Analysis of the bite force and mechanical design of the feeding mechanism of the durophagous horn shark Heterodontus francisci
1 Department of Biology, University of South Florida, 4202 E. Fowler Avenue,
SCA 110, Tampa, FL 33620, USA
2 Department of Mechanical Engineering, University of South Florida, 4202 E.
Fowler Avenue, ENB 118, Tampa, FL 33620, USA
3 Center for Shark Research, Mote Marine Laboratory, 1600 Ken Thompson
Parkway, Sarasota, FL 34236, USA
* Author for correspondence (e-mail: drhuber{at}mail.usf.edu)
Accepted 27 July 2005
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Summary |
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Key words: bite force, elasmobranch, feeding biomechanics, performance, durophagy, jaw suspension, Heterodontus francisci
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Introduction |
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The heterodontid sharks are the only family of elasmobranchs in which every
species is ecologically and functionally specialized for durophagy (Compagno,
1984a,
1999
;
Taylor, 1972
). The suite of
morphological characters associated with durophagy in the heterodontid sharks
includes robust jaws capable of resisting dorsoventral flexion under high
loading, molariform teeth and hypertrophied jaw adductor muscles
(Nobiling, 1977
;
Reif, 1976
;
Summers et al., 2004
). To
date, the concept of durophagy in the heterodontid sharks has mostly been
examined qualitatively (but see Summers et
al., 2004
). Neither the bite forces they are capable of producing
nor the subsequent loadings on the various articulations within their feeding
mechanisms have been quantified in any manner. Bite force is
particularly informative in regard to linking morphological, ecological and
behavioral variables associated with prey capture because biting capacity is
dictated by cranial morphology and is known to affect resource partitioning
(Verwaijen et al., 2002
;
Wiersma, 2001
), dietary
diversity (Clifton and Motta,
1998
; Wainwright,
1988
) and ontogenetic changes in feeding ecology
(Hernandez and Motta,
1997
).
Like most modern elasmobranchs, the heterodontid sharks possess a hyostylic
jaw suspension in which the mandibular arch indirectly articulates with the
chondrocranium via the hyomandibular cartilages, and the palatal
region of the upper jaw is suspended from the ethmoid region of the
chondrocranium via ligamentous connections
(Fig. 1A). However, a number of
variants on this arrangement exist, primarily in the superorder Squalea
(Gregory, 1904;
Shirai, 1996
;
Wilga, 2002
). The hexanchiform
sharks possess an orbitostylic jaw suspension in which the upper jaw
articulates with the ethmoidal, orbital and postorbital regions of the
chondrocranium, and the hyomandibula contributes little support to the jaws
(Fig. 1B). Conversely, the only
suspensorial element in the batoids is the hyomandibula (euhyostyly;
Fig. 1C;
Gregory, 1904
;
Maisey, 1980
;
Wilga, 2002
). These highly
divergent morphologies constitute independent mechanical systems, perhaps with
comparably divergent cranial loading regimes occurring during feeding.
Determining these loading regimes will help to establish the link, if any,
between elasmobranch jaw suspension and the functional diversity of their
feeding mechanisms.
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The purpose of this study was therefore to determine the biomechanical
basis of durophagy in the heterodontid sharks, as represented by the horn
shark Heterodontus francisci (Girard 1855), a primarily
shallow-water, nocturnal forager of molluscs, echinoderms and benthic
crustaceans (Segura-Zarzosa et al.,
1997; Strong,
1989
). Heterodontus francisci uses suction to capture
prey, which is grasped by the anterior cuspidate teeth and then crushed by the
posterior molariform teeth, effectively combining both suction and biting
feeding mechanisms (Edmonds et al.,
2001
; Summers et al.,
2004
). Through in situ bite performance measurements and
theoretical modeling of the forces generated by the cranial musculature of
H. francisci, the specific goals of this study were to: (1)
theoretically determine the forces generated by each of the cranial muscles
active during the gape cycle; (2) determine the distribution of forces
throughout the jaws and suspensorium and discuss the implications of these
loadings for jaw suspension; (3) compare theoretical bite force from
anatomical measures with those obtained during voluntary unrestrained feeding,
restrained biting and electrical stimulation of the jaw adductors; (4) relate
its bite performance to feeding ecology and (5) compare the bite force of
H. francisci with those of other vertebrates.
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Materials and methods |
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Morphological analysis
A theoretical model of the feeding mechanism of H. francisci was
designed by investigating the forces produced by the nine cranial muscles
involved in the abduction (coracomandibularis, coracohyoideus, coracoarcualis
and coracobranchiales), adduction (adductor mandibulae complex consisting of
the quadratomandibularis-preorbitalis complex, quadratomandibularis-
and preorbitalis-
) and retraction (levator palatoquadrati and levator
hyomandibularis) of the jaws and hyobranchial region
(Fig. 2). The
quadratomandibularis-preorbitalis complex consists of six individual heads of
the adductor mandibulae complex (Nobiling,
1977
). Difficulty in mechanically separating these heads led to
their analysis as a group. Using the tip of the snout as the center of a
three-dimensional coordinate system, the three-dimensional position of the
origin and insertion of each muscle was determined by measuring the distance
of these points from the respective X, Y and Z planes
intersecting the tip of the snout (Fig.
3A). Each muscle was then excised (unilaterally where applicable),
bisected through its center of mass perpendicular to the principal fiber
direction, and digital images of the cross-sections were taken (JVC DVL9800
camera). Cross-sectional areas were measured from these images using Sigma
Scan Pro 4.01 (SYSTAT Software Inc., Point Richmond, CA, USA). Center of mass
was estimated by suspending the muscle from a pin and tracing a vertical line
down the muscle. After repeating this from another point, the intersection of
the two line-tracings indicated the center of mass of the muscle.
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The three-dimensional coordinates of the center of rotation of the dual
(lateral and medial; Nobiling,
1977) quadratomandibular jaw articulation (hereafter referred to
as `jaw joint'), the ethmoidal articulation and the lateral and medial
articulations of the hyomandibula with the jaws and chondrocranium,
respectively, were determined with respect to the right side of the head of
each individual. Points corresponding to 0, 25, 50, 75 and 100% of the
distance along the functional tooth row on the lower jaw from the
posteriormost molariform tooth were also determined; 100% is the anteriormost
cuspidate tooth. The in-lever for jaw abduction from the center of rotation of
the jaw joint to the point of insertion of the coracomandibularis was
determined from the three-dimensional coordinates. In-levers for jaw adduction
from the center of rotation of the jaw joint to the points of insertion on the
lower jaw of the quadratomandibularis-preorbitalis complex,
quadratomandibularis-
and preorbitalis-
were determined in the
same manner. A weighted average of these in-levers was determined based on the
forces produced by their respective muscles. The abductive and weighted
adductive in-levers were divided by the out-lever distance from the center of
rotation of the jaw joint to the tip of the anteriormost tooth of the lower
jaw to determine mechanical advantage ratios for jaw opening and closing
(Fig. 3B). Due to the
quadratomandibularis-preorbitalis complex's broad surface attachment on the
lateral face of both the upper and lower jaws, an exact insertion point for
this muscle could not be identified. Its center of mass and principal muscle
fiber direction relative to the lower jaw were used to approximate its
mechanical line of action. The distance from the jaw joint to the intersection
of this line of action with the lower jaw served as the in-lever for this
muscle. Anatomical nomenclature is based on Daniel
(1915
), Motta and Wilga
(1995
,
1999
) and Nobiling
(1977
).
|
![]() | (1) |
Anatomical cross-sectional area was used in this analysis because
theoretical estimates of maximum bite force based on the anatomical
cross-sectional area of the parallel fibered jaw adducting musculature of the
spiny dogfish Squalus acanthias best approximated bite forces
measured during tetanic stimulation of the jaw adducting musculature
(Huber and Motta, 2004). Force
vectors for each muscle were constructed from their maximum tetanic forces and
the three-dimensional coordinates of their origins and insertions. The force
vectors of muscles excised unilaterally were reflected about the
Y-plane to represent the forces generated by the musculature on the
other side of the head.
Mathcad 11.1 software (Mathsoft, Inc., Cambridge, MA, USA) was used to
generate a three-dimensional model of the static forces acting on the jaws of
H. francisci during prey capture. Summation of the three-dimensional
moments acting on the lower jaw about the jaw joints (left and right)
determined the theoretical maximum bite force for each individual and the mean
maximum bite force for all individuals
(B;
Fig. 4). Maximum bite force was
modeled at points 0, 25, 50, 75 and 100% of the distance along the functional
tooth row from the posteriormost tooth to determine a bite force gradient
along the lower jaw. Additionally, the reaction force acting on the jaw joints
during bites occurring at 0 and 100% of the distance along the functional
tooth row was determined (FJR;
Fig. 4).
Loadings were determined at the ethmoidal and hyomandibular articulations
of the upper jaw with the chondrocranium and hyomandibula, respectively (Figs
1A,
4). For bites occurring at 0%
(posteriormost molariform tooth) and 100% (anteriormost cuspidate tooth) of
the distance along the functional tooth row, the moments acting on the upper
jaw about the ethmoidal articulation were summed to determine the forces
acting at the hyomandibular articulation (FH;
Fig. 4). In these analyses, the
hyomandibula was modeled as a two-force member, moveable about its
articulations with both the upper jaw and chondrocranium
(Hibbeler, 2004). Static
equilibrium analysis of the forces acting on the upper jaw was then used to
determine the forces acting at the ethmoidal articulation
(FE; Fig. 4).
Static equilibrium conditions for the forces acting on the lower
(FLJ) and upper jaws (FUJ) were:
![]() | (2) |
![]() | (3) |
where FB is the bite reaction force from a prey item,
FPO- is the force generated by the
preorbitalis-
, FQM-PO is the force generated by the
quadratomandibularis-preorbitalis complex, and FQM-
is the force generated by the quadratomandibularis-
. Forces generated
by the preorbitalis-
and quadratomandibularis-
are isolated to
the lower jaw because they originate on the chondrocranium and insert only
upon the lower jaw (Figs 2A,
4). Joint reaction forces
maintain the static equilibrium of feeding mechanisms by balancing the moments
acting upon the jaws via their associated musculature and contact
with prey items. The moment acting on the lower jaw during jaw opening
via the coracomandibularis muscle was used to determine the
theoretical maximum jaw opening force of H. francisci.
In situ bite performance measurements
Bite performance measurements were performed using a modified single-point
load cell (Amcells Corp., Carlsbad, CA, USA) with custom-designed stainless
steel lever arms, which was calibrated using a series of known weights.
Free-swimming H. francisci were trained to voluntarily bite the
transducer by wrapping the device with squid and presenting it to them after
several days of food deprivation. A P-3500 strain indicator (Vishay
Measurements Group, Raleigh, NC, USA) was used for transducer excitation and
signal conditioning. Data were acquired with a 6020E data acquisition board
and LabVIEW 6.0 software (National Instruments Corp., Austin, TX, USA).
Fifteen measurements of bite force were taken from each animal. Only events in
which the transducer was bitten between the tips of the jaws were kept for
analysis. The five largest bite force measurements for each individual were
analyzed for the following performance variables, as well as used in the
multivariate statistical analyses described below: maximum force (N), duration
of force production (ms), time to maximum force (ms), rising slope of
force-time curve (N s-1), duration at maximum force (ms), time from
maximum force to end of force production [hereafter referred to as `time away
from maximum force' (ms)], falling slope of force-time curve (N
s-1) and impulse (I), which is the integrated area under
the force-time curve (kg m s-1) from the initiation of force
generation to its cessation:
![]() | (4) |
where F is force and t is time. The impulse of a force is the extent to which that force changes the momentum of another body, in this case the force transducer, and therefore has the units of momentum (kg m s-1). For each individual, the single largest bite force and its associated performance measurements were used to create a profile of maximum bite performance for H. francisci, to compare the dynamics of the ascending and descending portions of the bite performance waveforms and to compare the maximum bite forces obtained from the theoretical, in situ, restrained and stimulated methods of determining bite force (see below).
In situ bite performance measurements were simultaneously filmed
with a Redlake PCI-1000 digital video system (Redlake MASD, San Diego, CA,
USA) at 250 frames s-1 to verify that bites on the transducer
occurred between the tips of the jaws (hereafter referred to as `transducer
bites'). The modified single-point load cell used in this study averages the
signals generated by four strain gages in a full Wheatstone bridge such that
the transducer is insensitive to the position on the lever arms at which the
bite is applied. Therefore, the point at which a shark bit the lever arms of
the transducer did not need to be determined from the digital video sequences
for appropriate calibration. To identify any behavioral artifacts associated
with biting a stainless steel transducer, H. francisci were also
filmed while consuming pieces of O. oglinum cut to the same size as
the biting surface of the force transducer (hereafter referred to as `fish
bites'). The following kinematic variables were quantified from transducer and
fish bites using Motionscope 2.01 (Redlake MASD, San Diego, CA, USA) and
SigmaScan Pro 4.01 software: distance, duration, velocity and acceleration of
lower jaw depression, lower jaw elevation, upper jaw protrusion, and head
depression; maximum gape; time to maximum gape; time to onset of lower jaw
elevation; time to onset of head depression; cranial elevation angle. All
kinematic variables were quantified using discrete cranial landmarks as
reference points (Edmonds et al.,
2001).
Restrained and stimulated bite performance measurements
At least one week after the in situ bite performance measurements,
four of the H. francisci were individually removed from the
experimental tank and restrained on a table. Once they had opened their jaws
an adequate distance, the transducer was placed between the anterior teeth,
which elicited an aggressive bite. Following a recovery period of
approximately 10-15 min, the shark was again removed from the tank and
anaesthetized with MS-222 (0.133 g l-1). The
quadratomandibularis-preorbitalis complex, quadratomandibularis- and
preorbitalis-
were implanted with stainless steel 23-gauge hypodermic
needles connected to a SD9 stimulator (Grass Telefactor, West Warwick, RI,
USA), and tetanic fusion of these muscles was accomplished via
stimulation (10 V, 100 Hz, 0.02 ms delay, 3 ms pulse width) while the bite
force transducer was placed between the tips of the anterior teeth. Three
measurements were taken from each individual in both of these experimental
protocols. Individuals were ventilated with aerated seawater between
measurements during muscle stimulation experiments. Maximum bite force, time
to maximum force, and time away from maximum force were quantified from all
restrained and stimulated bites.
Statistical analysis
All bite performance and kinematic variables were log10
transformed and linearly regressed against body mass to remove the effects of
size. Studentized residuals were saved from each regression for subsequent
analysis (Quinn and Keough,
2002). Principal components analyses (PCA) based on correlation
matrices were then used to (1) identify covariation in bite performance
variables and reduce these variables to a series of non-correlated principal
components, which were subsequently analyzed to assess the extent of
individual variability in these parameters, (2) identify covariation in
performance and kinematic variables from in situ bite performance
trials and (3) identify covariation in kinematic variables from fish and
transducer bites and reduce these variables to a series of non-correlated
principal components, which were subsequently analyzed to determine whether
there were any behavioral artifacts associated with biting the steel
transducer. Variables were considered to load strongly on a given principal
component (PC) if their factor scores were greater than 0.6. Non-rotated axes
described the greatest amount of variability in each PCA. For analyses 1 and
3, multivariate analysis of variance (MANOVA) was used to compare the factor
scores for the PCs with eigenvalues greater than 1.0. To determine whether
fish and transducer bites differed kinematically, a two-way, mixed-model
MANOVA was performed on the PCs from PCA 3, with `individual' as the random
effect and `prey type' as the fixed effect, which was tested over the
interaction mean square. Kinematic data from four individuals were included in
this analysis because a complete data set was lacking for one individual. To
determine the extent of individual variability within the bite performance
variables, a one-way MANOVA was performed on the PCs from PCA 1.
To determine whether the kinematic variables associated with biting the transducer were predictive of biting performance in H. francisci, stepwise (forward) multiple regressions were performed with kinematic variables measured from transducer bites as the multiple independent factors, and the eight bite performance variables as the individual dependent factors. Data from four individuals were included in this analysis because a complete kinematic data set was lacking for one individual. One-way ANOVA on Studentized residuals was used to identify significant differences among the theoretical, in situ, restrained and electrically stimulated methods of determining maximum bite force. A Student's t-test was used to identify differences between time to maximum force and time away from maximum force and between the rising and falling slopes of the force-time curves for in situ biting trials. One-way ANOVA was used to compare time to maximum force and time away from maximum force within and among in situ, restrained and electrically stimulated bite forces. Finally, bite forces at the anterior jaw (fish, reptiles and birds) or canine teeth (mammals) and body masses for various vertebrates were compiled from the available literature and grouped according to major taxonomic level. These bite forces, along with those of the horn sharks investigated in this study, were linearly regressed against body mass. Studentized residuals from this regression were then coded according to taxonomic level and compared with a one-way ANOVA. All significant differences were investigated post-hoc with Tukey's pairwise comparisons test. Linear regressions were performed in SigmaStat 2.03 (SYSTAT Software, Inc.) in order to obtain Studentized residuals. All other statistical analyses were performed in SYSTAT 10 (SYSTAT Software, Inc.) with a P-value of 0.05.
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Results |
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Summation of the moments acting on the lower jaw determined that the maximum theoretical bite force of H. francisci ranged from 128 N at the anterior teeth to 338 N at the posteriormost molariform teeth (Fig. 5; Table 2). The bite force at the posteriormost molariform teeth exceeded the resultant force generated by the adductive musculature (Table 2) because the mechanical advantage at this point along the jaw was 1.06. The resultant jaw closing mechanical advantage at the anterior teeth was 0.51, resulting in a dramatically lower bite force at this point.
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The ethmoidal articulation of H. francisci received a loading of
59 N per side during biting, regardless of whether biting occurred at the
anterior or posterior margin of the jaws (FE;
Fig. 4). The angle of incidence
of this force relative to the articular surface of the upper jaw at the
ethmoidal articulation was 80° (;
Fig. 4). For both anterior and
posterior biting, the majority of loading was directed ventrally into the
upper jaw, indicating compression between the ethmoid region of the
chondrocranium and the palatal region of the upper jaw
(Table 3).
The magnitude of loading at the hyomandibular articulation (36 N) was independent of bite point as well (FH; Fig. 4). The lower jaw was loaded posterodorsally and medially at its articulation with the hyomandibula during both anterior and posterior biting (Table 3). The reaction forces acting on the distal ends of the hyomandibula are equal to and opposite the forces acting at the jaws' articulation with the hyomandibula. Therefore, during biting, the hyomandibula was loaded anteroventrally and laterally. These local/internal loadings between the jaws and hyomandibula indicate that the hyomandibula is globally in tension. Modeling the hyomandibula as a two-force member assumed that the line of action of the force acting on the hyomandibula passed through its articulation with the jaws and chondrocranium. The hyomandibula is therefore loaded in pure tension, and the angle of incidence of the hyomandibular force cannot be determined.
The only muscle involved in abduction of the lower jaw is the coracomandibularis, which was capable of generating 31 N of force (Table 1). This muscle inserts on the caudal aspect of the lower jaw symphysis at 37° below the longitudinal axis of this jaw and has a mechanical advantage of 0.89. Despite this high mechanical advantage, indicative of force amplification in a class III lever system, its acute insertion angle caused the muscular force generating motion about the lower jaw (force component perpendicular to the lower jaw) to be 19 N (Table 2). After accounting for mechanical advantage, the resultant abductive force at the tip of the lower jaw was 16 N (Table 2). The abductive force lacks a component along the Z-axis because the coracomandibularis runs parallel to the longitudinal axis of the body. The other muscles involved in the expansive phase of the gape cycle generated considerably greater forces than the coracomandibularis (Table 1).
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PCA 2 of performance and kinematic variables yielded six PCs with eigenvalues greater than 1.0, which collectively explained 86.7% of the variance. All of the variables that loaded heavily on the first PC (30.5% of variance explained) were kinematic measurements (Table 5). These variables primarily demonstrated covariance in the timings and excursions of lower jaw depression and elevation. Performance measures were the only variables to load heavily on the second PC (19.5% of variance explained), indicating covariance between rates and durations of force application (Table 5). Maximum bite force did not load heavily until the fifth PC (7.8% of variance explained), and impulse did not load heavily on any of the PCs.
|
Stepwise multiple regressions yielded similar results to PCA 2 on kinematic and performance data. Only three of the bite performance variables were significantly related to individual kinematic variables. Force duration was significantly, though poorly, related to lower jaw elevation velocity (r2=0.226, F1,18=5.268, P=0.034). Similarly, time to maximum force (r2=0.389, F1,18=11.471, P=0.003) and the rising slope of the force-time curve (r2=0.410, F1,18=12.523, P=0.002) were significantly related to lower jaw elevation distance. Inclusion of additional kinematic variables did not improve the predictive ability of these regression models. The two variables indicative of the magnitude of bite force generated (maximum force, impulse) could not accurately be predicted by any combination of kinematic variables. Although kinematic variables were not predictive of bite performance variables, PCA 1 used to assess individual variability (see above) identified notable covariance in performance measures. Maximum in situ bite force exhibited a strong linear relationship with impulse (r2=0.758) and moderate linear relationships with force duration (r2=0.450) (Fig. 7) and time to maximum force (r2=0.489).
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PCA 3 reduced the set of kinematic variables measured from fish and transducer bites to a series of four PCs (73.3% of variance explained). MANOVA indicated no significant differences between the prey capture kinematics of H. francisci while biting fish or the transducer on any of the PCs for all individuals (Wilk's Lambda=1.0, F4,29=0.0, P=1.0). However, a single individual was found to differ from two other individuals on the first PC (F3,32=4.646, P=0.008). Variables that loaded heavily on the first PC were durations and distances of lower jaw depression and elevation, times to maximum gape, onset of lower jaw elevation, completion of lower jaw elevation and maximum gape distance. The acceleration of lower jaw elevation loaded heavily, but negatively, on the first PC.
Methodological comparison
In situ measurement of maximum bite force was a reasonably good
indicator of the maximum bite force of H. francisci. Using
size-corrected data, a single difference was found among the four methods of
determining maximum bite force (F3,14=4.358,
P=0.023). Restrained bite force (159-206 N) was significantly greater
than in situ bite force (60-133 N) (P=0.013). In
situ bite force was, however, equivalent to theoretical (107-163 N) and
electrically stimulated (62-189 N) bite forces. Restrained, electrically
stimulated and theoretical bite forces were equivalent
(Table 6). During restrained
bites, time to maximum force (522 ms) was greater than time away from maximum
force (339 ms) (t4=2.848, P=0.046). Time to
maximum force (285 ms) was shorter than time away from maximum force (556 ms)
for electrically stimulated bites (t8=-5.476,
P<0.001). Significant differences were detected between the in
situ, restrained and electrically stimulated methods for time to maximum
force (F2,10=4.996, P=0.031) and time away from
maximum force (F2,10=58.290, P<0.001). Time to
maximum force was greater for restrained bites than for electrically
stimulated bites (P=0.030), both of which were equivalent to the time
to maximum force of in situ bites. Time away from maximum force was
greater for electrically stimulated bites than restrained bites
(P=0.001), which was greater than that of in situ bites
(P=0.005).
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Bite forces among vertebrates
Bite forces and body masses were compiled for 113 species of vertebrates
(including H. francisci) from the available literature
(Binder and Van Valkenburgh,
2000; Cleuren et al.,
1995
; Clifton and Motta,
1998
; Erickson et al.,
2004
; Hernandez and Motta,
1997
; Herrel et al.,
1999
,
2001
,
2002
;
Huber et al., 2004
;
Huber and Motta, 2004
;
Korff and Wainwright, 2004
;
Ringqvist, 1972
;
Robins, 1977
;
Thomason et al., 1990
;
Thompson et al., 2003
;
van der Meij and Bout, 2004
;
Weggelaar et al., 2004
;
Wroe et al., 2005
; D. R.
Huber, M. N. Dean, and A. P. Summers, unpublished)
(Appendix I). Collectively,
bite force scaled to body mass with a coefficient of 0.60, which is below the
isometric scaling coefficient of 0.67 (Fig.
8). When the mammalian bite forces from Wroe et al.
(2005
) were excluded from this
analysis, bite force scaled with a coefficient of 0.66, approximating
isometry. This discrepancy is probably due to Wroe et al.
(2005
) having used the
dry-skull method of estimating muscle Acs, which can
underestimate Acs by 1.3-1.5x
(Thomason et al., 1991
).
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|
Fishes collectively had the highest mass-specific bite force of the four
vertebrate groups, followed by reptiles, mammals and birds, respectively
(F3,130=6.357, P<0.001). Mass-specific bite
force of the fishes was greater than those of the birds (P=0.002) and
mammals (P=0.013), while reptilian mass-specific bite force was
greater than that of the birds (P=0.009). The striped burrfish,
Chilomycterus schoepfi, had the highest mass-specific bite force,
followed by the Canary Island lizard, Gallottia galloti, and the
American alligator, Alligator mississippiensis
(Erickson et al., 2004;
Herrel et al., 1999
;
Korff and Wainwright, 2004
).
The hogfish, Lachnolaimus maximus, had the second highest
mass-specific bite force, but for biting with the pharyngeal jaws not the oral
jaws (Clifton and Motta,
1998
). The three lowest mass-specific bite forces were those of
the red-bellied short-necked turtle, Emydura subglobosa, the mata
mata turtle, Chelus fimbriatus, and the twist-necked turtle
Platemys platycephala (Herrel et
al., 2002
) (Fig.
8). Of the cartilaginous fishes in this analysis, the mean
mass-specific bite force of H. francisci was greater than those of
S. acanthias and the blacktip shark, Carcharhinus limbatus,
but less than that of the white-spotted ratfish, Hydrolagus
colliei.
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Discussion |
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The jaw closing mechanical advantage at the anterior teeth of H.
francisci is greater than that of the only other elasmobranch for which
values have been published, S. acanthias (0.28;
Huber and Motta, 2004), which
utilizes a combination of ram and suction feeding to consume soft-bodied prey
(Wilga and Motta, 1998
). Its
jaw closing mechanical advantage is greater than those at the anterior teeth
of nearly every actinopterygian fish investigated (
150), which include
prey from plankton to hard-shelled species
(Durie and Turingan, 2001
;
Turingan et al., 1995
;
Wainwright et al., 2004
;
Westneat, 2004
). The
durophagous species among these taxa do, however, have the highest jaw
adducting mechanical advantages. The durophagous parrot fishes (Scaridae) are
the only actinopterygian fishes with jaw adducting mechanical advantages
comparable with that of H. francisci
(Wainwright et al., 2004
;
Westneat, 2004
). Thus, there
is extensive evolutionary convergence on high leverage jaw adducting
mechanisms in fishes that consume hard prey.
The jaws of H. francisci are elliptical in transverse-section,
with their major axis oriented vertically, in-line with the compressive
stresses associated with feeding. Calcium reinforcement in the jaw cortex
increases posteriorly as the dentition becomes more molariform and is greatest
at the jaw joints (Summers et al.,
2004). Calcification and elliptical geometry increase the second
moment of area of the jaws with respect to the compressive loading of prey
capture and processing, which augments the jaws' ability to resist
dorsoventral flexion (Summers et al.,
2004
). The resolved force vector for jaw adduction also occurs
approximately in the region of the most robust molariform teeth of H.
francisci, where it can generate upwards of 338 N of bite force.
Therefore, maximum bite force is produced where both the dentition and jaw
cartilages are best able to resist compressive stresses.
Despite the high mechanical advantage (0.89) of the coracomandibularis
muscle in the lower jaw depression mechanism of H. francisci, its
acute insertion angle relative to the lower jaw causes most of its force to be
directed posteriorly, into the jaw joints
(Table 2.) This high mechanical
advantage is due to the insertion of the coracomandibularis on the posterior
margin of the mandibular symphysis, which is synapomorphic for elasmobranchs
(Wilga et al., 2000). Although
this mechanism is suited for force production, velocity production is
desirable for inertial suction feeding. Heterodontus francisci
nonetheless effectively uses suction to initially capture and reorient prey
(Edmonds et al., 2001
), which
may be due in part to its powerful hyoid and branchial abductors
(Table 1). These muscles
rapidly expand the floor of the buccopharyngeal cavity, which is critical to
suction feeding in elasmobranchs (Motta et
al., 2002
; Svanback et al.,
2002
). As in the nurse shark, Ginglymostoma cirratum
(Motta et al., 2002
), the
large labial cartilages of H. francisci considerably occlude its
lateral gape, theoretically augmenting suction ability
(Muller and Osse, 1984
;
Van Leeuwen and Muller,
1984
).
Three-dimensional resolution of the forces generated during jaw adduction
may reveal the mechanical basis of upper jaw protrusion in H.
francisci. The force driving the upper jaw into the ethmoidal
articulation has both dorsal and anterior components, causing the upper jaw to
slide through the anteroventrally sloping palatal fossa of the chondrocranium
and protrude (Fig. 4;
Table 2). This proposed
mechanism is based on the resolved force vector for all muscles involved in
jaw adduction. Differential activity of the heads of this complex may
facilitate modulation of protrusion. The quadratomandibularis- is the
likely candidate for control over protrusion because its acute insertion angle
relative to the lower jaw and anterior insertion point give it high leverage
over anterior motion (Fig.
2).
Activity of the quadratomandibularis-preorbitalis complex alone, which has
a broad insertion on the lateral face of both the upper and lower jaws, may
contribute to protrusion of the upper jaw as well. After the lower jaw has
been depressed, contraction of this muscle complex may simultaneously raise
the lower jaw and pull the upper jaw away from the skull. This mechanism has
been proposed for upper jaw protrusion in S. acanthias, G. cirratum
and the lemon shark, Negaprion brevirostris
(Moss, 1977;
Motta et al., 1997
;
Wilga and Motta, 1998
).
Protrusion by H. francisci, which may be used to chisel away at
attached benthic prey, occurs after the lower jaw has been depressed
(Edmonds et al., 2001
),
corroborating the role of the quadratomandibularis-preorbitalis complex in
this behavior.
Extensive calcification near the jaw joints of H. francisci
(Summers et al., 2004) would
apparently indicate high joint reaction forces during prey capture. Joint
reaction forces can exceed bite forces at the tip of the jaw depending on the
mechanical advantage of the given feeding mechanism and the force produced by
the associated musculature, which has been identified in numerous reptiles
(3-4x greater; Cleuren et al.,
1995
; Herrel et al.,
1998
). Although joint reaction force was greater than anterior
bite force in H. francisci, the ratio of these values (1.65) is
substantially lower than those found for reptiles. The ratio of joint reaction
force to posterior bite force in H. francisci was 0.43.
Low ratios of joint reaction force to bite force in H. francisci
are due to its high mechanical advantage jaw adducting mechanism. Humans,
which share this characteristic, have correspondingly low ratios of joint
reaction force to bite force (Koolstra et
al., 1988). Although some damping will occur in the connective
tissue associated with the jaw joint, loading occurring at the joint will be
transmitted to adjacent skeletal elements. Therefore, low ratios of joint
reaction force to bite force may be adaptive in H. francisci, and
elasmobranchs in general, because the posterior region of their jaws is
suspended from the cranium by mobile hyomandibulae, not a stable jaw
articulation as in other vertebrates. Minimizing loading at this articulation
may stabilize the feeding mechanism during prey capture and processing.
In heterodontiform sharks, the cranial stresses associated with prey
capture can be isolated to the ethmoidal and hyomandibular articulations.
Unlike carcharhinid sharks (Motta and
Wilga, 1995), the upper jaw of H. francisci does not
disarticulate from the chondrocranium during feeding, even during upper jaw
protrusion (Maisey, 1980
).
Therefore, in carcharhinid sharks, the hyomandibulae may receive all of the
suspensorial loading occurring during prey capture. Optimal loading at the
ethmoidal articulation would entail forces directed perpendicularly into the
articular surface of the upper jaw because cartilage is strongest in axial
compression (Carter and Wong,
2003
). The estimated forces at this articulation deviated from
optimal orientation by only 10° during anterior and posterior biting. The
ethmoidal articulation of H. francisci appears well designed for
withstanding this nearly axial compressive loading because the upper jaw
calcifies at this articulation early in ontogeny
(Summers et al., 2004
) and the
ethmoid region of the chondrocranium is one of the thickest parts of this
structure (Daniel, 1915
).
Additionally, maintenance of contact between the upper jaw and chondrocranium
in H. francisci will distribute stresses from the repetitive loading
associated with processing hard prey.
Although it is well known that the hyomandibulae support the posterior
margin of the jaws, the nature of the loading they receive has been a matter
of speculation. This mechanical analysis indicates that the hyomandibulae of
H. francisci are tensile elements, as suggested by Moss
(1972) and Frazzetta
(1994
). Consequently, the
hyomandibulae may regulate anterior movement of the jaws during feeding, such
as would occur during jaw protrusion. In this regulatory role, activity of the
levator hyomandibularis could hypothetically modulate resistance to anterior
motion of the jaws. Electromyographic analysis of the feeding musculature of
H. francisci would be required to verify this hypothesis.
The ligamentous attachments between the hyoid arch and the posterior end of
the jaws stabilize this articulation against the tensile stresses caused by
biting. The internal hyomandibular palatoquadrate and hyoideo-mandibulare
ligaments resist dorsoventral translation between the hyomandibula and jaws,
while the hyomandibuloceratohyal ligament prevents lateral translation between
these elements. The two slips of the median ligament
(Daniel, 1915) stabilize
against dorsoventral and lateral translation, respectively. Although this
analysis makes the assumption that the hyomandibulae are loaded as two-force
members in axial tension, they probably experience a more diverse loading
pattern in nature, necessitating this multidirectional support.
Increased hyomandibular loading may have played a role in the transition
from amphistylic to hyostylic jaw suspensions in modern elasmobranchs. As the
number and size of the articulations between the jaws and chondrocranium was
reduced, the hyomandibulae took on a greater role in suspending the jaws
(Carroll, 1988;
Maisey, 1980
;
Schaeffer, 1967
). Concomitant
with these changes in articulation, the hyomandibulae became shorter and more
mobile (Cappetta, 1987
;
Maisey, 1985
;
Moy-Thomas and Miles, 1971
;
Schaeffer, 1967
), oriented
more orthogonally to the chondrocranium
(Stahl, 1988
;
Wilga, 2002
) and had more
extensive ligamentous attachments with the jaws and chondrocranium
(Gadow, 1888
). Collectively,
these changes may have been associated with a shifting of the force of jaw
adduction to a more posterior region of the jaws. This may have resulted in
greater hyomandibular loading as well as a `freeing-up' of the anterior margin
of the jaws such that upper jaw kinesis was increased, facilitating jaw
protrusion and prey gouging (Maisey,
1980
; Moss, 1977
;
Wilga, 2002
).
Although the jaw suspension mechanism of H. francisci is
classified as hyostylic (Gregory,
1904; Wilga,
2002
), this analysis indicates that it is functionally
amphistylic. Heterodontus francisci exhibits considerable upper jaw
kinesis (reduces maximum gape by 39%), similar to other hyostylic
carcharhiniform sharks (Edmonds et al.,
2001
; Wilga et al.,
2001
). Despite this functional similarity, the upper jaw does not
disarticulate from the chondrocranium during protrusion in H.
francisci. Furthermore, in contrast to the hypotheses regarding
hyomandibular evolution (see above), H. francisci has considerable
loading at both the hyomandibular (tensile) and ethmoidal (compressive)
articulations. The term `hyostyly' should therefore be reserved for taxa in
which the upper jaw disarticulates from the chondrocranium during protrusion
such that hyomandibulae are the primary means of support and the ethmopalatine
ligaments are loaded in tension. Therefore, contemporary definitions of jaw
suspension should incorporate functional interpretations of loadings at the
various articulations between the jaws and cranium, as well as the
relationship between suspension type and upper jaw protrusion.
Methodological comparison
Although no differences were found between theoretical, restrained and
electrically stimulated bite force measurements using size-corrected data, the
absolute maximum bite force for each individual occurred during restrained
bite force measurements. No differences were found between theoretical and
electrically stimulated bite force measurements of S. acanthias
either (Huber and Motta,
2004). Therefore, restrained measurements appear to be the best
method of obtaining maximum bite force measurements from live elasmobranchs.
Small sample size might, however, account for the lack of statistical
significance found between different methods of determining bite force.
Nonetheless, the results of both this analysis and that of bite force
production in S. acanthias (Huber
and Motta, 2004
) indicate that theoretical estimates of bite force
in sharks are accurate in predicting maximum bite forces. This is fortunate
given the logistical problems associated with obtaining bite force
measurements from live elasmobranchs. Given the appropriate resources,
however, maximum bite force can be obtained through in situ methods,
as indicated by the equivalence of theoretical, electrically stimulated and
in situ bite forces in this study. In situ measurements
enable the quantification of biting dynamics as well, which is informative
regarding feeding performance and ecology (see below).
Static estimates of force production based on muscle architecture may
underestimate actual force production because active stretching of the jaw
adductors during the expansive phase of the gape cycle can increase force
production (Askew and Marsh,
1997; Josephson,
1999
). Furthermore, by modeling the primary jaw adductor as the
quadratomandibularis-preorbitalis complex instead of delineating the
individual heads of this complex, variations in muscle architecture of these
heads such as pinnate insertion points may have been overlooked. If this were
the case, a theoretical model of force production based on morphological
cross-sectional area alone could underestimate maximum force production.
The ratios of time to and away from maximum force for in situ
(1.52) and restrained (1.54) bites suggest that the application of bite force
by H. francisci takes longer than its release. However, the opposite
relationship for these variables occurred during electrically stimulated
bites. The ratio of time to and away from maximum force during electrically
stimulated biting (0.51) approximates the ratio of time for twitch tension
development to relaxation (0.42) for pectoral fin muscle of the cuckoo ray,
Raja naevus (Johnston,
1980). This suggests that force generation during voluntary or
stimulated biting is a function of the rate at which the adductor muscles
reach tetanic fusion. Gradual summation of motor unit recruitment during
voluntary biting results in a prolonged time to maximum force, whereas manual,
high-frequency electrical stimulation of the adductor muscles causes more
rapid tetani and subsequently shorter times to maximum force. Time away from
maximum force was longer for restrained measurements than for in situ
measurements, perhaps indicating motivational differences between these two
presentation methods.
Feeding performance
Several bite performance variables demonstrated patterns consistent with
the durophagous diet of H. francisci. The time to maximum bite force
application by H. francisci was longer than time away from maximum
force, the rising slope of the force-time curve was lower than the falling
slope, and maximum bite force was positively related to the time to maximum
force. These performance characteristics indicate that the application of bite
force is a slower, more deliberate action than its release by H.
francisci. Linear relationships of maximum bite force with impulse and
force duration further indicate that higher bite forces are associated with
slower, more deliberate closing of the jaws by H. francisci
(Fig. 7).
The impulse generated upon impact between two bodies is a measure of
momentum transfer and can be interpreted as the `effort' that each body exerts
on the other (Nauwelaerts and Aerts,
2003). Because momentum is conserved during impact, larger
impulses generated during biting transfer greater quantities of kinetic energy
from the jaws to the prey. Optimizing impulse by maximizing bite force output
per unit time will increase the amount of energy contributing to the
rupture/fracture of a prey item. Heterodontus francisci capitalizes
upon this when consuming hard prey with composite exoskeletons. Sustained
loading after a high-velocity initial impact is effective at fracturing
composite structures such as sea urchin exoskeletons (calcite ossicles linked
by collagenous ligaments) because composites harden to a saturation point upon
initial compression, after which crack nucleation occurs, followed by
structural failure (Christoforou et al.,
1989
; Ellers et al.,
1998
; Provan and Zhai,
1985
; Strong,
1989
).
The prevalence of multiple force peaks within a compressive waveform of a
single bite (32% of in situ bites) also indicates H.
francisci's behavioral specialization for exploiting hard prey
(Fig. 6). This behavior
maximizes the damage inflicted upon prey items during a given bite by ramping
up the applied force multiple times, especially when there are multiple bites
during a feeding event. The rate at which the strength of a composite
structure degrades is a power function of both the strain rate and number of
strain cycles (Hwang and Han,
1989). Multiple force peaks within a given bite indicate that
H. francisci may have evolved motor patterns specialized for
durophagy as well. High-frequency bursts of electrical activity associated
with rhythmic compression of prey items occur in the jaw adductor musculature
of the lungfish Lepidosiren paradoxa
(Bemis and Lauder, 1986
).
Prolonged jaw adductor activity occurs in the queen triggerfish, Balistes
vetula (Turingan and Wainwright,
1993
), and the bonnethead shark, Sphyrna tiburo, which
also uses repeated compressions of the jaws to process prey
(Wilga and Motta, 2000
). All
of these fish include hard prey in their diets
(Berra, 2001
;
Turingan and Wainwright, 1993
;
Wilga and Motta, 2000
). These
behavioral attributes demonstrate that the way in which force is applied to
prey items, and not just the magnitude of force, is likely to be a determinant
of feeding success.
Although covariation in several performance measures appears related to the
consumption of hard prey by H. francisci, covariation was lacking
between kinematic and performance variables from the in situ bite
performance trials. Both principal components and multiple regression analyses
demonstrated the inability of kinematic measures to predict bite performance
measures with any accuracy (Table
5). These findings beg the question, how are two series of
sequential behaviors so unrelated? One would assume that at least the
kinematics of lower jaw elevation (e.g. velocity, acceleration) would be
predictive of biting performance (e.g. maximum force, impulse). This lack of
covariation is probably due to the instantaneous position of the jaw adducting
muscles of H. francisci on the force-velocity curve relating muscle
tension to contraction velocity (Aidley,
1998). Based on this principle, when the adductor musculature is
elevating the lower jaw, it is contracting with high velocity and low force.
However, once contact is made with the bite force transducer, movement of the
lower jaw is impeded and the jaw adductors shift to the low-velocity,
high-force region of the force-velocity curve. In addition to high force,
maximum muscle power is generated at low velocity as well
(Askew and Marsh, 1997
).
Because of the dramatic differences in muscle function at either end of the
force-velocity curve, jaw kinematics and biting performance may vary
conversely and possibly be modulated independently. A predictive relationship
between cranial kinesis and performance kinetics is more likely to be found
for behaviors such as suction feeding in which kinesis and performance occur
simultaneously (cranial expansion and suction generation;
Sanford and Wainwright, 2002
;
Svanback et al., 2002
), not
sequentially, as is the case in biting performance (jaw adduction and bite
force application).
An additional behavior that may augment the biting performance of H.
francisci is the use of upper jaw protrusion to dislodge and chisel away
at hard prey, as was suggested by Edmonds et al.
(2001). While the restrained
bite force measurements of H. francisci indicate that they can
consume prey capable of resisting over 200 N using this behavior, in
situ bite force measurements suggest they would consume smaller, less
durable prey. An analysis of the forces necessary to crush various sizes of
hard prey items found in H. francisci's diet is needed to delineate
the prey it is theoretically capable of consuming (potential niche) from that
which it actually consumes (realized niche). Functioning at maximum capacity
would typically be an unnecessary expenditure of energy, especially when
feeding occurs in a niche such as durophagy that is relatively inaccessible to
sympatric taxa.
Feeding ecology
The cranial architecture and prey capture behavior of H. francisci
enable it to exploit hard prey, which is a relatively untapped ecological
niche for aquatic vertebrates. In fishes, durophagy has been associated with
high bite forces and low dietary diversity
(Clifton and Motta, 1998;
Wainwright, 1988
). Species
capable of consuming hard prey are morphologically segregated by relative
differences in bite force and ecologically segregated by the hardness of the
prey they can consume (Aguirre et al.,
2003
; Kiltie,
1982
). Therefore, durophagy appears to result in niche
specialization and competition reduction. This is the case in H.
francisci because hard prey (molluscs, echinoderms, benthic crustaceans)
comprises approximately 95% of its diet
(Segura-Zarzosa et al., 1997
;
Strong, 1989
). However,
Summers et al. (2004
)
suggested that H. francisci goes through an ontogenetic shift to
durophagy due to biomechanical changes in its jaw cartilages. It remains to be
seen if H. francisci undergoes a reduction in dietary diversity and
increased niche specialization over ontogeny, with associated changes in
feeding behavior and performance. A more detailed dietary analysis of neonate
and juvenile H. francisci would be needed to determine whether these
changes occur.
Biomechanical modeling and performance testing provide a morphological and
behavioral basis from which to interpret differences in organismal ecology.
These analyses determined that H. francisci is capable of generating
bite forces an order of magnitude higher than comparably sized S.
acanthias (Huber and Motta,
2004) and that H. francisci applies bite force in a way
suited for processing hard prey. Differences in the feeding performance of
H. francisci and S. acanthias directly coincide with the
different feeding niches they occupy (durophagy and piscivory, respectively;
Alonso et al., 2002
;
Segura-Zarzosa et al., 1997
).
Therefore, these analyses are of utility for understanding the diversity of
elasmobranch feeding mechanisms at numerous organismal levels (morphology,
behavior, ecology), as well as the selective pressures involved in the
evolution of these mechanisms.
Heterodontus francisci has the second highest mass-specific bite
force of the cartilaginous fishes in which bite force has been measured or
estimated (Huber et al., 2004;
Huber and Motta, 2004
;
Weggelaar et al., 2004
; D. R.
Huber, M. N. Dean and A. P. Summers, unpublished). Relative to body mass, the
hardest biting cartilaginous fish studied thus far is H. colliei,
which is also durophagous (Ebert,
2003
; Johnson,
1967
). Neither H. francisci nor H. colliei were
comparable in biting ability to the durophagous teleost fishes C.
schoepfi, L. maximus and the sheepshead, Archosargus
probatocephalus. The mass-specific bite forces of these teleost fishes,
which possess a battery of anatomical specializations associated with
durophagy (Clifton and Motta,
1998
; Hernandez and Motta,
1997
; Korff and Wainwright,
2004
), were considerably higher than those of the durophagous
cartilaginous fishes (Appendix
I). Comparative materials testing of the hard prey items in the
diets of these cartilaginous and teleost fishes would be required to determine
the ecological relevance of these differences in bite force. Nonetheless, the
bite forces of these fishes collectively indicate that high biting
performance, in addition to anatomical specialization, are associated with the
consumption of hard prey.
Conclusions
The heterodontiform sharks, as represented by the horn shark H.
francisci, possess a unique combination of morphological and behavioral
characteristics that enable them to consume hard prey. Although H.
francisci bites harder than the average vertebrate of comparable size, on
a mass-specific basis it is not the most powerful biter in the animal kingdom
(Fig. 8). Reptiles, mammals,
other fishes and even some birds are capable of performing as well as or
better than H. francisci when body mass is accounted for. These data
suggest that factors other than bite force magnitude play a significant role
in prey capture and processing ability. For H. francisci, these
factors are molariform teeth, robust jaws, a high leverage jaw-adducting
mechanism, and long duration, cyclically applied bite forces. The durophagous
feeding behavior of H. francisci is reflected in its extensive
ethmoidal articulation bracing the anterior portion of the upper jaw against
the chondrocranium during prey capture and processing. Although in
situ bite force measurements provided valuable information regarding its
feeding behavior and ecology, theoretical estimates and restrained bite force
measurements were the most effective means of estimating maximum bite force,
depending on the availability of deceased specimens and live individuals.
Because only a few investigations of biting performance in cartilaginous
fishes have been made (Evans and Gilbert,
1971; Huber et al.,
2004
; Huber and Motta,
2004
; Snodgrass and Gilbert,
1967
; Weggelaar et al.,
2004
), little is known about the role that bite force plays in the
ecological and evolutionary success of sharks. Combining theoretical and
performance analyses provides the basis for an in-depth understanding of the
link between morphology, behavior and ecology in sharks, and the role that
biomechanics plays in the form and function of shark feeding mechanisms.
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