Elasmobranch fishes (sharks, skates and rays) consume prey of a variety of sizes and properties, and the feeding mechanism typically reflects diet. Spotted ratfish, Hydrolagus colliei (Holocephali, sister group of elasmobranchs), consume both hard and soft prey; however, the morphology of the jaws does not reflect the characteristics typical of durophagous elasmobranchs. This study investigated the mechanical properties and morphological characteristics of the jaws of spotted ratfish over ontogeny, including strain, stiffness and second moment of area, to evaluate the biomechanical function of the feeding structures. Compressive stiffness of the jaws (E=13.51–21.48 MPa) is similar to that of silicone rubber, a very flexible material. In Holocephali, the upper jaw is fused to the cranium; we show that this fusion reduces deformation experienced by the upper jaw during feeding. The lower jaw resists bending primarily in the posterior half of the jaw, which occludes with the region of the upper jaw that is wider and flatter, thus potentially providing an ideal location for the lower jaw to crush or crack prey. The mechanical properties and morphology of the feeding apparatus of spotted ratfish suggest that while the low compressive stiffness is a material limit of the jaw cartilage, spotted ratfish, and perhaps all holocephalans, evolved structural solutions (i.e. fused upper jaw, shape variation along lower jaw) to meet the demands of a durophagous diet.

The class Chondrichthyes is composed of two subclasses, Elasmobranchii (sharks, skates and rays) and Holocephali (chimaeras), with species possessing a variety of morphologies and methods for capturing and processing a diversity of prey types (Huber et al., 2019). Despite this variation, all chondrichthyans face the mechanical challenge of feeding with jaws composed predominantly of unmineralized cartilage (Applegate, 1967; Kemp and Westrin, 1979; Dean and Summers, 2006; Seidel et al., 2020). Cartilage in vertebrates is typically a flexible connective tissue (Liem et al., 2001), and therefore does not seem an ideal material for jaws, being particularly counterintuitive for those species that feed on prey shelled in materials stiffer and stronger than cartilage (e.g. mollusks, echinoderms). Elasmobranch species exhibit a variety of morphological and musculoskeletal characters associated with durophagy (the eating of hard prey) (e.g. Summers, 2000; Summers et al., 2004; Dean et al., 2007, 2015; Rutledge et al., 2019; Seidel et al., 2021), but it is unclear what characters in holocephalan species relate to durophagy.

An array of morphological characteristics, including hypertrophied adductor muscles, robust jaws and molariform teeth, are typical of durophagous elasmobranchs (Wilga and Motta, 2000; Summers et al., 2004). Hypertrophied adductor muscles produce more force (Russell et al., 2000), which facilitates cracking, crushing and grinding hard prey. Molariform teeth provide a broad uneven surface for processing hard prey, and in species with heterodont dentitions, hard prey is moved to the molariform teeth before crushing (Fernandez and Motta, 1997; Wilga and Motta, 2000). As the teeth exert force on the hard prey, a bending moment is exerted on the jaws, and resistance to bending is a determinant of the force that can be brought to bear on the prey item. Durophagous sharks, like bonnetheads (Sphyrna tiburo) and horn sharks (Heterodontus spp.), share heterodont dentitions of anterior cuspidate and posterior molariform teeth (Nobiling, 1977; Cortes et al., 1996; Segura-Zarzosa et al., 1997; Harrington et al., 2016; Amini et al., 2020). The jaws of these and other durophagous elasmobranch species exhibit a similar pattern of higher second moment of area (I, a geometric property representing a cross-section's bending resistance) below the molariform teeth and/or adjacent to the jaw joint (Summers et al., 2004; Herbert and Motta, 2018; Rutledge et al., 2019).

Another strategy that has evolved in vertebrates that facilitates durophagous feeding is fusion of the upper jaw to the cranium. The loss of upper jaw kinesis in some bony fish taxa is considered a key specialization for durophagy (Turingan and Wainwright, 1993). Modern sauropsids (reptiles and birds) and modern synapsids (mammals) developed divergent mechanisms for jaw suspensions, associated with the evolutionary split (Russell and Thomason, 1993). Sauropsid taxa developed multiple cranial kinesis types typically accompanied by mobile upper jaws, while modern synapsids evolved a fused upper jaw (loss of cranial kinesis), which enabled an increased bite force as well as the ability to better hold large struggling prey (Russell and Thomason, 1993). Similarly, the elasmobranch and holocephalan evolutionary split resulted in divergent jaw suspension types. Elasmobranchs, like many early chondrichthyans, evolved a more mobile jaw suspension, while holocephalans (sister group to elasmobranchs) evolved a fused upper jaw (Huxley, 1876; Gregory, 1904). The functional consequences of a fused upper jaw in holocephalans have previously not been examined experimentally.

Additionally, some durophagous fish species develop or augment features during ontogeny which enhance feeding on hard prey. The diets of durophagous fishes tend to include harder and/or more complex prey as the feeding apparatus develops (Fernandez and Motta, 1997; Yamaguchi and Taniuchi, 2000; Fahle and Thomason, 2008; Fisher et al., 2011). Juvenile sheepshead fish (Archosargus probatocephalus) and lesser spotted dogfish (Scyliorhinus canicula) feed on small prey items with relatively larger, harder (e.g. shelled prey) and more complex prey (e.g. crab) increasingly included over ontogeny (Jardas, 1979; Lyle, 1983; Fernandez and Motta, 1997). The force produced by the adductor mandibulae of sheepshead fish increases with positive allometry over ontogeny and directly correlates with increased durophagous habits (Fernandez and Motta, 1997). The jaws of adult dogfish are significantly less viscoelastic (i.e. less flexible and less likely to deform over time) than the jaws of newborns, and perhaps this change in the material properties of the jaws is a contributing factor enabling the change in diet (Fahle and Thomason, 2008). More studies on the development of chondrichthyan skeletal tissues will shed light on whether this ontogenetic pattern is unique to durophagous species, while helping to understand how cartilage skeletons are modified through evolution and ontogeny to sustain high feeding loads.

Chondrichthyan cartilage is unique among vertebrates in being reinforced by tesserae, small mineralized blocks interconnected by ligaments that surround an inner core of hyaline-like cartilage (Liu et al., 2014; Seidel et al., 2016, 2020). The thickness of the layer of mineralization in tessellated cartilage varies among elasmobranch species and confers stiffness necessary for feeding, especially processing hard prey (Dean and Summers, 2006; Balaban et al., 2015). Although far less studied, mineralization in the cartilage of holocephalans apparently also takes the form of tiles, with a similar composition to elasmobranch tesserae (Seidel et al., 2020). However, recent work shows that holocephalan tesserae may not be as regularly patterned as elasmobranch tesserae (Fig. 1) (Seidel et al., 2020).

In this study, we examined a suite of skeletal characters in spotted ratfish (Hydrolagus colliei), to characterize morphological and mechanical strategies of durophagous holocephalan cartilage and contextualize it relative to the known properties of cartilage of elasmobranch species (e.g. Macesic and Summers, 2012; Balaban et al., 2015). Spotted ratfish have mass-specific bite forces comparable to those of durophagous elasmobranchs, but the jaw suspension and tooth plates are quite different and the jaw closing muscles are not obviously hypertrophied (Didier, 1995; Huber et al., 2008; Smith et al., 2019). Holocephalans have three pairs of continuously growing tooth plates, two pairs on the upper jaw and one pair on the lower jaw (Didier, 1995; Smith et al., 2019). In spotted ratfish, the tooth plates form a nipping or beak-like arrangement in the anterior, and an arrangement much like a utility cutter or gasket shear in the posterior (a vertical blade occluding with a wider, flat surface; Fig. 2). The tooth plates are thin and vertically aligned, in contrast to other holocephalan species where the plates can be more robust and have a proportionally larger working surface (Dean, 1906; Didier, 1995).

Our study investigated the following in spotted ratfish: (1) the strain of the upper and lower jaws under biologically relevant loads; (2) the compressive and flexural stiffness of the jaw cartilage; and (3) the second moment of area of the lower jaw. Given the weakly mineralized jaws, the indication that holocephalan tesserae may be disordered, and the lack of hypertrophied jaw muscles and molariform teeth characteristic of durophagous elasmobranchs, we expect the jaws of spotted ratfish to be modified in other structural ways to resist biting loads.

Research specimens

Spotted ratfish, Hydrolagus colliei Lay and E. T. Bennett 1839, were originally collected by otter trawl from Puget Sound, WA, USA, by the Washington Department of Fisheries and Wildlife on a survey cruise and stored in a −4°C freezer at the University of Washington's Friday Harbor Laboratories prior to the onset of this study. Standard length (SL) was measured from rostral tip to the base of the caudal fin (determined by the break between the elongated second dorsal fin and the caudal fin) and total length (TL) was measured from rostral tip to the tip of the caudal filament. Specimens ranged in size over 20 cm from juvenile to adult (SL=23–43 cm and TL=32.5–55.5 cm). Maturity was determined by body length and based on published size at maturity data (determined through morphometrics) for H. colliei from Barnett et al. (2009). The intact specimens were kept frozen until immediately prior to testing, when specimens were thawed and the cranium and jaws were removed for testing and immersed in elasmobranch Ringer's solution to prevent desiccation of the cartilage (Forster et al., 1972). The linear lengths of the upper and lower jaws, measured from symphysis to jaw joint, were recorded for comparison with the SL of each specimen.

Second moment of area

Crania of 25 H. colliei were scanned with a Bruker 1173 microCT scanner (Bruker, Kontich, Belgium) at the University of Washington Friday Harbor Laboratories. CT scans were made at 40 kV and 170 μA with a voxel resolution of 31 μm. Dissected specimens were wrapped in ethanol-soaked cheesecloth and placed in a tube to prevent movement and settling during scans. CT scans were reconstructed using NRecon (Bruker microCT). Ten virtual cross-sections of the left side of the upper and lower jaw were made with ImageJ Volume Viewer (National Institutes of Health, Bethesda, MD, USA). The slices were evenly spaced relative to the length of the jaw from the jaw joint to the symphysis.

Cross-sectional images were used to measure the second moment of area of the lower jaw. Second moment of area (I, mm4) is a measurement that describes the resistance of a beam's cross-section to bending (Vogel, 2003). Measuring second moment of area of the cross-sections of the lower jaw provides a quantitative evaluation of how well the jaw shape resists bending. We calculated second moment of area, Ix=∫y2dA, according to the direction of biting (i.e. parallel to the Y-axis of the jaw) (Fig. 3; Bailey et al., 2013). The neutral axis of the jaw cross-section was first determined, perpendicular to the line of applied force (i.e. the vertical axis of the jaw) and passed through the centroid of the cross-section (Beer et al., 2010). The line of applied force for the lower jaw of H. colliei was designated as parallel with the sagittal plane of the jaw, running dorsal to ventral. In the equation, y is the distance between an infinitesimal element of area, dA (e.g. a pixel of jaw tissue in the image), and the neutral axis of the cross-section of the jaw (Vogel, 2003; Beer et al., 2010).

Second moment of area was calculated for each cross-section using AutoCAD 2018 (AutoDesk) (Fig. 3). The material of the cross-sections of the jaw was assumed to be homogeneous for calculations of second moment of area, as the tesseral layer was thin and therefore is expected to contribute comparatively little to overall mechanical properties. The negligible thickness of the tesseral layer also meant it could not be accurately measured in our microCT data. Second moment of area was not measured for the upper jaw as it is fused completely to the cranium (identification of the dorsal, anterior and posterior margins would be largely arbitrary), making beam theory inapplicable.

Compression testing

Mechanical properties of the jaw cartilage of 20 H. colliei were measured with a material testing system (MTS Criterion Model 42, Eden Prairie, MN, USA) at two scales of structural organization: within the intact feeding apparatus and at the level of the cartilage material.

Strain experienced by the upper and lower jaws during feeding was measured by compression tests of the intact cranium (Fig. 4). The cranium was placed ventral-side up in elasmobranch Ringer's solution in the MTS, such that the upper platen of the MTS would close the lower jaw on its descent (Fig. 4). A base made from epoxy and a metal mending plate stabilized the cranium during tests. A thawed shrimp was placed between the jaws to simulate feeding conditions. Cartilage was compressed at 0.5 mm s−1, the observed minimum average jaw closing speed of H. colliei during prey processing. The minimum average jaw closing speed was used, as greater speeds caused excessive movement of the apparatus within the MTS. The jaw closing speed was measured from videos of two spotted ratfish (one male and one female) in an aquarium recorded with a GoPro Hero 5 (GoPro, San Mateo, CA, USA) at 60 frames s−1. Multiple feeding events (>5) were captured for each ratfish feeding on frozen shrimp and pieces of bony fish. The force used for the compression tests varied with SL of the specimen, according to the bite force regression equation for H. colliei in Huber et al. (2008). Half of the maximum bite force for each specimen was used for each test to simulate routine feeding conditions.

To quantify strain of the upper and lower jaws during compression, a pair of sonometric crystals (Sonometrics Corp., London, ON, Canada) were glued (Loctite Super Glue) at mid-length on each upper and lower jaw, vertically aligned to match the direction of the bite force. Crystals sized 1 or 2 mm were used depending on the size of the specimen. Each pair of crystals was attached approximately 2 mm apart. Sonometric crystals transmit and receive ultrasonic pulses, which allows the distance between two crystals to be measured. As the cartilage is compressed in solution in the MTS, the sonometric crystals recorded distance changes using speed of sound in water (1590 mm s−1), which were then used to calculate strain (Wilga and Sanford, 2008). SonoVIEW software (Sonometrics Corp.) was used to record the data from the sonometric crystals at a sampling rate of 122 Hz, transmit pulse of 250 ns and inhibit delay of 0.94 mm.

Sections at the mid-length of the upper and lower jaws were removed from the previously tested specimens to quantify compressive stiffness of the cartilage tissue itself (Fig. 4). Cross-sections of the cartilage (approximately 1.5 cm wide) were cut with a scalpel to encompass the locations of the sonometric crystals on the jaws in the previous tests. Jaw sections were stabilized with epoxy between two metal discs and compression tests were conducted, following Balaban et al. (2015). The discs were set parallel with each other to allow for even distribution of the force on the cartilage during compression. The force used for the compression tests was half of the predicted maximum bite force for each specimen. A pair of sonometric crystals was attached to each jaw section as described above, parallel to the line of applied force to record length changes testing local strains during simulated biting. Compressive stiffness (E, MPa), calculated as Young's modulus, was measured from the slope of the linear portion of the stress versus strain curve generated during compression tests. Stress equals the load divided by the cross-sectional area of the material. Cross-sectional area was measured for each jaw section tested using ImageJ (National Institutes of Health, Bethesda, MD, USA). Strain was calculated from sonomicrometry data as the change in the length of the material divided by the original length.

To calculate flexural stiffness (EI, N mm2) of the lower jaw at the anatomical location of compression testing, simulating a bite at mid-length of the jaw, the compressive stiffness (E) was multiplied by the second moment of area (I) of each lower jaw section used in the compression tests. The I of the lower jaw section was measured from the images of each cross-section in the same manner as described above for CT scan cross-sections. Flexural stiffness describes a beam's resistance to bending by accounting for both material (E) and structural (I) contributions, and the classical beam theory equation for flexural stiffness assumes a beam with constant cross-sectional shape (Vogel, 2003). The jaw of spotted ratfish does not have a constant cross-sectional shape. Therefore, the flexural stiffness calculated here only describes the section of the jaw used for compression tests but will be used to make inferences for the lower jaw as a whole.

Statistical analyses

All statistical analyses were performed in RStudio (https://www.rstudio.com/products/rstudio/). The relationship between the length of the upper and lower jaws and specimen standard length was tested with a linear regression. An ANOVA with a multiple comparisons test (Holm–Šidák) was used to determine the differences among second moment of area measurements at the 10 positions on the jaw (slices 1–10, symphysis to jaw joint). Additionally, the second moment of area of slices 6–10 in juvenile and adult specimens was compared by testing for differences between the regression coefficients of the resulting slopes (Zar, 1996). Normality was tested using the Shapiro–Wilk test; strain and compressive stiffness data violated the assumption of normality, and therefore non-parametric tests were used to analyze strain data and compressive stiffness (E). A Friedman test with pairwise Wilcoxon signed-rank tests with Bonferroni correction was used to detect differences between the four strain measurements (upper jaw/lower jaw intact/sectioned). A Mann–Whitney–Wilcoxon test was used to compare the compressive stiffness of the upper and lower jaw.

Scaling

The length of the upper and lower jaw scaled isometrically with SL (Table 1, Fig. 5). The scaling results of the mechanical properties measured in this study with SL are discussed below and presented in Table 1 (see also Fig. 5).

Cross-sectional shapes and second moment of area

Analysis of the lower jaw cross-sections and the upper jaw (Fig. 6) from the CT scans of H. colliei showed a distinct shift in jaw aspect ratio from the symphysis to the jaw joint. The upper jaw is tall and thin at the symphysis (Fig. 6, a) and the jaw joint (Fig. 6, c), but wide and flat between the symphysis and jaw joint (Fig. 6, b). The lower jaw cross-sections become taller and narrower from the symphysis to slice 7 and then widen closer to the jaw joint.

Mean second moment of area (I) of the lower jaw for the 25 specimens tested increased from slice 1 (symphysis) to 6 and then decreased from slice 6 to 10 (jaw joint) (Fig. 7). The largest increase occurred from slice 5 to 6 (P<0.05). The multiple comparisons test revealed slices 1–5 and 10 had a lower I than slices 6–8, slices 1–4 had a lower I than slice 9, and slices 1–3 had a lower I than slices 5 and 10 (P<0.05 for each pairwise comparison).

The lower jaws of juveniles (SL<31 cm, n=13) and adults (SL>31 cm, n=12) showed the same rostrocaudal trend of second moment of area, with I increasing from slice 1 (symphysis) to 6 and decreasing to slice 10 (jaw joint) (Fig. 7). Mean I of the lower jaw of juveniles was lower than mean I of the lower jaw of adults (P=0.008, F=11.313), which is to be expected. The slope of I from slice 6 to slice 10 was steeper in adults than in juveniles (|t|≥tα(2),v) (Zar, 1996), meaning that in adults, the bending resistance of the jaw decreases more rapidly toward the jaw joint.

Compression testing

Strain was significantly different at each repeated measure (χ23=41.0, P<0.0001). Mean (±s.d.) strain values of the upper and lower jaws during compression of the intact cranium were similar at 0.03±0.02 and 0.03±0.03, respectively (P>0.05). Mean strain of the upper jaw was greater than that of the lower jaw during compression of jaw sections at 0.11±0.05 and 0.05±0.02, respectively (P<0.0001), meaning that upper jaw sections deformed more than twice as much under compression. Pairwise comparisons of strain are depicted in Fig. 8.

Compressive stiffness (E) of the upper jaw cartilage was 21.48±15.47 MPa (mean±s.d.), greater than that of the lower jaw cartilage at 13.51±7.00 MPa (P=0.048). Average flexural stiffness (EI) of the lower jaw was 3077.5±1754.7 N mm2, and flexural stiffness scaled negatively allometrically with SL (P<0.05) (Table 1, Fig. 9). The log-scaled equations and predicted scaling exponents for isometry are presented in Table 1.

Gut analyses of spotted ratfish portray an opportunistic diet with a wide range of prey, including hard prey (e.g. shrimp, mollusks, sea urchins) and soft prey (e.g. annelids, bony fish), vertebrates and invertebrates, and even conspecifics (Johnson and Horton, 1972; Fresh et al., 1979; Miller et al., 1977; Ebert, 2003). Generally, juvenile and adult spotted ratfish are thought to have similar diets (Johnson and Horton, 1972) and this is reflected in our data. The material properties of spotted ratfish jaws (e.g. stiffness) showed largely no relationship with animal size, therefore not scaling with positive allometry, as might be expected for an ontogenetic dietary shift to harder prey (e.g. Rutledge et al., 2019). Rather, the negatively allometric change in flexural stiffness with age alludes instead to a shift from harder to softer prey, but again, this is not supported by gut analyses (Johnson and Horton, 1972). Additionally, the low r2 values and high P-values indicate that SL, here a proxy for ontogeny, does not adequately describe the large amount of variation present in the measurements of strain and compressive stiffness of the jaws (Table 1).

A specialist can be defined as a species restricted to a narrow range of resources because it is mechanically constrained to that subset (Ferry-Graham et al., 2002). A durophagous specialist would therefore be confined to hard prey because its feeding mechanism is best suited for hard prey. Spotted ratfish, however, lack the array of characteristics expected for durophagous elasmobranchs, but still capture and process hard prey. Such contradictory feeding ecomorphology is not unheard of in durophagous elasmobranchs. White-spotted bamboo sharks (Chiloscyllium plagiosum) have sharp clutching teeth, but their teeth can be depressed to create a crushing surface for durophagy (Ramsay and Wilga, 2007). Notoriously durophagous cownose rays (Rhinoptera bonasus), with robust flat teeth and gape-limited jaws, can eat oysters even larger than their gapes by nibbling the flattened edge of the shells instead of crushing the mollusk at its deepest points (Fisher et al., 2011), but are also known to feed opportunistically on soft-bodied prey (Collins et al., 2007). Similarly, the jaws of several large-bodied batoid fishes (Rhynchobatus, Pristis, Glaucostegus), although possessing teeth more associated with durophagy, are also thought to feed on stingrays, once the batoids grow large enough to escape the constraint of gape width (Dean et al., 2017). Our results show that although spotted ratfish are durophagous, their jaw skeletons bear no marked specializations for durophagy. Moreover, not only is their jaw morphology atypical for a durophagous chondrichthyan (e.g. jaws with low compressive stiffness, vertical rather than horizontal tooth plates), their small gapes and largely akinetic jaws even seem poorly suited for a generalist diet, which allows for the exploitation of many different resources (Ferry-Graham et al., 2002). More feeding observations and biomechanics data for holocephalan species are sorely needed to solve this conundrum.

The flexibility of spotted ratfish jaw cartilage suggests the jaws do not resist compression well and that tessellation in holocephalan cartilage contributes less to compressive stiffness than it does in elasmobranch cartilage, as also suggested by the thin tessellation we and others (Seidel et al., 2020; Pears et al., 2020) have observed in holocephalan skeletons. At a compressive stiffness (E) of 21.48±15.47 and 13.51±7.00 MPa (means±s.d.), the upper and lower jaws of spotted ratfish are considerably less stiff than elasmobranch cartilage (elasmobranch propterygium cartilage: E=140–2533 MPa: Macesic and Summers, 2012; elasmobranch jaw cartilage: E=41–106 MPa: Balaban et al., 2015). This is surprising as stiffer jaws should be advantageous for durophagous species, on account of the large reaction forces that occur when consuming hard prey (Huber et al., 2005).

We speculate that the lower compressive stiffness (E) of spotted ratfish cartilage relative to elasmobranch cartilage is offset by its bending resistance (I). Together, E and I create flexural stiffness. The flexural stiffness of the lower jaw of spotted ratfish has a negative allometric relationship with body length. The mean value is comparable with that of the walking legs (pereopods) of aquatic blue crabs (Callinectes sapidus) (EI=4000 N mm2; Taylor, 2018), which support the body mass of the crab during both aquatic and terrestrial locomotion (Taylor, 2018). This is in stark contrast to the low flexural stiffness (EI=60–180.2 N mm2) of the pelvic appendages (propterygia) of batoid species that ‘punt’ (use their propterygia to locomote along the sea floor; Macesic and Summers, 2012). Propterygia are made of tessellated cartilage, like the jaws of spotted ratfish; perhaps the difference in direction and magnitude of force experienced during punting versus durophagous biting and the extreme compressiform morphology of the ratfish jaw can explain the dissimilarity in flexural stiffness values. Also, the flexural stiffness of the pereopods and propterygium were calculated via three-point bending tests, which results in one combined value of EI, not deconstructed into discrete values of E and I, and therefore may only represent the properties of a limited region of the tested element (Macesic and Summers, 2012; Taylor, 2018). It should be noted that although the calculation of flexural stiffness from independently derived values of E and I (as in our study) can provide a more location-specific concept of flexural stiffness relative to the three-point bending approach, it can also oversimplify the morphology of the element and thus misrepresent the true EI value (Taylor, 2018). Therefore, the flexural stiffness of the jaws of spotted ratfish calculated within this study can serve as a useful baseline for comparison but should still be interpreted with caution.

Bending resistance (I, second moment of area) differs along the jaws and changes throughout ontogeny of spotted ratfish, as it does in horn sharks (Heterodontus francisci) and Xingu River rays (Potamotrygon leopoldi) (Summers et al., 2004; Rutledge et al., 2019). Second moment of area is greatest mid-length and in the posterior half of the lower jaw, suggesting that prey crushing occurs in this area, similar to some durophagous elasmobranchs (Summers et al., 2004; Herbert and Motta, 2018). The mean I of the lower jaw increases from juvenile to adult spotted ratfish, while still maintaining the same trend along the jaw, with higher I values in the posterior half of the jaw. The shape of the upper jaw ranges from thinner and taller at the symphysis and jaw joint to wider and shorter under the nasal capsule (a–c in Fig. 6). The posterior half of the lower jaw comes into contact with the wider area of the upper jaw (Fig. 2 and Fig. 6, b of the upper jaw against 3–6 of the lower jaw), which would facilitate cracking, crushing or cutting prey, leaving the anterior portion of the jaws to pierce and nip prey.

While I was not measured for the upper jaw, its fusion to the cranium should greatly increase its bending resistance, given the increase in cranial material in line with the loading axis (Vogel, 2003; Beer et al., 2010). As expected, the strain experienced by the upper jaw when loaded in the natural state (intact – fused to the cranium) was less than the strain experienced by the upper jaw when loaded isolated from the cranium (Fig. 8). The strain experienced by the lower jaw when loaded in the natural state was similar to the strain experienced by the upper jaw when loaded in the same state (Fig. 8). When both the upper and lower jaw were loaded isolated from the cranium, the strain experienced by the upper jaw was greater than that of the lower jaw (Fig. 8). This underscores the importance of the evolution of the fused upper jaw in ratfish, as the arrangement limits deformation. Therefore, in addition to allowing increased bite force (Russell and Thomason, 1993), a fused upper jaw reduces the strain during feeding in spotted ratfish by distributing the force through the cranium. Similarly, the large vertical toothplates of the lower jaw may alter the force experienced by the lower jaw during biting, provide additional support to the cartilage, and limit the deformation. Low compressive stiffness (and perhaps a thin tessellation) could be a material limit for ratfish cartilage, so the aforementioned anatomical features could represent architectural solutions to facilitate the processing of hard prey.

The feeding apparatus of spotted ratfish is quite different from those of hard prey specialists, demonstrating again the multiple mechanisms for accomplishing the same tasks that have evolved in chondrichthyans and more broadly across fish taxa. We suggest that in the evolutionary split between elasmobranchs and holocephalans, the strategies for building cartilage skeletons evolved in different directions, involving modifications to jaw suspension and tooth arrangement, but also skeletal mineralization and jaw cross-sectional morphology. In particular, differences in the material properties of the cartilage of these groups may have given rise to different morphological adaptations for durophagy. The low compressive stiffness of the jaws of spotted ratfish may be a constructional constraint, so to meet the demands of a durophagous diet, multiple structural strategies evolved that reduce bending and deformation of the flexible jaw cartilage. The high bending resistance in the posterior half of the lower jaw suggests that is where ratfish process and crush prey, and where we also suspect the large lower jaw tooth plates (spanning from symphysis to jaw joint) reduce cartilage deformation and brace the jaw during biting. Future studies should focus on the role that the distinct tooth plates of holocephalans play in durophagous feeding and perhaps in augmenting cartilage properties.

The authors thank the two anonymous reviewers for their helpful suggestions that improved the manuscript. We would also like to thank Friday Harbor Laboratories for access to and assistance with scanning.

Author contributions

Conceptualization: A.M.H., C.D.W.; Methodology: A.M.H., C.D.W.; Formal analysis: A.M.H., C.D.W.; Investigation: A.M.H.; Resources: A.M.H., A.P.S., C.D.W.; Writing - original draft: A.M.H.; Writing - review & editing: A.M.H., M.N.D., A.P.S., C.D.W.; Visualization: A.M.H., M.N.D., A.P.S., C.D.W.; Supervision: C.D.W.; Funding acquisition: A.M.H., C.D.W.

Funding

This research was supported by a National Science Foundation grant to C.D.W. (IOS-1631165). A.M.H. received funding from University of Alaska Anchorage LGL Graduate Student Research Award, the PADI Foundation, and the Friday Harbor Laboratories Wainwright Fellowship.

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Competing interests

The authors declare no competing or financial interests.