved together, according to the museum. The two skeletons are among the best-preserved examples of each species, and the T. rex's skeleton is the only example of a 100 percent complete specimen ever unearthed." https://sea.mashable.com/science/13317/i...ic-display |
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