Batoid wing skeletal structure: Novel morphologies ... · 18/04/2005 · High-resolution radiography re- ... across the wing during steady swimming (Rosen-berger, 2001). Oscillators

Batoid Wing Skeletal Structure: Novel Morphologies,Mechanical Implications, and Phylogenetic PatternsJustin T. Schaefer* and Adam P. Summers

University of California, Irvine, Department of Ecology and Evolutionary Biology, Irvine, California 92697-2525

ABSTRACT The skeleton of the “wings” of skates andrays consists of a series of radially oriented cartilaginousfin rays emanating from a modified pectoral girdle. Eachfin ray consists of small, laterally oriented skeletal ele-ments, radials, traditionally represented as simple cylin-drical building blocks. High-resolution radiography re-veals the pattern of calcification in batoid wing elements,and their organization within the fin ray, to be consider-ably more complex and phylogenetically variable thanpreviously thought. Calcification patterns of radials var-ied between families, as well as within individual pectoralfins. Oscillatory swimmers show structural interconnec-tions between fin rays in central areas of the wing. Mor-phological variation was strongly predictive of locomotorstrategy, which we attribute to oscillatory swimmersneeding different areas of the wing stiffened than do un-dulatory swimmers. Contributions of various forms of cal-cification to radial stiffness were calculated theoretically.Results indicate that radials completely covered by min-eralized tissue (“crustal calcification”) were stiffer thanthose that were calcified in chain-like patterns (“catenatedcalcification”). Mapping this functionally important vari-ation onto a phylogeny reveals a more complicated patternthan the literature suggests for the evolution of locomotormode. Therefore, further investigation into the phyloge-netic distribution of swimming mode is warranted. J. Mor-phol. 264:298–313, 2005. © 2005 Wiley-Liss, Inc.

KEY WORDS: cartilage; calcification; tesserae; swim-ming; undulation; oscillation; flapping; robotics

Batoid fishes (stingrays, skates, sawfishes, andguitarfishes), are cartilaginous fishes (Chondrich-thyes) characterized by dorsoventrally compressedbodies ranging in shape from circular to rhomboidal(Compagno, 1977). They inhabit all the oceans of theworld and have invaded freshwater systems on fivecontinents (Lovejoy, 1996; Compagno, 2001). Theirpectoral fins are greatly enlarged and fused to thecranium, forming large, wing-like structures. Thesehighly modified pectoral fins are usually used as theprimary locomotor propulsors (Klausewitz, 1964;Heine, 1992).

Some basal batoids, such as sawfish and electricrays, do not use their pectoral fins to swim, insteadrelying on the plesiomorphic caudal fin-based loco-motor mode of their shark relatives. However, themajority of batoid fishes use their pectoral fins toswim and fall on a continuum from undulatory to

oscillatory locomotion. These swimming strategiescan be described by the number of waves (f) movingacross the wing during steady swimming (Rosen-berger, 2001). Oscillators appear to fly through thewater, flapping their wings such that f is less than0.5 at any given time (Heine, 1992). In contrast,undulators often have many waves (f � 1) movingalong the wing. Fish that swim with f between 0.5and 1 have been categorized as “semi-oscillatory”.

The wing skeleton upon which these locomotorwaves are propagated consists of an array of seriallyrepeating cartilaginous elements (Fig. 1). The carti-laginous skeleton of batoids is mineralized to vary-ing degrees, usually taking the form of a thin layerof tiles, tesserae, arranged on the surface of an un-mineralized core (Applegate, 1967; Kemp and We-strin, 1979; Clement, 1992; Summers et al., 2003; DeCarvalho et al., 2004). The wing skeleton originateson the craniocaudally expanded pectoral girdle andis formed by many long, tapering fin rays (Mivart,1878; Compagno, 1999). Each fin ray is composed ofcylindrical skeletal elements, radials, stacked end-to-end, much like carpals. The fin rays of most ba-toids bifurcate once or twice before reaching theedge of the wing (Fig. 1).

This complicated skeleton is actuated by long thinmuscles that run from the craniocaudally expandedpectoral girdle along each of the fin rays, insertingon every radial (Liem and Summers, 1999). Duringlocomotion, the radials are flexed dorsally by dorsaladductor muscles and ventrally flexed by less mas-sive ventral abductors. Although the range of motionbetween any two adjacent radials in a fin ray issmall (�15°) (Schaefer, pers. obs.), there are enoughradials, and therefore interradial joints, that thewingtips of rapidly swimming oscillatory rays often

Contract grant sponsor: National Science Foundation (NSF); Con-tract grant number: IBN-0317155 (to A.P.S.); Contract grant spon-sors: Teledyne Corp.; Mr. and Mrs. R. Schaefer.

*Correspondence to: Justin Schaefer, 321 Steinhaus Hall, Univer-sity of California, Irvine, Irvine, CA 92697-2525.E-mail: [email protected]

Published online 18 April 2005 inWiley InterScience (www.interscience.wiley.com)DOI: 10.1002/jmor.10331

JOURNAL OF MORPHOLOGY 264:298–313 (2005)

© 2005 WILEY-LISS, INC.

touch behind their back (Rosenberger, 2001). Thisimplies a morphological constraint: the interradialjoints must be mobile to give the wing flexibility, yetthe radials must be stiff to transmit the force of thewing musculature.

During locomotion individual radials function asend-loaded cantilevered beams. The deflection(Ymax) of a cantilevered beam is:

Ymax �FL3

3EI (1)

where F is the force of the muscle, L is the length ofthe radial, E is the material stiffness and I is thesecond moment of area, a measure of the distribu-tion of material around an object’s neutral axis (Vo-gel, 2003). Deflection of a loaded beam can be de-creased in several ways: by making it shorter,increasing its material stiffness, or increasing thesecond moment of area. Decreasing radial length,and thus stiffness, in this system is confounded byincreasing numbers of interradial joints between themore numerous radials. In contrast, changing eithermaterial properties or second moment of area of a

radial is independent of total wing flexibility, aschanges in one can be counteracted by changes inthe other.

If we assume that the mineralized cartilage ismaterially the same among species and is far stifferand stronger than unmineralized cartilage, then theflexural stiffness of the wing skeleton should be de-pendent primarily on the amount and arrangementof the mineralized tissue. In this study we investi-gate the pattern of mineralization in the wing skel-eton of 12 families of batoid fishes. Our goals wereto: 1) describe previously unknown mineralizationpatterns in radials; 2) qualitatively compare miner-alization patterns; 3) describe functionally signifi-cant variation in the distribution of joints betweenradials; and 4) place this variation in a functionaland phylogenetic context.

MATERIALS AND METHODSDorsoventral radiographs of adult specimens of 56 batoid spe-

cies from 12 families and three orders were obtained from variousmuseum collections, supplemented by specimens from the firstauthor’s personal collection (Appendix). Additional radiographswere performed with a cabinet radiograph (Hewlett Packard,Faxitron series) using Kodak Bio-Max MR film. Voltage andexposure times for radiographs varied depending on the thick-ness of the specimen.

Specimens for clearing and staining were obtained by beachseine at Seal Beach, California (California Dept. of Fish andGame permit #801060-02) and stored in a –30°C freezer prior topreparation. Tissue was dissected from the skeleton prior toclearing and staining. Specimens were cleared and stained usinga standard staining procedure which allowed for visualization ofall mineralized portions of the skeleton (Dingerkus and Uhler,1977). Specimens were stored in glycerin and photographed in aglycerin bath to minimize glare. Dorsal and cross-sectional im-ages were taken with a Nikon Coolpix 950 digital camera fitted toa Zeiss dissection scope. Digitized radiographs (1200 DPI resolu-tion) and images of cleared and stained samples (Appendix) wereoptimized for visual clarity in Adobe PhotoShop 7 (San Jose, CA),and anatomical drawings were created in Adobe Illustrator 10.

Phylogenetic analysis was based on the phylogeny presented byMcEachran and Aschliman (2004), a strict consensus tree of 10most parsimonious trees generated from 82 characters and 39taxa. We collapsed the operational taxonomic units into familiesbased on the tentative classification presented in the same arti-cle. We used Mesquite (Maddison and Maddison, 2004) to tracethe most parsimonious evolution of the morphological charactersdescribed here as well as the swimming modes described inRosenberger and Westneat (1999).

It is important to keep in mind that for the majority of speci-mens examined for this study, radiographs were the primarysource of information. For this reason, only those structures thatwere mineralized were evident. This does not mean that other,soft tissue structures serving the same purpose as calcified struc-tures were not present in some specimens. Another caveat tothese data is that the ages of the specimens are not known. Incases where morphology varies among specimens of the samespecies, (e.g., Pteroplatytrygon violacea) or morphological varia-tion is exhibited by a single species in a family (e.g., Urotrygonmicropthalmum), this variation might be due to the age of thespecimen, which would be evident through examination of spec-imens of various sizes (Table 1).

RESULTS

We found extensive interspecies and intraindi-vidual variation in the mineralization patterns and

Fig. 1. Cleared and stained embryo of Gymnura marmorata.Dorsal view of left side of animal is shown. Red areas indicatecalcification, blue is cartilage. From these images and those ofother cleared and stained embryos, we can infer that the calcifi-cation in batoids increases in intensity medially to laterally withage.

299NOVEL MORPHOLOGIES IN BATOID WING SKELETONS

joint arrangement of batoid wing skeletons. Varia-tion occurred at several levels of organization: finescale (calcification patterns), medium scale (shapeand structure of individual radials), and large scale(arrangement of radials).

Fine Scale–Calcification Patterns

All of the radials examined were covered intesserae to some extent. The radials of basal batoids,including torpedinids, narcinids, pristids, platyrhin-ids, and rhinobatids were covered with a continuousand complete layer of small (�1 mm dia.) tesserae.We call this form of calcification “crustal” (Fig. 2)(Table 1). Crustal calcification is also seen in theaxial skeleton of batoids and other cartilaginousfishes, as well as the radials of some derived species(Gymnuridae and Myliobatidae).

In several families (Dasyatidae, Potamotry-gonidae, Rajidae, Urotrygonidae, and Urolophidae)we found an alternative form of calcification inwhich the coverage of tesserae was greatly reduced(Table 1). In these taxa, calcification did not coverthe entire radial but instead occurred as a variablenumber of chains of tesserae on the dorsal, ventral,anterior, and posterior surfaces of the radial, fan-ning out to form plates of tesserae that cap theproximal and distal ends of the radial (Figs. 2, 3).Patterns of noncrustal calcification are termed “cat-enated” in reference to their chain-like appearance.

The degree of catenated calcification varied withposition in the wing. Medial elements were moreheavily calcified and had more complex patterns ofmineralization (Figs. 2, 3). In extremely mineralizedradials, tesserae were arranged as a basket of wovenchains covering the element (Fig. 2). The number ofchains and their interconnectivity decreased with

increasing distance from the pterygial complex (Ta-ble 2). Calcification in immature animals appearedto spread from the body axis toward the margins ofthe wing, as evidenced by its absence at the wingedge in cleared and stained juveniles (Fig. 1). At thedistal end of a fin ray, the calcification often con-sisted of a single chain traversing the middle of theskeletal element, or a scattering of tesserae over thesurface of the terminal radial (Fig. 3).

The most heavily mineralized form of this calcifi-cation pattern was seen in the Dasyatidae, and con-sisted of nearly complete coverage of the proximalelements and extending to the first radial bifurca-tion, after which it condensed to one chain on thedorsal, ventral and lateral sides of the radial for atotal of four chains (Table 2). Calcification was re-duced in the rajids, consisting of a single chain onthe dorsal and ventral sides of the radial on all partsof the wing (Figs. 2, 3). Apart from the skates, manyspecies of batoids demonstrated paired chains on thedorsal and ventral surfaces, which were often inter-connected by bridges of tesserae.

Medium Scale–Individual Radials

Variation in the shape of individual radials tooktwo main forms: 1) cross-sectional and dorsoven-trally projected shape of the radials; and 2) associa-tions with adjacent fin rays.

The cross-section of radials varied within andamong species and ranged from square, triangular,or circular to dorsoventrally compressed ovals (Fig.3). Within individuals, the cross-sectional shape ofthe radials changed with position on the wing, be-coming more dorsoventrally compressed distally.

In addition, in some species we found interradialconnections, which we term “cross-braces,” that con-

TABLE 1. Family level distribution of batoid wing morphology (number of species with listed morphological characteristics aregiven for each family, with specific exceptions listed below). Presence of characters is indicated with “X”.

Family name SpeciesCross-bracing

Jointstaggering Calcification

Torpedinidae Torpedo californica – – crustalNarcinidae 4 spp. – – crustalPristidae Pristis microdon – – crustalRhinobatidae 2 spp. – – crustalRajidae 4 spp. – – catenatedPlatyrhinidae Platyrhinoidis triseriata – – crustalUrolophidae 4 spp. – – catenated

exceptions Plesiobatis daviesi – – crustalUrotrygonidae 12 spp. X – catenated

exceptions Urotrygonmicropthalmum,Urotrygon reticulata

– – catenated

Dasyatidae 9 spp. – X catenatedexceptions Himantura pacifica,

Pteroplatytrygonviolacea

– – catenated

Potamotrygonidae 8 spp. – – catenatedGymnuridae 3 spp. X – crustalMyliobatidae 5 spp. X – crustal

300 J.T. SCHAEFER AND A.P. SUMMERS

nected radials in adjacent fin rays in some areas ofthe wing (Figs. 4, 5). Cross-bracing was seen only inthe medial areas of the wing of semi-oscillatory(Gymnuridae) and oscillatory (Myliobatidae) swim-mers. Cross-bracing was also found in the Urotry-gonidae, but there are no data on swimming mode,so they are listed as undulatory based on field ob-servation of the closely related Urobatidae (J.Schaefer, pers. obs.). However, the ability to switch

between undulatory and oscillatory swimmingmodes has been documented in Dasyatidae (Rosen-berger and Westneat, 1999), and we suggest thatfurther research may find this to be the case withthe Urotrygonids.

In some species the area of cross-bracing was ex-tensive enough to leave only a thin margin of un-braced radials at the edges of the wing (e.g., Gym-nura crebripunctata) (Fig. 5). Cross-braces occurred

Fig. 2. Calcification patterns in: column A) Platyrhinoidis triseriata, column B) Urobatis halleri, and column C) Amblyraja radiataat various positions on the wing (colored boxes). Calcified material is stained red. Platyrhinoidis triseriata demonstrates crustalcalcification. Urobatis halleri and A. radiata show two variations of catenated calcification. The curvature of the outer margin of thewing of A. radiata is due to an attempt to accelerate clearing through heat application, but did not damage the calcification. All scalebars � 1 mm.


Fig. 3. Cross-section of calcification in Amblyraja radiata, Platyrhinoidis triseriata, Urobatis halleri, and Myliobatis californicaskeletal elements from proximal, mid, and distal portions of the wing. Species are arranged in rows. Silhouettes at bottom showapproximate area of wing from which sections were taken. Platyrhinoidis triseriata demonstrates crustal calcification. Two-chaincatenated calcification is represented by A. radiata, while four-chain catenated calcification is demonstrated by M. californica and U.halleri. The occurrence of both crustal and catenated calcification patterns in M. californica is representative of the mediolateralprogression of calcification in an immature individual (disk width � 17 cm). Location of section in relation to joints is given byschematic in lower right corner of each panel. All scale bars � 1 mm.

contralaterally and at opposite ends of the radial,with the proximal brace on the anterior side. Thisstaggering of connections is consistent throughoutthe area in which the cross-bracing occurs. Thispattern is maintained on both sides of the animal,giving the cross-bracing a handedness, and the po-tential for side-specific effects on locomotor move-ment. Cross-braces varied in size among species,and in some species did not join between radials.Gaps between cross-braces were more common be-tween distal radials. Species that had calcified lat-

eral extensions from the ends of their radials thatdid not touch in the great majority of instances werenot considered to have cross-bracing.

The projected shape of the radials, although gen-erally rectangular, varied among species. Lateralexpansion of the radials resulted in projected shapesranging from narrow rectangles to rough squares,sometimes with recurved sides (Figs. 6, 7). In undu-latory swimmers, radials usually decreased in sizeisometrically with distance from the body axis (Fig.6). In some oscillators, radial shape differed drasti-

TABLE 2. Morphology of catenated calcification in batoid wings

Family name Species nameProximal DV

chainsDistal DV

chainsLateralchains

Dasyatidae Dasyatis americana c 1 yDasyatidae Dasyatis brevis c 1 yDasyatidae Dasyatis centroura c 1 yDasyatidae Dasyatis guttata c 1 yDasyatidae Dasyatis longa c 2� yDasyatidae Dasyatis margaritella 2 1 yDasyatidae Dasyatis sabina c 1 yDasyatidae Himantura jenkinsii c 1 yDasyatidae Himantura pacifica c 1 yDasyatidae Himantura schmardae c 1 yDasyatidae Pteroplatytrygon violacea 2� 2� yDasyatidae Pteroplatytrygon violacea 0 0 nDasyatidae Pteroplatytrygon violacea c 1 yDasyatidae Taeniura lymma c 1 yDasyatidae Taeniura lymma c 1 yPotamotrygonidae Paratrygon aiereba c 1 yPotamotrygonidae Paratrygon aiereba c 2� yPotamotrygonidae Plesiotrygon iwamae 2 1 yPotamotrygonidae Potamotrygon castexi 2 2 yPotamotrygonidae Potamotrygon falkneri c 1 yPotamotrygonidae Potamotrygon magdalenae 2 1 yPotamotrygonidae Potamotrygon motoro 2 2 yPotamotrygonidae Potamotrygon motoro c 1 yPotamotrygonidae Potamotrygon orbignyi 2 1 yPotamotrygonidae Potamotrygon orbignyi 2 1 yPotamotrygonidae Potamotrygon sp. 2� 2 yRajidae Amblyraja radiata 1 1 nRajidae Bathyraja interrupta 1 1 nRajidae Dipturus tengu 2 2 nRajidae Rajella eisenhardti 1 1 nUrolophidae Plesiobatis daviesi 0 0 yUrolophidae Urolophus aurantiacus 1 1 yUrolophidae Urolophus cruciatus 1 1 yUrolophidae Urolophus cruciatus 1 1 yUrolophidae Urolophus fuscus 1 1 yUrotrygonidae Urobatis concentricus 2 1 yUrotrygonidae Urobatis concentricus c 1 yUrotrygonidae Urobatis halleri 2� 1 yUrotrygonidae Urobatis halleri c 1 yUrotrygonidae Urobatis halleri c 1 yUrotrygonidae Urobatis jamaicensis c 1 yUrotrygonidae Urobatis maculatus c 1 yUrotrygonidae Urobatis tumbesensis c 1 yUrotrygonidae Urobatis tumbesensis c 1 yUrotrygonidae Urotrygon micropthalmum 1 1 yUrotrygonidae Urotrygon munda 1 1 yUrotrygonidae Urotrygon nana 1 1 yUrotrygonidae Urotrygon rogersi 0 1 yUrotrygonidae Urotrygon sp. 0 1 y

Proximal DV chains, number of chains on dorsal and ventral surfaces of 2nd radial after pterygium. Distal DV chains, number of dorsaland ventral chains on 2nd radial after major bifurcation. C, complete (crustal) coverage.Lateral chains are chains on anteroposterior sides of radial, scored as yes/no due to dorsal view of animals.


cally depending on position in the wing, rangingfrom short and stout to extremely elongate and grac-ile (Fig. 7). Near the leading edge of the wing of someoscillators, radials were laterally expanded to thepoint that they fit closely together and formed anearly solid plate.

Large Scale–Interradial Relationships

Radial lengths in batoids varied, causing thejoints between them to vary spatially. In undulators,radials at the same proximodistal position were rel-atively uniformly sized, causing the joints betweenthem to follow the shape of the pterygial complex. Ifthese joints are plotted spatially, they form concen-tric lines around the pterygial complex (Fig. 6). Incontrast, the radials of oscillators at a given medio-lateral position (e.g., 3rd radial lateral to the ptery-gial complex) varied extensively in length, causingthe joints to form nonconcentric patterns. Radials incentral areas of the wings of oscillators were oftenelongated, and in all areas of the wing were gener-ally much shorter following bifurcation of the fin ray(Fig. 7).

In the undulating dasyatids, the joints betweenthe radials in the most distal aspects of the wingwere staggered. That is, the joints were arranged ina lattice-like network such that any joint would beopposed on either side by the middle of a radial (Fig.

8). This pattern, “joint staggering,” was only seen atthe edge of the wing after the first radial bifurcation.

DISCUSSION

We have found hitherto unappreciated variationin the wing skeleton of batoid fishes. Locomotormode is a good predictor of morphology, leading us tobelieve that this variation has important functionalconsequences for the flexural stiffness of the wing.

Ontogenetically, it appears that calcificationspreads from proximal to distal. This is based on thepattern observed in embryonic specimens in whichproximal areas of the skeleton calcify first (Fig. 1).This may imply that the catenated patterns seen inmature animals are neotonic states, and that crust-ally calcified species may show catenated calcifica-tion as juveniles.

Evolution of the Wing Skeleton

Crustal calcification is the basal character state, aconclusion supported by its occurrence in sharks,the sister group to the batoid clade (Douady et al.,2003). Catenated calcification arose twice, once inthe Rajidae and again in the group containing Urolo-phidae, Urotrygonidae, Dasyatidae, and Potamotry-gonidae, and was subsequently lost in Gymnuridaeand Myliobatidae (Fig. 9).

Although we have treated calcification as a two-state character (crustal/catenated), there is exten-sive variation in calcification patterns among thefamilies and species. The most important observa-tion from the present data is that the majority ofspecies have complete or nearly complete coverage ofthe proximal radials. Coverage then decreases untilthe first bifurcation of radials, at which point it isreduced to one chain per side. The exceptions to thispattern are Rajidae, Urotrygonidae, and some spe-cies of Urolophidae, in which the catenated calcifi-cation does not “fill in” in the proximal areas of thewing (Table 2).

Between-radial relationships vary phylogeneti-cally. For example, joint staggering was restricted tothe Dasyatidae, but not all species in that grouppossessed this morphology (Table 1). If it is con-firmed that only dasyatids have this morphology,then we have identified a synapomorphy of the cladethat may prove to be a useful character for phyloge-netic analysis. Cross-bracing appears in the batoidsin two separate clades, among Urotrygonidae and inthe Gymnuridae � Myliobatidae. Although they oc-cur in Urotrygonidae, the cross-braces themselvesare relatively slight when compared with those ofthe more oscillatory swimmers. Partial cross-bracing, in which the cross-braces did not meet be-tween the fin rays, occurred in the Dasyatidae,Urolophidae, and in some species of Urotrygonidae.However, increased calcification around the moreproximal interradial joints in these families is evi-

Fig. 4. Schematic of cross-bracing. Fin ray “A” is joined to finray “B” by a cartilaginous extension (CB). This inhibits the bend-ing of normal radial joints j1 and j2. When the joint betweenradials B1 and B2 tries to bend, radial A1 will be forced to bendalong with them, effectively eliminating the ability of j2 to bend.These cross-braces are arranged in diagonal patterns such thatthe entire area is reinforced and stiffened.


dent, and probably has functional consequencessuch as joint stiffening.

Swimming Mode and Skeletal Structure

In undulatory swimmers there is reduced (cate-nated) calcification and joint staggering (Dasyatids),while crustal calcification is characteristic of oscilla-tory and axial-undulatory swimmers. Cross-bracingis found only among the oscillatory swimmers andthe Urotrygonidae. These differences are not unex-pected, given that we believe that undulatory andoscillatory swimming put very different stresses onthe skeleton, and require different flexural stiffness.

Oscillatory swimming (Myliobatidae, Gymnuri-dae) requires large amplitude deformations of thewing (Heine, 1992; Rosenberger, 2001). Because thebending of the wing of oscillatory swimmers is con-

centrated proximally, we expect greater stiffening inthis area. In contrast, the shorter wavelength anddecreased amplitude in the wings of undulatoryswimmers (Urolophidae, Urotrygonidae, Potamotry-gonidae) concentrate bending stresses near theedges.

The morphology of the wing skeleton will have aneffect on wing stiffness, and we note variation infunctionally critical areas of the wing (joint stagger-ing, cross-bracing), as well as whole-wing variations(catenated calcification). Joint staggering, presentonly in the undulatory dasyatids, is associated withthe marginal areas of the wing critical for undula-tory propulsion; likewise, cross-bracing is found onlyin the medial areas of the wing that are load-bearingin oscillatory swimmers. The presence of cross-bracing in Urotrygonidae is interesting since theseare solely undulatory swimmers, and the lack of

Fig. 5. Cross-bracing in oscil-latory swimmers. Red zones onthe wings of 1) Pteromylaeus as-perrimus (CAS 11895), 2) Gym-nura crebripunctata (CAS SU11587), and 3) Mobula thurstoni(LACM 38433-1) indicate the ar-eas in which cross-bracing isfound. All pictures of whole ani-mals are radiographs except forM. thurstoni, for which a fullbody radiograph was not avail-able. Magnified images of thewing appear next to the speciesand demonstrate variations inthe cross-bracing found in manyspecies of oscillatory swimmers.The sample for M. thurstoni con-sisted of a dried strip of wing,and thus allows observationaldata from only that strip(shaded). Hypothesized extent ofcross-bracing is outlined indashed lines. Figures not toscale.


cross-bracing in the related and also undulatoryUrolophidae may be an indication of unappreciateddifferences in swimming kinematics.

The pelagic stingray, Pteroplatytrygon violacea,has evolved a completely pelagic lifestyle from aclade of benthically oriented species (McEachran

Fig. 6. Schematic outline and joint position of the wing skeleton of Urobatis halleri (UCI). A: Radiograph of the left side of U.halleri. Dark indicates radio-opacity. Anterior is at top of page. B: Outline of individual skeletal elements from radiograph. Differentcolors denote origins of radials from different skeletal elements of the pterygial complex. C: Dots showing the location of joints on thewing. Joints are arranged in lines that run craniocaudally.


Fig. 7. Schematic outline and joint position of the wing skeleton of Gymnura crebripunctata (CAS SU 11587). The discontinuity inthe fin rays proximal to the pterygial complex is a cut made in the museum specimen during preservation. A: Radiograph of left sideof G. crebripunctata, dark indicates radio-opacity, anterior is at top of page. B: Outlines of skeletal elements based on radiograph.Different colors denote origin of radials from different skeletal elements of the pterygial complex. C: Dots showing the location of jointson the wing. Blue shading indicates presence of cross-bracing.


and Aschliman, 2004). In so doing, it has become amore oscillatory swimmer (f � 0.78) (Rosenberger,2001). While P. violacea does not have cross-bracinglike other oscillators, the chains of calcification onits robust radials are very broad and highly miner-alized. In addition, it has lost the joint-staggeringpattern that is indicative of the family’s other, moreundulatory species. This leads to the interpretationthat a more highly calcified skeleton is beneficialduring oscillatory swimming.

Catenated cartilage has two potential benefits tobatoid fishes over crustal calcification. First, it isprobable that it is energetically less expensive toconstruct a lightly calcified skeleton. Batoids mustinvest far more in their skeletons than do sharksdue to their more extensive appendicular skeleton;therefore, calcification of the pectoral skeleton may

represent a greater energetic burden in batoids thanit does in sharks. Second, it is energetically lesscostly to move a lighter skeleton, and the develop-ment of catenated cartilage may have been a re-sponse to a decreased need for stiffness in the medialarea of the wing.

Second Moment of Area and RadialStiffness

The musculature that powers swimming in ba-toids originates on the pectoral girdle and inserts onserially arrayed radials. Each radial, therefore, actsas a cantilevered beam, transferring the force of themuscle to the surrounding fluid as well as to otherskeletal elements. Therefore, the efficiency of thisforce transmission is tied to the stiffness of the ra-

Fig. 8. Radiograph of Dasyatis margaritella (CAS SU 68915) demonstrating staggering of joints between skeletal elements. Blueareas on wing margin indicate occurrence of joint staggering. The inset is a magnification of the marginal area of the wing. The topof the inset is toward the wing edge. Red dots are placed on joints that are in line, while blue dots are placed on joints that arestaggered.


dials. Using Equation 1, we can calculate the deflec-tion of a cantilevered beam under load, and we as-sume that the Young’s modulus (E) of cartilage doesnot vary between species; therefore, variations incalcification geometry and distribution (second mo-ment of area – I) will impact flexural stiffness. Todetermine the effect of mineralization, the relativecontribution of different calcification patterns toflexural stiffness of the radial was determined. Wecalculated the second moment of area of radials withcrustal and catenated (two-chain and four-chain)calcification assuming a constant area of mineraliza-tion (Beer and Johnston, 1977). A second set of cal-culations examined the amount of mineralization

required to maintain a constant stiffness (constantsecond moment of area) (Fig. 10).

To calculate the second moment of area (I) of acrustally calcified radial, we used the equation forthe second moment of area for a cylinder of variablewall thickness (Fig. 10). For the purposes of calcu-lation, the inner and outer radii of crustal calcifica-tion were set to 4 and 5 units, respectively (as seenin Platyrhinoidis triseriata) (Fig. 3). These numberswere chosen (and only the ratio between them isimportant) because they closely approximate thevalues estimated from the cleared and stained spec-imens. For the second moment of area of two-chaincatenated calcification (i.e., Rajidae), we used the

Fig. 9. Cladogram depicting the families of batoids sampled and their use of axial-undulatory, undulatory, and oscillatorylocomotion strategies. Also shown are the families in which joint staggering (blue outline), cross-bracing (red outline), and crustal andcatenated calcification were found. Note the grouping of cross-bracing with the oscillatory swimmers, and the grouping of catenatedcalcification patterns with undulatory swimmers.


equation for an off-axis, solid, circular cross-sectionbeam modified to reflect the dorsal and ventralchains found in this family. By adding another term

to represent the lateral chains, we calculated the I ofa four-beam catenated calcification scheme. Holdingthis total area of calcification constant, we calcu-

Fig. 10. A comparison of the mechanical behavior of different calcification schemes. The center circles represent cross sections ofradials with crustal (top), two-chain catenated (middle), and four-chain catenated (bottom) calcification. Schematics of calcification aredrawn to scale for equal area of calcification. Formulae for area of calcification (A) and second moment of area (I) for each calcificationtype are given below the diagrams. Neutral axes are shown with dashed lines. The left side of the figure shows the response of thesecond moment of area when the area of calcification is held constant. The right side shows the calculated area of calcification whenthe second moment of area is held constant. Both sides show the calculated radius of the internal calcification (in the case of catenatedcalcification) or uncalcified cartilage (for crustal calcification). The external radius of the radial (ro) remained 5.0 in all calculations.Second moment of area is calculated for two-chain catenated calcification when the neutral axis is opposed 90° and force is applied inthe plane represented by the arrows.


lated the radius of the catenated chains, and fromthis the second moment of area (Fig. 10).

When the area of calcification is held constant, thedifferent distributions of material through the cross-section of the radial affect the structural properties.In two-chain catenated calcification, the second mo-ment of area decreased by 8%, resulting in an in-crease in maximum flexion of 8.6%. In four-chaincalcification, the material in each rod is againhalved, and two of the rods are positioned on theneutral axis and thus contribute less to the struc-tural stiffness. For these reasons, second moment ofarea decreased by 35% relative to crustal calcifica-tion in four-chain catenated calcification, resultingin a 54% increase in flexion. Since the second mo-ment of area is integral to the flexural stiffness ofthe radial, we can say that for a radial of a givenlength and material stiffness, holding the cross-sectional area of calcification constant, crustally cal-cified radials will be stiffer than those with cate-nated calcification.

If the second moment of area is held constant andthe calcified area is allowed to vary, different pat-terns emerge. Crustal calcification again forms thebasis for comparison, with an inner radius of 4 andan outer radius of 5. The area of calcification intwo-chain catenated calcification must be increasedby 17% to attain the same second moment of area ascrustal calcification. The calcified area in four-chaincatenated calcification must be increased by 45%.

From Equation 1 we can see that it is possible tooffset a decrease in second moment of area by de-creasing the length of the element. A decrease inlength of just 2.8% in a two-chain catenated radialwould increase its stiffness to that of a crustallycalcified radial. Four-chain catenated calcificationwould require a decrease in length of 13.2% toachieve the stiffness of crustal calcification.

To this point, we have assumed that the neutralaxis is determined purely by the action of the mus-cle. That is, it is in the horizontal plane. Crustalcalcification is symmetrical, and the orientation ofthe neutral axis does not matter. However, two-chain and four-chain catenated calcification are notsymmetrical, and so lateral forces that would tend toreorient the neutral axis are potentially important.For example, in the extreme case of the neutral axisbeing oriented parallel, or in line with the muscleaction, the second moment of area of crustal andfour-chain catenated calcification would remain un-changed, but the second moment of area of two-chain catenated calcification would decrease 88%,from 266 to 32 (Fig. 10).

We wonder whether the calcification in two-chaincatenated radials implies that forces are usuallyoriented perfectly dorsoventrally, while in the othercalcification patterns the direction of loading may bemore variable. It may be that the ontogenetic pro-gression of calcification in batoids reflects this rela-tionship. Partially calcified radials typically have

catenated patterns, distributing the calcification op-timally and adding calcification so that the coverageeventually approaches a crustal configuration (Figs.2, 3).

SUMMARY

We have found previously undescribed variationin the morphologies of the wing skeleton of batoidelasmobranchs. These morphologies consist of vari-ation in structural aspects of calcification, shape,and spatial relationships of radials. There appearsto be a phylogenetic pattern in the distribution ofthese morphologies and associated swimming styles.All the morphologies described above appear to betied to stiffening the appendicular skeleton, and cal-culations of structurally important variables showthat, at least for calcification variability, morphologyimpacts the mechanical properties of the skeleton.We believe these results have interesting implica-tions for the design and construction of aquatic ro-bots.

ACKNOWLEDGMENTS

We thank R. Jacinto for data collection, N. Lovejoyfor access to his radiograph collection, S. Kajiura, M.Dean, the physiology group, and the biomechanicslab at UCI for critical discussions and input ondrafts of the manuscript, D. Catania at the Ichthy-ology collection of the California Academy of Sci-ence, R. Feeney and J. Seigel at the Los AngelesCounty Museum of Natural History, and C. Loweand his lab for specimens.

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APPENDIX. Materials examined. All samples were radiographed, scanned, and then digitally optimized using Adobe Photoshop v.7.0.

Order Family Genus speciesSpecimen catalog

number

Pristiformes Pristidae Pristis microdon CAS SU 12670Rajiformes Dasyatidae Dasyatis americana LACM 22324Rajiformes Dasyatidae Dasyatis brevis LACM 31759-16Rajiformes Dasyatidae Dasyatis centroura ROM 42578Rajiformes Dasyatidae Dasyatis guttata ROM 23096Rajiformes Dasyatidae Dasyatis longa ROM 66847Rajiformes Dasyatidae Dasyatis longa ROM 66840Rajiformes Dasyatidae Dasyatis longa ROM Uncat.Rajiformes Dasyatidae Dasyatis margaritella CAS SU 68915Rajiformes Dasyatidae Dasyatis sabina ROM 46549Rajiformes Dasyatidae Himantura jenkinsii ROM 23011Rajiformes Dasyatidae Himantura pacifica ROM 66838Rajiformes Dasyatidae Himantura schmardae ANSP 103478Rajiformes Dasyatidae Pteroplatytrygon violacea LACM 31753-1Rajiformes Dasyatidae Pteroplatytrygon violacea LACM 38242-1Rajiformes Dasyatidae Pteroplatytrygon violacea ROM 43223Rajiformes Dasyatidae Taeniura lymma ROM 39404Rajiformes Dasyatidae Taeniura lymma ROM 50295Rajiformes Gymnuridae Gymnura crebripunctata CAS SU 11587Rajiformes Gymnuridae Gymnura marmorata LACM 48891-3*Rajiformes Gymnuridae Gymnura marmorata UCI -Rajiformes Gymnuridae Gymnura micrura USNM 222598Rajiformes Myliobatidae Mobula thurstoni LACM 38433-1Rajiformes Myliobatidae Mobula thurstoni LACM 39276-67Rajiformes Myliobatidae Myliobatis californica UCI -Rajiformes Myliobatidae Myliobatis californica USNM 26781Rajiformes Myliobatidae Myliobatis californica LACM 6899-1Rajiformes Myliobatidae Myliobatis longirostris USNM 222686Rajiformes Myliobatidae Pteromylaeus asperrimus CAS 11895Rajiformes Myliobatidae Rhinoptera bonasus FMNH 40224*Rajiformes Platyrhinidae Platyrhinoidis triseriata UCI -Rajiformes Potamotrygonidae Paratrygon aiereba UMMZ 204840Rajiformes Potamotrygonidae Paratrygon aiereba USNM 264005Rajiformes Potamotrygonidae Plesiotrygon iwamae FMNH 94500Rajiformes Potamotrygonidae Potamotrygon castexi LACM 39934-1Rajiformes Potamotrygonidae Potamotrygon falkneri UMMZ 206379Rajiformes Potamotrygonidae Potamotrygon motoro UMMZ 207766Rajiformes Potamotrygonidae Potamotrygon motoro LACM 42359-1Rajiformes Potamotrygonidae Potamotrygon magdalenae UMMZ 211755Rajiformes Potamotrygonidae Potamotrygon orbignyi ROM 26182Rajiformes Potamotrygonidae Potamotrygon orbignyi UMMZ 211262Rajiformes Potamotrygonidae Potamotrygon sp. LACM 39931-1*Rajiformes Rajidae Amblyraja radiata UCI -Rajiformes Rajidae Bathyraja interrupta LACM 30342-1Rajiformes Rajidae Bathyraja spinosissima CAS SU 46500Rajiformes Rajidae Dipturus tengu CAS SU 12912Rajiformes Rajidae Rajella eisenhardti CAS CAS 86817Rajiformes Rhinobatidae Rhinobatus percellens CAS SU 11851


Order Family Genus speciesSpecimen catalog

number

Rajiformes Urolophidae Plesiobatis daviesi BPBM 30909Rajiformes Urolophidae Urobatis concentricus LACM 6962-2Rajiformes Urolophidae Urobatis concentricus ROM 66839*Rajiformes Urolophidae Urobatis halleri UCI -Rajiformes Urolophidae Urobatis halleri CAS SU 2948Rajiformes Urolophidae Urobatis halleri USNM 181313Rajiformes Urolophidae Urobatis jamaicensis ROM 28276Rajiformes Urolophidae Urobatis maculatus USNM 119751Rajiformes Urolophidae Urobatis tumbesensis AMNH 44021Rajiformes Urolophidae Urolophus aurantiacus USNM 026543Rajiformes Urolophidae Urolophus cruciatus LACM 52122-2Rajiformes Urolophidae Urolophus cruciatus LACM CSUF 67-17Rajiformes Urolophidae Urolophus fuscus USNM 151756Rajiformes Urotrygonidae Urotrygon

micropthalmumUSNM 222693

Rajiformes Urotrygonidae Urotrygon munda CAS 51835Rajiformes Urotrygonidae Urotrygon nana ROM 66837Rajiformes Urotrygonidae Urotrygon reticulata USNM 321478Rajiformes Urotrygonidae Urotrygon rogersi CAS SU 11700Rajiformes Urotrygonidae Urotrygon sp. UMMZ 190227Torpediniformes Narcinidae Diplobatis ommata CAS CAS 5444Torpediniformes Narcinidae Diplobatis ommata LACM 48971-3Torpediniformes Narcinidae Narcine bancroftii CAS IU 00987Torpediniformes Narcinidae Narcine brasiliensis LACM 6262Torpediniformes Narcinidae Narcine entemedor CAS SU 11699Torpediniformes Torpedinidae Torpedo californica LACM 26485

BPBM � Bernice P. Bishop Museum, Honolulu, Hawaii. UCI � University of California, Irvine (first author’s collection), CAS �California Academy of Science, San Francisco, California, LACM � Los Angeles County Museum of Natural History, Los Angeles,California, ROM � Royal Ontario Museum, Toronto, Ontario, USNM � National Museum of Natural History, Smithsonian Institu-tion, Washington, D.C., ANSP � Academy of Natural Sciences, Philadelphia, Pennsylvania, UMMZ � Museum of Zoology, Universityof Michigan, Ann Arbor, Michigan, FMNH � Field Museum of Natural History, Chicago, Illinois, AMNH � American Museum ofNatural History, New York, New York. Uncat. � uncatalogued. Asterisks indicate specimens that were cleared and stained.


APPENDIX (Continued)

Documents

Batoid wing skeletal structure: Novel morphologies ... · 18/04/2005 · High-resolution radiography re- ... across the wing during steady swimming (Rosen-berger, 2001). Oscillators