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. 2019 Oct 30;236(2):210–227. doi: 10.1111/joa.13102

The morphological diversity of the quadrate bone in squamate reptiles as revealed by high‐resolution computed tomography and geometric morphometrics

Alessandro Palci 1,2,✉, Michael W Caldwell 3, Mark N Hutchinson 1,2, Takuya Konishi 4, Michael S Y Lee 1,2
PMCID: PMC6956442  PMID: 31667837

Abstract

We examined the morphological diversity of the quadrate bone in squamate reptiles (i.e. lizards, snakes, amphisbaenians). The quadrate is the principal splanchnocranial element involved in suspending the lower jaw from the skull, and its shape is of particular interest because it is potentially affected by several factors, such as phylogenetic history, allometry, ecology, skull kinesis and hearing capabilities (e.g. presence or absence of a tympanic ear). Due to its complexity, the quadrate bone is also considered one of the most diagnostic elements in fragmentary fossil taxa. We describe quadrates from 38 species spread across all major squamate clades, using qualitative and quantitative (e.g. geometric morphometrics) methods. We test for possible correlations between shape variation and factors such as phylogeny, size, ecology and presence/absence of a tympanum. Our results show that the shape of the quadrate is highly evolutionarily plastic, with very little of the diversity explained by phylogenetic history. Size variation (allometric scaling) is similarly unable to explain much shape diversity in the squamate quadrate. Ecology (terrestrial/fossorial/aquatic) and presence of a tympanic ear are more significant, but together explain only about 20% of the diversity observed. Other unexplored and more analytically complex factors, such as skull biomechanics, likely play additional major roles in shaping the quadrates of lizards and snakes.

Keywords: disparity, ecology, lizards, morphology, quadrate, snakes

We describe the morphological diversity of the quadrate bone in squamate reptiles, using both qualitative and quantitative methods. We found that ecology (especially fossorial) and the loss of a tympanic membrane are two important correlates of shape disparity.

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Introduction

Squamate reptiles are one of the most diverse groups of vertebrates on the planet, with well over 10 000 extant species (Uetz et al. 2018). The group is represented by forms with many different habitats (e.g. aquatic, fossorial, arboreal), trophic specializations (carnivores, omnivores, herbivores) and body plans (e.g. limbed, limbless, short‐bodied, elongate). This great diversity of ecological and morphological specialisations is also reflected in all aspects of their phenotype, from general body shape to skull anatomy.

The quadrate bone of reptiles is the sole element articulating the lower jaw with the suspensorial elements of the dermatocranium. In squamate reptiles it also typically has a kinetic (i.e. movable) dorsal joint with the squamosal and supratemporal (dermatocranial bones), a condition referred to as streptostyly, which permits a wide range of lower jaw movements (Frazzetta, 1962; Evans, 2008). Various degrees of modification to the amplitude of potential movements of the quadrate, including the extreme of akinesis in some taxa (Evans, 2008; LeBlanc et al. 2013), have likely contributed to shape variation in this element.

The quadrate also contributes to areas of insertion for muscles involved in the opening and closing of the jaws. One of the major jaw‐opening muscles, the musculus (= m.) depressor mandibulae, attaches extensively along the posterior surface of the quadrate, whereas one of the main jaw‐closing muscles, the m. adductor externus, originates in part from the dorsal portion of the quadrate. The anterior surface of the quadrate may also serve as a point of origin for the m. levator anguli oris in some taxa (Frazzetta, 1962).

Furthermore, the quadrate of most squamates is constrained anteroventrally by the quadratomaxillary ligament, which connects it to the posterior end of the maxilla and/or jugal (Iordansky, 1996), and is also constrained medioventrally by a connection with the pterygoid, which in some taxa is a fairly tight sliding contact (synovial joint) (e.g. Lacerta viridis; Frazzetta, 1962), whereas in others it is a very loose ligamentous connection (e.g. snakes; Frazzetta, 1966; see also Evans, 2008).

To complicate matters even further, the quadrate is also involved, directly or indirectly, in sound reception. This is because the quadrate is a major supporting element for membranes and cartilages of the outer and middle ear of squamates: the attachment point for the anterior and superior portions of the tympanic membrane (posterior and inferior membrane attachments are with soft tissues), ligaments associated with one or more extracolumellar cartilages and, where the tympanum is absent, may be in a direct contact with the cartilaginous distal portions of all of the extracolumellar cartilages in a wide variety of morphologies (Wever, 1978; Rieppel, 1980; Caldwell, 2019).

The great diversity of shapes observed in the quadrate of squamate reptiles likely resulted from the complex mechanical interactions impacting this bone. Phylogenetic history, allometric scaling, ecology, dietary preferences, variations in the degree and mode of streptostyly, as well as presence/absence of an external tympanic membrane may all have contributed to the observed morphological disparity of the quadrate. A combination of some of these factors has in fact been found to be responsible for the great morphological diversity of the quadrate bone within gekkotan lizards (Paluh & Bauer, 2018). This diversity also means that the quadrate bone is a potentially important element for diagnosing and identifying fragmentary fossil taxa (Russell, 1967; Estes, 1983).

Here we describe, first quantitatively and later qualitatively, a broad sample of squamate quadrates (38 species) from representatives of all major clades within this very diverse group of animals. In our quantitative analysis we use geometric morphometrics to test for possible correlations between shape variation, phylogeny, ecology, size and presence/absence of a tympanum in our sample.

Materials and methods

For the geometric morphometrics component of this study, 38 taxa were selected across the phylogenetic tree of squamate reptiles, to provide a good coverage of the morphological diversity of the quadrate bone within all major clades. While we attempted to sample across all major squamate clades, sampling of the specimens was also partially opportunistic (i.e. based on specimen availability in the collections of the SAMA or from previous studies). All sampled specimens were considered adults (based on adult body size for the species). Sex was unknown in most cases; however, when present in squamates, sexual dimorphism mostly affects relative head size rather than shape (Olsson et al. 2002), and we assumed that shape differences between sexes (or more in general, intraspecific variation) would be negligible compared with the morphological differences that reflect relatively distant phylogenetic relationships.

A complete list of taxa selected for high‐resolution computed tomography (micro‐CT) is provided in Supporting Information Data S1 (refer to this file also for list of taxonomic authorities). Most of the micro‐CT data were obtained from specimens in the collections of the South Australian Museum, Adelaide (South Australia), or loaned from other institutions within Australia (Melbourne Museum, Melbourne, Victoria; Australian Museum, Sydney, New South Wales), and data for eight specimens were kindly provided by O. Rieppel and J. Maisano (Deep Scaly Project, NSF grant EF‐0334961). A CT scan of Plesioplatecarpus planifrons was made available by the University of Alberta Laboratory for Vertebrate Palaeontology (UALVP). All new scan data were obtained using a Skyscan 1076 at the micro‐CT scanning facility at Adelaide Microscopy, University of Adelaide, South Australia. The software nrecon (Bruker microCT) was used to reconstruct stacks of images (in bitmap format) from the micro‐CT scan data, and a digital surface model of the right quadrate was produced for each specimen via segmentation in avizo v. 9.0 (http://www.fei.com/software/avizo3d) and exported in polygon file format (.ply) for subsequent analyses.

Rendered images of the quadrate surface models were obtained after removing parallax distortion (i.e. parallel rendering mode) in avizo v. 9.0 (http://www.fei.com/software/avizo3d) and orienting the volume‐rendered skull in lateral, medial and posterior views. After the skull was positioned as if lying flat on a horizontal surface, the volume rendering of the skull was switched off, leaving only the surface model of the quadrate in its life‐like orientation. This procedure was meant to ensure that the depicted orientation of the quadrate was in a natural position and preserved any original tilting observed inside the skull. The only exception was Plesioplatecarpus, where the quadrate was not in its natural position due to postmortem compression of the skull.

The digital surface models were then landmarked in landmark editor v. 3.6 (Wiley et al. 2007; http://www.idav.ucdavis.edu/research/EvoMorph) using the following procedure (Fig. 1):

  • a fixed landmark was placed at the posterior end of the sutural surface of the dorsal quadrate epiphysis (a point that in most lizards corresponds to the posterior tip of the suprastapedial process);

  • four evenly spaced semilandmarks were placed along the cephalic condyle of the quadrate, following the sutural surface of the dorsal epiphysis towards its most anterior end;

  • a second fixed landmark (landmark #6; L6) was placed at the anterior end of the sutural surface of the dorsal epiphysis (anterior end of the cephalic condyle);

  • four evenly spaced semilandmarks were placed along the anterior margin of the shaft (i.e. the main portion between mandibular and cephalic condyles) of the quadrate, to approximate a gentle curve that joins the anterior end of the cephalic condyle with the lateral end of the mandibular condyle;

  • a third fixed landmark (L11) was placed on the lateral end of the mandibular condyle of the quadrate;

  • a fourth fixed landmark (L12) was placed in the most concave point of the saddle‐shaped articular surface of the mandibular condyle; when the surface was not saddle‐shaped (convex) the landmark was then placed in the centre (circumcentre) of the condyle;

  • the last fixed landmark (L13) was placed on the medial end of the mandibular condyle of the quadrate.

Figure 1.

Figure 1

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Rendered surface model of the right quadrate bone of Cercosaura schreibersii in lateral (left) and posterior (right) view to illustrate the landmarking scheme and the main anatomical terminology adopted in this study. Fixed landmarks in red, sliding semilandmarks in blue. ae, anterior edge of quadrate shaft; cc, cephalic condyle; mc, mandibular condyle; mr, medial ridge; pa, pterygoid attachment surface (may develop into an articulary facet in forms where the pterygoid is tightly attached to the quadrate); pe, posterior edge of quadrate; ssp, suprastapedial process; tc, tympanic crest; tco, tympanic conch. Additional anatomical features are highlighted in Figs 4, 5, 6.

The amount of error in placing the landmarks on the digital surface models was evaluated by repeating the same landmarking procedure on five randomly selected digital surface models five times each, and then by comparing the results in a PCA as well as by running a repeatability test (Arnqvist & Mårtensson, 1998) in geomorph v. 3.1.2 (Adams & Otárola‐Castillo, 2013; Adams et al. 2019).

The landmark configurations (five fixed landmarks, eight sliding semilandmarks) were scaled and aligned with a generalized Procrustes superimposition using the R v. 3.6.1 (R Core Team, 2019; https://www.r-project.org) package geomorph v. 3.1.2 (Adams & Otárola‐Castillo, 2013; Adams et al. 2019). Analyses of the dataset were carried out in R v. 3.6.1 (R Core Team, 2019; https://www.r-project.org) using a combination of the packages geomorph v. 3.1.2 (Adams & Otárola‐Castillo, 2013; Adams et al. 2019), RRPP (Collyer & Adams, 2018, 2019), morpho v. 2.4.1.1 (Schalger, 2016), phytools v. 0.6‐99(Revell, 2012) and phylotools v. 0.2.2 (Zhang et al. 2012), and morphoj v. 1.06d (Klingenberg, 2011, http://www.flywings.org.uk/MorphoJ_page.htm) was used for visualization of the principal components analysis (PCA). The landmark configurations of all specimens are provided in Supporting Information Data S2.

We assessed the effect of phylogenetic signal using the function ‘physignal’ (Adams, 2014a) in the package geomorph v. 3.1.2 (Adams & Otárola‐Castillo, 2013; Adams et al. 2019). The test was performed with 10 000 random permutations.

The phylogenetic tree adopted for the test of phylogenetic signal (Fig. 2) was the dated molecular tree from Zheng & Wiens (2016), where unsampled species were pruned out and the fossil taxon P. planifrons was added using mesquite v. 3.2 (Maddison & Maddison, 2017; https://www.mesquiteproject.org). All branch lengths (proportional to time) between extant taxa from the original tree were retained. Plesioplatecarpus was positioned according to the topology in Reeder et al. (2015) and inserted midway along the relevant branch, i.e. halfway between the nodes representing the most recent common ancestors of snakes (Serpentes) and of toxicoferans [(Anguimorpha, Iguania), Serpentes]. The tip‐age of the Plesioplatecarpus terminal was based on the date provided for the specimen in Konishi & Caldwell (2007).

Figure 2.

Figure 2

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Phylogenetic tree illustrating the relationships of the squamates sampled for the quantitative analyses using 3D geometric morphometrics. The phylogeny of extant taxa is from Zheng & Wiens (2016), where the extinct taxon Plesioplatecarpus was added manually based on the work of Reeder et al. (2015) (see main text for details). Branch lengths are proportional to time (units to the right are millions of years). Blue dots represent aquatic taxa, black dots represent generalist taxa, and pink dots represent fossorial taxa. Stars mark taxa that lack a tympanum. Ac, Acrodonta; Al, Alethinophidia; An, Anguimorpha; C, Caenophidia; Ge, Gekkota; Ig, Iguania; La, Lacertoidea; Pl, Pleurodonta; ‘S’, ‘Scolecophidia’; Sc, Scincoidea; Se, Serpentes.

To test for a possible allometric pattern in the data, we tested for a correlation between the values of the first principal component (PC1), a potential proxy of shape variation, and overall size of the quadrate (measured as centroid size). Three tests were performed using the cor.test function in R v. 3.6.1 (R Core Team, 2019; https://www.r-project.org), and included Pearson’s, Spearman’s and Kendall’s methods (Hollander & Wolfe, 2014). Additionally, we also performed a phylogenetic regression between Procrustes shape coordinates and centroid size in geomorph v. 3.1.2 (Adams & Otárola‐Castillo, 2013; Adams et al. 2019). The phylogenetic regression was run with randomization of null model residuals, 10 000 permutations, and Type I sum of squares.

To test for differences in mean shape between groups based on ecological habits and presence/absence of an external tympanic membrane, we carried out non‐phylogenetic and phylogenetic Procrustes analyses of variance (anova) using a randomized residual permutation procedure (10 000 iterations) (Goodall, 1991; Anderson, 2001; Adams, 2014b; Collyer & Adams, 2018, 2019).

The degree of morphological disparity of each of the ecological categories, and of taxa with and without a tympanic ear, was evaluated using the morphol.disparity function in geomorph v. 3.1.2 (Adams & Otárola‐Castillo, 2013; Adams et al. 2019) with 10 000 randomized residual permutations for evaluation of statistical significance.

Information about the ecological preferences and presence/absence of an external tympanic membrane of the selected species was obtained from a survey of the literature (Data S1). Presence/absence of an external tympanic membrane could also be confirmed directly for extant species included in this study.

The R scripts and settings used for our analyses are available in Supporting Information Data S3. The table files used to slide the semilandmarks during Procrustes superimposition (curveslide.csv) and read data relevant to the analyses in R (species.csv) are available in Supporting Information Data S4 and S5, respectively.

Results

Quantitative analyses

There was negligible error in the placement of the landmarks, as confirmed by five landmarking replicates for five randomly selected individuals: the spread of the data points in the first three principal components of a PCA always fell well inside the maximum range of 0.05‐unit‐wide intervals on any axis (see Supporting Information Data S6: Fig. S1), and the repeatability measure returned a value of R = 0.9945 (R = 0.986, P = 0.0001), i.e. negligible measurement error (most variance is found between, rather than within, individuals; Arnqvist & Mårtensson, 1998).

Principal components analysis (PCA; Fig. 3) revealed that the first three components (PCs) explain 76.2% of the total variance in the data. All the species appear to be fairly evenly distributed in shape space, regardless of whether they are snakes or lizards, although snakes tend to have negative values for PC2, with the only exception being the typhlopid Anilios (Ramphotyphlops).

Figure 3.

Figure 3

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Results of principal components analysis. Top, plot of principal component 2 (PC2) against principal component 1 (PC1); centre, plot of PC2 against principal component 3 (PC3); bottom, plot of PC1 against PC2 where taxa that lack a tympanum are highlighted in red. The amount of variance explained by each component is shown next to each axis. Wireframe diagrams of the landmarked quadrates are used to illustrate the amount of morphological change across each axis, in right lateral (left) and antero‐posterior (right) views. Taxon names are abbreviated to the sixth letter (for a list of full taxonomic names see Data S1). Snake names are shown in blue and lizard names in orange. The colour of the dots in the top two plots corresponds to the ecological category of the taxon: blue dots represent aquatic taxa, black dots represent generalist taxa, and pink dots represent fossorial taxa. Red dots in the bottom plot indicate taxa that lack a tympanum.

Positive values of PC1 characterize quadrates with a relatively long and narrow shaft, while negative values correspond to quadrates that have a relatively short and broad shaft and a long area for articulation of the dorsal epiphysis (long cephalic condyle; ~ long suprastapedial process where this is present).

Positive values of PC2 characterize quadrates where the anterior edge of the shaft is convex, and where the cephalic condyle is concave laterally. Negative values correspond to an almost vertical quadrate shaft and a cephalic condyle that is convex laterally. Most taxa that lack a tympanic membrane also have negative values of PC2 (Fig. 3).

Positive values of PC3 characterize quadrates where the cephalic condyle forms a sharp right angle with the quadrate shaft, whereas negative values correspond to quadrates where the cephalic condyle forms a continuous curve with the anterior lateral outline of the shaft (question‐mark shape).

The test for phylogenetic signal returned a lack of statistically significant phylogenetic signal under a Brownian motion model of evolution (K = 0.59696, P = 0.2361; based on 10 000 permutations). This is consistent with the PCA results (Fig. 3), where even closely related sampled taxa are often very widely separated in shape space.

The test for a possible allometric correlation between shape (represented by the shape component in PC1) and size (represented by centroid size) returned non‐significant results under all three tests performed (i.e. no statistically significant correlation was found: Pearson’s method, t 36 = −1.2846, corr = −0.2093556, P = 0.2071; Spearman’s method, S = 9510, ρ = −0.04059525, P = 0.8084; Kendall’s method, T = 341, τ = −0.02987198, P = 0.8028). The phylogenetic regression of Procrustes shape coordinates vs. centroid size returned a similar result (i.e. a lack of correlation between the two variables; R 2 = 0.056, F = 2.15, P = 0.1074).

We then used both ordinary and phylogenetic Procrustes anovas to test for significant differences in group means where the grouping factors consisted of ecology (generalist, fossorial or aquatic) and presence/absence of an external tympanic membrane. Both methods found statistically significant differences between ecological groups, but only the ordinary Procrustes anova found the differences between tympanic/atympanic groups to be statistically significant. The results of these analyses are summarized in Table 1.

Table 1.

Results of ordinary and phylogenetic Procrustes anovas used to test for possible effects of (i) ecology and (ii) presence of an external tympanic membrane (tympanum) on shape.

  R 2 F‐value Pr
OPanova Fa = ecology 0.1264 2.5322 0.0189
OPanova Fa = tympanum 0.09313 3.6968 0.0107
PPanova Fa = ecology 0.13287 2.6814 0.0132
PPanova Fa = tympanum 0.05019 1.9025 0.0933
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Fa, factor; OPanova, Ordinary Procrustes anova; PPanova, Phylogenetic Procrustes anova; R 2, squared correlation coefficient; Pr, percentage of F‐ratios from permutated data that are equal or greater than the observed F‐value (significant values in bold).

Null hypothesis: the factor tested does not affect shape (F = 1); 37 degrees of freedom.

Because a significant difference was found between the group means of the three ecological categories, to determine whether this difference was driven by a single category we also ran a post‐hoc pairwise comparison (with 10 000 permutations for significance testing) in geomorph v. 3.1.2 (Adams & Otárola‐Castillo, 2013; Adams et al. 2019). The result showed that the greatest distance between group means was that between the fossorial and the generalist groups (d = 0.1830) and this was also the only pairing where the distance between means was statistically significant (95% confidence interval = 0.145, Z = 3.14, P = 0.006). This pairing was followed closely by that consisting of fossorial and aquatic groups, with a distance d = 0.180, although this was not found to be statistically significant (95% confidence interval = 0.202, Z = 1.35, P = 0.097). These results suggest that the category that drives the difference in group means is the fossorial one.

For the sake of completeness, we additionally ran a phylogenetically informed combined analysis (multifactorial analysis) to test for an interaction effect of ecology and absence of a tympanum affecting quadrate shape (with residual randomization, type I sums of squares and cross products, and 10 000 permutations for significance testing). The result of this analysis confirmed that ecology is the principal driver of Procrustes shape variance in the dataset (R 2 = 0.145, P = 0.0038; R 2 = 0.05, P = 0.0537 for tympanic/atympanic grouping; R 2 = 0.084, P = 0.0112 for combined effect of ecology and absence of a tympanum on Procrustes shape variance).

The analysis of morphological disparity of each of the ecological groups showed that the group with the largest Procrustes variance (= disparity) is the fossorial category (0.111), followed by the aquatic (0.084) and then the generalist (0.038). The largest pairwise difference between variances was that between the fossorial and the generalist group, a difference that, unlike all others, was found to be statistically significant (P = 0.0008). With regard to presence vs. absence of a tympanum, the taxa that retain a tympanum have almost half the Procrustes variance of those that have lost it (0.0457 vs. 0.0855), and the difference is statistically significant (P = 0.0386).

Qualitative descriptions

The results of our quantitative analysis, and in particular our PCA, showed that the observed diversity of quadrate morphologies is partly the result of the combination of six main shape components (corresponding to the extremes of the first three PC axes). However, the observed diversity is also generated by additional variable features (not mapped by our landmarking scheme, as they are not always present). These features include the presence or absence of additional processes, crests and/or articular facets. In the following section we will provide an overview of the occurrence of these additional features in the quadrates of the same squamate species that had been sampled for the quantitative analyses (Figs 4, 5, 6) following the phylogeny in Fig. 2. These descriptions will be complemented by information provided by the literature where necessary. With regard to mosasauroids, only P. planifrons was sampled as a representative taxon (it was the only mosasauroid for which we had access to CT scan data). However, it should be noted that although Plesioplatecarpus is representative of the general and rather plesiomorphic morphology of the mosasauroid quadrate (relatively short and broad quadrate shaft with elongate suprastapedial process), the presence, length and orientation of various processes and crests add a great deal of morphological variation within the group (Russell, 1967; Caldwell & Palci, 2007).

Figure 4.

Figure 4

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Plate showing a selection of squamate right quadrates in right lateral, medial and posterior views. The order follows the tip order in the phylogeny in Fig. 2 (from left to right); boxes enclose taxa from the major clades named in Fig. 2: (b–d) Gekkota; (e–h) Scincoidea; (i–l) Lacertoidea. (a) Dibamus novaeguineae. (b) Delma australis. (c) Coleonyx variegatus. (d) Chatogekko amazonicus. (e) Xantusia vigilis. (f) Gerrhosaurus nigrolineatus. (g) Cordylus rhodesianus. (h) Acontias meleagris. (i) Holcosus undulatus. (j) Cercosaura schreibersii. (k) Gymnophthalmus leucomystax. (l) Amphisbaena alba. alp, anteromedial lappet for articulation with pterygoid; ccn, cephalic condyle notch; exg, groove for ‘extracolumella’; ptf, pterygoid facet; pps, process for articulation with pterygoid and stapes; pvp, posteroventral process.

Figure 5.

Figure 5

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Plate showing a selection of squamate right quadrates in right lateral, medial and posterior views. The order and boxes follow the phylogeny in Fig. 2 (continued from Fig. 4): (a) Lacertoidea; (b–h) Anguimorpha; (i,j) Acrodonta; (k,l) Pleurodonta. (a) Lacerta viridis. (b) Heloderma suspectum. (c) Xenosaurus grandis. (d) Anniella pulchra. (e) Anguis fragilis. (f) Shinisaurus crocodilurus. (g) Lanthanotus borneensis. (h) Varanus eremius. (i) Rhampholeon spectrum. (j) Agama anchietae. (k) Ctenosaura similis. (l) Tropidurus hispidus. adp, anterodorsal process; alp, anteromedial lappet for articulation with pterygoid; est, extrastapes? (ossified element partially embedded within quadrate); ptf, pterygoid facet.

Figure 6.

Figure 6

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Plate showing a selection of squamate right quadrates in right lateral, medial and posterior views. The order and boxes follow the phylogeny in Fig. 2 (continued from Fig. 5): (a) Pleurodonta; (c–e) ‘Scolecophidia’; (f–l) basal Alethinophidia; (m,n) Caenophidia. (a) Phrynosoma modestum. (b) Plesioplatecarpus planifrons. (c) Trilepida dimidiatum. (d) Anilios bicolor. (e) Liotyphlops beui. (f) Anilius scytale. (g) Cylindrophis ruffus. (h) Teretrurus sanguineus. (i) Xenopeltis unicolor. (j) Aspidites ramsayi. (k) Morelia viridis. (l) Eunectes murinus. (m) Acrochordus granulatus. (n) Natrix natrix. ap, anterior process; sty, stylohyal process; vlp, ventrolateral process.

Overview of quadrate morphological diversity in squamates

Dibamidae – Dibamus (Fig. 4a)

The quadrate of Dibamus is a fairly flat and anteroposteriorly expanded element, with a broad cephalic condyle and a large, triangular, posteroventral process (pps in Fig. 4a). The posteroventral process is closely associated with the posterolateral end of the quadrate ramus of the pterygoid as well as the distal end of the stapedial shaft (Fig. 7a). According to Rieppel (1980, 1984) the medial side of the posteroventral process of the quadrate in Dibamus is covered by cartilage and forms a synovial joint with a cartilaginous distal expansion of the stapes. The ventral portion of the quadrate process also forms a loose ligamentous connection with the distal portion of the quadrate ramus of the pterygoid (Fig. 7a; Rieppel, 1984).

Figure 7.

Figure 7

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Relationships between quadrate, stapes and pterygoid in a selection of lizards. (a) Dibamus novaguineae, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and posterolateral (and slightly ventral) views. (b) Acontias meleagris, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and posterolateral views. (c) Amphisbaena alba, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and posteroventral views. (d) Xenosaurus grandis, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and posterolateral views. (e) Anniella pulchra, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and posterolateral views. (f) Rhampholeon spectrum, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior, posterolateral and posteromedial views. Quadrate is coloured red, stapes is coloured green, and pterygoid is coloured yellow. Amphisbaena has two additional elements that are highlighted: a calcified distal portion of the stapes (blue) and the epihyal (light green).

Gekkota – Delma, Coleonyx and Chatogekko (Fig. 4b–d)

The quadrate of gekkotans is rather variable in shape. Generally, the main components of variation are: the presence or absence of a large foramen in the anteroventral region of the tympanic conch (e.g. Delma australis; Fig. 4b); presence or absence of a deep posterolateral emargination of the cephalic condyle (e.g. Coleonyx variegatus and Chatogekko amazonicus; Fig. 4c,d); and overall width of the tympanic conch, which can be relatively broad (e.g. Coleonyx) or narrow (e.g. Chatogekko). The same main aspects of variation have also been described in a recent paper focused on the morphological diversity within a large sample of gekkotan species (Paluh & Bauer, 2018). In miniaturized species like C. amazonicus the quadrate shaft also appears to be fairly straight and is oriented almost vertically (Fig. 4d), likely as a result of its unusual suspension from the skull (the quadrate articulates dorsally directly with the basicranium, because the squamosal and paroccipital processes are extremely reduced; Gamble et al. 2011). On the medial surface of the mandibular condyle, all gekkotan quadrates examined show a facet for articulation with the quadrate ramus of the pterygoid.

Scincoidea – Xantusia, Gerrhosaurus, Cordylus, Acontias (Fig. 4e–h)

The quadrates of Xantusia, Gerrhosaurus and Cordylus look fairly similar overall, both in shape and orientation within the skull: there is the same degree of anteroventral tilting in lateral view, a lack of mediolateral tilting, a similar relative size of the suprastapedial process, the presence of a distinct narrow anterodorsal corner between quadrate shaft and cephalic condyle, and a similar degree of development of the tympanic conch and associated lateral crest (tympanic crest). The quadrates of Xantusia and Gerrhosaurus also share the presence of a lateral notch in the cephalic condyle that in Xantusia is closed by a thin bridge of calcified cartilage (possibly of epiphyseal origin). Xantusia also possesses a short anterodorsal projection along the medial side of the cephalic condyle (‘accessory process’ of Gauthier et al. 2012). The atympanic ear of Acontias (Fig. 4h) is characterized by a quadrate that looks quite distinct from those of the above‐mentioned taxa: it lacks a tympanic conch and crest, has a much better developed suprastapedial process and also possesses a very well developed teardrop‐shaped articular surface for the quadrate ramus of the pterygoid (Fig. 7b). A similar articular surface is present in Cordylus (Fig. 4g), but in Acontias it also produces a distinct process posteriorly, whereas in the former taxon it produces a thin flange (or lappet) anteromedially. Despite the lack of an external tympanic membrane (Wever, 1978; Vitt & Caldwell, 2009), the stapes of Acontias still projects laterally below the suprastapedial process of the quadrate, but does not contact the quadrate directly as in some other squamates that lack a tympanic membrane (e.g. snakes, Dibamus, Feylinia; Wever, 1978; Rieppel, 1980).

Lacertoidea – Holcosus, Cercosaura, Gymnophthalmus, Amphisbaena, Lacerta (Figs 4i–l and 5a)

With the exception of Amphisbaena, the quadrate (and overall skull) morphology of which deviates substantially from the general lacertilian pattern, all other lacertoid quadrates look fairly similar: there is a similar degree of anteroposterior tilting, only slightly more accentuated in Gymnophthalmus, a mediolateral tilting very limited (mandibular condyle slightly shifted laterally in Holcosus and medially in Cercosaura) or absent (Gymnophthalmus and Lacerta), a similar relative size of the suprastapedial process, a similar degree of development of the tympanic conch and tympanic crest, and a similar anteroposterior curvature of the quadrate shaft. Holcosus, Cercosaura and Gymnophthalmus also share the presence of a distinct lateral open notch on the cephalic condyle (weakly developed in Lacerta). Medial to the mandibular condyle, Holcosus, Cercosaura and Lacerta also share the presence of a posteroventral lappet for articulation with the quadrate ramus of the pterygoid (lappet very well developed in Holcosus; Fig. 4i). Amphisbaena (Figs 4l and 7c), on the other hand, possesses a stout, rod‐like quadrate dorsally expanded and bearing a deep ventrolateral groove for passage of the ‘extracolumella’ (an element that is unlikely to be truly homologous with the extracolumella of other squamates, and is more likely the homologue of the epihyal; Wever & Gans, 1972, 1973). Medioventrally, the quadrate of Amphisbaena bears a large articular surface for the quadrate ramus of the pterygoid, and this surface projects slightly anteroventrally as well as dorsomedially to produce small crests/processes. These processes accentuate the concavity of the surface. The shaft of the quadrate of Amphisbaena is pierced by a large foramen dorsally, and the cephalic condyle is strongly concave, not only for the lodging of the dorsal epiphysis (which is possibly not yet fully ossified in this specimen) but also to accommodate a synovial joint with a convex surface on the posterior part of the braincase (Evans, 2008; Fig. 7c). Although the quadrate of Amphisbaena looks strikingly different from that of other squamates, more basal genera within Amphisbaenia, such as Bipes (possibly the most basal amphisbaenian genus if Rhineuridae falls outside of the clade, e.g. molecular analyses in Wiens et al. 2010; but see combined data analyses in Wiens et al. 2010, and also Gauthier et al. 2012, Pyron et al. 2013, and Reeder et al. 2015), retain a quadrate that is more reminiscent of the original squamate configuration, with a subtriangular lateral profile and lack of an enlarged ‘extracolumellar’ element (Wever & Gans, 1972).

Anguimorpha – Heloderma, Xenosaurus, Anniella, Anguis, Shinisaurus, Lanthanotus, Varanus (Fig. 5b–h)

With the exception of Varanus and Anniella, the quadrates of all sampled anguimorphs are characterized by a fairly robust shaft and a short, blunt suprastapedial process. The tympanic conch and crest are very well developed in Heloderma and Xenosaurus, moderately developed in Shinisaurus, Lanthanotus and Varanus, and absent in Anniella and Anguis. All sampled anguimorphs, similarly to scincoids, are characterized by the presence of a distinct narrow anterodorsal corner between quadrate shaft and cephalic condyle. A lateral open notch in the cephalic condyle is present in Xenosaurus and Lanthanotus, but absent in the other sampled taxa (Fig. 5b–h). Very distinct, concave facets for articulation with the quadrate ramus of the pterygoid are visible on the medial side of the mandibular condyle in Heloderma, Xenosaurus (see also Fig. 7d), Anniella (see also Fig. 7e) and Anguis. The facets are not as strongly developed in Shinisaurus, Lanthanotus and Varanus, but in the first two they are extended anteromedially to produce a distinct lappet. The quadrate of Anniella (Figs 5d and 7e) shares with that of Dibamus the presence of an enlarged posteroventral process that contacts the stapes medially and the quadrate ramus of the pterygoid ventrally. Unlike the process in Dibamus, however, this process in Anniella is likely derived from a separate ossified element that originally connected the stapes to the quadrate. Evidence for the fact that this process was originally an element distinct from the quadrate shaft comes from parasagittal sections through the quadrate of Anniella (see Data S6: Fig. S2). This element has been interpreted as the internal process of the stapes by Wever (1978), but as the extracolumella by McDowell (1967) and Rieppel (1980). Unlike the quadrates of other examined anguimorphs, the quadrate of Anniella has a suprastapedial process that is relatively long and tapers posteriorly to a point, a condition similar to the one observed in the burrowing skink Acontias (cf. Figs 4h and 5d).

Iguania: Acrodonta – Rhampholeon and Agama (Fig. 5i,j)

The quadrate of Rhampholeon is highly representative of the unusual shape of this bone in chamaeleonids. The shaft is rod‐like and lacks a tympanic conch but it does possess a thin vertical crest where a tympanic membrane would be expected to attach (despite the absence of an external ear opening). The quadrate sits in the skull in an almost vertical position, and the cephalic condyle is expanded anterodorsally into a broad cylindrical process. The quadrate shaft has a thin medial flange, which closely approaches the quadrate ramus of the pterygoid (Fig. 7f).

The shape of the quadrate of Agama is much more similar to that of most other lizards, with a distinct tympanic conch, a short suprastapedial process, and a deep lateral emargination on the cephalic condyle. Unlike all other sampled squamates, however, the cephalic condyle of the quadrate in Agama is greatly expanded mediolaterally relative to the shaft (Fig. 5j), making the quadrate appear much wider mediolaterally than anteroposteriorly. This is a feature observed also in distantly related agamids (e.g. the amphibolurine Ctenophorus; Palci et al. 2016). A distinct facet for articulation with the pterygoid is absent in Agama.

Iguania: Pleurodonta – Ctenosaura, Tropidurus, Phrynosoma (Figs 5k,l and 6a)

The quadrates of Ctenosaura and Tropidurus look fairly similar, although in the latter the tympanic crest extends further laterally, and the shaft is more slender as well as distinctly tilted anteroventrally in lateral view (almost vertical in Ctenosaura). Both taxa have a lateral notch in the cephalic condyle of their quadrate. Phrynosoma (Fig. 6a), on the other hand, possibly as a result of its lack of an external ear opening, presents a very simplified quadrate morphology, where there is no suprastapedial process, tympanic conch or crest. The quadrate is mostly a rod‐like element with a somewhat expanded dorsal end, and is strongly tilted anteroventrally in lateral view.

Mosasauridae – Plesioplatecarpus (Fig. 6b)

The quadrates of mosasaurs can be quite diverse in the details of their anatomy (Russell, 1967) but overall they tend to have an elliptical to oval lateral profile, a well‐developed suprastapedial process, a deep, sometimes bowl‐shaped, tympanic conch and a well‐developed tympanic crest. Unlike extant squamates, the mosasaur quadrate is characterized by the presence of a shallow oval to bean‐shaped depression, called the stapedial pit, located on the medial side of the shaft and at the base of the suprastapedial process (Russell, 1967). In an articulated skull, a mosasaur quadrate is either erect or tilted posteroventrally, depending on the species (e.g. Camp, 1942; Konishi et al. 2012, 2014).

Serpentes: ‘Scolecophidia’ – Trilepida, Anilios, Liotyphlops (Fig. 6c–e)

All snakes lack a tympanic membrane (Wever, 1978) and as a result they lack a tympanic conch and a tympanic crest. Scolecophidians are relatively conservative in the shape of their quadrates, which are all rod‐like and strongly tilted anteroventrally (with the mandibular condyle facing anteriorly) (see also taxa sampled in Rieppel et al. 2009). In scolecophidians the stapedial shaft typically lies medial to the posterodorsal end of the quadrate (Fig. 8a; see also Rieppel et al. 2009). Leptotyphlopids, here represented by Trilepida dimidiata (Fig. 6c), have a very simple, needle‐shaped quadrate, with a distinct foramen piercing the dorsal end of the shaft. The anomalepidid Liotyphlops (Fig. 6e) also has a very similar quadrate, but it lacks the dorsal foramen and is somewhat broader dorsoventrally. The quadrate of typhlopoid snakes, here represented by Anilios (Ramphotyphlops) bicolor (Fig. 6d), can be distinguished from those of leptotyphlopids and anomalepidids by the presence of a robust triangular projection that protrudes anterodorsally from the anterior half of the quadrate shaft (anterior process). A small foramen pierces the base of this process in Anilios bicolor, but such a foramen is variably present within typhlopoid snakes (absent in Typhlops jamaicensis for example; Rieppel et al. 2009).

Figure 8.

Figure 8

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Relationships between quadrate, stapes and pterygoid in a selection of snakes. (a) Anilios bicolor, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and posterolateral (and slightly ventral) views. (b) Teretrurus sanguineus, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and ventrolateral (and slightly posterior) views. (c) Xenopeltis unicolor, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and posteroventral views; a calcified element articulating with the distal end of stapes is coloured light blue. (d) Eunectes murinus, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and posteromedial views; partially calcified cartilaginous element ventral to stylohyal process is coloured greenish‐blue. (e) Acrochordus granulatus, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and posterolateral views (last view is a further close‐up of the previous image to show the stapedial shaft pointing dorsally towards the quadrate cephalic condyle). (f) Natrix natrix, right lateral view of the skull and close‐ups of the quadrate and adjacent bones in lateral, posterior and posterolateral views. Quadrate is coloured red, stapes is coloured green, and pterygoid is coloured yellow.

Serpentes: basal Alethinophidia – Anilius, Cylindrophis, Teretrurus, Xenopeltis, Aspidites, Morelia, Eunectes (Fig. 6f–l)

These snakes can be subdivided into two main morphofunctional categories: snakes with adaptations for a larger gape, usually referred to as ‘macrostomatans’ (i.e. ‘large mouths’), and snakes that lack such adaptations. In the past ‘macrostomatans’ were considered a monophyletic group, but more recent molecular phylogenetic studies highlighted how various lineages of snakes may have actually independently evolved morphological features that allow ingestion of relatively large prey items (see Palci et al. 2016; Scanferla, 2016 for recent reviews of this topic). In terms of quadrate morphology, this morphofunctional dichotomy translates into two distinct types of snake quadrates. Snakes that lack the capacity to swallow very large prey items, such as Anilius, Cylindrophis, Teretrurus and Xenopeltis, are characterized by a quadrate bone that has a relatively short, stout subvertical shaft and that retains a suprastapedial process. ‘Macrostomatan’ snakes, on the other hand, have quadrates that are strongly tilted posteroventrally (i.e. in the opposite direction to that in ‘scolecophidians’ and most lizards with a tilted quadrate) and/or where the mandibular condyle is distinctly displaced laterally. This is the case in Aspidites (quadrate tilted laterally; Fig. 6j), Morelia (quadrate tilted posteroventrally and laterally; Fig. 6k) and Eunectes (quadrate tilted posteroventrally and bent laterally; Fig. 6l).

With only a few exceptions, the quadrate of alethinophidian snakes possesses a distinct process for articulation with the distal cartilaginous portion of the stapes. This process, termed the stylohyal process or articulatory process, is derived from ossification of a stylohyal cartilage (Parker, 1879) and has been considered homologous with the intercalary or with part of the processus internus of the extrastapes of lizards (Kamal & Hammouda, 1965; McDowell, 1967; Caldwell, 2019). Rieppel (1980) argued in favour of the former interpretation (intercalary), while the processus internus of lizards would be incorporated into the distal cartilaginous portion of the ophidian stapes. The stylohyal occurs on the distal portion of the suprastapedial process in snakes that still have this process (e.g. Figs 6f–i and 8b,c), while it is located at various points along the posteromedial side of the quadrate shaft in snakes that have lost the suprastapedial process (i.e. ‘macrostomatans’) (e.g. Figs 6j–l,n and 8d). The ventral shift of the stylohyal is linked to the considerable increase in length of the quadrate shaft in macrostomatan forms during ontogeny (Genest‐Villard, 1966; Palci et al. 2016; Scanferla, 2016), where addition of bone below the dorsal epiphysis pushes the connection with the stapes further ventrally as the cephalic condyle extends dorsally. However, this does not seem to be the case in the caenophidian Acrochordus (see below). Interestingly, the lateral shift of the mandibular condyle in the quadrate of Eunectes is not achieved via a lateral tilting of the quadrate shaft, but by its lateral bending. Moreover, the stylohyal process is located on a triangular wing‐like crest that extends medially to maintain the contact between stylohyal and stapes (Fig. 8d). The quadrate of some basal alethinophidians is also characterized by the presence of a ventrolateral process or tuberosity in the area where the quadratomaxillary ligament and the m. retractor quadrati attach, just lateral to the mandibular condyle (Frazzetta, 1966). A tuberosity can be observed in Anilius and Cylindrophis (Fig. 6f,g), whereas a more pronounced triangular process can be observed in Aspidites, Morelia and Eunectes (Fig. 6j–l).

Serpentes: Caenophidia – Acrochordus and Natrix (Figs 6m,n and 8e,f)

The quadrates of caenophidian snakes, here represented by the basal form Acrochordus and by the colubroid Natrix, are typically very elongate, posteroventrally tilted elements with expanded sub‐triangular cephalic condyles. Caenophidians often have an anterodorsal and/or a posterodorsal process on the quadrate head; in Natrix the posterodorsal corner of the cephalic condyle is very gently rounded, but in other caenophidian species a distinct posterior process is present (e.g. Notechis, Ephalophis and Lampropeltis; see Cundall & Irish, 2008; figs. 2.95, 2.96, 2.102). This condition can, however, be reversed to a short vertical quadrate shaft in some burrowing forms (e.g. Aparallactus, Homoroselaps and Phyllorhynchus; see Cundall & Irish, 2008; figs. 2.85, 2.90, and 2.104). A median stylohyal process is again typically present in the middle of the quadrate shaft of caenophidians, but this is not the case in Acrochordus, where the stapedial shaft faces posterodorsally, towards the posterior end of the cephalic condyle (as in some basal alethinophidians such as Xenopeltis; compare Fig. 8c,e), and a stylohyal process is absent. In Natrix the stylohyal process is poorly developed and the cartilaginous extension of the stapes makes contact with a short longitudinal crest on the posteromedial side of the quadrate shaft (Figs 6n and 8f). Other advanced colubroid snakes show a much better developed stylohyal process (e.g. Elaphe longissima; Rieppel, 1980).

Discussion

As described above, squamates show extreme disparity in the morphology of their quadrate bones, and this disparity is likely the result of a complex interaction between several factors. We tested the effect of four factors that are most likely to contribute to the observed disparity, namely, phylogenetic history, size, ecology and presence/absence of a tympanic ear (other potential factors such as variations in the degree of streptostyly could not be tested, due to a lack of precise data in the literature). Interestingly, we found that phylogenetic history is not a significant predictor of the morphology of the quadrate bone for our 38 species sampled across major squamate clades. Furthermore, in a recent study focused on gekkotans, there was a similar absence of phylogenetic signal, despite the closer relationship of the taxa under study (Paluh & Bauer, 2018).

Size also did not prove to be an important factor responsible for quadrate disparity within Squamata as a whole, as shape variation was not significantly affected by size in our sample. However, size was shown to have a strong effect on some closely related species within Squamata: allometric scaling was found to be significant in determining quadrate shape in gekkotans (Paluh & Bauer, 2018), and more generally in determining head shape in Anolis (Sanger et al. 2011) and Varanus (Openshaw & Keogh, 2014). The lack of significant signal for allometric scaling in squamates as a whole is presumably due to the great range of shapes in morphospace shown by our broad sample (Fig. 3).

It is still possible that allometric scaling may affect individual squamate clades, and yet not be detectable in squamates as a whole. Even with increased sampling (i.e. after including several representatives from each major clade) different allometric patterns across major clades may cancel out or confound the signal. Studies on ontogenetic shifts in the quadrates of snakes (Palci et al. 2016; Scanferla, 2016) and geckos (Paluh et al. 2018) have shown that morphological changes due to ontogeny can be quite different. If evolutionary allometry in squamates reflects at least in part patterns of ontogenetic allometry (as suggested in some cases; Sherratt et al. 2019), then there may well be multiple allometric patterns within Squamata.

Both ecological preferences and presence/absence of a tympanic ear were found to drive shape variation within Squamata. This correlation was somewhat expected, as squamates with a burrowing ecology often lose the tympanic membrane and external ear opening and this transformation is likely to affect quadrate morphology. However, ecology was found to be the main driver of Procrustes shape variance (disparity) in the dataset. In particular, the post‐hoc pairwise comparison revealed that the fossorial category is the one mainly responsible for driving the overall significance in difference between group means. This is consistent with the observation that elongate limbless burrowers such as Teretrurus, Acontias and Anniella all share a similarly elongated and posteriorly directed suprastapedial process, possibly as a result of streamlining of the skull for head‐first burrowing. Absence of an external tympanic membrane was found to have a ‘weaker’ effect on Procrustes shape variance (significant only in the ordinary anova) than ecology (possibly the presence of a tympanum is more structured by phylogeny compared with ecology).

This suggests that: (1) the loss of the external tympanic membrane can precede major morphological changes in the shape of the quadrate (quite evident in Lanthanotus, the quadrate of which is not too dissimilar to that of other related squamates that still retain a tympanic ear, e.g. Heloderma; Fig. 5b,g); and (2) that ecological factors are affecting quadrate disparity beyond the simple loss of a tympanic ear often driven by a fossorial lifestyle. This could possibly be related to dietary preferences and morphofunctional requirements connected to lifestyles in surface‐dwelling terrestrial vs. fossorial vs. aquatic environments.

Interestingly, the fossorial group shows the greatest disparity (i.e. largest Procrustes variance: is spread over the largest portion of morphospace) and is significantly different from the other groups (in terms of both group mean and variance). This could be due to the strong selective pressure imposed on fossorial taxa, which often show considerable morphological divergence from their non‐fossorial close relatives (e.g. amphisbaenians vs. lacertids).

Taxa that have lost a tympanum were found to have almost twice the Procrustes variance of those that have retained it. This is likely due to the release of constraints on the quadrate once the tympanum is lost, which allows for diversification of this bone into novel morphologies. The fact that burrowing taxa often lack a tympanic membrane could, at least in part, explain the greater morphological disparity of the fossorial group.

Our survey of the morphological diversity of squamate quadrates also highlighted a number of processes, crests and flanges that could be of use in phylogenetic analyses that rely on morphological characters, as well as in identifying fragmentary fossil taxa. Qualitative traits such as these have been identified as diagnosing major squamate clades (e.g. Gauthier et al. 2012). Furthermore, although we show that the quantitative (GM landmark) data has relatively little power to discriminate between major groups of squamates (see also Paluh & Bauer, 2018), more phylogenetic signal and discriminatory power might be preserved in analyses of clades that consist of taxa that share a relatively close most‐recent common ancestor.

Conclusions

In this study we illustrated and described a broad sample of the morphological diversity that is present in the shape of the quadrate of squamate reptiles. Geometric morphometric analysis indicates that the morphology of the quadrate is extremely evolutionarily plastic and does not retain significant phylogenetic signal when considered across all squamates. We have demonstrated that such diversity is at least in part correlated with ecological preferences and is strongly influenced by a fossorial lifestyle. Absence of an external tympanic membrane was also found to affect quadrate disparity in squamates, although this effect was less pronounced than the effect of ecology. Together, ecology and presence/absence of a tympanic ear explained up to about 20% of the observed morphological diversity (see R 2 values in Table 1). The fact that other tested factors (phylogenetic history and size variation) were not found to have left a significant signal in the morphological diversity of the quadrate of squamates means that up to 80% of such diversity is caused by unexplored factors. These factors are most likely correlated with biomechanics of the lower jaws (including the length relative to the skull that would affect the orientation of the quadrate), degree of streptostyly, and ultimately dietary preferences (likely the main driver of variation in the first two). These effects are more difficult to quantify, compared with those of the relatively simple discrete traits tested here. Future studies should therefore focus on gathering detailed information on diet and jaw‐quadrate biomechanics, so that a fuller understanding of the causes of variation in the shape of the quadrate bone of squamates can be achieved.

Conflict of interest

The authors have no conflict of interest to declare.

Author contributions

A.P. and M.W.C. conceived the study. A.P. collected the data, carried out the quantitative analyses, and drafted the article. All authors read, commented on and approved the final version of the article.

Supporting information

Data S1. List of taxa examined, taxonomic authorities, data on external tympanic membrane and ecology, and bibliographic sources.

Click here for additional data file. (19.1KB, xlsx)

Data S2. Raw landmark data for all taxa in this study.

Click here for additional data file. (15.6KB, txt)

Data S3. R scripts used to run the analyses.

Click here for additional data file. (5.7KB, txt)

Data S4. Table to slide semilandmarks during Procrustes superimposition (curveslide.csv).

Click here for additional data file. (81B, csv)

Data S5. Table containing data used in R (species.csv).

Click here for additional data file. (1.2KB, csv)

Data S6. Supplementary figures.

Click here for additional data file. (547.8KB, pdf)

Acknowledgements

We would like to thank Adelaide Microscopy (University of Adelaide) and Microscopy Australia, as well as R. Williams for the assistance provided while using the micro‐CT scanning facility at the University of Adelaide; we are grateful to O. Rieppel, M. Kearney, J. Maisano and M. Colbert for providing the micro‐CT scan data of some of the species included in this study (data acquired under the Deep Scaly Project, NSF grant EF‐0334961); we thank two anonymous reviewers for their valuable comments and suggestions; A.P. and M.S.Y.L. thank the Australian Research Council for financial support (grant no. DP160103005); M.W.C. thanks the Natural Sciences and Engineering Research Council of Canada (grant no. 23458) and a Chairs Research Allowance for financial support.

Data availability

The surface (.ply) files of all sampled quadrates are openly available from the Dryad Digital Repository (https://doi.org/10.5061/dryad.m905qftwz) (Palci et al. 2019).

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Data S1. List of taxa examined, taxonomic authorities, data on external tympanic membrane and ecology, and bibliographic sources.

Click here for additional data file. (19.1KB, xlsx)

Data S2. Raw landmark data for all taxa in this study.

Click here for additional data file. (15.6KB, txt)

Data S3. R scripts used to run the analyses.

Click here for additional data file. (5.7KB, txt)

Data S4. Table to slide semilandmarks during Procrustes superimposition (curveslide.csv).

Click here for additional data file. (81B, csv)

Data S5. Table containing data used in R (species.csv).

Click here for additional data file. (1.2KB, csv)

Data S6. Supplementary figures.

Click here for additional data file. (547.8KB, pdf)

Data Availability Statement

The surface (.ply) files of all sampled quadrates are openly available from the Dryad Digital Repository (https://doi.org/10.5061/dryad.m905qftwz) (Palci et al. 2019).

Articles from Journal of Anatomy are provided here courtesy of Anatomical Society of Great Britain and Ireland

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