Variation in the skulls of Elgaria and Gerrhonotus (Anguidae, Gerrhonotinae) and implications for phylogenetics and fossil identification

Background There are limited data on intra- and interspecific osteological variation for many squamate clades. Those data are relevant for phylogenetic analyses that use osteological characters and for apomorphic identifications of fossils. We investigate whether morphological features in the skulls of extant gerrhonotine lizards can be used to distinguish taxa at the species- and genus-level and assess whether newly discovered intra- and interspecific osteological variation alters the utility of previously reported apomorphic features. We examined skulls of species belonging to the gerrhonotine genera Elgaria and Gerrhonotus. These genera contain 17 extant species, but the cranial osteology of only a few species was previously examined. As a result, intra- and interspecific osteological variation of these gerrhonotines is poorly understood. Methods We employed high-resolution x-ray computed tomography (CT) to scan 25 alcohol-preserved specimens. We provide data on the skulls of all eight species of Elgaria, four for the first time, and five species of Gerrhonotus, three for the first time. We examined 3-D reconstructed skulls of the scanned specimens as well as dry, traditionally prepared skeletons (when they were available). Results We found that the purported diagnostic utility of many previously described morphological features is impacted because of substantial morphological variation between and within species. We present an assessment of osteological differences that may be useful to differentiate species of Elgaria and Gerrhonotus, many of which are present on isolated cranial elements commonly recovered as fossils, including the premaxilla, maxilla, parietal, pterygoid, prootic, dentary, and surangular. We demonstrate the importance of documenting patterns of osteological variation using large sample sizes, and the utility of examining disarticulated cranial elements of the squamate skull to identify diagnostic morphology. This study adds to a growing body of literature suggesting that extensive documentation of morphological variation is needed to further our understanding of the phylogenetic and diagnostic utility of morphological features across vertebrate clades. Efforts in that direction likely will benefit from examination of disarticulated skeletal elements.


INTRODUCTION
There is currently a paucity of data on patterns of intra-and interspecific osteological variation for many squamate clades (Evans, 2008). A firm understanding of patterns of variation in extant taxa aids in discovering and describing morphological features that are useful for identifying fossils (Bhullar, 2012;Pérez Ben, Gómez & Báez, 2014). An understanding of variation is also paramount for reconstructing phylogenetic relationships among extant and extinct taxa using osteological characters (e.g., Conrad, 2008;Bhullar, 2011;Gauthier et al., 2012) and for studies that use phylogenetic reconstructions based on osteological characters to inform taxonomy (e.g., Conrad et al., 2011). Analysis of variation aids in the repeatability and testability of phylogenetic hypothesis (Poe & Wiens, 2000), in that studies of osteological variation can assess the constancy of characters upon which phylogenetic analyses of osteological data are based (Joyce & Bell, 2004;Bever, 2009). Accordingly, new data on osteological variation can alter our understanding of the reliability of reported apomorphies or other morphological features that were used to diagnose and identify fossils (Bever, 2005), leading to reevaluations of previous biogeographic or evolutionary hypotheses based on data from the fossil record (e.g., Good, 1988a).
The dearth of knowledge on intra-and interspecific osteological variation in squamates in particular was partly attributed to the relatively minor emphasis placed on maintaining and growing modern skeletal collections (Bell & Mead, 2014). A robust sample size in the number and type of specimens (e.g., those that preserve data on size, sex, and geographic location of collection) and variety of sampled taxa is necessary to account for different types of variation, including ontogenetic and individual variation, bilateral asymmetry, polymorphism within monophyletic lineages, teratologies, pathologies, ecophenotypic plasticity, and sexual dimorphism (Jones & German, 2005). In recent years, there has been a growing body of literature dedicated to understanding patterns of osteological variation in squamates (e.g., Bell, Evans & Maisano, 2003;Nance, 2007;Bell, Mead & Swift, 2009;Čerňanský et al., 2019;Paparella et al., 2020;Takesh et al., 2020) many utilizing x-ray computed tomography (CT) methods (partially reviewed by Broeckhoven & du Plessis, 2018). The use of x-ray computed tomography to scan wet alcohol-preserved specimens has the potential to partially supplement the lack of traditionally prepared dry skeletons (Bell & Mead, 2014). CT is also useful for producing osteological data for species for which skeletal data are rare or difficult to obtain as is often the case for species known from only a few specimens or species that are now near extinction. Here, we utilize CT data to document morphology of the skulls of several species of gerrhonotine lizards.
Gerrhonotinae is a diverse clade of anguid lizard that contains over 50 species. Lizard species in this group are ecologically diverse and inhabit a large geographical area from British Columbia to Panama (Lamar et al., 2015;Leavitt et al., 2017). Gerrhonotine fossils are known from early Eocene deposits (Smith, 2009) and possibly from late Cretaceous sediments (Estes, 1964;Good, 1988a;Longrich, Bhullar & Gauthier, 2012). Crown gerrhonotines are known from at least the middle Miocene (Scarpetta, 2018). The osteology of the group was previously studied by several researchers (Cope, 1892;Tihen, 1949;McDowell & Bogert, 1954;Romer, 1956;Criley, 1968;Meszoely, 1970;Rieppel, 1980;Gauthier, 1982;Good, 1987;Good, 1988a); however, only a few species from each group within Gerrhonotinae were sampled. Variation in gerrhonotine osteology was previously reported in studies of ontogenetic variation (Good, 1995) and timing of fusion relative to sexual maturity (Maisano, 2002) in Elgaria coerulea, and an osteological description of the skull of Elgaria panamintina (Ledesma & Scarpetta, 2018). However, intra-and interspecific variation in other gerrhonotine species was not previously documented or was not described in detail. In this study we present variation in the skulls of the gerrhonotine lizard genera Elgaria and Gerrhonotus. We selected Elgaria and Gerrhonotus because the two clades were described as morphologically similar (Tihen, 1949), although the two genera are hypothesized to form a grade as opposed to a clade (Stebbins, 1958;Good, 1987;Pyron, Burbrink & Wiens, 2013;Zheng & Wiens, 2016).
Our sample includes all eight species of Elgaria and five species of Gerrhonotus, representing the most taxonomically extensive osteological dataset of these genera. We provide the first discussion of variation in the skulls of four species of Elgaria (Elgaria cedrosensis, Elgaria nana, Elgaria paucicarinata, and Elgaria velazquezi) and three species of Gerrhonotus (Gerrhonotus lugoi, Gerrhonotus ophiurus, and Gerrhonotus parvus). We discuss variation in previously reported diagnostic and apomorphic morphology, as well as variation in previously undescribed morphology. We comment on the phylogenetic and taxonomic implications of variation discovered in our sample, and the efficacy of those features for diagnosing taxa at the genus and species levels based on our new variation data.
parentheses to facilitate interpretation. Abbreviations for anatomical features that appear in figures can be found in the figure captions.

CT sample and scanning information
Our sample includes both dry skeletal specimens and CT-scans of alcohol-preserved specimens (Table 1). Most specimens were relatively large individuals, but we also examined some smaller specimens of Elgaria multicarinata (TxVP M-8578, TxVP M-8982), Elgaria kingii TxVP M-8582, and Gerrhonotus liocephalus TCWC 9896. The heads of all alcohol-preserved specimens were scanned at the University of Texas High-Resolution CT Facility (UTCT) except for E. kingii UF 74645 (https://www.morphosource.org/Detail/ MediaDetail/Show/media_id/24786) and E. coerulea UF 152969 (https://www. morphosource.org/Detail/MediaDetail/Show/media_id/24778) which were downloaded from http://www.MorphoSource.org. Most specimens were scanned individually, but in some cases, specimens were scanned together, including scans of the two Elgaria multicarinata, the two Elgaria coerulea, the two Gerrhonotus infernalis, Gerrhonotus liocephalus TCWC 9896 with Gerrhonotus lugoi CM 49012, and Gerrhonotus ophiurus TCWC 35604 with Gerrhonotus liocephalus TCWC 8585. CT scanning specifications for specimens scanned at the UTCT are provided (see Table 2). Isotropic voxel sizes for scanned specimens range from 9.62 mm to 25.8 mm. We examined at least two specimens of each species with the exception of G. ophiurus, for which only a single specimen could be acquired. All raw CT data for the image-processed skulls used in this study are available for download without restrictions at http://www.MorphoSource.org. All CT-scanned specimens were digitally reconstructed in Avizo 3D 8.1 or 9.1 software. The skulls were segmented (digitally disarticulated) into individual cranial elements in Avizo using the magic wand tool or manual selections. Gray-scale values used to make magic wand selections varied substantially among datasets and are not directly comparable between datasets, but bone gray-scale values largely fell into the range of 18,000-30,000. We did not segment separate cranial elements when two or more elements were largely fused to one another and/or there was no distinct boundary between the bones in the CT slices. Our evaluations of morphology were based on observations of both volume-and surface-renderings. All figures are surface renderings because surface renderings of segmented bones provide higher quality images. Care was taken to ensure that the surface rendering represent the true morphology of the bones; however, some thin bones (e.g., the septomaxilla) may have small holes as the result of the smoothing process in generating the surface models.
Measurements of CT specimens were conducted in Avizo 3D 8.1 in orthographic view, and all figures are also in orthographic view. Shrinkage of dry skeletal specimens may create contact between bones (McDowell, 1967). Therefore, when bones had a small space between them (likely connected by a small amount of soft tissue) in CT specimens, we considered those bones to be in contact (i.e., features 1, 30, and 40). A largely immovable sutural contact was not required for bone contacts to be scored as present. Snout-ventlength (SVL) measurements for alcohol preserved specimens were taken from photographs of the specimens positioned next to a ruler with 1 mm subdivisions. We calibrated the images based on the ruler in the photographs in ImageJ and drew and measured a line starting from the snout along the middle of the body to the vent (see Table 1 for measurements).

Taxonomic framework
The genus Gerrhonotus was first described by Wiegmann (1828), who accommodated six species within the genus, including coeruleus (now Elgaria coerulea), deppei (now Abronia deppii), imbricatus (now Barisia imbricata), liocephalus (Gerrhonotus liocephalus), rudicollis (now Barisia rudicollis), and taeniatus (now Abronia taeniata). The genus Elgaria was erected by Gray (1838), who assigned to it two species, Elgaria kingii and E. multicarinata. The species coerulea and 12 other forms, including subspecies, were placed in Elgaria by Tihen (1949), but all of those taxa were placed in the genus Gerrhonotus by Stebbins (1958). That proposal placed species previously assigned to Elgaria in the subgenus Gerrhonotus, but classified E. coerulea in the subgenus Barisia (Stebbins, 1958). External scale characters were used by Waddick & Smith (1974) to support the classification of Tihen (1949) in which Elgaria and Gerrhonotus are treated as distinct genera. Although Criley (1968) identified no features of the skull to distinguish gerrhonotine genera and support the classification of either Tihen (1949) or Stebbins (1958), Good (1987) identified features of the skull that permitted generic differentiation that largely supported the generic classification by Tihen (1949). There are up to eight currently recognized species of Elgaria (Table 3). Elgaria nana was considered a distinct species by Grismer (2001) because the size at which E. nana reaches sexual maturity is smaller than that of E. multicarinata, but some recent authors considered E. nana to be conspecific with E. multicarinata (Feldman & Spicer, 2006;Leavitt et al., 2017). The taxonomy of E. nana requires further investigation, but for our analysis we maintained E. nana as a separate species. Elgaria cedrosensis, previously a subspecies of E. paucicarinata (Grismer, 1988), was elevated to species status by Grismer & Hollingsworth (2001). Genetic data revealed that E. cedrosensis likely only occurs on Isla Cedros (from where the specimens in our sample were collected) and not on the mainland Baja California peninsula (Leavitt et al., 2017). A novel phylogenetic hypothesis was recently proposed in which E. panamintina is nested within Elgaria multicarinata as currently circumscribed, and there are distinct northern and southern lineages of E. multicarinata (Leavitt et al., 2017). Elgaria multicarinata is currently considered a single species. The two distinct lineages are E. multicarinata webbii for populations in the south There are 10 currently recognized species of Gerrhonotus (including Gerrhonotus (=Coloptychon) rhombifer) ( Table 3). Gerrhonotus parvus was described by Knight & Scudday (1985) but was subsequently assigned to Elgaria and was thought to be closely related to E. kingii based on external morphology (Smith, 1986;Good, 1988b). Phylogenetic analysis of molecular data suggested that G. parvus is most closely related to species in Gerrhonotus (Conroy et al., 2005;Leavitt et al., 2017). The monophyly of Gerrhonotus and the inclusion of both G. parvus and G. lugoi within Gerrhonotus was questioned in a more recent analysis (García-Vázquez et al., 2018a). Those authors found that the phylogenetic position of G. parvus as sister to all Gerrhonotus, excluding G. lugoi, was not strongly supported in all analyses. Additionally, G. lugoi was recovered with weak support as either sister to Barisia or as an early diverging member of Gerrhonotus (García-Vázquez et al., 2018a). Gerrhonotus lugoi was previously included in the genus Barisia (Waddick & Smith, 1974;Smith, 1986). In our study, we treated G. lugoi and G. parvus as separate taxa within the genus Gerrhonotus pending further investigation. A paraphyletic Gerrhonotus infernalis also was previously inferred (García-Vázquez et al., 2018a). All specimens of G. infernalis included in our study are from Texas. The genus Mesaspis was recently found to be paraphyletic with respect to Abronia, and it was suggested that species previously placed in Mesaspis should now be placed in Abronia (Gutiérrez-Rodríguez et al., 2021). We follow the suggestion of Gutiérrez-Rodríguez et al. (2021).

Morphological matrix
We provide descriptions of all examined morphological features in our "Results" section below. We also provide a matrix (see Table S1) that contains scorings for features that were counts and features that we discretized into distinct states. However, this matrix as Table 3 The constituent species of Gerrhonotus and Elgaria as recognized in this study.
Gerrhonotus farri Bryson & Graham, 2010 #+ Elgaria cedrosensis (Fitch, 1934a) presented is not intended for phylogenetic analysis, but rather as a convenient and now-familiar way to summarize morphological data. We use the term 'morphological feature' to emphasize this distinction because the term 'character' is now almost inextricably associated with morphological features that are assessed specifically for their utility for phylogenetic analysis. Although we discuss the systematic significance of some features, the features we evaluated herein are not explicitly framed for that purpose. Instead, our overarching goal was to document and report variation and to assess the impact of variation on the reliability of previous statements made in the literature, especially about the potential utility of features in diagnosing Elgaria and Gerrhonotus.
Our work builds on the foundation laid by those who previously worked on these groups. They did so in the face of limited availability and sample sizes of skeletal specimens of many species, and without the benefit of digital technologies such as X-ray computed tomography. The limited taxonomic sampling reflected availability of specimens at the time the authors were writing, when the skeletal system of rare taxa could only be studied through destructive sampling, or at a minimum the removal of skin and removal or alteration of tissues surrounding the skeleton. For taxa known only from a type specimen or a small number of specimens (e.g., Gerrhonotus rhombifer; Gerrhonotus parvus) such destructive sampling was not possible. As our own work unfolded over the last several years, our taxon sampling became less complete when new species were described (e.g., Gerrhonotus lazcanoi in 2017, Gerrhonotus mccoyi in 2018). In addition to those two species previous authors also did not have access to E. velazquezi, named in 2001 and included in our sample, or Gerrhonotus farri, which was named in 2010, is known only from the type specimen (Meiri et al., 2018), and is not included in our study.
When we review statements made by previous authors, we do so with the understanding that those statements that addressed diagnostic features of particular genera or higher taxa are to be interpreted as statements that apply to the species of those genera that were available for study at the time. The same is true for our own work. Although we have expanded the taxon sampling relative to the samples available to our predecessors, our coverage is not complete, and our sample size remains low for many species. Our statements must, therefore, be interpreted by readers and subsequent authors as applying only to the specimens we examined (see Table 1). This general issue of interpreting the literature in its historical context is exacerbated by the fact that the taxonomic arrangement of species into more inclusive taxa such as genera also changes through time. Although the extant taxa included within Elgaria appear now to be stable, the same is not true for Gerrhonotus, the taxonomic makeup and monophyly of which are not yet well established (García-Vázquez et al., 2018a). For those reasons we made an effort here to indicate particular specimens and/or species to which our comments apply, especially for those currently placed in Gerrhonotus.

RESULTS
We found considerable morphological variation among specimens for most cranial elements. The following section is organized first by bone; with morphological features for a particular bone organized chronologically by publication. We discuss skeletal features that we found to vary or that were previously reported to vary among Elgaria or Gerrhonotus and also evaluated features for which variation was not previously addressed. Features that begin with a number indicate ones that we summarized in our matrix ('scored') in discrete states. Features that begin with a letter represent ones that we did not score.
There were several reasons that we did not score features, including non-independent morphology resulting in identical scorings for multiple features, our inability to identify or comprehend previous descriptions made by other researchers, and ambiguous or inconsistent scoring resulting from the way in which a previously described feature was constructed or described. We also recognized continuous variation in some features, making qualitative character states arbitrary and/or difficult to create and score. Premaxilla 1. Contact between the premaxilla and the frontal with the nasals removed: 0=no contact, Fig. 1A; 1=contact, Fig. 1B (Tihen, 1949;modified from Good (1987), character 9).
Contact between the nasal process of the premaxilla and the frontal was reported in Barisia, Abronia (=Mesaspis) gadovii, and Abronia (Good, 1987). In these taxa, the nasal process of the premaxilla was reported to separate the nasals completely from one another. We found that when the nasals are removed, the nasal process of the premaxilla contacts the frontal in some specimens of Gerrhonotus, although the nasal process of the premaxilla does not separate the nasals completely from one another. It would be difficult to determine whether the premaxilla and frontal contact on a traditionally prepared skull in which the nasals overlie the anterior portion of the frontal and the posterior portion of the nasal process of the premaxilla. The nasal process and frontal do not contact in all Gerrhonotus, but in specimens that lack contact, the space separating the bones is relatively small. The premaxilla and frontal do not contact in specimens of Elgaria.
An ossified bridge was reported to occur in all gerrhonotines besides Elgaria and Abronia (Good, 1987). Ossified projections extending laterally from the nasal process but failing to connect with the alveolar plate were reported in Abronia (Good, 1987). We found that some Elgaria also possess ossified projections extending from the nasal process or have ossified projections that extend dorsally from the alveolar plate (e.g., E. kingii SDNHM 27895, Fig. 2D). We excluded the lateral projections from the discrete scoring of this feature due to continuous variation in distinctiveness of these projections. We scored a 1 if there were ossified projections extending dorsally from the lateral portion of the alveolar plate on one or both sides of the premaxilla, and we scored a 2 if there was a bridge on one or both sides of the premaxilla. Among Elgaria, a bridge is present on the left side of the premaxilla in E. kingii SDNHM 24252 (Fig. 2C), on the right side in E. kingii UF 74645 and E. multicarinata TxVP M-8993, and on both sides of the premaxilla of E. kingii TxVP M-8981. Asymmetry of the ossified bridge was also observed in G. lugoi LACM 116254 (Fig. 2F), which possesses the bridge on only the left side of the premaxilla. Specimens that have an ossified bridge on only one side of the premaxilla always possess non-connecting ossifications on the other side, supporting the homology of those features as was suggested by other authors (Campbell & Frost, 1993). Although an ossified bridge was reported to occur in Gerrhonotus (Good, 1987), both specimens of G. parvus and G. lugoi CM 49012 do not have a bridge nor ossified projections on either side of the premaxilla.
3. Midline foramen on the anterior surface of the alveolar plate of the premaxilla (anterior premaxillary foramen of Ledesma & Scarpetta, 2018): 0=absent, Fig. 2A; 1=present, Fig. 2B (Smith, 2009;Scarpetta, 2018). We observed intraspecific variation in E. kingii, with one specimen (E. kingii CAS 266265) lacking a foramen, while all other specimens of that species have a foramen. A unique condition was observed in E. kingii SDNHM 24252, which has two foramina on the anterior surface (Fig. 2C). A foramen is absent from all specimens of E. panamintina and E. cedrosensis. All other species of Elgaria possess the foramen and most Gerrhonotus except for two specimens of G. infernalis (TxVP M-11411, TxVP M-13441) lack the foramen. However, in G. infernalis TxVP M-11411, the foramen is minute and more ventrally located.
4. Number of premaxilla tooth positions (Conrad et al., 2011, character 406). The presence of four bilateral tooth positions on the premaxilla was previously considered an unambiguous synapomorphy of Anguidae, including anguines, anniellines, gerrhonotines, and glyptosaurines (Conrad et al., 2011). However, we observed that same morphology in one specimen of the anguimorph Xenosaurus grandis (TxVP M-8960), corroborating a finding by Bhullar (2011). The shape of the posterior end of the nasal process of the premaxilla in specimens of G. parvus and G. lugoi is characterized by a thin extension of the ventral keel of the premaxilla that is not present on other specimens. All specimens that have a thin posterior extension of the premaxilla ventral keel also have the premaxilla and frontal in contact.
A. Width of the nasal process (Good, 1987, characters 7 and 8) The nasal process was described by Good (1987) as parallel-sided between the nares in all gerrhonotines except for Barisia, in which it narrows posteriorly, and in Gerrhonotus, in which it narrows anteriorly in some specimens. We found intraspecific variation in the width of the nasal process in Elgaria, as did Good (1987). However, there were no specimens of Gerrhonotus that have a nasal process that significantly narrows anteriorly with the possible exception of G. lugoi LACM 116254 (Fig. 2F) and G. parvus SRSU 5538, which have a nasal process that is slightly widened midway along the process. However, several specimens of Elgaria also have a slight widening midway along the nasal process (e.g., E. cedrosensis SDNHM 27702, Fig 2A). The nasal process is widest relative to the anterior portion of the nasal process in E. coerulea TNHC 14643 (Fig. 2B), E. coerulea TNHC 58792, and E. multicarinata TNHC 35666. Interestingly, some specimens of E. kingii have a nasal process that is somewhat widened at the posterior end and narrows anteriorly (Fig. 2C); however, the nasal process is parallel-sided in E. kingii UF 74645 and is less distinctly widened at the posterior end in E. kingii TxVP M-8981. We chose not to score this feature due to the continuous variation we observed among specimens, confounding creation of qualitative states.  (Tihen, 1949;Good, 1987, character 17).
Contact between the maxilla and the frontal was reported to occur in Gerrhonotus and Abronia (Good, 1987). We found contact between the maxilla and the frontal in specimens of G. infernalis, G. ophiurus, and G. lugoi, but not in specimens of G. parvus nor G. liocephalus. The maxilla and frontal do not contact in any specimens of Elgaria, but the  maxilla comes closer to contacting the frontal in specimens of E. paucicarinata relative to other species of Elgaria. Absence of contact between the maxilla and frontal in Elgaria and Barisia was reported by Tihen (1949). Variation in this morphology was noted by Criley (1968), but he did not specify whether variation in maxilla-frontal contact was found in Elgaria, Barisia, or both genera.
7. Number of anterior openings of the superior alveolar canal at the base of anterior edge of the facial process (anterior inferior alveolar foramen of the maxilla of Oelrich, 1956;Smith, 2009) (Oelrich, 1956;Smith, 2009). Several specimens of Elgaria and Gerrhonotus were found to have two openings for the superior alveolar canal and some were found to be bilaterally asymmetrical in the number. One specimen (E. cedrosensis SDNHM 27702, Fig. 4A) possesses three anterior openings for the superior alveolar canal on the right maxilla.
8. In a dorsal view, presence of a distinct medial projection at the anterior end of the palatine facet on the palatine process of the maxilla: 0=present, Fig. 3A; 1=absent, Fig. 3E (derived from Good, 1987, character 22) Gerrhonotus lugoi is unique in our sample in that the maxillary shelf lacks a distinct medial projection where the maxilla articulates with the maxillary process of the palatine; however, the right maxilla of G. lugoi CM 49012 possesses a subtle projection. There is variation in the distinctiveness of a projection which ranges from being quite distinct (Elgaria velazquezi SDNHM 68678, Fig. 3A) to subtle (E. nana SDNHM 17102, Fig. 3C). 9. Number of maxillary tooth positions (Good, 1987, character 95).
A count of 21-24 maxillary tooth positions reportedly differentiates Gerrhonotus from other gerrhonotine genera, which were described as having 14 to 18 tooth positions (Good, 1987). We found that many specimens of Elgaria overlap with the count reported for Gerrhonotus. For example, E. velazquezi SDNHM 68677 has 23 maxillary tooth positions on each maxilla and E. kingii SDNHM 27895 has 21 tooth positions on the left maxilla and 22 on the right. Specimens of G. parvus have a maximum of 18 tooth positions and G. lugoi has a maximum of 19 tooth positions, both of which fall short of the number of tooth positions previously reported for Gerrhonotus. We hypothesize that the smaller adult body size of G. parvus and G. lugoi accounts for their reduced maxillary tooth position number relative to specimens of G. infernalis and large specimens of Elgaria that we examined. The number of teeth on the maxilla was shown to vary ontogenetically (indicated by head length) in E. coerulea (Good, 1995). The influence of body size on the number of teeth is corroborated by the fact that smaller specimens in our sample (e.g., G. liocephalus TCWC 9896) have fewer tooth positions than larger individuals of the same species. Gerrhonotus infernalis TxVP M-7129 has the most tooth positions of any specimen with 26 tooth positions on the right maxilla and 25 on the left. 10. Number of labial nutrient foramina on the maxilla (Good, 1987).
The number of nutrient foramina on the maxilla varies intraspecifically among gerrhonotines, as was found previously (Good, 1987). In our sample, the number of foramina in a line running parallel to the tooth row ranges from four to eight. Additional foramina were occasionally present in variable positions on much of the lateral face of the maxilla (e.g., E. velazquezi SDNHM 68678, Fig. 5D). Multiple rows of foramina on the lateral surface of the facial process were observed in other anguimorphs (Bhullar, 2011 (2008)) and lateral to the palatine process (Smith, 2009). The number of trigeminal foramina on the maxilla is two to three ( Fig. 3A) with many specimens exhibiting bilateral asymmetry.
12. Spur on the anterior edge of the facial process of the maxilla: 0=absent, Fig. 5E   B. Shape of the overlap between the maxilla and the prefrontal (Good, 1987, character 16). The junction between the maxilla and the prefrontal was described as straight in Gerrhonotus (Fig. 6C), a lopsided 'w' shape in Abronia, or a 'v' shape ( Fig. 6A) in all other gerrhonotines (Good, 1987). We did not score this feature because the 'v' shape contact can only be present in specimens which lack contact between the maxilla and the frontal (feature 6 of this study and character 17 of Good, 1987) (Figs. 6A and 6B).
C. Presence of sculpturing on the lateral surface of the maxilla (Conrad et al., 2011, character 8).
D. Location of the midpoint of the apex of the facial process of the maxilla (Conrad et al., 2011, character 28) A midpoint of the apex of the facial process (nasal process of Conrad et al., 2011) located posterior to the longitudinal midpoint of the maxilla was reported as an unambiguous synapomorphy for Elgaria (Conrad et al., 2011). However, we found that the orientation in which we measured the maxilla affected whether the apex was anterior or posterior to the longitudinal midpoint of the maxilla. We measured the total length of the maxilla and the length from the anterior tip of the maxilla to the level of the midpoint of the apex of the facial process along a line parallel to the tooth row from a view directly lateral to the maxilla (Figs. 6D and 6E). With this method of measurement, the midpoint of the apex of the facial process is located just anterior to the longitudinal midpoint of the maxilla in both specimens of E. velazquezi, in E. nana SDNHM 52886, and in E. multicarinata TNHC 4478. In other specimens of Elgaria the midpoint of the apex of the facial process is located only slightly posterior to the longitudinal midpoint of the maxilla. The farthest posterior extent was seen in E. panamintina MVZ 191076 and G. parvus SRSU 5538, in which the midpoint/apex was located posteriorly at 55% of the total anterior-posterior length of the maxilla. We also measured the location of the midpoint of the apex of the facial process from a view lateral to the entire skull on several specimens so that the maxilla was oriented obliquely. This is the view that would likely be examined on an articulated, traditionally prepared skull. We found that the midpoint of the apex shifted about 2-3% more posteriorly with regard to the total anterior-posterior length of the maxilla. This is because the facial process is curved medially, making the location of the apex dependent on the orientation of the maxilla. We view this character as ambiguous, which results in inconsistent scoring. Because the location of the midpoint of the apex is always close to the longitudinal midpoint of the bone, having a midpoint of the apex that is just posterior to the midpoint is not a reliable diagnostic character of Elgaria. Furthermore, we found that some specimens of Gerrhonotus also have a midpoint of the apex of the facial process that is located posterior to the midpoint along the maxilla.
E. The inclination of the anterior edge of the facial process (Conrad et al., 2011, character 29).
The inclination of the anterior edge of the facial process, resulting from the relative degree of distinction between the ventral and posterior border of the naris, was used as a character in a large-scale phylogenetic analysis of squamates (Conrad et al., 2011). The condition reported for Elgaria, a weakly inclined anterior edge of the facial process (nasal process of Conrad et al., 2011), was recovered as an unambiguous synapomorphy of  the genus (Conrad et al., 2011). However, we found that most of the specimens of Elgaria have an inclined anterior edge of the facial process that most closely resembles that of Heloderma suspectum as depicted by Conrad (2008, figure 26B), which was scored as having a steeply inclined facial process. We had difficulty scoring this character because of the ambiguity of the exemplar conditions provided by Conrad (2008) as well as the high degree of variation in the morphology of the anterior edge of the facial process. This resulted in specimens not easily being circumscribed into the different character states based on the character descriptions in their current form. Elgaria velazquezi SDNHM 68677, for example, has a morphology that is fully intermediate between a steep or shallowly inclined anterior edge of the facial process (Fig. 5C). Gerrhonotus infernalis TNHC 18988 (Fig. 5E) has a shallowly inclined anterior edge of the facial process while G. infernalis TNHC 92262 has a more distinct contrast between the anterior edge of the facial process and the dorsolateral edge of the premaxillary process. Specimens of G. lugoi and G. parvus have a more steeply sloped condition similar to that in most Elgaria. Like other authors (Simões et al., 2017), we were unable to score this character objectively, and do not recommend use in its current form in phylogenetic analyses of Gerrhonotinae.
F. Condition of the posterodorsal edge of the facial process of the maxilla from a lateral view (new feature). There is significant variation in the shape of the posterior portion of the facial process among specimens of Elgaria and Gerrhonotus. In many specimens, the posterodorsal region of the facial process is rounded (e.g., E. coerulea TNHC 14643, Fig. 5A). The posterodorsal portion of the facial process is a broad posteriorly directed sheet in G. parvus SRSU 5538 (Fig. 5F). Other species have a distinct posterodorsal projection on the facial process. This projection is most distinct in specimens of E. cedrosensis (Fig. 6D), E. nana SDNHM 17102, and G. infernalis TxVP M-13441. We did not score this feature in discrete states because the length of the posterodorsal projection is continuously variable and the distinctiveness may be contingent on the presence of notches on the posterior edge of the facial process (e.g., E. paucicarinata SDNHM 45106, Fig. 5B).
G. Notch in the posterior edge of the facial process of the maxilla where the lacrimal articulates (new feature).
Specimens of G. infernalis, except for G. infernalis TxVP M-7129, have a notch in the posterior edge of facial process where the lacrimal articulates (Fig. 5E). This notch is also found in G. ophiurus TCWC 35604, on the right maxilla of G. liocephalus TCWC 8585, and a more subtle notch is present on the right maxilla of E. kingii TxVP M-8981. Other specimens possess a small projection above the lacrimal articulation facet which creates a smaller notch (e.g., E. paucicarinata SDNHM 45106, Fig. 5B), have a thin lamina of bone where a notch would be present otherwise (e.g., E. kingii SDNHM 27895), or have no notch (e.g., E. coerulea TNHC 14643, Fig. 5A). We did not score this feature in distinct states because of continuous variation in the distinctiveness of a notch and because we found many ways in which a notch is formed, none of which are mutually exclusive.
H. Length of a medially projecting lappet on the maxilla (new feature).
There is significant variation in the morphology of a medially projecting lappet on the maxilla. The lappet ranges from being elongated (e.g., E. cedrosensis SDNHM 27702, Fig. 4A), short (e.g., E. coerulea TNHC 14643, Fig. 4C), or minute (e.g., G. infernalis TNHC 92262, Fig. 4B). We observed substantial variation in length of the lappet among specimens of both Elgaria and Gerrhonotus, but we note that the lappet is shortest in two specimens of G. infernalis (TNHC 18988, TNHC 92262) and G. liocephalus TCWC 9896. The lappet may also be incompletely or completely pierced by a foramen (e.g., left lappet of G. infernalis TNHC 18988, Fig. 4D, and the right lappet of E. coerulea TNHC 14643, Fig. 4E). We did not score this feature because a continuous spectrum of variation in length prevented us from reliably separating specimens into discrete qualitative states.
Complete separation of the nasals from one another was reported in Barisia, Abronia (=Mesaspis) gadovii, and Abronia (Good, 1987). We observed a large separation between the nasals near their anterior-posterior midpoint only in specimens of G. lugoi (Fig. 7B).
14. Position of the anterior nasal process in dorsal view relative to the anteromedial inflection of the premaxillary process of the maxilla: 0=close to the anteromedial inflection of the premaxillary process of the maxilla, Fig  Contact between the cristae cranii and the palatines was reported as a synapomorphy of Anguidae (Conrad, 2008), as a synapomorphy of Gerrhonotinae + Diploglossinae (Gauthier, 1982), and as an unambiguous synapomorphy of gerrhonotines excluding Elgaria (Conrad et al., 2011). In the CT scans, the frontal and the palatine may not directly contact each other as they often do in dry skulls, so we modified this feature to instead describe the relative positions of the frontal and palatine. We found that the crista cranii extend ventrally below the dorsal apex of the palatine in many specimens of Elgaria and Gerrhonotus and some specimens were bilaterally asymmetric (e.g., E. cedrosensis SDNHM 27702). It was more recently claimed that this feature could not be scored qualitatively because of the continuous range of the ventral extent of the cristae cranii (Simões et al., 2017). A clear distinction can be made between the character states within our sample. Shrinkage caused by skeletal preparation of specimens may also influence the position of the crista cranii relative to the palatine. This would make comparisons between dry skeletal data and CT data problematic; however, the wide range in this morphology in both skeletal and CT specimens suggests that observed differences are not solely tied to specimen preparation.
The frontal of gerrhonotine lizards was reported previously to have constricted interorbital margins (Meszoely, 1970;Gauthier, 1982;Good, 1988a). Other authors reported linear and parallel interorbital margins in gerrhonotines (Conrad et al., 2011). These conflicting reports coincide with the variation  discovered within our sample. We did not score specimens in discrete qualitative states because specimens exhibit a continuous range of variation from having an interorbital region that is distinctly narrower than the anterior region (e.g., specimens of G. infernalis, Fig. 8E), an interorbital region is only slightly narrower (e.g., E. nana SDNHM 52886, Fig. 8D), and an interorbital width is the same as the anterior width (e.g., E. nana SDNHM  17102, Fig. 8C). The width of the interorbital region reportedly varies ontogenetically in many lizards (Evans, 2008). In juvenile specimens of Elgaria the interorbital region appears constricted.
J. Condition of the anterolateral processes on the frontal (Evans, 2008).
The anterolateral processes on the frontal are relatively indistinct in E. cedrosensis SDNHM 30296 (Fig. 8A) and on the left side of E. cedrosensis SDNHM 27702. We did not score this feature in discrete qualitative states because there is a continuous range in the distinctiveness of those processes in our sample. It was previously noted that the processes may be variably developed in gerrhonotines (Evans, 2008).
K. Length of nasal facets of the frontal (new feature).
The nasal facets on the frontal in CT scans of E. kingii (SDNHM 28795, SDNHM 24252) appear somewhat shortened relative to the nasal facets of other specimens (Fig. 8B). However, there is not a clear distinction between short or long nasal facets in our sample and the shape and length of the nasal facet varies continuously within our sample.
L. Condition of the lateral edge of the frontal (new feature).
When viewed dorsally, the frontal of some specimens has a lateral margin with a notch in which the posterior tip of the orbital process of the prefrontal articulates (e.g., G. liocephalus TCWC 8585, Fig. 8F). In some specimens, the presence of a notch is bilaterally asymmetrical. We did not score this feature because the distinctiveness of a notch varies continuously and because co-ossified osteoderms may affect whether a notch is visible.  (Good, 1987, character 43).
It was previously reported that the parietal extends posterior to the anterior end of the braincase in Gerrhonotus (Good, 1987). We interpreted this as the parietal extending posteriorly relative to the anterior end of the supraoccipital, because the parietal overlaps parts of the sphenoid and the alar process of the prootic in all specimens. We found that in most specimens of Gerrhonotus the parietal does not overlap the anterior end of the supraoccipital; only in some specimens of G. infernalis (TxVP M-7129, TxVP M-11411, TxVP M-11412) is overlap present. In other specimens of G. infernalis (TNHC 18988, TxVP M-7525, TxVP M-12353) the parietal comes close to overlapping the anterior end of the supraoccipital (Fig. 10C), but that condition is similar to that observed in several specimens of Elgaria. The parietal does overlap the anterior end of the supraoccipital in   recess that is not defined ventrally like in other specimens. This feature may vary ontogenetically, because in E. multicarinata only specimens with a snout-vent-length over 140 mm have a deep recess.
M. Shape of the parietal table in dorsal view (Good, 1987, character 41). The parietal table of Abronia (=Mesaspis) moreletii is reportedly broadened compared to its length (Good, 1987). Most specimens of Elgaria and Gerrhonotus have a parietal table that is trapezoidal in shape, but we found that some specimens have a parietal with anterolateral and posterolateral edges that are similar in lateral extent, giving the parietal a square-shaped appearance (e.g., G. parvus SRSU 5538, Fig. 10D). We did not assign discrete qualitative states to specimens because of a continuous spectrum of variation that may be due to ontogenetic variability. The shape of the parietal table was shown to vary ontogenetically in E. multicarinata (Bhullar, 2012), and juvenile specimens of Elgaria in our sample have a square-shaped parietal table.  N. Condition of the proximal medial edge of the postparietal processes (modified from Good, 1987, character 43). The edges on either side of the posterior notch in the parietal were reported to "twist sharply downwards in M.
[Mesaspis] gadovii…" (Good, 1987:289). Based on the description and illustrations of Abronia (=Mesaspis) gadovii provided by Good (1987) we interpret this as being the same as having a proximal medial edge of the postparietal processes that is steeply and ventromedially slanted. Specimens of Elgaria and Gerrhonotus exhibit a continuous range of morphological variation in the feature, including having a steeply slanted medial edge of the postparietal processes (e.g., specimens of E. velazquezi and E. cedrosensis, Fig. 11D) to having a flat medial edge (e.g., G. parvus SRSU 5538, Fig. 11A).
O. Border of the pit for the processus ascendens on the ventral surface of the parietal (Villa & Delfino, 2019).
The morphology of ridges that laterally border the pit for the processus ascendens on the ventral surface of the parietal varies intra-and interspecifically. Specimens exhibit a continuous range of variation in morphology of the ridge which ranges from being developed into a prominent crest that merge with the ventrolateral crests anteriorly (e.g., most specimens of G. infernalis, E. panamintina MVZ 75918, E. velazquezi SDNHM 68677, and E. multicarinata TNHC 35666) (Figs. 11E and 11F), absent (e.g., specimens of G. parvus and juvenile specimens of Elgaria) (Fig. 11A), or having an intermediate morphology (e.g., E. nana SDNHM 52886, Fig. 11C). The condition of the ridges appeared to vary with size, and larger specimens of G. infernalis possess a prominent crest while smaller species like G. parvus and G. lugoi do not have a ridge or have a ridge with only a minimal ventral extent.     In several specimens of G. infernalis there is a small medial projection at the anterior end of the medial shelf of the lacrimal that articulates with the anterior surface of the posteroventral process of the prefrontal. This feature is present but less distinct in E. kingii SDNHM 24252 (Fig. 14A). P. Length of the posterior end of the lacrimal (new feature).
There is substantial variation in the overall shape of the lacrimal. The posterior end of the lacrimal appears shortest in specimens of E. panamintina (Fig. 15C), G. parvus, G. infernalis TNHC 18988, and in some specimens of E. multicarinata (TNHC 35666, TxVP M-9005, TxVP M-8990). We observed continuous range in length and chose not to discretize this feature into distinct qualitative states.
Q. Condition of a notch between a posterior extension of the medial shelf of the lacrimal and the posterior process of the lacrimal (new feature).
A posterior projection extending from the medial shelf of the lacrimal creates a notch on the posterior end of the lacrimal in several specimens of Elgaria and Gerrhonotus.  The distinctiveness of this notch ranges from being quite distinct (e.g., E. kingii SDNHM 24252, Fig. 15A), relatively indistinct (e.g., E. paucicarinata SDNHM 45106, Fig. 15D), completely absent (e.g., E. velazquezi SDNHM 68678, Fig. 15B), or bilaterally asymmetric (e.g., E. multicarinata TNHC 35666). We did not separate these morphologies into discrete qualitative states because we found continuous variation in the distinctiveness of a notch.
R. Condition of a notch on the anterior end of the lacrimal (new feature).
In some specimens of Elgaria and Gerrhonotus the anterior end of the lacrimal has a notch where the bone articulates with the maxilla. The morphology of the notch ranges from being distinct (Figs. 14A-14C and 15D), to less distinct (e.g., E. multicarinata TNHC 4478, Fig. 14B), to absent (e.g., E. velazquezi SDNHM 68678, Fig. 14D). In some specimens, the notch is indistinct but there is an elongate projection on the anterior end of the lacrimal that articulates with the medial surface of the maxilla (e.g., G. liocephalus TCWC 8585, Fig. 14F). We observed continuous range in the distinctiveness of a notch and chose not to discretize this feature into distinct qualitative states.
Lateral overhang (outward bending of Good (1987)) of the jugal and lacrimal where the two bones articulate dorsal to the maxilla was reported in Elgaria, Gerrhonotus, and Barisia (Good, 1987). In most specimens within our sample, there is some degree of lateral overhang of the lacrimal and the jugal dorsal to the maxilla (Fig. 16F). Specimens are variable on a continuous spectrum, making it difficult to discretize this feature into qualitative states; however, we note that the overhang is subtle or indistinct in many specimens (e.g., E. coerulea TNHC 58792, Fig. 16E).

Postfrontal
T. Overlap between the postfrontal and the postorbital (new feature).
In many specimens, the lateral portion of the postfrontal distinctly overlies the postorbital (Fig. 17A). However, in some specimens including E. coerulea UF 152969, specimens of G. parvus, specimens of G. lugoi, and some G. infernalis (TxVP M-7129, TxVP M-1732, TxVP M-11412) there is minimal overlap between the postfrontal and the postorbital (Fig. 17B). The amount of overlap varies continuously among specimens, so we did not score this feature in discrete qualitative states.
U. Condition of the lateral edge of the inflection point on the postfrontal (new feature).
The jugal process of the postorbital was reported to lie anterior to the jugal only in Elgaria (Good, 1987). We found that the jugal process of the postorbital lies anterior to the jugal only in specimens of E. cedrosensis (Fig. 18B)  It was reported that having a postorbital extending more than 75% of the length of the supratemporal fenestra (upper temporal fenestra of Evans (2008)) is an unambiguous synapomorphy of Elgaria (Conrad et al., 2011). Previous authors noted issues in the  construction of this character (Simões et al., 2017). We note that there is also the problem of consistently determining the anterior-posterior length of the supratemporal fenestra because of variation in the length of the fenestra due to variation in the width of postorbital at the anterior end of the supratemporal fenestra, and variation in the length of the fenestra due to the anterior extent and orientation of the supratemporal. We chose to examine the posterior extension of the postorbital relative to the anterior tip of the supratemporal because we were able to score specimens in discrete states. The postorbital extends posterior to the anterior tip of the supratemporal in E. panamintina MVZ 75918, E. kingii SDNHM 24252 (Fig. 18C) . Both the length of the postorbital and the supratemporal influenced our scoring of the feature and we note that the length of the supratemporal was documented to vary ontogenetically in E. coerulea (Good, 1995) and generally in lizards (Evans, 2008).
W. Condition of the anterior surface of the quadrate (new feature). We found a continuous range of variation in the shape of the concave medial portion of the anterior surface of the quadrate (Figs. 19D,19E,and 19F). The concave medial portion is relatively shallow in specimens of G. parvus (Fig. 19F) and E. multicarinata TxVP M-8988. Ontogenetic changes in the shape of the quadrate were reported in lacertid lizards (Barahona & Barbadillo, 1998) and in Anolis (Bochaton et al., 2017). Juvenile specimens of Elgaria (e.g., E. multicarinata TxVP M-8982) have a shallow concave medial portion of the quadrate.  Pterygoid 28. Pterygoid teeth: 0=no teeth, Fig 20A; 1=small number of tooth positions present in a single row or a small patch, Fig. 20B; 2=many tooth positions present in a large patch, Fig. 20C (Tihen, 1949;modified from Good, 1987, character 91 and 92). Pterygoid teeth were reported to occur in Gerrhonotus and Elgaria, albeit reduced in number in E. coerulea (Good, 1987) and some Gerrhonotus (Criley, 1968). Most specimens have a large number of pterygoid teeth arranged in a large patch; however, a reduced number of pterygoid teeth arranged in a single row or small patch is present in some specimens of E. multicarinata, E. cedrosensis, G. parvus, G. infernalis, and G. ophiurus. Juvenile specimens of E. multicarinata (TxVP M-8982, TxVP M-8578) possess a single row of pterygoid teeth, but a juvenile E. kingii (TxVP M-8582) has a large patch of teeth. An unusual condition was observed in E. panamintina MVZ 75918, in which pterygoid teeth are absent, but a rugose texture and empty tooth sockets are present on the ventral surface of the palatal plate (see figure 10A of Ledesma & Scarpetta (2018)). Gerrhonotus infernalis TxVP M-13440 is the only specimen in which pterygoid teeth appear to be completely absent (Fig. 20A). Pterygoid teeth were also reported to be absent in one specimen of E. coerulea (Stebbins, 1958). High variability in the presence and number of pterygoid teeth was previously documented in Podarcis (Skawi nski, Borczyk & Turniak, 2017), and ontogenetic variation in the number of rows of pterygoid teeth was reported in Iguana iguana (Bochaton et al., 2016b). An increased sample size of Elgaria and Gerrhonotus could capture a greater range of variation in this feature for these genera. Some specimens of Elgaria possess a dorsal ridge that is distinct from the lateral edge of the pterygoid, which serves as the insertion point for the superficial pseudotemporal muscle (Villa & Delfino, 2019), and the palatal plate. This ridge is most distinct in specimens of E. panamintina, E. paucicarinata (but only the left pterygoid of E. paucicarinata SDNHM 45100, Figs. 21F and 21H), E. velazquezi SDNHM 68678, the left pterygoid of E. kingii SDNHM 27895, and in G. liocephalus TCWC 8585. A raised surface on the posterior surface of the palatal plate is present on some specimens (e.g., the right pterygoid of E. kingii SDNHM 27895, Figs. 21E and 21G) but it is short and does not extend anteriorly to the ectopterygoid facet on the pterygoid flange.
X. Condition of the border of the fossa columella on the pterygoid (new feature).
The border of the fossa columella varies continuously among specimens. The border ranges from being developed into tall prominent ridges surrounding the fossa (e.g., E. kingii SDNHM 24252, Fig. 20E) to being close to level with the surrounding area on the pterygoid (e.g., E. coerulea TNHC 58792, Fig. 20D).   (1954)). Contact between the epipterygoid and the parietal is only seen in the three CT scanned specimens E. multicarinata TNHC 35666 (Fig. 22B), E. kingii UF 74645, and G. parvus SRSU 5537. However, eight dry skeletons of Elgaria have contact between the bones. This discrepancy may be a result of shrinkage during the skeletonization process in which bones are pulled together by the drying of tissue. It may also be a result of ontogenetic variation, with older and younger specimens having an epipterygoid that is closer or farther away from the parietal, respectively (Evans, 2008).
A curved, "u-shaped" (Good, 1987: 289), contact between the ectopterygoid and the pterygoid was reported in Elgaria and Gerrhonotus (Good, 1987). We found that the shape of the contact between the ectopterygoid and pterygoid was curved in all specimens; however, we note that the condition of G. infernalis TxVP M-1723 and the left side of E. kingii SDNHM 27895 (Fig. 20C) closely resembles the straight condition illustrated by Good (1987) for species belonging to other gerrhonotine genera. Furthermore, exemplars of the straight condition illustrated by Good (1987) were not all depicted as having strictly straight contact, and some were depicted as being bilaterally asymmetrical (e.g., figs. 2A and 3B of Good, 1987 Y. Length of a lateral 'spur' on the ectopterygoid where the bone meets the maxilla. (Good, 1987, character 38). An elongate lateral 'spur' on the ectopterygoid was reported to differentiate Elgaria from other gerrhonotines (Good, 1987). We found that the presence of a spur is related to whether the bone is viewed in articulation or in isolation. A 'spur' may be a distinct projection in the isolated ectopterygoid, as in E. panamintina MVZ 191076 (Figs. 23A, 23D, and 23G). In many specimens, there is no distinct projection or 'spur' on the isolated ectopterygoid; however, when observed in ventral view on an articulated skull, the posterior orbital process of the maxilla fits into a notch on the anterior end of the ectopterygoid making the portion of the ectopterygoid just lateral to this notch resembles a distinct projection or 'spur' (e.g., E. velazquezi SDNHM 68677, Figs. 23B, 23E, and 23H). The lateral portion of this notch is most indistinct in some specimens of G. infernalis (TxVP M-11411, THNC 18988) (Figs. 23C, 23F, and 23I) and E. velazquezi SDNHM 68678. Juvenile specimens of E. multicarinata also do not have a distinct lateral portion of the ventral notch (e.g., E. multicarinata TxVP M-8982). We chose not to score this feature in discrete states because we could not make a clear qualitative distinction among specimens in the shape and distinctiveness of the notch or spur. However, we note that the notch on the ectopterygoid in many specimens of Gerrhonotus is not unlike that present in most specimens of Elgaria.
The posterior process of the septomaxilla is shortened in E. coerulea TNHC 58792 and in specimens of G. lugoi relative to other specimens of Elgaria and Gerrhonotus.
A dorsally curved posterior process of the septomaxilla was reported previously to diagnose Elgaria (Good, 1987). We found that the posterior process is straight in many specimens of Elgaria, including specimens of E. cedrosensis (only the left septomaxilla of SDNHM 30296, Fig. 24D), E. kingii (SDNHM 24252, the left septomaxilla of SDNHM 27895), E. paucicarinata SDNHM 45100, E. coerulea (CAS 14509, UF 152969), and some specimens of E. multicarinata (TNHC 35666, TNHC 4478, TxVP M-8975). Furthermore, a dorsally curved posterior process of the septomaxilla is present on the left septomaxilla of G. lugoi LACM 116254 and the right septomaxilla of G. infernalis TxVP M-11414. Care should be employed when scoring this feature in anterolateral view on an articulated skull (i.e., viewed through the naris) because a non-linear ventral border of the posterior process of the septomaxilla may give the impression that the process curves farther dorsally than it appears in lateral view (e.g., E. cedrosensis SDNHM 30296, Fig 24G).   (Good, 1987, character 60).
An anterolateral 'spur' on the septomaxilla was reported in Elgaria and Gerrhonotus and was hypothesized to be homologous to a flange on the septomaxilla present in other   anguids (Good, 1987). All specimens have some type of anterolateral projection; however, the morphology of such a projection varies considerably among specimens. The projection may be thin and elongated (e.g., E. paucicarinata SDNHM 45106, Fig. 24B) or it may be broad (e.g., G. lugoi LACM 116254, Fig. 24C). The morphology of the projection may  also be bilaterally asymmetrical (e.g., E. velazquezi SDNHM 68677). It is possible that the shape of the spur varies ontogenetically, and Evans (2008) noted that in lizards generally flanges and processes on the septomaxilla result from an increased ossification through ontogeny.
Vomer 35. Angle that the foramen for the medial palatine nerve penetrates the vomer: 0=penetrates at an anteriorly inclined angle, Fig. 25H; 1=penetrates vertically through the bone, Fig. 25I (Good, 1987, character 28). All gerrhonotines besides Mesaspis (now synonymized with Abronia) reportedly possess a medial palatine nerve that pierces the vomer via an anteriorly angled foramen (Good, 1987). We found that in most examined specimens of Elgaria and Gerrhonotus, the foramen pierces the bone at an inclined angle. The foramen on the left vomer of G. ophiurus TCWC 35604 and the left vomer of E. nana SDNHM 17102 (Fig. 25I) pierces the bone vertically. In E. multicarinata TNHC 35666, the left foramen is not inclined and instead pierces the bone horizontally and empties anteriorly into a large hole in the vomer that we did not observe in any other specimen (Fig. 25B). The foramen on the right vomer of E. kingii SDNHM 27895 penetrates closer to vertical relative to its contralateral element.
The vomers of E. multicarinata TNHC 35666 are unusual with respect to other gerrhonotines in that they have a small spur on the ventral surface of the palatine processes. This morphology is similar to bony spurs reported in Diploglossus and Ophiodes (Evans, 2008; e.g., Ophiodes striatus CAS 231485, Fig. 25C).
37. Condition of a lamina or projection on the lateral edge of the posterior palatine process of the vomer: 0=short or absent, Fig. 25K; 1=tall or long, Fig. 25G (new feature).
The morphology of a lamina on the dorsolateral surface of the posterior palatine process of the vomer is variable among specimens. Most specimens of Elgaria possess a tall lamina that may extend into a posterodorally pointed projection (e.g., E. paucicarinata SDNHM 45100, Fig. 25G) or may not have a pointed projection (e.g., E. coerulea and E. nana). A tall lamina without a pointed projection is also present in G. liocephalus TCWC 9896 (Fig. 25J) and G. lugoi CM 49012. Specimens of G. parvus are unique in having a short lamina (Fig. 25K).
We found that there is a large foramen near the posterolateral margin of the vomeronasal concavity in E. kingii SDNHM 27895 and on the right vomer of E. coerulea TNHC 14643 (Fig. 25E).
Z. Length of the palatine process of the vomer (Good, 1987, character 25).
The palatine process of the vomer of Gerrhonotus was described as being elongated relative to other gerrhonotines (Good, 1987). While the lengths of the vomers of specimens of G. infernalis and possibly G. lugoi appear somewhat different than those of specimens of Elgaria and G. parvus, when we isolated the vomers, we did not observe an unambiguous qualitative distinction between a short and a long palatine process (Figs. 25H and 25I). Future studies using quantitative methods like geometric morphometrics may discover distinct differences related to this morphology.
AA. Condition of the posterolateral border of the vomeronasal concavity on the vomer (new feature).
The posterolateral border of the vomeronasal concavity is characterized by a steep and distinct ridge that separates the nasal and vomeronasal regions of the vomer in most specimens of Elgaria (e.g., E. cedrosensis SDNHM 30296, Fig. 25D). In some specimens of G. infernalis (TNHC 18988, TNHC 92262) and G. lugoi LACM 116254 this ridge is somewhat shorter resulting in a shallowly inclined posterolateral border of the vomeronasal concavity and a less distinct separation from the nasal region (Fig. 25F). We did not score this character because all specimens have a ridge and variation is continuous which results in specimens not easily being separated into distinct qualitative states.
Species of Elgaria (then classified in the genus Gerrhonotus) were reported by Fitch (1938) to possess palatine teeth. No specimen in our sample has palatine teeth and it is likely that the author intended to reference teeth on the pterygoid instead.
The prefrontal was reported previously to exclude contact between the palatine and jugal in Gerrhonotus and Mesaspis (now synonymized with Abronia) (Good, 1987). The lacrimal excludes contact between the palatine and the jugal in E. kingii SDNHM 24252 (Fig. 26B) and the left side of E. coerulea TNHC 58792, a condition unique among our sample of gerrhonotines. Among Elgaria, the palatine and jugal contact each other only in E. panamintina and in most specimens of E. multicarinata and E. coerulea. Among specimens of Gerrhonotus, the palatine and jugal are in contact in G. infernalis TNHC 92262, G. parvus SRSU 5538, and on the right side of G. parvus SRSU 5537 (the condition on the left side could not be determined due to bone deterioration). In other specimens of G. infernalis There is a separate foramen on the lateral surface of the choanal groove that opens posteriorly into the infraorbital foramen on the left palatine of E. cedrosensis SDNHM 30296 (Fig. 26C), the left palatine of E. paucicarinata SDNHM 45100, and the right palatine of E. multicarinata TxVP M-8987. The presence of two anterior openings for the infraorbital canal was previously reported in other lizards (e.g., Cordylus mossambicus)   ; however, the presence of two anterior openings has not been previously reported in gerrhonotines.
42. Presence of a flange of bone proximal to the anterior opening of the infraorbital foramen: 0=absent (right palatine of E. cedrosensis SDNHM 30296), Fig. 26C; 1=present (left palatine of E. cedrosensis SDNHM 30296), Fig. 26C (new feature). In E. coerulea TNHC 58792, the right palatine of E. cedrosensis SDNHM 30296 (Fig. 26C), and G. infernalis TxVP M-13441, there is a small flange of bone near the anterior opening of the infraorbital foramen. It is possible that the presence of a flange may be related to the presence of two anterior openings for the infraorbital canal because E. cedrosensis SDNHM 30296 has a flange on the right palatine and a foramen on the left palatine; however, on all other specimens either a flange or two openings for the infraorbital canal are present.
AB. Shape of the maxillary process of the palatine (modified from Good, 1987, character 32).
The maxillary process of the palatine was described as robust in Gerrhonotus, Elgaria, and Barisia relative to Mesaspis (now synonymized with Abronia) and Abronia (Good, 1987). We found considerable intra-and interspecific variation in the shape of the maxillary process among Elgaria and Gerrhonotus. The maxillary process extends farthest posteriorly and is posteriorly pointed in specimens of E. panamintina (Fig. 26F), G. liocephalus, most specimens of E. multicarinata except for E. multicarinata (TxVP M-8993, TxVP M-8987), and most specimens of G. infernalis except for G. infernalis (TxVP M-7129, TNHC 18988, Fig. 26G). In other species, the shape of the process varies intraspecifically and is somewhat shorter and blunter (Fig. 26E). Variation in whether the maxillary process possesses a more laterally or posteriorly oriented tip may influence whether the process is interpreted as short or long in articulated specimens. The morphology of the maxillary process of the palatine may also influence whether the palatine and jugal contact one another (our feature 40). Most specimens with an elongate maxillary process also possess contact between the palatine and the jugal. This is exemplified by G. infernalis TxVP M-7129, which has contact on the left side where the maxillary process is somewhat longer but not on the right side where the process is shorter. An elongated maxillary process may, therefore, result in the contact with the jugal; however, this is contradicted by E. multicarinata (TxVP M-9005, TxVP M-9007) and G. infernalis TxVP M-12353, in which an elongated maxillary process of the palatine does not contact the jugal. We did not score this character because a continuous spectrum of variation in the shape and length of the maxillary process of the palatine among specimens did not allow for consistent assignment to distinct states.
AC. Condition of a dorsomedial flange on the vomerine process of the palatine (Good, 1987, character 33).
A "pronounced dorsomedial flange, present on the dorsal surface of the vomerine process…" was reported in Gerrhonotus, Elgaria, and Barisia (Good, 1987:289). We were unable to determine which flange Good (1987) referred to because there were multiple features on the dorsomedial surface of the vomerine process of the palatine that could have been referenced. When the palatine is viewed anteriorly, the anterior end of an upturned medial edge of the palatine has the appearance of a dorsomedial flange (see figure 17 of Ledesma & Scarpetta (2018)). This is similar to examining an articulated skull in anterior view through the naris. When we viewed the palatine in isolation, we found that there are also small projections on the medial surface of the vomerine process in some specimens that are variable in size and position (e.g., E. kingii SDNHM 24252, Fig. 26B). We chose not to score this feature because of our uncertainty as to which structure was intended by Good (1987).
AD. Posterior extension of the lateral edge of the posterior palatine process (Good, 1987, character 34).
It was reported that in ventral view, "…the lateral edge of the pterygoid process [=posterior palatine process] projects much farther posteriorly in all other genera than in Gerrhonotus…" (Good, 1987:289). This morphology was likely scored by Good (1987) with the pterygoid and palatine in articulation. We did not observe a difference in the posterior extent of the lateral edge of the posterior palatine process between specimens of Elgaria relative to specimens of Gerrhonotus. We instead found that the nature of articulation between the palatine and pterygoid is variable, likely because of the kinetic nature of the articulation between the two bones (Frazzetta, 1983). When we examined the palatine in isolation, we found a large amount of intraspecific variation and bilateral asymmetry in the lengths of the two projections on the posterior palatine process. The medial projection ranges from projecting far posteriorly relative to the lateral projection (e.g., specimens of E. paucicarinata, Fig. 26E) to being relatively equal in posterior extent to the lateral projection (e.g., specimens of E. panamintina, Fig. 26F). Some specimens exhibit bilateral asymmetry in this feature (e.g., G. infernalis TNHC 18988, Fig. 26G). There was a continuous spectrum of variation in the lengths of the projections on the posterior palatine process which prevented us from scoring this feature in discrete qualitative states.
The head of the orbitosphenoid is bifurcated in specimens of E. panamintina, E. kingii SDNHM 24252, E. paucicarinata SDNHM 45106, and E. coerulea TNHC 14643 (Fig. 27A). Although the morphology of the orbitosphenoid changes with ontogeny in iguanines (de Queiroz, 1987), the morphology of the orbitosphenoid was reported to be independent of ontogeny in polychrotids (Torres-Carvajal, 2003). Further investigation is needed to evaluate patterns of ontogenetic variation in the shape of the orbitosphenoid in gerrhonotines. the posterolateral tip is located slightly closer to the posterior-most extent of the supraoccipital compared to other Elgaria.
AE. Width of supraoccipital and shape of anterior margin in dorsal view (Good, 1987, character 71).  The supraoccipital in Abronia (=Mesaspis) moreletii was reported to be wider and shorter than the supraoccipital of other gerrhonotines (Good, 1987). We found that many specimens of Elgaria and Gerrhonotus possess a morphology similar to that description, in which the supraoccipital is much wider than it is long (e.g., G. parvus SRSU 5538, Fig. 28C). The shape of the supraoccipital was reported to vary ontogenetically in other anguimorphs (Bever, Bell & Maisano, 2005) and we found that the shape of the supraoccipital is wide relative to its anteroposterior length in juvenile specimens of Elgaria and small specimens of Gerrhonotus. This provides evidence that the relative width-to-length of the supraoccipital varies ontogenetically and may help explain the continuous spectrum of variation observed in our sample. Additionally, we noticed that the anterolateral end of the supraoccipital projects far anteriorly relative to the base of the ascending process in several specimens with a wide and short supraoccipital (e.g., G. parvus and E. multicarinata TxVP M-12129). This morphology may be correlated to how wide the bone is perceived to be relative to its length; however, in E. multicarinata TxVP M-8992, which has a supraoccipital that is not especially wide relative to its length, the anterolateral part of the supraoccipital projects far anteriorly relative to the base of the ascending process (Fig. 28D). Elgaria paucicarinata SDNHM 45100 is unusual in that long projections are present on either side of the ascending process (Fig. 28F).
AF. Angle between the ascending process (processus ascendens of Evans, 2008) and the main body of the supraoccipital (Good, 1987, character 72).
Gerrhonotus was reported to possess an ascending process (medial ascendant process of Good, 1987) that "…at its anterior end makes a sharper angle with the main body of the element…" (Good, 1987:291). We had difficulty consistently examining the angle between the process and the main body of the bone for several reasons. First, because the dorsal surface of the supraoccipital is not flat, it is difficult to determine a horizontal plane by which to measure the angle consistently. Second, the inclination of the dorsal surface of the supraoccipital varies among specimens. Some specimens (e.g., E. velazquezi SDNHM 68677 and G. infernalis TNHC 18988) have an inclined anterior end of the supraoccipital (Fig. 28G), which confounds a comparison between the angle between the ascending process and the main body of the supraoccipital between all specimens. Nonetheless, we did not observe a distinct qualitative difference in the angle of the ascending process between specimens of Gerrhonotus and Elgaria. Sphenoid 45. In anterior view, direction of the anterior opening for internal carotid foramen: 0=opening faces anteromedially, Figs. 27A and 27F; 1=opening faces anteriorly, Fig. 27B (new feature).
In all examined specimens of Elgaria, the anterior openings for the internal carotid foramina face anteromedially. In most specimens of G. infernalis, the anterior openings for the internal carotid foramina face anteriorly. However, the opening for the right internal carotid foramen on G. infernalis TNHC 18988 (Fig. 27B) and left internal carotid foramen in G. infernalis TxVP M-13442 and G. infernalis TxVP M-13441 are oriented somewhat anteromedially. In G. infernalis TxVP M-13440, the left anterior opening for the internal carotid foramen is much larger than the right opening. In other species of Gerrhonotus the internal carotid foramina face anteromedially.
AG. Anterior extent of the basipterygoid processes of the sphenoid relative to the main body of the bone (new feature).
In several specimens of Gerrhonotus and Elgaria, the basipterygoid processes extend far anteriorly (e.g., E. coerulea TNHC 58792 and G. parvus SRSU 5538) (Fig. 27C) compared to other specimens (Fig. 27E). We observed a continuous range of variation in the anterior extent of the basipterygoid processes among specimens and we choose not to score this feature in discrete qualitative states. Some specimens that have basipterygoid processes that extend relatively far anteriorly (e.g., G. parvus SRSU 5538) also have a sphenoid that is somewhat wider in anterior view (Fig. 27D) suggesting a correlation between the two features. However, in E. multicarinata TxVP M-8990 and E. coerulea (TxVP M-9008, TxVP M-8965) the basipterygoid processes extend far anteriorly, but the sphenoid does not appear wide in anterior view. In one juvenile specimen (E. multicarinata TxVP M-8982), the basipterygoid processes extend far anteriorly and the sphenoid is not widened in anterior view, but in another juvenile specimen (E. multicarinata TxVP M-8578), the basipterygoid processes do not extend far anteriorly but the sphenoid is relatively wide in anterior view. The shape of the sphenoid was shown to vary ontogenetically in Shinisaurus (Bever, Bell & Maisano, 2005). An increased sample of juvenile gerrhonotines is necessary to shed further light on patterns of ontogenetic variation in sphenoid morphology.
The supratrigeminal process was reported to divide the incisura prootica in Gerrhonotus and some Elgaria (Evans, 2008). We found that a supratrigeminal process is present on all Elgaria except for E. multicarinata TxVP M-8980 and the right prootic of E. multicarinata TNHC 35666. The process is not visible in lateral view in many specimens. A small supratrigeminal process is present in specimens of G. parvus, G. lugoi LACM 116254, and G. liocephalus TCWC 8585. The process is absent in G. ophiurus and G. infernalis except for the presence of a small supratrigeminal process in G. infernalis TxVP M-7129. Additionally, on the right prootic of G. infernalis TNHC 18988 and on both sides of G. liocephalus TCWC 9896, a foramen is present in the same location where a supratrigeminal process would be (Fig. 29D).
In many specimens of Elgaria there is a small foramen located near the posterior acoustic foramen that opens posteriorly into the cavum capsularis. This foramen is present on only one side in some specimens (e.g., E. kingii SDNHM 24252) and is not fully enclosed by bone in others (e.g., left prootic of E. cedrosensis SDNHM 30296). Two anterior acoustic foramina were reported in Ctenosaura pectinata (Oelrich, 1956).
However, it is not clear whether the foramen observed in Elgaria represents a second anterior acoustic foramen, because it is located near to and may merge with the posterior acoustic foramen, as seen in E. cedrosensis SDNHM 30296.
An enclosed canal for the perilymphatic duct was reported on the prootic of E. panamintina (Ledesma & Scarpetta, 2018 Figure  AH. Condition of the alar process of the prootic (Good, 1987). Variation in the shape of the alar process was previously reported in gerrhonotines (Good, 1987). Our data corroborate those observations. Many specimens have long alar processes (e.g., G. infernalis TNHC 18988, Fig. 29F), but several specimens (e.g., G. parvus, Fig. 29E) have a relatively short alar process of the prootic. We observed continuous variation in the length of the alar process. The length of the alar process of the prootic was shown to vary through ontogeny in E. multicarinata (Bhullar, 2012) and in other anguimorphs (Bever, Bell & Maisano, 2005). One juvenile specimen (E. multicarinata TxVP M-8578) also has a short alar process.  Figure    Elgaria kingii SDNHM 27895 and G. parvus SRSU 5538 (Fig. 31B) have the unusual condition of having a foramen on the left otooccipital that opens dorsal to the vagus foramen and empties into an enclosed hollow chamber in the otooccipital located medial to the posterior semicircular canal (Fig. 31A).
50. Extent of a crest on the posterior edge of the supraoccipital extending onto the posterior surface of the otooccipital: 0= crest does not extend to the ventral margin of the paroccipital processes, Fig. 31E; 1= crest reaches the ventral margin of the paroccipital processes, Fig. 31C (new feature).
There is variation in the length of a crest extending from the posterior edge of the supraoccipital onto the posterior surface of the otooccipital. This crest extends to the ventral edge of the paroccipital process in some specimens of G. infernalis (e.g., G. infernalis TNHC 18988, TNHC 92262). Among Elgaria, the crest is longest in E. panamintina MVZ 75918 (Fig. 31F) and some specimens of E. multicarinata. The crest is somewhat shorter in other specimens of Elgaria (e.g., E. coerulea TNHC 58792, Fig. 31E). There is a continuous spectrum of variation in the length of the crest in Elgaria which is likely a result of some degree of ontogenetic variation because juvenile specimens of Elgaria all have a short crest. Although E. cedrosensis SDNHM 30296 lacks a continuous crest running from the supraoccipital to the ventral margin of the paroccipital processes, that specimen does have a short crest near the ventral margin of the paroccipital processes that continuous as a small lateral projection.
The length of the paroccipital process is variable among specimens of Elgaria and Gerrhonotus. The paroccipital process is shortest in G. parvus SRSU 5538 (Fig. 31D) and longest in E. paucicarinata SDNHM 45106 and some specimens of G. infernalis (Fig. 31C). We chose to not score this feature as discrete qualitative states due to continuous variation in length.
It was reported previously that the dentary contributes to both the dorsal and anterior bordering of the anterior inferior alveolar foramen in Anguidae ). However, it was also reported that in all gerrhonotines except for Elgaria the dentary contributes only to the dorsal margin of the anterior inferior alveolar foramen (Conrad et al., 2011). We found that in most specimens the dentary contributes to both the anterior and dorsal margin of the anterior inferior alveolar foramen. Interestingly, the dentary does not contribute to the anterior inferior alveolar foramen in E. velazquezi SDNHM 68678 (Fig. 32C), in some specimens of E. kingii (SDNHM 27895, on the left side of SDNHM 24252), and on the left side of E. multicarinata TxVP M-8990 because the anterior inferior alveolar foramen is enclosed entirely within the splenial. In those specimens, the dentary is lacking a posterior-facing spine that usually forms the anterior and a small portion of the ventral margin of the anterior inferior alveolar foramen. An elongate projection of the splenial dorsal to the anterior inferior alveolar foramen excludes the dentary from contributing to the dorsal border of the foramen in E. velazquezi SDNHM 68677 (Fig. 32B)  52. Number of tooth positions on the dentary (Good, 1987, character 95).
Gerrhonotus was described as unique compared to other gerrhonotine genera in having between 27-30 tooth positions on the dentary, compared to the 18-23 tooth positions reported for other genera (Good, 1987). We found that large specimens of Elgaria have 19-26 tooth positions on the dentary and specimens of G. infernalis have 25-28 tooth positions. Specimens of G. parvus and G. lugoi have 21-23 tooth positions and G. liocephalus and G. ophiurus have between 20 and 26 tooth positions. 53. Number of labial nutrient foramina on the dentary (Evans, 2008).
We found intraspecific variation and bilateral asymmetry in the number of nutrient foramina on the lateral surface of the dentary with specimens ranging from having four to nine foramina (G. liocephalus TCWC 9896, Fig. 32F).
In E. paucicarinata SDNHM 45106 (Fig. 32D) and on the left dentaries of E. paucicarinata SDNHM 45100, G. liocephalus TCWC 8585, and Gerrhonotus ophiurus TCWC 35604 there are two posteriorly oriented projections of the intramandibular septum. This condition was not observed in any other specimens.
Coronoid 55. Extension of the visible portion of the anteromedial process of the coronoid relative to the last tooth position on the dentary when in articulation with the splenial; 0=anteromedial process is posterior relative to the last tooth position, Fig. 33B; 1=anteromedial process extends anterior to the last tooth position, Fig. 33C (modified from Good (1987), character 86).
Elgaria and Gerrhonotus reportedly possess an anteromedial process of the coronoid that projects anterior relative to the posterior margin of the posterior-most tooth position on the dentary (Good, 1987). We modified this character because the original description did not specify whether the character was scored for the entire anteromedial process of the coronoid or only the part visible when in articulation with the splenial. We inferred that the latter was more likely because the entire anteromedial process of the coronoid projects anteriorly much farther than the last tooth position of the dentary in all specimens. We found that the visible portion of the anteromedial process of the coronoid fails to extend anteriorly past the last tooth position on the dentary when in articulation with the splenial in G. parvus SRSU 5538 (Fig. 33B), G. lugoi CM 49012 (Fig. 33A), and the left side of E. nana SDNHM 52886. The condition in G. parvus SRSU 5537 cannot be determined due to the deteriorated condition of the bones.
All gerrhonotines besides Elgaria were reported to lack a lateral process of the coronoid (coronoid labial flange of Conrad et al., 2011). We found that a lateral process is present in all specimens of Elgaria and Gerrhonotus.
A coronoid contribution to the external border of the anterior surangular foramen was reported as an unambiguous synapomorphy of the least inclusive clade containing Parophisaurus pawneensis, Paragerrhonotus ricardensis, Gerrhonotinae, and Glyptosaurinae clade (Conrad et al., 2011). It was difficult to determine what constituted a contribution to the anterior surangular foramen, so we modified the states to describe the relative position  of the coronoid to the anterior surangular foramen. We found that the anterior surangular foramen is located proximal to the coronoid in all specimens except for E. multicarinata TNHC 35666. Additionally, we found that the coronoid possesses a distinct notch corresponding to the dorsal border of the anterior surangular foramen on one or both sides in many specimens of Elgaria and some Gerrhonotus (e.g., E. velazquezi SDNHM 68677).
AK. Angle of the posteromedial coronoid process with respect to the horizontal axis of the mandible (Good, 1987, character 84). A more ventrally directed posteromedial coronoid process (posteroventral process of Good, 1987) was reported in Gerrhonotus (Good, 1987). The orientation of the  posteromedial coronoid process in specimens varies on a continuous spectrum, but the posteromedial coronoid process is oriented most ventrally in G. lugoi LACM 116254 (Fig. 35B). Some specimens of Elgaria also have a posteromedial coronoid process that is oriented somewhat ventrally (e.g., the right coronoid of E. multicarinata TxVP M-9005).
All other specimens of Gerrhonotus more closely resembled the condition typical of Elgaria in having a more posteriorly-facing posteromedial coronoid process (Fig. 35A).   (Good, 1987, character 80).
Gerrhonotus was reported to have a ventral bulging on the prearticular anterior to the retroarticular process (Good, 1987). What we interpret as a ventral bulging is present in about half of the specimens of G. infernalis but not in other species of Gerrhonotus. Elgaria multicarinata TxVP M-8993 also has a ventral bulging, which suggests that this feature may be correlated with larger size, since that specimen is the largest specimen of Elgaria that we examined. The notion that size is related to the presence of a ventral bulge is further supported by the fact that a similar ventral expansion was found in large individuals of Lacerta viridis (see figure 52 of Villa & Delfino, 2019).
The dorsal surface of the surangular is relatively flat in most specimens of G. infernalis (Fig. 35E), G. liocephalus TCWC 9896, and G. ophiurus TCWC 35604. In G. infernalis (TxVP M-13440, TxVP M-13442) and on the left side of G. liocephalus TCWC 8585 the dorsal surface of the surangular is more raised and curved similar to that of Elgaria.
Lack of fusion between the surangular and articular (including the prearticular) was reported as an unambiguous synapomorphy of anguines, anniellines, gerrhonotines, and glyptosaurines (Conrad et al., 2011), but one researcher reported fusion of the articular and surangular in some gerrhonotines (Criley, 1968). Other authors noted that the bones are fused in most anguid genera (McDowell & Bogert, 1954) or reported that they were not fused (Rieppel, 1980). The surangular and articular are unfused in several specimens of Elgaria and Gerrhonotus. Juvenile specimens of Elgaria and some smaller specimens of Gerrhonotus have an unfused surangular and articular suggesting ontogenetic variation in the amount of fusion. This variation is consistent with previously reported intraspecific variation in fusion in E. kingii (Meszoely, 1970) and bilateral asymmetry of fusion in E. multicarinata (Evan, 2008). The articular and prearticular are fused in all specimens. Conrad et al., 2011, character 172).

Number of anterior surangular foramina (modified from
A distinct anterior surangular foramen was recovered as an unambiguous synapomorphy of Elgaria and was coded as absent in G. liocephalus (Conrad et al., 2011). We found that a distinct surangular foramen is present in all specimens of Elgaria and Gerrhonotus. In fact, there are two distinct anterior surangular foramina on one or both surangulars in several specimens of Elgaria and Gerrhonotus (e.g., G. liocephalus TCWC 8585, Fig. 34C). The presence of two anterior surangular foramina that pierce the coronoid was reported previously in Xenosaurus platyceps (Bhullar, 2011).
AL. Width of the surangular shelf anterior to the articular surface (Good, 1987, character 82).
Gerrhonotus was reported to have a relatively broader and overall, more robust surangular (Good, 1987). We observed that the surangular in specimens of G. infernalis and G. ophiurus TCWC 3560 was broadest among specimens we examined; that may be related to the fact that in those specimens the surangular crest runs anteroposteriorly along the dorsolateral edge of the bone (e.g., G. infernalis TNHC 18988, Figs. 34D and 35F). Other specimens of Gerrhonotus do not appear as broad laterally and also do not have as distinct a crest along the dorsolateral edge of the bone (Fig. 34C). Specimens of Elgaria have a somewhat less broad surangular and have a surangular crest that either slants ventrally along the anterior portion of the bone or becomes indistinct anteriorly (e.g., E. cedrosensis SDNHM 30296, Fig. 35H). The width of the surangular shelf and distinctiveness of the surangular crest vary continuously among specimens.
An expansion on the dorsal surface of the surangular was reported to occur in all gerrhonotines except for Gerrhonotus (Good, 1987). We were unable to identify the feature referenced in this character, partly because our specimens did not differ in that way at that region of the surangular.
AN. Curvature of the posterior end of the surangular and articular complex (new feature).
The surangular and articular complex, including the retroarticular process, tends to be most strongly curved in G. infernalis (Fig. 34D) relative to other species (Fig. 34B); however, specimens vary along a continuous spectrum.
It was reported that the anterior inferior alveolar foramen was farther from the anterior mylohyoid foramen in Gerrhonotus relative to other gerrhonotines (Good, 1987). When we looked at specimens of Elgaria and Gerrhonotus we did not observe clear qualitative differences in the distance between the foramina in these genera (Figs. 32A-32C and 33A-33C) and observed continuous variation in this feature.

DISCUSSION
We evaluated a total of 104 cranial features, including 38 features not previously discussed in gerrhonotines that we found to vary within our sample of specimens (Fig. 37). We discovered substantial variation in previously described osteological features. Much of that variation was previously undocumented, which speaks to the need for more in-depth investigations into osteological variation in squamate clades. Furthermore, we found that most purported systematically informative skeletal features for Elgaria and Gerrhonotus are subject to intra-and interspecific variation, which alters the diagnostic utility of those features. For many features, specimens varied on a continuous spectrum. This made it difficult to discretize that variation into meaningful and/or objective categories, especially qualitative categories. For features originally described with states involving the presence or absence of some morphology, larger sample sizes sometimes revealed many intermediate variations of the 'presence' of a given structure which made it especially difficult to discretize features into objective categories (e.g., features F, G, and Q).  For several features that vary on a continuous spectrum (e.g., features A, F, and I), future investigations using linear or geometric morphometric techniques (e.g., Rej & Mead, 2017;Gray et al., 2017) may provide a more objective means of evaluating those features quantitatively.
We also found that for some features, the orientation of skeletal elements influences scorings (e.g., features 33 and D). It is therefore imperative for researchers to be cognizant of how scorings may be impacted by the way they are viewing a feature. Furthermore, we discovered that for some previously described features it was unspecified whether the feature was originally scored on an isolated element or in articulation with multiple elements (e.g., feature 55). Additionally, we were unable to confidently identify some previously described features (e.g., features AC and AM). Our findings emphasize the need for researchers to effectively describe and communicate the way they are conceptualizing a feature in their descriptions. Explicit figures illustrating the described feature are essential in this regard; a distinct advantage of CT scanning is that the digital models can readily be manipulated for orientation, cross-sectional anatomy, or other desired aspects that greatly facilitate the construction of informative figures.
Several features that were used as characters in phylogenetic analyses of squamate or anguimorph relationships (e.g., features 15, 23, 41, C, D, E, I) and for which a given character state was reported to be an apomorphy of Gerrhonotinae, Elgaria, or Gerrhonotus have decreased utility when a larger sample of specimens and taxa are examined. That is because character matrices framed for eliciting higher-level relationships are generally different from those used to infer lower-level relationships (e.g., Augé & Guével, 2018;Marsh et al., 2019) and because taxon sampling and number of specimens examined in large-scale analyses are not as dense at lower taxonomic levels (i.e., a single species per genus; Gauthier et al., 2012). We identified many new features that are potential apomorphies of different gerrhonotine taxa (see discussion below). The study of variation is a part of the primary process of morphological discovery, but investigations into morphological variation often only assess previously described features or only report on variation that is seen as being systematically informative. We found a substantial amount of intraspecific variation in our sampled gerrhonotine genera, including evidence for ontogenetic variation in many features (e.g., features 9, 17, 18, 26, 52, 58, 60, C, I, M, O, W, AE, AG, AH, and AI). Our results demonstrate that continued study of many different types of variation at lower taxonomic resolution is valuable for understanding broader patterns of morphological variation to inform systematics and fossil identifications. For our study we made observations on articulated and disarticulated dry skeletal specimens as well as CT-scanned alcohol-preserved specimens. CT data facilitated a unique opportunity to examine both articulated and disarticulated cranial elements on a single specimen, which allowed us to make exceptionally detailed observations of morphological variation. The use of CT allows us to report many morphological features that were not previously discussed in gerrhonotines (e.g., features 5, 11, 12, 18, 19, 22, 27, 29, 36, 37, 41, 43, 44, 45, 50, F, G, H, L, Q, R, V, W, X, and AA), and some features that were not documented or were poorly discussed in squamates in general (e.g., features 42, 43, 47, and 48). Many of these features would previously have been impossible or difficult to access on dry skeletal specimens, especially articulated specimens.
In a previous study of gerrhonotine cranial osteology Good (1987) reported three features that diagnose Elgaria (see features 25, 31, and 33) and eight features that diagnose Gerrhonotus (see features 52, 58, 59, A, Z, AD, AF, and AK). An analysis of anguimorph relationships (Conrad et al., 2011) listed five cranial features that were purportedly unambiguous synapomorphies of Elgaria (see features 26, 62, D, E, and AJ). We found that osteological variation in our sample altered the utility of almost all of those previously reported features. We sampled all species of Elgaria and five species of Gerrhonotus. Although we sampled at least two specimens of each species, except for G. ophiurus, to account for some measure of intraspecific variation, future investigations with increased sample sizes will almost certainly reveal additional sources of variation. Based on our current sample we found that no one particular cranial element could be used to identify a particular species of Elgaria; however, a few potential autapomorphies on some elements exist for a few species of Gerrhonotus. We found few clear differences useful to differentiate between Elgaria and Gerrhonotus and none were unambiguous. Many differences between species of Elgaria and between species of Gerrhonotus are subject to intraspecific variation reducing their utility in unambiguously differentiating taxa. Here we present a preliminary assessment of notable osteological differences, including differences subject to relatively smaller amounts of intraspecific variation, that may be useful to differentiate species of Elgaria and Gerrhonotus.
Differences between Elgaria and Gerrhonotus present in at least 60 percent of specimens for each genus 1. Most Elgaria (except for some specimens of E. kingii and E. multicarinata) lack an ossified bridge on the premaxilla that encloses the medial ethmoidal foramen.
7. Most specimens of G. infernalis have a medial projection at the anterior end of the medial shelf of the lacrimal (Feature 22).
8. Gerrhonotus lugoi has a relatively short posterior process of the septomaxilla compared to other Gerrhonotus (Feature 32). 9. Gerrhonotus parvus has a relatively short lamina on the lateral edge of the posterior palatine process of the vomer compared to other Gerrhonotus (Feature 37). 10. In most specimens of G. infernalis the posterolateral tip is positioned level or nearly level to the posterior-most extent of the supraoccipital where the bone forms a part of the margin of the foramen magnum. In other species of Gerrhonotus, the posterolateral tip of the dorsal surface of the supraoccipital is positioned anterior to the posterior-most extent of the supraoccipital (Feature 44).
11. In most G. infernalis the anterior openings for the internal carotid foramen face anteriorly. In other species of Gerrhonotus the anterior openings for the internal carotid foramen face anteromedially (Feature 45).
12. Most specimens of G. infernalis have a crest on the posterior edge of the supraoccipital that reaches the ventral margin of the paroccipital processes (Feature 50).
13. The posterior end of the surangular and articular complex of G. infernalis has a propensity to have the strongest lateral curvature among our sample of Gerrhonotus (Feature AN).

Taxonomic considerations
Continued taxonomic revisions, newly described species, and novel phylogenetic hypotheses based on molecular data (e.g., Leavitt et al., 2017;Zheng & Wiens, 2016) change interpretations and conceptualizations of known morphological features. Conversely, morphology is also useful for hypothesizing phylogenetic relationships and framing taxonomy. It is therefore valuable to assess whether variation in the skulls of Elgaria and Gerrhonotus provides support for phylogenetic hypotheses and taxonomy of those groups. Elgaria multicarinata recently was found to be paraphyletic with respect to E. panamintina (Leavitt et al., 2017). However, we found no consistent differences in the skulls of the northern and southern E. multicarinata lineages inferred by Leavitt et al. (2017). We also found no consistent differences between E. nana and E. multicarinata and found one morphological feature (feature 63) shared between those two species to the exclusion of all other species of Elgaria. The monophyly of Gerrhonotus including G. lugoi and G. parvus is currently undetermined (García-Vázquez et al., 2018a). We found several features shared by G. lugoi and other species of Gerrhonotus (e.g., features 2, 6, and 7). However, some of those features are present in other gerrhonotine genera according to Good (1987) (e.g., feature 2 and 6). Furthermore, we found several morphologies that, within our sample, are specific to G. parvus (e.g., feature 37), G. lugoi (e.g., features 8, 13, 14, and 32), or both species (feature 5). The phylogenetic position of G. lugoi is particularly interesting, because it was recovered in some analyses as being sister to Barisia (García-Vázquez et al., 2018a). We found that G. lugoi shares several features reported to occur in Barisia, Mesaspis (now synonymized with Abronia), or Abronia (Good, 1987), including a marked separation of the nasals from one another (although only near the midpoint of the nasals of G. lugoi) (feature 13) and the reduction of the length of the posterior process of the septomaxilla (feature 32).

CONCLUSIONS
Our study represents the most exhaustive investigation into the cranial osteology of the gerrhonotine genera Elgaria and Gerrhonotus. We sampled all extant species of Elgaria and five of the nine species of Gerrhonotus. Most previously reported systematically informative skeletal features for Elgaria and Gerrhonotus are subject to intra-and interspecific variation, which alters their diagnostic utility. We report 38 new variable features for Elgaria and Gerrhonotus and present a preliminary assessment of osteological differences that may be useful to differentiate species and genera. Several cranial features may support phylogenetic hypotheses and taxonomy of Elgaria and Gerrhonotus. Much of the variation that we report in Elgaria and Gerrhonotus was previously undocumented including some features that were unknown or were poorly discussed in squamates in general. Our findings demonstrate that there is a need for more detailed investigations into patterns of morphological variation in squamate clades to facilitate an increased understanding of patterns of osteological variation for interpreting the fossil record, a conclusion that is broadly applicable across vertebrate clades.
The systematic utility of intraspecifically variable features was previously noted (Wiens, 1999), yet few authors have reported or emphasized such features. In part, that is because methods for integrating polymorphic characters into phylogenetic analyses are not straightforward. Nevertheless, continued investigations into morphological variation have yielded new insights into phylogenetic relationships and morphological evolution of squamates (e.g., Bhullar, 2011;Čerňanský, Smith & Klembara, 2014;Díaz-Fernández, Quinteros & Lobo, 2017;Stilson, Bell & Mead, 2017;Hernández Morales et al., 2019). Investigations into other vertebrate clades including turtles (Joyce & Bell, 2004), frogs (Bever, 2005), birds (Kirchner-Smith, 2015), and mammals (Gould, 2001) have also shown that substantial amounts of previously unreported morphological variation exist, some of which alter the diagnostic utility of previously reported features. Data on morphological variation in vertebrate clades serves as the foundation for interpretation of the fossil record, especially for taxa deeper in time for which genetic data are not available. Continued investigations into morphological variation are needed to better understand patterns of variation, including but not limited to intra-and interspecific variation, ontogenetic variation, and sexual dimorphism. Documenting these patterns of variation will greatly advance our ability to interpret patterns of morphological variation in the fossil record and may provide useful insights for systematics (e.g., Olori & Bell, 2012;Bhullar, 2012).
We highlight the need for researchers to effectively describe and communicate the way in which they are conceptualizing morphological features. Clear morphological descriptions and guiding figures will greatly facilitate continued investigations into morphological variation. Lastly, we reaffirm that X-ray computed tomography provides a unique opportunity to examine both articulated and disarticulated elements of the same specimen and can facilitate novel insights into patterns of morphological variation.