A re-assessment of the osteology and phylogenetic relationships of the enigmatic, large-headed reptile Sphodrosaurus pennsylvanicus (Late Triassic, Pennsylvania, USA) indicates archosauriform affinities

Most Triassic terrestrial diapsids belong to two clades, Lepidosauromorpha or (the more diverse) Archosauromorpha. Nevertheless, the phylogenetic relationships of some Triassic diapsids have remained uncertain for decades because of the lack of preservation of phylogenetically relevant anatomical regions or because of unusual combinations of features. One of these enigmatic forms is the small-sized Sphodrosaurus pennsylvanicus from the Upper Triassic Hammer Creek Formation of the Newark Supergroup in Pennsylvania (USA). It was first identified as a procolophonid parareptile, later as a probable rhynchosaur archosauromorph, and more recently as an indeterminate neodiapsid. Here we revise the anatomy of Sphodrosaurus pennsylvanicus in order to include it for the first time in a quantitative phylogenetic analysis, which is focused on Permo–Triassic neodiapsids. Sphodrosaurus pennsylvanicus is recovered in this analysis as a doswelliid proterochampsian within Archosauromorpha. As a result, this taxon is added to the list of doswelliids known from the Carnian–Norian of the eastern and south-western USA. Previous authors recognized that the most unusual feature of Sphodrosaurus pennsylvanicus is its proportionally very large skull. Phylogenetic generalized least squares regressions confirmed that Sphodrosaurus pennsylvanicus has a larger skull than the vast majority of Permo–Triassic diapsids. Optimization in the phylogeny of the skull width to presacral length ratio shows the most likely scenario is that the extremely broad skull of Sphodrosaurus pennsylvanicus is autapomorphic, but it is not unique among archosauromorphs, being paralleled by hyperodapedontine rhynchosaurs and the proterochampsian Proterochampsa barrionuevoi. Exploration of a morphospace of linear measurements shows that Sphodrosaurus pennsylvanicus shares strong similarities with the probably semi-aquatic Proterochampsa barrionuevoi, suggesting that the former species may have had a similar mode of life. A linear discriminant analysis of ungual functional categories found that the only preserved ungual of Sphodrosaurus pennsylvanicus was suitable for digging or some other way of substrate processing.


Introduction
Most Late Triassic continental tetrapod assemblages are numerically dominated by diapsid reptiles. The vast majority of species that represent this diapsid diversity belong to different lepidosauromorph and archosauromorph groups (e.g. rhynchocephalians, tanystropheids, rhynchosaurs, allokotosaurs, dinosaurs, phytosaurs, aetosaurs, 'rauisuchians') (Brusatte et al. 2010;Evans & Jones 2010;Langer et al. 2010;Nesbitt et al. 2013Nesbitt et al. , 2022Ezcurra & Butler 2018;Ezcurra et al. 2021a;Spiekman et al. 2021). However, some taxa could not be clearly referred to any of these groups, resulting in uncertain phylogenetic relationships, or their phylogenetic positions have been controversial in recent decades (e.g. Pachystropheus rhaeticus: Huene 1935; Elachistosuchus huenei : Janensch 1949;Sphodrosaurus pennsylvanicus: Colbert 1960; Colobops noviportensis: Pritchard et al. 2018). These species are generally represented by specimens with limited anatomical information, which is the main reason for their uncertain phylogenetic position. Some of these Late Triassic enigmatic diapsids have been re-examined recently using modern technologies (e.g. computed tomography scanning) and/or updated comparisons with more recently described specimens (e.g. Sobral et al. 2015;Pritchard et al. 2018;Pritchard & Sues 2019;Scheyer et al. 2020). An improved understanding of the affinities of these species is important to account for the phylogenetic diversity of diapsids during their evolutionary radiation in the Late Triassic and to determine how the Triassic-Jurassic mass extinction impacted different clades.
Here we revise the phylogenetic relationships of one of these enigmatic Late Triassic diapsids, Sphodrosaurus pennsylvanicus from the Upper Triassic (Norian) Hammer Creek Formation in Lancaster County, Pennsylvania, USA (Fig. 1). The holotype of Sphodrosaurus pennsylvanicus consists of a partial skeleton originally preserved mostly as a natural mould in a block of hornfelsed mudstone (Fig. 2). This specimen was first reported by Price (1956) who, based on observations of colleagues, referred it to the procolophonoid parareptile Hypsognathus fenneri, but provided no anatomical justification for this identification. Subsequently, Colbert (1960) described and discussed the anatomy of the specimen in detail andalthough he initially had identified it as a specimen of Hypsognathusfound enough differences with other procolophonids to propose a new genus and species, Sphodrosaurus pennsylvanicus. Colbert (1960) based the procolophonid affinities of Sphodrosaurus pennsylvanicus mainly on the presence of a large skull and a 'frill' in the posterior region of the cranium, composed of what he considered quadratojugals, squamosals and tabulars, which resembled that of the most deeply nested procolophonids. Nevertheless, he noted that the great length and robustness of the hindlimb and the long, sharp pedal unguals clearly differ from the condition present in other known procolophonids.
The placement of Sphodrosaurus pennsylvanicus as a procolophonid was followed by Kuhn (1969) and Ivakhnenko (1979) in their systematic overviews of the group. Baird (1986) was the first to express doubts regarding the procolophonid affinities of Sphodrosaurus pennsylvanicus and instead considered this species a probable rhynchosaur. After this radical proposal, Paul Olsen (Lamont-Doherty Earth Observatory, Columbia University) removed the remaining fragments of bone in some regions of the natural mould. Subsequently, Peter Kroehler (National Museum of Natural History, Washington, DC) generated high-quality latex casts that presented exquisite and previously unavailable details of the anatomy of Sphodrosaurus pennsylvanicus. Sues et al. (1993) redescribed the skeletal structure and revised its phylogenetic affinities based on the information provided by these new casts. They concluded that the purported procolophonid-like 'frill' of the skull actually comprises the posterior regions of the hemimandibles and, thus, there was no evidence to support procolophonid affinities. They also could not find evidence in support of either rhynchosaurian or archosauromorph affinities. However, Sues et al. (1993) considered that the species could be referable to Neodiapsida based on the presence of an atlanto-occipital joint apparently positioned well anterior to the craniomandibular articulation, a slender and sigmoid femoral shaft, and possibly a forelimb proportionally shorter than the hindlimb and ventral keels on the cervical and anterior dorsal centra. As a result, Sues et al. (1993) interpreted Sphodrosaurus pennsylvanicus as Neodiapsida incertae sedis, but clearly distinguishable from other known diapsids because of a unique combination of character states, namely the presence of a proportionally very large head, atlanto-occipital joint anterior to craniomandibular joint, external surface of mandibular bones distinctly ornamented, and cervical and anterior dorsal centra with strongly developed ventral keels. The phylogenetic relationships of Sphodrosaurus pennsylvanicus among neodiapsids have remained enigmatic ever since. Here we revise the phylogenetic relationships of Sphodrosaurus pennsylvanicus based on new observations of its anatomy, comparisons with the large amount of new data about Triassic diapsids that have become available in the last three decades, and its inclusion for the first time in a quantitative phylogenetic data set focused on Permo-Triassic neodiapsids.

Phylogenetic analysis
To test the phylogenetic relationships of Sphodrosaurus pennsylvanicus, we scored this species in the phylogenetic data matrix of the CoArTreeP (the Complete Figure 2. Holotype of Sphodrosaurus pennsylvanicus. A, photograph in natural colour and B, inverted colour. Abbreviations: lcr, left cervical ribs; lhm, left hemimandible; lpt, left pterygoid; lra, left radius; lsg?, possible left shoulder girdle; lul, left ulna; mttI-III, metatatsals I-III; PS23, presacral vertebra 23; rco, right coracoid; rcr, right cervical ribs; rdII, right digit II; rfe, right femur; rhm, right hemimandible; ril, right ilium; ris, right ischium; rpt, right pterygoid; rpu, right pubis; rsc, right scapula; rti, right tibia; S1, sacral vertebra 1. Units in the rulers are in cm. Archosauromorph Tree Project; see Ezcurra [2016] for the first iteration of this project). This is the most extensive phylogenetic dataset currently available for Permian and Triassic archosauromorphs, and it has been shown to be useful for determining the relationships of taxa either within Archosauromorpha and/or their inclusion among early Lepidosauromorpha or non-saurian neodiapsids (e.g. Scheyer et al. 2020;Ezcurra et al. 2022). The character and taxonomic sample of this matrix has been expanded multiple times in recent years (e.g. Ezcurra et al. 2017Ezcurra et al. , 2020aEzcurra et al. , b, 2021aNesbitt et al. 2017;Sengupta et al. 2017;Ezcurra & Butler 2018;Wynd et al. 2019;Scheyer et al. 2020;Sues et al. 2021). Some of these expansions were conducted independently, and there is no currently available data matrix that integrates all the information in a single data set. Thus, we merged all of these recent datasets in this paper. We deactivated the following 40 terminals before the tree searches because they were scored only for the purpose of morphological disparity analyses, are not diagnostic at the species level, or are combinations of operational Characters 9 and 119 were also removed (following Ezcurra et al. [2017] and Butler et al. [2019a]).
We also modified 60 characters, added 40 characters, and added seven terminals that were not present in previous versions of this data matrix: the Palaeozoic diapsid Orovenator mayorum, the lepidosauromorphs Marmoretta oxoniensis and Huehuecuetzpalli mixtecus, the pseudosuchian archosaur Revueltosaurus callenderi, and the enigmatic diapsids Elachistosuchus huenei, Feralisaurus corami and Sphodrosaurus pennsylvanicus.
The matrix of discrete morphological characters was analysed under equally weighted (eqWs) and implied weighted (IWs; k ¼ 3, 7, 10) maximum parsimony using TNT v. 1.5 (Goloboff et al. 2008;Goloboff & Catalano 2016). The search strategy initially used a combination of the tree-search algorithms sectorial searches, drifting (five iterations), and tree fusing (one round) for each replication, until 100 hits (using four initially unconstrained replications as starting point) of the same minimum tree length were achieved (not collapsing trees during search, multiplying trees by fusing after hitting best score, and saving no more than one tree per replication)all these parameters are default settings. The shortest trees obtained and retained in memory were then subjected to a final round of tree bisection and re-connection branch swapping. Zerolength branches in any of the recovered most parsimonious trees (MPTs) were collapsed into polytomies. Branch support was quantified using decay index (Bremer support) values and a bootstrap resampling analysis, with 1000 pseudo-replicates and reporting both absolute and GC ('Group present/Contradicted'; i.e. the difference between the frequencies of recovery in pseudo-replicates of the clade in question and the most frequently recovered contradictory clade) frequencies (Goloboff et al. 2003). Finally, analyses forcing topological constraints were conducted to find the minimum number of steps necessary to force alternative sub-optimal positions for Sphodrosaurus pennsylvanicus. The monophyletic groups and specific positions in which Sphodrosaurus pennsylvanicus was forced are detailed in the Discussion section.

Skull size analyses
The proportionally large skull of the holotype of Sphodrosaurus pennsylvanicus is one of the most unusual features of this species. However, previous discussions about the relative size of the skull were based on qualitative comparisons and lacked an explicit phylogenetic context (Colbert 1960;Sues et al. 1993). Unfortunately, the skull of Sphodrosaurus pennsylvanicus is represented only by the posterior region of the palate and both hemimandibles. Thus, it is not straightforward to determine how large the skull is in comparison to those of other Triassic diapsids and how allometry may have influenced its proportional size in comparison to the postcranium.
The preserved posterior region of the skull of Sphodrosaurus pennsylvanicus only allows the measurement of widths to use as proxies for skull size. The maximum cranial width is more commonly recorded for Triassic diapsids than the maximum mandible width because the hemimandibles are commonly disarticulated and displaced from each other. We lack direct information regarding the cranial width of Sphodrosaurus pennsylvanicus because the bones of the lower temporal region are not preserved. However, the right hemimandible seems to be in natural position with respect to the palate, because the external edge of the lateral ramus of the pterygoid is overlapped by the hemimandible and the quadrate ramus of the pterygoid is directed towards the glenoid region of the hemimandible. In particular, the latter indicates that the hemimandible is not displaced posteriorly or skewed anteromedially to posterolaterally with respect to the palate, because the quadrate ramus of the pterygoid and the pterygoid ramus of the quadrate would form a relatively straight line between the main body of the pterygoid and the mandibular glenoid fossa. Since the maximum width of the mandible is slightly narrower than the cranium in articulated diapsid skulls, we calculated the maximum skull width of Sphodrosaurus pennsylvanicus as twice the maximum width between the lateral-most margin of this hemimandible and the mid-width of the palate. This should be considered an estimate of maximum skull width, possibly slightly lower than the actual value, because slight displacement of the hemimandible with respect to the palate cannot be completely ruled out. We choose the  Sues et al. (1993). Abbreviations: I-III, pedal digits I-III; ga, gastralia; lcr, left cervical ribs; lhm, left hemimandible; lpu, left pubis; lra, left radius; lsg?, possible left shoulder girdle; lul, left ulna; pt, pterygoid; rcr, right cervical ribs; rfe, right femur; rhm, right hemimandible; ril, right ilium; ris, right ischium; rpu, right pubis; rsc, right scapula; rti, right tibia; S1, sacral vertebra 1; sr, sacral rib. Scale bar: 5 cm. total length of the presacral vertebral series as a proxy for postcranial size because it is completely preserved in Sphodrosaurus pennsylvanicus. Previous studies of archosauromorph body size have used the femoral length as a proxy (e.g. Sookias et al. 2012;Turner & Nesbitt 2013;Pradelli et al. 2022), but the proximal end of the femur of Sphodrosaurus pennsylvanicus is damaged (Fig. 3). Nevertheless, we also conducted the following analyses using femoral length as the independent variable to test whether the results were congruent with those recovered using the presacral vertebral length.
We used phylogenetic generalized least squares (pGLS) regressions between these variables to explore whether Sphodrosaurus pennsylvanicus is an outlier, accounting for the phylogenetic non-independence of species, in a broad taxonomic sample of Permo-Triassic diapsid taxa scored in our phylogenetic analysis. The regressions were conducted for the complete sample of MPTs found under eqWs and IWs (k ¼ 10) (5600 and 75 MPTs, respectively; see Results). The regressions were conducted with the function 'gls' of the R package nlme (Pinheiro et al. 2021) with an expected covariance under a Brownian model and a variance function with fixed variances from the diagonal of the variance-covariance matrix of the time-calibrated phylogenetic tree. Each of these trees was time-calibrated using the minimum branch length (mbl) method with three different minimum branch lengths: 0.1, 0.5 and 1 million yearshigher mbl values resulted in a calibration of the origin of Archosauromorpha older than that estimated by previous studies (i.e. >260 Mya; Ezcurra et al. 2014). The time calibrations were conducted with the function 'timePaleoPhy' of the R package paleotree (Bapst 2012). Species without either of the two measurements used for these regressions were pruned only after the time calibration of the trees to retain the temporal information provided by all taxa. To reduce computational times, the topology and branch lengths of the pruned trees were compared to each other with the function 'unique.multiPhylo' of the R package ape (Paradis & Schliep 2019), and repeated trees were deleted. The pGLS regressions were conducted on these trees. We selected manually two of the MPTs recovered under eqWs and one of the trees found under IWs (k ¼ 10), because they include the topological differences in the interrelationships among the species more closely related to Sphodrosaurus pennsylvanicus, each calibrated with mbl values of 1 My and 0.1 My, to graph the pGLS residuals more clearly.
The ratio between skull width and presacral vertebral length was optimized on one of the two topologies found under equal weights and the topology recovered under implied weights (to reduce computational times), each calibrated with mbl values of 1 My and 0.1 My, using the 'contMap' function of the R package phytools, which uses maximum likelihood as the optimality criterion (Revell 2012). Finally, the phylogenetic signal, local indicator of phylogenetic association (local Moran's I), and phylogenetic correlogram of the skull width-presacral length ratio were calculated for the two above-mentioned phylogenies calibrated with mbl of 1 My and 0.1 My using the 'phyloSignal', 'lipaMoran' and 'phyloCorrelogram' functions, respectively, of the R package phylosignal (Keck et al. 2016). All these analyses and graphics were conducted in R 4.1.1 (R Development Core Team 2021), and the files and codes are available in Supplemental material 3.

Morphospace exploration
We used the femoral and tibial length in addition to the skull width and presacral length to build a three-dimensional morphospace of linear measurements and expand the quantitative comparisons with other taxa beyond the skull width-to-postcranium relationship. The partially preserved skeleton of Sphodrosaurus pennsylvanicus limits the number of informative measurements that could be taken from the specimen. Thus, we decided to use the ratio of femoral length to tibial length and the ratio of femoral þ tibial length to presacral length to generate a biplot showing the relationship between the posterior stylopodium and zeugopodium and the postcranial presacral length. A heatmap depicting the ratio of skull width to presacral length was superimposed on the biplot to generate a three-dimensional morphospace to show the interrelationships among the skull, presacral vertebral, and hindlimb variables. The heatmap was built with the function 'filled.contour' of the R package akima (Akima & Gebhardt 2021), and the graphic was built in R 4.1.1 (R Core Team 2021) after the log10 transformation of the variables. Files and codes are available in Supplemental material 4.

Pedal ungual functional morphology analysis
The possible function of the only available pedal ungual of Sphodrosaurus pennsylvanicus was studied quantitatively using the database and analyses described by Thomson & Motani (2021). This analysis was originally based on a data set of keratinous claw sheaths of extant amniote specimens, but there is a strong correlation between the shape of the bony ungual and the keratinous sheath. Mann et al. (2021) recently used this analysis to assess the functional morphology of the ungual of a late Carboniferous eureptile, and this procedure is followed here (see Mann et al. [2021] for a discussion of the caveats associated with the use of bony unguals in this analysis). Due to preservational limitations (see Mann et al. 2021), we used nine linear measurements and one angular variable to sample the shape of the unguals. These variables were quantified for 76 extant amniote species and Sphodrosaurus pennsylvanicus following the methods described by Thomson & Motani (2021). The two outlier taxa (Gopherus and Cyclopes) were removed from the data set prior to the analyses to avoid biasing the results (Mann et al. 2021). The data set was log 10 transformed and subjected to a pGLS regression, with the dorsal curve length of the ungual as the independent variable, using the 'procD.pgls' function of R package geomorph v. 3.3.1 (Adams et al. 2021). The phylogeny used for the pGLS was taken from Thomson & Motani (2021) with the addition of Sphodrosaurus pennsylvanicus after the results of our phylogenetic analyses. Subsequently, the pGLS residuals were subjected to a linear discriminant analysis (LDA) using the 'lda' function of the R package MASS v. 7.3.51.6 (Venables & Ripley 2002) to determine the major axes of between-group variation in the extant taxa and whether the ungual of Sphodrosaurus pennsylvanicus could be assigned to any of the eight functional groups proposed by Thomson & Motani (2021): amplectorial (grasping), cursorial (running or hopping), generalist (multipurpose), gryporial (hook-and-pull digging), scalporial (scratch digging), scansorial (climbing), suspensorial (hanging) and tenasorial (grappling). The misidentification rate of the LDA was calculated using a confusion matrix. The pGLS residuals for Sphodrosaurus pennsylvanicus were projected into a plot showing the first two linear discriminant axes using the function 'predict' of R employing all equal priors (prob ¼ 0.125). All these analyses and graphics were Abbreviations: an, angular; an.tub, angular tuberosities; co, coronoid; dt, dentary; dt.tub, dentary tuberosities; FIC, foramen intermandibularis caudalis; gr, groove; pra, prearticular; rap, retroarticular process; ri, ridge; spl, splenial. Scale bars: A, B ¼ 5 mm; C-F ¼ 2 mm. conducted in R 4.1.1 (R Core Team 2021) using the codes of Thomson & Motani (2021). Files and codes are available in Supplemental material 4.
Emended diagnosis. Sphodrosaurus pennsylvanicus is a small-sized reptile (presacral vertebral column length c. 136 mm and femoral length c. 57 mm) that differs from other known neodiapsids in the following combination of character states (autapomorphies among non-archosaurian archosauriforms indicated with an asterisk): skull proportionately very large, with a skull width-presacral vertebral series length ratio of c. 0.44 (similar ratio present in hyperodapedontine rhynchosaurs and a larger ratio present in Proterochampsa barrionuevoi); absence of external mandibular fenestra (shared by Doswellia kaltenbachi); external surface of posterior mandibular bones distinctively sculptured by longitudinal ridges and grooves (also present in Proterochampsa barrionuevoi); angular with laterally projecting ridge that separates lateral and ventral sides on the ventrolateral surface of the bone (also present in Tropidosuchus romeri and rhadinosuchines); ridge on the ventrolateral surface of the angular and posterior end of dentary with rounded, low tuberosities Ã ; angular and posterior end of the dentary with a well-defined longitudinal groove that has a smooth surface Ã ; angular and prearticular with sub-equal dorsoventral contribution to the medial wall of the postdentary region of the hemimandible Ã (also present in phytosaurs); retroarticular process restricted to the ventral half of the hemimandible Ã (also present in phytosaurs) and ventrolaterally oriented in lateral view Ã ; presacral vertebrae 3-12 with large parapophysis occupying half or more of the anteroposterior length of the centrum/base of neural arch Ã ; cervical rib shafts plate-like, strongly compressed Ã ; dorsal vertebrae with a well-developed ventral keel restricted to the anterior two-thirds of the series Ã ; proportionally short posterior dorsal vertebrae, with a centrum length-height ratio of $1.33 (measured on the 19th presacral vertebra; also present in Chanaresuchus bonapartei and several other archosauriforms); dorsal vertebrae with ventral margin of synapophysis positioned partially on lateral surface of centrum Ã ; scapula with distal half of the blade with a convex anterior margin Ã ; plate-like pubis without anterior apron (also present in Doswellia kaltenbachi); and metatarsal II with a deeply grooved anteromedial surface for reception of metatarsal I (also present in Tropidosuchus romeri).

Anatomical revision
The holotype of Sphodrosaurus pennsylvanicus has previously been described in detail by Colbert (1960) and Sues et al. (1993). The latter authors corrected some previous misinterpretations and added a substantial number of new anatomical details based on the repreparation of the specimen and new latex casts. Thus, we consider that it is not necessary to provide another complete redescription of Sphodrosaurus pennsylvanicus.
Here we will focus on anatomical regions that required a more detailed description or where we provide a different interpretation from that by previous authors. These descriptions are complemented with comparisons with other Triassic terrestrial diapsids, mainly those published during the last 30 years. These re-descriptions and comparisons are intended to provide new information to discuss the phylogenetic relationships of Sphodrosaurus pennsylvanicus.
General state of preservation. The holotype of Sphodrosaurus pennsylvanicus is preserved as a natural mould of a partial skeleton in ventral view (Figs 2, 3). As a result, the dorsal surface of the palate, the dorsal margins of the hemimandibles, the neural arches of the vertebrae, and the lateral surfaces of the femur and tibia are not exposed. Some of the bones are partially preserved or embedded in matrix, as is the case for part of the shoulder girdle, left anterior zeugopodium, right posterior autopodium and some ribs. No osteoderms could be identified in the specimen.
Palate. The right pterygoid of Sphodrosaurus pennsylvanicus preserves the lateral ramus and the proximal half of the posterolateral (or quadrate) ramus (Figs 2, 3; Table 1). The posterior margin of the lateral ramus extends directly laterally based on the orientation of the vertebral series and the relationship with the right hemimandible and the preserved region of the left pterygoid. A laterally oriented lateral ramus of the pterygoid occurs in most archosauromorphs (Ezcurra 2016 Gower 1999). There is no evidence of palatal teeth on the lateral ramus of the pterygoid of Sphodrosaurus pennsylvanicus, and palatal teeth are absent in this region in lepidosauromorphs, some tanystropheids, Malerisaurus langstoni, rhynchosaurs, Teyujagua paradoxa, erythrosuchids and eucrocopod archosauriforms (Ezcurra 2016;Schoch & Sues 2018;Simões et al. 2018;Pinheiro et al. 2020;Nesbitt et al. 2022).
Lower jaw. The lateral surface of the hemimandibles bears a series of prominent ridges that have an anteroposterior main axis and generally form an anastomizing pattern (Fig. 4A, B; Table 1). This kind of ornamentation closely resembles that present in the proterochampsian Proterochampsa barrionuevoi (PVSJ 77). Coarse ornamentation is also present on the lateral surface of the postdentary bones of the doswelliids Doswellia kaltenbachi and Rugarhynchos sixmilensis (Dilkes & Sues 2009;Wynd et al. 2019). However, the mainly anteroposteriorly oriented ridges of Rugarhynchos sixmilensis are restricted to the posterior region of the surangular (Wynd et al. 2019) and the sculpture of Doswellia kaltenbachi is extensive but it has a reticular pattern (Dilkes & Sues 2009). The postdentary bones of rhadinosuchine proterochampsids have a mostly smooth external surface, with the exception of a ridge that extends along the suture between the surangular and angular and another ridge that extends along the ventrolateral surface of the angular (Dilkes & Arcucci 2012). The position of the suture between the surangular and angular, and thus the presence of the former ridge, cannot be determined in Sphodrosaurus pennsylvanicus. However, a ridge in the same position as the ventrolateral ridge on the angular of rhadinosuchines occurs in Sphodrosaurus pennsylvanicus (Fig. 4A, B: ri), but this structure also extends onto the dentary in the latter species (see below). The posterior end of this ridge has a flat, smooth surface in Sphodrosaurus pennsylvanicus, but, more anteriorly, it bears a series of rounded, very low and laterally oriented tuberosities ( Fig. 4C: an.tub).
A longitudinal groove with a smooth surface is present immediately dorsal to the ventrolateral ridge on both hemimandibles of Sphodrosaurus pennsylvanicus (Fig. 4A, B: gr) and, as far as we are aware, this feature seems to be unique for this species. The posterior end of this groove narrows dorsoventrally and bows dorsally, matching the slightly dorsally concave ventral margin of this region of the hemimandible. Sues et al. (1993) reported that the retroarticular process was not distinct in Sphodrosaurus pennsylvanicus. We confirm that the retroarticular process is very short, and it is also dorsoventrally very low, being restricted to the ventral third of the hemimandible (Fig. 4A, B: rap). A similar, ventrally restricted retroarticular process is present in phytosaurs (e.g. Stocker et al. 2017), but the process is slightly ventrolaterally oriented in Sphodrosaurus pennsylvanicus. No suture between bones can be identified on the lateral surface of the hemimandibles of Sphodrosaurus pennsylvanicus, which is probably due to the coarse ornamentation on the bones.
The right hemimandible preserves a more anterior region than the left one, and it is inferred that it should include the posterior portion of the dentary ( Fig. 4B; see below). The ventrolateral groove of the angular does not extend onto this region of the mandible and the external surface of the dentary is sculptured by very shallow but well-defined, sub-circular to sub-oval depressions of variable size and distributed without a distinct pattern. The dorsal margin of the dentary bears four rounded tuberosities, which have an anteroposterior main axis ( Fig. 4B: dt.tub). The three anterior tuberosities are arranged close to each other and separated by a transverse groove. There is no evidence to suggest that these tuberosities are the bases of broken teeth, and thus they are identified here as bony sculpturing.
The medial surface of the hemimandibles was not described in previous accounts of the anatomy of Sphodrosaurus pennsylvanicus, but it is well preserved and informative (Fig. 4E, F). The dorsal regions of both hemimandibles are obscured due to a lack of preservation or the bone entering into the matrix. In contrast to the heavily sculptured external surface, the inner surface of the lower jaw is smooth. The posterior region of the hemimandible is sub-equally divided dorsoventrally by a mostly longitudinal and slightly sigmoidal suture between the prearticular and the angular. A similarly extensive contribution of the angular to the medial surface of the hemimandible, ventral to the adductor fossa, Abbreviations: I-1, pedal phalanx I-1; ac, acetabulum; dfe, damaged femoral margin; fe, femur; ft, fourth trochanter; il, ilium; is, ischium; isp, ischial peduncle; mc, medial condyle; mttII, metatarsal II; popa, postacetabular process; pu, pubis; ti, tibia. Scale bars: A, D ¼ 5 mm; B ¼ 2 mm; C ¼ 1 mm.
is also present in phytosaurs (Bona et al. 2022). The suture between the prearticular and angular cannot be identified on the posterior tip of the hemimandible and terminates anteriorly on the posterior margin of an anteromedially facing foramen intermandibularis caudalis (Fig. 4E, F: FIC). This foramen occurs in disparate diapsid clades, being present in the non-saurians Orovenator mayorum (Ford & Benson 2019), Claudiosaurus germaini (Carroll 1981) : Norman 2020). Both prearticular and angular contribute to the posterior margin of the FIC, resembling the condition in Gephyrosaurus bridensis, Trilophosaurus buettneri and phytosaurs. As in Trilophosaurus buetteneri and early archosaurs, the anterior margin of the FIC of Sphodrosaurus pennsylvanicus is delimited by the splenial. By contrast, the FIC is completely enclosed by the prearticular in non-saurian diapsids and at least the vast majority of hyperodapedontine rhynchosaurs.
Both the prearticular and angular have a sub-triangular, anteriorly tapering anterior end in medial view. The anterior end of the prearticular fits between the coronoid bone and the posterior end of the splenial and the angular fits between the splenial and the dentary. The presence of an unexpanded and straight anterior end of the prearticular resembles the condition in Proterochampsa barrionuevoi (PVSJ 77) and phytosaurs (e.g. Nicrosaurus kapffi: NHMUK PV R42744). The presence of a coronoid bone in Sphodrosaurus pennsylvanicus is established here because of distinct sutures separating it from the splenial and prearticular as well as the presence of a distinctly convex surface that is absent in surrounding bones. The presence of a coronoid bone as an independent post-embryonic mandibular ossification occurs in non-saurian Palaeozoic neodiapsids, choristoderans, early-diverging lepidosauromorphs and Triassic archosauromorphs with the exception of aetosaurs and pterosaurs (Bona et al. 2022), whereas the coronoid bone has not been identified to date in the archosauromorph genus Tanystropheus .
The more anterior regions of both hemimandibles of Sphodrosaurus pennsylvanicus have a distinct longitudinal suture that separates the broadly exposed splenial from another, ventrally restricted bone in medial view. This suture is anterior to the FIC, extends anterior to the level of the coronoid bone, and then reaches the anterior end of the preserved portion of the hemimandible. As a consequence, this is strong evidence for the preservation of the dentaries in Sphodrosaurus pennsylvanicus. One of the most interesting implications of the preservation of the posterior region of the dentary is that there is no external mandibular fenestra. Such a mandibular opening is present in Teyujagua paradoxa (Pinheiro et al. 2016), and it is a symplesiomorphy of Archosauriformes (Gauthier et al. 1988). The loss of an external mandibular fenestra is uncommon among known Triassic archosauriforms, occurring only in Doswellia kaltenbachi (Weems 1980;Dilkes & Sues 2009) and pterosaurs (with the exception of Austriadraco dallavecchiai; Wellnhofer 2003). The suture between the dentary and splenial curves gradually ventrally towards the anterior end of the lower jaw, and, at the anterior end of the preserved region of the right hemimandible, it is already positioned on the ventral margin (Fig. 4D).
Position of the atlanto-occipital joint. Colbert (1960) described the posterior region of the skullboth hemimandiblesof Sphodrosaurus pennsylvanicus as extending as far back as about the fourth or fifth cervical vertebra. This condition, and the recognition of both pterygoids as very likely in natural position with respect to each other and the hemimandibles, led Sues et al. (1993) to suggest that, although the basicranial region was not preserved, the atlanto-occipital joint would have been placed well forward of the craniomandibular joint. However, we doubt that this condition can actually be determined in Sphodrosaurus pennsylvanicus. The basal articulation between the pterygoid and basipterygoid process of the basisphenoid or parabasisphenoid is positioned level with the base of the posterolateral (or quadrate) ramus of the pterygoid in diapsids. In Sphodrosaurus pennsylvanicus, the atlas is positioned only a few millimetres posterior to the level where the basal articulation should be located (Figs 2, 3). This does not leave room for the basicranial bones and, thus, we interpret that the vertebral series is preserved forward from its natural position. The parasphenoid/basisphenoid and basioccipital have different proportional lengths in diapsids and, as a result, we think that the position of the atlanto-occipital joint with respect to the craniomandibular articulation cannot be determined with confidence.
Presacral vertebrae. We confirm the count of 23 presacral vertebrae of Sues et al. (1993;contra Colbert 1960), and the first sacral vertebra is articulated with the presacral series (Colbert 1960) (Figs 2, 3, 5; Table  2). The length of the cervical series is 29.8 mm, that of the dorsal series is 106.2 mm, and that of the complete presacral series is 136.0 mm (lengths measured as the sum of each of the centrum lengths). The identification of the position of the cervico-dorsal transition is difficult because of the limited exposed surface of each vertebra and the dorsoventral compression of the specimen, which has affected the orientation of the ribs. It is possible that Sphodrosaurus pennsylvanicus has seven cervical vertebrae based on the location of the shoulder girdle with respect to the vertebral series and the position of the first rib with an orientation mainly orthogonal to the vertebral series (Figs 2, 3). However, this count should be considered speculative. The atlantal intercentrum is displaced a few millimetres anterior to the axial intercentrum and centrum (Fig. 5A, B). It (Fig. 5B: atlint) has a transversely concave posteroventral surface for the reception of the axial intercentrum. A poorly preserved bone to the left of the atlantal intercentrum may represent an atlantal neural arch, but it cannot be confidently identified ( Fig. 5B: atlna?). A transversely elongated bone, with a ventral median apex, is preserved on the right half of the anteroventral margin of the axial centrum. This bone is interpreted as the axial intercentrum ( Fig. 5B: axint), and its displacement relative to the midline indicates that it was not fused to the axial centrum. The right lateral surface of the axial centrum has an anteriorly positioned, sub-triangular parapophysis with a posterior apex. The pronounced median longitudinal keel of the axis (Sues et al. 1993) extends ventrally slightly beyond the ventral rims of the centrum, as also on the fourth and sixth to ninth presacral vertebrae (the condition on the fifth cervical vertebra cannot be determined due to damage; Fig. 5A The anterior or posterior articular surface of the centrum is sufficiently exposed on presacral vertebrae 13, 14 and 17-19 to determine that they are amphicoelous and not notochordal (Fig. 5D, E). By contrast, notochordal centra occur in Palaeozoic non-saurian diapsids, rhynchocephalian lepidosauromorphs and the Permian archosauromorph Aenigmastropheus parringtoni . We confirm the absence of postaxial intercentra in Sphodrosaurus pennsylvanicus, which is an apomorphy of Archosauromorpha present in most Permo-Triassic species Ezcurra 2016).
The cervical vertebrae are proportionally short anteroposteriorly (Figs 2, 3; Table 2), contrasting with the elongated cervical vertebrae of Protorosaurus speneri (Gottmann-Quesada & Sander 2009), tanystropheids and dinocephalosaurids (Spiekman et al. 2021), some allokotosaurs (Sen 2003;Nesbitt et al. 2022), Prolacerta broomi (Gow 1975), Litorosuchus somnii (Li et al. 2016), the doswelliids Jaxtasuchus salomoni, Doswellia kaltenbachi and Rugarhynchos sixmilensis (Weems 1980;Dilkes & Sues 2009;Schoch & Sues 2014;Wynd et al. 2019) and most archosaurs. The parapophysis quickly migrates dorsally in the cervical series and is placed on the anterodorsal corner of the centrum by the sixth vertebra (Fig. 5A: pa). It is anteroposteriorly long, occupying the anterior half or more than half of the anteroposterior length of the centrum from the third to the twelfth presacral vertebrae (Fig. 5A, C: pa). This condition differs from that in other known diapsids. The diapophysis is well exposed on the left side of the fifth and sixth cervical vertebrae (Fig. 5A: di). It is completely situated on the neural arch and extends slightly laterally beyond the level of the lateral margin of the respective centrum. No other diapophyses are exposed, but the position of the ribs with respect to the vertebrae, including a rib with its capitulum articulated to its respective parapophysis in presacral 11 (Fig. 5C), indicates that the diapophyses of the middle dorsal vertebrae are considerably shorter than those of Doswellia kaltenbachi (Dilkes & Sues 2009). The anterior-middle dorsal vertebrae have a shallowly concave surface between the ventral keel and dorsolateral margin of the centrum, lacking the well-defined lateral fossa present in several suchian pseudosuchians (Ezcurra 2016). There is no subcentral foramen on the presacral vertebrae of Sphodrosaurus pennsylvanicus. The presence or absence of laminae cannot be determined because of the limited exposure of the neural arches.
Presacral ribs. Cervical ribs are preserved along both sides of and parallel to the cervical vertebrae (Colbert 1960;Sues et al. 1993; Figs 2, 3, 5A; Table 2). One of the left ribs has a slightly expanded proximal end, probably representing the part that bears an articular facet for its respective vertebra (Fig. 5A: per). Only the shafts are exposed on the other cervical ribs; three rib shafts are preserved on the right side and four or five on the left side (the probable fifth shaft is only a fragment with its major axis parallel to the other shafts). The presence of an accessory anterior process, which is an archosauromorph synapomorphy Ezcurra 2016), cannot be determined on the preserved elements. The cervical rib shafts extend parallel to each other and overlap the ventromedial surface of the preceding element in ventral view. The ribs are very long, in which the longest rib is four times the length of the anterior-middle postatlantal cervical vertebrae (Colbert 1960). As a result, four or more cervical rib shafts extend parallel to each other at the same anteroposterior level of the neck. The presence of elongated cervical ribs, two or more times longer than their respective vertebrae and parallel to the neck, is a condition widely distributed among archosauromorphs, but it is absent in non-saurian neodiapsids and lepidosauromorphs (Gauthier 1986;Nesbitt 2011;Pritchard et al. 2015;Ezcurra 2016). The cervical rib shafts of Sphodrosaurus pennsylvanicus are strongly dorsoventrally compressed, contrasting with the rod-like shafts of early diapsids and saurians.
The posterior cervical and dorsal rib shafts are gradually bowed throughout their length, contrasting with the sharp, right-angle bent present in the anterior and middle dorsal ribs of the doswelliids Doswellia kaltenbachi and Jaxtasuchus salomoni (Dilkes & Sues 2009;Schoch & Sues 2014). The posterior surface of the middle dorsal rib shafts of Sphodrosaurus pennsylvanicus has a welldefined longitudinal groove. The proximal ends of the dorsal ribs are sufficiently exposed to determine that they are dichocephalous back to at least the 17th presacral position, where a very short capitulum and a longer tuberculum are present. Dichocephalous anterior and middle dorsal ribs are also present in erythrosuchids and eucrocopods (Hughes 1963;Ezcurra 2016). By contrast, nonsaurian diapsids and lepidosauromorphs all have holocephalous dorsal ribs, and most non-archosauriform archosauromorphs have dichocephalous ribs restricted to the anterior third of the trunk series.

Gastralia and sacrum.
There is no new anatomical information or comparison to provide here about these anatomical regions.
Shoulder girdle. Colbert (1960) and Sues et al. (1993) identified a partially exposed and crushed right shoulder girdle (Figs 2, 3, 6A, B, D; Table 3). We agree with this interpretation. The anterior end of the proximal end of the scapula is not exposed, and only the posterior Table 2. Measurements (in mm) of the postcranial axial skeleton on the latex cast of the holotype of Sphodrosaurus pennsylvanicus. Asterisks indicate incomplete measurements, where the value given is the maximum measurable. Abbreviations: PS, presacral; S, sacral. The maximum deviation of the digital calliper is 0.02 mm, but measurements were rounded to the nearest 0.1 mm. Atlantal intercentrum width 5.5 Axial centrum length 5.7 PS3 centrum length 5.7 PS4 centrum length 5.5 PS5 centrum length 5.0 PS6 centrum length 4.9 PS7 centrum length 5.0 PS8 centrum length 4.6 PS9 centrum length 5.3 PS10 centrum length 5.8 PS11 centrum length 5.8 PS12 centrum length 5.9 PS13 centrum length 6.5 PS14 centrum length 5.1 Ã PS15 centrum length 6.4 PS16 centrum length 6.0 PS17 centrum length 6.4 PS18 centrum length 6.9 PS19 centrum length 6.8 PS20 centrum length 6.8 PS21 centrum length 7.0 PS22 centrum length 6.5 PS23 centrum length 6.3 PS9 centrum posterior width 6.7 PS12 centrum posterior width 6.1 PS13 centrum posterior width 6.2 S1 centrum length 6.6 Longest cervical rib length 22.1 Ã Longest dorsal rib length (PS7/8) 55.3 margin of the base and the anterior and anterodistal margins of the distal end of the scapular blade are exposed (Fig. 6B). This shows that the scapular blade is very long (Colbert 1960), the anterior margin of its distal half is convex, and it does not expand anteriorly at its distal end. However, we cannot determine the complete anteroposterior width of the blade at its base or whether the distal end of the blade expands posteriorly, because these regions are covered with matrix. The absence of an anterior expansion of the distal end of the scapular blade resembles the condition in non-saurian diapsids (e.g.  Nesbitt et al. 2009). By contrast, rhynchosaurs, allokotosaurs, non-archosaurian eucrocopods, Triassic pseudosuchians and most early avemetatarsalians have an anterodistal expansion that gives the anterior margin of the blade a concave profile in side view (Nesbitt 2011;Nesbitt et al. 2015;Ezcurra 2016). The proximal end of the right scapula of Sphodrosaurus pennsylvanicus is strongly overlapped by poorly preserved partial bones. One of those was interpreted as a forelimb bone by Colbert (1960), but we cannot determine its identity. The posterior end of the proximal surface of the scapula is deeply depressed and likely represents part of the glenoid surface. A rod-like, partially exposed bone is preserved immediately next to the proximal surface of the scapula. Because of its position it could be part of a clavicle, but it could also be part of a rib shaft (Fig. 6B: dr/cl). A blocky bone is preserved immediately next to and partially in contact with the probable glenoid region of the scapula (Fig. 6A, B, D: co). Its size and position suggest that it could be a coracoid. In agreement with this interpretation, there is a foramen on the most extensively exposed surface of the bone, whose size, position and orientation are congruent with the coracoid foramen of other diapsids (Fig. 6D: cf). The closest edge to this foramen should be the proximal margin of the coracoid, and it is partially well exposed, showing that the scapula and coracoid are not fused to each other. Following this interpretation, the coracoid lacks a posterior expansion, resembling the condition in most hyperodapedontine rhynchosaurs (Chatterjee 1974;Benton 1983 : Wild 1979), in which the height of the coracoid is two-thirds or more the length of the scapula. An unidentified plate-like bone is exposed between the coracoid and the vertebral series ( Fig. 6B: ?).
In a very similar position to that of the shoulder girdle but on the left side of the skeleton, there are bones that have been interpreted as a humerus and an indeterminate element (Colbert 1960;Sues et al. 1993). The putative humerus lacks clear features providing strong support for this interpretation and, alternatively, this bone could be the left scapula (Figs 2, 3, lsg?, 6C; Table 3). Its putative proximal end and shaft are not dissimilar to the proximal end and base of the scapular blade of the right scapula. A low, blade-like ridge next to one of the margins of the expanded area of the bone may represent an acromion ridge ( Fig. 6C: ac?) similar to that present in proterochampsids (e.g. Proterochampsa barrionuevoi: PVSJ 606; Gualosuchus reigi: PULR 05). If the identification as the left scapula is correct, it shows that the scapular blade lacks the strong bend of the posterior margin present in non-saurian diapsids, non-crocopodan archosauromorphs, some allokotosaurs, Mesosuchus browni, Prolacerta broomi, proterosuchids and Sarmatosuchus otschevi Ezcurra 2016). The indeterminate bone preserved next to this possible scapula could be a poorly exposed left coracoid ( Fig. 6C: lco?).
Ulna and radius. The distal regions of the left ulna and radius are exposed (Colbert 1960;Sues et al. 1993; Fig.  6E, F; Table 3). The distal end of the ulna is not much expanded, with a slightly convex articular surface (Sues et al. 1993), several times transversely broader than anteroposteriorly deep (Fig. 6F). A slightly convex distal articular surface of the ulna is widely distributed among diapsids, but the distal end is squared off, with a flat articular surface, in erythrosuchids and several suchian pseudosuchians (Nesbitt 2011;Ezcurra 2016). The distal end of the radius is narrower than that of the ulna and its articular surface is also slightly convex but sub-circular in distal view (Fig. 6F). The end of a bone preserved next to the distal ends of the radius and ulna possibly represents a metacarpal ( Fig. 6E: mtc).
Ilium. Most of the acetabular region of the right ilium is exposed and the base of the postacetabular process is preserved (Fig. 7A, B; Table 4). The acetabular wall is ventrally developed and, thus, the acetabulum was presumably completely (or nearly completely) closed. The acetabulum is deeply concave, with a smooth surface.
There is no raised antitrochanter on the posterior region of the acetabulum, contrasting with its presence in several ornithodiran archosaurs (Nesbitt 2011;Ezcurra 2016;Ezcurra et al. 2020a). The ischial peduncle lacks a posterior expansion or heel (Fig. 7B: isp). The base of the postacetabular process suggests that it was distinctly posterodorsally oriented ( Fig. 7B: poap), but this observation is tentative because part of the acetabulum is not exposed and thus the orientation for the ilium cannot be definitively determined.
Pubis. The pubis is plate-like without an anterior apron ( Fig. 7A;

Ischium.
The single preserved ischium of Sphodrosaurus pennsylvanicus is severely damaged, but it can be determined that it is a plate-like bone, as reported by previous authors (Colbert 1960;Sues et al. 1993). A plate-like ischium is present in other Permo-Triassic diapsids, with the exception of several paracrocodylomorph pseudosuchians and saurischian dinosaurs, which have rod-like ischial shafts (Nesbitt 2011).
Femur and tibia. The preserved right femur lacks the proximal end of the bone (Colbert 1960;Sues et al. 1993). The femur has an overall sigmoid profile in medial view, with an anteriorly curved proximal half and a posteriorly curved distal half ( Fig. 7A; Table 4). This is a common condition among neodiapsids (Benton 1985;Sues et al. 1993). The femur of Sphodrosaurus pennsylvanicus has a distinct fourth trochanter ("prominent ventral ridge" of Sues et al. 1993, p. 251; Fig. 7A: ft). Colbert (1960, p. 16) reported that "there is obviously no fourth trochanter", but the structure in Sphodrosaurus pennsylvanicus differs from the internal trochanter present in non-eucrocopod diapsids in the absence of a trochanteric fossa and a proximal extension that does not get close to the proximal end of the bone (Nesbitt 2011;Ezcurra 2016). The fourth trochanter of Sphodrosaurus pennsylvanicus is positioned on the proximal half of the bone. It is mound-like at its base, relatively low, proximodistally symmetrical and posteromedially oriented. As a result, the size, shape and  (Nesbitt 2011;Ezcurra 2016). The length of the tibia is approximately 0.69-0.74 times the length of the femur ( Fig. 7D; Table 4), a ratio similar to that of several Permo-Triassic diapsids. The proximal end of the tibia is distinctly anteroposteriorly expanded with respect to the shaft, resembling the condition in some eucrocopodan archosauriforms (e.g. Chanaresuchus bonapartei: PVL 4575; Lewisuchus admixtus: Ezcurra et al. 2020c; Herrerasaurus ischigualastensis: PVJ 373). It cannot be determined whether a cnemial crest was present, because most of the proximal surface of the bone is not exposed. The anteromedial surface of the distal region of the tibia is mostly flat, whereas the posteromedial surface is anteroposteriorly convex. The distal end of the tibia is slightly anteroposteriorly expanded, but considerably less than the proximal end, and the distal articular surface is mostly straight and slants slightly anteriorly in medial view, as in Chanaresuchus bonapartei (PVL 4575). The medial margin of the tibia is continuously convex in distal view, without any notch or facet for reception of an astragalar process. The rest of the distal surface of the tibia is not exposed.
Metatarsus. Metatarsals I, II and III are partially exposed, mainly in ventromedial view ( Fig. 8; Table 4). Metatarsal I is a robust element with a strongly asymmetrical distal end, in which the medial condyle is considerably narrower transversely and less distally extended than the lateral one ( Fig. 8A: ldc, mdc). This asymmetry should have resulted in a distinctly medially oriented first pedal digit (Sues et al. 1993), and a similar condition is also present in several Triassic archosauriforms (e.g. Antarctanax shackletoni: Peecook et al.
Lagerpeton chanarensis: PVL 4619). Metatarsal II is approximately as broad as metatarsal I at their midshafts, contrasting with the presence of a proportionally more robust metatarsal II in proterochampsids (Romer 1972;Arcucci 1990). The anteromedial surface of metatarsal II has a deeply concave surface that extends longitudinally from the proximal margin up to approximately the mid-length of the bone. As a result of this concavity, a flange-like portion of bone extends along the posteromedial margin of the metatarsal II and forms a nearly right-angled inflexion with the rest of the medial margin of the bone in proximal view (Fig. 8B: minf), as in Tropidosuchus romeri (PVL 4601). By contrast, the medial margin of metatarsal II of Chanaresuchus bonapartei (MCZ 4035, PVL 4575) and Gualosuchus reigi (PULR 05) is shallowly concave in proximal view. The distal end of metatarsal II and most of metatarsal III are not exposed. Pedal phalanges. The first phalanx of digit I, the complete digit II and the first two phalanges of digit III are exposed (Fig. 8A, C; Table 4). Phalanx I-1 has welldeveloped dorsal and ventral proximal lips, which should have allowed a broad range of flexion and extension of the digit. Phalanx II-2 closely resembles phalanx I-1 in structure, including the presence of a well-developed proximal ventral lip (the dorsal lip is not exposed). The ungual of digit II is longer than the other phalanges of the same digit, as in Azendohsaurus madagaskarensis , rhynchosaurs (e.g. Mesosuchus browni: SAM-PK-7416; Stenaulorhynchus stockleyi: Huene 1938), proterosuchids (Proterosuchus fergusi: SAM-PK-K140; 'Chasmatosaurus' yuani: IVPP V4067) and most proterochampsids (e.g. Proterochampsa barrionuevoi: PVSJ 606; Tropidosuchus romeri: PVL 4601; Chanaresuchus bonapartei: PVL 4575). The only preserved pedal ungual of Sphodrosaurus pennsylvanicus is very slightly recurved and proportionally long, without a distinct flexor tubercle. Immediately distal to the proximal end, the ventral margin of the ungual, below the lateral groove for the claw sheath, expands slightly laterally. As a result, the ventral surface of this area is transversely broader than that of the proximal end. The morphology of this ungual resembles that of proterochampsids (e.g. Proterochampsa barrionuevoi: PVSJ 606), but it seems to be less cylindrical in cross-section.

Phylogenetic analyses
The analysis of the phylogenetic data matrix under equal weights (eqWs) found 5600 MPTs of 6279 steps with a consistency index (CI) of 0.18697 and a retention index (RI) of 0.64183. The strict consensus tree (SCT) generated from these trees is generally well resolved, with only a few polytomies (Fig. 9). The high-level relationships depicted in this SCT are completely congruent with those of previous iterations of this dataset, although there are a few differences regarding the interrelationships of some low-level taxa or species (see Discussion). The species added here to this dataset are well resolved in the SCT: Orovenator mayorum is nested as the sister taxon to all other species with the exception of the species used to root the trees (Petrolacosaurus kansensis). Marmoretta oxoniensis, Feralisaurus corami and Elachistosuchus huenei are found as non-lepidosaurian lepidosauromorphs, Huehuecuetzpalli mixtecus is resolved as the sister taxon to Salvator rufescens within Squamata, and Revueltosaurus callenderi is found as the sister taxon to Aetosauria. Regarding Sphodrosaurus pennsylvanicus, this species is recovered as deeply nested within Archosauromorpha and Archosauriformes and as a member of Proterochampsia. Within the latter clade, Sphodrosaurus pennsylvanicus is positioned as the earliest-branching member of Doswelliidae (Fig. 10A) (Fig. 10B), as was the case in the eqWs analysis. However, a constant difference between the SCTs generated under IWs and that under eqWs is the position of Proterochampsa barrionuevoi as the sister taxon to Doswelliidae (Fig. 10B). Other major differences between the results of these analyses are: (1) the position of Prolacertoides jimusarensis in a polytomy with Allokotosauria and crownward archosauromorphs (IWs k ¼ 3) instead of as one of the earliest-branching crocopods (eqWs, IWs k ¼ 7, 10); (2) the position of Asperoris mnyama as an erythrosuchid (IWs k ¼ 3) instead of being one of the earliest-branching eucrocopods (eqWs, IWs k ¼ 7, 10); (3) the position of the clade Litorosuchus somnii þ Vancleavea campi as the sister taxon to Proterochampsia þ crownward archosauriforms (IWs k ¼ 3) instead of being early-branching proterochampsians (eqWs, IWs k ¼ 7, 10); (4) the position of Polymorphodon adorfi þ Dorosuchus neoetus as the sister taxa to Euparkeria capensis and crownward archosauriforms (IWs k ¼ 3) instead of being an early proterochampsian and an early eucrocopod, respectively (eqWs, IWs k ¼ 7, 10); (5) the position of Phytosauria as the sister taxon to Archosauria (IWs k ¼ 3) instead of being the earliest-branching pseudosuchians (eqWs, IWs k ¼ 7, 10); (6) the position of Ornithosuchidae as the sister taxon to Gracilisuchidae þ Paracrocodylomorpha (IWs k ¼ 3) instead of forming a clade with Erpetosuchidae and Aetosauriformes (eqWs, IWs k ¼ 7, 10); (7) the position of Ticinosuchus ferox and Youngosuchus sinensis as early-branching poposauroids (IWs k ¼ 3 in the case of both taxa and IWs k ¼ 7, 10 only for the case of Youngosuchus sinensis) instead of being one of the sister taxa to Paracrocodylomorpha and the earliest-branching Loricata, respectively (eqWs); and (8) the position of the clade Austriadactylus cristatus þ Preondactylus buffarinii as the earliest-branching pterosaurs (IWs k ¼ 3) instead of being more deeply nested in the clade (eqWs, IWs k ¼ 7, 10).

Skull width analyses
The estimated maximum skull width of Sphodrosaurus pennsylvanicus accounts for 0.44 times the total length of the presacral series. This value is twice as high as the median for the taxa sampled here for this ratio (mean ¼ 0.2182, standard deviation ¼ 0.1279). The pGLS regressions show that Sphodrosaurus pennsylvanicus distinctly departs from the regression lines (p < 0.0001 for the 616 regressions using the pruned time-calibrated trees [mbl ¼ 1, 0.5 and 0.1 My] derived from those found under equal weights and the 65 regressions using the pruned time-calibrated trees [mbl ¼ 1, 0.5 and 0.1 My] derived from those found under implied weights; Fig. 11A), with a skull width (59.8 mm) approximately twice the presacral length predicted for the species (28.3-30.6 mm). The high pGLS residual values of Sphodrosaurus pennsylvanicus cluster it with species of the hyperodapedontine genus Hyperodapedon, which have skull width-presacral length ratios ranging from 0.37-0.42; the proterochampsian Proterochampsa barrionuevoi is the only species with a pGLS residual value higher than those of the aforementioned taxa (ratio ¼ 0.61; Fig. 11D). The pGLS regressions between skull width and femur length show fairly congruent results with those reported using presacral length, in which hyperodapedontine rhynchosaurs, Proterochampsa barrionuevoi, Machaeroprosopus pristinus, rhynchocephalian lepidosauromorphs, 'Chasmatosaurus' yuani and Sphodrosaurus pennsylvanicus show the highest values of positive residuals.
The optimization of the skull width-presacral length ratio on the phylogeny found under equal weights (with a traditional monophyletic Proterochampsidaei.e. Proterochampsa þ rhadinosuchines) shows a slight increase of the ancestral ratio of Proterochampsia with respect to that of its most recent ancestral node (i.e. Proterochampsia þ Archosauria: 0.21!0.25 for the calibration with mbl ¼ 1 My, and 0.19!0.21 for the calibration with mbl ¼ 0.1 My). The high values for Sphodrosaurus pennsylvanicus (0.44) and Proterochampsa barrionuevoi (0.61) are optimized as independent acquisitions of large skulls from the ancestral conditions of Doswelliidae and Proterochampsidae, respectively, using maximum parsimony (state 1!states 3 and 4) and maximum likelihood optimality criteria (0.21 [mbl ¼ 0.  11C). In the phylogeny found under implied weights (k ¼ 10; in which Proterochampsa is recovered as the sister taxon to Doswelliidae) with a maximum likelihood optimization, the ancestral ratio of Proterochampsia increases substantially from the value of its most recent ancestral node (0.21!0. . By contrast, the optimization of the ratio as a discrete character in the phylogeny found under implied weights shows an ambiguous result, in which the condition of Sphodrosaurus pennsylvanicus (state 3) could be a retention of the ancestral condition of Doswelliidae or an apomorphy derived from a lower ratio (ambiguous optimization as states 1, 2 and/or 3).
The phylogenetic signal of the skull width-presacral length ratio is significant (p < 0.05 for all the alternative methods used to compute phylogenetic signal) for all the analysed trees and both mbl calibration methods (1 My and 0.1 My). A more detailed exploration through each species of the trees found that the phylogenetic signal is significantly strong in tanystropheids and some early dinosaurs (reduced skull widths) and hyperodapedontine rhynchosaurs (increased skulls widths) (Fig.  11B). By contrast, the phylogenetic signal of Sphodrosaurus pennsylvanicus (phySig ¼ 0.733-0.954) and Proterochampsa barrionuevoi (phySig ¼ 0.991-0.998) is non-significant in all trees. Finally, the phylogenetic correlograms show that the phylogenetic signal of skull width change is lost no more than 10 My after its acquisition during the evolution of the species sampled here.

Morphospace plot
The plot of the hindlimb and presacral length variables shows that Sphodrosaurus pennsylvanicus, Proterochampsa barrionuevoi and Chanaresuchus bonapartei are positioned close to each other (Fig. 12A). In particular, the similarity between the former two species is highlighted when considering the skull width to presacral length ratio. Hyperodapedontine rhynchosaurs, which also have very broad skulls, are separated from Sphodrosaurus pennsylvanicus and Proterochampsa barrionuevoi by a 'valley' of lower skull width vs presacral length values (cooler colours in Fig. 12A). Species such as the early archosauriforms Chanaresuchus bonapartei and Euparkeria capensis are positioned in this valley. All the other species included in this plot show more dissimilar body proportions with respect to those of Sphodrosaurus pennsylvanicus.

Ungual functional category analysis
The LDA found that the shape of the preserved pedal ungual of Sphodrosaurus pennsylvanicus can be predicted as gryporial with a 99% probability. The second most probable category, scalporial, is considerably less likely (prob ¼ 0.7%). This result is consistent with the graphical exploration of the plots showing the distribution of the linear discriminant axes 1-3 (91.75% of accumulated variance), in which Sphodrosaurus pennsylvanicus is positioned close to the convex hulls of the gryporial and scalporial categories (Fig. 12B, C). The confusion matrix shows an overall misidentification of 27.0%, in which only one of the gryporial species was misidentified as scalporial and two of the scalporial species were misidentified as generalist. No species was misidentified as gryporial when it was not. As a result, the identification of the ungual of Sphodrosaurus pennsylvanicus as gryporial seems to be a robust result.

Discussion
The phylogenetic relationships of Sphodrosaurus pennsylvanicus and other results of the cladistic analyses The phylogenetic relationships of Sphodrosaurus pennsylvanicus have changed substantially since its initial description as a procolophonid parareptile (Price 1956;Colbert 1960), being subsequently interpreted as a probable rhynchosaur (Baird 1986) and more recently as an indeterminate neodiapsid (Sues et al. 1993). Our results indicate for the first time that Sphodrosaurus pennsylvanicus is an archosauriform and that it belongs to Doswelliidae (Figs 9, 10), a clade that has been previously identified in other Upper Triassic formations of the eastern and south-western United States (Weems 1980;Heckert et al. 2012;Lucas et al. 2013). Thus, the phylogenetic position of Sphodrosaurus pennsylvanicus as a doswelliid removes this species as a potentially unusual component of the Triassic vertebrate assemblages of North America. In the eqWs analysis, the position of Sphodrosaurus pennsylvanicus within the clade Doswelliidae þ Proterochampsidae is supported by the presence of cervical vertebrae with a median longitudinal keel that extends ventral to the centrum rims on at least one anterior cervical vertebra (character 327: 1!2) and pedal unguals of digits II-IV longer than all nonungual phalanges of the same digit (889: 0!1). Sphodrosaurus pennsylvanicus shares with other doswelliids the following synapomorphies: external mandibular fenestra absent (262: 1!0); posterior cervical and anterior dorsal ribs with short tuberculum (347: 1!0); pubis plate-like, with approximately constant transverse width anteroposteriorly (476: 1!0); and pubis without anterior apron (477: 1!0). By contrast, the absence of the following two synapomorphies excludes Sphodrosaurus pennsylvanicus from the clade composed of more deeply nested doswelliids: anterior-middle dorsal ribs with sharp flexure close to an angle of 90 between the proximal end and the rib shaft in anterior or posterior view (367: 0!1) and at least some anterior-middle dorsal ribs with lateral surface of the proximal half bearing a rugose ridge or flange (878: 0!1).
Under topological constraints with eqWs, the following numbers of additional steps are necessary to force placement of Sphodrosaurus pennsylvanicus into alternative phylogenetic positions: two steps to place it (i) as a proterochampsid (sister taxon to the genus Proterochampsa) or (ii) as a non-doswelliid, non-proterochampsid proterochampsian; four steps to place it (iii) within Pseudosuchia (as an early phytosaur) or (iv) as a non-archosauriform archosauromorph (as the earliestbranching archosauromorph); five steps to place it (v) as the earliest-branching proterochampsian or (vi) within Avemetatarsalia (as the earliest-branching avemetatarsalian or an early pterosauromorph); and seven steps to place it (vii) as a non-proterochampsian, non-archosaurian archosauriform (as the sister taxon to Proterochampsia þ Archosauria), (viii) as a lepidosauromorph (as a non-lepidosaurian lepidosauromorph), or (ix) as a non-saurian neodiapsid (as the sister taxon to Sauria). As a result, the phylogenetic position of Sphodrosaurus pennsylvanicus as a proterochampsian is 3 Figure 11. Results of the phylogenetic generalized least squares (pGLS) regressions and phylogenetic signal analyses. A, bivariate plot of log 10 (skull width) vs log 10 (presacral length) showing the regression lines of 681 different pGLS regressions (corresponding to different time calibrations with a minimum branch length (mbl) of 0.1, 0.5 and 1 My of all different topologies found under equal and implied weights analyses after taxonomic pruning); B, ratio of skull width to presacral length in each sampled taxon, in which red bars indicate significant local indicators of phylogenetic association in the tree calibrated using mbl of 1 My; C, optimization of the ratio between skull width and presacral length in the diapsid phylogeny calibrated using an mbl of 1 My; and D, univariate plot of the pGLS residuals of the regression using an mbl of 1 My. Figure 12. Morphospace plot and results of the linear discriminant (LD) analysis of ungual functional categories. A, morphospace built from a bivariate plot of log 10 (femoral length/tibial length) vs log 10 (femoral length þ tibial length/presacral length) and adding a heatmap showing the log 10 (skull width/presacral length); B, bivariate plot of LD2 vs LD1; and C, bivariate plot of LD3 vs LD1. relatively well supported by our dataset and non-archosauromorph affinities are distinctly sub-optimal.
Contrasting with the eqWs results, the analyses under IWs found the genus Proterochampsa as the sister taxon to Doswelliidae (Fig. 10B), matching some recent results under a Bayesian framework (Wynd et al. 2019; see below) based on the presence of the following synapomorphies: strongly dorsoventrally compressed skull with mainly dorsally facing antorbital fenestrae and orbits (3: 0!1); foramina for the entrance of the cerebral branches of the internal carotids on the ventral surface of the bone close to the suture between basioccipital and parabasisphenoid (241: 0!1); axis with dorsoventrally very low neural spine (328: 0!1); jugal with height below the most ventral level of the orbit equal to or greater than half of the maximum height of the orbit in lateral view (625: 0!1); surangular-angular with distinct coarse ornamentation on the lateral surface (861: 0!1; present in Sphodrosaurus pennsylvanicus); and prearticular with ventral margin posterior to its contact with the splenial straight or ventrally curved on the anterior half of the bone in medial/ lateral view (868: 1!0, present in Sphodrosaurus pennsylvanicus). By contrast, Proterochampsa is excluded from Doswelliidae (i.e. the clade composed of Sphodrosaurus pennsylvanicus and more deeply nested doswelliids) by the absence of the following synapomorphies: external mandibular fenestra absent (262: 1!0), posterior cervical and anterior dorsal ribs with short tuberculum (347: 1!0), and pubis without anterior apron (477: 1!0). The absolute bootstrap frequencies of the clade Proterochampsa þ Doswelliidae are similar (21-24%) under the three different concavity constants tested here, but the GC bootstrap frequencies get sequentially more negative values (2% to À8% to À16%) when the k values are increased. This indicates that a higher penalization of homoplasy results in lower conflictive evidence for the clade. The branch supports for the clade Proterochampsa þ Doswelliidae are always very low and those of a monophyletic Proterochampsidae under eqWs are considerably higher.
The vast majority of the differences between eqWs and IWs occur only when using a very low concavity constant (k ¼ 3) and, thus, a strong downweighting of homoplasy. As a consequence, these results should be taken as extreme cases, but an exception is the position of the genus Proterochampsa as the sister taxon to Doswelliidae because it occurs with the three different k values tested here.
Beyond the interrelationships within Proterochampsia, the expansion and modifications in the phylogenetic matrix produced some different results in comparison to those reported in previous versions of this data set (Fig.   9). The main differences are the following (present in all trees under eqWs and IWs unless otherwise stated): (1) the non-saurian neodiapsids Hovasaurus boulei and Acerosodontosaurus piveteaui are sister taxa to each other (which would represent a monophyletic Tangasauridae, although Tangasaurus mennelli is not included in the data set to test this hypothesis) instead of in a polytomy with Youngina capensis (contra Ezcurra et al. 2022); (2) Paliguana whitei is recovered as the sister taxon to a clade comprising Marmoretta oxoniensis þ Fraxinisaura rozynekae þ more crownward lepidosauromorphs instead of being the sister taxon to Fraxinisaura rozynekae (contra Ezcurra et al. 2022); (3) the Permian archosauromorphs Aenigmastropheus parringtoni and Protorosaurus speneri are found as sister taxa to each other instead of these species being successive sister taxa to more deeply nested archosauromorphs (contra Ezcurra 2016); (4) Prolacertoides jimusarensis is recovered as one of the earliest-branching crocopods (but under IWs k ¼ 3 it is found as an early allokotosaurian or sister taxon to Allokotosauria þ crownward archosauromorphs) and not as a member of the clade Jesairosaurus þ Dinocephalosauridae þ Tanystropheidae or an early allokotosaurian (contra Ezcurra 2016); (5) Boreopricea funerea is found as the earliest-diverging prolacertid and not as the sister taxon to Prolacertidae þ more crownward archosauromorphs (contra Ezcurra 2016, but this position is recovered under IWs k ¼ 3); and (6) Youngosuchus sinensis is positioned as the earliestbranching loricatan instead of being the sister taxon to all other poposauroids (contra Ezcurra et al. 2017; but the poposauroid affinities are recovered in all the trees under IWs). The assessment of these different phylogenetic positions goes beyond the scope of this study and will be discussed elsewhere.
The enigmatic Triassic neodiapsids Feralisaurus corami and Elachistosuchus huenei were included in the CoArTreeP data set for the first time here (Fig. 9). Feralisaurus corami was recovered in previous phylogenetic analyses as a non-saurian neodiapsid or as a non-lepidosaurian lepidosauromorph, and the authors of the original description of this species preferred the latter hypothesis based on the morphology of the specimen (Cavicchini et al. 2020). Our results support the assignment of Feralisaurus corami to Lepidosauromorpha and outside Lepidosauria. However, under sub-optimal topological constraints, only one additional step forces the position of Feralisaurus corami as a non-saurian neodiapsid, but five steps are necessary to place this species within Archosauromorpha (as its earliest-branching member). In the case of Elachistosuchus huenei, previous analyses of its phylogenetic relationships recovered conflicting results, as a pseudosuchian archosaur (Janensch 1949), a rhynchocephalian (Walker 1966), a non-lepidosaurian lepidosauromorph (as the sister taxon to Choristodera), a non-saurian neodiapsid or a nonarchosauriform archosauromorph (Sobral et al. 2015). The results of our study favour the lepidosauromorph hypothesis, but the branch support for the clade that includes Elachistosuchus huenei and other lepidosauromorphs is very weak (minimum Bremer support and bootstrap frequencies <10% under eqWs). Indeed, only one additional step forces the placement of Elachistosuchus huenei as the earliest-branching archosauromorph, and two extra steps places it as a choristoderan outside of Sauria. These alternative, slightly sub-optimal results are congruent with those recovered by Sobral et al. (2015). As a result, the phylogenetic relationships of both Feralisaurus corami and Elachistosuchus huenei remain extremely poorly supported in the context of our dataset, although the archosauromorph affinities of the former species are definitely sub-optimal.
Is the skull of Sphodrosaurus pennsylvanicus autapomorphically large?
Our revision of the anatomy of Sphodrosaurus pennsylvanicus shows that this species can be easily distinguished from other archosauromorphs (see Diagnosis). Our analyses also demonstrate that Sphodrosaurus pennsylvanicus does have a proportionately larger skull than the vast majority of Permo-Triassic diapsids (Figs 11A, C, 12A), considering the length either of the presacral vertebral series or of the femur as proxies for postcranial size, as claimed by previous authors (Colbert 1960;Sues et al. 1993). However, the condition of Sphodrosaurus pennsylvanicus is not unique among archosauromorphs, as it is paralleled by hyperodapedontine rhynchosaurs (e.g. Chatterjee 1974;Benton 1983) and the proterochampsian Proterochampsa barrionuevoi (Trotteyn 2011) (Figs 11D, 12A). Although Sphodrosaurus pennsylvanicus and Proterochampsa barrionuevoi are found to be closely related to each other (both as members of Proterochampsia), most phylogenetic scenarios and optimization methods indicate that the two species developed unusually broad skulls independently (e.g. Fig. 11C). In addition, a considerably lower proportional skull width increase is also recovered at the base of Proterochampsia in several of our analyses. Nevertheless, if the genus Proterochampsa is the sister taxon to Doswelliidae, one possible scenario is that a skull as broad as that of Sphodrosaurus pennsylvanicus would be ancestral for this family and Doswellia kaltenbachi has an autapomorphically narrower skull. As a consequence, the results of our analyses indicate the most likely hypothesis is that the extremely broad skull of Sphodrosaurus pennsylvanicus is autapomorphic.

Do proterochampsid skull widths show positive interspecific allometry?
Regarding the relative size of the skull of proterochampsids (considering a monophyletic Proterochampsidae), Proterochampsa barrionuevoi is the largest known species and has the proportionally largest skull, whereas the smallest species, Tropidosuchus romeri and Pseudochampsa ischigualastensis, have proportionally smaller skulls. Thus, it can be argued that the relationship between skull width and presacral length has a positive allometry in proterochampsids. However, Cerritosaurus binsfeldi is one of the smallest known proterochampsids (Pradelli et al. 2022) and it seems to have a relatively large skull. The holotype and only known specimen of Cerritosaurus binsfeldi preserves a complete skull articulated to 15 presacral vertebrae (Trotteyn et al. 2013). The skull width is 52.7 mm and the preserved presacral vertebral length is 80.1 mm. If we assume a complete presacral vertebral series composed of 24 vertebrae, as in other proterochampsids (e.g. MCZ 4037), the estimated presacral length of Cerritosaurus binsfeldi would be c. 127 mm (based on the length of the preserved anterior-middle dorsal vertebrae). This estimate results in a skull width-presacral length ratio of 0.41, which is considerably higher than the ratio in Chanaresuchus bonapartei (0.20: PVL 4575, with skull width of 91.4 mm). The pGLS regressions between the skull width and presacral length of proterochampsids, including Cerritosaurus binsfeldi, are not significant (p ¼ 0.2134-0.5452 using the three different mbl values), and Cerritosaurus binsfeldi and Proterochampsa barrionuevoi represent clear outliers above the regression lines (see Supplemental material 3). Indeed, the pGLS residual of Cerritosaurus binsfeldi in the regression using the time-calibrated tree with mbl of 1 My is considerably higher (0.12) than those of other proterochampsids (À0.08 to À0.32), with the exception of the very high value for Proterochampsa barrionuevoi (0.40). In the regression using an mbl of 0.1 My, the pGLS residual of Cerritosaurus binsfeldi (0.11) is very similar to that of Chanaresuchus bonapartei (0.09), and considerably lower than that of Proterochampsa barrionuevoi (0.61). In conclusion, we reject here the hypothesis of positive interspecific allometry in the skull size of proterochampsids. Instead, it seems that the earliest-branching proterochampsids (Proterochampsa barrionuevoi and Cerritosaurus binsfeldi) have proportionally larger skulls and that this has more to do with phylogeny than with scaling related to the overall body size of the species.

Implications for the taxonomic content and evolutionary history of Doswelliidae and Proterochampsidae
The identification of Sphodrosaurus pennsylvanicus as a doswelliid adds a new species to this clade (Fig. 10). The first version of the phylogenetic dataset of the CoArTreeP recovered Vancleavea campi as the earliestbranching member of Doswelliidae (Ezcurra 2016), but analyses of more recent iterations of this data set found Vancleavea campi and its sister taxon, Litorosuchus somnii, within Proterochampsia but outside the Doswelliidae þ Proterochampsidae dichotomy (e.g. Wynd et al. 2019;Ezcurra et al. 2020a;). An independent phylogenetic data set alternatively recovered Doswellia kaltenbachi as more closely related to Archosauria than to the clade Vancleavea campi þ Litorosuchus somnii (Li et al. 2016). However, it should be noted that the character and taxon sampling of the latter matrix is poorer than that of the CoArTreeP for this part of the tree. As a result, the position of Vancleavea campi and Litorosuchus somnii within Doswelliidae seems unlikely based on current available information and is considerably sub-optimal in our analyses. The gracile and longlimbed reptile Scleromochlus taylori has been recently recovered as a doswelliid (Bennett 2020). However, this hypothesis has been found strongly sub-optimal in a more recent revision of its phylogenetic relationships, and Scleromochlus taylori has been recovered as the earliest-branching pterosauromorph (Ezcurra et al. 2020a). As a consequence, our study increases the known taxonomic richness of Doswelliidae to at least five nominal species: Jaxtasuchus salomoni, Doswellia kaltenbachi, Rugarhynchos sixmilensis, Ankylosuchus chinlegroupensis and Sphodrosaurus pennsylvanicus.
The phylogenetic placement of Proterochampsa barrionuevoi seems to be more problematic (Fig. 10). This species and Proterochampsa nodosa have historically been grouped with Cerritosaurus binsfeldi, Chanaresuchus bonapartei and Gualosuchus reigi in a monophyletic Proterochampsidae (see Trotteyn et al. 2013). However, recent studies have found an alternative hypothesis in which Proterochampsa is the sister taxon to Doswelliidae, using a Bayesian inference analysis under rate heterogeneity (gamma distribution, with four rate categories, ¼ Mk þ G4 model; Wynd et al. 2019) and using a maximum parsimony analysis under IWs ; the maximum parsimony analyses under eqWs of these same datasets recovered a monophyletic Proterochampsidae. Thus, downweighting the influence of homoplastic characters favours the position of the genus Proterochampsa as the sister taxon to Doswelliidae under both maximum parsimony and model-based phylogenetic analyses.
Our phylogenetic analyses repeated the same results found by  under eqWs and IWs. However, in our phylogenetic analysis under IWs (k ¼ 10), the absolute bootstrap frequencies of the clade Proterochampsa þ Doswelliidae remained virtually unchanged after the a priori exclusion of Sphodrosaurus pennsylvanicus (21% vs 25%), but the GC bootstrap frequencies changed from À25% to À16% after the inclusion of Sphodrosaurus pennsylvanicus. This indicates that the inclusion of Sphodrosaurus pennsylvanicus decreases the amount of conflicting information in support of the clade Proterochampsa þ Doswelliidae. Similarly, under equal weights, two additional steps are necessary to force the clade Proterochampsa þ Doswelliidae when including Sphodrosaurus pennsylvanicus, but three extra steps are required if Sphodrosaurus pennsylvanicus is excluded a priori. Thus, the anatomical information provided by Sphodrosaurus pennsylvanicus seems to reduce to some degree the anatomical gap between doswelliids and Proterochampsa, and the non-monophyly of a traditional Proterochampsidae seems to be more likely than before. However, additional information about doswelliid anatomy and early proterochampsians is needed to shed more light on the phylogenetic relationships of Proterochampsa.
With the exception of Jaxtasuchus salomoni from the late Middle Triassic (late Ladinian) of Germany, all of the currently recognized doswelliid species are from Late Triassic formations of the United States. The Sphodrosaurus pennsylvanicus-bearing Hammer Creek Formation is dated as late early to early middle Norian, thus being stratigraphically younger than the late Carnian strata that yielded the specimens of Doswellia kaltenbachi (Dilkes & Sues 2009). Ankylosuchus chinlegroupensis is assigned to the Otischalkian land-vertebrate faunachron and thus dated close to the Carnian-Norian boundary (<221.76 ± 0.23 Ma, based on a date close to the base of the Blue Mesa Member of the Chinle Formation; Rasmussen et al. 2021). Rugarhynchos sixmilensis comes from the 'Bluewater Creek Formation', which correlates to the uppermost Blue Mesa Member up to the middle Sonsela Member of the Chinle Formation (Ramezani et al. 2014), and thus it is approximately constrained to 220.54 ± 0.96-215.67 ± 0.67 Ma (Rasmussen et al. 2020). As a result, the chronostratigraphic uncertainty of Sphodrosaurus pennsylvanicus probably overlaps those of Ankylosuchus chinlegroupensis and Rugarhynchos sixmilensis, the youngest known doswelliids (Fig. 10).
The biochron of Proterochampsa barrionuevoi is dated to within 231.4 ± 0.3 to 227.24 þ 1.27, À1.97 Ma (Rogers et al. 1993;Desojo et al. 2020) and, thus, it potentially overlaps the chronostratigraphic uncertainties of Sphodrosaurus pennsylvanicus, Doswellia kaltenbachi and Ankylosuchus chinlegroupensis (Fig. 10). If the genus Proterochampsa belongs to a traditionally monophyletic Proterochampsidae, this means that proterochampsids became extinct (or their currently known youngest records occur) at least five million years before the youngest doswelliid occurrence. On the other hand, if Proterochampsa is the sister taxon to Doswelliidae, its biochron would be congruent with those of doswelliids, but it would be the only evidence that the lineage that led to this clade also evolved in south-eastern Pangaea.
The anatomy of Sphodrosaurus pennsylvanicus in the context of the proterochampsian body plan Sphodrosaurus pennsylvanicus and Proterochampsa barrionuevoi have broader skulls than other Permo-Triassic diapsids with a similar snout-vent length, and this should have important palaeobiological implications. For example, bite force correlates with head size in at least some extant reptiles (e.g. scincid and lacertid lizards; Verwaijen et al. 2002;Le Guilloux et al. 2020), and it has been reported that proportionally large heads might be advantageous during agonistic competitive intraspecific interactions (Wegener et al. 2019). However, the largely unknown skull structure of Sphodrosaurus pennsylvanicus prevents us from further discussing the possible function(s) of its broad skull. Regarding the rest of the body, the partially preserved postcranium of Sphodrosaurus pennsylvanicus also limits the number of comparisons that can be made with other taxa, being mostly restricted to the presacral vertebral series and hind limb. The morphospace plot shows that the body proportions of Sphodrosaurus pennsylvanicus are similar to those of Proterochampsa barrionuevoi, including the presence of a relatively short posterior stylopodium and zeugopodium in relation to the presacral length and a longer femur than tibia in addition to the proportionally very broad skull (Fig. 12A).
Beyond the measurements included in the morphospace plot, the presence in Sphodrosaurus pennsylvanicus of a proportionally short pubis and an incipiently recurved and long pedal ungual also closely resembles the condition in Proterochampsa barrionuevoi. In particular, the only available pedal ungual of Sphodrosaurus pennsylvanicus (Fig. 8A, C) has been identified by the LDA as gryporial or much less likely scalporial among the functional categories of Thomson & Motani (2021). Gryporial unguals are adapted for hook-and-pull digging (extant examples are most anteaters and armadillos), whereas scalporial unguals are adapted for scratch-digging (extant examples are pangolins, meerkats and aardvarks) (Thomson & Motani 2021). As a consequence, the LDA robustly identifies the ungual of Sphodrosaurus pennsylvanicus as adapted for substrate processing (likely digging). A similar function could also be inferred for Proterochampsa barrionuevoi and other proterochampsids because of their pedal ungual morphology (see Trotteyn 2011), which is very similar to that of Sphodrosaurus pennsylvanicus.
Our observations and analyses indicate that Sphodrosaurus pennsylvanicus and Proterochampsa barrionuevoi probably occupied a similar ecological role in their respective palaeocommunities. Proterochampsa barrionuevoi has been historically interpreted as a semiaquatic animal based on its cranial features (e.g. dorsally facing external nares and orbits, long rostrum, strongly ornamented external bone surfaces ;Reig 1959;Sill 1967;Romer 1971) and this hypothesis is still broadly supported (Arcucci 2011;Trotteyn 2011;Trotteyn et al. 2013). In particular, the more recent description of a fairly complete skeleton of Proterochampsa barrionuevoi has confirmed the proportionally huge size of the skull (see Results; Trotteyn 2011) and may support the semi-aquatic hypothesis. As a result, semi-aquatic life habits could be hypothesized for Sphodrosaurus pennsylvanicus based on its similarities to Proterochampsa barrionuevoi. However, a more complete specimen of Sphodrosaurus pennsylvanicus is needed to test this hypothesis properly and shed more light on the mode of life of this species.
In conclusion, our results suggest that both Sphodrosaurus pennsylvanicus and Proterochampsa barrionuevoi could have been semi-aquatic reptiles that were able to swallow relatively large prey (if Sphodrosaurus pennsylvanicus was actually a predatory form) and were adapted for digging or at least using their hind limbs to process the substrate in some way. A semi-aquatic life habit is congruent with previous inferences for other proterochampsian species (Romer 1972;Bonaparte 1978;Weems 1980;Sues et al. 2013;Schoch & Sues 2014;Wynd et al. 2019). Nevertheless, a more terrestrial habit has been recently suggested at least for rhadinosuchine proterochampsids, because of the absence of clear evidence supporting a locomotor style associated to a semiaquatic behaviour and palaeohistological features associated to semi-aquatic forms (Arcucci et al. 2019;Ezcurra et al. 2021c). There is a substantial disparity in the proterochampsian body plan: long-limbed (Pseudochampsa ischigualastensis) to short-limbed forms (Chanaresuchus bonapartei), species with a posterior zeugopodium as long as the stylopodium (Tropidosuchus romeri) to ones with a proportionally very short zeugopodium (Sphodrosaurus pennsylvanicus and Proterochampsa barrionuevoi), and large-headed forms (Sphodrosaurus pennsylvanicus and Proterochampsa barrionuevoi) to relatively smallheaded forms (Pseudochampsa ischigualastensis) (Fig.  12A). Thus, it seems that there was a variety of lifestyle strategies among proterochampsians, possibly including different feeding behaviours and habitats ranging from semi-aquatic (e.g. Proterochampsa and doswelliids) to more terrestrial (e.g. Tropidosuchus romeri and rhadinosuchine proterochampsids).

Supplemental material
Supplemental material for this article can be accessed here: https://doi.org/10.1080/14772019.2022.2057820. The data that support the findings of this study are openly available in Zenodo here: http://doi.org/10.5281/ zenodo.5879789.