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Smilodon populator

Guatemala GuateGojira Offline
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(04-26-2022, 05:15 PM)GreenGrolar Wrote: Also does anyone know how aggressive a smilodon would be? 

Male sabertoothed cats were pussycats compared to macho lions.


*This image is copyright of its original author

*This image is copyright of its original author

Close up view of a saber tooth cat head on display at the American Natural History Museum, New York. Image: Wikipedia.

Despite their fearsome fangs, male sabertoothed cats may have been less aggressive than many of their feline cousins, says a new study of male-female size differences in extinct big cats.

Commonly called the sabertoothed tiger, Smilodon fatalis was a large predatory cat that roamed North and South America about 1.6 million to 10,000 years ago, when there was also a prehistoric cat called the American lion. A study appearing in the November 5 issue of the Journal of Zoology examined size differences between sexes of these fearsome felines using subtle clues from bones and teeth.

The researchers report that while male American lions were considerably larger than females, male and female sabertoothed cats were indistinguishable in size. The findings suggest that sabertooths may have been less aggressive than their fellow felines, researchers say.


In species where males fight for mates, bigger, heavier males have a better chance of winning fights, fending off their rivals and gaining access to females. After generations of male-male competition, the males of some species evolve to be much larger than their mates.

Most big cats have a form of sexual dimorphism where males are bigger than females, said co-author Julie Meachen-Samuels, a biologist at the National Evolutionary Synthesis Center in Durham, NC. So she and Wendy Binder of Loyola Marymount University in Los Angeles wanted to know if extinct sabertooths and American lions showed the same size patterns as big cats living today.


When it comes to fossils, sorting males from females can be tricky. "It's hard to tell who's a male and who's a female in the fossil record," said Blaire Van Valkenburgh, a biologist at UCLA who has studied these animals extensively but was not an author on the paper. "Unless you're lucky enough to get some DNA, or you're working with an animal where males have horns and females don't."
For species that keep growing into adulthood, simply separating the fossils into two groups by size may not do the trick, either. "It's easy to get a younger, smaller male confused with an older, larger female if you're just dividing them by size," Meachen-Samuels said.

The researchers accounted for continued growth using subtle clues from fossilized teeth. "Teeth fill in over time," said Binder. "In young animals the tooth cavity is basically hollow, but as they get older it fills in with dentin. It won't give you an exact age, but it can give you a relative age in terms of young, middle aged or old," Binder added.


Meachen-Samuels and Binder x-rayed the lower teeth and jaws of 13 American lions and 19 sabertoothed cats recovered from the La Brea Tar Pits in Los Angeles. To account for growth over time, they measured tooth cavity diameter and plotted it against jaw length for each species. Plotted this way, the data for the American lion fell easily into two groups, regardless of age. The researchers concluded that "the little ones were females and the big ones were males," said Van Valkenburgh.


In contrast, sabertoothed cat sizes seemed to be governed solely by age. It would appear that the males were indistinguishable from their mates. "Even by incorporating a measure of age, you can't distinguish males and females," said Meachen-Samuels.


Size differences between the sexes tend to be more impressive in species where male aggression is more intense, and in the extinct American lion, size differences between the sexes were even more dramatic than in lions living today.


The closest living relative of the American lion, "African lions engage in aggressive takeovers where one to several males will take over an entire pride - the males have battles to the death," said Van Valkenburgh.


"Living lions have huge sexual dimorphism," said Meachen-Samuels.

Based on their findings, the researchers think the American lion probably lived in male-dominated groups, where 1-2 males monopolized and mated with multiple females. "My guess would be that the American lion was similar to African lions, where males guard groups of females," said Meachen-Samuels.


"But we don't see that in the sabertoothed cat," Binder said. The size similarity in sabertoothed cats suggests that male sabertooths may have been less aggressive than their larger cousins. "Rather than males having harems of females, the males and females in a group might have been more equal," Binder said.


More information: Meachen-Samuels, J. and W. Binder (2009). "Sexual Dimorphism and Ontogenetic Growth in the American Lion (Panthera atrox) and Sabertoothed Cat (Smilodon fatalis) from Rancho La Brea." Journal of Zoology.


Source: Duke University (news : web)

https://phys.org/news/2009-11-male-sabertoothed-cats-pussycats-macho.html

From Carnivora.

https://carnivora.net/siberian-tiger-v-smilodon-fatalis-female-t10344.html#p193586


Food for thought, animals with greater sexual dimorphism seems to be more aggressive in general.

Actually those conclutions were already challenged, check this study from 2012 Variation in Craniomandibular Morphology and Sexual Dimorphism in Pantherines and the Sabercat Smilodon fatalis

Abstract:
Sexual dimorphism is widespread among carnivorans, and has been an important evolutionary factor in social ecology. However, its presence in sabertoothed felids remains contentious. Here we present a comprehensive analysis of extant Panthera and the sabertoothed felid Smilodon fatalis. S. fatalis has been reported to show little or no sexual dimorphism but to have been intraspecifically variable in skull morphology. We found that large and small specimens of S. fatalis could be assigned to male and female sexes with similar degrees of confidence as Panthera based on craniomandibular shape. P. uncia is much less craniomandibularly variable and has low levels of sexual size-dimorphism. Shape variation in S. fatalis probably reflects sexual differences. Craniomandibular size-dimorphism is lower in S. fatalis than in Panthera except P. uncia. Sexual dimorphism in felids is related to more than overall size, and S. fatalis and the four large Panthera species show marked and similar craniomandibular and dental morphometric sexual dimorphism, whereas morphometric dimorphism in P. uncia is less. Many morphometric-sexually dimorphic characters in Panthera and Smilodon are related to bite strength and presumably to killing ecology. This suggests that morphometric sexual dimorphism is an evolutionary adaptation to intraspecific resource partitioning, since large males with thicker upper canines and stronger bite forces would be able to hunt larger prey than females, which is corroborated by feeding ecology in P. leo. Sexual dimorphism indicates that S. fatalis could have been social, but it is unlikely that it lived in fusion-fission units dominated by one or a few males, as in sub-Saharan populations of P. leo. Instead, S. fatalis could have been solitary and polygynous, as most extant felids, or it may have lived in unisexual groups, as is common in P. leo persica.

Link to full aticle and Support information: https://journals.plos.org/plosone/articl...ne.0048352

Just a taste of it:

*This image is copyright of its original author


There is much more information in that document. A "most read" paper for Smilodon lovers.
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Guatemala GuateGojira Offline
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(04-27-2022, 12:01 AM)Spalea Wrote: That being said, I didn't believe that the size difference between sexes was greater among lions than among tigers. Thus, are tigers especially macho too ? Tigers are solitary animals but the males don't seem to be as rough towards females as in the case of lions.

After lions, tigers are the more sexually dimorphic, so much that Dr Sunquist stated that the skulls of males and females may be so different in some cases that they look like different species.

Tigers are solitary but are not antisocial, they have several ways to communicate each other in they large and normally close habitats, where a roar can't be heard more than 3 km. Male tigers had the same schedule of life as male lions, they need to grow and get a territory, rise cubs and try to stay alive, with the only difference that they need to do it alone. The tenure may be relatively longer (or shorter, depending of the "social" situation in the are, check the case of Chitwan, for example) but they face the same dangers, as a younger stronger male can kill you and kill your cubs. The only difference is that tigers need to travel trough they terrirtory and can't stay to much time in a single area as male lions do (terrirorial marks do not last more than 7 days), also they are more "polite"with tigresses with cubs as tiger society shows "priority rights" over the animal that made the kill (with some exceptions, of course), so cubs are allowed to eat even before the dominant male.

Finally, on the size, they have the same difference as in lions, with males been over 50% bigger than females.
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@GuateGojira 

About #108: " so cubs are allowed to eat even before the dominant male " . Unthinkable as concerns the pride of lions, even if, sometimes, the males are able to leave the cubs eating before the females.
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Guatemala GuateGojira Offline
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(04-27-2022, 01:57 AM)Spalea Wrote: About #108: " so cubs are allowed to eat even before the dominant male " . Unthinkable as concerns the pride of lions, even if, sometimes,  the males are able to leave the cubs eating before the females.

Correct, and that is something that is very interesting in tigers. This observations were made in Kanha and Ranthambore, thanks to its relativelly open habitat. In Chitwan it was not possible to check, habitat is too close for direct observations, except for baiting sites. Other behaviours like taking care of they cubs has been observed in Ranthambore and Panna and in the case of Chitwan, Sunquist found that the young adult M104 (previous to its independance) spend more time with its father M105 than with his mother or sister, although keeping a good distance most of the time. 

What I like the most is that tigers seems to recognize they relatives at some degree. Let's remember the case of the 9 tigers together in Ranthambore, the matriarc (oldest female ) with her cubs of that season, togheter with the dominant male of the area and her previous daughters and her cubs, a "tiger pride", and all of them ate in order, not fighting, all ate they part and the dominant tigress directed the entire activity. Valmik Thapar provided some of the most ground breaking observations ever!
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(04-26-2022, 04:58 PM)GreenGrolar Wrote: Book, Smilodon: the iconic sabertooth.

Wroe (2008) suggestes that Smilodon lumbar vertebrae are ursid-like in being shorter craniocaudally than most felids, but still have transverse processes oriented in the matter of felids, giving them BETTER ACCELERATION AND LESS STABILITY THAN URSIDS.



*This image is copyright of its original author


https://books.google.com.au/books?id=fmBVDwAAQBAJ&pg=PT297&dq=Ursids+are+superior+than+felids&hl=en&sa=X&redir_esc=y#v=onepage&q=Ursids%20are%20superior%20than%20felids&f=false

I know there  is data which says a smilodon has more robust limbs at parity. However, this might only apply when comparing smilodons with younger brown bears up to six to eight years old. Brown bears at nine years old are fully grown and more robust than their own kind at six years old. Smilodons reach their probably from 5 to 7 years old like modern days big cats.

bears in some areas probably are proportionally more robust than populator, but i think when it comes to the humerus and femur populator was proportionally more robust in both, although populators femur isnt more robust to the same degree as its humerus is
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(04-27-2022, 01:57 AM)I’m Spalea Wrote: @GuateGojira 

About #108: " so cubs are allowed to eat even before the dominant male " . Unthinkable as concerns the pride of lions, even if, sometimes,  the males are able to leave the cubs eating before the females.

(04-27-2022, 02:08 AM)GuateGojira Wrote:
(04-27-2022, 01:57 AM)Spalea Wrote: About #108: " so cubs are allowed to eat even before the dominant male " . Unthinkable as concerns the pride of lions, even if, sometimes,  the males are able to leave the cubs eating before the females.

Correct, and that is something that is very interesting in tigers. This observations were made in Kanha and Ranthambore, thanks to its relativelly open habitat. In Chitwan it was not possible to check, habitat is too close for direct observations, except for baiting sites. Other behaviours like taking care of they cubs has been observed in Ranthambore and Panna and in the case of Chitwan, Sunquist found that the young adult M104 (previous to its independance) spend more time with its father M105 than with his mother or sister, although keeping a good distance most of the time. 

What I like the most is that tigers seems to recognize they relatives at some degree. Let's remember the case of the 9 tigers together in Ranthambore, the matriarc (oldest female ) with her cubs of that season, togheter with the dominant male of the area and her previous daughters and her cubs, a "tiger pride", and all of them ate in order, not fighting, all ate they part and the dominant tigress directed the entire activity. Valmik Thapar provided some of the most ground breaking observations ever!

It’s an interesting observation that ties into lions’ and tigers’ different growth strategies in the wild. The member “Acinonyx Sp” posted an interesting paper in the “Comparing Cats” thread recently that touched on this, in comparison with Smilodon fatalis (a cat that may have combined the growth strategies of lions and tigers):

https://www.sciencedirect.com/science/article/pii/S2589004220311135

Quote:The saber-toothed cat Smilodon fatalis is known predominantly from “predator trap” deposits, which has made many aspects of its life history difficult to infer. Here, we describe an association of at least two subadult and one adult S. fatalis from Pleistocene coastal deposits in Ecuador. The assemblage likely derived from a catastrophic mass mortality event, and thereby provides insights into the behavior of the species. The presence of a P3 in the subadult dentaries suggests inheritance, a rare instance of familial relatedness in the fossil record. The siblings were at least two years old and were associated with an adult that was likely their mother, indicating prolonged parental care in S. fatalis. Comparison with the growth of pantherine cats suggests that S. fatalis had a unique growth strategy among big cats that combines a growth rate that is similar to a tiger and the extended growth period of a lion.

'For example, high levels of sociality in S. fatalis have been considered plausible by some authors (Akersten (1985)Carbone et al. (2009)Christiansen and Harris (2012)Friscia et al. (2008)Gonyea (1976)Meachen-Samuels and Binder (2010)Van Valkenburgh and Sacco (2002)), but unlikely by others (Kiffner (2009)McCall et al. (2003)). Furthermore, it has been argued that S. fatalis would not have lived in polygynous groupings because of its putative reduced sexual dimorphism, but the possibility of social groups where polygamy or monogamy are the primary mating system cannot be discounted (Christiansen and Harris (2012)Meachen-Samuels and Binder (2010)Van Valkenburgh and Sacco (2002)).'

'At two years old, tigers (Panthera tigris) have been independent from their mothers for at least six months and weigh between 68% (males) and 94% (females) of their asymptotic body mass (Jones et al. (2009)Slaght et al., 2005). Meanwhile, two-year-old lions are nearly a year from independence and weigh from 58% (males) to 72% (females) of asymptotic body mass (Jones et al. (2009)Smuts et al. (1980)).'

(In captivity though, it’s a different story, as lions grow faster and reach puberty far earlier than their wild counterparts do. The difference in nutrition at an early age really makes a big impact!)

Quote:A major finding in this study was that captive male lions appear to reach puberty at a younger age than wild counterparts. Based on when males first show mounting behaviors, wild males reach sexual maturity at 2.2 years (26 months), but do not typically breed until they take over a pride at the average age of 4 [26,49] or 5 [23,50] years. Still, individuals as young as 3.3 years have been observed to control prides in the Serengeti and Ngorongoro Crater [11]. In wild lions, males 1.6–1.8 years of age were considered pre-pubertal because they produced lower serum testosterone than young adults and adults, weighed only ~88 kg, and were aspermic [11]. Histologic evaluation of testicular tissue from wild males further demonstrated that the onset of spermatogenesis begins at about 2.5 years of age (range: 2.2–2.8 years) [23]. Our study found that although the peripubertal age group had lower FAM concentrations compared to older age categories, the youngest males that tested positive for spermaturia were 105 kg at 1.2 years of age.

The growth kinetics presented in the present study indicate that captive-born lion cubs develop at a faster rate than wild-born cubs, which could account for the early puberty. Wild cubs are heavier for the first few months after birth, but between 3–5 months of age the growth patterns were the same to our captive cubs. Both captive and wild cubs begin to taste/consume meat a few months after birth and are usually weaned by 0.5 years [22,27,50]. However, after weaning, the plane of nutrition appears to diverge between wild- and captive-born cubs and the ADG rate is no longer synchronous, perhaps a result of feeding captive cubs meat daily. There is substantial variability in growth rate in wild African lions [22], and the rate at which lion cubs grow is correlated with food availability once they are weaned [50,51]. Cubs are dependent on adults for food [7,22], but when prey is scarce, young lions go without food for extended periods [50–52] and starvation is a common cause of death at that age [7,22,53]. Captive cubs likely experience an early onset of puberty and reach adult body weight earlier as a result of the consistent feedings they are provided [22,50,54]. For most mammals, the onset of puberty is associated with attaining a threshold body weight [55–59] and acquiring adequate fat reserves [60]. Under-nutrition can delay onset of puberty while over-conditioned animals often attain puberty at an earlier age.
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( This post was last modified: 04-28-2022, 10:06 PM by LonePredator )

@tigerluver How did they estimate the size of Smilodon Populator when it was so different from currently living felids? Like it’s morphology was entirely different from the living cats.

Can you tell me the equations which has been used for it and are all these allometric equations similar in different kinds of uses? For example, is an allometric equation to find the weight of smilodon populator similar to say Cave Bear? Can you tell me a little bit about this?
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(04-28-2022, 10:05 PM)LonePredator Wrote: @tigerluver How did they estimate the size of Smilodon Populator when it was so different from currently living felids? Like it’s morphology was entirely different from the living cats.

Can you tell me the equations which has been used for it and are all these allometric equations similar in different kinds of uses? For example, is an allometric equation to find the weight of smilodon populator similar to say Cave Bear? Can you tell me a little bit about this?


You make an excellent observation and truly, no publication has really been able to address the limitation.

The oldest estimates from Anyonge used circumferences of the long bones. Christiansen and Harris (2005) did similar but also added many other dimensions of the bone. Both used extant felids as the source of the regression equations and cannot actually account for the unique proportions of Smilodon. The hope is that circumference has minimal interspecific different in estimating body mass in these. While Campione et al. (2012) did show circumference is best correlated with body mass across taxa, the percent error is still actually quite significant. Another example of the problem of Smilodon is that it is front heavy, therefore there is a comparatively disproportionate amount of weight supported by the forelimbs as compared to hindlimbs (while in extant cats the distribution is more even). If we think about this theoretically, this would result in the humerus robusticity overestimating (a greater percentage of the body weight is stressing the forelimbs, so they will be proportionately thicker for the total weight) while femur robusticity (a lesser percentage of the body weight is stressing the hindlimbs, so they would be proportionately thinner for the body weight) would underestimate.

The allometric equations were based on felids. Separate equations have been made for bears. When we compare the estimates from the equations, the results are different. This means an allometric equation applied to a felid cannot really apply accurately to a bear.

The giant Smilodon skull was estimated using a regression developed from felid skulls. The issue here is that Smilodon had a smaller skull for its body as compared to extant felids. Therefore, this estimate is probably a significant underestimate.

So there is no perfect formula for Smilodon. Volumetric estimation can be attempted but it gets exposed to subjectivity as the model is essentially art subject to the artist's thoughts.
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( This post was last modified: 04-30-2022, 06:14 AM by LonePredator )

(04-29-2022, 02:33 AM)tigerluver Wrote:
(04-28-2022, 10:05 PM)LonePredator Wrote: @tigerluver How did they estimate the size of Smilodon Populator when it was so different from currently living felids? Like it’s morphology was entirely different from the living cats.

Can you tell me the equations which has been used for it and are all these allometric equations similar in different kinds of uses? For example, is an allometric equation to find the weight of smilodon populator similar to say Cave Bear? Can you tell me a little bit about this?


You make an excellent observation and truly, no publication has really been able to address the limitation.

The oldest estimates from Anyonge used circumferences of the long bones. Christiansen and Harris (2005) did similar but also added many other dimensions of the bone. Both used extant felids as the source of the regression equations and cannot actually account for the unique proportions of Smilodon. The hope is that circumference has minimal interspecific different in estimating body mass in these. While Campione et al. (2012) did show circumference is best correlated with body mass across taxa, the percent error is still actually quite significant. Another example of the problem of Smilodon is that it is front heavy, therefore there is a comparatively disproportionate amount of weight supported by the forelimbs as compared to hindlimbs (while in extant cats the distribution is more even). If we think about this theoretically, this would result in the humerus robusticity overestimating (a greater percentage of the body weight is stressing the forelimbs, so they will be proportionately thicker for the total weight) while femur robusticity (a lesser percentage of the body weight is stressing the hindlimbs, so they would be proportionately thinner for the body weight) would underestimate.

The allometric equations were based on felids. Separate equations have been made for bears. When we compare the estimates from the equations, the results are different. This means an allometric equation applied to a felid cannot really apply accurately to a bear.

The giant Smilodon skull was estimated using a regression developed from felid skulls. The issue here is that Smilodon had a smaller skull for its body as compared to extant felids. Therefore, this estimate is probably a significant underestimate.

So there is no perfect formula for Smilodon. Volumetric estimation can be attempted but it gets exposed to subjectivity as the model is essentially art subject to the artist's thoughts.

Thankyou very much. A very well detailed explanation. I will check out those sources. As far as I remember, I think that the oldest estimates which came from Anyonge were gross overestimations and I’ll check out the rest.

Just one more question, do you think that the isometric scaling of extant felids by scaling the the mass cubically in relation to scaling the length linearly give an accurate enough bodymass estimate? I’m aware it’s just a law of physics which only works on objects of similar proportions but...

What if I do the same for the shoulder height, chest girth and head body length. I linearly scale all these dimensions to the dimensions of the big Tiger and then cubically scale the mass and then average out all the three mass estimates then will it practically hold up?

Do you think that will give a good enough estimate of the mass of the big Tiger and can you roughly predict a percentage error that I could get in my result?

And once again, thanks a lot for your detailed explaination.
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( This post was last modified: 04-30-2022, 02:35 AM by tigerluver )

(04-29-2022, 02:41 AM)LonePredator Wrote:
(04-29-2022, 02:33 AM)tigerluver Wrote:
(04-28-2022, 10:05 PM)LonePredator Wrote: @tigerluver How did they estimate the size of Smilodon Populator when it was so different from currently living felids? Like it’s morphology was entirely different from the living cats.

Can you tell me the equations which has been used for it and are all these allometric equations similar in different kinds of uses? For example, is an allometric equation to find the weight of smilodon populator similar to say Cave Bear? Can you tell me a little bit about this?


You make an excellent observation and truly, no publication has really been able to address the limitation.

The oldest estimates from Anyonge used circumferences of the long bones. Christiansen and Harris (2005) did similar but also added many other dimensions of the bone. Both used extant felids as the source of the regression equations and cannot actually account for the unique proportions of Smilodon. The hope is that circumference has minimal interspecific different in estimating body mass in these. While Campione et al. (2012) did show circumference is best correlated with body mass across taxa, the percent error is still actually quite significant. Another example of the problem of Smilodon is that it is front heavy, therefore there is a comparatively disproportionate amount of weight supported by the forelimbs as compared to hindlimbs (while in extant cats the distribution is more even). If we think about this theoretically, this would result in the humerus robusticity overestimating (a greater percentage of the body weight is stressing the forelimbs, so they will be proportionately thicker for the total weight) while femur robusticity (a lesser percentage of the body weight is stressing the hindlimbs, so they would be proportionately thinner for the body weight) would underestimate.

The allometric equations were based on felids. Separate equations have been made for bears. When we compare the estimates from the equations, the results are different. This means an allometric equation applied to a felid cannot really apply accurately to a bear.

The giant Smilodon skull was estimated using a regression developed from felid skulls. The issue here is that Smilodon had a smaller skull for its body as compared to extant felids. Therefore, this estimate is probably a significant underestimate.

So there is no perfect formula for Smilodon. Volumetric estimation can be attempted but it gets exposed to subjectivity as the model is essentially art subject to the artist's thoughts.

Thankyou very much. A very well detailed explanation. I will check out those sources. As far as I remember, I think that the oldest estimates which came from Anyonge were gross overestimations.

Just one more question, do you think that the isometric scaling of extant felids by scaling the the mass cubically in relation to scaling the length linearly give an accurate enough bodymass estimate? I’m aware it’s just a law of physics which only works on objects of similar proportions but...

What if I do the same for the shoulder height, chest girth and head body length. I linearly scale all these dimensions to the dimensions of the big Tiger and then cubically scale the mass and then average out all the three mass estimates then will it practically hold up?

Do you think that will give a good enough estimate of the mass of the big Tiger and can you roughly predict a percentage error that I could get in my result?

And once again, thanks a lot for your detailed explaination.


Isometry is the most parsimonious when are comparing animals of the same species so I prefer it.

Isometry works with 3 dimensions (length, width, height). Therefore, if you use three measurements that are surrogates for these dimensions, cubically scale the mass, then average them together, you should get an estimate that ideally accurately estimates the mass/volume. There is no real way to calculate percent error unfortunately. 

Another way to do it is to multiple the difference ratio of length by the difference ratio of width and the difference ratio of height. This is based on the formula for volume (length * width * height). For instance, if a tiger is 1.2x longer, 1.1x width, and 1.4x taller than another tiger, you would do:

Mass bigger tiger = Mass smaller tiger * (1.2 * 1.1 * 1.4) = Mass smaller tiger * 1.848

This way is mathematically more accurate than averages the cubically scaled masses together.
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@tigerluver 

About #116:

You wrote: " Mass bigger tiger = Mass smaller tiger * (1.2 * 1.1 * 1.4) = Mass smaller tiger * 2.002 ".

Sorry but 1,2 X 1,1 X 1,4 = 1,848 and not 2,002.
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(04-30-2022, 02:10 AM)tigerluver Wrote:
(04-29-2022, 02:41 AM)LonePredator Wrote:
(04-29-2022, 02:33 AM)tigerluver Wrote:
(04-28-2022, 10:05 PM)LonePredator Wrote: @tigerluver How did they estimate the size of Smilodon Populator when it was so different from currently living felids? Like it’s morphology was entirely different from the living cats.

Can you tell me the equations which has been used for it and are all these allometric equations similar in different kinds of uses? For example, is an allometric equation to find the weight of smilodon populator similar to say Cave Bear? Can you tell me a little bit about this?


You make an excellent observation and truly, no publication has really been able to address the limitation.

The oldest estimates from Anyonge used circumferences of the long bones. Christiansen and Harris (2005) did similar but also added many other dimensions of the bone. Both used extant felids as the source of the regression equations and cannot actually account for the unique proportions of Smilodon. The hope is that circumference has minimal interspecific different in estimating body mass in these. While Campione et al. (2012) did show circumference is best correlated with body mass across taxa, the percent error is still actually quite significant. Another example of the problem of Smilodon is that it is front heavy, therefore there is a comparatively disproportionate amount of weight supported by the forelimbs as compared to hindlimbs (while in extant cats the distribution is more even). If we think about this theoretically, this would result in the humerus robusticity overestimating (a greater percentage of the body weight is stressing the forelimbs, so they will be proportionately thicker for the total weight) while femur robusticity (a lesser percentage of the body weight is stressing the hindlimbs, so they would be proportionately thinner for the body weight) would underestimate.

The allometric equations were based on felids. Separate equations have been made for bears. When we compare the estimates from the equations, the results are different. This means an allometric equation applied to a felid cannot really apply accurately to a bear.

The giant Smilodon skull was estimated using a regression developed from felid skulls. The issue here is that Smilodon had a smaller skull for its body as compared to extant felids. Therefore, this estimate is probably a significant underestimate.

So there is no perfect formula for Smilodon. Volumetric estimation can be attempted but it gets exposed to subjectivity as the model is essentially art subject to the artist's thoughts.

Thankyou very much. A very well detailed explanation. I will check out those sources. As far as I remember, I think that the oldest estimates which came from Anyonge were gross overestimations.

Just one more question, do you think that the isometric scaling of extant felids by scaling the the mass cubically in relation to scaling the length linearly give an accurate enough bodymass estimate? I’m aware it’s just a law of physics which only works on objects of similar proportions but...

What if I do the same for the shoulder height, chest girth and head body length. I linearly scale all these dimensions to the dimensions of the big Tiger and then cubically scale the mass and then average out all the three mass estimates then will it practically hold up?

Do you think that will give a good enough estimate of the mass of the big Tiger and can you roughly predict a percentage error that I could get in my result?

And once again, thanks a lot for your detailed explaination.


Isometry is the most parsimonious when are comparing animals of the same species so I prefer it.

Isometry works with 3 dimensions (length, width, height). Therefore, if you use three measurements that are surrogates for these dimensions, cubically scale the mass, then average them together, you should get an estimate that ideally accurately estimates the mass/volume. There is no real way to calculate percent error unfortunately. 

Another way to do it is to multiple the difference ratio of length by the difference ratio of width and the difference ratio of height. This is based on the formula for volume (length * width * height). For instance, if a tiger is 1.2x longer, 1.1x width, and 1.4x taller than another tiger, you would do:

Mass bigger tiger = Mass smaller tiger * (1.2 * 1.1 * 1.4) = Mass smaller tiger * 2.002

This way is mathematically more accurate than averages the cubically scaled masses together.

This makes it much more simpler. Thanks a lot! I was calculating with all three dimensions separately and then averaging them out and even though it was working well, I’ll try this out now.

Just one more question. I’ve seen in some studies which show that the bite force of Jaguar is 3/4th that of a Bengal Tiger while the bodymass of the Jaguar is only half of the Tiger.

But can we really say that Jaguar has pound for pound stronger bite? Because when we scale the Jaguar to the same weight as the Tiger (by 2x) then the bite force would only increase by 1.777 times, right? Because the cross sectional area would only increase by an exponent of 2 while the mass increases by an exponent of 3.

And I calculated this and found that when mass of the Jaguar is scaled to 200kg from 100 then the force would still be about 12% weaker. Don’t you also think that the Jaguar would still have a weaker bite force than the Tiger if we scale a Jaguar by 2 times to make it equal in weight as the Tiger??
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tigerluver Offline
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(04-30-2022, 02:18 AM)LonePredator Wrote:
(04-30-2022, 02:10 AM)tigerluver Wrote:
(04-29-2022, 02:41 AM)LonePredator Wrote:
(04-29-2022, 02:33 AM)tigerluver Wrote:
(04-28-2022, 10:05 PM)LonePredator Wrote: @tigerluver How did they estimate the size of Smilodon Populator when it was so different from currently living felids? Like it’s morphology was entirely different from the living cats.

Can you tell me the equations which has been used for it and are all these allometric equations similar in different kinds of uses? For example, is an allometric equation to find the weight of smilodon populator similar to say Cave Bear? Can you tell me a little bit about this?


You make an excellent observation and truly, no publication has really been able to address the limitation.

The oldest estimates from Anyonge used circumferences of the long bones. Christiansen and Harris (2005) did similar but also added many other dimensions of the bone. Both used extant felids as the source of the regression equations and cannot actually account for the unique proportions of Smilodon. The hope is that circumference has minimal interspecific different in estimating body mass in these. While Campione et al. (2012) did show circumference is best correlated with body mass across taxa, the percent error is still actually quite significant. Another example of the problem of Smilodon is that it is front heavy, therefore there is a comparatively disproportionate amount of weight supported by the forelimbs as compared to hindlimbs (while in extant cats the distribution is more even). If we think about this theoretically, this would result in the humerus robusticity overestimating (a greater percentage of the body weight is stressing the forelimbs, so they will be proportionately thicker for the total weight) while femur robusticity (a lesser percentage of the body weight is stressing the hindlimbs, so they would be proportionately thinner for the body weight) would underestimate.

The allometric equations were based on felids. Separate equations have been made for bears. When we compare the estimates from the equations, the results are different. This means an allometric equation applied to a felid cannot really apply accurately to a bear.

The giant Smilodon skull was estimated using a regression developed from felid skulls. The issue here is that Smilodon had a smaller skull for its body as compared to extant felids. Therefore, this estimate is probably a significant underestimate.

So there is no perfect formula for Smilodon. Volumetric estimation can be attempted but it gets exposed to subjectivity as the model is essentially art subject to the artist's thoughts.

Thankyou very much. A very well detailed explanation. I will check out those sources. As far as I remember, I think that the oldest estimates which came from Anyonge were gross overestimations.

Just one more question, do you think that the isometric scaling of extant felids by scaling the the mass cubically in relation to scaling the length linearly give an accurate enough bodymass estimate? I’m aware it’s just a law of physics which only works on objects of similar proportions but...

What if I do the same for the shoulder height, chest girth and head body length. I linearly scale all these dimensions to the dimensions of the big Tiger and then cubically scale the mass and then average out all the three mass estimates then will it practically hold up?

Do you think that will give a good enough estimate of the mass of the big Tiger and can you roughly predict a percentage error that I could get in my result?

And once again, thanks a lot for your detailed explaination.


Isometry is the most parsimonious when are comparing animals of the same species so I prefer it.

Isometry works with 3 dimensions (length, width, height). Therefore, if you use three measurements that are surrogates for these dimensions, cubically scale the mass, then average them together, you should get an estimate that ideally accurately estimates the mass/volume. There is no real way to calculate percent error unfortunately. 

Another way to do it is to multiple the difference ratio of length by the difference ratio of width and the difference ratio of height. This is based on the formula for volume (length * width * height). For instance, if a tiger is 1.2x longer, 1.1x width, and 1.4x taller than another tiger, you would do:

Mass bigger tiger = Mass smaller tiger * (1.2 * 1.1 * 1.4) = Mass smaller tiger * 2.002

This way is mathematically more accurate than averages the cubically scaled masses together.

This makes it much more simpler. Thanks a lot! I was calculating with all three dimensions separately and then averaging them out and even though it was working well, I’ll try this out now.

Just one more question. I’ve seen in some studies which show that the bite force of Jaguar is 3/4th that of a Bengal Tiger while the bodymass of the Jaguar is only half of the Tiger.

But can we really say that Jaguar has pound for pound stronger bite? Because when we scale the Jaguar to the same weight as the Tiger (by 2x) then the bite force would only increase by 1.777 times, right? Because the cross sectional area would only increase by an exponent of 2 while the mass increases by an exponent of 3.

And I calculated this and found that when mass of the Jaguar is scaled to 200kg from 100 then the force would still be about 12% weaker. Don’t you also think that the Jaguar would still have a weaker bite force than the Tiger if we scale a Jaguar by 2 times to make it equal in weight as the Tiger??


In the literal sense your math would be right. However, as skulls get bigger there are allometric effects such as increase in the length of the masseteric fossa which would increase the bite force. 

Therefore, regressions are made to account for the allometric changes. Wroe et al. finds the jaguar's bite force is above the regression line:


*This image is copyright of its original author


The positioning of where the point is as compared to the regression line is measured by the bite force quotient (BFQ). In the study, the jaguar's BFQ is 1.37 and the tiger's 1.27. A weakness of the study is that actual weights of animals are not used, just estimates. Therefore, the BFQ may not be accurate.

A more fruitful measurement would probably be bite force over skull length. I ran the regression quickly (can't figure out how to label datapoints, if I have time later I will update the post):


*This image is copyright of its original author


Based on the second graph, the jaguar has significantly stronger bite than predicted for its skull length.
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LonePredator Offline
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( This post was last modified: 04-30-2022, 03:24 AM by LonePredator )

(04-30-2022, 03:09 AM)tigerluver Wrote:
(04-30-2022, 02:18 AM)LonePredator Wrote:
(04-30-2022, 02:10 AM)tigerluver Wrote:
(04-29-2022, 02:41 AM)LonePredator Wrote:
(04-29-2022, 02:33 AM)tigerluver Wrote:
(04-28-2022, 10:05 PM)LonePredator Wrote: @tigerluver How did they estimate the size of Smilodon Populator when it was so different from currently living felids? Like it’s morphology was entirely different from the living cats.

Can you tell me the equations which has been used for it and are all these allometric equations similar in different kinds of uses? For example, is an allometric equation to find the weight of smilodon populator similar to say Cave Bear? Can you tell me a little bit about this?


You make an excellent observation and truly, no publication has really been able to address the limitation.

The oldest estimates from Anyonge used circumferences of the long bones. Christiansen and Harris (2005) did similar but also added many other dimensions of the bone. Both used extant felids as the source of the regression equations and cannot actually account for the unique proportions of Smilodon. The hope is that circumference has minimal interspecific different in estimating body mass in these. While Campione et al. (2012) did show circumference is best correlated with body mass across taxa, the percent error is still actually quite significant. Another example of the problem of Smilodon is that it is front heavy, therefore there is a comparatively disproportionate amount of weight supported by the forelimbs as compared to hindlimbs (while in extant cats the distribution is more even). If we think about this theoretically, this would result in the humerus robusticity overestimating (a greater percentage of the body weight is stressing the forelimbs, so they will be proportionately thicker for the total weight) while femur robusticity (a lesser percentage of the body weight is stressing the hindlimbs, so they would be proportionately thinner for the body weight) would underestimate.

The allometric equations were based on felids. Separate equations have been made for bears. When we compare the estimates from the equations, the results are different. This means an allometric equation applied to a felid cannot really apply accurately to a bear.

The giant Smilodon skull was estimated using a regression developed from felid skulls. The issue here is that Smilodon had a smaller skull for its body as compared to extant felids. Therefore, this estimate is probably a significant underestimate.

So there is no perfect formula for Smilodon. Volumetric estimation can be attempted but it gets exposed to subjectivity as the model is essentially art subject to the artist's thoughts.

Thankyou very much. A very well detailed explanation. I will check out those sources. As far as I remember, I think that the oldest estimates which came from Anyonge were gross overestimations.

Just one more question, do you think that the isometric scaling of extant felids by scaling the the mass cubically in relation to scaling the length linearly give an accurate enough bodymass estimate? I’m aware it’s just a law of physics which only works on objects of similar proportions but...

What if I do the same for the shoulder height, chest girth and head body length. I linearly scale all these dimensions to the dimensions of the big Tiger and then cubically scale the mass and then average out all the three mass estimates then will it practically hold up?

Do you think that will give a good enough estimate of the mass of the big Tiger and can you roughly predict a percentage error that I could get in my result?

And once again, thanks a lot for your detailed explaination.


Isometry is the most parsimonious when are comparing animals of the same species so I prefer it.

Isometry works with 3 dimensions (length, width, height). Therefore, if you use three measurements that are surrogates for these dimensions, cubically scale the mass, then average them together, you should get an estimate that ideally accurately estimates the mass/volume. There is no real way to calculate percent error unfortunately. 

Another way to do it is to multiple the difference ratio of length by the difference ratio of width and the difference ratio of height. This is based on the formula for volume (length * width * height). For instance, if a tiger is 1.2x longer, 1.1x width, and 1.4x taller than another tiger, you would do:

Mass bigger tiger = Mass smaller tiger * (1.2 * 1.1 * 1.4) = Mass smaller tiger * 2.002

This way is mathematically more accurate than averages the cubically scaled masses together.

This makes it much more simpler. Thanks a lot! I was calculating with all three dimensions separately and then averaging them out and even though it was working well, I’ll try this out now.

Just one more question. I’ve seen in some studies which show that the bite force of Jaguar is 3/4th that of a Bengal Tiger while the bodymass of the Jaguar is only half of the Tiger.

But can we really say that Jaguar has pound for pound stronger bite? Because when we scale the Jaguar to the same weight as the Tiger (by 2x) then the bite force would only increase by 1.777 times, right? Because the cross sectional area would only increase by an exponent of 2 while the mass increases by an exponent of 3.

And I calculated this and found that when mass of the Jaguar is scaled to 200kg from 100 then the force would still be about 12% weaker. Don’t you also think that the Jaguar would still have a weaker bite force than the Tiger if we scale a Jaguar by 2 times to make it equal in weight as the Tiger??


In the literal sense your math would be right. However, as skulls get bigger there are allometric effects such as increase in the length of the masseteric fossa which would increase the bite force. 

Therefore, regressions are made to account for the allometric changes. Wroe et al. finds the jaguar's bite force is above the regression line:


*This image is copyright of its original author


The positioning of where the point is as compared to the regression line is measured by the bite force quotient (BFQ). In the study, the jaguar's BFQ is 1.37 and the tiger's 1.27. A weakness of the study is that actual weights of animals are not used, just estimates. Therefore, the BFQ may not be accurate.

A more fruitful measurement would probably be bite force over skull length. I ran the regression quickly (can't figure out how to label datapoints, if I have time later I will update the post):


*This image is copyright of its original author


Based on the second graph, the jaguar has significantly stronger bite than predicted for its skull length.

Is this allometric variation seen in the Jaguars? I mean do the bigger Jaguar skulls have these allometric variations compared to the smaller Jaguar species of the same population.

And was this allometric variation also seen in the prehistoric subspecies of Jaguars which were as big as Bengal Tigers? Would their bite force be stronger or weaker than the Tiger’s?

What about a Sumatran Tiger? Do you think a 120kg Sumatran Tiger’s bite force be higher or lower than a 120kg Jaguar assuming that the Sumatran’s morphology is the same as Bengals but they just have a bigger skull for their body (which I am assuming is the actual case as well since isometric equations with Bengals and Sumatrans as surrogates have been used to estimate Ngandong and the Borneo Tiger)
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tigerluver Offline
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( This post was last modified: 04-30-2022, 04:04 AM by tigerluver )

(04-30-2022, 03:14 AM)LonePredator Wrote:
(04-30-2022, 03:09 AM)tigerluver Wrote:
(04-30-2022, 02:18 AM)LonePredator Wrote:
(04-30-2022, 02:10 AM)tigerluver Wrote:
(04-29-2022, 02:41 AM)LonePredator Wrote:
(04-29-2022, 02:33 AM)tigerluver Wrote:
(04-28-2022, 10:05 PM)LonePredator Wrote: @tigerluver How did they estimate the size of Smilodon Populator when it was so different from currently living felids? Like it’s morphology was entirely different from the living cats.

Can you tell me the equations which has been used for it and are all these allometric equations similar in different kinds of uses? For example, is an allometric equation to find the weight of smilodon populator similar to say Cave Bear? Can you tell me a little bit about this?


You make an excellent observation and truly, no publication has really been able to address the limitation.

The oldest estimates from Anyonge used circumferences of the long bones. Christiansen and Harris (2005) did similar but also added many other dimensions of the bone. Both used extant felids as the source of the regression equations and cannot actually account for the unique proportions of Smilodon. The hope is that circumference has minimal interspecific different in estimating body mass in these. While Campione et al. (2012) did show circumference is best correlated with body mass across taxa, the percent error is still actually quite significant. Another example of the problem of Smilodon is that it is front heavy, therefore there is a comparatively disproportionate amount of weight supported by the forelimbs as compared to hindlimbs (while in extant cats the distribution is more even). If we think about this theoretically, this would result in the humerus robusticity overestimating (a greater percentage of the body weight is stressing the forelimbs, so they will be proportionately thicker for the total weight) while femur robusticity (a lesser percentage of the body weight is stressing the hindlimbs, so they would be proportionately thinner for the body weight) would underestimate.

The allometric equations were based on felids. Separate equations have been made for bears. When we compare the estimates from the equations, the results are different. This means an allometric equation applied to a felid cannot really apply accurately to a bear.

The giant Smilodon skull was estimated using a regression developed from felid skulls. The issue here is that Smilodon had a smaller skull for its body as compared to extant felids. Therefore, this estimate is probably a significant underestimate.

So there is no perfect formula for Smilodon. Volumetric estimation can be attempted but it gets exposed to subjectivity as the model is essentially art subject to the artist's thoughts.

Thankyou very much. A very well detailed explanation. I will check out those sources. As far as I remember, I think that the oldest estimates which came from Anyonge were gross overestimations.

Just one more question, do you think that the isometric scaling of extant felids by scaling the the mass cubically in relation to scaling the length linearly give an accurate enough bodymass estimate? I’m aware it’s just a law of physics which only works on objects of similar proportions but...

What if I do the same for the shoulder height, chest girth and head body length. I linearly scale all these dimensions to the dimensions of the big Tiger and then cubically scale the mass and then average out all the three mass estimates then will it practically hold up?

Do you think that will give a good enough estimate of the mass of the big Tiger and can you roughly predict a percentage error that I could get in my result?

And once again, thanks a lot for your detailed explaination.


Isometry is the most parsimonious when are comparing animals of the same species so I prefer it.

Isometry works with 3 dimensions (length, width, height). Therefore, if you use three measurements that are surrogates for these dimensions, cubically scale the mass, then average them together, you should get an estimate that ideally accurately estimates the mass/volume. There is no real way to calculate percent error unfortunately. 

Another way to do it is to multiple the difference ratio of length by the difference ratio of width and the difference ratio of height. This is based on the formula for volume (length * width * height). For instance, if a tiger is 1.2x longer, 1.1x width, and 1.4x taller than another tiger, you would do:

Mass bigger tiger = Mass smaller tiger * (1.2 * 1.1 * 1.4) = Mass smaller tiger * 2.002

This way is mathematically more accurate than averages the cubically scaled masses together.

This makes it much more simpler. Thanks a lot! I was calculating with all three dimensions separately and then averaging them out and even though it was working well, I’ll try this out now.

Just one more question. I’ve seen in some studies which show that the bite force of Jaguar is 3/4th that of a Bengal Tiger while the bodymass of the Jaguar is only half of the Tiger.

But can we really say that Jaguar has pound for pound stronger bite? Because when we scale the Jaguar to the same weight as the Tiger (by 2x) then the bite force would only increase by 1.777 times, right? Because the cross sectional area would only increase by an exponent of 2 while the mass increases by an exponent of 3.

And I calculated this and found that when mass of the Jaguar is scaled to 200kg from 100 then the force would still be about 12% weaker. Don’t you also think that the Jaguar would still have a weaker bite force than the Tiger if we scale a Jaguar by 2 times to make it equal in weight as the Tiger??


In the literal sense your math would be right. However, as skulls get bigger there are allometric effects such as increase in the length of the masseteric fossa which would increase the bite force. 

Therefore, regressions are made to account for the allometric changes. Wroe et al. finds the jaguar's bite force is above the regression line:


*This image is copyright of its original author


The positioning of where the point is as compared to the regression line is measured by the bite force quotient (BFQ). In the study, the jaguar's BFQ is 1.37 and the tiger's 1.27. A weakness of the study is that actual weights of animals are not used, just estimates. Therefore, the BFQ may not be accurate.

A more fruitful measurement would probably be bite force over skull length. I ran the regression quickly (can't figure out how to label datapoints, if I have time later I will update the post):


*This image is copyright of its original author


Based on the second graph, the jaguar has significantly stronger bite than predicted for its skull length.

Is this allometric variation seen in the Jaguars? I mean do the bigger Jaguar skulls have these allometric variations compared to the smaller Jaguar species of the same population.

I haven't seen enough jaguar skulls but I see the trend in tigers and lions, so I infer it's also in jaguars.
(04-30-2022, 03:14 AM)LonePredator Wrote:
(04-30-2022, 03:09 AM)tigerluver Wrote:
(04-30-2022, 02:18 AM)LonePredator Wrote:
(04-30-2022, 02:10 AM)tigerluver Wrote:
(04-29-2022, 02:41 AM)LonePredator Wrote:
(04-29-2022, 02:33 AM)tigerluver Wrote:
(04-28-2022, 10:05 PM)LonePredator Wrote: @tigerluver How did they estimate the size of Smilodon Populator when it was so different from currently living felids? Like it’s morphology was entirely different from the living cats.

Can you tell me the equations which has been used for it and are all these allometric equations similar in different kinds of uses? For example, is an allometric equation to find the weight of smilodon populator similar to say Cave Bear? Can you tell me a little bit about this?


You make an excellent observation and truly, no publication has really been able to address the limitation.

The oldest estimates from Anyonge used circumferences of the long bones. Christiansen and Harris (2005) did similar but also added many other dimensions of the bone. Both used extant felids as the source of the regression equations and cannot actually account for the unique proportions of Smilodon. The hope is that circumference has minimal interspecific different in estimating body mass in these. While Campione et al. (2012) did show circumference is best correlated with body mass across taxa, the percent error is still actually quite significant. Another example of the problem of Smilodon is that it is front heavy, therefore there is a comparatively disproportionate amount of weight supported by the forelimbs as compared to hindlimbs (while in extant cats the distribution is more even). If we think about this theoretically, this would result in the humerus robusticity overestimating (a greater percentage of the body weight is stressing the forelimbs, so they will be proportionately thicker for the total weight) while femur robusticity (a lesser percentage of the body weight is stressing the hindlimbs, so they would be proportionately thinner for the body weight) would underestimate.

The allometric equations were based on felids. Separate equations have been made for bears. When we compare the estimates from the equations, the results are different. This means an allometric equation applied to a felid cannot really apply accurately to a bear.

The giant Smilodon skull was estimated using a regression developed from felid skulls. The issue here is that Smilodon had a smaller skull for its body as compared to extant felids. Therefore, this estimate is probably a significant underestimate.

So there is no perfect formula for Smilodon. Volumetric estimation can be attempted but it gets exposed to subjectivity as the model is essentially art subject to the artist's thoughts.

Thankyou very much. A very well detailed explanation. I will check out those sources. As far as I remember, I think that the oldest estimates which came from Anyonge were gross overestimations.

Just one more question, do you think that the isometric scaling of extant felids by scaling the the mass cubically in relation to scaling the length linearly give an accurate enough bodymass estimate? I’m aware it’s just a law of physics which only works on objects of similar proportions but...

What if I do the same for the shoulder height, chest girth and head body length. I linearly scale all these dimensions to the dimensions of the big Tiger and then cubically scale the mass and then average out all the three mass estimates then will it practically hold up?

Do you think that will give a good enough estimate of the mass of the big Tiger and can you roughly predict a percentage error that I could get in my result?

And once again, thanks a lot for your detailed explaination.


Isometry is the most parsimonious when are comparing animals of the same species so I prefer it.

Isometry works with 3 dimensions (length, width, height). Therefore, if you use three measurements that are surrogates for these dimensions, cubically scale the mass, then average them together, you should get an estimate that ideally accurately estimates the mass/volume. There is no real way to calculate percent error unfortunately. 

Another way to do it is to multiple the difference ratio of length by the difference ratio of width and the difference ratio of height. This is based on the formula for volume (length * width * height). For instance, if a tiger is 1.2x longer, 1.1x width, and 1.4x taller than another tiger, you would do:

Mass bigger tiger = Mass smaller tiger * (1.2 * 1.1 * 1.4) = Mass smaller tiger * 2.002

This way is mathematically more accurate than averages the cubically scaled masses together.

This makes it much more simpler. Thanks a lot! I was calculating with all three dimensions separately and then averaging them out and even though it was working well, I’ll try this out now.

Just one more question. I’ve seen in some studies which show that the bite force of Jaguar is 3/4th that of a Bengal Tiger while the bodymass of the Jaguar is only half of the Tiger.

But can we really say that Jaguar has pound for pound stronger bite? Because when we scale the Jaguar to the same weight as the Tiger (by 2x) then the bite force would only increase by 1.777 times, right? Because the cross sectional area would only increase by an exponent of 2 while the mass increases by an exponent of 3.

And I calculated this and found that when mass of the Jaguar is scaled to 200kg from 100 then the force would still be about 12% weaker. Don’t you also think that the Jaguar would still have a weaker bite force than the Tiger if we scale a Jaguar by 2 times to make it equal in weight as the Tiger??


In the literal sense your math would be right. However, as skulls get bigger there are allometric effects such as increase in the length of the masseteric fossa which would increase the bite force. 

Therefore, regressions are made to account for the allometric changes. Wroe et al. finds the jaguar's bite force is above the regression line:


*This image is copyright of its original author


The positioning of where the point is as compared to the regression line is measured by the bite force quotient (BFQ). In the study, the jaguar's BFQ is 1.37 and the tiger's 1.27. A weakness of the study is that actual weights of animals are not used, just estimates. Therefore, the BFQ may not be accurate.

A more fruitful measurement would probably be bite force over skull length. I ran the regression quickly (can't figure out how to label datapoints, if I have time later I will update the post):


*This image is copyright of its original author


Based on the second graph, the jaguar has significantly stronger bite than predicted for its skull length.

And was this allometric variation also seen in the prehistoric subspecies of Jaguars which were as big as Bengal Tigers? Would their bite force be stronger or weaker than the Tiger’s?

No jaguar skull has been found that is much larger than an extant jaguar so we cannot actually say.


(04-30-2022, 03:14 AM)LonePredator Wrote:
(04-30-2022, 03:09 AM)tigerluver Wrote:
(04-30-2022, 02:18 AM)LonePredator Wrote:
(04-30-2022, 02:10 AM)tigerluver Wrote:
(04-29-2022, 02:41 AM)LonePredator Wrote:
(04-29-2022, 02:33 AM)tigerluver Wrote:
(04-28-2022, 10:05 PM)LonePredator Wrote: @tigerluver How did they estimate the size of Smilodon Populator when it was so different from currently living felids? Like it’s morphology was entirely different from the living cats.

Can you tell me the equations which has been used for it and are all these allometric equations similar in different kinds of uses? For example, is an allometric equation to find the weight of smilodon populator similar to say Cave Bear? Can you tell me a little bit about this?


You make an excellent observation and truly, no publication has really been able to address the limitation.

The oldest estimates from Anyonge used circumferences of the long bones. Christiansen and Harris (2005) did similar but also added many other dimensions of the bone. Both used extant felids as the source of the regression equations and cannot actually account for the unique proportions of Smilodon. The hope is that circumference has minimal interspecific different in estimating body mass in these. While Campione et al. (2012) did show circumference is best correlated with body mass across taxa, the percent error is still actually quite significant. Another example of the problem of Smilodon is that it is front heavy, therefore there is a comparatively disproportionate amount of weight supported by the forelimbs as compared to hindlimbs (while in extant cats the distribution is more even). If we think about this theoretically, this would result in the humerus robusticity overestimating (a greater percentage of the body weight is stressing the forelimbs, so they will be proportionately thicker for the total weight) while femur robusticity (a lesser percentage of the body weight is stressing the hindlimbs, so they would be proportionately thinner for the body weight) would underestimate.

The allometric equations were based on felids. Separate equations have been made for bears. When we compare the estimates from the equations, the results are different. This means an allometric equation applied to a felid cannot really apply accurately to a bear.

The giant Smilodon skull was estimated using a regression developed from felid skulls. The issue here is that Smilodon had a smaller skull for its body as compared to extant felids. Therefore, this estimate is probably a significant underestimate.

So there is no perfect formula for Smilodon. Volumetric estimation can be attempted but it gets exposed to subjectivity as the model is essentially art subject to the artist's thoughts.

Thankyou very much. A very well detailed explanation. I will check out those sources. As far as I remember, I think that the oldest estimates which came from Anyonge were gross overestimations.

Just one more question, do you think that the isometric scaling of extant felids by scaling the the mass cubically in relation to scaling the length linearly give an accurate enough bodymass estimate? I’m aware it’s just a law of physics which only works on objects of similar proportions but...

What if I do the same for the shoulder height, chest girth and head body length. I linearly scale all these dimensions to the dimensions of the big Tiger and then cubically scale the mass and then average out all the three mass estimates then will it practically hold up?

Do you think that will give a good enough estimate of the mass of the big Tiger and can you roughly predict a percentage error that I could get in my result?

And once again, thanks a lot for your detailed explaination.


Isometry is the most parsimonious when are comparing animals of the same species so I prefer it.

Isometry works with 3 dimensions (length, width, height). Therefore, if you use three measurements that are surrogates for these dimensions, cubically scale the mass, then average them together, you should get an estimate that ideally accurately estimates the mass/volume. There is no real way to calculate percent error unfortunately. 

Another way to do it is to multiple the difference ratio of length by the difference ratio of width and the difference ratio of height. This is based on the formula for volume (length * width * height). For instance, if a tiger is 1.2x longer, 1.1x width, and 1.4x taller than another tiger, you would do:

Mass bigger tiger = Mass smaller tiger * (1.2 * 1.1 * 1.4) = Mass smaller tiger * 2.002

This way is mathematically more accurate than averages the cubically scaled masses together.

This makes it much more simpler. Thanks a lot! I was calculating with all three dimensions separately and then averaging them out and even though it was working well, I’ll try this out now.

Just one more question. I’ve seen in some studies which show that the bite force of Jaguar is 3/4th that of a Bengal Tiger while the bodymass of the Jaguar is only half of the Tiger.

But can we really say that Jaguar has pound for pound stronger bite? Because when we scale the Jaguar to the same weight as the Tiger (by 2x) then the bite force would only increase by 1.777 times, right? Because the cross sectional area would only increase by an exponent of 2 while the mass increases by an exponent of 3.

And I calculated this and found that when mass of the Jaguar is scaled to 200kg from 100 then the force would still be about 12% weaker. Don’t you also think that the Jaguar would still have a weaker bite force than the Tiger if we scale a Jaguar by 2 times to make it equal in weight as the Tiger??


In the literal sense your math would be right. However, as skulls get bigger there are allometric effects such as increase in the length of the masseteric fossa which would increase the bite force. 

Therefore, regressions are made to account for the allometric changes. Wroe et al. finds the jaguar's bite force is above the regression line:


*This image is copyright of its original author


The positioning of where the point is as compared to the regression line is measured by the bite force quotient (BFQ). In the study, the jaguar's BFQ is 1.37 and the tiger's 1.27. A weakness of the study is that actual weights of animals are not used, just estimates. Therefore, the BFQ may not be accurate.

A more fruitful measurement would probably be bite force over skull length. I ran the regression quickly (can't figure out how to label datapoints, if I have time later I will update the post):


*This image is copyright of its original author


Based on the second graph, the jaguar has significantly stronger bite than predicted for its skull length.

What about a Sumatran Tiger? Do you think a 120kg Sumatran Tiger’s bite force be higher or lower than a 120kg Jaguar assuming that the Sumatran’s morphology is the same as Bengals but they just have a bigger skull for their body (which I am assuming is the actual case as well since isometric equations with Bengals and Sumatrans as surrogates have been used to estimate Ngandong and the Borneo Tiger)

Intrinsically, if an animal has a bigger skull for its body, then its mass-based BFQ will be higher.

I ran a hypothetical with a smaller tiger skull, and while the gap between tiger and jaguar decreases, it's still large.


*This image is copyright of its original author


This is assuming the smaller tiger scales isometrically with the larger tiger. If it has a bigger head, than the skull length based BFQ would be higher. Note these graphs are bite force versus skull length, not weight.

If I recall correctly, jaguar have wider arches than tigers. This intrinsically would give the higher bite force per skull length.
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