A new extinct species of alligator lizard (Squamata: Elgaria) and an expanded perspective on the osteology and phylogeny of Gerrhonotinae

Alligator lizards (Gerrhonotinae) are a well-known group of extant North American lizard. Although many fossils were previously referred to Gerrhonotinae, most of those fossils are isolated and fragmentary cranial elements that could not be placed in a precise phylogenetic context, and only a handful of known fossils are articulated skulls. The fossil record has provided limited information on the biogeography and phylogeny of Gerrhonotinae. We redescribe a nearly complete articulated fossil skull from the Pliocene sediments of the Anza-Borrego Desert in southern California, and refer the specimen to the alligator lizard genus Elgaria. The fossil is a representative of a newly described species, Elgaria peludoverde. We created a morphological matrix to assess the phylogeny of alligator lizards and facilitate identifications of fossil gerrhonotines. The matrix contains a considerably expanded taxonomic sample relative to previous morphological studies of gerrhonotines, and we sampled two specimens for many species to partially account for intraspecific variation. Specimen-based phylogenetic analyses of our dataset using Bayesian inference and parsimony inferred that Elgaria peludoverde is part of crown Elgaria. The new species is potentially related to the extant species Elgaria kingii and Elgaria paucicarinata, but that relationship was not strongly supported, probably because of extensive variation among Elgaria. We explored several alternative biogeographic scenarios implied by the geographic and temporal occurrence of the new species and its potential phylogenetic placements. Elgaria peludoverde is the first described extinct species of Elgaria and provides new information on the biogeographic history and diversification of Elgaria. Our research expands the understanding of phylogenetic relationships and biogeography of alligator lizards and strengthens the foundation of future investigations. The osteological data and phylogenetic matrix that we provided will be critical for future efforts to place fossil gerrhonotines. Despite limited intraspecific sampled sizes, we encountered substantial variation among gerrhonotines, demonstrating the value of exploring patterns of variation for morphological phylogenetics and for the phylogenetic placement of fossils. Future osteological investigations on the species we examined and on species we did not examine will continue to augment our knowledge of patterns of variation in alligator lizards and aid in phylogenetics and fossil placement.

Background Alligator lizards (Squamata: Gerrhonotinae) compose a widely distributed group in North America with a relatively ancient history. There are approximately 60 extant species and a handful of known extinct alligator lizard taxa [1][2][3]. Extant gerrhonotines are found in southeastern Canada, across the western United States, throughout Mexico, and in Central America south to Panama [4][5][6]. Gerrhonotines inhabit a wide range of habitats including cloud-forests, temperate pine-oak forests, grasslands, and desert refugia [7][8][9]. Some extant taxa are habitat generalists, including several species of Elgaria [6], but others exhibit specialized ecologies, including arboreal species of Abronia [8,10].
The cranial osteology of gerrhonotine lizards was examined by several researchers [11][12][13][14][15][16] and gerrhonotines were incorporated into a number of phylogenetic analyses of morphological data [17][18][19][20][21]. Some researchers previously noted difficulty in differentiating gerrhonotine genera based upon osteological morphology [11]. Most previous investigations into the osteology of gerrhonotines focused on identifying osteological features that would serve to distinguish the various genera. Those studies were based on limited sample sizes with relatively low taxon sampling. More recently, patterns of intra-and interspecific variation were documented in Elgaria and Gerrhonotus to increase our understanding of osteological variation in the skulls of extant gerrhonotines and to explore the potential consequences of that variation for phylogenetic analysis of osteological data [13,14], with the goal of facilitating identifications of fossil gerrhonotines. Variation has also been documented in the external morphology of gerrhonotines [22].
We know of only three formally described articulated fossil skulls referred to Gerrhonotinae or placed via phylogenetic analysis in that clade [1,12,17,33,39]. One of those skulls, LACM (Natural History Museum of Los Angeles County, formerly the Los Angeles County Museum) 10601, is a well-preserved fossil from Pliocene sediments of the Anza-Borrego Desert of southern California [33]. Although many cranial elements are visible on LACM 10601, most of the previously established apomorphies of gerrhonotines [4] were reported to be obscured on the physical specimen, preventing a refined identification [33]. The fossil was found in an area that is currently inhabited by species of the genus Elgaria, which are found in Canada, the United States, and Mexico ( Fig. 1) [5,6], although that alone does not preclude its assignment to any of the other gerrhonotine genera [40]. LACM 10601 was more recently examined by Ledesma [41]; he provided a new description of the fossil using x-ray computed tomography, and investigated the evolutionary relationships of the fossil with phylogenetic analyses that included all species of Elgaria and several species of Gerrhonotus. Those analyses indicated that LACM 10601 was referable to Elgaria, and that the fossil may have a close relationship with species of Elgaria that are endemic to the Baja California Peninsula [41]. Recent molecular phylogenies indicate that extant species of Elgaria that are today endemic to Baja California are not all each other's closest relatives. Elgaria cedrosensis and E. velazquezi are hypothesized to be sister taxa, but E. paucicarinata is hypothesized to be sister to the mainland taxon E. kingii, which currently inhabits the Sierra Madre Occidental in western Mexico and parts of the southwestern United States [5,6].
Here, we expand upon the work of Ledesma [41]. We provide a redescription and a new diagnosis of LACM 10601 and formally designate it as a representative of a new extinct species of Elgaria. We examined the cranial osteology of a significantly expanded sample of gerrhonotine taxa, which includes many extant gerrhonotine species and clades. We created a phylogenetic character matrix that includes revised characters from the literature and characters that are new to the literature, and which is designed specifically for investigating phylogenetic relationships of Gerrhonotinae and for identifying fossil alligator lizards. In that process, we identified some characters that we excluded from phylogenetic analyses of Gerrhonotinae. Additionally, we provide new morphological data that may help inform the relationships of several systematically enigmatic gerrhonotines (e.g., G. lugoi, G. parvus). Using automated binning, we discretized several continuous morphological features into discrete character states. We conducted phylogenetic analyses Keywords: Gerrhonotinae, Phylogenetics, Morphology, Osteology, Elgaria, Fossils, Anza-Borrego, Pliocene, Biogeography

Holotype
The holotype, LACM 10601, is a nearly complete and articulated fossil skull. The specimen is reposited in the paleontology collections of the Natural History Museum of Los Angeles County (LACM).

Etymology
Named in honor of Harry W. Greene, an extraordinary educator, author, and tireless promoter of a greater appreciation of natural history, who has cultivated in his career a deep personal appreciation of the fossil record and of alligator lizards. "Peludo Verde" was the name he took while working in Costa Rica; from the Spanish, peludo ('hairy') and verde ('green').

Diagnosis
LACM 10601 (Fig. 3) is referred to Squamata based on the presence of pleurodont tooth implantation, a single premaxilla, and a splenial, as well as the absence of a quadratojugal and vomerine teeth [19,57,58]. We note that not all of those character states are present in all squamates (e.g., Pseudopus can have vomerine teeth and some skinks have a paired premaxilla) [19]. The fossil is a member of Anguimorpha given the presence of an open and ventrally-facing Meckel's canal, non-compound cephalic osteoderms, and an anterior inferior alveolar foramen that is located between the splenial and the dentary (Figs. 3,4) [28,59]. The specimen is referred to Anguidae because it possesses laterally imbricating osteoderms, a free posteroventral margin of the intramandibular septum (although the free posteroventral margin is absent in extant anguines) [28,38], a maxillary lapet, and a squamosal that is not mediolaterally expanded (Figs. 3a-f, 4, 5a, b) [60].
The anguid clades Diploglossinae and Anguinae possess distinct palatal processes of the premaxilla, which are absent in LACM 10601. LACM 10601 has a fused frontal  Fig. 3e-f ), which is an apomorphy of Gerrhonotinae among extant Anguidae (including Gerrhonotinae, Anniellinae, Diploglossinae, and Anguinae) [28,38]. A fused frontal is present in some taxa in the extinct anguid clade Glyptosaurinae, but that clade is unique among anguids in possessing tubercular-textured osteoderms [28], which are absent in LACM 10601. The frontals are also fused in the extinct European anguine Pseudopus laurillardi [61], although a suture line is still evident in that species and the frontal tapers uniformly in width anteriorly. LACM 10601 is referable to Gerrhonotinae. LACM 10601 possesses a large patch of pterygoid teeth (Fig. 6), which is present in Elgaria and some Gerrhonotus (see "Phylogenetic character list" in "Materials and methods"). The fossil lacks vermiculate and heavily sculptured osteoderms, which are characteristic of many species of Abronia, and also lacks contact of the premaxilla and the frontal, contact of the maxilla and the frontal,  BMC Ecol Evo (2021) 21:184 and an ossified bridge between the nasal process and the body of the maxilla (Figs. 3,7); those features are present in many species of Gerrhonotus, Barisia, and Abronia ("Phylogenetic character list" in "Materials and methods"). The above evidence suggests that the fossil is part of total clade Elgaria. We evaluated the relationships of LACM 10601 via phylogenetic analysis of a morphological character matrix that we created, and we ultimately referred the fossil to the crown clade of Elgaria. The new taxon is diagnosed from other Elgaria in possessing the following unique combination of character states: a supralabial groove on the maxilla (not used as a phylogenetic character), a ventral lamina on the lateral surface of the orbital process of the jugal, a distinct surangular process of the dentary, and a ridge on the dorsal surface of the pterygoid (on the pterygoid flange anterior to the fossa columella).
Remarks LACM 10601 was previously assigned to Gerrhonotinae based on the presence of an anterior process of the surangular, possession of long anterior and posterior maxillary processes, elongate and thin supratemporals, a fused frontal, and the fusion of the prearticular, articular, and surangular [33]. LACM 10601 was reported to resemble Abronia in having a supralabial groove on the maxilla [33]. We agree that there is a groove on the posterior portion of the maxilla, and that this feature seems to be unique in the fossil with respect to other Elgaria. However, we did not observe that groove in any of the Abronia that we examined. It was also suggested that LACM 10601 resembled Abronia in the reduction of the lateral concave surface of the quadrate [33]. We do not find that there is a reduction of the lateral concave surface of the quadrate of LACM 10601. Another reportedly derived feature of the fossil was a lacrimal and jugal everted at the maxillary suture [33], although the systematic meaning of that character was not specified. It was previously reported that eversion of the jugal and lacrimal only occurred in Elgaria, Gerrhonotus, and Barisia [12]. A relationship between LACM 10601 and Abronia was contradicted by the lack of a sublabial groove of the dentary on the fossil [33]. We agree that the 'sublabial' groove is absent on the fossil, and found the groove in some species of Abronia and Barisia (see Phylogenetic Character List). We interpret LACM 10601 as a mature individual because of the well-developed osteodermal crust on the parietal, constriction of the parietal table, relatively long paroccipital processes, and relatively long supraoccipital in dorsal view [14,62].

Description Premaxilla
The right portion of the premaxilla is missing, and the nasal process is laterally curved to the left side due to taphonomic deformation (Figs. 3,7). The premaxilla is rotated to the left so that it faces anterolaterally. As a result, contact of the premaxilla with adjacent bones was difficult to determine. We inferred the spatial relationship of the nasal process relative to the frontal by rotating the premaxilla in Avizo Lite so that the left maxillary facet on the lateral edge of the palatal shelf was aligned with the corresponding articulation surface of the intact maxilla, and determined that contact with the frontal could not have been present (Fig. 7). That observation is supported by the lack of a posterior extension of the ventral keel of the nasal process of the premaxilla (see "Phylogenetic character list" in "Materials and methods"). The nasal process is not especially wide or narrow (Fig. 7a). The anterior surface of the nasal process is flat, and the process tapers in width posteriorly. The incisive process projects anteroventrally below the palatal process, and has a midline groove that gives the process a concave appearance ventrally. The preserved left portion of the palatal process preserves the medial ethmoidal foramen just lateral to the base of the nasal process. The foramen likely transmits the ophthalmic branch of cranial nerve five [63]. Some of the anterior face of the premaxilla is sheared away. An anterior midline foramen is evident ventral to the nasal process, but it is not clear whether the foramen would be open anteriorly because of the missing anterior portion of the premaxilla.
Most of the teeth are missing. There is one partial tooth and four or potentially five total tooth positions.

Septomaxilla
The right septomaxilla is preserved, but is broken into a few pieces (Figs. 3f, 5c). On one of the pieces, a foramen penetrates the bone horizontally. This piece has a flattened medial surface where it would have contacted or closely approached its contralateral element. Another piece of the septomaxilla preserves an anterolateral projection that is also present in many extant gerrhonotines. The posterior process is evident, and is long posteriorly.

Nasal
The anterior process and premaxillary facet of the left nasal are preserved. The anterior process is well-developed (Fig. 5d). An indistinct piece of bone on the right side of the skull may be a piece of the right nasal.

Maxilla
The left maxilla is mostly preserved, but only the orbital process of the right maxilla is present. The orbital process is long relative to the premaxillary process of the left maxilla. The facial process is broad (Figs. 3a, b, 5a), and is inflected medially (Fig. 5b). The anterior edge of the facial process possesses a small anterior spur. The premaxillary process is bifurcated with a medial maxillary lappet that is short and fragmented. The anterolateral portion of the premaxillary process is also short and is located above a distinct facet for the lateral edge of the palatal process of the premaxilla. The crista transversalis connects with the anteromedial surface of the facial process and extends anteriorly towards the base of the premaxillary process. There is a distinct recess at the base of the medial surface of the facial process (medial recess for the nasal sac) just posterior to the crista transversalis. The superior alveolar foramen and/or maxillary trigeminal foramen [64] emerge from a groove on the dorsal surface of the palatal shelf.
The palatine process is a distinct and substantial medial projection from the palatal shelf, and is thickened relative to the rest of the shelf (Fig. 5a, b). There is a small but deep articulation surface on the palatine process for the palatine.
There are five nutrient foramina on the lateral surface of the maxilla and the posteriormost foramen is noticeably larger (Fig. 3a, b). Smaller foramina are located more dorsally on the anterior half of the facial process. Posterior to the nutrient foramina, there is a shallow anteriorposterior depression along the anterior portion of the orbital process. The ventrolateral part of the facial process is covered with sculpturing, particularly the ventral part of the process. There are 20 tooth positions on the left maxilla.

Lacrimal
Both lacrimals are present, but only the left lacrimal is well-preserved (Fig. 3a, b). The posterior end of the bone is elongate and forms a posterior process that articulates with a facet at the anterior end of the jugal. The lacrimal is excavated medially and has a projection extending dorsally from the medial shelf which forms part of the medial border of the lacrimal foramen (Fig. 8h). The lacrimal lacks lateral sculpturing (Fig. 3b).

Prefrontal
The main body of the prefrontal is broad with a rounded anterior edge. The anterior half of the lateral surface of the main body is defined by an articulation surface for the facial process of the maxilla (Fig. 8a). There is a distinct ridge posterior to the articulation facet for the facial process that extends posterodorsally onto the ventral edge of the orbital process of the prefrontal. The orbital process articulates with the lateral surface of the frontal (Fig. 3b, d). The medial surface of the orbital process has a defined groove that continues anteriorly onto the main body of the prefrontal. The posteroventral process extends posteriorly to contact the jugal and contribute to the border of the lacrimal foramen. There are two foramina on the lateral surface of the prefrontal just dorsal to the lateral ridge.

Jugal
The anterior and posteriormost portions of the right jugal are highly fragmented or missing, but both jugals are otherwise complete (Fig. 3a, d). The postorbital (temporal) process has a posteromedial articulation facet for the postorbital. The jugal is broadened at the ventral inflection point in lateral view. Anterior to the inflection point, the maxillary (orbital) process narrows abruptly. The postorbital process narrows more gradually. There is a distinct ventral lamina on the orbital process to articulate with the orbital process of the maxilla (Fig. 8b). A jugal spur is present, as are two lateral foramina and one medial foramen near the inflection point.

Frontal
The frontal is a single midline element (Fig. 3e, f ). The dorsal surface is moderately sculptured with a pitted and somewhat undulose texture. The bone widens posteriorly to meet the parietal, and there is a slight constriction between the orbits. The anteriormost tip of the bone is missing, but some part of all three anterior processes are preserved as are portions of the nasal facets, suggesting that only a small portion of the anterior tip is missing. Due to the shifting of the palatines within the skull, it is not possible to determine whether the crista cranii project below the dorsal surface of the palatine (Fig. 9). There is an anterolateral facet that articulates with the prefrontal, which has a well-developed ridge that slots into a groove on the prefrontal. The posterolateral edge of the frontal has an articulation facet for the postfrontal (Fig. 9).

Parietal
The parietal table is broad, flattened, and roughly trapezoidal (Fig. 3e, f ). The anterodorsal surface of the parietal table is sculptured with osteodermal crust. The parietal foramen is present on the anterior sculptured portion of the parietal table. The anterior edge of the bone has a straight linear contact with the frontal. The post-parietal processes converge towards one another anteriorly where they connect with the main body of the bone, but do not contact (Fig. 8e). LACM 10601 lacks recesses on each side of the posterior surface of the parietal table (Fig. 8e).
On the ventral surface, there are distinct ventrolateral crests (epipterygoid processes) as well as well-developed ridges that define the lateral edges of the pit for the ascending process of the supraoccipital. Although the bones appear to have shifted in their positions, the epipterygoid processes of the parietal and the left epipterygoid are far from contacting one another. The posterior edge of the parietal between the post-parietal processes has a slight notch.

Postfrontal
The lateral edge of the left postfrontal overlaps with the anteromedial portion of the left postorbital. The left postfrontal has a lateral expansion near the inflection point between the anterior and posterior process of the element (Fig. 8c), while the right postfrontal is characterized by a corner at the inflection point. Both postfrontals are rotated ventrally. The medial surface of the postfrontal has a facet for articulation with the frontal and parietal. There are three foramina on the dorsal surface of the posterior process (Fig. 8c).

Postorbital
The postorbitals are well-preserved, but are shifted ventrally. The jugal process projects ventrally along the medial surface of the jugal and bears a distinct articulation facet for the jugal. The postfrontal process is somewhat shorter than the jugal process. The postorbital is not markedly widened along its length; however, the left postorbital is missing a portion of the medial edge (Fig. 8d). The postorbital extends posterior to the anterior tip of the supratemporal as well as the posterior edge of the parietal between the post-parietal processes. The right postorbital and supratemporal contact one another, although this may be a result of the fossilization process (Fig. 3f ).

Squamosal
Most of the right squamosal is well-preserved except for the posterior end of the bone (Fig. 8g). Both the anterior and posterior processes of the squamosal curve ventrolaterally, and the anterior end tapers to a point. The squamosal contacts the lateral surface of the supratemporal and the posterior portion of the postorbital. The posterior end of the squamosal is fragmented and we could not determine whether it curved anteriorly.

Supratemporal
Both supratemporals are present, but only the right is well-preserved (Fig. 3f ). Posteriorly, the supratemporal broadens mediolaterally and increases in height. Anteriorly, the supratemporal tapers to a single point.

Vomer
Both vomers are present, but are fragmented (Fig. 3h). The anterior portion of the left vomer is shifted ventrally. The posterior palatine processes are in close proximity, and possess a facet for the anterior vomerine process of the palatine. There is a well-developed posterodorsal lamina (Fig. 5e). The medial ridge is tall and steeply inclined. On the left vomer there is a ridge that runs anterolaterally from the medial ridge of the vomer. The foramen for the medial palatine nerve appears to be present on the left vomer, but the angle at which the foramen penetrates the bone could not be determined.

Palatine
Both palatines are translated and rotated so that they medially overlap one another (Figs. 3h, 6b). The prefrontal blocks contact between the palatine and the jugal on the left side. The lateral maxillary process of the palatine is pointed posterolaterally. The bifurcated posterior process has medial and lateral projections that are short and blunt, with the lateral projection extending slightly farther posteriorly. The palatine has a deep choanal groove. The maxillary process of the left palatine has a concave facet for articulation with the maxilla. Just above that facet, the bone is pierced horizontally by the large infraorbital foramen. On the anterior portion of the dorsal surface of the palatine there is a distinct articulation facet for the prefrontal. The vomerine process of the palatine has a ventral ridge at the posterior margin of the articulation facet for the vomer (Fig. 6b). Scarpetta et al. BMC Ecol Evo (2021) 21:184 Ectopterygoid Both ectopterygoids are well-preserved (Fig. 6a). The anterior end of the bone has a deep concave facet for the orbital process of the maxilla. The posterior end of the bone is bifurcated with dorsal and ventral processes that form a tight articulation with the pterygoid flange (Fig. 6a). Viewed dorsally, the left ectopterygoid has a distinct lateral bulge which is less developed on the right ectopterygoid. There is a foramen on the ventral surface of the ectopterygoid just anterior to the suture line with the pterygoid. On the left ectopterygoid, there is a single foramen within the articulation facet for the transverse flange of the pterygoid, and there are two foramina on the right ectopterygoid.

Pterygoid
Both pterygoids are present, but the posteriormost portions of the quadrate processes are not completely preserved especially on the left side (Fig. 6c, d). The anterior portion of the bone has a flattened palatal plate that tapers anteriorly. The anterior end of the palatal plate has a facet on the dorsal surface for the medial posterior palatine process. There is an anterolaterally projecting pterygoid flange that is flattened laterally and curves to slot into the articulation facet of the ectopterygoid. There is a distinct anteroposteriorly directed ridge on the dorsal surface of the pterygoid, anterior to the fossa columella (Fig. 6c). The quadrate process of the pterygoid has a well-defined groove on the dorsal surface that begins just posterior to the fossa columellae, and on the right pterygoid a well-developed posterodorsal ridge is evident (Fig. 6c). A small foramen is visible just posterior to the fossa columella on the left pterygoid. There is a broad patch of blunt teeth and tooth implantation sites on the left pterygoid, and a similar patch of implantation sites on the right pterygoid (Fig. 6d).

Quadrate
Both quadrates are present, and the right quadrate is nearly complete (Fig. 10), but the left quadrate is highly fragmentary. The tympanic crest is well-developed but incompletely preserved. The conch is deep (contra Norell [33]) and is substantially wider dorsally than ventrally (Fig. 10b). The cephalic condyle and squamosal notch are both present but portions of each structure are missing. The quadrate column widens near its base. There is a medial expansion of the pterygoid lamina dorsal to the articulation surface for the the quadrate process of the pterygoid. The anterior surface of the quadrate possesses a deep excavation medial to the convex anterior surface of the conch (Fig. 10a).

Epipterygoid
The left epipterygoid is preserved (Fig. 3b, d). The epipterygoid articulates in the fossa columella of the pterygoid and possesses a slight lateral groove at its ventral end. Although the epipterygoid does not contact the ventrolateral crest (epipterygoid process) of the parietal, it does contact the alar process of the prootic.

Sphenoid
The sphenoid is fragmented (Fig. 11). The sphenoid contacts the prootic dorsolaterally and the basioccipital posteriorly. There is a shallow depression on the ventral surface in between the basipterygoid processes. The left basipterygoid process is missing, but the right side is well-preserved and projects ventrolaterally from the main body of the bone, and has a prominent posterior spur. The alar process of the sphenoid projects anteriorly and is rounded. Between the alar processes the crista sellaris overhangs the pituitary fossa. Only the base of the parasphenoid process is preserved. A depression (sella turcica) is located between the trabeculae (crista trabecularis of Oelrich [65]), but the depression ends abruptly before reaching the posterior wall of the pituitary fossa. The depression is replaced posteriorly with a sloped surface of the dorsum sella that contains a carotid foramen on either side, which each open anteromedially. Only the right vidian canal is preserved and the anterior opening is located lateral to the trabecula. The posterior opening of the vidian canal is obscured by bone fragments and matrix. The openings for the abducens foramina are not preserved.

Supraoccipital
The supraoccipital is well-preserved (Fig. 11b). The suproccipital contacts the prootic anterolaterally and the otooccipital posterolaterally. On the dorsal surface, the ascending process projects anterodorsally and rises at a relatively low angle with respect to the bone. A tall medial crest (sagittal crest of McDowell and Bogert [66]) continues posteriorly on the dorsal surface (Fig. 11a). The base of the ascending process connects to the body of the supraoccipital close to the level of anterior extent of the anterolateral tips of the bone. The paths for the anterior and posterior semicircular canals are filled with matrix of a similar density to the fossil, which can be seen in the CT slices. Those paths become obscured at the osseous common crus where the bone is fragmented. An endolymphatic foramen is located on the medial (external) surface of the supraoccipital portion of the cavum capsularis. The supraoccipital appears to be largely fused to the otooccipital posteriorly.

Prootic
The prootics are present but fragmented (Fig. 11a,  b). The prootic contacts the supraoccipital posterodorsally, the otooccipital posteriorly, the basioccipital ventrally, and the sphenoid anteroventrally. The alar process is long with a squared end that, on the left side, contacts the epipterygoid. The external surface of the anterior ampullar recess is large and bulbous, forming part of the dorsal border of a narrow incisura prootica. An elongate anterior inferior process that lies on the sphenoid forms the ventral border of the incisura prootica, and has a dorsal margin that is oriented horizontally. A well-developed supratrigeminal process is present, but is obscured in lateral view by the anterior ampullar recess (Fig. 11a). A well-defined crista prootica is preserved on the right prootic. Neither prootic is preserved well enough to distinguish the location of the facial foramen, but the prootic contribution to the anterior border of the fenestra ovalis is somewhat preserved. On the medial surface on the right prootic, the acoustic recess is visible. The medial opening for the facial foramen as well as the openings for the anterior and posterior acoustic foramina are not preserved.

Otooccipital
Portions of the otooccipitals are preserved (Fig. 11). The otooccipital contacts the supraoccipital dorsally and dorsomedially, although the exact contact between the bones is unclear due to fusion and fragmentation. The otooccipital contacts the basioccipital ventromedially and the prootic anteriorly. The posterior surface of the otooccipital is fragmented and the vagus and hypoglossal foramina were not identified. Much of the paroccipital processes are missing, but a depression is visible on the dorsal surface where the paroccipital process is continuous with the bone (Fig. 11c). A portion of the crista interfenestralis is preserved, thus preserving part of the otooccipital contribution to the lateral aperture of the recessus scala tympani.

Basioccipital
Parts of the left and posterior portions of the basioccipital are missing. The basioccipital contacts the sphenoid anteriorly, the prootic laterally, and the otooccipital posterolaterally. The ventral surface is convex ventrally, and a preserved basal tubercle is oriented ventrolaterally on the right side. The dorsal surface of the basal tubercle constitutes the ventral margin of the lateral aperture for the recessus scala tympani (Fig. 11c). The occipital condyle is incomplete.

Dentary
Portions of both dentaries are preserved, but much of the right dentary is missing (Fig. 3a-d). The dentary has a short dorsoventral height, and tapers gradually in height posterior to the ramus. The Meckelian groove is open, and faces medially along its posterior portion and ventromedially along its anterior portion. There is a welldeveloped, free posteroventral projection of the intramandibular septum (Fig. 4c).
The posteroventral portion of the left dentary is fragmented and so the development of the angular process was not possible to ascertain. The coronoid process is a pronounced triangular projection that articulates with the anterodorsal surface of the anterolateral process of the coronoid. There is also a discrete surangular process that is separate from the coronoid process (Fig. 4c). There are five or six nutrient foramina on the lateral surface of the bone. There are 24 tooth positions visible on the left dentary (Fig. 4a).

Coronoid
Both coronoids are well-preserved. The posteromedial process of the coronoid slants posteroventrally and terminates just anterior to the adductor fossa (Fig. 4b). The coronoid (dorsal) process is long in lateral view and possesses a ridge on the lateral surface anterior to a depression where adductor muscles would attach. The lateral process (labial process of Evans [63]) is a small projection that, together with the anteromedial process, creates a notch in which the surangular process of the dentary articulates. The anteromedial process extends below the dental shelf and reaches anteriorly past the third most distal tooth position of the dentary (Fig. 4a). Midway along this process there is a foramen that penetrates ventrally. The right coronoid does not contribute to the border of the anterior surangular foramen (Fig. 3c-d).

Surangular and articular
The right surangular and articular are well-preserved, but the left elements are largely absent besides some anterior fragments. The surangular and the articular (including the prearticular) are indistinguishable in CT slices and segmented surfaces. The lateral surface of the surangular has a crest that runs anteroventrally. The dorsal surface of the surangular is raised and is sloped on both its lateral and medial surfaces (Fig. 4d). The surangular possesses an anterior surangular foramen as well as a posterior foramen on the lateral surface under the surangular crest. The adductor fossa faces medially and is deep. The retroarticular processes are absent, but the articular surface for the quadrate is present.

Splenial
Fragmented pieces of both splenials are present (Fig. 4a,  b). The splenial has a small anterior projection dorsal to the anterior inferior alveolar foramen. The left splenial has a preserved posterodorsal process that articulates with a facet on the lateral surface of the anteromedial process of the coronoid.

Dentition
Teeth and tooth crowns in particular are absent or poorly preserved due to over-preparation prior to the original examination of the specimen by Norell [33]. Those that are present on the dentary are 'chisel-shaped' (see Gauthier [28]) to nearly bicuspid, in that the distal portion of the crown attains a higher dorsal or ventral extent than the mesial portion of the crown (Fig. 4a-c).

Osteoderms
The osteoderms laterally imbricate and have a distinct anterior gliding surface ( Fig. 4a-f ). Osteoderms become more rectangular and regular in shape posteriorly. The osteoderms are moderately sculptured, and have a dorsal pattern of scattered lines with some pits. The cranial osteoderms lack keels. Sculpturing on the parietal and frontal is similar to the osteoderms. The frontoparietal shields of the frontal are distinct, and are separated by a triangular interparietal shield. There is an osteoderm that partially covers the left frontoparietal shield (Fig. 3d). On the right side that osteoderm appears to have fallen off, because there is an apparent facet for an osteoderm like the one present on the left side of the frontal. No ventral or lateral osteoderms are preserved.

Phylogenetic analyses
We employed Bayesian inference and parsimony on our novel dataset to infer phylogenetic relationships among gerrhonotines and ascertain the placement of Elgaria peludoverde with respect to extant gerrhonotines. We performed analyses without any topological constraints, and two sets of analyses with scaffolds based on previously published molecular phylogenies (see "Materials and methods").

Relationships among extant gerrhonotines
The unconstrained phylogenies (Fig. 12) were similar in many ways to published molecular and morphological phylogenies, although many posterior probability values were low in the Bayesian analyses (Fig. 12a)    A. gadovii, A monticola, and A. moreletti) were sister to the rest of Abronia as in previous osteological analyses [12], as opposed to the paraphyletic 'Mesaspis' inferred by recent phylogenomic analyses [10]. We also found a monophyletic Barisia and a monophyletic keeled-scale clade of Gerrhonotus (represented here by G. infernalis, G liocephalus, and G. ophiurus) [26]. In the unconstrained Bayesian analysis, the keeled-scale clade of Gerrhonotus was sister to Abronia (Fig. 12a), but in the parsimony analysis (both the strict and majority-rule consensus trees) there was a polytomy among the major gerrhonotine clades (Fig. 12b). Gerrhonotus lugoi was consistently placed as the sister taxon of Barisia, a relationship found in some of the analyses by García-Vázquez et al. [26]. This is the first osteological phylogeny to infer a close relationship between G. lugoi and Barisia, and substantiates our previous observations [14]. Unconstrained analyses replicated several other relationships inferred in previous studies. Those include monophyly of species placed in the subclade Auriculabronia (represented here by A. campbelli and A. lythrochila) [8,10], relationships among the keeled-scale Gerrhonotus, a close relationship between G. parvus and the keeled-scale Gerrhonotus ( [26]; but see below), and a close relationship between E. multicarinata and E. nana [5].
In the unconstrained analyses, conspecific specimens were generally inferred to be sister taxa with high or moderate support, except for among Elgaria, in which only E. multicarinata and E. nana were consistently placed together (Fig. 12). Additionally, external morphological and phylogenomic studies suggest a close relationship between or a species complex of individuals referred to A. graminea and A. taeniata [10,22]. In the unconstrained analyses from this study, however, A. taeniata was placed as sister to other Abronia (excluding species previously placed in Mesaspis).
Elgaria was not monophyletic in both unconstrained analyses here (Fig. 12), but monophyly for the genus is strongly supported by molecular data [5,25]. Elgaria cedrosensis was outside Elgaria in the unconstrained analyses (see below). Two specimens of Elgaria were sister to all other gerrhonotines in the unconstrained Bayesian analysis, and in the parsimony analysis, Barisia and G. lugoi were nested in Elgaria. The difficulty we encountered with Elgaria aligns with our previous work in which we found substantial and sometimes excessive intra-and interspecific variation in Elgaria, including features that were purportedly diagnostic or apomorphic for the clade with respect to other gerrhonotines [14].
In all unconstrained and scaffold analyses G. lugoi was sister to Barisia (Figs. 12,13,14). The position of A. ornelasi varied. In all Bayesian analyses and the unconstrained parsimony analysis (Figs. 12, 13a, 14a), the species was sister to ((A. graminea, A. taeniata), A. mixteca) or (A. graminea, A. mixteca), but in the constrained parsimony analyses it was sister to species of Auriculabronia (Figs. 13b, 14b). The latter result is more consistent with previous analyses of morphological and molecular datasets [8,25,67]. The position of G. parvus was even more variable, mirroring difficulties previously encountered by researchers attempting to infer the relationships of the species [26]. Gerrhonotus parvus and G. lugoi, which are both part of the 'smooth-scale' group of Gerrhonotus, were never inferred to be sister taxa. In the unconstrained parsimony analysis G. parvus was sister to E. cedrosensis, and that clade was sister to the keeled-scale Gerrhonotus (Fig. 12b). In the unconstrained Bayesian analysis, E. cedrosensis was sister to the clade (G. parvus, keeled-scale Gerrhonotus) (Fig. 12a). In the constrained Bayesian analyses in which G. parvus could attach anywhere (Fig. 13a), the species was placed as sister to Elgaria. In the constrained parsimony analysis that allowed G. parvus to attach anywhere, the taxon was placed in a polytomy with the keeled-scale Gerrhonotus + the clade (Abronia, (Barisia, G. lugoi)) in the majority rule consensus tree (Fig. 13b), but was in a polytomy with many gerrhonotines in the strict consensus tree (see Additional file 1: Fig. S1). Gerrhonotus parvus is similar to Elgaria in lacking contact of the maxilla and the frontal and in lacking an ossified bridge between the nasal process and the body of the premaxilla, but possesses several features that are largely restricted to Abronia or Barisia, including contact of the premaxilla and the frontal, a low posterodorsal lamina of the vomer, reduced sublabial osteoderms, and the absence of a supratrigeminal process on the prootic. Contact of the premaxilla and the frontal and the absence of a supratrigeminal process were also observed in some specimens of G. infernalis and G. lugoi.
We note that for the parsimony analyses, the tree length of the scaffold trees was distinctly but not greatly longer than that of the unconstrained analyses. The tree length of the unconstrained parsimony tree was 324 steps, and the length of both constrained parsimony trees was 343 steps.

Relationships of Elgaria peludoverde
Elgaria peludoverde was always inferred to be part of crown Elgaria. Relationships of E. peludoverde among Elgaria were largely consistent, but were poorly supported. Almost all relationships among Elgaria, including sister taxon relationships that were strongly supported by molecular analyses [5] and that were constrained here in scaffold analyses, were poorly supported (Figs. 12,13,14).    In strict consensus trees from the parsimony analyses, E. peludoverde was in a polytomy with other species of Elgaria (excluding E. coerulea), or in a polytomy with other many gerrhonotines (Additional file 1: Figs S1-S3). In the majority rule trees from the constrained parsimony analyses, E. peludoverde was sister to E. paucicarinata, occuring in 66.7% of most parsimonious trees (MPTs) in both consensus trees (Figs. 13b, 14b), and in the unconstrained analysis the new taxon was sister to E. paucicarinata SDNHM 45106 (Fig. 12b). In the other MPTs from the parsimony analyses, E. peludoverde was sister to E. panamintina. In the unconstrained Bayesian analysis, E. peludoverde was sister to (E. kingii SDNHM 27895, E. velazquezi SDNHM 68678) (Fig. 12a). In the Bayesian scaffold analysis that allowed G. parvus to attach anywhere, E. peludoverde was sister to (E. kingii, E. paucicarinata) (Figs. 13a, 15b). In the Bayesian scaffold analysis in which G. parvus was placed as the sister taxon of the keeled-scale Gerrhonotus, E. peludoverde was placed as the sister taxon of the clade ((E. cedrosensis, E. velazquezi), ((E. multicarinata, E. nana), E. panamintina)) (Figs. 14a, 15a). That relationship was similar to the majority rule scaffold tree from Ledesma [41]. Although the relationships of E. peludoverde were not well-supported in any analysis, a close relationship with E. paucicarinata and/or E. kingii was recurring.

Phylogenetic relationships of alligator lizards
We inferred relationships among gerrhonotine lizards using specimen-based phylogenetic analyses of a new osteological dataset. We corroborated several well-supported relationships previously inferred in phylogenetic analyses (see "Results"). Although we observed substantial inter-and intraspecific variation among many gerrhonotines (see "Phylogenetic character list" in "Materials and methods"), the main difficulty we encountered estimating phylogenetic relationships among extant gerrhonotines was with the interrelationships of Elgaria. That result was expected given the high amount of intraspecific variation in that genus that we documented previously [14].
The phylogenies and osteological data that we present here will be helpful towards future efforts to illuminate the relationships of two systematically enigmatic species of Gerrhonotus, G. parvus and G. lugoi. In both unconstrained analyses, G. parvus was in a clade with the keeled-scale Gerrhonotus, a relationship previously found by Conroy et al. [68], García-Vázquez et al. [26], and Zheng and Wiens [25]. In the partially constrained analyses which allowed G. parvus to attach anywhere, the species was placed in a polytomy with Abronia, Barisia, and the keeled-scale Gerrhonotus in the parsimony analysis ( Fig. 13b), but the species was inferred to be the sister taxon of Elgaria in the Bayesian analysis (Fig. 13a). The former result is more consistent with previous molecular phylogenies and the presence of several shared features between G. parvus and Abronia, Barisia, and Gerrhonotus; the latter result may reflect convergence in shared character states between G. parvus and some species of Elgaria. Phylogenomic data may be required to provide resolution to the relationships of G. parvus. In all of our analyses, G. lugoi was the sister taxon of Barisia, a novel relationship first inferred by García-Vázquez et al. [26]; we provide the first osteological phylogeny supporting that relationship. That said, the presence of extensive patches of pterygoid teeth in G. lugoi is surprising given a close relationship between that species and Barisia, because we interpret a reduction of the pterygoid teeth as a derived character state in the clade containing Barisia and Abronia.
One notable discrepancy between our unconstrained phylogenies and recently published molecular phylogenies is the relationships among Abronia. We accept a recent phylogenomic hypothesis indicating paraphyly between Abronia and the previously recognized genus Mesaspis [10], but we did not find a paraphyletic Abronia (as it was previously circumscribed) in the present study. Instead, the terrestrial ('Mesaspis') and arboreal ('Abronia') morphotypes were monophyletic and were sister taxa, as was previously inferred from morphological data [8,12]. The repeated appearance of those morphotypes and their associated ecologies is a fascinating issue that will hopefully be addressed in future genomic, ecological, and morphological studies.

Osteological apomorphies of gerrhonotine lizards
Here, we list some morphological character states that we interpret as apomorphic of specific alligator lizards. These character states are interpreted through the constrained trees based on previously published molecular phylogenies and the taxonomies that reflect those phylogenies [5,10,26], not through the unconstrained trees from this study. We recommend that none of these characters be used individually in the absence of other morphological characters to frame a morphological diagnosis   for any given fossil. Instead, we recommend that combinations of characters be assessed in a qualitative apomorphy-based diagnosis, or that a phylogenetic analysis be performed using the matrix that we provide here. We observed inter-and/or intraspecific variation in most character states that we consider apomorphic of a given species or clade. Thus, our interpretation of a character state as an apomorphy does not imply that the character state is present in all of the members of the specified clade. This list is intended to guide fossil identifications but is not intended to be an unambiguous key or a comprehensive summary of our findings. It is necessary to review the "Phylogenetic character list" in "Materials and methods") and/or the matrix itself to determine whether a character state can be used to identify a fossil via apomorphy-based diagnosis given the variation that we observed. Additionally, should a tree topology different from those employed here be leveraged to evaluate a fossil using the morphological characters from our matrix, topological discrepancies and any resulting differences in interpretation would need to be assessed and accounted for [69,70]. Finally, we note that although our study contains a much broader taxonomic sample of gerrhonotines than any previous osteological survey, including several species for which osteological data were not previously available, we only sampled one or two specimens per species because in most cases no skeletons were available and relatively few alcohol-preserved specimens were available. Future studies with increased sample sizes for each species will augment our knowledge of patterns of variation for the morphological characters that we examined [14].
Character states that we observed only in a given species or clade among gerrhonotines are marked with a *. The phylogenetic character number and apomorphic character state number are listed following the brief character state description in the format '(phylogenetic character; apomorphic character state)' . We consider the phylogenetic position of G. lugoi and G. parvus to be ambiguous for the time being. However, each species exhibits character states that we consider to be apomorphic of other gerrhonotine clades, so in those cases we note the presence of those states in G. lugoi and/or G. parvus.

Elgaria
-Presence of a midline foramen on the anterior surface of the premaxilla (5; 1). -Presence of a large patch of pterygoid teeth (46; 2).
This character state is also present in G. lugoi.

Unnamed clade containing Gerrhonotus, Barisia and Abronia
-Presence of a bridge between the nasal process and the body of the premaxilla (2; 1). This character state is present in G. lugoi but is absent in G. parvus.

Barisia
-Relatively long distance between anterior margin of the nasals and the premaxillary process of the maxilla (13; 1). This character state is also present in G. lugoi.

Eastern clade of Abronia (Auriculabronia and the moreletii clade)
-Presence of a midline foramen on the anterior surface of the premaxilla (5; 1).

moreletti clade (represented here by Abronia moreletti and Abronia monticola)
-Presence of a ventrolateral plate on the vomerine process of the palatine (44; 1)*.

Abronia graminea species complex (Abronia graminea and Abronia taeniata)
-Absence of a bridge between the nasal process and the body of the premaxilla (2; 0).

Phylogenetic relationships of Elgaria peludoverde
Based on our phylogenetic analyses E. peludoverde is a member of crown Elgaria, and so is the oldest known fossil of the crown clade. The new species was generally inferred to be sister to or closely related to E. paucicarinata and/or E. kingii, but in one of the majority rule consensus trees from a Bayesian analysis, the new taxon was sister to the clade ((E. cedrosensis, E. velazquezi), ((E. multicarinata, E. nana), E. panamintina)) (see "Results"). Neither of those hypotheses were well supported by nodal posterior probabilities, nor were relationships among extant species of Elgaria regardless of constraints on the tree topology. The difficulty we encountered inferring relationships among Elgaria including E. peludoverde corroborates our previous study of variation among Elgaria [14]. Despite that variation, the alternative hypotheses for the relationships of E. peludoverde were recurring, and so we are able to provide a discussion of the potential biogeographic impacts of the discovery (see below).

Diversification and biogeographic history of Elgaria
Fossils that do not occur within the modern-day distributions of extant relatives can provide important biogeographic insights that can not be inferred from the distributions of extant species [71,72]. Extant species of Elgaria inhabit parts of southern British Columbia and much of the western U.S., and range as far south as the city of Jalisco, Mexico as well as onto the Baja California peninsula [73,74] (see Fig. 1). One extralimital occurrence of Elgaria is known from Wyoming during the middle Miocene [24]. Previously, a paucity of fossils identified to Elgaria using apomorphies made interpretation of the biogeographic history of the genus largely reliant on molecular or other non-paleontological information [4,5]. Additionally, hypotheses of relationships among Elgaria fluctuated greatly over the years, and correspondingly, biogeographic hypotheses changed as well (e.g., compare hypotheses proposed by Good [4] with those proposed by Leavitt et al. [5]). We investigated the phylogenetic relationships of E. peludoverde with respect to other species of Elgaria and in the context of modern phylogenetic hypotheses based on molecular data [5]. We inferred two alternative hypotheses of the relationships of E. peludoverde (Figs. 13, 14, 15). Here, we discuss the evolutionary and biogeographic history of Elgaria based on those hypotheses, published molecular phylogenies and divergence time estimates for Elgaria [5], modern species distributions (Fig. 1), and Neogene tectonic events in the southwestern U.S. and northern Mexico. Elgaria peludoverde is currently the only described extinct species of Elgaria. The locality in Anza-Borrego Desert State Park from which the type specimen was recovered is today inhabited by E. multicarinata, which now ranges from Washington south to the west coast of Baja California. Divergence-time analyses indicate that E. coerulea diverged from other species of Elgaria in the Miocene circa 15 Ma (95% highest posterior density interval 19.1-11.8 Ma) [5]. That age coincides with and may be related to an episode of basin and range extension in the Nevada portion of the Great Basin region that is estimated to have started 17-16 Ma and ended 12-10 Ma [75]. The clade (E. kingii, E. paucicarinata) was estimated to have diverged from the other species of Elgaria between 8.7 and 5.5 Ma [5]. That divergence may be related to an episode of basin and range deformation in the southwestern U.S. and parts of northern Mexico lasting from about 15-12 Ma to around 6 Ma [76,77]. Elgaria kingii and E. paucicarinata were estimated to have diverged from each other between 6.8 and 2.1 Ma [5]. A trans-gulfian vicariance event [78] resulting from the rifting of the Baja California Peninsula from mainland Mexico was hypothesized to play a role in the divergence between E. kingii and E. paucicarinata [5]. The initial rifting of the Baja California peninsula is estimated to have begun around 14-12 Ma, with sea waters first separating the southern peninsula by 8 Ma, and by 6.3 Ma the Gulf of California seaway was fully developed [79].
Elgaria cedrosensis and E. velazquezi are thought to have diverged from each other between 5.3 and 2.9 Ma [5]. The divergences between these two species and between the clades (E. cedrosensis, E. velazquezi) and (E. multicarinata, E. panamintina) in the late Miocene to early Pliocene were hypothesized to be related to the presence of a mid-peninsula seaway or marine incursion that may have existed near present day San Ignacio and Santa Rosalina [5,80,81]. Elgaria cedrosensis only occurs on Isla Cedros, so a vicariant event related to an uplift of Isla Cedros during the late Pliocene to Pleistocene [82] may have been involved in the divergence of E. cedrosensis from E. velazquezi [5]. The southern population of E. multicarinata and E. panamintina were estimated to have diverged from each other during the Pliocene [5], although Banta [7] previously envisioned a possible split as late as the Pleistocene.
LACM 10601 was deposited between 3.33 Ma and 3.22 based on correlation of the magnetozone at which the fossil was collected with chron 2An.2r. In many of our phylogenetic analyses, including the constrained Bayesian analysis in which G. parvus could attach anywhere, the majority-rule tree from the unconstrained parsimony analysis, and the majority-rule trees from both constrained parsimony analyses, E. peludoverde was inferred to be sister to E. paucicarinata or to the clade (E. paucicarinata, E. kingii). If E. peludoverde is indeed most closely related to these extant species, it is possible that E. peludoverde represents a northern population of total clade E. paucicarinata that diverged because of the development of the mid-Miocene mid-peninsula seaway. If E. peludoverde is more closely related to E. kingii, E. peludoverde may represent a western population of total clade E. kingii that diverged because of marine incursions during which the Gulf of California reached much farther north and partly isolated the Baja California peninsula and parts of southern California from the mainland (c. 4-3 Ma) [83]. Alternatively, E. peludoverde may be a stem member of the clade (E. kingii, E. paucicarinata) that diverged as a result of the basin-and-range deformation in the southwest U.S. and parts of northern Mexico mentioned above.
In the Bayesian analysis in which G. parvus was constrained to be the sister taxon of the keeled-scale Gerrhonotus, E. peludoverde was a stem member of the clade ((E. cedrosensis, E. velazquezi), ((E. multicarinata, E. nana), E. panamintina)). That clade was previously estimated to have a basal divergence age around 6-4 Ma [5]. It is unknown how long the lineage of E. peludoverde persisted, but under this hypothesis it would have diverged before 6-4 Ma. The location of E. peludoverde in southern California during the Pliocene and its position as a stem member of the ((E. cedrosensis, E. velazquezi), ((E. multicarinata, E. nana), E. panamintina)) clade would support a scenario of a southward dispersal of species within this clade onto the Baja California Peninsula, similar to the proposal of Welsh [84], although southern dispersal likely occurred prior to the Pleistocene scenario suggested by Welsh [84].
We provided some discussion on the evolutionary and biogeographic history of Elgaria, but our data are not exhaustive. Future biogeographic and phylogenetic analysis aided by well-supported fossil identifications will continue to shape interpretations of the biogeographic history of Elgaria. However, large amounts of intraspecific variation among species of Elgaria will likely make unambiguous identification of fossils to clades within crown Elgaria difficult [14]. Future investigations may benefit from using techniques such as geometric morphometrics, which have shown promise for identification of fossil lizards [85,86] and may prove useful for interpreting the fossil record of Elgaria.

Variation and fossil identifications
We sampled a broad range of gerrhonotine species in order to identify LACM 10601, ultimately concluding that the fossil represents a previously undescribed and extinct species of Elgaria. We examined all described extant species of Elgaria as well as many representatives from other gerrhontotine lineages. Our sampling strategy allowed us to gain a broad perspective of patterns of variation in the skulls of extant gerrhonotines. One limitation that we faced was a paucity of skeletal specimens for many gerrhonotine species. We partially overcame this limitation by CT-scanning alcohol preserved specimens of species for which skeletal information was scarce or lacking altogether. Although our dataset sampled many species, it is evident that there is much to be gained by sampling additional species as well as increasing sample sizes within sampled species (e.g., Ledesma et al. [14]). Our work as paleontologists will be greatly aided by continued efforts to understand patterns of osteological variation in extant taxa because investigating patterns of variation in extant taxa helps us to recognize and confidently identify extinct taxa. Documentation of variation in extant taxa is therefore an immensely valuable undertaking and indeed for many extant taxa, and for squamates generally, we have much to learn about patterns of osteological variation [87]. Before we investigate variation, we must address the need for comparative material. This need can be met by growing and maintaining dry skeletal collections [87]. CT data can also serve to increase the number of available comparative skeletal specimens, especially for rare, endangered, or otherwise underrepresented taxa in collections (e.g., most species of Abronia). However, the use of CT data can be restrictive because scanning and scan-processing software and hardware are costly and previously acquired CT data may not be readily available to all researchers [88]. We made all CT data used in our study freely and readily available at Mor-phoSource.org so that other researchers can build upon what we have learned and advance our understanding of osteological variation in gerrhonotines.

Conclusions
The fossil record of gerrhonotines includes many specimens, but most of those specimens are isolated and fragmented cranial elements. Thus, there is limited potential for phylogenetic placement of most fossil alligator lizards. Articulated skulls like the one described here therefore yield new and critical insights. For example, we were able to provide a biogeographic assessment of Elgaria that was not possible from previously described fossils. That is especially important because the biogeography of Elgaria cannot be comprehensively inferred from the modern distributions of the extant taxa alone. Alternative biogeographic hypotheses informed by the new species of Elgaria are consistent with the geological history of the western U.S. and western Mexico including the Baja California peninsula. The results of our study reemphasize the importance of fossils for developing more holistic perspectives of evolutionary history.
A refined interpretation of the skull LACM 10601, first described in 1989 [33], had to await computed tomography, which revealed the full cranial anatomy of the fossil and allowed the production of an expanded osteological dataset of the alligator lizards from Baja California and other areas south of the contiguous US. Many of those species are rare and not widely available in collections, certainly not as skeletons. Our effort to CT-scan alcoholpreserved specimens to elucidate patterns of variation within and among gerrhonotines was a necessary step towards developing a reliable interpretation of the fossil. That endeavor resulted in a significantly expanded understanding of the osteology and phylogeny of alligator lizards and the biogeography of Elgaria, including a new phylogenetic matrix and an assessment of the phylogenetic utility of previously used morphological characters. The osteological dataset contains many more species of gerrhonotine lizards than were previously examined in phylogenetic analyses of osteological data, and the matrix will be instrumental for future efforts to describe and systematically place fossil gerrhonotines.
Patterns of skeletal variation among gerrhonotines, and especially among Elgaria, are complex. Although our taxonomic sample was more robust than those of previous studies, we still do not have a full appreciation of patterns of skeletal variation in alligator lizards. Our sample size was low (n = 1) for several species (largely due to specimen availability), yet we still encountered variation in many skeletal elements. We performed specimen-based phylogenetic analyses to account for that variation and avoid condensing our observations of multiple specimens to single terminal taxa. Broadly, our study underscores the need for greater efforts to expand osteological datasets for gerrhonotines and for squamates generally and for renewed efforts to integrate variable morphological characters into phylogenetic analyses. Small sample sizes remain inadequate for addressing many questions about the biogeography and evolutionary morphology of squamates. Multiple representatives of lineages should be sampled in morphological studies-the future of morphological and paleontological research relies on greater understanding of the extent and consequences of variation in the skeletal system.

High-resolution computed tomography
Scanning information for specimens of Abronia, Barisia, LACM 10601, and outgroup anguids is in Table 1. Scanning information for all specimens of Elgaria and Gerrhonotus was provided by Ledesma et al. [14]. Digital segmentation was performed in Avizo Lite (8 and 9) by DTL and SGS. For the fossil LACM 10601, we segmented out as many elements as possible, but left those for which we could not separate the matrix from bone. We used the magic wand tool with a lower value of 25,000 or higher. Manual selections were often necessary to separate bone from the matrix. For extant specimens, we segmented all elements, generally with the magic wand and a gray-scale range of 18,000 to 30,000, but we occasionally segmented using manual selections when bones were in close contact. Unless otherwise noted, all images are surface renderings in orthographic view.

Phylogenetic analysis
Celestus enneagrammus FMNH 108860 was treated as the outgroup in all analyses, following the topology of Burbrink et al. [89]. We performed unconstrained analyses, and analyses with scaffolds based on published molecular phylogenies. In the scaffold analyses, relationships among Elgaria follow Leavitt et al. [5], those among Gerrhonotus follow García-Vázquez et al. [26], and those among Abronia follow Gutiérrez-Rodríguez et al. [10]. Relationships among the major clades (Elgaria, (keeled-scale Gerrhonotus, (Barisia, Abronia))) follow Zheng and Wiens [25]. The phylogenetic positions of G. lugoi and G. parvus were uncertain with respect to other Gerrhonotus in the analyses performed by García-Vázquez et al. [26]. Previous morphological analyses placed G. parvus in Elgaria [4,90], although later work using molecular data rejected that hypothesis [68]. Abronia ornelasi was not sampled by Gutiérrez-Rodríguez et al. [10]. We performed analyses in which we allowed A. ornelasi, G. lugoi, and G. parvus to attach anywhere on the tree. We also performed analyses in which A. ornelasi and G. lugoi could attach anywhere, but G. parvus was constrained to be the sister taxon of the keeled-scale Gerrhonotus, a recurring relationship in the analyses by García-Vázquez et al. [26] that was also found by Conroy et al. [68] and Zheng and Wiens [25]. Relationships among Barisia were allowed to vary in all analyses. We performed Bayesian analyses in MrBayes v. 3.2.7 [91]. We ran analyses for two runs of 2,000,000 generations and four MCMC chains sampled every 1000 generations. The symmetric dirichlet hyperprior was set at infinity and lset coding was set to variable. We used Tracer v 1.7 [92] to confirm convergence of each run (effective sample size values > 200). The posterior distributions of trees were summarized as 50% majority rule consensus trees (sumt command). We conducted the parsimony analyses in PAUP* 4.0 [93] using a heuristic search, 10,000 replicates, random taxon addition, and with multistate codings treated as polymorphic. The resulting MPTs were summarized as strict consensus trees and 50% majority rule consensus trees. For all analyses, characters were treated as unordered and equally weighted, and should be treated as such in all future analyses of this matrix.

Phylogenetic matrix construction Taxon sampling
Apomorphy-based diagnosis established that LACM 10601 is a gerrhonotine (see "Results"). In the new matrix presented here, we only included CT-scanned gerrhonotines and CT-scanned diploglossine and anguine outgroups. We also only scored skeletally mature specimens for phylogenetic analyses. We examined supplemental CT-scanned specimens of juvenile gerrhonotines and adult Xenosaurus, and traditionally prepared skeletal material of gerrhonotines, diploglossines, anguines, and Xenosaurus (see Additional file 1).
Skeletal maturity was assessed via comparison to individual bone ontogenies described by Bhullar [62] and supplemented by our previous observations in Elgaria and Gerrhonotus [14]. Specifically, we established whether specimens were mature by examining the development of the parietal (constriction of the parietal table present, well-developed osteodermal crust on parietal present), otooccipital (relatively long paroccipital processes present), and supraoccipital (bone long relative to its width in dorsal view). Both specimens of G. parvus and A. campbelli UTA 35945 lack the constriction of the parietal table that is associated with skeletal maturity. The specimens of G. parvus (SRSU 5538 and SRSU 5537, the holotype and the paratype, respectively) are known to be adults because previous examination of the ovaries of the holotype indicated a mature individual, and the paratype was kept alive in captivity for five years prior to preparation in alcohol [94]. Abronia campbelli UTA 35945 is a large and robust specimen comparable in size to the other specimen of A. campbelli, and the other ontogenetic measures indicate a skeletally mature individual.
Our sample of extant gerrhonotines scored for the phylogenetic matrix consists of 25 species and 42 specimens. We examined all eight species of Elgaria, five species of Gerronotus, three species of Barisia, and nine species of Abronia (three of which were until recently placed in the genus Mesaspis). For outgroups, we sampled the anguids Ophisaurus mimicus, Pseudopus apodus, and Celestus enneagrammus (n = 1 for each). When possible, we scanned, examined, and scored two specimens of each species of gerrhonotine to accommodate at least some intraspecific variation. We sampled several lineages within each nominal genus, recognizing that several of those genera are not/may not be monophyletic. Although our sampling represents a substantial improvement over previous studies that examined the phylogeny of gerrhonotines from an osteological perspective, we emphasize that the sample is not exhaustive in terms of species nor is it robust in terms of number of specimens sampled.
The northern and southern populations of E. multicarinata were paraphyletic with respect to E. panamintina in the analyses of Leavitt et al. [5], so we restricted our CT data for E. multicarinata to the southern population. We did not observe consistent osteological differences between the northern and southern populations in a previous study [14]. Additionally, E. nana was not treated as a species separate from E. multicarinata by Leavitt et al. [5], but we treat it as a separate species here following Grismer [74] and pending further investigation. We sampled two specimens of each species of Elgaria.
Gerrhonotus is putatively non-monophyletic. A recent molecular phylogeny indicated that G. lugoi may be more closely related to Barisia than to other species of Gerrhonotus, and support for a sister-taxon relationship between G. parvus and the keeled-scale species of Gerrhonotus (e.g., G. infernalis, G. liocephalus, and G. ophiurus) was recurring but weak [26]. Gerrhonotus infernalis is probably paraphyletic as well [26]; both of our CT-scanned specimens are from Texas and so can be confidently ascribed to the same lineage.
For Barisia, we sampled B. levicollis (n = 2), B. ciliaris (n = 1), and B. imbricata (n = 1). The specimens of B. ciliaris and B. imbricata are both identified as B. imbricata ciliaris, but only one (FMNH 30707) falls within the range of B. ciliaris, in Nuevo León. The other specimen (TNHC 76984) was collected in the state of Hidalgo well within the currently recognized range of B. imbricata [95].
Abronia is paraphyletic with respect to the previously recognized genus Mesaspis. In a phylogenetic study of external morphological data, monophyly of Abronia (excluding Mesaspis) was supported but was not considered unambiguous [8]. Monophyly of Abronia (excluding Mesaspis) was also supported by a phylogenetic study of osteological data [4]. In molecular studies of Sanger-sequenced exonic and mitochondrial data, Abronia and Mesaspis were paraphyletic with respect to each other, but most relationships among the two groups were inferred with poor support [25,67,96]. Most recently, the authors of a phylogenomic study that used double-digest restriction site-associated (ddRADseq) data presented persuasive evidence of wide-spread paraphyly of Abronia and Mesaspis with respect to each other [10]. Those authors found two major clades distributed on either side of the Isthmus of Tehuantepec, each containing multiple clades of 'Abronia' and 'Mesaspis. ' That result indicated that the geography of Mesoamerica explains the phylogeny of extant species Abronia and Mesaspis, as opposed to life history, the existing genus-level taxonomy, or previously proposed morphological apomorphies and/or diagnostic features, and consequently, the authors [10] recommended that species of Mesaspis Cope, 1877 [97] be placed in Abronia Gray, 1838 [57].
We endeavored to sample multiple clades that are or were placed in Abronia, Mesaspis, and Gerrhonotus. We follow the recommended taxonomy of Gutiérrez-Rodríguez et al. [10]; we consider all species formerly assigned to Mesaspis to be part of the genus Abronia. We sampled the clades Abaculabronia (A. ornelasi, n = 1), Auriculabronia (A. campbelli, n = 2; A. lythrochila, n = 1), members of the taeniata complex (A. graminea, A. taeniata, n = 2 for both), and a member of the oaxacae group (A. mixteca, n = 2). For species of Abronia previously placed in Mesaspis, we sampled A. gadovii (n = 2) and the moreletti group (A. moreletti and A. monticola, n = 1 for both species). In total, we sampled six of the eleven major subclades of Abronia, including five of the eight subclades sampled by Gutiérrez-Rodríguez et al. [10] and one of three other putative subgenera (Aenigmabronia, Lissabronia, and Abaculabronia). For Gerrhonotus, we sampled several species of the keeled-scale clade (G. infernalis, n = 2; G. liocephalus, n = 1; G. ophiurus, n = 1) and two smooth-scale species (G. lugoi and G. parvus, n = 2 for both species).

Specimen sampling
For the most part, we scored specimens that were scanned at UTCT specifically for this project or for related research projects [13,14]. Pseudopus apodus YPM 12870 and C. enneagrammus FMNH 108860 were previously scanned at UTCT for the Squamate Tree of Life Project, and those data were downloaded from MorphoSource.org. One specimen each of A. graminea (CAS 138886), B. ciliaris (FMNH 30707), and O. mimicus (NCSM 25699) were also downloaded from Morpho-Source.org, and were scanned at CAS, FMNH, and UF, respectively.

Character sampling
Here, we outline our character selection criteria (see Poe and Wiens [98]). The matrix has 80 characters and 75 parsimony informative characters. All phylogenetic characters pertain to the skull because LACM 10601 is a fossil skull, and reported fossil gerrhonotines are almost exclusively cranial elements [38]. We included previously described cranial characters that could not be scored on the fossil, with the intent that those characters will be useful for future efforts to systematically place skulls or isolated cranial elements of fossil gerrhonotines. We used autapomorphic characters of individual species, characters that varied among species, and characters that varied within individual specimens. We did not establish new invariant characters. We scored some previously published characters that diagnose Anguidae with respect to Xenosauridae and which identified LACM 10601 as an anguid (see "Diagnosis"), and those characters are listed in the matrix description as Invariant. We made a concerted effort to not use a priori groupings (i.e., the present genus-level taxonomy or previously published phylogenies) to frame morphological characters or character state values.
We investigated the systematic utility of some variable morphological features that we ultimately decided to exclude from the phylogenetic matrix. We provide a list of excluded characters at the end of the character list, including our rationale for excluding those characters. That list includes both characters used in previous phylogenetic analyses and features not previously investigated for gerrhonotine systematics.
Character state numbers were assigned arbitrarily, and no character state transformations are treated as ordered. Characters that were bilaterally asymmetric within an individual specimen were treated as polymorphic (e.g., '(01)'). The study from which we derived a character is listed in parentheses after the description. In some cases, the systematic or diagnostic utility of a character was described previously without being explicitly framed for phylogenetic analysis, but those references are still listed.
Specimen numbers for individual specimens are listed when appropriate, including for species represented by only one specimen. In cases for which both examined specimens of a given taxon exhibit a morphological character, the species name is listed by itself (as opposed to repeatedly listing both specimen numbers).

Remarks.
Gerrhonotines and diploglossines have a raised ossification on the dorsal surface of the alveolar plate posterolateral to the medial ethmoidal foramen, but the ossification is absent in examined anguines. The space between the nasal process and the alveolar plate is more heavily ossified in Barisia than in other gerrhonotines (see character 2), so the raised dorsal ossification is difficult to distinguish in anterior view (Fig. 16e, f ). (Good 1987 [12], characters 1 and 2; see Campbell and Frost 1993 [8]): 0 = absent (Fig. 16b, c, h); 1 = present (Fig. 16d-f, i). Barisia, Gerrhonotus (except G. parvus  and G. lugoi CM 49012), Abronia (except A. taeniata,  A. graminea, and A. moreletti TNHC 29675), and E. kingii SDNHM 24252, an ossified bridge connects the alveolar plate of the premaxilla to the nasal process. A bridge is absent in anguines and diploglossines. Ossification between the alveolar plate and the nasal process is more extensive in Barisia and some specimens of Gerrhonotus relative to other gerrhonotines, so the  Bilateral asymmetry is present on E. kingii SDNHM 24252 (Fig. 17a) and G. lugoi LACM 116254, in which the bridge is present on the left side but not the right side. Those specimens were scored as polymorphic. In E. kingii SDNHM 27895 (Fig. 16a) and A. moreletti TNHC 29675, distinct projections from both sides of the nasal process nearly connect to the raised dorsal ossification, which attains an unusually tall height in both specimens. Those specimens are also scored as polymorphic. We also note that we and another author previously observed a prepared skeleton of E. multicarinata that has a fully ossified bridge [14,61] Fig. 17c).

Remarks.
Incomplete tooth positions of 0.5 or over were rounded to the next whole number (e.g., if the nasal process of the premaxilla was 3.5 tooth positions wide, that value was rounded up to 4 tooth positions). The tooth count spanning the nasal process was normalized by dividing the number of teeth spanned by the nasal process by the total number of premaxillary tooth positions. Gerrhonotines usually possess nine tooth positions on the premaxilla, but occasionally the central position is missing or an extra position is present on one side, resulting in eight or ten tooth positions, respectively. Elgaria panamintina MVZ 75918 and E. coerulea TNHC 14643 have eight premaxillary tooth positions, and E. kingii SDNHM 24252 has ten premaxillary tooth positions.
We used an automated classification method to assign our continuous data to discrete character states. We selected three states for the character and used the function 'bin' in the machine learning package OneR [99,100] to bin the data into discrete states. We used the method 'length, ' which splits the data into bins of equal length. We emphasize that these categories are specific to the specimens measured here. Should other specimens be scored for this character (and other characters that we discretized using this method), the categorization analysis would need to be repeated and revised character state boundaries established.
Given those categories, we found that the nasal process is narrow in most gerrhonotines in our sample. The nasal process is comparatively wider in A. mixteca, A. gadovii, A. monticola TNHC 32083, B. levicollis, G. infernalis, G. ophiurus TCWC 35604, and a few specimens of Elgaria (e.g., E. multicarinata TNHC 35666, E. coerulea TNHC 14643). The nasal process is exceptionally broad in C. enneagrammus FMNH 108860, B. ciliaris FMNH 30707, and B. imbricata TNHC 76984. In B. imbricata TNHC 76984, there are two projections from the ossified bridge that appear to be part of the nasal process in anterior view (see Fig. 17c), but that we do not consider to be part of the nasal process.

Remarks.
Contact is scored as present when the premaxilla and the frontal are in contact, or overlap anteroposteriorly but are narrowly separated in the dorsoventral dimension. Contact is scored as absent when the premaxilla and frontal are not close to contacting, or are close to contacting but do not overlap in the anteroposterior dimension. Premaxilla-frontal contact is present in A. graminea, A. mixteca, A. taeniata TCWC 30660, A.  gadovii, A. monticola TNHC 32083, Barisia, G. infernalis TNHC 92262, G. lugoi, and G. parvus. In most of those taxa, contact is present because there is a long and thin extension of the nasal process of the premaxilla posterior to the main body of the nasal process [14]. The posterior extension is absent in G. infernalis TNHC 92262. The nasal process appears elongated in Barisia relative to Elgaria and other gerrhonotines that lack the posterior extension of the nasal process, but in Barisia there is little width differentiation between the anterior and posterior portions of the process, especially in B. levicollis. Thus, the presence or absence of the posterior extension is unclear in Barisia. (Scarpetta 2018 [24]; Smith 2009 [23]): 0 = absent (Fig. 16d-i); 1 = present (Fig. 16a-c).

Remarks.
A single anterior midline foramen is present on the anterior surface of the premaxilla in most species of Elgaria, but is absent in E. cedrosensis and E. panamintina. The foramen is also present in A. moreletti TNHC 29675, A. campbelli, and Ophisaurus [24]. Like Scarpetta [24], we interpret the foramen as separately derived in Ophisaurus and gerrhonotines. Elgaria kingii SDNHM 24252 is singular among examined specimens in that there are two midline foramina in close proximity and in a dorsoventral row. We assume that the two foramina of E. kingii SDNHM 24252 are homologous to the single foramen of other gerrhonotines and scored the specimen as state 1. In E. paucicarinata SDNHM 45100, a single midline foramen is divided by an anterior midline septum.

Remarks.
In anguines the premaxilla is convex anteriorly, protruding well past the alveolar margin. In gerrhonotines and diploglossines, the anterior face of the premaxilla is nearly flush with the alveolar margin.

Remarks.
The dorsal surface of the nasal process is convex or almost flat in most gerrhonotines, but is concave in Barisia. 8. Morphology of the posterior portion of the nasal process of the premaxilla (Ledesma et al. 2021 [14]): 0 = posterior portion of the nasal process tapers relative to the immediately proximal portion of the process (Fig. 16a-e, g-i); 1 = posterior margin of the nasal process is broad and does not taper (Fig. 16f ).
Remarks. The posterior end of the nasal process tapers in width in most gerrhonotines, both in taxa with a posterior extension and in those without. In B. levicollis, the posterior portion of the nasal process does not taper and retains a width similar to the anterior portion of the process.  [60], character 24): 0 = present (Fig. 19a, b); 1 = absent (Fig. 19c).
Remarks. The ventral keel on the nasal process is welldeveloped in gerrhonotines, and is absent in examined anguines and diploglossines.

Remarks.
In gerrhonotines, the alveolar plate is a single surface from which distinct palatal processes do not extend. In anguines and diploglossines, there are discrete processes that meet the maxilla laterally and the vomers posteriorly that create an anterior fontanelle between the premaxilla and the maxilla.

Remarks.
In most gerrhonotines, the premaxillary facet of the nasal has a subtriangular anteromedial process that articulates with the nasal process of the premaxilla. The anteromedial process of the nasal is absent in B. levicollis. Good 1987 [12], characters 53 and 54). 0 = relatively short (Fig. 20c, d); 1 = relatively long (Fig. 20a, b).

Remarks.
In most gerrhonotines, the distance between the anterior margin of the nasal and the anteriormost inflection of the premaxillary process of the maxilla is short. That distance is substantially longer in Barisia and G. lugoi. The scoring of this character is not dependent on the presence or absence of the anteromedial process because the distance is long in G. lugoi, B. ciliaris FMNH 30707, and B. imbricata TNHC 76984 in addition to B. levicollis (see character 12). Good 1987 [12], character 54): 0 = nasals contact (Fig. 20a); 1 = nasals are separated (Fig. 20b-d).

Contact of the nasals with one another near their anterior-posterior midpoint (derived from
Remarks. The nasals are separated near their anterior-posterior midpoint in A. graminea, A. mixteca, A. ornelasi UTA R-6220, A. gadovii, Barisia, and G. lugoi. Contact between the nasal process of the premaxilla and the frontal was previously hypothesized to exclude contact of the nasals in Abronia, Barisia, and Abronia (Mesaspis) gadovii [12]. We did not find that separation of the nasals was tied to the contact of the premaxilla and the frontal, and so consider those features to be separate characters. For example, the nasals of G. parvus SRSU 5538 and A. taeniata TCWC 30660 are in close contact anteriorly and near their longitudinal midpoint, but the premaxilla and frontal are in broad contact. In A. ornelasi UTA R-6220, the nasals are broadly separated anteriorly and near their midpoint, but the premaxilla and frontal do not contact.

Remarks. The anterolateral projection of the septomaxilla is absent in
Remarks. An anterodorsal projection of the facial process is present in most specimens of Elgaria (excluding E. cedrosensis), G. lugoi, G. ophiurus TCWC 35604, Barisia (excluding B. imbricata TNHC 76984), A. campbelli (although both specimens are bilaterally asymmetric), A. taeniata, A. gadovii, A. monticola TNHC 32083, and A. moreletti TNHC 29675. The projection is absent in other Abronia and in G. infernalis, G. liocephalus, and G. parvus. 18. Relative width of the facial process of the maxilla (left maxilla), measured in tooth positions spanning the facial process divided by the total number of tooth positions (modified from Good 1988 [38]). The posterior margin of the facial process was marked at the anterior margin of the lateral exposure of the lacrimal foramen, and the anterior margin was marked at the end of a line drawn from the posterior margin that is perpendicular to the horizontal access of the maxilla. The number of teeth under that line was counted and divided by the total number of tooth positions: 0 = < 0.305 (narrow; Fig. 23a); 1 = 0.305-0.375 (intermediate; Fig. 23b); 2 = > 0.375 (wide; Fig. 23c).

Remarks.
A narrow facial process is distinctive of species previously assigned to Mesaspis and was previously considered to be derived in Mesaspis and Abronia [38].  However, it is not straightforward to standardize the posterior and anterior points at which that narrowness is perceived and measured. We created a standardized line to examine the width of the facial process (see above). Instead of measuring the length of the line, we counted the number of tooth positions present under the line, and divided that number by the total number of tooth positions. Measuring the relative width of the facial process using tooth count is easier to score for fossils in which the premaxillary and/or orbital processes of the maxilla are warped or broken (both of which are frequent occurrences in our experience), and removes controversy over which length to measure (i.e., maximum length, length perpendicular to the tooth row, length of the tooth row, etc.). Incomplete tooth positions of 0.5 or over were rounded to the next whole number (e.g., if the facial process was 3.5 tooth positions wide, that value was rounded up to 4 tooth positions). The data were binned and assigned to three states of equal length with the function 'bin' with the 'length' method, as in Character 3. 19. Medial inflection of the facial process (new): 0 = present (Fig. 24a, b); 1 = absent; the facial process faces almost straight dorsally (Fig. 24c).
Remarks. State 0 accommodates a wide range of variation, especially among Abronia and Elgaria. Some species have a distinct inflection point creating a dorsal lamina (e.g., A. campbelli), while others have a relatively uniform curvature (e.g., E. cedrosensis). State 1 is restricted to Barisia levicollis. 20. Large posterior projection on the posterior edge of the facial process of the maxilla between the posterodorsal apex and the posteroventral margin of the process; the latter is defined by the anterior margin of the lacrimal foramen in lateral view (modified from Good 1987 [12], character 16): 0 = absent (Fig. 22a); 1 = present (Fig. 22b).

Remarks.
A projection ventral to the apex of the dorsal lamina is present in A. mixteca and G. ophiurus TCWC 35604. This character accommodates the morphology of the maxilla-prefrontal suture that was previously described by Good [12] as a "lop-sided W pattern. " We did not examine the other species of Abronia that were described as having that pattern (A. oaxacae and A. deppii). 21. Morphology of the palatine process of the maxilla (modified from Good 1987 [12], character 22): 0 = palatine process has a well-developed medial projection (Fig. 24d); 1 = palatine process has a well-developed medial projection that faces posteriorly (Fig. 24e); 2 = palatine process lacks a discrete medial projection (Fig. 24f ).

Remarks.
Osteoderms fused to the skull may prevent accurate scoring of this character on traditionally prepared skulls. Contact is best observed from CT scans that have been digitally disarticulated to show only the maxilla and the frontal. Contact was observed in some species of Abronia (e.g., A. lythrochila TNHC 112900, A. campbelli) and Gerrhonotus (e.g., G. infernalis, G. lugoi). Good 1987 [12], character 21): 0 = present (Fig. 22a), 1 = absent.

Remarks.
The medial shelf of the lacrimal contributes both medially and ventrally to the lacrimal foramen in most gerrhonotines. In G. parvus SRSU 5537, the medial shelf extends dorsally to fuse with the lateral wall of the lacrimal, completely enclosing the lacrimal foramen. The medial shelf contributes only ventrally to the lacrimal foramen in E. paucicarinata, G. infernalis TNHC 18988, G. lugoi LACM 116254, and A. monticola.

Remarks.
A distinct anterior projection of the posteroventral process of the prefrontal is present in A. campbelli, A. lythrochila TNHC 112900, A. mixteca UTA 30324, A. ornelasi UTA R-6220, A. gadovii TCWC 9907, and Gerrhonotus (except in G. ophiurus TCWC 35604). The projection is absent in Barisia and in most species of Elgaria, but is present in both specimens of E. cedrosensis and E. paucicarinata. Several specimens have a projection on one side but not the other (e.g., A. lythrochila TNHC 112900, E. kingii SDNHM 27895).

Postnatal fusion of the frontal bones
Remarks. The frontals are fused early in postnatal development in gerrhonotines [19], but remain unfused throughout ontogeny in diploglossines and all extant anguines. Remarks. Abronia (excluding Mesaspis) was previously described as possessing a less elongate frontal compared to other gerrhonotines [3]. We standardized that qualitative observation by taking measurements that we then binned into discrete morphological character states.
We took continuous measurements of the maximum width and the maximum length of the frontal and then divided the length by the width for each specimen to assign a single value to address frontal proportions. The data were binned and assigned to three states of equal length using the function 'bin' with the 'length' method, as in Character 3 and Character 18. We again emphasize that the values described here are specific to this analysis   (Fig. 29); 1 = present (Fig. 28b).
Remarks. The frontals of gerrhonotines were previously characterized as 'hour-glass' shaped due to constriction between the orbits [28,66]. Interorbital constriction relative to both the anterior and posterior sections of the bone is present in gerrhonotines as previously reported, but we note that marked interorbital constriction occurs in members of many squamate clades, including varanids, xenosaurids, iguanians, and scincomorphs [19]. There is substantial variation in the degree of interorbital constriction among gerrhonotines (Fig. 29). The interorbital region is constricted in C. enneagrammus FMNH 108860 to a degree comparable to some gerrhonotines (e.g., Barisia). The interorbital region of examined anguines is constricted relative to the posterior face of the bone only, but the anterior portion of the bone tapers to a point; P. apodus YPM 12870 and O. mimicus NCSM 25699 were scored as state 0.  [14]): 0 = absent (Fig. 30a); 1 = present (Fig. 30b).
Remarks. The recess is present in E. cedrosensis, E. velazquezi SDNHM 68677, E. multicarinata TNHC 4478, G. lugoi, and the right side of the parietal of G. infernalis TNHC 92262. Juvenile E. multicarinata always lack a bilateral recess [14]. Remarks. All gerrhonotines have separate postorbital and postfrontal elements in the posterior orbital region, but some diploglossines were reported previously to have a single element called the postorbitofrontal [63]. In squamates it is generally assumed that the postorbitofrontal represents a fusion between the postorbital and postfrontal, but we do not discount the possibility that some taxa may simply lack either the postorbital or the postfrontal, and so the single element filling that portion of the orbital region does not represent a fusion. Examined CT-scanned anguines and C. enneagrammus FMNH 108860 have separate postorbital and postfrontal elements.  (Fig. 30f ).

Remarks.
A posterior mediolateral expansion of the squamosal is present in Xenosaurus and is absent in Anguidae.
Remarks. The supratemporal has two anterior projections in A. campbelli and has a single projection in other gerrhonotines and in other examined anguids.  (Fig. 31b, c); 1 = vomeronasal region is ventral to the posterior nasal region (Fig. 31a).
Remarks. This character is observed in lateral view and with respect to the horizontal axis of the isolated vomer, instead of with respect to the horizontal axis of the skull. In A. campbelli, A. graminea, A. lythrochila TNHC 112900, and A. gadovii TCWC 9907, the anterior vomeronasal region of the vomer is ventrally displaced from the posterior nasal portion of the element. (Good 1987 [12], character 28): 0 = foramen penetrates the bone from a posterior angle and opens anteriorly on the ventral surface of the vomer (Fig. 31d); 1 = foramen penetrates the bone dorsally and exits ventrally (Fig. 31e).

Remarks. In
Remarks. In most gerrhonotines there is a slight to a moderate thickening of the palatine dorsal to the anterodorsal portion of the choana. In several species, there is also a triangular flange above the choana. The flange is present and particularly large in Barisia, but is also present in G. infernalis TNHC 92262, G. liocephalus TCWC 8585, E. cedrosensis SDNHM 27702, and E. paucicarinata SDNHM 46106.
Remarks. An extension of the palatal process of the pterygoid is present in anguines and is absent in diploglossines and gerrhonotines.

Remarks.
A posterodorsal ridge on the quadrate process of the pterygoid is present in all gerrhonotines but is reduced in height (to the point of being nearly absent) in A. campbelli and in A. taeniata.

51.
Width of the conch of the quadrate in posterior view (new): 0 = dorsal portion of the conch is substantially wider than the ventral portion (Fig. 36a); 1 = dorsal portion of the conch is roughly the same width as the ventral portion (Fig. 36b).
Remarks. The conch of the quadrate is markedly wider dorsally than ventrally in most examined gerrhonotines. The conch does not markedly widen dorsally relative to the ventral portion of the conch in A. campbelli, A. lythrochila TNHC 112900, A. gadovii, B. ciliaris FMNH 30707, and B. levicollis MVZ 68782. The conch of P. apodus YPM 12870 is poorly developed, so that specimen was scored as '?' (Fig. 36c).
Remarks. The anteromedial surface of the quadrate is concave, especially dorsally, in most gerrhonotines and in other anguids. That surface is nearly flat in A. campbelli and A. graminea UTA 38831.
53. Dorsomedial narrowing of the quadrate (new): 0 = absent (Fig. 36a, b); 1 = present (Fig. 36c).  Remarks. In Anguinae, the dorsomedial margin of the quadrate abruptly narrows such that the dorsal portion of the quadrate is considerably narrower in anterior and posterior view relative to the ventral and middle portions of the element.
Remarks. The anterior opening of the internal carotid foramen is directed anteromedially in most gerrhonotines. In G. infernalis and B. levicollis MVZ 68782, the opening is directed anteriorly. of the dorsal surface of the supraoccipital is much narrower than the posterior portion (a roughly trapezoidal supraoccipital in dorsal view) (Fig. 37b).  (Fig. 37f ).

Remarks.
The supratrigeminal process is located on the medial surface of the prootic, and often bisects the incisura prootica in lateral view. Bilateral asymmetry is present in some specimens (e.g., E. multicarinata TNHC 35666) in which the process is moderately developed on one prootic but nearly undetectable on the other prootic. The supratrigeminal process is absent in A. graminea, A. mixteca, Barisia, G. lugoi, G. infernalis, and G. parvus.
Remarks. The dorsal excavation on the otooccipital is present on both otooccipitals in all specimens. Abronia graminea, A. mixteca, and A. ornelasi UTA R-6220 exhibit a shallow depression.
58. Crest extending from the posterior edge of the supraoccipital onto the posterior surface of the otooccipital (new): 0 = extends to the base of the paroccipital process (Fig. 38a); 1 = extends well onto the paroccipital process (Fig. 38c).

Remarks.
A free posteroventral margin of the intramandibular septum was previously considered to be an apomorphy of all Anguidae [28] or Anguidae exclusive of Diploglossus bilobatus [18].  [18], character 186): 0 = the angular process of the dentary terminates anterior to the coronoid process of the dentary (Fig. 40a, c-f ); 1 = the angular process of the dentary extends at or posterior to the coronoid process of the dentary (Fig. 40b).
Remarks. This character is best scored on a disarticulated dentary. The angular process extends posterior to the coronoid process in A. mixteca, A. gadovii TCWC 9907, and B. levicollis.
The posterior extent of the angular process was framed relative to the extent of the surangular process by Gauthier [28] and Conrad et al. [18], and it was noted by Gauthier [28] that the surangular process is well-developed plesiomorphically in anguimorphs. Relatively few species of gerrhonotine have a distinct and well-developed surangular process (see character 61). We frame the relative length of the angular process relative to the coronoid process of the dentary, because the coronoid process is always present and well-developed in gerrhonotines. 61. Distinct surangular process of the dentary (modified from Gauthier 1982 [28]): 0 = present (Fig. 40c-f ); 1 = absent (Fig. 40a, b).  (Fig. 40f ) and the right dentary of G. infernalis TNHC 18988 possess a distinct process, and those specimens are scored as polymorphic (01). Anguines have a well-developed surangular process.

Remarks. All gerrhonotines except for A. graminea
have an anterodorsal projection of the splenial. The projection is also absent in anguines. The projection is present but relatively reduced in length in B. imbricata TNHC 76984 and A. mixteca. In E. velazquezi SDNHM 68678 and E. kingii, the projection extends ventrally to enclose the anterior inferior alveolar foramen, although only on the left splenial of E. kingii SDNHM 24252.

Coronoid
64. Extension of the medial exposure of the anterior medial process of the coronoid relative to the last tooth position on the dentary. This character is scored when the splenial is in articulation with the dentary (Good 1987 [12], character 86): 0 = process does not extend anterior to the last tooth position (Fig. 42a); 1 = process extends anterior to the last tooth position (Fig. 42b).

Remarks.
We also examined this character when the splenial was not in articulation, and found that without exception the anterior medial process of the coronoid extends far anterior to the last tooth position. In articulation, however, the medial exposure of the anterior medial process failed to extend past the last tooth position in A. graminea, A. taeniata TCWC 30660, A. mixteca, A. ornelasi UTA R-6220, and A. gadovii, paralleling the results of Good [12]. Additionally, the medial exposure of the anterior medial process failed to extend past the last tooth position in G. parvus, in which the process extended to, but not past, the last tooth position.
This character was somewhat ambiguous in E. paucicarinata SDNHM 45100 and E. multicarinata TNHC 4478. In those two specimens, one (but not both) of the dentaries lacked a distinct posteriormost tooth position where a position was present at the analogous location on the other dentary of those specimens. If a tooth position is truly absent, these specimens would be bilaterally asymmetric, but we scored the specimens as character state 1. Elgaria nana SDNHM 52886 is clearly bilaterally asymmetric; the left anterior medial process is close to, but does not extend past, the last tooth position. That specimen is scored as polymorphic (01).

65.
Elements that contribute to the anterior margin of the anterolateral mandibular foramen (anterior surangular foramen) (modified from Conrad et al. 2011 [18], characters 172 and 173): 0 = the foramen is bordered only by the surangular (Fig. 43a); 1 = the lateral process of the coronoid contributes to the anterior margin of the foramen (Fig. 43b); 2 = the surangular process of the dentary contributes to the anterior margin of the foramen (Fig. 43c).

Remarks.
A coronoid contribution to the anterior border of the anterolateral mandibular foramen is present in   Good 1987 [12], character 82; see Ledesma et al. 2021 [14]): 0 = dorsal surface of the surangular shelf is raised and slopes to face medially and laterally (Fig. 41d); 1 = dorsal surface of the surangular shelf is flat (Fig. 41e).

Remarks.
A flat surangular shelf is present in G. infernalis, G. ophiurus TCWC 35604, and B. ciliaris FMNH 30707. The dorsal surface of the surangular is not flat in all adult specimens of G. infernalis [14]. The left surangular of G. liocephalus TCWC 8585 is slightly rounded, but the specimen is scored as state 1.
Remarks. The posterior process of the coronoid has a small but distinct contribution to the anterior margin of the adductor fossa in A. graminea, E. coerulea TNHC 58792, and in anguines.

Tooth morphology of maxillary teeth (adapted from
Remarks. Almost all of the maxillary teeth of A. mixteca, A. graminea, G. parvus, and O. mimicus NCSM 25699 are unicuspid and the crowns are pointed. The teeth of B. levicollis and E. velazquezi SDNHM 68677 are blunt to bicuspid. Other examined gerrhonotines exhibit heterodonty, possessing sharp and unicuspid mesial teeth and blunt, sometimes bicuspid distal teeth. All but the mesialmost teeth are molarized in P. apodus YPM 12870.

Osteoderms
General remarks on osteoderm characters. Besides sculpturing texture and imbrication morphology, osteoderms were not extensively used for systematic purposes in gerrhonotines [12,28]. We identified and labelled osteoderms with spatial reference to overlying scales figured by Campbell and Frost [8] and Waddick and Smith [101]. Although many cranial osteoderms are similar to overlying scales, we note that osteoderms do not always recapitulate the shape, contacts, and fusions of the overlying scales, and some scales are not represented by underlying osteoderms (e.g., the presence of a rostral osteoderm is highly variable among examined specimens). Thus, these characters should not be viewed as homologous to scale characters previously used to differentiate gerrhonotines from each other. 70. Laterally imbricating osteoderms with a distinct gliding surface (Invariant, Gauthier 1982 [28]): 0 = absent; 1 = present.
Remarks. The presence of laterally imbricating osteoderms is an apomorphy of anguids with respect to other anguimorphs. Good 1987 [12], character 97;Norell, 1989 [33]): supraciliary and the median supraciliaries on the right side of the skull of E. kingii SDNHM 24252 and the posterior supraciliaries are absent on the left side of the skull Elgaria nana SDNHM 52886; those specimens are scored as polymorphic (01). In Elgaria panamintina MVZ 191076, the left supraciliaries are strongly developed and span the entire orbit, but there are no supraciliaries on the right side of the skull. That specimen is scored as polymorphic (02). The supraciliaries are especially wellossified in B. imbricata TNHC 76984 (Fig. 47c) and B. ciliaris FMNH 30707. The supraciliary osteoderms may be fused to the osteoderms in the supraorbital semicircle in Barisia levicollis; those specimens are scored as '?. '

Dorsal and lateral osteoderm texture (modified from
In most specimens of Abronia, the supraciliary osteoderms span a lesser portion of the orbit compared to Elgaria and Gerrhonotus; there are one or two anterior supraciliaries, but the posterior supraciliaries are weaklyossified and far-spaced or are absent. The supraciliaries span most of the orbit in A. mixteca UTA 30324, and that specimen is scored as state 0. Supraciliary osteoderms are absent in the anguine and diploglossine outgroups and A. gadovii TCWC 9907. 76. Osteoderm overlying the frontoparietal shield (new): 0 = present (Fig. 45a-d); 1 = absent (Fig. 45e).

Remarks.
There is an osteoderm overlying some or most of each frontoparietal shield in Elgaria, Gerrhonotus, Barisia, A. gadovii, A. monticola TNHC 32083, and A. moreletti TNHC 29675. An osteoderm overlies the left side of the frontal of A. taeniata TCWC 30660 but there is no frontoparietal osteoderm on the other side of the skull; the specimen is scored as polymorphic. The frontoparietal osteoderm is absent in other specimens of Abronia. The frontoparietal shield is itself indistinct in B. imbricata TNHC 76984 and A. monticola TNHC 32083, but an osteoderm overlying the frontoparietal region is clearly present. Campbell and Frost 1993 [8]): 0 = absent (Fig. 45c); 1 = present (Fig. 45a, b, d-e).

Remarks.
In Barisia, the posterior internasal and prefrontal osteoderms possess medial contact along their length, excluding the presence of a frontonasal osteoderm. The presence and morphology of the frontonasal are variable among other gerrhonotines, particularly Elgaria, but the frontonasal region is open in all gerrhonotines besides Barisia. Frontonasal region morphology ranges from a relatively small, single, but distinct osteoderm in A. graminea and A. taeniata, a large, multi-osteoderm region in the keeled-scale Gerrhonotus and many specimens of Elgaria, to two reduced and separated osteoderms in several specimens of Elgaria and in A. gadovii TCWC 9907. Waddick and Smith 1974 [101]): 0 = absent (Fig. 45a, c-e); 1 = present (Fig. 45b).

Contact between the posterior internasal and the prefrontal osteoderms (new; inspired by
Remarks. Contact between the posterior internasal and the prefrontal osteoderms on both sides of the skull is present in Abronia (exclusive of species previously referred to Mesaspis and A. ornelasi UTA R-6220) and in Barisia. Elgaria nana SDNMH 17102 has a unique condition among examined specimens, in which the left posterior internasal is posteriorly offset from its contralateral element, and is also posteriorly elongated (or potentially fused to a piece of another osteoderm) to narrowly contact the left prefrontal osteoderm. Campbell and Frost 1993 [8]): 0 = absent (Fig. 45a, c-e); 1 = present (Fig. 45b).

Separation of the anterior and posterior internasals by the supranasal (new; inspired by
Remarks. Separation of the internasals by the supranasal osteoderm is present in A. campbelli, A. lythrochila TNHC 112900, A. gadovii TCWC 11384, and the keeledscale Gerrhonotus.

Remarks.
The presence of a small foramen or foramina lateral to the medial ethmoidal foramen was reported to be an apomorphy of Barisia [12]. There can be a variety of small openings in the bony tissue connecting the alveolar plate and the nasal process in most gerrhonotines in which a premaxillary bridge is present (character 2 of this study), not just in Barisia as reported by Good [12]. We did not score this character because there are multiple foramina to which this character could refer and the homology between them is not clear.  Remarks. Mediolateral expansion of the postorbital is present in all specimens of Elgaria and in almost all other gerrhonotines, but is most substantial in E. panamintina [13]. Elgaria velazquezi SDNHM 68678 has a medially pointed shelf instead of the rounded shelf present in other Elgaria, which is similar to the morphology of A. ornelasi UTA R-6220 and G. infernalis TNHC 18988.
There is no expansion in A. graminea UTA 38831, A. taeniata TCWC 4911, and G. parvus. The postorbital of G. parvus is extremely narrow across its length and there is little width differentiation between the posterior and anterior ends. In A. taeniata TCWC 4911, the postorbital is relatively short and narrow, but maintains the same width throughout its length except at its posteriormost end, where it tapers in width abruptly. In A. graminea UTA 38831, the postorbital is narrow across its length, but is slightly wider posteriorly.

Remarks.
We excluded this character because of a discrepancy between data derived from CT scans and dry skeletons. We previously found that only dry skeletons of Elgaria displayed contact between the squamosal and postparietal process, likely because of shrinkage of soft tissue bringing the squamosal and postparietal process into contact [14].
Remarks. The squamosal forms part of the margin of the upper temporal fenestra in all gerrhonotines examined. In B. levicollis, A. gadovii, A. monticola TNHC 32083, A. moreletti TNHC 29675, E. kingii SDNHM 24252, and E. panamintina, the squamosal is nearly excluded from the upper temporal fenestra. However, this character encompasses several morphological features (i.e., length of supratemporal, length of postorbital, length of squamosal, directionality and morphology of the postparietal processes) that each vary among gerrhonotines.
E17. Medial contact of the palatine processes of the vomers (modified from Good 1987 [12], character 26): 0 = Contacting or nearly contacting; 1 = Not close to contacting and often broadly divergent at the posteriormost ends.
Remarks. The palatine processes of the vomer were reported to be divergent from one another in Abronia (excluding species previously placed in Mesaspis), although with substantial variation [12]. We also found that the palatine processes of the vomer are separated in most specimens of Abronia, but we observed that morphology in many other specimens that we examined (e.g., B. imbricata TNHC 76894, E. kingii SDNHM 24252, A. gadovii TCWC 9907, G. infernalis TNHC 92262).
E18. Development of an anterolaterally directed ridge that separates the vomeronasal region from the nasal region of the vomer (Ledesma et al. 2021 [14]): 0 = well-developed with high dorsal extent; 1 = poorly-developed with low dorsal extent.
Remarks. Some specimens of Abronia and Gerrhonotus have a somewhat low dorsal ridge separating the vomeronasal region from the nasal region of the vomer relative to other specimens of Gerrhonotus, Abronia, and most specimens of Elgaria. We had difficulty defining the boundary between relatively low and relatively high for this morphological character, and so excluded it from our analyses.

Remarks.
The absence or reduction of a dorsomedial flange was reported to be a derived feature of Abronia and Mesaspis [12]. We were not able to identify the feature on the vomerine process of the palatine reported by Good [12].