A functional morphological approach to the scaling of the feeding system in the African catfish, Clarias gariepinus
1 Dept Biology, University of Antwerp, Universiteitsplein 1, B-2610
Antwerpen, Belgium
2 Institute of Zoology, University of Ghent, K.L. Ledeganckstraat 35,
B-9000, Ghent, Belgium
* Author for correspondence (e-mail: anthony.herrel{at}ua.ac.be)
Accepted 15 March 2005
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Summary |
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Key words: scaling, fish, feeding, muscle, bone, cross-sectional area, fibre length
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Introduction |
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Although numerous experimental studies have attempted to test these models
by investigating the effects of size on the movements of skeletal elements
during locomotion and feeding (for example, see
O'Reilly et al., 1993;
Reilly, 1995
;
Richard and Wainwright, 1995
;
Quillin, 1999
,
2000
; Nauen and Shadwick,
1999
,
2001
;
Meyers et al., 2002
;
Toro et al., 2003
), relatively
little is known about the scaling of the functional properties of muscles and
bones causing the actual movements. Yet, this is important because the scaling
of muscles and bones relates back to the basic premises and assumptions of
many of these scaling models. For example, in many models
(Hill, 1950
;
Richard and Wainwright, 1995
)
geometric similarity is assumed whereby the capacity to generate force
increases to the second power (i.e. proportional to the cross-sectional area
of muscles), but segmental masses increase to the third power of linear
dimensions. Hill's predictions for the scaling of movements
(Hill, 1950
), for example, are
based on the discrepancy between the available muscle force [proportional to
body length (L)2] and the force needed to accelerate a
given segmental mass (proportional to L3) that arises as a
consequence of geometric similarity. Consequently, any departure from
geometric similarity during growth in muscle properties or segmental masses
will probably have an impact on the expected scaling relationships. Because
ectotherms typically display indeterminate growth, they are assumed to confer
to the assumptions of geometric similarity
(O'Reilly et al., 1993
;
Meyers et al., 2002
). However,
this is not always the case as subtle changes in shape may take place (e.g.
Birch, 1999
). Also, during the
early ontogeny of fish and amphibians, distinct shape changes in the cranial
system take place (e.g. Osse,
1990
; Reilly,
1995
; Hernandez,
2000
; Hunt von Herbing,
2001
). Such shape changes are important as they are often related
to changes in functional properties (e.g.
Birch, 1999
).
Despite the large body of work dealing with the effects of size on the
functioning of musculo-skeletal systems, no consensus has been reached on
which scaling patterns to expect. Studies investigating suction feeding in
aquatic vertebrates are exemplary in this regard as different scaling
relationships were observed in nearly every single study (see
Richard and Wainwright, 1995;
Reilly, 1995
;
Deban and O'Reilly, 1996
;
Wainwright and Shaw, 1999
;
Hernandez, 2000
;
Robinson and Motta, 2002
).
Although this may be a real phenomenon, it must be clear that an understanding
of the scaling of the underlying musculo-skeletal system is crucial to be able
to explain the observed diversity in scaling relationships. Surprisingly,
relatively little is known of how the actual muscles and muscle properties
(e.g. fibre length, cross-sectional area, intrinsic shortening velocity) scale
as a function of animal size during ontogeny. Despite it being crucial to our
understanding of musculo-skeletal function, only a few studies have examined
these issues (e.g. Richard and Wainwright,
1995
; Hernandez and Motta,
1997
; James et al.,
1998
; Robinson and Motta,
2002
). Given that no or little changes in the muscular activation
pattern appear to take place with increasing size
(Wainwright and Richard, 1995
;
but see Wakeling et al., 1999
)
and that sarcomere length does not change with size in fish
(James et al., 1998
), studies
investigating the scaling of muscle properties such as cross-sectional area
and fibre length may be especially insightful and could potentially allow us
to fine-tune existing scaling models and make more precise predictions
regarding the scaling of movements.
In the present study, we investigate the scaling of external morphology,
the dimensions of skeletal elements involved in suction feeding and some
functional attributes of a number of cranial muscles in the catfish
Clarias gariepinus to understand how these scaling patterns may
affect the movements observed during suction feeding in animals of different
size. Additionally, we use previously published biomechanical models
(Herrel et al., 2002;
Van Wassenbergh et al., 2005a
)
to investigate how the observed changes in morphology may affect aspects of
feeding function (i.e. bite force and jaw closing velocity). Finally, we
compare the scaling of bite force and jaw closing velocity to previously
published dietary data for a size series of wild-caught animals (see
Bruton, 1979
).
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Materials and methods |
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Morphological data
External body and head dimensions were quantified using a ruler and digital
callipers (Absolute Digimatic; Mitutoyo, Sakato, Japan). External measurements
included head length (measured from the tip of the premaxilla to the posterior
aspect of the supraoccipital spine), head width (measured both at the level of
the eyes and at the level of the pectoral fins) and head depth (measured at
the highest point of the head, just posterior to the eyes). The total length
(the distance from the tip of the head to the tip of the caudal fin) and
standard length (the distance from the tip of the head to the base of the
caudal fin) of the fish were quantified by stretching out a piece of rope
along the ventral midline of the fish. The rope was then measured using a
ruler.
Muscles and bones of interest were exposed by dissecting away the skin, the bony elements covering the jaw adductors and some superficial musculature. Muscles were detached at their origin and insertion and stored in a 70% aqueous ethanol solution. The hypaxial muscles were cut at the level of the pectoral fins in all fish. Given that the exact portion of the hypaxial muscles involved in suction feeding is not known, we considered this approach valid as it provided us with a homologous measurement across all fish. Three fishes had been partly dissected previously and no longer had the hypaxial muscles and m. sternohyoideus (hyoid retractor). Muscles and bones were weighed using electronic scales (AND type FX 3200; ±0.01 g used for the larger fish; Mettler MT 5; ±0.0001 g used for the smaller fish).
Next, muscles were submersed in a 30% aqueous nitric acid solution for 24 h. After 24 h, the nitric acid was removed and replaced by a 50% aqueous glycerol solution. Muscle fibres were teased apart using blunt-tipped glass needles, and at least 20 fibres were selected randomly and drawn using a Wild Heerbrugg (M3Z) binocular scope with camera lucida. A scale bar was included on each drawing. Drawings were scanned, and fibre lengths calculated using NIH image. Muscle volume was obtained by dividing the mass by 1050 kg m-3, and physiological cross-sectional area was obtained by multiplying muscle volume by the cosine of the pennation angle (where relevant) and dividing this by the mean fibre length.
Digital pictures were taken during all stages of the dissection using a
Nikon Coolpix digital camera. These pictures were used to estimate the
pennation angle of the A2A3'. However, as
pennation angles varied widely within a single muscle (see
Herrel et al., 2002), an
average angle was calculated and used to scale muscle physiological
cross-sectional area. As pennation angle did not change with fish size, the
same average angle of 30° (see also
Herrel et al., 2002
) was used
for the A2A3' in all fish. Additionally, X-ray
pictures were taken of the lower jaw, hyoid and cleithrum in situ
using a Philips Optimus X-ray system coupled to a Redlake Motion Pro
high-resolution camera. These pictures were used to measure the angle made by
the bones of the left and right sides. The in-lever for jaw opening and
in-lever for jaw closing were determined using digital callipers (Mitutoyo;
±0.01 mm) as described in Richard and Wainwright
(1995
). A number of linear
dimensions of skeletal elements were determined using digital callipers
(Mitutoyo; ±0.01 mm; see Fig.
1).
|
Jaw closing velocity was calculated for each fish using the dynamic jaw
closing model of Van Wassenbergh et al.
(2005a), where lower jaw
adduction is modelled as the rotation of a half-elliptic surface. As input for
the model, the length and half-width of the lower jaw, the length of the
in-lever for jaw closing, the angle between the line of action of the muscle
and the in-lever, the muscle length, the physiological cross-sectional area,
the pennation angle and the fibre length of the jaw closers
(A2A3' and A3'') are needed. For a
detailed description of the model, we refer to Van Wassenbergh et al.
(2005a
). Simulations were run
for a jaw closure starting at a gape angle of -32° and ending at
-11.8° when the jaws typically impact on the prey (values based on actual
kinematics of jaw closure in C. gariepinus; see Van Wassenbergh et
al., 2004
,
2005a
). Peak mouth closing
velocity was calculated for each individual and used as input for our
regression analysis. To calculate mouth closing velocities, we made the
following assumptions: (1) we set the activation rise time to 20 ms in the
smallest individual and scaled it with cranial length to the power of 0.31 in
accordance with James et al.
(1998
); (2) we set
Vmax (muscle lengths s-1) to 10 for the
smallest individual and scaled it with cranial length to the power of -0.34
(see James et al., 1998
).
|
To test if the observed slopes differed from the theoretical predictions of a geometric scaling model, the 95% confidence limits were calculated. If the predicted slope fell outside the calculated limits, the slope was considered significantly different from the predictions. All analyses were performed using SPSS (v.11.5).
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Results |
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The adductor mandibulae complex
The adductor mandibulae complex consists of the
A2A3' and A3'' muscles. This
muscle complex connects the suspensorium with the mandibula. Caudally, the
muscles A2A3' and A3'' are
separated from each other by the musculus levator arcus palatini
(Fig. 2A). The function of the
adductor complex is mouth closure (Adriaens
and Verraes, 1996; Adriaens et
al., 2001
).
The hyoid muscles
The m. protractor hyoidei is formed by the fusion of the posterior part of
the m. intermandibularis and the anterior part of the m. interhyoideus. The
protractor hyoidei connects the hyoid bars to the mandibula and the mandibular
barbels (Fig. 2B). The function
of the protractor hyoidei is mouth opening, elevation of the hyoid bars and
displacement of the mandibular barbels
(Adriaens and Verraes, 1997;
Adriaens et al., 2001
).
The m. sternohyoideus connects the pectoral girdle to the hyoid bars. The
sternohyoideus originates at the rostral aspect of the cleithrum and inserts
on the parurohyale (Fig. 2B).
The m. sternohyoideus contributes to mouth opening, the abduction of the
suspensoria and the depression of the hyoid
(Adriaens and Verraes, 1997;
Adriaens et al., 2001
).
The m. levator arcus palatini connects the lateral ethmoid, the
infraorbitale IV and the frontale to the suspensorium
(Fig. 2A) and is responsible
for the abduction of the lateral sides of the orobranchial cavity
(Adriaens and Verraes, 1997;
Adriaens et al., 2001
).
The m. levator operculi connects the dorsal part of the operculare to the neurocranium (Fig. 2A) and presumably causes the depression of the mandibula by the opercular four-bar system.
The hypaxial muscles attach at the posterior margin of the cleithrum (Fig. 2B) and cause the retraction of the pectoral girdle.
Scaling of external head dimensions
Whereas all head dimensions scaled with significant negative allometry
(Fig. 3), the slopes of the
regression of total length on standard length did not deviate from the
predictions of geometric similarity (Table
1).
|
|
Scaling of skeletal elements
Linear dimensions
The linear dimensions of the skeletal elements generally scale in
proportion to skull length in accordance with the predictions of the geometric
similarity model (Table 2;
Fig. 4). Notable exceptions are
the length of the hyoid and cleithrum, which scale with small, but
significant, positive allometry (Table
2; Fig. 4).
|
|
Angles
In contrast to the predictions of the geometric similarity model, all
slopes differed significantly from 0. Whereas the angle of the lower jaw and
hyoid display small, but significant, positive allometry, the angle of the
cleithrum decreased marginally with overall fish size
(Table 2;
Fig. 4).
Masses
The masses of all skeletal elements examined increased with a slope
significantly greater than the predicted slope of 3. Thus, in large fish, the
masses of the segments that need to be moved are relatively larger
(Table 2;
Fig. 4).
Scaling of muscles
When examining the scaling of muscle properties, it becomes apparent that
different scaling relationships can be recognised for different muscles (see
Table 3).
|
Muscle masses
Whereas the increase in the mass of the jaw adductors with cranial size did
not deviate from isometry, the mass of all other muscles examined scaled with
significant positive allometry (Table
3; Figs 5,
6).
|
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Physiological cross-sectional areas
Because of the scaling of muscle mass and fibre lengths, the physiological
cross-sectional areas in all muscles increased with significant positive
allometry with slopes being close to or larger than 3 (compare to the
predicted slope of 2; see Table
3; Figs 5,
6). Thus, larger fish have
relatively stronger muscles than smaller fish.
Performance
Our analyses show that bite force, as estimated by the static bite force
model (see Herrel et al.,
2002), increases with cranial length with a slope significantly
steeper than the expected slope of 2 (R2=0.96; slope=3.0;
intercept=-4.54; see Fig. 7A).
However, a closer inspection of the relationship of bite force to cranial
length suggests the presence of a breakpoint at a cranial length of
65 mm
(Fig. 7B). For fish with
cranial lengths greater than 65 mm only, bite force increases with a slope of
2.58 (R2=0.96; intercept=-3.72). Below the breakpoint,
bite force increases more rapidly with fish cranial size with a slope of 3.92
(R2=0.92; intercept=-6.05; see
Fig. 7B).
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Discussion |
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The shape of the hyoid, the lower jaw and cleithrum also changed with
increasing size for the fish included in our study. Specifically, whereas the
angle between the two hyoid bars and lower jaw elements increased with
increasing fish size, the angle between the two halves of the cleithrum
decreased. Given that the starting position of the hyoid is crucial in
determining suction performance in cichlid fish (see De Visser and Barel,
1996,
1998
), this suggests that
smaller fish may be optimising their feeding system towards suction feeding
(i.e. more adducted, and thus more potential for expansion). However, in
contrast to cichlids, a large part of the expansion of the buccal cavity in
C. gariepinus is due to ventral rotation of the hyoid rather than to
the abduction of the hyoid bars (Van
Wassenbergh et al., 2004
). Moreover, as the angle between the two
halves of the lower jaw also increases in larger fish, the relatively small
change in hyoid angle with size may just be part of an overall change in shape
of the cranial system in C. gariepinus. The change in angle of the
cleithrum, although significant (Table
2), is marginal and may reflect individual differences rather than
scale effects. Note, for instance, the distinct difference in shape of the
cleithra depicted in Fig. 4,
with one of the intermediately sized animals having the smallest angle.
Unexpectedly, the masses of the skeletal elements examined increased with
positive allometry relative to fish cranial length. As there is no a
priori reason to expect relative increases in segmental masses, this
suggests that the bones get more robust to be able to cope with the increased
muscular forces (see also Hernandez and
Motta, 1997). Histological sections of, for example, the hyoid
bars show an increasing formation of bony apolamellae, perpendicular to the
outer surface during ontogeny, thus also increasing hyoid rigidity (D.A.,
personal observation).
In contrast to data for other aquatic vertebrates
(Richard and Wainwright, 1995;
Hernandez and Motta, 1997
;
Robinson and Motta, 2002
), the
scaling of muscle masses in C. gariepinus differed for different
cranial muscles. Whereas the increase of the mass of the jaw closers did not
deviate from isometry, the masses of all other muscles increased with
significant positive allometry. This is not unique to the fish studied here,
as different scaling patterns were also observed for different muscles in
toads (Birch, 1999
).
Apparently, in aquatic vertebrates, no uniform scaling patterns of jaw muscle
mass are observed, as isometry (Richard
and Wainwright, 1995
; Robinson
and Motta, 2002
), positive allometry
(Hernandez and Motta, 1997
)
and mixed scaling patterns (present study) have all been documented. Thus,
predictions of the scaling of movements based on general models seem at first
sight problematic given the already large amount of variation observed in the
scaling of the underlying muscle mass.
Similarly to muscle masses, muscle fibre lengths also showed mixed scaling
patterns, with both negative allometric scaling (jaw closers, m. protractor
hyoidei) and isometry (other muscles) being present in C. gariepinus
(Table 3). Although we are
unaware of other studies examining the scaling of muscle fibre lengths,
sarcomere lengths do not appear to change with body size in fish
(James et al., 1998). If
sarcomere lengths remain constant, then this implies that larger fish have
relatively fewer sarcomeres in series in some of the important compressive (m.
protractor hyoidei, jaw adductors) muscles. This in turn suggests that the
velocity of jaw closure would increase with fish size but get
relatively slower in the largest fish (i.e. slope less than one).
However, the estimates of angular jaw closing velocity based on the dynamic
jaw closing model suggest that velocity actually decreases with size (see
Fig. 7). Moreover, kinematic
data on linear jaw closing velocities show that linear velocities are
independent of fish size (Van Wassenbergh
et al., 2005b
). These observations thus suggest that the actual
velocity of movement cannot be extrapolated from changes in muscle fibre
lengths.
The muscle cross-sectional area, however, increased with significant
positive allometry in all muscles examined, with slopes roughly equal to three
(Table 3). This is due to the
positive allometry or isometry in muscle mass combined with the negative
allometry or isometry in fibre length. The substantial positive allometry
observed for the muscle cross-sectional area, in turn suggests that the jaw
system in large fish is geared towards high force output. Indeed, our bite
force estimates indicate that static bite forces increase much faster with
fish cranial size than expected for simple geometrically growing systems
(Fig. 7A,B). The increase in
physiological cross-sectional area of the muscles may theoretically also
increase the velocity of the feeding event (see
Van Wassenbergh et al., 2005a)
although this is not fully supported by the results of the dynamic jaw closing
model (Fig. 7C,D). The positive
allometries of physiological cross-sectional areas observed for C.
gariepinus do not appear to be a general feature of the scaling in fish
cranial systems. Despite the fact that a positive allometry of cross-sectional
area (of the jaw adductors) was observed in the study by Hernandez and Motta
(1997
), in other suction
feeders such as the nurse shark, muscle cross-sectional area increased
isometrically with increases in linear dimensions (slope=2; see
Robinson and Motta, 2002
).
Thus, no general trend appears to be present despite the similarity in feeding
mechanism (all suction feeders) of these animals.
Effects of changes in morphology on performance
Our model calculations suggest that the observed changes in morphology have
a significant effect on two potentially important performance traits: bite
force and jaw closing velocity. Bite forces increase rapidly with fish cranial
size, especially in the smallest individuals
(Fig. 7B). Interestingly
enough, published diet accounts (see
Bruton, 1979) suggest that, for
smaller fish (roughly up to a total length of 300 mm), crustaceans, insects
and larval fish make up the bulk of the diet. At a size of 300 mm, the catfish
switches to a diet composed primarily of adult fish
(Bruton, 1979
). The size at
which this dietary switch occurs (300 mm total length; 75 mm cranial length)
corresponds closely to the size at which the break point appears in the
relationship between cranial length and bite force (±65 mm cranial
length). This suggests that the demand for high bite forces in smaller fish is
tightly linked to their diet of predominantly hard prey (i.e. crustaceans). At
the point where the C. gariepinus switches to evasive prey that are
swallowed whole, the increase in bite force with cranial length decreases
dramatically (see Fig. 7B).
Thus, the growth of the cranial system appears geared towards high bite forces
for smaller life history stages and is reflected in the significant positive
allometry of the physiological cross-sectional area of the jaw closer muscles
(Fig. 5).
Given the switch towards more evasive prey in the diet at a size of 75
mm cranial length, we could expect the feeding system to be geared towards
high jaw closing velocities. This appears, however, not to be the case, as
suggested by our model output. Rather, angular jaw closing velocity decreases
with cranial size across all fish. When analyzing data for small and large
fish separately, it becomes clear that jaw closing velocity is independent of
size in the smallest individuals but decreases rapidly (slope of -0.78) for
fish larger than 65 mm cranial length. At first sight, this appears rather
paradoxical as it is the larger fish that appear to be specializing on evasive
prey (and for which high jaw closing velocities would probably be relevant).
By contrast, the smaller fish seem to be exploiting the cranial system in such
a way that they benefit from a rapid increase in bite force without a
concomitant drop in jaw closing velocity. This should not be surprising as
previous model calculations have already suggested that a hypertrophy of the
jaw adductors has a positive effect on jaw closing velocity as well as static
bite force (Van Wassenbergh et al.,
2005a
).
Although our data on jaw closing velocity might initially suggest some
constraint on the further development of the cranial musculature, preventing
the larger fish from optimising their feeding system towards improved suction
performance, this is not necessarily so. Previous models have demonstrated
that, when C. gariepinus becomes larger, the expansive phase of
suction is prolonged, resulting in a longer sustained flow of water into the
mouth (Van Wassenbergh et al., in
press). This flow also reaches further in front of the mouth,
roughly proportional to head size. Moreover, forward dynamic simulations
indicate that the absolute distance from which a given prey can be sucked into
the mouth, as well as the maximum potential prey diameter, increases
substantially with increasing head size
(Van Wassenbergh et al., in
press
) despite the decrease in angular mouth closing velocity, as
estimated here. Consequently, the range of potential prey that can be captured
through suction feeding continues to increase during growth in C.
gariepinus, despite the observed decrease in jaw closing velocity.
Can suction-feeding kinematics be predicted based on scaling of morphology?
Previous models, such as the ones proposed by Hill
(1950) and Richard and
Wainwright (1995
), appear
inadequate in explaining the movements of structures, as the scaling of the
underlying morphology and function often deviates from the assumptions of
geometric similarity. However, if the scaling of morphology is known, as in
the present case, can the scaling of movements be predicted?
If the inertia of the system dominates the dynamics, acceleration capacity,
at least, should be predictable based on knowledge of the scaling of muscle
cross-sectional area and segmental mass
(O'Reilly et al., 1993). In
geometrically similar systems, this would imply a decrease in the capacity to
accelerate a load because of the discrepancy of the scaling of mass
vs cross-sectional area (O'Reilly
et al., 1993
). In C. gariepinus, the increase in
cross-sectional area of the muscles is roughly proportional to the increase in
segmental mass, and thus the acceleration of the cranial elements should be
identical across fishes of different sizes. Whereas in terrestrial systems
(e.g. Meyers et al., 2002
)
accelerations can indeed be predicted if the scaling of forces is known, in
the present case this does not hold as peak acceleration decreases linearly
with fish head size (Van Wassenbergh et
al., 2005b
). Additionally, our data for the scaling of fibre
length in C. gariepinus suggest that mouth opening velocity should
increase isometrically relative to cranial length. Thus, the time needed to
execute a proportionally similar displacement should be independent of cranial
length (e.g. mouth opening). Even though the magnitude of linear displacements
is indeed proportional to size, the time needed to execute a given
displacement increases with positive allometry (see
Van Wassenbergh et al.,
2005b
). Thus, our predictive ability appears limited even when the
scaling of morphology and functional properties is known.
However, it can be questioned whether inertial forces dominate in aquatic
systems and especially during rapid and explosive events such as suction
feeding. Previous workers (Muller et al.,
1982; Aerts et al.,
1987
), for instance, concluded that the hydrodynamic power
requirements, rather than inertial forces, are the predominant constraint
acting on the feeding system during the generation of suction. Indeed, also
for fish fast-starts, it was deduced that body-mass-specific hydrodynamic
power requirements increase with fish size and that, consequently,
size-dependent increases in muscle power output are needed and observed
(Wakeling et al., 1999
). If
hydrodynamic power requirements are indeed driving the scaling of the muscle
properties during explosive events such as suction feeding then the predictive
ability based on morphology alone may be intrinsically limited. This suggests
that more complex mechanical models that take into account the physical
constraints of generating negative pressures are needed to better understand
the scaling of power requirements during suction feeding
(Van Wassenbergh et al.,
2005b
). Moreover, such models may allow us to make more accurate
predictions of the scaling of feeding kinematics in aquatic vertebrates.
Conclusions
The data on the scaling of the feeding system in the African catfish,
Clarias gariepinus, show that neither the head nor the cranial
elements themselves scale according to geometric similarity models. Moreover,
relative to head size, distinct changes in the mass and configuration of the
feeding structures (muscles and bones) take place that affect feeding
function. Unexpectedly, different cranial muscles show different scaling
patterns, which ultimately all lead to a positive allometry of muscle
cross-sectional area relative to fish head size. Our data thus show that (1)
the scaling of the cranial elements cannot be predicted a priori,
even when the scaling of external head dimensions is known, (2) the scaling
patterns may differ for different muscles within a single functional system
and (3) the feeding system is optimised towards high bite force in the smaller
size classes, which is correlated to the natural diet of these animals. The
scaling of the feeding system in the largest fish (over 65 mm cranial length)
appears to be dictated by the need to produce high power outputs while
generating negative pressure in the buccal cavity during suction feeding.
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Acknowledgments |
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References |
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