Temnospondyli are a morphologically varied and ecologically diverse clade of tetrapods that survived for over 200 million years. The body mass of temnospondyls is a key variable in inferring their ecological, physiological, and biomechanical attributes. However, estimating the body mass of these extinct creatures has proven difficult because the group has no extant descendants. Here we apply a wide range of body mass estimation techniques developed for tetrapods to the iconic temnospondyls Paracyclotosaurus davidi and Eryops megacephalus. These same methods are also applied to a collection of extant organisms that serve as ecological and morphological analogues. These include the giant salamanders Andrias japonicus and Andrias davidianus, the tiger salamander Ambystoma tigrinum, the California newt Taricha torosa, and the saltwater crocodile, Crocodylus porosus. We find that several methods can provide accurate mass estimations across this range of living taxa, suggesting their suitability for estimating the body masses of temnospondyls. Based on this, we estimate the mass of Paracyclotosaurus was between 159 and 365 kg, and Eryops was between 102 and 222 kg. These findings provide a basis for examining body size evolution in this clade across their entire temporal span.

Graphic Double Integration. Silhouettes of all seven taxa were created based on lateral and dorsal views of the 3-dimensional skeletal meshes. The extent of soft tissue surrounding the skeletons was reconstructed based on comparisons with living examples (following Witzmann and Brainerd 2017). Pixel measurement of these silhouettes was carried out in GIMP v2.10.8 (The Gimp Development Team, 2019). Here, lines were drawn across the lateral and dorsal silhouettes (effectively creating dorsal and lateral cross-sections), and the number of pixels for each was recorded.

Three estimates were generated to accommodate variable body density assumptions. For the extant taxa, this included the raw estimate above (calculated assuming a neutral specific gravity of 1.0) and a second estimate based on the specific gravity of amphibians (1.05 for the salamanders) or crocodiles (1.06 for C. porosus) as outlined by Larramendi et al. (2020). The median of the two estimates above was calculated to generate a “mid” estimate for the extant taxa. For the temnospondyls, the specific gravities of amphibians and crocodiles were both applied to the volume estimate, which served to provide lower, middle, and upper estimates. 

Convex Hull. The 3-dimensional meshes of each specimen were split into functional elements, including the head, trunk, forelimb, hindlimb, and tail regions using MeshLab v2020.12 (Cignoni et al. 2008). The tail was divided into sections for skeletons with curved tails. Each element was converted to a convex hull polygon using Meshlab’s “Convex Hull” function (Figs. 1B, 1D, 1F, 1H, 1J, 1L, 1N) and saved as a point cloud. The point cloud was imported into MATLAB vR2021a (The Mathworks Inc., 2010), and the minimum convex hull volume was calculated using the “convhull” command. An additional convex hull estimate was generated for each of the four salamanders, employing a model which incorporated the head and body as a single functional element, instead of two separate elements. This was done to simulate the appearance of the animal in life. For the extant taxa, volumes were converted to mass by multiplying volumes by the specific gravity calculated by Larramendi et al. (2020) for amphibians and crocodiles. The temnospondyls were calculated using the specific gravity of crocodiles. The minimum convex hull volumes for each body region were summed and the total multiplied by 1.091, 1.206, and 1.322 (as per Sellers et al. 2012) to generate lower, mean, and upper body mass estimates, respectively.

Extant-scaling. Four extant-scaling algorithms originally devised for extant salamanders were applied (Pough 1980; Santini et al. 2018). The anteroposterior length from the end of the rostrum to the sacrum was used as an osteological correlate for snout-to-vent length (SVL), as the exact location of the cloaca cannot be obtained from skeletons. Pough’s second formula uses total length (TL) as the independent variable (see Pough 1980 for formulae). Santini et al. (2018) developed two length-to-mass scaling equations for salamanders, also using SVL, for paedomorphic and non-paedomorphic taxa (see Santini et al. 2018 for formulae). The mean absolute percentage error (MAPE) of these formulae, given by Santini et al. (2018), is 44.792%. This error was applied to all mass estimates based on Santini’s model to generate upper and lower error bounds.

Crocodyliform body mass has historically been estimated through several methods (see O’Brien et al. 2019 and references therein) that primarily focus on cranial or femoral dimensions. O’Brien et al. (2019) provide an extant-scaling equation (see O’Brien et al. 2019 for details) for predicting body mass based on head width (HW). Upper and lower estimates were calculated utilising the error of 0.193, as given by O’Brien et al. (2019). The second set of estimates was produced by reducing these results by 25%, as suggested by O’Brien et al. (2019). 

Farlow et al. (2005) outlined a range of measurements based on the femur of Alligator mississippiensis to create growth trajectories for estimating the mass of extinct mesoeucrocodylians. In our study, we use the equations based on femur length (FL), femur distal width (Fdw), femur distal height (Fdh), maximum diameter of proximal end of femur (Fpmx), minimum diameter of proximal end of femur (Fpmn), femoral minimum midshaft circumference (Fc), and distance from proximal articular end to fourth trochanter (Ftr). We followed the method outlined in Farlow et al. (2005, figure 2), to make these measurements. Furthermore, Farlow et al. (2005) also give regression equations for TL and head length (HL) and a multivariate equation (which utilises Ftr and FL). Refer to Farlow et al. (2005) for all formulae.

Finally, the body masses of included taxa were calculated using the stylopodial regression formula of Campione and Evans (2012), calculated using the “QE” function within the R v4.0.4 (R Core Team, 2021) package MASSTIMATE v2.0-1 (Campione et al. 2014; Campione 2020), wherein lower and upper estimates were also generated, based on a 25% Percentage Prediction Error (PPE). PPE was calculated using the “PE” function, also within the MASSTIMATE v2.0-1 (Campione et al. 2014; Campione 2020) package.