THE MORPHOLOGY AND BIOMECHANICS OF JAW STRUCTURES IN CHONDRICHTHYES

The skeletons of chondrichthyans (sharks, skates, rays, and chimeras) are composed entirely of cartilage, yet must still provide the skeletal support that bone does in other vertebrates. There is also an incredible range of diversity in the morphology of the cartilaginous skeleton of the feeding apparatus in Chondrichthyans. The goal of this research is to provide insight into the morphological evolution and biomechanical function of the cranial skeleton in chondrichthyans. Feeding style changes can occur with morphological changes in the skeletal elements of the shark feeding apparatus. In chapter one, to increase our understanding of how the feeding skeletal morphology has evolved with the of feeding style of sharks, the length, width, and angles of the elements of the feeding apparatus are measured in four species (white-spotted bamboo, Chiloscyllium plagiosum; spiny dogfish, Squalus acanthias; sandbar, Carcharhinus plumbeus; and dusky smoothhound, Mustelus canis). These species encompass a wide phylogenetic range, and include suction and bite feeders as well as two different orientations of the hyomandibula, the major jaw supporting element. A principle components analysis is used to identify relationships among the skeletal elements by species, and linear regressions are then used to test the effect of hyomandibula length on the other morphological variables. Strong relationships were discovered between the length of the hyomandibula and the lengths of all other skeletal elements and the angle of the hyomandibula. The bite feeders have longer elements and appear to maximize the size of the oral cavity, allowing larger prey to be swallowed. Suction feeders have shorter elements, which restrict the size of the oral cavity and mouth opening, but can concentrate suction forces. Based on the strong relationship between hyomandibula length and angle on feeding morphology, the mechanical properties of the hyomandibular cartilages in the same four shark species is investigated in chapter two. Young’s modulus, a measure of stiffness, and Poisson’s ratio, a measure of three-dimensional shape change, of the hyomandibular cartilages are compared. While Poisson’s ratio is similar among the species, Young’s modulus increases with mineralization and is larger in the suction feeders. Though sharks have a cartilaginous skeleton, some species have higher mineralization of elements that are under higher stress.


Abstract
Sharks have an incredible diversity of feeding mechanisms for a group with so few extant species. To understand the relationship between the morphology of the shark feeding apparatus and feeding style, length, width, and angle of the ten skeletal elements in the feeding apparatus are measured in four shark species (white spotted bamboo, Chiloscyllium plagiosum; spiny dogfish, Squalus acanthias; sandbar, Carcharhinus plumbeus; and dusky smoothhound, Mustelus canis). These species encompass a wide phylogenetic range, and include suction and bite feeders as well as two different orientations of the hyomandibula, the primary jaw support element. A principle components analysis is used to identify relationships among the skeletal elements by species, and linear regressions are then used to test the effect of hyomandibula length on the other morphological variables. Strong relationships were discovered between the length of the hyomandibula and the lengths of all other skeletal elements and the angle of the hyomandibula. Bite feeders have longer elements and appear to maximize the size of the oral cavity, allowing larger prey to be swallowed. Suction feeders have shorter elements, which restrict the size of the oral cavity and mouth opening, but can concentrate suction forces. Significant regressions of all skeletal elements may be of use for future paleontological studies.

Introduction
Sharks are known as effective predators, yet they have a relatively simple feeding apparatus compared to bony fishes (Motta & Huber 2012). The ten skeletal elements ( Fig. 1) (Gregory 1904, Wilga 2002, Wilga et al. 2011.
Shark jaws are not fused to the cranium, and can protrude away from the cranium during a feeding event (Gregory 1904, Maisey 1980, Wilga 2001. The jaws are suspended posteriorly from the cranium by the hyomandibular cartilages, which articulate with the lower jaw, and by one to three anterior craniopalatine ligaments that connect the upper jaw with the cranium (Gregory 1904, Maisey 1980, Wilga 2008, Fig. 1). At rest, the hyomandibula projects laterally from the cranium, and may be oriented directly lateral, posterolateral, or anterolateral in different taxonomic groups , Wilga 2008. The distal tips of laterally oriented hyomandibulae are at a maximal distance from the cranium at rest, and are moved medially as they swing ventrally during jaw opening (Wilga 2008(Wilga , 2010. Shark species in the orders Heterodontiformes, Orectolobiformes and Squaliformes have short, laterally oriented hyomandibulae (Wilga 2008  . Posteriorly oriented hyomandibulae are long and swing ventrolaterally, which increases the width of the oral cavity, allowing large prey to pass through with minimal obstruction , Wilga 2008. Suction feeding sharks have short jaws with short, laterally oriented hyomandibulae, while bite feeding sharks have long jaws with long, posteriorly oriented hyomandibulae , Wilga 2008. The ceratohyal cartilages are medial to Meckel's cartilages and articulate with the hyomandibulae proximally and the basihyal distally. The coracohyoideus and coracoarcualis muscles depress the basihyal posteroventrally, which in turn depresses the ceratohyal posteroventrally (Marion 1905, Motta et al., 1997Motta 1998, 2000). In a study of 19 shark species, the ceratohyal of suction feeding sharks had a higher second moment of area (a measure of resistance to bending) than ram feeders (Tomita et al. 2011). The coracohyoideus and coracoarcualis muscles of suction feeders generate large forces to rapidly rotate the ceratohyal posteroventrally, expanding the oral cavity, which creates a large negative pressure to pull prey into the mouth. These forces place bending stress on the ceratohyal, and the large second moment of area helps to resist the forces. Aspect ratio (length/width) of an element may indicate the resistance to bending; ratios greater than 20:1 have greater bending and shear deformation (Spatz et al. 1996).
Basic morphological relationships among the elements of the shark feeding apparatus can provide a greater understanding into how a group of organisms with so few skeletal elements has evolved such functional diversity. To this end, the morphology of the skeletal elements involved in the feeding apparatus is quantified in four species of sharks to identify relationships in length, width, and hyomandibula angle among species with different feeding methods (bite, suction), hyomandibular cartilage orientation (lateral, posterior), and phylogenetic position. Several hypotheses will be addressed. 1) The length of the hyomandibulae will be shorter (relative to cranial length) in suction feeding species with lateral hyomandibula orientation.
2) The length of the hyomandibula will vary in direct proportion with the length of the jaws, the length of the ceratohyal, and the angle of the hyomandibula.
3) The width of the basihyal and the intracranial distance between the hyomandibula articulations will vary in proportion with the other morphological variables and be larger in bite feeders (increasing mouth width for swallowing large prey items). 4) The aspect ratio (length/width) of the ceratohyal will be larger in suction feeders than bite feeders.

Morphology
The following measurements were taken for each shark using either dial calipers or by taking digital images and taking measurements using the software program ImageJ

Statistics
A principal components analysis was run to test for variation among the species.
The following morphological measurements were included for analysis: length of the HY, CH, BH, MC, PQ, and ICR normalized to cranial length; aspect ratio of the HY, CH, and BH; and HY angle. Linear regressions were then run to test for the relationships between the morphological variables, using the normalized and non-normalized lengths of the HY, CH, BH, MC, PQ, and ICR, as well as the HY angle and aspect ratios of the HY, CH, and BH. To test hypotheses one and four ANOVAs were run to test for differences in CH aspect ratio and normalized HY length among species.

Results
Principal components one and two account for 86% of the variance among the variables, while PC3 contributes 8% of total variance. All four species cluster in different areas of morphospace in a plot of PC1 by PC2 (Fig. 3). Since all length measurements were normalized to cranial length (CL), size was not a factor for any of the axes.
Ceratohyal (CH) and hyomandibula (HY) aspect ratios are the only variables that load negatively on PC1 (Table 1), while all other variables load positively and are close together. Chiloscyllium plagiosum and S. acanthias load highly negative on PC1. M.
canis loads closer to zero on the positive side of PC1 while C. plumbeus loads highly positive. Basihyal (BH) length loads highly negative on PC2, while BH and HY aspect ratios load highly positive, and all other variables load close to zero (Table 1). C.
plagiosum and M. canis overlap on PC2, and they range from loading close to zero

Abstract
Sharks have an incredible diversity of feeding mechanisms for a group with so few extant species. To understand the relationship between the morphology of the shark feeding apparatus and feeding style, length, width, and angle of the ten skeletal elements in the feeding apparatus are measured in four shark species (white spotted bamboo, Shark jaws are not fused to the cranium, and can protrude away from the cranium during a feeding event (Gregory 1904, Maisey 1980, Wilga 2001. The jaws are suspended posteriorly from the cranium by the hyomandibular cartilages, which articulate with the lower jaw, and by one to three anterior craniopalatine ligaments that connect the upper jaw with the cranium (Gregory 1904, Maisey 1980, Wilga 2008, Fig. 1). At rest, the hyomandibula projects laterally from the cranium, and may be oriented directly lateral, posterolateral, or anterolateral in different taxonomic groups , Wilga 2008, Fig. 2). The distal tips of laterally oriented hyomandibulae are at a maximal distance from the cranium at rest, and are moved medially as they swing ventrally during jaw opening (Wilga 2008(Wilga , 2010. Shark species in the orders Heterodontiformes, Orectolobiformes and Squaliformes have short, laterally oriented hyomandibulae (Wilga 2008). Anteriorly oriented hyomandibulae are found only in batoids (skates and rays) carcharhiniform sharks . Posteriorly oriented hyomandibulae are long and swing ventrolaterally, which increases the width of the oral cavity, allowing large prey to pass through with minimal obstruction , Wilga 2008. Suction feeding sharks have short jaws with short, laterally oriented hyomandibulae, while bite feeding sharks have long jaws with long, posteriorly oriented hyomandibulae , Wilga 2008.
The ceratohyal cartilages are medial to Meckel's cartilages and articulate with the hyomandibulae proximally and the basihyal distally. The coracohyoideus and coracoarcualis muscles depress the basihyal posteroventrally, which in turn depresses the ceratohyal posteroventrally (Marion 1905, Motta et al., 1997Motta 1998, 2000). In a study of 19 shark species, the ceratohyal of suction feeding sharks had a higher second moment of area (a measure of resistance to bending) than ram feeders (Tomita et al. 2011). The coracohyoideus and coracoarcualis muscles of suction feeders generate large forces to rapidly rotate the ceratohyal posteroventrally, expanding the oral cavity, which creates a large negative pressure to pull prey into the mouth. These forces place bending stress on the ceratohyal, and the large second moment of area helps to resist the forces. Aspect ratio (length/width) of an element may indicate the resistance to bending; ratios greater than 20:1 have greater bending and shear deformation (Spatz et al.

1996).
Basic morphological relationships among the elements of the shark feeding apparatus can provide a greater understanding into how a group of organisms with so few skeletal elements has evolved such functional diversity. To this end, the morphology of the skeletal elements involved in the feeding apparatus is quantified in four species of sharks to identify relationships in length, width, and hyomandibula angle among species with different feeding methods (bite, suction), hyomandibular cartilage orientation (lateral, posterior), and phylogenetic position. Several hypotheses will be addressed. 1) The length of the hyomandibulae will be shorter (relative to cranial length) in suction feeding species with lateral hyomandibula orientation.
2) The length of the hyomandibula will vary in direct proportion with the length of the jaws, the length of the ceratohyal, and the angle of the hyomandibula.
3) The width of the basihyal and the intracranial distance between the hyomandibula articulations will vary in proportion with the other morphological variables and be larger in bite feeders (increasing mouth width for swallowing large prey items). 4) The aspect ratio (length/width) of the ceratohyal will be larger in suction feeders than bite feeders.

Morphology
The following measurements were taken for each shark using either dial calipers or by taking digital images and taking measurements using the software program ImageJ

Statistics
A principal components analysis was run to test for variation among the species.
The following morphological measurements were included for analysis: length of the HY, CH, BH, MC, PQ, and ICR normalized to cranial length; aspect ratio of the HY, CH, and BH; and HY angle. Linear regressions were then run to test for the relationships between the morphological variables, using the normalized and non-normalized lengths of the HY, CH, BH, MC, PQ, and ICR, as well as the HY angle and aspect ratios of the HY, CH, and BH. To test hypotheses one and four ANOVAs were run to test for differences in CH aspect ratio and normalized HY length among species.

Results
Principal components one and two account for 86% of the variance among the variables, while PC3 contributes 8% of total variance. All four species cluster in different areas of morphospace in a plot of PC1 by PC2 (Fig. 3). Since all length measurements were normalized to cranial length (CL), size was not a factor for any of the axes.
Ceratohyal (CH) and hyomandibula (HY) aspect ratios are the only variables that load negatively on PC1 (Table 1), while all other variables load positively and are close together. Chiloscyllium plagiosum and S. acanthias load highly negative on PC1. M.
canis loads closer to zero on the positive side of PC1 while C. plumbeus loads highly positive. Basihyal (BH) width loads highly negative on PC2, while BH and HY aspect ratios load highly positive, and all other variables load close to zero (Table 1). C.
plagiosum and M. canis overlap on PC2, and they range from loading close to zero  Correlation matrix up to highly positive. S. acanthias and C. plumbeus also overlap on PC2, though S. acanthias ranges from slightly to highly negative, while M. canis ranges from around zero to highly negative. canis and C. plumbeus were not different from one another but were lower than the other two species at 5.94 ± 0.16 and 6.11 ± 0.01, respectively.

Discussion
The length of the hyomandibula accounts for most of the variation in the skeletal morphology of the shark feeding apparatus. Bite capturers (C. plumbeus and M. canis) have longer elements relative to head length, than the suction capturing C. plagiosum or the intermediate capturing S. acanthias. These longer elements have been noted previously and likely allow for larger bites , Wilga 2008. Bite feeders also have posteriorly oriented (larger angle) hyomandibulae, which are longer because of the orientation (Fig. 2). The ceratohyal cartilage, which is medial to and parallels the lower jaw, necessarily lengthens with the jaws.
The length of the hyomandibula explained a significant amount of variation in the width of the basihyal and the intracranial width between the hyomandibula articulations (ICR). Although the regression of the hyomandibula to the basihyal was significant, the R 2 values were low (0.38), indicating that much of the variance in the width of the basihyal is due to some factor other than the length of the hyomandibula. However, much of the variance in the intracranial width between hyomandibula articulations was due to the length of the hyomandibula (R 2 = 0.82). These are likely functionally coupled and relate to feeding style. Bite feeding sharks have long, posteriorly oriented hyomandibulae and long jaws to help bite and swallow large prey items , Wilga 2008. A relatively wider cranium and basihyal would create a wider gape to allow larger prey to be consumed. Conversely, suction feeders have short, laterally oriented hyomandibulae with short jaws that are occluded laterally during suction, and that create a small mouth opening that can concentrate suction pressure , Wilga 2008.
The aspect ratio of the ceratohyal cartilages is lower in the two species that can use suction to capture (C. plagiosum and S. acanthias) than those that always bite capture (C. plumbeus and M. canis) (F=22.59, p<0.001). In a previous study of 19 shark species, suction feeders were found to have ceratohyal cartilages that are more resistant to bending than sharks with other feeding styles (Tomita et al. 2011). Although this study uses a different metric (aspect ratio rather than second moment of area), the ceratohyal cartilages with lower aspect ratios (shorter and thicker) were found in the suction feeding species. Bending forces on short, squat elements also shear the elements (Spatz et al. 1996), and low aspect ratio ceratohyals resist bending forces better than the relatively gracile higher aspect ratio ceratohyals of bite feeders.
Most of the elements in the species studied here have significant linear relationships to one another. This indicates that variation in any of the morphological variables measured here will be reflected in most of the other variables. This is potentially significant for paleontological research because other than teeth, fossil data from sharks is limited because cartilage does not fossilize well (Shimada 2005

Introduction
The skeletons of chondrichthyans (sharks, skates, rays, and chimeras) are composed entirely of cartilage and must provide the stiff skeletal support that bone does in other vertebrates. Bone has two main advantages over cartilage: it can remodel and repair. In remodeling, the cortical layer thickens in areas of high stress or trabecular rods are created in the planes where force is applied to reinforce bone strength (Thompson, 1917;Goldstein, 1987). Though cartilage cannot remodel or repair (Kemp & Westrin, 1979), shark jaws must resist substantial forces generated during feeding. The chondrichthyan jaw is strengthened by the uniquely layered composition of the cartilage.
In the non-vertebral skeleton of chondrichthyans, an inner core of unmineralized hyaline cartilage is surrounded externally by a mosaic of mineralized hexagonal tiles called tesserae (Kemp & Westrin, 1979;Dean and Summers, 2006). In tessellated cartilage, the thickness of the tesseral layer can lead to differences in the functional properties of different skeletal elements (Summers 2000).
The vertebral centrum of sharks has areolar calcification, which forms in concentric rings and permeates the entire cartilaginous structure , Dean & Summers, 2006, Porter et al. 2006. Minerals are distributed throughout areolar cartilage, and thus may have different properties than tessellated cartilage, which is only mineralized in the outer layer. The vertebral centra of several shark species have a Young's moduli between 323 and 563 MPa (Porter et al. (2006). Young's modulus is a measure of stiffness, which is calculated by testing a structure in compression or tension.
The slope of the linear portion of a plot of force per unit area (N/m 2 (Pa)), or stress, placed on the structure by the resultant strain (change in length/original length) is a measure of Young's modulus, whereby the larger the modulus, the stiffer the structure, and the greater resistance to shape change. Young's modulus for bony tissue is between 10-20 GPa, while values for non-shark cartilage range from 0.21 to 2.6 MPa (Currey 2010, Korhonen et al. 2002, Jin & Lewis 2004, Stolz et al. 2004).
The propterygia, a skeletal element associated with the pelvic girdle in batoids, has tessellated cartilage (Dean & Summers 2006, Macesic & Summers 2012. Batoids that punt (use the propterygia to push off of the sea floor) have stiffer propterygia than those of non-punters (Macesic & Summers 2012). Young's modulus was not measured in the propterygia because they were tested in bending, rather than compression or tension (Macesic & Summers 2012), however flexural stiffness ranged from 140-2533 MPa.
When a cube is compressed in one dimension, it will expand in the other two dimensions. The ratio of compression along one axis and expansion in the other two is called Poisson's ratio. There is a wide range of values for Poisson's ratio in biological tissues, with cartilage ranging from 0.15 to 0.503 (Korhonen et al. 2002, Jin & Lewis 2004, and bone ranging from 0.09 to 0.5 (Shahar et al. 2007, Wirtz et al. 2000. There are no measured values for Poisson's ratio in shark cartilage.
Shark jaws are not fused to the cranium, and can protrude away from the cranium during a feeding event (Gregory 1904, Maisey 1980, Wilga 2001. The jaws are suspended posteriorly from the cranium by hyomandibular cartilages that articulate with Meckel's knob of the lower jaw and anteriorly by one to three craniopalatine ligaments that connect the upper jaw with the cranium (Gregory 1904, Maisey 1980, Wilga 2008).
The orientation of the hyomandibula may affect the orientation of the forces on the cartilage when the hyomandibula swings ventrally during feeding (Huber 2006, Wilga 2008. At rest, the hyomandibular cartilages can be directed laterally, anterolaterally, or posteolaterally with respect to the midline , Wilga 2008, Fig. 2). The distal tips of laterally and anterolaterally oriented hyomandibulae move medially as they swing ventrally during jaw opening, whereas posterolaterally oriented hyomandibulae move anterolaterally as they swing ventrally (Wilga 2008). Horn sharks, Heterodontus francisci, which have laterally oriented hyomandibulae, capture prey using suction and is durophagous (eats hard bodied prey) , Wilga 2008.
The hyomandibulae of horn sharks are thought to be loaded in tension during biting, opposing the forces generated in the lower jaw (Huber 2006). In lemon sharks, Negaprion brevirostris, which have posterolaterally oriented hyomandibulae, the hyomandibulae are thought to be loaded weakly in compression when the jaws are not protruded, but loaded with stronger compression when the upper jaws are protruded when bite feeding (Wilga 2008, Huber 2006.
The mechanical properties of the hyomandibular cartilages are measured in compression by calculating Young's modulus and Poisson's ratio. This will provide an understanding of how tesselated shark cartilage responds to compressive forces, and to give insight into the material properties of shark cartilage. The mechanical properties of the hyomandibular cartilage are compared among four shark species with two different hyomandibula orientations (lateral vs posterior) and two different feeding styles (bite vs suction). The percent of cross-sectional area that is mineralized is also compared to test whether mineralization influences the mechanical properties. Three hypotheses will be tested. 1) Young's modulus of the hyomandibular cartilage will increase as mineralization increases. 2) Bite feeders will have a higher modulus than suction feeders. 3) Laterally oriented hyomandibulae will have a higher modulus than posteriorly oriented hyomandibulae. 4) Poisson's ratio will be similar among the species.

Animals
Four shark species were used in this study (Fig.  2)   hyomandibulae were dissected from previously frozen whole animal specimens. Freezing does not alter the mechanical properties of vertebrate skeletal tissue (Macesic and Summers, 2012;Porter et al., 2006).

Young's modulus
The mechanical properties of each hyomandibular cartilage was measured using a materials testing machine (MTS Synergie 100, software TestWorks 4, version 4.08 B) to measure compressive strength (Fig. 3). The hyomandibula was placed upright on a metal disc and glued in place with hardening putty (Loctite repair putty, multi-purpose).
Another disc was placed on top of the hyomandibula and glued in place with putty. A large flat plate was placed on the top disc to ensure that the putty hardened with the discs parallel to one another. The apparatus was placed into elasmobranch ringer's solution (Forster et al., 1972) for at least 30 minutes to allow the putty to set. Once set, the putty had an elastic modulus of 3.19 GPa, which is three orders of magnitude higher than the modulus of articular cartilage and about one order of magnitude higher than that of previously tested shark cartilage (Korhonen et al. 2002, Jin & Lewis 2004, Stolz et al. 2004, Porter et al. 2006, Macesic & Summers 2012. The hyomandibulae were then placed in the materials testing machine so the discs were parallel with two metal plates and the hyomandibulae could be loaded on the longitudinal axis. The top plate was connected to a force transducer. The hyomandibulae were compressed at a rate of 0.5 mm/s until the slope of the linear portion of the ascending force curve was apparent (50 to 100 N of force). Data was collected at a frequency of 120 Hz. Compression tests were conducted five times (2 pre-conditioning trials, and three test trials), with three minutes between trials. The hyomandibulae were kept in ringer's solution at all times after excision except for a short period (no more than five minutes) used to attach the sonometric crystals (see Poisson's Ratio section below).
The hyomandibulae were then bisected at the narrowest point to measure the cross sectional area at the region of maximal stress (Fig 4). To ensure that all hyomandibulae within a species was cut along the same plane, the cut was made at a fixed percentage of hyomandibular cartilage length from the proximal end.
One half of the bisected hyomandibula was placed in modeling clay and arranged so the cut surface was parallel to the  area. A stress/strain curve was plotted using the force data, the surface area, and the strains calculated from the material tests. The elastic modulus was calculated as the slope of the linear portion of the curve. The modulus of each element was measured as the average of the last three compression trials (Fig. 5). Cross-sectional aspect ratio was then measured using ImageJ (National Institutes of Health, Bethesda, MD, USA) as the anteroposterior length of each cross-section divided by the dorsoventral width. ratio. Paired t-tests were used to test for differences between species in both of these measures. area mineralized has an effect on the Young's Modulus among the species (Young's modulus=-5.807+(4.108* % Cross-section mineralized), (R 2 =0.59, p <0.001); Fig. 8).

Cross-sectional aspect ratio
The aspect ratio of the cross sectional area differed among the species (ANOVA, F=313.88, p<0.001). The cross-sectional aspect ratio is higher in the generalist species, S. acanthias (4.85±0.14), than all other species. The bite feeding species, C. plumbeus (3.24±0.02), has the next highest crosssectional aspect ratio, which is larger than the other two species.
The aspect ratio of the bite feeder,

Poisson's ratio
Data for Poisson's ratio in C. plagiosum and C. plumbeus was not used for analysis because the noise level was too high to detect the signal. Poisson's ratio is similar between the generalist, S. acanthias (0.168±0.026), and the bite feeder, M. canis (0.099±0.014) (Fig. 9).

Discussion
Mineralization plays the greatest role in increasing the stiffness of the hyomandibular cartilages in the four species studied here. C. plagiosum has a higher Figure 9. Poisson's ratio by species. Black lines are the median and the boxes range from the 25 th to the 75 th percentile. Values for cartilage and bone are ranges from (Korhonen et al. 2002, Jin & Lewis 2004, Shahar et al. 2007, Wirtz et al. 2000 Young's modulus (140 MPa) than the other three species (56-70 MPa) (Fig. 7). This stiffness appears to be due to a higher degree of mineralization and a rounder crosssection, which may prevent buckling (Fig. 8). Though the modulus of the hyomandibular cartilage in S. acanthias was similar to that of M. canis and C. plumbeus, S. acanthias hyomandibula have a higher mineralization level. S. acanthias were expected to have a higher Young's modulus than either of the bite feeders because of this mineralization; however, the relatively high cross-sectional aspect ratio likely decreases compressive strength in S. acanthias and increases the potential for buckling.
Mineralization and compressive strength are directly related in shark vertebrae (Porter et al., 2006), as are mineralization and bending strength in the pelvic fin propterygia of batoids (Macesic and Summers, 2012). The values of Young's modulus for shark vertebrae range from 323 to 563.9 MPa (Porter et al., 2006), which is higher than that for the hyomandibulae in bamboo sharks. However, vertebrae likely experience higher levels of cyclical compressive stress from anguilliform swimming. Torpedo rays, which swim using axial undulation like sharks, are benthic (live on the sea floor), and swim more slowly than the shark species (Porter et al. 2006). The mean Young's modulus for torpedo ray vertebrae is 25.5 MPa, which is lower than the modulus for hyomandibular cartilage (56-140 MPa). However, the mean Young's modulus of the vertebrae in sandbar sharks, Carcharhinus plumbeus, is 396.9 MPa (Porter et al. 2006), which is larger than that of the hyomandibulae (70.013 MPa). Stiff vertebrae help transfer energy from muscles to swimming motions (Porter et al. 2006), and may contribute to selection for higher mineralization in vertebrae. However, the mineralization pattern of vertebrae differs from that of the non-vertebral endoskeleton, such as the hyomandibula.
Vertebral cartilage may be stiffer because areolar cartilage is not mineralized only around the outer edge like non-vertebral cartilage, but rather minerals are distributed throughout the structure (Dean & Summers 2006).
Bony tissues have a Young's modulus between 10-20 GPa, (Currey 2010), which is two orders of magnitude greater than the average maximum value (140 MPa) for shark hyomandibulae, and over an order of magnitude greater than shark vertebrae (0.5 GPa).
Young's moduli for bovine articular cartilage ranges from 0.29 to 1.79 MPa (Korhonen et al. 2002;Jin & Lewis 2004), and from 0.21 to 2.6 MPa for porcine articular cartilage (Stolz et al. 2004). Unmineralized shark cartilage is expected to have a similar modulus as articular cartilage. The mineralized outer layer of tessellated cartilage likely has a higher modulus than the unmineralized core, yet the relatively harder tesserae probably interacts with the relatively softer unmineralized core to give the whole element a value between articular cartilage and bone.
Within the tesseral layer are mineralized polygonal tesserae connected by collagenous fibers (Kemp & Westrin 1979, Dean & Summers 2006. Under compression, the tesserae abut one another and stress is distributed throughout the tesseral layer, while the fibers allow the tesserae to separate when in tension (Liu et al. 2010). The interactions within the tesseral layer as well as between the tesseral layer and the unmineralized core may provide tessellated shark cartilage with a pliable supportive element that is unlikely to crack yet is strong enough to resist forces incurred during feeding. This is a particularly important property for cartilage because of the limited ability to repair. In homogenous materials, once a crack forms the sharp end of the crack acts as a force multiplier so minimal energy is required to continue the crack until the structure fails (Vogel 2003). However, shark cartilage is not homogenous. Brittle, crack sensitive tesserae are surrounded by more pliable fibers, all of which surround a soft, pliable core (Kemp & Westrin, 1979).

Conclusion
Young's modulus is greater in hyomandibular cartilages with a relatively higher percentage of cross-sectional mineralization than those with less mineralization. There appears to be a relationship to feeding style in the four species studied here, where the suction feeding species has a stiffer hyomandibula than the bite feeders or the generalist.
One possible reason is that stiff elements can resist larger forces and transmit energy from muscle to movement effectively (Porter et al. 2006). Suction feeders rapidly expand the buccal and pharyngeal cavities to generate negative pressure that draws prey into the mouth (Lauder 1983, Wilga & Sanford 2008. Though the hyomandibulae of bite feeders were hypothesized to have a higher Young's modulus, the large forces generated during suction may necessitate stiffer hyomandibular cartilages than those of bite feeders.