What about MUCPv-95?

[intro] Back in the late 90s and early 2000s, Giganotosaurus (Coria and Salgado 1995), and specifically MUCPv-95, the second, alledgedly larger specimen of that taxon (Calvo and Coria 1998), was all the rage. It now appears to have been superseded by a revived hype for Tyrannosaurus, fueled by the recognition that the largest T. rex specimens are actually the largest reliably documented theropods, at least in terms of mass (e. g. Persons et al. 2020).

However, in the plethora of recent works dealing with theropod body size (especially mass), something that’s entirely absent is MUCPv-95. Obviously the specimen doesn’t have a femur, nor anything else except for a large, isolated dentary, and is therefore naturally excluded from any analysis that is based on femoral dimensions or circumference, which were most of them in recent years. The actual size of the fossil has also come under increased scrutiny as time went on, with several conflicting scalings for it now circulating on the internet.
When originally publishing the specimen, an almost complete, but isolated dentary, Calvo and Coria claimed it was 8% larger than the holotype. Considering the emphasis they put on this figure, as well as its supposed relevance on account of it being hailed as the largest known theropod, one would have thought they’d have conclusively documented how they arrived at those 8%, but sadly the opposite is the case. While Calvo and Coria do give a number of measurements of the dentary, most notably the length at 61 cm, minimum depth at 14 cm and maximum depth at 18 cm, what they did not do was provide any comparative figures for the holotype, or ever explain how exactly they compared them to arrive at the "8% larger" figure (length? tooth row lenght? depth? a combination?). With them being quite vague about it, there were basically three camps from then on out;
1) Some people accepted the 8% at face value (which understandably appears to have been a declining sentiment ever since)

2) Others tried to figure out the relative sizes on their own based on the limited information given in Calvo and Coria (1998) and Coria and Salgado (1995), and later Coria and Currie’s (2006) description of Mapusaurus, which lists the relative minimum dentary depths as 135 and 138 mm respectively. Taking the latter alone would imply a size difference of just 2.2%. Scott Hartman came up with an alternative scaling of the two specimens that resulted in a difference of 6.5%.
3) Lastly, at some point most people just started disregarding the specimen entirely and focusing on the osteologically almost undescribed, smaller, but much more complete holotype specimen MUCPv-Ch1 for comparisons between giant theropods, often treating it as if it was the largest specimen of the genus.

While that is understandable, it is also a pity, because it ends up ignoring a direly needed datapoint for the size distribution of one of the largest known theropods, in analyses that already suffer from a severe lack of consideration for sample sizes and statistical biases. Which led me to continue being interested in this specimen, even if it is just a dentary. I even asked both Calvo and Coria about it’s actual size. Coria sadly doesn’t recall how exactly the 8% was calculated any more (but suggested that 5% might be reasonable), and from Calvo I never got a reply. So how to proceed?

[m&m] Instead of choosing a single measurement to compare the two bones, which might give varying results due to slight shape variations, I chose to use a more comprehensive approach based on geometric morphometrics. For this, I took the best available images for both specimens, and scaled them according to the best available measurements. For the holotype, that was the minimum depth of 135 mm given by Coria and Currie (2006), while for the large dentary that was the length of 61 cm. Based on this, the scalebar in Calvo and Coria (1998) is actually really accurate (which surprised me), whereas that in Salgado and Coria (1995) doesn’t even come close (it’s undersized by more than a factor of 2…maybe it was supposed to be 5 cm rather than the stated 10?). For the images, I used the flipped medial view for MUCPv-95 (because it doesn’t matter for the landmarks in question, and allowed a better view of the tooth positions) and the lateral (and only available) view for MUCPv-Ch1 and made sure each image had an accurate scalebar. I then imported these two images in geomorph (Adams et al. 2022) and digitized the scalebars and 8 landmarks each, which were:

1) anterodorsal corner of dentary

2-4) distal bases of 3rd, 5th and 7th tooth

5) ventral margin of jaw on a vertical line below landmark 4

6) same for landmark 3

7) anteroventral corner of dentary

8) sliding semi-landmark on anterior margin of dentary between landmarks 8 and 1

Based on these landmarks, I calculated a procrustes-fit in geomorph, which gave me the centroid sizes for both landmark configurations (the centroid size is a measure of size used in geometric morphometrics, calculated as the square root of the sum of all squared distances of individual landmarks from their centroid).

Figure 1: Comparisons of MUCPv-95 (top) and MUCPv-Ch1 (bottom), with corresponding landmark configurations on the anterior dentary, used to calculate procrustes fit and centroid size. Semi-landmark coloured circle, all other landmarks black circles. Bottom: Procrustes superimposition and mean shape between the two specimens.

The images and R code used in the analysis plus a tps file with the digitized landmark configurations and a plot with the raw results can be found here.

[results & discussion] The result is this:
centroid size for MUCPv-Ch1: 33.54746 cm
centroid size for MUCPv-95: 35.28684 cm
ratio: 1.051848

So in other words, the larger specimen ends up approximately 5% larger than the holotype (which incidentally lines up well with what Coria told me). What does this imply?
While this still doesn’t give us any progress on determining where the 8% actually came from (nor does it rule it out), this does provide a more objective and repeatable way to compare the sizes of these two specimens based on the best publicly available data. It supports the notion that MUCPv-95 is a bit larger than MUCPv-Ch1, or conversely (and more importantly) it demonstrates that MUCPv-Ch1, commonly treated as if it were the only individual, is not large for its species.

The results of the morphometric comparison also demonstrate a fairly good fit between the two individuals’ dentary shapes, which would seem to support them both being the same taxon (obviously helpful), but also that the landmark placement appears to be fairly consistent. There is one landmark that differs a bit more markedly than the others, which is landmark 3, which is markedly "recessed" in MUCPv-95. Here it appears that the margin of the dentary, and perhaps also the tooth, may be somewhat incomplete, which if true, would mean I end up slightly underestimating the size for MUCPv-95, but in order to stay on the conservative side I left the landmark as it is instead of estimating it.
So what are the implications?
Firstly, regarding the scaling of skeletal elements:
Most recently, Canale et al. (2022), in their description of the coeval, giant carcharodontosaurid Meraxes gigas, numerically estimated the skull length of the G. carolinii holotype at 163.4 cm. If the second specimen was 5 % bigger, as implied by the centroid sizes in the morphometric comparison, then that means its skull would have been 171.9 cm long, meaning Giganotosaurus likely retains the title for longest theropod skull quite decisively, even based on known specimens (and compared to all other truly giant theropods, Giganotosaurus is tied with Tyrannotitan for the lowest sample size, at 2 for each). That being said, there’s a good argument to be had that the largest specimens of Mapusaurus and Spinosaurus might have had skulls equally long, or even longer (the largest bone fragment of Mapusaurus is still 10% bigger than the equivalent in G. carolinii), though only for the latter is that size actually based on cranial material.
The holotype femur of G. carolinii is 136.5 cm long (Carrano et al. 2012), so the 5% bigger MUCPv-95 would be expected to have a femur 143.6 cm long (incidentally this is very close to the initially reported larger femoral measurement for the holotype, at 143 cm). Femur circumference for the holotype is  521 mm according to Campione et al. 2014, so it would be estimated at 548 for the larger specimen.

 
Secondly, this also implies that body size estimates exclusively based on the holotype likely underestimate the species as a whole in terms of average, and especially maximum size (or rather, highlight that the holotype definitely isn’t representative of maximum size at all, as it is the slightly smaller of two individuals known, which are likely both a far cry from the maximum size).
Usually, the focus of analyses has been on finding the largest specimens (and often the largest femoral specimens) for various species of giant theropods, a comparison in which, by virtue of being known from a multitude of large, well-preserved skeletons T. rex is predestined to end up at the top of the list. However it has been acknowledged previously that this is not an apples to apples comparison for that very reason, with Persons et al. 2020 going so far as to note that, by femur circumference, the G. carolinii holotype actually outsizes most T. rex specimens. The mean of the 12 T. rex femur circumferences given in their table 1 is 504.8 mm, vs 521 mm for G. carolinii. Obviously, this trend becomes even more pronounced when we figure in the second Giganotosaurus, in which case mean femur circumference for G. carolinii becomes 534.5 mm, 3% larger than the average of T. rex. In other words, it can be expected that, on average, Giganotosaurus was likely the heavier animal.

Comparing mass estimates between the two, The two specimens of Giganotosaurus end up as follows when using Campione et al.’s cQE (phylocor regression, with a correction factor of 2.01, for the femoral eccentricity of 1.1, seen in the holotype):
femur_circ      cQE_pcor_2.01

1        521          6349

2        548          7296

And the 12 specimens of T. rex end up as follows, using exactly the same settings for the mass estimation function to keep the comparison simple:
femur_circ      cQE_pcor_2.01

1         590          8942

2         534          6794

3         580          8531

4         515          6149

5         495          5514

6         505          5826

7         520          6315

8         483          5153

9         460          4505

10        480          5066

11        469          4752

12        426          3647

So even though the largest T. rex specimens, like Scotty (RSMP 2523.8, femur circumference 590 mm) and Sue (FMNH PR 2081, femur circumverence 580 mm), quite clearly seem to outmass even the bigger Giganotosaurus specimen by well over a ton, Giganotosaurus is actually about 0.9 t heavier on average (6.8 vs 5.9 t). And this is being cautious, because the T. rex specimens for which this is listed in Campione et al.,  tend to have higher femoral eccentricities than the 1.1 of G. carolinii used here, which would result in slightly lower mass estimates if accounted for (hence why the figures above ended up slightly higher than the published figures for T. rex.)

As for overall body size of the larger Giganotosaurus specimen, the holotype has been variously estimated at something from 12.2 m (e.g. Coria and Currie 2006) to 12.5 m (e.g. Coria and Salgado 1995). So this means an estimated total length somewhere between 12.8 and 13.1 m for the larger specimen. If we prefer a volumetric mass estimate, Hartman (2013, online) estimated the holotype at 6.8 t, so scaling up isometrically that would put us at about 7.9 t for MUCPv-95 (slightly higher than what is implied by the femur scaling, but hardly an extreme difference).

[summary] So in conclusion: I tried to estimate the relative size of the larger Giganotosaurus specimen in a reproducible manner using centroid sizes derived from geometric morphometrics, and it came out at approximately 5% larger than the holotype. Considering this, and that these are the only two substantial (there may be a few isolated teeth referred to it, but nothing major) fossils of Giganotosaurus, we can wager a good guess that these specimens represent fairly normal-sized individuals. While they are both likely considerably smaller (by mass) than the largest known T. rex individuals, Sue and Scotty, they appear to be demonstrably larger (by both mass and length) than the average T. rex, which has some bearing on the question of which is actually the largest theropod.

---Refs:

Adams, D., Collyer, M., Kaliontzopoulou, A. and Baken, E. 2022. geomorph: Geometric Morphometric Analyses of 2D/3D Landmark Data. .

Calvo, J.O. and Coria, R. 1998. New specimen of Giganotosaurus carolinii (Coria & Salgado, 1995), supports it as the largest theropod ever found. Gaia 15: 117–122.
Campione, N.E., Evans, D.C., Brown, C.M. and Carrano, M.T. 2014. Body mass estimation in non-avian bipeds using a theoretical conversion to quadruped stylopodial proportions. Methods in Ecology and Evolution 5 (9): 913–923.
Canale, J.I., Apesteguía, S., Gallina, P.A., Mitchell, J., Smith, N.D., Cullen, T.M., Shinya, A., Haluza, A., Gianechini, F.A. and Makovicky, P.J. 2022. New giant carnivorous dinosaur reveals convergent evolutionary trends in theropod arm reduction. Current Biology 32 (14): 3195-3202.e5.
Carrano, M.T., Benson, R.B.J. and Sampson, S.D. 2012. The phylogeny of Tetanurae (Dinosauria: Theropoda). Journal of Systematic Palaeontology 10 (2): 211–300.

Coria, R.A. and Currie, P.J. 2006. A new carcharodontosaurid (Dinosauria, Theropoda) from the Upper Cretaceous of Argentina. Geodiversitas 28 (1): 71–118.

Coria, R.A. and Salgado, L. 1995. A new giant carnivorous dinosaur from the Cretaceous of Patagonia. Nature 377 (6546): 224.

Persons, W.S., Currie, P.J. and Erickson, G.M. 2020. An older and exceptionally large adult specimen of Tyrannosaurus rex. The Anatomical Record 303 (4): 656–672.