DOI: 10.5061/dryad.zcrjdfnfd
title: Dataset for: On the estimation of body mass in temnospondyls: A case study using the large-bodied Eryops and Paracyclotosaurus

description: 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.
description: <em>Graphic Double
 Integration</em>. 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
 <em>C. porosus</em>) as outlined by Larramendi <em>et
 al</em>. (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.  <em>Convex
 Hull</em>. 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 <em>et al.</em>
 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
 <em>et al.</em> (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 <em>et
 al.</em> 2012) to generate lower, mean, and upper body mass
 estimates, respectively.
 <em>Extant-scaling</em>. Four extant-scaling
 algorithms originally devised for extant salamanders were applied (Pough
 1980; Santini <em>et al.</em> 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 <em>et al.</em> (2018) developed two
 length-to-mass scaling equations for salamanders, also using SVL, for
 paedomorphic and non-paedomorphic taxa (see Santini <em>et
 al.</em> 2018 for formulae). The mean absolute percentage error
 (MAPE) of these formulae, given by Santini <em>et al.</em>
 (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 <em>et al.</em> 2019 and
 references therein) that primarily focus on cranial or femoral dimensions.
 O’Brien <em>et al.</em> (2019) provide an extant-scaling
 equation (see O’Brien <em>et al.</em> 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
 <em>et al.</em> (2019). The second set of estimates was
 produced by reducing these results by 25%, as suggested by O’Brien
 <em>et al.</em> (2019).  Farlow
 <em>et al.</em> (2005) outlined a range of measurements based
 on the femur of <em>Alligator mississippiensis</em> 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 <em>et al.</em> (2005, figure 2), to make
 these measurements. Furthermore, Farlow <em>et al.</em> (2005)
 also give regression equations for TL and head length (HL) and a
 multivariate equation (which utilises Ftr and FL). Refer to Farlow
 <em>et al.</em> (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 <em>et al.</em> 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 <em>MASSTIMATE</em> v2.0-1
 (Campione <em>et al.</em> 2014; Campione 2020)
 package.