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Post by theropod on Aug 20, 2019 23:56:20 GMT 5
^Yes, but the Mapusaurus tibia’s proximal end is not complete, and it is likely from a considerably smaller individual than Sue.
Weird regarding Gorgosaurus, you’re right about that.
Holtz (2004) states "The tibia, although powerfully built, is never as robust and stocky as in carnosaurs and other basal tetanurans (fig. 5.19CD)."
Holtz, T.JR. 2004. Tyrannosauroidea. In: Weishampel, D.B., Dodson, Peter and Osmólska, Halszka (eds.), The Dinosauria, 2nd Ed., 111–136. University of California Press, Berkely, Los Angeles, London.
But as I said, I was arguing that the calves should be equally robust, not necessarily more. Just in response to the inclusion in Verdugo’s quote from Hartman, because I don’t think that’s actually something on account of which Hartman was too conservative with his T. rex restoration (not that it would have a major impact on the overall mass though).
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Post by Verdugo on Aug 21, 2019 5:32:36 GMT 5
theropod I haven't looked at tibia morphology or calf muscle architecture in details so i really just took Hartman's statement at face value. I suppose you're probably correct in this regard. Though i think it's really odd for someone like Hartman to make such mistake, wouldn't he already be too familiar with Theropod bone morphology and muscle architecture?
Infinity Blade I did not necessarily mean that estimates from Larramendi are unreasonable or unrealistic. I only mean that it may represent the lower-end (more conservative) estimate. For example, the estimate of Stan from Larramendi is consistent with the min model from Hutchinson (2011) who used a rather low density for their minimum models, lower than from most workers i have seen: "Resulting whole-body density values for all five minimal models overlap those of previous studies [28], [30]: ∼840–890 kg m−3; vs. less plausible values of ∼970 kg m−3 for the maximal models" Larramendi also stated that he used Paul's restoration (which means that it's probably not his model/work, he merely did the GDI) and Paul's models are regarded by some as slightly shrink-wrapped. I just don't understand why you consider the lower-end, more conservative estimates realistic and reasonable while the upper-end, more liberal estimates such as that from Franoys (even though the result from Franoys is congruent with Bates 2009) too unrealistic and unreasonable. My argument is that i don't think we should label either upper or lower-end estimates as too unrealistic, especially since both estimates from Franoys and Larramendi are congruent with published volumetric estimates from Hutchinson 2011 and Bates 2009; and both estimates are obtained from using reasonable methods. Anyway, in the end of the day, which weight estimates would you use for Stan if you are to remake your scale? What do you think of the equation in my previous post? How did you get the whole body density value though? I suppose you did not just average the sum of density values from each segments? (which is not mathematically correct). Anyway we can calculate the whole body density based on the whole body volume and body mass:  Density = 8400/9200 = 0.913 kg/dm^3 I merely address this, not that it really matters much to the discussion though
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Post by theropod on Aug 21, 2019 6:10:21 GMT 5
Verdugo: Hmm yes, but on the other hand, wouldn't Holtz as well? I'll readily concede that the difference is fairly insignificant, I'm just saying it looks more like carnosaurs have more robust calves than the reverse. Which is a tad unusual, since of course rexy has both the more robust thighs and is more massive overall for a similar tibial length. Those things might have led Hartman to assume the tyrannosaur should have the thicker calves (it is the bigger specimen, after all), but they have pretty similar tibial lengths (112 vs 114 cm), and it doesn't look like the carnosaurs tibia should be thinner or less muscled at similar length. Also, hope you two don't mind me weighing in on that, but I don't think infinity actually called Franoys' figure unrealistic or unreasonable or suggested that another figure is preferable, he even used Franoys' figure over the others after all. If I'm understanding him correctly, he's merely making the point that it is the highest in a number of volumetric estimates. Saying that it "might" be too high is not necessarily implying you think it is, it can just be rigor in pointing out that lower estimates exist. So both of you are probably already on the same page about that. Good point on overall density of the model, I was going to point that out myself but you got there first. The density is really up for debate though, I still tend to think that for a giant theropod, values above .9 are a bit high. The net density for the torso segment in Allosaurus (Bates et al. 2009) was quite a bit lower (around .8) than the one Hartman assumed (.9). And there is clear osteological evidence suggesting T. rex should have relatively more extensive pneumaticity, not less. So those lower densities are probably indeed more realistic. But the difficulty is in getting the absolute value correct, because the absolute size of the respiratory structures and the absolute density they imply are hard to quantify. Its easier to say whether one taxon appears to be similarly or more extensively pneumatized than another one. Of course we know jaguars aren't pneumatized at all except for their lungs and some cranial sinuses, that much is obvious, so here we have to make some sort of best guess as to how much lower a theropod's density would be.
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Post by Infinity Blade on Aug 21, 2019 6:50:45 GMT 5
Verdugo What theropod basically said above. I didn't mean to suggest that Franoys' estimate is unreasonable, and if I ever sounded like I was saying that, I apologize for that. Franoys does pretty good work, which is why I do think his estimate is reasonable. I just think it's probably the highest volumetric estimate that I think is still reasonable for Stan. Well, I picked Franoys' estimate simply to give us a fairly conservative idea of how large Stan's head would be compared to a same-sized jaguar (i.e. if Stan was heavier overall with a given skull size, its skull would be relatively smaller; but if it were lighter overall with that same given skull size, its skull would be relatively bigger). At first glance I think this would suggest the only logical step would be to assume a smaller body mass for Stan, but if one can argue that say, Hutchinson's average mass estimate for the specimen (i.e. 8385 kg) doesn't strain plausibility I could create a comparison that incorporates that mass estimate too ( theropod what do you think of the estimate?). I have a question about the equation. I can easily punch in log 10(*insert hypothetical T. rex body mass here*), but what does the =2.762±0.426 part mean? Also, I'm assuming that the body mass you plug into the body mass equation assumes it's in kilograms, but what unit does the skull length equation assume? Centimeters or millimeters? I hate to admit this but...that is kind of what I did ((0.8+0.9+1.0)/3). Somehow I overlooked Hartman's actual total volume estimate and didn't realize I could have just done what you did (i.e. 8400/9200). Forgive me, this was a really idiotic blunder of mine.
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Post by theropod on Aug 21, 2019 16:06:31 GMT 5
Infinity Blade: The ± probably means either the standard error or a 95% confidence band. You can add or substract those from the coefficients to get a range (prediction interval), or just ignore them and calculate a point estimate. Regarding Hutchinson et al.’s average mass estimates, I think they are too high. You can see it in their anterior views, the lower estimate looks a bit anorexic, but for the higher ones they simply added enormous amounts of flesh all around it (added to other problems, especially ribcage articulation). The lower estimate in Stan’s case may be too low though. Bates et al.’s model looks better (a range between the 7.6t 'best estimate' and -7.5% model at 6.9t seems reasonable), even if the model’s belly is still a bit on the fleshy side compared to skeletal-based reconstructions.
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Post by Infinity Blade on Aug 21, 2019 16:10:50 GMT 5
Yeah, but there's an =2.762 part that I'm not entirely understanding. Do I add or subtract that constant too?
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Post by theropod on Aug 22, 2019 15:30:32 GMT 5
Yeah, but there's an =2.762 part that I'm not entirely understanding. Do I add or subtract that constant too? This is the equation without the ± error margins (I assume you want the mean estimate anyway). Log 10(BM[kg]) = 2.762 * Log10(SL[mm])-4.638 This equates to Log 10(BM[kg]) = Log 10(SL[mm]^2.762 * 10 ^ -4.638) ⇒ BM[kg] = 10^-4.638 * SL[mm]^2.762 So skull length is (BM[kg]/10^-4.638)^(1/2.762) = SL[mm] However, as always with an allometric equation, extrapolation is a lot more problematic than interpolation. Since the skull is positively allometric according to this model, this will result in a proportionately larger skull when scaled beyond the data range (and perhaps excessively so). For a body mass of 7700kg, this equation would give us a skull length of 1220mm. But for a 100kg body mass, we get a skull length of 253mm. But if you scale up the latter isometrically, to result in a mega-jaguar with the same proportions as a real jaguar, you get a skull length of just 1077mm at 7700kg, so the allometric skull is 13% longer than the isometric one would be. |
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Post by Infinity Blade on Aug 22, 2019 16:21:26 GMT 5
Yeah, but there's an =2.762 part that I'm not entirely understanding. Do I add or subtract that constant too? This is the equation without the ± error margins (I assume you want the mean estimate anyway). Log 10(BM[kg]) = 2.762 * Log10(SL[mm])-4.638 This equates to Log 10(BM[kg]) = Log 10(SL[mm]^2.762 * 10 ^ -4.638) ⇒ BM[kg] = 10^-4.638 * SL[mm]^2.762 So skull length is (BM[kg]/10^-4.638)^(1/2.762) = SL[mm] However, as always with an allometric equation, extrapolation is a lot more problematic than interpolation. Since the skull is positively allometric according to this model, this will result in a proportionately larger skull when scaled beyond the data range (and perhaps excessively so). For a body mass of 7700kg, this equation would give us a skull length of 1220mm. But for a 100kg body mass, we get a skull length of 253mm. But if you scale up the latter isometrically, to result in a mega-jaguar with the same proportions as a real jaguar, you get a skull length of just 1077mm at 7700kg, so the allometric skull is 13% longer than the isometric one would be. Ah thanks! I was trying to find out what would happen if you scaled the jaguar up isometrically. I'm not surprised to learn that cat skulls apparently grow with positive allometry (I think big predatory dinosaur skulls do too(?), but I'm not sure), but then, of course, just about everything else about a multi-ton jaguar would have to change if you scaled it up in accordance to the square cube law. |
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Post by Verdugo on Aug 22, 2019 18:35:46 GMT 5
Infinity Blade Well my impression is because of this comment: I thought you intended to imply that anything above 7.2 tonnes are considered unrealistic and thus should be rejected. But if you did not intend to imply so then it's all good for me, just a little misunderstanding. I am glad we're on the same page, like i said,i was not proposing higher estimates either. I merely think we should treat them as equally valid. Since Theropod already did everything, i just want to remind you that the Skull length here is measured by premaxilla - occipital condyle (so the Greatest skull length should a bit longer), just a little thing to keep in mind if you have not already aware about it of course. Like Theropod said, this is extrapolation way beyond the data size range so yeah, it's fun to think about it but certainly not the most realistic. I don't know if a T-rex sized Jaguar could even carry a head of that size with its current skeletal morphology. For what it's worth, Hutchinson 2011 did state that their minimal models are the most plausible: "Importantly, our minimal models are much more plausible reconstructions than our maximal models, especially for the Carnegie and Sue specimens, considering the realistic density (see above; similar to extant archosaurs'; [31]), less ridiculously rotund appearance (Figs. 2, 3, 4) and smaller masses (closer to previous studies' estimates) of the minimal models (Table 6). We certainly do not contend that our maximal models are results that should be assumed to be equally as valid as our minimal models. Rather, they form extreme upper end values on a spectrum of “fleshiness.” The actual mass of individual Tyrannosaurus specimens should have fallen well below these extremes and much closer to our minimal models', but how much below may never be known."
theropod Holtz merely commented on the bone morphology (robusticity) while Hartman directly talked about the muscle architecture (calf muscle). I know it might sound rather counterintuitive but i'm not sure if high robusticity always means larger muscle, especially since the Rex in this case is almost 2000 kg than the Carnosaur at similar tibia length. Anyway, since you mention this: It reminds me about some paper on how body mass may actually be more related to muscle mass than just bone morphology. Binder 2006 measured the in vivo bite force of Hyena and they remarked this: "Interestingly, bite strength continued to increase
beyond the age at which skull growth seemed to have
stopped and the adult dentition was fully in place (i.e.
20 months of age) (Fig. 3a). It even continued well
beyond the point at which adult body sizes are reached
in the wild, between 24 and 36 months of age (Mills,
1990). This suggests that the jaw adductor musculature
continued to increase beyond the cessation of skeletal
growth. Our inability to detect this beyond 20 months
suggests that our external measurements were insuf®-
cient."Older (presumably larger) Hyenas tend to bite harder (having larger jaw muscle) despite not having any larger skull. Also, in Erickson 2012 for Crocodilians: " We found negligible support for the commonly held view that bite forces correlate strongly with rostral form – a proxy for strength. Rather, bite forces vary independently of rostral morphology, so much so that in some cases same-sized taxa from the extreme bounds of crocodilian rostal morphology and dietary ecology (e.g. the slender-snouted, Crocodylus johnsoni and robust-snouted, Caiman latirostris; Figure 1) show “pound for pound” comparable molariform bite forces (Figure 3A)."Body mass is also a stronger predictor for bite force than skull morphology, suggesting than body mass may be more related to muscle mass than just bone morphology. Obviously, jaw muscles and calf muscles are not the same thing. However, it's reasonable to think that calf muscles would be even more related to body mass than jaw muscles (since heavier animals need stronger legs just to walk around). I'm not saying that Hartman is 100% correct but if he was assuming that Sue had larger calf muscle than a smaller Carnosaur of similar tibia dimensions, then his assumption is not unreasonable and baseless. Not that having larger calf would affect the body mass much, i don't know why i keep discussing with you about calf muscle. On the other, the density on the head that i have seen in publications is usually higher than the 0.8 that Hartman assumed: Bates 2009: T-rex head density up to 0.99 Witmer 2008 (Table 2): T rex head density can be calculated at ~0.966 (515528/533698.5) I have no idea why this is the case though. I merely point this out.
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Post by theropod on Aug 22, 2019 20:18:29 GMT 5
Yes I was wondering about that myself. Indeed, the skull has a lot of very dense bone tissue in it, I don’t really understand why Hartman assigned it the lowest density in the entire body when it should probably be among the densest parts. Well, of course he correctly assumes there are lots of sinuses in the skull, but that doesn’t really explain why he makes the skull lighter, there are air sacs in the torso and neck as well. However increasing the density of the head appropriately likely won’t outweigh lowering the density of the torso, considering the latter is far more voluminous.
You are mixing up ontogeny with taxonomy. That the skeleton can reach final size before the muscles do during ontogeny does not imply that muscle size has nothing to do with the size of the underlying bones–on the contrary, the final skeletal size is the limiting factor on the size of the musculature. If you look at the hyaenas, larger skull size clearly does correlate with greater bite force, it’s just that there is developmental asynchrony regarding the growth of the skeleton and musculature. But if you were to look at a sample of fully developed hyaenas, you’d certainly find that larger skulls also correlate with larger bite forces.
That externally measurable skeletal measurements cease growth also does not mean the bones or muscle insertions don’t continue to grow more robust later on (especially in dinosaurs). I’m not talking about tibial length (obviously, that of Giganotosaurus is marginally shorter than that of sue) talking about robusticity and the size for muscle attachments. The only way we have to infer the volume of muscles in fossil specimens is to look at these factors, it’s as simple as that. So if two animals have equally robust, similar-sized tibiae implying similar muscle volumes, we should assume they had similarly muscular calves, not that one had relatively larger muscles than its bones imply, or the other relatively smaller ones.
As Hartman wrote, this is needed to keep estimates comparable.
It would also be a bit circular to reason that since animal A is bigger than animal B, every body part of it must have been bigger, irrespective of what the bones suggest. We wouldn’t know it was bigger in the first place if we thought along these lines, after all, the animal seeming smaller could just have had more flesh relative to what its bones suggest.
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Post by dinosauria101 on Aug 24, 2019 16:53:58 GMT 5
Kronosaurus vs Brygmophyseter by creature386  |
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Post by creature386 on Aug 24, 2019 16:59:11 GMT 5
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Post by dinosauria101 on Aug 24, 2019 17:00:49 GMT 5
Good catch on the 2nd. I found the 1st while hunting for size charts, but not the 2nd
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Post by jdangerousdinosaur on Aug 24, 2019 18:10:14 GMT 5
Carcharodontosauride comparison chart by koprX (he has updated most of the outdated size comparisons on wiki he does good work) www.deviantart.com/koprx |
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Post by dinosauria101 on Aug 24, 2019 19:25:54 GMT 5
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