Biomechanical behaviour of lizard osteoderms and skin under external loading

Animals can be subjected to traumatic events that damage their tissues, sometimes with lethal consequences (e.g. Jennings, 2009; Tanke and Currie, 1998; Thomas and Cole, 1996). Physical stresses are generated in biological tissues when an individual impacts the ground or objects in its environment, but damage may also occur under the action of an opponent's or predator's claws, teeth, beak, tail, hoofs or horns, for example (e.g. Mukherjee and Heithaus, 2013; Song et al., 2011). As such strong loading regimes likely induce different patterns of loading, one could hypothesize that they probably create a wide range of species-specific selective pressures and, consequently, may have promoted the diversity of protective structures that have evolved in animals (see also Connors et al., 2019). For example, loading during agonistic interactions and falls likely constrained the cranial design of primates (e.g. Carrier and Morgan, 2014; Hylander and Johnson, 1997; Hylander et al., 1991).

A potential shielding strategy against traumatic events involves the incorporation of dermal bony plates also known as osteoderms (Vickaryous and Sire, 2009). Such plates are present in several distantly related vertebrate taxa (Yang et al., 2013), yet are particularly common and diverse among extant lizards (Vickaryous and Sire, 2009; Williams et al., 2021). Osteoderms with various shapes and types of organization have been reported for many lizard families (see Williams et al., 2021, for an exhaustive list) including scincids (e.g. Canei and Nonclercq, 2020; Oliver, 1951), lacertids (Arnold, 1973, 1989), gekkonids (e.g. Laver et al., 2020; Paluh et al., 2017), anguids (e.g. Strahm and Schwartz, 1977; Zylberberg and Castanet, 1985), gerrhosaurids and cordylids (e.g. Broeckhoven et al., 2018a; Marques et al., 2019).

Lizard osteoderms have classically been considered to have a protective function against predators (Williams et al., 2021), but this simplistic view has been challenged, notably by results from phylogenetically informed comparative studies on cordylids (Broeckhoven, 2022; Broeckhoven et al., 2018a,b; Stanley, 2013). Indeed, the covariation between osteoderm expression, distribution or morphology and ecological factors such as climate suggests that osteoderms likely have a multi-functional nature including thermoregulation (e.g. Clarac et al., 2019; but see Inacio Veenstra and Broeckhoven, 2022) and mineral storage (Broeckhoven and du Plessis, 2022). To date, our understanding of osteoderm function(s) suffers from a lack of data relating osteoderm structural features and their biomechanical and thermal properties. The sole empirical data available for lizard osteoderms were provided by Broeckhoven et al. (2015, 2017) and suggest that the resistance of cordylid skin to predator bites increases with osteoderm thickness. Simulations using single osteoderms reconstructed from high resolution micro-computed tomography (µCT) scans have also proven insightful (Broeckhoven et al., 2017; Iacoviello et al., 2020), highlighting, for example, how vascularization or material density can impact stress magnitude and distribution. Surprisingly, two simpler yet fundamental questions have never been addressed: (1) are there interspecific differences in the in toto deformation of lizard osteoderms under external loading?; and (2) can these differences be quantified? Aside from improving our understanding of osteoderm function and evolution, answers to these questions would also be useful for applied research. Lizard osteoderms are regarded as valuable models for the development of biomimetic materials such as protective clothing (Broeckhoven et al., 2017; Iacoviello et al., 2020; Liang et al., 2021) but are rarely the topic of biomimetic studies. Insights into the biomechanics of the lizard body ‘armour’ and the forces that have driven the evolution of their diversity could provide valuable insights for the bioinspiration of protective materials.

In this study, we measured deformation in morphologically different osteoderms. To do so, we instrumented temporal osteoderms of formalin-fixed specimens from 11 species of lizards with different osteoderm shapes and distribution patterns (Fig. 1). Next, we applied two loading regimes roughly mimicking either a bite or an impact on different locations of the head. Our goals were to test: (1) whether loading applied at different locations of the head generated strain in the instrumented osteoderm, (2) whether species differed in the relative stiffness of their osteoderm and skin, and (3) whether the two loading regimes (‘static’ versus ‘dynamic’) differed, thus providing insights into the morphological features and the patterns of organization driving variation in osteoderm stiffness.

Our experimental setup required specimens with at least one osteoderm that was larger than the smallest strain gauge available. We worked on temporal osteoderms because they are generally larger than the body and tail osteoderms and are not fused with skull bones. Data were collected for 11 species with 2–6 individuals per species (Table 1). All the specimens were adults that had been formalin fixed and preserved in 70% ethanol, and are housed at the Muséum National d'Histoire Naturelle (MNHN) in Paris. Small differences in the fixation protocol (e.g. time spent in formalin, formalin concentration) cannot be excluded for the specimens from the MNHN collections, causing the intraspecific variability to increase.

An osteoderm located in the temporal area was instrumented for every specimen (Fig. 2). The epidermis and the periosteum of the target osteoderm were removed with a scalpel and the surface of the osteoderm was cleaned with hydrogen peroxide, allowing the strain gauge to be glued to the external surface of the osteoderm using cyanoacrylate glue.

The smallest model of rectangular rosette strain gauge (item code: MMF402103; gauge total surface: 1.33 mm×2.9 mm; grid resistance: 350 Ω; gauge factors: 1.7–1.9) manufactured by Micro-Measurements (Vishay Measurements Group France, Chartres, France) was selected for these experiments. The rosette configuration was favoured because it bears three recording units and therefore can provide tensile, compressive and shear strain in every direction of the gauge plane which here corresponds to the external surface of the instrumented osteoderm.

The target osteoderm was loaded by applying an external force orthogonally to the surface at 14 different locations of the animal head (Fig. 3A). Loading was applied directly on the instrumented osteoderm (when the osteoderm surface was not entirely covered by the gauge), on several neighbouring osteoderms, and to the rostral area. First, force was applied for a very short period of time (<0.1 s; Fig. 2B) using a piezoelectric hammer (Model 086E80, PCB Piezotronics S.A., Saint Aubin, France). As the force–time slope was very steep, we refer to this loading regime as ‘dynamic’ loading. Second, force was applied slowly and for a relatively long period of time (>0.5 s; Fig. 2B) using a metal pin mounted on a Kistler piezo-sensor. The signal generated by the piezo-electric sensor and amplified by a 5011B charge amplifier (Kistler Instrumente AG, Winterthour, Switzerland) provided the magnitude of the load. As the force was gently increased by hand, we will refer to this experimental set-up as the ‘static’ loading condition hereafter. For each loading location, the procedure was repeated on average 33 times for the static loading and 104 times for the dynamic loading. More data points were collected during the dynamic loading because of the apparent lower consistency in the recording of the force magnitude. In both cases, care was taken to administer forces across the widest possible range of magnitudes (0.01–36.5 N for the static loading and 0.01–5.3 N for the dynamic loading).

Strain recorded in toto may not only reflect interspecific differences in the features of the osteoderms themselves. Indeed, the distribution of stresses between osteoderms may be dependent on the thickness and nature of the tissues underlying the osteoderms. Therefore, we tested whether similar trends could be observed in an experimental setup with fewer confounding factors. Six specimens (two Pseudopus apodus, one Heloderma horridum, one Heloderma suspectum, two Tiliqua scincoides, two Tiliqua rugosa and two Corucia zebrata) with at least one temporal osteoderm that was large enough to drill small holes on its rostral and caudal ends (see Fig. 2C) were selected for this experiment. In each case, temporal osteoderms of one side of the head were dissected out and the largest osteoderm was cleaned of any underlying soft tissue and instrumented. Note that, because of the destructive nature of dissections, several specimens from the MNHN collections that are listed in Table 1 were not included in the sampling for this experiment.

Next, two single-element gauges (item code: MMF402183, Micro-Measurements; gauge total surface: 2.41 mm×2.6 mm; 350 Ω; gauge factor: 1.9) were glued to the dissected osteoderm, one on its external side and the other on its internal side. Single gauges can only provide compressive, tensile and shear strain along their long axis; here, the anteroposterior axis of the osteoderm. They were, however, appropriate considering the goal of this second set of experiments and the loading applied to the osteoderms.

Two small holes (0.8 mm) were drilled through the osteoderms. They were located along the anteroposterior axis of the osteoderm near the edges. One of these holes was used to hang the osteoderm from a stand (Fig. 2C). The second hole was used to load the osteoderm with a series of weights (100 g, 200 g, 500 g and 700 g) using a thin wire. Consequently, the force vector resulting from the weight and the long axis of the gauge were aligned. The force applied to the osteoderm was obtained by multiplying the mass by the gravitational acceleration (F=m×g). In a second experimental setup, the osteoderm was held horizontally using forceps and the weight vector was oriented perpendicular to the anteroposterior axis of the osteoderm (Fig. S1). This experiment was conducted on an even smaller sample of individuals because some osteoderms were too small to be held using forceps.

The instrumented osteoderms were prepared following the polishing protocol reported by Marghoub et al. (2022) and sectioned along the axis of the force vector in a way that ensured the drilled holes were in view. Sections performed at the level of the gauges were imaged using a KEYENCE Vhx 7000 Digital Microscope to illustrate the thickness and shape of the osteoderms, and the multi-partite morphology of compound osteoderms (characteristic of some skink species), and to document the presence and proportion of capping tissue (i.e. osteodermine) described by Marghoub et al. (2022) and Kirby et al. (2020).

The gauges were connected with a 2310 signal conditioning amplifier (Vishay, Malvern, PA, USA) set up to feed the gauges with a 1.4 V current. Changes in the resistance of the gauges caused by changes in the gauge length resulted in voltage variations that were captured and amplified by the differential amplifier. The output signals from the amplifier were then converted from analog to digital and synchronized in a MP150 data acquisition and analysis system (BIOPAC Systems Inc., Goleta, CA, USA). For the in toto experiment, the force signal recorded from the piezoelectric sensors was synchronized with the recordings of strain using the MP150 data acquisition system. The output of the BIOPAC system was recorded on a laptop using AcqKnowledge 4 software (BIOPAC Systems Inc.).

Using calibration data and a series of custom-written Igor (Wavemetrics, Inc., Portland, OR, USA) procedures, the force and strain signals were calibrated, transformed and analysed. For strain recorded from the rectangular rosette gauges (experiment 1), the data recorded from each element of the gauge were used to calculate the maximal principal strain (maximal tensile strain in the plane of the gauge), the minimal principal strain (maximal compressive strain in the plane of the gauge), the shear strain (maximal−minimal principal strain), and the angle between the element A of the gauge and the maximal principal strain. The procedure used for the analysis first located the peaks of force then measured the maximal force and the largest strain associated with each peak. Strain values recorded from the tensile test experiment were measured manually using AcqKnowledge software. Here, the compressive and tensile strain caused by the attached weight were recorded as soon as the signal became stable.

We ran linear mixed models (LMMs) using the maximal tensile and compressive strain recorded at the level of the outer surface of the instrumented osteoderm and the following covariates: loading force, loading location, species, specimen and specimen head length. For each of the next four hypotheses, several models were run in R (http://www.R-project.org/) with the lmer function of the lme4 package (Bates et al., 2018).

Hypothesis 1: for a given loading force, the largest strain amplitudes are always measured when the loading was applied directly on the instrumented osteoderm (versus other locations in the head). Here, we considered the covariates ‘location’, ‘loading force’ and their interaction as fixed factors and the covariates ‘species’, ‘specimen’ and ‘head length’ as random effects. The interaction between specimen and location was also considered as a random effect to deal with the pseudo-replications.

Hypothesis 2: there are interspecific differences in the stiffness of the ‘skin system’ (i.e. osteoderm and soft tissues of the skin). Here, the covariates species, loading force and their interaction were considered a fixed factor while the other covariates were modelled as random effects.

For the purpose of testing hypotheses 3 and 4, a variable ‘group’ was added to the dataset. This group variable had four different levels: (0) loading at the rostral end of the head (Fig. 3A; 11–14), (1) loading on osteoderms that are separated from the instrumented osteoderm by one osteoderm (Fig. 3A; 8–10), (2) loading on osteoderms that are adjacent to the instrumented osteoderm (Fig. 3A; 4–7), and (3) loading on the instrumented osteoderm (Fig. 3A; 1–3). Matobosaurus validus specimens were excluded from these models because we were not able to load the instrumented osteoderm directly (i.e. gauges occupied most of the osteoderm surface).

Hypothesis 3: there are interspecific differences in the stiffness of osteoderms. Here, we focused on strain measured for loading locations that are on the instrumented osteoderm (group 3) to exclude the effects of factors such as stress transmission between osteoderms and skull morphology, for example. The data obtained from the tensile test experiment were also used to test hypothesis 3.

Hypothesis 4: there are interspecific differences in the transmission of the force between neighbouring osteoderms. Here, we investigated relative differences in strain predicted for groups 0, 1, 2 and 3 within each species to determine which species transmit more force from the loading location to the instrumented osteoderm. For each model, the compressive and tensile strain predicted (using the median loading forces) for each combination of species and group were normalized between 0 and 1. This was achieved by dividing the strain values predicted for each combination of species and group by the highest values predicted for a group of the same species. These data provide a sense of the relative changes in the strain recorded in the instrumented osteoderm when the same loading force was moved from group 3 to 0. The underlying idea is that in some species the strain could decrease by small increments (e.g. 100% of the strain when the instrumented osteoderm is loaded directly, 90% when the adjacent osteoderms are loaded, and 70% when the osteoderms separated from the instrumented osteoderm by one osteoderm are loaded), while in some other species the increments would be very large (e.g. 100%, 50% and 10%, respectively).

The strain and loading force were log-transformed to fit a normal distribution of the residuals. Visual inspection of the model residuals did not reveal strong violations of parametric conditions (normality and homogeneity of variances). Small to moderate residuals correlations were still observed (from 0.2 to 0.4), which should not affect our interpretation of the models. We performed type III ANOVA to check whether the fixed effects and their interactions had significant impacts on the measured strain. Next, we used the models to predict the strain under a unique value of loading force. We chose the median applied force value observed in both the static and dynamic loading experiment.

Loading force and loading location significantly impacted the maximal tensile and compressive strain in both the static and dynamic models (Table S1A; P<0.0001). Compressive strain predicted for the static and dynamic data tended to confirm our hypothesis that loading of the instrumented osteoderm induced the largest strain amplitudes recorded at the outer surface of this structure (triangles in Fig. 3Bii,Cii). However, loading of the adjacent osteoderms (diamonds in Fig. 3Bii,Cii) can also generate large compressive strain in the instrumented osteoderm. This was mostly true when the osteoderm located at the ventral rim of the instrumented osteoderm (Fig. 3Bii and Ci, diamond 4) was loaded.

The highest tensile strain in the dynamic model was predicted for loading on the instrumented osteoderm (Fig. 3Bi). However, tensile strain with similar magnitude was predicted for loading on the osteoderm located at the ventral rim of the instrumented osteoderm (Fig. 3Bi, diamond 4). Considering the static data, the model even predicts greater tensile strain when the loading is applied on adjacent osteoderms (diamond in Fig. 3Ci) instead of the instrumented osteoderm (triangles in Fig. 3Ci).

For both the dynamic and static loading conditions, the models predict much smaller tensile and compressive strain in the instrumented osteoderm when the loaded osteoderm is separated by at least one osteoderm from the instrumented osteoderm (Fig. 3). In the case of loading at the rostral end of the head, the strain generally barely exceeded the background noise (Fig. 3B,C). It is also worth mentioning that loading osteoderms located ventrally or posteriorly to the instrumented osteoderm generally produced larger strain than loading osteoderms that were located anteriorly or dorsally (see location 4 versus 5, 6 and 7; and location 8 versus 9 and 10 in Fig. 3B,C).

Our data showed that the largest compressive strain was observed when the instrumented osteoderm was loaded directly even though loading of adjacent osteoderms also generated large compressive strain. Loading of the adjacent osteoderms produced tensile strain that was similar to (dynamic data) or even larger than (static data) that observed when the instrumented osteoderm was loaded.

The static and dynamic models confirmed interspecific variation in osteoderm strain (species effect: P<0.05; Table S1B) considering all the loading locations. Species can be placed along a stiffness gradient based on the predicted tensile and compressive strain (Fig. 4). This gradient also becomes apparent when looking at the strain predicted for groups 1–3 (Figs 5 and 6) and species order is highly similar using the different models (Figs 4, 5 and 6). The osteoderms of T. rugosa and the two Heloderma species were stiffer than those of Timon lepidus, P. apodus, Tribolonotus gracilis, T. scincoides and, in some instances, C. zebrata, whereas the three-remaining species (Tribolonotus novaeguineae and the gerrhosaurids B. major and M. validus) showed intermediate strain values. Our second hypothesis was confirmed, with T. rugosa standing out as a species with a very stiff skin system whereas the skin of T. lepidus, T. gracilis and P. apodus appears the least stiff. However, the question remains as to whether these differences are due to the structure or mechanical behaviour of the osteoderm itself.

The group variable had a significant effect on strain in every model (Table S1C). When considered alone, species did not have a significant effect on strain. However, when considered in combination with loading force and/or group, its impact was always significant (Table S1C).

Very similar gradients of species were obtained with the four models (Figs 5, 6 and 7). With the exception of tensile strain predicted for H. suspectum during static loading (Fig. 7Bi), the tensile and compressive strain predicted for T. rugosa and the two Heloderma species were always very small. In contrast, large compressive and tensile strain amplitudes were predicted for T. lepidus, T. gracilis, P. apodus and C. zebrata (except for tensile strain predicted under static loading). Intermediate values of strain were predicted for B. major, T. scincoides and T. novaeguineae. The species order along the stiffness gradients is very similar irrespective of whether all loading locations or direct loading is considered, suggesting that the features of the osteoderms strongly impact the biomechanical proprieties of the skin system.

The strain recorded on the external and internal sides of the dissected osteoderms during the tensile test experiment was several orders of magnitude (at least with the highest weights) larger in C. zebrata, T. scincoides and P. apodus than in the two Heloderma species or in T. rugosa (Fig. 8). The experimental setup, similar to a classical tensile test, confirmed the trends observed in toto even though, in the present case, osteoderms appear more elastic in C. zebrata and T. scincoides than in P. apodus. Notably, P. apodus is the only species for which we recorded tensile strain on the external surface of the osteoderm. For the other species, we recorded compressive strain on this side of the osteoderm. This was most likely explained by the more convex shape of their osteoderms (Fig. 8). On the internal side, tensile strain was recorded for every species.

Our third hypothesis was confirmed because there were clear interspecific differences in the strain recorded when the instrumented osteoderm was directly loaded. Tiliqua rugosa again stood out as having very stiff osteoderms whereas the temporal osteoderms of T. lepidus, T. gracilis and P. apodus were the least stiff. Based on the tensile test experiment, osteoderms of T. scincoides and C. zebrata, in particular, were also less stiff.

We also took advantage of the results provided by the models described for hypothesis 3 above (‘Hypothesis 3: there are interspecific differences in the stiffness of osteoderms’) to test our fourth hypothesis. During dynamic loading, large proportions of the forces causing tensile strain in the instrumented osteoderm were transferred between the different groups of osteoderms in T. rugosa and H. horridum and to some extent in T. lepidus, T. novaeguineae and T. scincoides (upper half of schemes under the hammer shapes in Fig. 9). Forces causing compressive strain (lower half of schemes under the hammer shapes in Fig. 9) were transmitted in the two Heloderma species and in T. rugosa. In contrast, forces causing tensile and compressive strain were rapidly dissipated between the groups of osteoderms in T. gracilis, C. zebrata, P. apodus and B. major.

During static loading, the forces causing tensile strain in the instrumented osteoderm seemed high in every species, at least between groups 1–3 (upper half of schemes under the hand shapes in Fig. 9). There were, however, differences in the transmission of forces causing compressive strain, with H. suspectum, H. horridum, T. scincoides, P. apodus and T. lepidus showing high levels of transmissions and the two Tribolonotus species, B. major, C. zebrata and T. rugosa showing much lower levels of force transmission (lower half of schemes under the hand shapes in Fig. 9).

In addition to the interspecific differences, some species seemed to show differences in the transmission of the force depending on the type (static versus dynamic) of loading. In T. rugosa, more force was transmitted under dynamic loading (Fig. 9). This was especially striking when investigating the compressive strain. In B. major, P. apodus and C. zebrata, force transmission seemed larger during static loading, especially when tensile strain was considered (Fig. 9).

During the last seven decades, strain gauges have been used extensively to quantify minute length changes in loaded human bones (Grassi and Isaksson, 2015). They have also been used to quantify the level of mechanical strain, subject to different loading regimes, across various bones of mammals (e.g. Hylander, 1984; Thomason, 1991; Weijs and De Jongh, 1977) and, more recently, of fish (Markey et al., 2006) and reptiles (Dutel et al., 2021; Metzger et al., 2005; Porro et al., 2013, 2014; Ross et al., 2018; Smith and Hylander, 1985). Here, we used strain gauges to record maximal compressive, tensile and shear strain (shear strain is illustrated in Tables S1 and S2 and Figs S2 and S3) in temporal osteoderms of 11 lizard species. We observed that large strain amplitudes can be recorded when the instrumented osteoderm is directly loaded but also when force is applied to neighbouring osteoderms. We also recorded large strain amplitudes on the external and internal side of the dissected osteoderms during a tensile test. Although it may seem counterintuitive that we recorded compressive strain on the external surface for every species but P. apodus, this could be explained by the convex shape of the osteoderms (Fig. 8). A clear species gradient emerged from our analyses. The two helodermatids (H. suspectum, H. horridum) and T. rugosa had stiff skin and osteoderms. Timon lepidus, P. apodus and T. gracilis were at the other end of the spectrum, with less stiff skin and osteoderms. The osteoderms of T. scincoides and C. zebrata had mechanical features more similar to those of T. lepidus, P. apodus and T. gracilis, and very large strain amplitudes were recorded for these two species when dissected osteoderms were subjected to a tensile test. The two gerrhosaurids (B. major and M. validus) and the scincid T. novaeguineae had temporal osteoderms with an intermediate stiffness.

In most cases, the stiffness of the osteoderms appeared to be related to their overall shape. The relatively elastic osteoderms of T. scincoides, T. lepidus, P. apodus and C. zebrata were thin and slightly to markedly elongated along the anteroposterior axis, whereas the stiff osteoderms of T. rugosa and the two helodermatids were proportionally thicker and more rounded (Fig. 1A). The osteoderms of the two gerrhosaurids had an intermediate shape and biomechanical properties (Fig. 1A). Among cordylids, thicker osteoderms have been shown to provide better resistance against puncture during predator bites (Broeckhoven et al., 2015, 2017). We therefore propose that thickness, inherent mechanical properties and protection against puncture are correlated, and that the dermal armour of T. rugosa and the Heloderma species should better resist puncture.

Focusing on the five scincid species, at least three additional features of the gross morphology of the osteoderms likely explain why T. rugosa and T. novaeguineae had stiff osteoderms compared with C. zebrata and T. scincoides. First, the length of the overlapping section of adjacent osteoderms was greater in T. rugosa than in all the other species, which may have helped increase the overall stiffness of the skin system (Fig. 1A). Second, the temporal osteoderms of C. zebrata and T. scincoides have a compound morphology (Fig. 1A), with each element being composed of several smaller bony pieces (termed osteodermites) sutured together with fibrous connective tissue (Williams et al., 2021). This compound organization likely contributed to a reduction in their overall stiffness. In contrast, the temporal osteoderms of T. rugosa and T. novaeguineae were consolidated elements without intervening fibrous sutures. Third, the midline keel observed in T. novaeguinae has previously been suggested to reduce vertical stress, at least in crocodylomorph osteoderms (Clarac et al., 2019).

Unexpectedly, osteoderms from the two Tribolonotus species (Fig. 1A) demonstrated different loading properties (we recorded larger strain for T. gracilis as compared with T. novaeguineae), despite sharing a similar large size (relative to snout–vent length) and shape (with a strong, midline keel). Investigating structural features of osteoderms may help explain this discrepancy, as histological composition and structural heterogeneity likely alter resistance to external loads (see Iacoviello et al., 2020). For example, an enamel-like capping tissue with a high Young's modulus has been reported in the dorsal osteoderms of some lizards (Kirby et al., 2020; Marghoub et al., 2022). The thickness of this tissue varies across species (including H. suspectum and P. apodus) but was absent from the osteoderms of Varanus komodoensis. For the temporal osteoderms, we observed a tissue similar to the capping tissue in every species investigated in the tensile test experiment although it was much thinner and sparsely distributed in C. zebrata (Fig. 8). The variation in osteoderm stiffness observed among these species underscores the need for systematic reporting of the presence, thickness, distribution and functional properties of this capping tissue. In particular, the morphological and functional diversity of scincid osteoderms stands out as an important target for future evolutionary and biomimetic studies of body armour. The biomechanical and morphological data gathered here offer a first glimpse of the knowledge that will be gained from such studies and the features that could be mimicked to improve the stiffness or elasticity of materials used in the production of armour, vehicles or helmets, for example.

Using a drop weight impact test on biomimetically manufactured skin sheets of the dorsum of H. suspectum, P. apodus and C. zebrata, Liang et al. (2021) found that the skin of the last of these species absorbed the most energy. They suggested that it was related to the compound nature of the osteoderm. Our histology and tensile test showed that temporal osteoderms of C. zebrata are relatively elastic, compared with those of P. apodus and H. suspectum, and have only a thin layer of capping tissue (Fig. 8). These observations are particularly interesting given that C. zebrata is the only arboreal species in our sample and is potentially at risk of falling. However, the stiffness of C. zebrata osteoderms in toto was intermediate between that of H. suspectum and P. apodus. Moreover, the osteoderms of C. zebrata did not stand out when it came to their response to dynamic loading. As the shape, size and imbrication pattern differ between the temporal, ventral and dorsal skin areas of every species studied, investigating the ventral and dorsal osteoderms in toto and using tensile tests may help improve our understanding of the interspecific differences in the biomechanical properties and energy absorption of the lizard skin.

When we consider biomechanical properties of lizard osteoderms it is important to keep in mind that they are only one part of a complex skin system. Our study showed that external loading of neighbouring osteoderms generally causes larger tensile than compressive strain in the instrumented osteoderm, with the exception of H. suspectum (Fig. 9). Overall, however, our force transmission data did not reveal any obvious phylogenetic or morphological trends. For example, H. horridum showed a pattern of compressive and tensile strain distinct from that of the morphologically similar sister taxon H. suspectum. As differences during development have been reported for helodermatid osteoderms (Moss, 1969), we cannot exclude the possibility that intraspecific rather than interspecific variation caused the observed differences. Further, given the large amount of overlap between osteoderms, we were expecting a proportionally greater transmission of force between the temporal osteoderms of T. rugosa and P. apodus compared with the other studied species (Fig. 1A). However, neither species demonstrated relatively high levels of force transmission during static loading, and only T. rugosa showed high force transmission levels during the dynamic loading. Force transmission during dynamic loading was also relatively high in the two Heloderma species, but relatively low in P. apodus, C. zebrata and T. gracilis, which had stiff and elastic osteoderms, respectively. We therefore hypothesize that force transmission during dynamic loading is only partly impacted by the stiffness of the osteoderms. Force transmission between osteoderms is probably impacted by several other factors, including the presence and organization of the large collagen bundles (Sharpey's fibres) that anchor the osteoderm within the skin (and interconnected osteodermites of compound osteoderms; see Williams et al., 2021). In order to better understand what role (if any) Sharpey's fibres and other microstructural components play in the context of force transmission, future investigations integrating detailed histological descriptions and functional analyses are needed.

Other anatomical features of the head (e.g. muscle and bones of the skull) likely impacted our results as well. For example, the osteoderms located ventrally or posteriorly to the instrumented osteoderm were more often positioned adjacent to jaw muscles, while the anterior and dorsal osteoderms generally covered parts of the skull. We observed that larger strain amplitudes were generally recorded from osteoderms that covered muscles (Fig. 3), suggesting that the nature of the underlying tissue could greatly impact the transmission of force between neighbouring osteoderms. As we worked on fixed specimens, the underlying muscles were probably stiffer than they would have been in live animals, thus possibly leading to an overestimation of the stiffness of the skin system in toto. However, live individuals may be able to increase the stiffness of their skin by contracting the jaw adductor muscles. Additional experiments should be conducted on anaesthetized and live specimens to investigate this topic further.

Based on our sample, it is impossible to formally assess the degree to which biomechanical properties of osteoderms are conserved among and between the different clades of lizards. It is, however, worth mentioning that we observed large differences in osteoderm stiffness between species of Tiliqua and Tribolonotus but not between the two helodermatids or the two gerrhosaurids.

Stiffer osteoderms could be advantageous during conspecific fighting and/or interspecific interactions with predators or prey by preventing lethal or sublethal injuries. However, they most likely represent higher maintenance and energetic costs, and may impair locomotor performance (e.g. higher mass resulting in a lower endurance, lower flexibility possibly reducing mobility in fossorial species). The trade-off observed between locomotor performance and the degree of armature in cordylid lizards (Losos et al., 2002) provides some evidence for this.

In our sampling, osteoderms were confined to the head only in T. lepidus but covered large/most parts of the body and head in the other species. Timon lepidus is likely the fastest lizard among the studied species (see Beck et al., 1995; Gans and Gasc, 1990; John-Alder et al., 1986; Main and Bull, 2000; Van Damme and Vanhooydonck, 2001; Vanhooydonck et al., 2014, for maximum sprint speeds), suggesting that evolutionary constraints related to speed are probably stronger than those favouring skin stiffness of the body in this species. Such differences in osteoderm distribution as well as those reported in this study for osteoderm stiffness could be related to interspecific differences in the balance between selective pressures associated with locomotor performance and protection against external loads.

Conspecific bites near or on the head have been reported for most of the studied species (e.g. Beck, 1990; Beck and Ramirez-Bautista, 1991; Jablonski, 2018; McCoy, 2006; Turner, 2010) or some of their close relatives (Pietruszka, 1988). In T. rugosa, conspecific bites to the head are common during male fights, often causing scale damage and sometimes breaking bones such as the mandible (Kerr and Bull, 2002; Murray and Bull, 2004). Considering the stiff temporal osteoderms of that species, we hypothesized that stiff temporal osteoderms evolved in species capable of strong bites during interactions with conspecifics. A rapid evaluation of the bite forces recorded for eight out of the 11 species investigated here (Fig. S4) suggests that the data do not unequivocally support this hypothesis because there is no obvious correlation between temporal osteoderm stiffness and bite force; H. suspectum had low bite forces despite having stiff temporal osteoderms while T. rugosa, T. scincoides and C. zebrata had strong bites of similar magnitude despite the differences in the stiffness of their osteoderms. In addition, both Heloderma species have stiff osteoderms although their fights are highly ritualized compared with those observed in most other lizards (Beck and Ramirez-Bautista, 1991). We would expect ritualized fights to reduce the occurrence of biting during agonistic interactions. Data suggest that this could be true for H. suspectum where bites are occasional, but not for H. horridum, where the males can bite each other tenaciously and the dominant individual typically bites the jaw of the subordinate male at the end of each fighting bout, sometimes causing bleeding (Beck and Ramirez-Bautista, 1991). In this respect, it may be relevant that the lower jaw is covered with osteoderms in H. horridum but not in H. suspectum (Fig. 1). Again, more morphological, behavioural and biomechanical data from a much larger sample of species would be needed to formally test our hypothesis but the data available suggest that the functional roles of osteoderms are likely diverse.

Temporal osteoderms show interspecific differences in their stiffness and those differences can be quantified using strain gauges. Specimens investigated here were all formalin-fixed which mostly likely increased the stiffness of the osteoderms and the underlying tissues. Therefore, differences in strain recorded for this study should be considered as relative differences. Future studies should explore strain in osteoderms of fresh specimens but also record strain during in vivo experiments to improve our understanding of the biomechanical properties and the ecological role of osteoderms. Our discussion also highlights the need for more ecological data in order to be able to interpret the functional role(s) of the lizard osteoderms.

We are very grateful to Prof. Callum Ross and Prof. Boris P. Chagnaud who provided templates and help during the writing of our Igor procedures. Prof. Ross and Ludovic Hallery (Vishay Group) also provided helpful tips for the recording of strain data. We also thank Dr Nicolas Vidal and Dr Marc Herbin who provided the specimens from the collections of the MNHN. We are also thankful to Kelia Isalas for her help with the tensile test experiment.