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Freak Felids - A Discussion of History's Largest Felines

Indonesia WaveRiders Offline
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tigerluver
 
 
You wrote
 
 
“You on the other hand like to slide accusations of bias and a lack of brain to those who disagree with you”
 
 
I am sorry if this was really meant that way towards you. So far you did nothing wrong against me, you behaved correctly and I can say I definitely appreciate a lot what you are doing, your great interest in these topics and your commitments. You are still a student and it would be totally unfair to criticize a student badly because students are still in a fast learning process and I have no titles to do that in a contest of a forum. I have also an advantage because you disclose nearly every detail of what you do while I do not for a number of reasons.
 
Although there could have likely been an initial impulse coming from a slightly different motivation, my major aim in raising possibly serious doubts about your weight estimate of the 480 mm femur tiger individual from the Pleistocene of Ngandong was and is in hopefully trying to be helpful to your studies following my knowledge and understanding. If this is retained arrogance by somebody nicknamed WaveRiders, and it could be in principle, please consider that Per Christiansen wrote in an e-mail to GuateGojira (or somebody else) dated a few years ago “no tiger was ever 470 kg that is absolutely certain”.



You wrote

“please bring some numbers on your bones in that contradicts databases like that of Christiansen”
 
 
Apart form a few data inconsistencies I do not definitely contest or have contested Christiansen database like it seems to me you you did stating that some tigers are underweight and a lion is overweight and I do not really see where I contradicted Christiansen. At most in some considerations which I have not touched here so far and in the methodologies I developed I could say that I believe to have gone farer then him. If this is actually the case this would not be unusual in research. If I could do it 10 years ago it has also been thanks to the work Christiansen performed between 10 and over 15 years ago. Christiansen did not develop further his methodologies after that as he concentrated on other topics, but he could have easily done if he wanted.
 
You are actually right as I have a really voluminous database in many areas, but not in all of them to the extent I would like of course. There are still margins of uncertainties, sometimes small, sometimes that could be substantial and need experience, careful and expertise to manage them properly hopefully. After all in most sciences nothing is really certain and nothing can be really proved as certain. Making research is a process that needs to be learnt with time. There is the need to open the mind, focus on details that can reveal a lot and bring illuminations and be as less biased as possible. Sometimes one can have things under his nose and does not realize he has.
 
If I raise doubts and force you to check your procedure and find in case some inaccuracies I got my target. The estimate of the 480 mm femur individual at 500 kg is really my major issue and unfortunately it casts possibilities we are both biased in opposite directions. I can understand that, but from my side I can say that I retain myself rather neutral or should I be retained biased because I firmly believe that no tiger was ever close to that weight as also Per Christiansen firmly believes?
 
 
Now let’s move on hopefully constructively for our mutual benefit
 
 
1)   post # 27 and post #108
 
You wrote
 
“You have a habit of taking estimates that fit your definition for the tiger's size as reality, and ignore actual weights at those greatest lengths and you know which ones I'm referring to.”
 
 
I definitely reject the weight of the Hasinger tiger even accounting for a full belly and would never include it in any database to build allometric regressions like you did. I also doubt the length measurements of that tiger as the skull is ridiculously small (14 x 9 inches) for its alleged total length (11 ft 1 in along curves and 10 ft 7 in between pegs).
 
The fact that I refuse to trust all 11 footer tigers along the curves but a few exceptions and all 12 footers along curves do not make me feel at all uncomfortable.
 
Overall I do not feel trapped in underestimating tiger size and weights. Furthermore including extreme unreliable data can screw up a database and any statistical analyses based on that to an extent depending how much this database is small and spread.
 
A database should be randomly taken and made by as many as possible accurate and reliable data hopefully with no outliers. If the datapoints for any reason are undervalued in the low range and overvalued in the high range or viceversa the slope of the regression, most affected from datapoints at the its extremes to an variable extent depending from sample size and data spread, may result to be significant overestimated or underestimated.
 
I am not convinced the tiger database you used in post # 27 is the best possible as there are many ore weights vs total lengths available from literature that would allow you to obtain a more realistic regression slope. Just to mention one among the very many more data available for instance you did not use the tiger shot by Gordon (3226 mm and 222.7 kg) and you instead used the tiger shot by Hasinger (3226 mm and 388.7 kg) which is clearly a not realistic weight (a bias?).
 
In my opinion a somewhat biased database is the reason why you obtained a significantly higher then expectable allometric coefficient of Body Mass vs Total Length of 3,9878. You estimated the 480 mm femur individual to be 347 cm in total length and the body mass based on total length therefore to be 446 kg.
 
 
2)   You wrote
 
“All long bones mentioned are nothing but above average. Untrue, take the 465 mm ulna for example, a 203 kg lion's ulna is 79mm shorter than the P. fossilis specimen, that is a huge difference in terms of mass. The same goes for the other large long bones of Pleistocene cats. On body length, my values are close to yours. You disregard isometric and allometric relations, that probably explains why none of the long dimensions produce a very large specimen in your mind.”
 
 
The fundamental aspects to consider for a correct application of allometric scaling in zoology are theoretical, mathematical, biomechanical and database related.
 
                                                                                           
Below I will discuss a few among the considerations you did that in my opinion need to be addressed differently.
 
 
2A)
 
Humerus, femur and tibia lengths in Christiansen & Harris (2005) are articular (functional) lengths and not greatest lengths. Greatest length is only the one used for ulna. In the case of tiger femur the articular length in a few cases may be about the greatest length, but normally is marginally smaller. Humerus and ulna articular lengths are generally smaller then greatest lengths.
 
All weight estimates using equations and database from Christiansen & Harris (2005) that I have seen done by you and GuateGojira so far are therefore conceptually not correct as you always used greatest length (the error is generally however marginal). Christiansen (1999) regressions instead used greatest lengths of limb bones.
 
 
2B)
 
Humerus and femur distal widths in Christiansen & Harris (2005) are articular widths (mediolateral width across condyles) and not epicondylar (greatest mediolateral) widths.
 
All weight estimates using equations and database from Christiansen & Harris (2005) that you have done so far using epicondylar (greatest mediolateral) of fossil specimens are therefore conceptually not correct.
 
 
2C)   Your post #1
 
“Mazak et al. (2011) used a species averaged database to prevent confusion between intra- and inter-specific allometry. Though, in reducing the sample size, the distribution of data became uneven, causing the size-related bias mention above.
 
I constructed a logarithmically scaled graph using the same database of specimens from Mazak et al. (2011), but had each individual specimen to represent a data point rather than a specie average representing a data point. This produced a plot with an even distribution of data points. The resulting equation:
log(body mass in kg) = 2.6725*log(condylobasal length in mm) - 4.4587
 
An implication of this equation is that skull size grows more rapidly than body mass. Furthermore, the data sample used can be more safely applied to P. spelaea as P. spelaea is a distinct species, rather than a subspecie of anomalous species in terms of relative proportions and body mass (e.g. P. t. soloensis to P. tigris), and thus one can assume P. spelaea follows the growth trend of Panthera in general. I realize the wording in this paragraph may be a bit confusing, so just ask if any further clarification is needed on the point I am making.
 
Finally, the equation discussed yields a theoretical body mass for the 484.7 mm skull of approximately 387 kg.
 
The Femur
 
The femur estimate you got is similar to the one I have found with regression. I assumed that P. spelaea had a build midway between tigers and lions and thus based the regression off a database of only tigers and lions. The database for the formula is based off of 6 specimens, the equation:
log(mass) = 3.6775*log(femur length) - 7.2568
The 470 mm femur would have a mass of 371 kg accordingly.
 
The Ulna
Finally, I will go over the ulna in this short post.
 
 
As I stated before, an ulna of 465 mm is certainly from a record breaking specimen. To predict the body mass without encounter false negative allometry, I again used a database of tigers and lions, with six specimens in total. The equation:
log(mass) = 2.8965*log(ulna length) - 5.1318”



 
It seems that you are convinced that building an allometric relationship mixing individuals of different species can prevent a size-related bias when a species average allometry create it. Well, as Christiansen and Mazak suggest, I also advice not to mix intraspecific and interspecific allometry using single individuals even if taking care to the same number of individuals for each species like you did for the femur and the ulna. The fundamental reason is that it is conceptually wrong, can lead to substantial errors and may not be necessary for what you want to achieve.
 
 
Condylobasal Length of Skull
 
Using Panthera leo, tigris, onca, pardus, uncia species average (neglecting Neofelis nebulosa) you got a body mass vs condylobasal regression nearly identical to the one you used. The two equations becomes basically the same enlarging the Christiansen database. For the 484.7 mm skull from Chateau you calculated 387 kg (myself with your equation 372 kg likely due to a smaller estimated CbL). while the species average gives (using CN5698 BM = 220 kg) 365 kg (allometric scaling exponent 2.63792) to 385 kg (allometric scaling exponent 2.75170) depending from the database.
 
The Mauer 442 mm skull individual was pretty much an average size Cromerian male lion I estimate at around 310 kg. There is no much question on its about average size considering the size margin given by the 465 mm and the 484.7 mm skulls from Chateau. That individual has generally been retained an Upper Middle Pleistocene lion of large size even because since 1912 and for over 60 years it has been the only Cromerian lion skull relatively complete unearthed (to date I am aware there are only 5 of them of which 3 actually substantially intact and complete).
 
My body mass estimate for the 484.7 mm skull from Chateau is around 355 kg.
 
 
Femur
 
For the femur you obtained a very positive allometric coefficient of body mass vs length of 3.6775 using 3 P. leo individual and 3 P. tigris altaica individuals. Inevitably you made a choice and you introduced a bias related to the individuals you chose. Assuming P. (leo) spelaea spelaea had a built between the tiger and the lion you therefore obtained a body mass of 371 kg assuming 470 mm is the articular length (which conceptually is not although very close) or nearly a couple of % less estimating the articular length.
 
Considering instead species average allometry using P. leo, P. tigris tigris and P. tigris altaica the allometric coefficient results to be 3.01601 for CN5698 body mass = 230 kg or 3.08298 for CN5698 BM = 220 kg. The body mass estimate for the P. (leo) spelaea spelaea 470 mm femur results to be 318 kg or 311 kg respectively based on femur length only and considering the articular length estimated from the greatest length.
 
The Panthera (leo) spelaea spelaea 470 mm femur individual from Mladec Cave was a male individual that within the spelaea form as a whole spanning over 300 KY is rated by me to be no more then of large size. Following biostratigraphy analysis and looking at him under the perspective to actually likely be a Late Pleistocene Eurasian Panthera (leo) spelaea spelaea it could then be classified as a very large male. With my methodology my body mass estimate for the 470 mm femur individual is 295+ kg.
 
Within the spelaea form there are quite a number of individuals larger and even significantly larger then the 470 mm femur individual. I estimate its greatest skull length around 445 mm, therefore likely nearly the size of the San River Skull (451 mm), but significantly smaller then the massive ca. 475 mm Ural skull (CbL = 422.0 mm, BM = ca 320 kg, HBLstraight approaching 2350 mm). The largest spelaea individuals I am aware would have had a greatest skull length likely in the range 490-500 mm with a couple of them seemingly even up to around 510 mm and head-and-body length straight around 2450 mm (it must be considered that the number of specimens of Panthera (leo) spelaea spelaea unearthed is much higher then any other fossil lion form, particularly of fossilis and vereshchagini).
 
No Panthera (leo) atrox fossil individual unearthed so far that I am aware reaches this size, being the largest and heaviest the 467.5 mm skull 14001 (CbL = 424.3 mm), approaching 2350 mm in straight head-and-body length and ca. 320 kg in body mass.
 
 
Ulna
 
For the ulna you obtained a nearly isometric coefficient of body mass vs length of 2.8965 using again a bias choice of 3 P. leo individual and 3 P. tigris altaica individuals and you obtained a body mass of 393 kg assuming again that P. (leo) spelaea fossilis had a built between the tiger and the lion. In your last computation (post #94) and assuming isometry with modern P. leo from database of Christiansen & Harris (2005) and applying the robustness index you calculated comparing the fossil ulna with a single modern ulna you obtained 347 * 1.0837^2.5 = 423 kg.
 
Considering instead P. leo, P. tigris tigris and P. tigris altaica species average the allometric coefficient of ulna length results to be 2.50902 for CN5698 body mass = 220 kg and a body mass estimate of 340 kg.
 
My methodology estimates the 465 mm ulna P. (leo) spelaea fossilis individual body mass to be around 325 kg.
 
You retain the 465 mm ulna individual a huge one, while among Cromerian male lions I retain it an individual above average size but not properly considerable of large size, definitely not very large or huge. I estimate the greatest skull length of this individual to have likely been 455+ mm and possibly approached 460 mm, but unlikely more then that. Therefore in my opinion it was likely slightly smaller in size then the 465 mm skull from Chateau, significantly smaller then the other skull from Chateau measuring 484.7 mm and much smaller then the 192 mm MT3 individual. However without a doubt the bone is quite more robust then an ulna of a modern lion.

 
2D)   192 mm Metatarsal 3
 
In post #89 you wrote
 
“On the MT3 reported by WaveRiders of 192 mm of P. fossilis, in accord with the ratios published by Day and Jane (2006), that specimen would be of 115 cm at the hip and 97 cm at the shoulder, assuming lion built, and a bit shorter assuming the other species' builts. Day and Jane (2006) use a pictoral method for their data, so there might be room for error as those numbers look too small to me. Furthermore, higher MT/Femur ratios is directly correlated to increased cursoriality, another piece suggesting how cursorial P. fossilis was.”
 

It seems you forgot to include the scapula contribution for the shoulder height and the distance from the acetabulum to the top of the ilium in its anatomical position for the hip height. Considering the anatomical position of the forelimb and the scapula, the skin and pad thicknesses and the proper contribution of the forefoot an Eurasian Pleistocene lion individual with a 192 mm MT3 should have had a standing shoulder height between 1350+ and 1400 mm, a head-and-body length in straight line most likely pretty much around 2500 mm and a greatest skull length most likely around 525 mm -10 mm / +5 mm. In spite of his huge size I estimate such a monstrous Cromerian male lion to have weighed in the region of 400 kg (at empty stomach of course).
 
 
2E)   Assumed Outlier
 
To build the BM vs Femur Length intraspecific regression for tigers you took out the presumed oddity tiger datapoint CN5697 (femur length 429.5 mm, body mass 230 or 220 kg). You assumed it is an outlier following the fact that the remaining 4 datapoints are well correlated while CN5697 substantially deviates. In my opinion in this case removing this presumed outlier datapoint contributed to lead you to unrealistic results as the regression departs from slight positive body mass allometry to femur length (exponent 3.14751 using 230 kg or  3.08233 using 220 kg) to an hardly justifiable significant positive allometry of 3.68654. It is a quite hazardous to remove a data in a sample of only 5 datapoints with the result to get farer and quite far from isometry and assume that having a sample of well fit 4 individuals the intraspecific allometry is more realistic. If you would have got closer to isometry instead of quite farer, removing an outlier could have cautiously been acceptable. The point is that CN5697 femur is not retainable a genuine outlier.
 
Furthermore that body mass of the other individual CN5698 is given by Christiansen in two papers at 220 kg and in other 2 papers at 230 kg (evisceration does account for nothing in this case as the difference would be much higher and the year of issue of the papers seems not correlated to one figure or the other). Therefore there is no evidence that 230 kg must be the correct figure and not 220 kg. Although the difference is marginal using 220 kg for CN5698 would make the suspected oddity CN5697 less odd.
 
Anyway, why you convinced yourself that the scaling exponent 3.68654 should be more correct then 3.14751? I found out and below is I reconstruct the procedure you have gone through.
 
I have seen that in AVA thread “Body size of the Ngandong tiger (Panthera tigris soloensis“ you were using power law instead of the logarithmic transformations that you are using recently.
 
In your post #346 sent on Fri, Jul 19, 2013 1:28 AM of thread “Body size of the Ngandong tiger (Panthera tigris soloensis)” in http://animalsversesanimals.yuku.com/top...PNmFS5mr5w pag 18
 
You wrote the comment
 
 
“Significant error, significant underestimation for both lion and tiger data”
 
 
after applying the formula you got from body mass vs femur length regression for tigers on the tiger dataset used to get the regression as well as to the lion individuals. The formula is shown in the graph you posted and it is Y= 1E-06 x^3,1475. I checked your tiger individual BM estimates and it resulted you actually used exactly that formula.
 
Being unsatisfied of the results you then removed tiger datapoint CN5697 and you found that with the new formula Y= 5E-08 x^3,6865 you got better results when applied on the database used to get the regression (which is a procedure to be done to get statistical parameters of accuracy of the prediction such as PE% and SEE%).
 
For this latest regression, you wrote
 
 
“Overall, not too bad for lions and tigers. The equation supports well the little data we have when applied only to lions and tigers. Now, is it a safe bet to extend it over to the larger prehistoric felids? This is open to discussion.
Interestingly, neither equation applied properly to jaguars. The tiger equations gave severe underestimates.
So, questions, comments, corrections?”

 
 
Now it comes the correction from me with the aim to be useful for you in the future as nobody told you that (apparently even your professor).
 
 
A much more correct formula using 5 datapoints (and 230 kg) then the one you wrote Y= 1E-06 x^3,1475
 
is
 
Y= 0.0000012738 x^3.1475073474
 
 
How I got it? Simply using 10 decimals in the Excel graph instead of the 6 only that you used.
 
It is immediate to understand that depending from chosen units and figures involved it is sometimes necessary to use a very high number of decimals above all when non log-transforming. Using only 6 instead of the 10 I showed you (much more correct) in this case you underestimated body masses by 27.38% (coefficient of 0.000001 instead of 0.0000012738) !!!
 
 
Using BM = 220 kg the formula for tiger femur length would be BM = 0.0000018622 FL^3.0823275490
 
 
With 6 decimals you would have had an overestimation by about 13.78% as your constant would have appeared in the Excel graph as 0.000002.
 
In recent posts I noticed you started to use logarithmic transformations. Data transformation are performed for inference statistics. Logarithmic transformation “linearizes” datapoints and improve homoscedasticity to apply statistics linear analysis methods. You also got rid from those small numbers and avoided the aforementioned kind of problem, but you did not check your previous results and stick to not consider the presumed oddity tiger datapoint CN5697 keeping the scaling exponent of 3.68654 which is far too high (either 3.08233 or 3.14751 appear to me a more accurate solution within the tiger database from Christansen & Harris, 2005).
 
 
2F)   480 mm Pleistocene Tiger Femur from Ngandong

Your posts # 72 and #96
 

“I've more indicators on the sheer robustness of P.t. soloensis after some more research. For one, a value I did not discuss that was published by vK himself was the AP diameter of the head. It was 59 mm. That is extremely massive. Let's put it into perspective. P. leo and its clad (P. atrox, P. speleaea, P. fossilis) is at least 10%-20% relatively more robust than P. tigris in the proximal end of the femur (Dawkins et al. 1866). An exceptionally robust P. atrox specimen had an AP diameter of head of 54.3 mm and length of 455 mm, an index of 0.119. The Ngandong tiger specimen had an index of 0.123. Considering how much more slender tiger bones are, the Ngandong tiger proximal AP diameter is absurdly thick. This published AP diameter of the head also supports my personal extropolated DAW and greatst proximal breadth, as a 59 mm diameter can only be of a bone with such dimensions (beyond the fact that vK actually differentaited between DAW and distal diameter in his book). But in terms of mass estimation, I don't have enough specimens to produce a good trendline, so no number will be produced by the AP diameter of the femoral head. Another measurement published by vK was the diameter of the distal notch of 23 mm. The DAW scales about 4.5-4.8 times the notch diameter, within the range of my DAW measurement of 107 mm.
 
On a good note, I was able to find a third comparitive diameter of the Ngandong tiger femur, the lateromedial diameter of the midshaft. Christiansen and Harris (2005) list this diameter at the point of least circumference. The word "least" is a bit misleading. Egi (2001) clarifies the point of measurement, which is the 1/2 point of the length of the bone (AKA the midshaft) in femur and tibia and the 55% length point in the humerus as follows:
 
Thus, I extropolated the third Ngandong femur measurement compatible with published databases, LM diameter of the shaft. The measure was 42 mm, much more robust than modern tigers and a bit shy of the most robust P. atrox femur.
 
Thus, from the measurements of the femur length (480 mm, est. 409 kg), DAW (107 mm, est. 531 kg), and LM diameter of shaft (42 mm, 559 kg), the calculated mass of this specimen is 500 kg.”

 
 
The picture of the 480 mm femur is much likely distorted because the minimum diameter of the femur results to be close to the proximal epiphysis while it should be around mid-shaft and the distal epiphysis appears much larger then the proximal epiphysis. It seems to me that the plane of the bone is not perpendicular to the sight direction. There might also be a minor rotation along its major axis.
 
The supposed proximal and distal widths based on reconstruction from the picture assuming the 480 mm length is correct should not be considered as in my opinion is a significant speculation. The distal mediolateral width you estimated at 107 mm is far above any regression of modern tiger and Pleistocene tiger femora giving a robustness with no corroboration from any other bone either femur or anything else.
 
I therefore retain your estimate of distal width 107 mm and minimum mediolateral diaphisis width of 42 mm the result of a speculation on a picture assuming that the length 480 mm is correct. As I pointed out above in my opinion the proximal epiphysis is farer from the observer then the distal epiphysis. While for sure there is something wrong in either the angles of the pictures or in the length or widths, first of all it could be the length. Considering either modern tigers femora and other Pleistocene tiger femora solidity regressions, the distal width provided by Koenigsvald (1933) at 88 mm matches pretty much a femur length of ca. 430-440 mm and with reasonable probability up to 460 mm. Similar trend is considering the proximal epiphysis mediolateral diameter given at 94 mm (estimated femur length 415-450 mm and with reasonable probability up to 460 mm). Considering the other dimensions (proximal sagittal diameter of 59 mm and distal sagittal diameter of 82 mm) that femur appears of build lighter then average, particularly as a male, although within the typical solidity range of modern tigers (therefore not an outlier).
 
My conclusion is that while I definitely do not rule out that the length figure of 480 mm or one or more diameters might be wrong, till updated info for the large 480 mm femur from Ngandong will emerge I would stick with all the measurements provided by Koenigsvald (1933) meaning femur length of 480 mm, proximal sagittal diameter of 59 mm, distal sagittal diameter of 82 mm and distal mediolateral width of 88 mm. The tiger individual owner of that 480 mm femur should therefore be retained as a very large but not heavily build individual. For sure other individuals as large and larger and bulkier then him existed, but that particular individual was not and it must not be forgotten that the weight estimate must refer to that particular fossil individual.
 
I still retain that there is no clear evidence the Ngandong Pleistocene tiger form was any more robust then modern Indian/Nepal tigers if possibly marginally in the forelimbs (see my comments in AVA in January 2012). In the Pleistocene lions compared to modern lions this feature is very much evident.
 
I currently estimate the 480 mm Ngandong tiger femur individual to have weighed around 315 kg (most likely range 300-335 kg) with a head-and-body length of 2300+ mm (up to 2350 mm) and a standing shoulder height of around 1200 mm. There is no question that the occurrence of such a fossil remain much larger then the average within a very small sample of various kind of cranial and postcranial remains is a very high unusual circumstance that would require much deeper investigation.
 
 
 
I do realize my body mass estimates could be retained underestimates. Perhaps some or all of them are like that by 10% or something and even 20% in a few circumstances and they are therefore pretty much stable for quite a number of years. I do feel comfortable with my methodologies and I am quite confident in what I have done despite the inevitable benefit of doubt and the only thing I really know for sure being that they can be improved.
 
 
I hope my discussion and observations have been useful to you at least to force you to reflect. This is what I really would like you to do it. I normally do it when something does not match my thoughts. I have no ambition and/or expectation to illuminate you and this is also the reason why I refrain to open my big book however worth it can be. It is going to be up to you to build yours, but I can guarantee you that once you will do it by your own you will have greater satisfactions.
 
 
I may come back to cursoriality and speciation at a later stage.


                                 WaveRiders
 

 
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Messages In This Thread
RE: Freak Felids - A Discussion of History's Largest Felines - WaveRiders - 03-07-2015, 10:07 PM
Sabertoothed Cats - brotherbear - 06-11-2016, 11:59 AM
RE: Sabertoothed Cats - peter - 06-11-2016, 04:28 PM
Ancient Jaguar - brotherbear - 01-04-2018, 12:45 AM



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