Ontogeny of feeding function in the gray short-tailed opossum Monodelphis domestica: empirical support for the constrained model of jaw biomechanics
1 Department of Biological Sciences, Ohio University, Athens, OH 45701,
USA
2 Department of Biomedical Sciences, Ohio University College of Osteopathic
Medicine, Athens, OH 45701, USA
3 Department of Biological Sciences, University of Cincinnati, Cincinnati,
OH 45221, USA
* Author for correspondence (e-mail: biknevic{at}ohio.edu)
Accepted 29 November 2002
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Summary |
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Key words: bite force, ontogeny, gray short-tailed opossum, Monodelphis domestica
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Introduction |
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Craniofacial structures also differ in juvenile and adult mammals. Compared
with the adult masticatory apparatus, juveniles typically have absolutely
smaller masticatory musculature, house fewer teeth in their jaws, and have
substantially distinct jaw configurations. For example, puma Felis
concolor and spotted hyena Crocuta crocuta juveniles have short,
wide jaws compared to their adult counterparts
(Biknevicius, 1996), and this
shape difference contributes to the reduced bite force production of juveniles
(Binder and Van Valkenburgh,
2000
). Functional inadequacies of the juvenile masticatory
apparatus are initially counteracted by maternal provisioning of food (milk
and then solids) to the offspring. This extended period of parental care
allows more time for the development of the feeding apparatus, thereby
ensuring that weaned juveniles are adequately equipped to compete effectively
for meat, and thus increasing survival of offspring
(Mills, 1990
).
An extended period of parental care is not ubiquitous among mammals.
Juveniles of many species must forage independently for food soon after
weaning, as is the case for gray short-tailed opossums, Monodelphis
domestica. Indeed, juvenile M. domestica may be directly
competing with adults for similar foods as no resource-partitioning between
age groups has been documented (Parker,
1977). The present study explores the configuration of the upper
jaw of M. domestica in order to assess whether or not juvenile jaws
display adaptations, allowing for bite force production, as in adults. The
analysis is based on the constrained model of lever mechanics of the jaws.
Constrained model of lever mechanics
A constrained model of lever mechanics was developed in the 1970s and is
largely associated with the work of Walter Greaves
(1978,
1982
,
1988
; see also
Bramble, 1978
;
Spencer and Demes, 1993
;
Spencer, 1998
,
1999
). Three points of
resistance (`triangle of support') occur during unilateral biting: one at each
temporomandibular joint (TMJ) and one at the bite point
(Fig. 1A). The side of the jaw
where the bite occurs is known as the working (biting) side and the
contralateral side is the balancing side. The model assumes that the adductor
muscle resultant force (the bilateral sum of the adductor muscle forces,
Fm) is positioned to limit distractive forces at the TMJ,
as there is no evidence of regular loading of TMJs by large tensile stresses
(Hylander, 1979
). Accordingly,
the muscle resultant is assumed to lie within the triangle of support and no
further anterior than the distal margin of the caudalmost tooth (for more
details, see Greaves, 1978
;
Spencer and Demes, 1993
).
Furthermore, the adductor muscle resultant force lies in the sagittal plane
when jaw adductor muscles act bilaterally and equally.
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A line trajectory that originates at the balancing-side TMJ and passes
through a point representing a midline muscle resultant will intersect the
working-side toothrow at the Region I-II boundary
(Fig. 1A;
Spencer and Demes, 1993). This
intersection distinguishes the jaw into Region I anteriorly and Region II
posteriorly. According to the constrained model, maximal bite force magnitudes
obey different mechanical rules in Regions I and II.
Bite force magnitudes in Region I follow simple lever mechanics, that is, bite forces are inversely proportional to the leverage of the bite force but directly proportional to both the muscle resultant force and its leverage. Because the triangle of support is large, masticatory muscles can contract bilaterally and maximally when biting with teeth located in Region I. The muscle resultant is, therefore, located sagittally and no further anterior than the caudalmost molars. Bite force magnitudes are expected to increase caudally along Region I in response to decreases in mechanical advantage of the lever system (ratio of in-lever to out-lever, with the in-lever measured as the distance from the interglenoid line to Fm and the out-lever as the distance from the interglenoid line to the bite; Fig. 1B). Maximal bite force values are obtained at the Region I-II boundary.
Different mechanics control bite force magnitudes in Region II. According
to the constrained model's original conception, bite forces do not continue to
increase caudally across Region II, but rather are equal in magnitude to the
maximal value obtained at the Region I-II boundary
(Greaves, 1978). This is
because a midline muscle resultant would be excluded from the triangle of
support when biting with Region II teeth, and repositioning it within the
triangle of support necessitates a reduction in balancing-side muscle activity
(shifting the vector laterally toward the working-side jaw;
Fig. 1C). While maximal muscle
resultant forces are lower in Region II than in Region I, high bite forces are
maintained across Region II because lower muscle forces are paired with
reduced out-lever lengths. More recent work has challenged the expectation of
equal and maximal bite force within Region II. While electromyographic (EMG)
data of jaw adductor muscles in humans show the ratio of
balancing-side-to-working-side activity fell within Region II (as expected to
keep the muscle resultant within the smaller triangle of support), activity
levels of both working- and balancing-side activity levels fell when biting
with more posterior teeth, suggesting that bite force magnitudes may actually
decrease caudally within Region II
(Spencer, 1999
). Mathematical
modeling for estimating bite force magnitudes also anticipate a posteriorly
decreasing bite force within Region II
(Kieser et al., 1996
). This is
precisely the pattern found in one study of bite forces in humans
(Pruim et al., 1980
), although
other human studies found increasing bite forces posteriorly (Mansour and
Reynick, 1975; van Eijden, 1991).
One of the appeals of the constrained model of masticatory function is that
it enables specific predictions of bite force potentials in skulls of
differing configurations, as might occur during ontogeny. Bite force potential
at the Region I-II boundary is of great interest because this represents the
highest bite forces potential across the jaw
(Greaves, 1978;
Kieser et al., 1996
;
Spencer, 1999
). Mechanical
advantage, or the ratio of the lever arm length of the muscle resultant
(in-lever) to that of the bite point at the Region I-II boundary (out-lever),
strongly influences bite force maxima. While certain changes in craniofacial
dimensions have straightforward affects on mechanical advantage (e.g. a
shortened out-lever to the bite point increases mechanical advantage), others
are more complicated. For example, simply elongating the muscle resultant
lever arm (broken lines in Fig.
2A) does not improve mechanical advantage because it is
accompanied by a proportionately equivalent elongation of the Region I-II
boundary lever arm (see Discussion and Appendix I). Mechanical advantage may
also be affected by differential widening of the skull components. Increasing
interglenoid width (by shifting laterally the glenoid fossae; broken lines in
Fig. 2B) will shorten the
leverage to the Region I-II boundary because this configurational shift drives
a more acute trajectory to the working-side jaw (W. S. Greaves, personal
communication; Spencer, 1999
).
By contrast, the out-lever length to the bite point will decrease if the cheek
teeth move medially (narrowing the palate; broken lines in
Fig. 2C) because the shorter
trajectory from the balancing-side TMJ will intersect the working-side tooth
row more caudally. Narrowing the palate also has the effect of allowing higher
bite force magnitudes within Region II as a relatively smaller reduction in
balancing-side muscle activity is adequate to move the muscle resultant back
into the triangle of support when biting with the caudalmost teeth
(Spencer and Demes, 1993
).
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The constrained model has been used to explain the adaptive significance of
orofacial configurations as varied as Neandertals and Inuits
(Spencer and Demes, 1993) and
carnivorous marsupials (Werdelin,
1987
). And while it has also been used to evaluate age-dependent
craniofacial changes in carnivorans
(Biknevicius, 1996
) and to
explain the great biteforce potential in ferrets Mustela putorius
(Dessem and Druzinsky, 1992
),
the constrained model has never been rigorously tested in non-human mammals.
Therefore, the first objective of the present study is to provide empirical
support for the constrained model of jaw mechanics using voluntary bite force
data in adult gray short-tailed opossums Monodelphis domestica. Then,
ontogenetic changes in the jaw of M. domestica are documented in
order to explain differences in maximal bite force potential in M.
domestica juveniles and adults.
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Materials and methods |
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Bite force transducers were designed after the models of Binder and Van
Valkenburgh (2000) and McBrayer
and White (2002
). The
transducers were composed of two parallel steel plates (tines) that were
cantilevered to a brass handle. Four foil strain gauges were firmly bonded on
each surface of each tine at the cantilevered end, and these were configured
into a full Wheatstone bridge. The tips of the tines were tapered so to allow
specificity of tooth use. The distal end of each tine was also covered with a
rubber coating to protect the teeth of the opossums during forceful biting
(Rubberize-It!, Rhodes American, Chicago, IL, USA). Two bite force transducers
were built, each differing only in the dimensions of the tines: the distal end
of the smaller transducer (including the rubber coating) was 3.2 mm in width
whereas the larger transducer was 4.8 mm wide. Biting on the force transducer
caused the tines to bend toward one another and thus altered the voltage
output of the Wheatstone bridge. Analog outputs were amplified (National
Instruments SCXI 1000 and 1121, Austin, TX, USA) and then converted to a
digital format (National Instruments NB-M10-16L). Voltage changes were
recorded with a Lab View 5.0 (National Instruments) virtual instrument data
acquisition program (designed by S. M. Reilly, Ohio University, USA). Data
were collected at 500 Hz for 20 s. The transducers were calibrated each trial
day by simultaneously loading the tines with known weights (0.05-0.5 kg); the
resulting voltage outputs were then regressed against weight (in N) to
determine the calibration factor between the variables
(McBrayer and White,
2002
).
The opossums either readily bit on the bite force transducers or were induced to bite by pinching the nape of their necks (which caused them to open their jaws). Only unilateral bites were recorded. The position of the transducer along the jaw was determined videographically using a 60 Hz Hi-8 camcorder (Sony CCD-TR400). Three bite locations were identified: incisor or canine, premolar (excluding the deciduous premolar in juveniles), and Region II (molars plus deciduous premolar in juveniles; Fig. 3A). The tines of the smaller bite force transducer were sufficiently narrow to localize bite forces from individual molars within Region II in the adult opossums (M1, M2 and M3 only; the caudalmost molar was difficult to visualize).
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Morphological sample
Linear measurements of the upper jaws were obtained from longitudinal sets
of dorsoventral radiographs of Monodelphis domestica in order to
assess how geometric differences in the orofacial complexes of juveniles and
adults arise. These radiographs represented eleven individuals from three
different litters (Maunz and German,
1996). The animals were weaned at 48 days of age, similar to the
time of weaning in the wild (50 days of age;
Parker, 1977
). The animals
were radiographed at 2-day intervals starting from 50 days of age until 160
days old, after which radiographs were taken every 10-20 days until the
animals reached 395 days of age. Although M. domestica stops gaining
weight at around 250 days of age (Maunz
and German, 1996
), periodic radiography continued through 395 days
to ensure that skeletal growth was complete.
The radiographs were imported into the computer by either downloading digital images captured with a Kodak DC265 digital camera or scanning the radiographs directly into the computer using a Hewlett Packard ScanJet HDF scanner; these techniques produced equivalent results. Nine landmarks were identified along the skull, primarily on the upper jaw (Fig. 3B, Table 1). Of the nine, five were homologous landmarks on the juvenile and adult skulls (landmarks 1, 7, 3, 5 and 4). The remaining landmarks were influenced by dental eruption. The caudal borders of the distalmost molars (landmarks 2 and 6) necessarily shift caudally with successive molar eruption. Consequently, the assumed location of the midline muscle resultant (landmark 8), determined by landmarks 2 and 6, also shifts caudally with dental eruption. Finally, an oblique line was drawn from the right TMJ (landmark 7), through the midline muscle resultant; the intersection of this trajectory with the contralateral tooth row determines the location of the Region I-II boundary (landmark 9, or the location of maximal bite force potential).
Landmarks were digitized using the Thin Plate Spline digitizing program (TPS dig) and were used to define the following linear measurements (Fig. 3C). Palatal width was calculated as the width of the palate distal to P3. A baseline axis was drawn between the centroids of the glenoid fossae, the length of which was used as the interglenoid width. Jaw length was calculated as the perpendicular distance from the baseline axis to the I1-I1 interdental gap. The resultant adductor muscle force lever arm (in-lever) and the Region I-II lever arm (out-lever) were calculated as the perpendicular distances from the baseline axis between the glenoid fossae to landmarks 8 and 9, respectively.
Morphometric analyses
Reduced major axis regressions were run on log10-transformed
variables using the SYSTAT 9 statistics package
(Wilkinson, 1998). The first
set of regressions explored the relationship between skull width measurements
and jaw length. The second set evaluated the relationship among lever arms and
jaw length. This latter analysis was complicated because caudal tooth eruption
caused a punctuated change in the lengths of the both lever arm (see
Fig. 5B). Therefore, the data
were split into two samples according to eruption pattern (those with a fully
erupted M3, i.e. adults, versus those without, i.e.
juveniles and sub-adults) and separate regression coefficients were calculated
for each age group. Significant allometric patterns were identified by
inspection of the 95% confidence intervals for each regression slope (isometry
indicated by a slope of 1).
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Gompertz parameters were determined for jaw length, palatal width and
interglenoid width for each individual M. domestica. Significant
differences between these Gompertz parameters were quantified by running
one-way ANOVAs; patterns of variation were confirmed with the Tukey
post-hoc test using the NCSS statistics package
(Hintze, 1998). Parameters
were identified as being significantly different from each other if
P<0.05.
Maximal masticatory force potentials for M. domestica
juveniles and adults
Bite force data were also collected from eight M. domestica
juveniles (all female) that were 70-80 days of age, i.e. these animals were
weaned but were still anatomically and reproductively immature
(Parker, 1977;
Maunz and German, 1996
). These
juveniles were unrelated to the opossums used to obtain the adult bite force
sample. Body mass range was 30-40 g, mean 35.5 g. As with the adults, bite
force data were captured during multiple trials over several days, but only
the maximal voluntary bite force recorded for incisor/canine, permanent
premolars and Region II teeth (including the deciduous premolar) from each
individual was used in the analysis. Unfortunately, the smaller mouths of
juveniles provided limited visibility for discriminating Region II teeth,
therefore only pooled data on bites from Region II are reported. Bite force
data for juveniles were compared with those obtained for adults, with position
and age-related variation in maximal bite force determined via
repeated-measures ANOVA followed by Bonferroni pairwise comparisons using
SYSTAT 9 (Wilkinson,
1998
).
In order to further compare bite force potentials of juveniles and adults, it was assumed that biting at the Region I-II boundary represented a functionally equivalent event in juveniles and adults, because this is where the greatest maximal voluntary bite forces are expected to be generated according to the constrained model of jaw mechanics. Mechanical advantage, or the ratio of lever arm of the muscle resultant to that of the tooth located at the Region I-II boundary, was determined using dorsoventral radiographs of juvenile and adult M. domestica; animals were first anesthetized by isoflurane inhalation prior to radiography in order to minimize movement artifacts. Finally, scaling coefficients of mechanical advantage and bite force against body mass (Mb) were determined by reduced major axis regression. A slope of 0 meets the expectation of geometric similarity for mechanical advantage. Because muscle force is proportional to the cross-sectional area of the muscle, isometry expectations are met when muscle and bite forces scale with Mb0.67.
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Results |
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Variation of bite force along the jaw in adult M.
domestica
Maximal voluntary bite forces varied significantly with respect to tooth
position in M. domestica (Fig.
4; Table 2). Among
adults, bite force magnitudes of Region II teeth were, on average, greater
than those of Region I (P<0.002). Within Region I, bites generated
with the premolars were stronger than those with the incisors or canines
(P<0.02). By contrast, maximal bite forces did not vary
significantly within Region II, so that bites with M1,
M2 or M3 were equivalently strong
(P>0.17).
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Craniofacial allometry
The longitudinal growth series revealed that both palatal width and
interglenoid width scale with negative allometry relative to jaw length in
M. domestica (Fig. 5A;
Table 3). Furthermore, palatal
width scales with negative allometry with respect to interglenoid width.
Therefore, skull widths (particularly palatal widths) become relatively
narrower as M. domestica develop.
Scaling relationships for either the muscle resultant lever arm or Region I-II lever arm length against jaw length consistently demonstrated positive allometry in both juvenile and adult age-groups (Fig. 5B; Table 3). In other words, older individuals (within each age group and across both groups) exhibit relatively longer lever arms. Additionally, positive allometry was found for the regression of muscle leverage against bite point leverage, indicating that the elongation of Region I-II lever arm falls behind that of the muscle resultant through ontogeny.
Finally, positive allometry was found for regression of lever arm lengths on cranial width in both the juvenile and adult sample (Table 3). Consequently, compared with juveniles, adult orofacial proportions emphasize length over width.
Ontogenetic trajectories
Growth curves for jaw length, palatal width and interglenoid width obtained
from the longitudinal growth series are shown in
Fig. 6;
Table 4 lists the associated
Gompertz parameters. Palatal width at the onset of rapid growth (b)
is significantly smaller (P<0.001), indicating an earlier onset of
rapid growth for palatal width but delays in rapid growth of jaw length and
interglenoid width. The instantaneous rate of growth (I) of jaw
length is significantly larger than either width measurement. There was no
significant difference between the measurements in the rate of growth decay
(k). However, the time of growth cessation (Tf)
was significantly earlier in palatal width. Therefore, while palatal width has
an earlier onset of rapid growth it also ceases growth earlier than either
interglenoid width or jaw length. Furthermore, although growth of interglenoid
width and jaw length is delayed, both parameters have faster initial rates of
growth in comparison to palatal width.
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Age-based differences in masticatory forces
As was found in the adult sample, bite force magnitudes of Region II teeth
were significantly greater than those of Region I teeth in M.
domestica juveniles (P<0.002;
Table 2;
Fig. 4); however, juveniles did
not display caudally increasing bite forces within Region I because there were
no significant differences in bite forces obtained in the incisor/canine
region versus the non-Region II premolars.
Maximal bite forces in adults exceeded juvenile values when comparable dental regions were examined (P<0.001; Table 2). Scaling relationships of maximal bite forces generated by Region II teeth fit isometric expectations (Mb0.77, 95% confidence interval ±0.20). By contrast, mechanical advantage for biting at the Region I-II boundary scales with positive allometry (Mb0.34, 95% confidence interval ±0.26).
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Discussion |
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Reduced bite force potential when biting with
M1M3 in humans may be due to the decline in tooth
root surface area and complexity, which may limit the ability of the
posteriormost teeth to withstand high occlusal loads
(Spencer, 1998). Opossums may
circumvent these constraints because overall tooth size increases from
M1 to M3, potentially enabling M. domestica
adults to maintain fairly high activity levels of the working-side musculature
and therefore avoid the caudal decline in bite forces across Region II found
in humans. While the caudalmost molar of M. domestica is
substantially smaller than the other molars, we were unable to unequivocally
verify bite forces with this tooth and thus could not provide data to
empirically test Spencer's dental complexity hypothesis.
Age-based differences in masticatory function
Based on theoretical (Greaves,
1978; Kieser et al.,
1996
) and empirical (Spencer,
1998
; this study) grounds, bite force magnitudes using teeth
located at the Region I-II boundary are likely to represent the greatest
values across all teeth. Maximal bite forces are directly affected by the
adductor muscle resultant force (its magnitude and lever arm) and are
inversely related to the lever arm to the Region I-II boundary. If maximizing
bite forces provide animals with some selective advantage then jaws should be
configured with a high mechanical advantage for biting with teeth located at
the Region I-II boundary. Yet the present study shows that M.
domestica juveniles do not compensate for their absolutely smaller
masticatory muscles by enhancing their adductor muscles' mechanical advantage
as mechanical advantage was found to increase with body size
(Mb0.34) and, hence, with age.
Improvements in mechanical advantage with age in M. domestica can not be explained by simple increases in the leverage of the jaw adductor muscle resultant. The constrained lever model specifies that any rostral shift of the muscle resultant will necessarily drive the Region I-II boundary even further rostrally as the trajectory from the balancing-side TMJ becomes less acute (Fig. 2A). The resulting proportionate elongation of the bite point lever arm should negate any lengthening of the muscle resultant lever arm (Appendix I). In other words, simple changes to the in-lever length alone can not improve mechanical advantage. A review of other ontogenetic changes of the orofacial complex reveals that relative palatal narrowing has a potent effect on masticatory leverages in M. domestica adults (Appendix II). Specifically, the trajectory from the balancing-side TMJ intersects a narrower palate more caudally than in a wider palate, resulting in a more caudal Region I-II boundary and, thus, a reduced out-lever length (Fig. 2C). Therefore, the relatively narrow palatal widths of adults help to temper elongation of the outlever to the bite point that necessarily accompanies any increase in muscle lever arm length. This combination of elongated muscle leverage with a disproportionately smaller elongation of the bite point leverage results in an enhanced mechanical advantage for biting with the Region I-II teeth in M. domestica adults.
The increase in mechanical advantage with size (and age) reported here for
the jaw adductor muscle resultant of M. domestica concurs with
scaling relationships found for the superficial masseter and internal
pterygoid muscles in Rattus norvegicus (although the mechanical
advantages of other craniomandibular muscles in rats were not found to change
significantly with growth; Hurov et al.,
1988). What implications do lower mechanical advantages have on
juvenile animals? The present study has shown that bite forces scale
isometrically in M. domestica so that the poor leverage of the
juvenile masticatory systems must be compensated for by relatively greater
muscular effort. Indeed, jaw adductor resultant muscle force in M.
domestica is proportional to Mb0.43 (bite
force/mechanical
advantage=Mb0.77/Mb0.34),
falling below Mb0.67 expected for
geometrically-similar animals.
While the scaling of maximal bite forces with body mass provides a window
into understanding the physiological (muscular) cost of generating bite
forces, it is absolute bite force values that determine, to a large degree,
feeding performance. Data reported here verify that juvenile opossums have
absolutely weaker bite forces than adults. It is also unarguably true that the
components of the orofacial complex are absolutely smaller in juveniles.
Paradoxically, absolutely narrower palates may provide juveniles
with some functional bonus, i.e. narrow jaws have been associated with smaller
reductions in balancing-side muscle activity when biting with the teeth
located in Region II (Spencer and Demes,
1993; Spencer, 1995). If balancing-side activity need not drop as
much in narrow jaws then muscle resultant forces and bite forces for Region II
teeth are correspondingly enhanced. Hence, bite force magnitudes of M.
domestica juveniles might actually be even weaker if their dental arcades
were absolutely wider.
Although absolutely weaker bite forces of M. domestica juveniles
may appear to place younger animals at competitive disadvantage relative to
adults when feeding on similar foods, it is important to remember that force
magnitudes alone are unlikely to adequately reflect the ability of animals to
comminute food. Because crack development in foods is, in large part, a
function of the stress applied to the surface of the food, and because stress
is determined by the quotient of bite force and area of force application
(Lucas and Luke, 1984), the unworn cusps and shearing crests of newly erupted
teeth may enhance stress development in juveniles. In other words, the
topography of the newly erupted molariform teeth may partially compensate for
the lower absolute bite forces in juveniles. Other characteristics of
masticatory behavior may also help equilibrate juvenile and adult feeding
performance (e.g. several rapid bites may cause food fracture quickly even if
each bite is of weaker force). Finally, it is also possible that M.
domestica age groups partition foods by choosing items of different sizes
or toughness (e.g. grubs versus adult insects) even if they
customarily choose similar types of foods (e.g. invertebrates), as has been
demonstrated in other taxa (Dumont,
1999; Strait,
1993
).
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Appendix I |
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Similarly, in the adult condition,
tan+k=LMa/(
IGW)=LRIIa/(
IGW+
PW), resulting in an
adult mechanical advantage of (LMa/LRIIa) = IGW/(IGW+PW).
In other words, simply elongating the muscle resultant lever arm does not improve mechanical advantage because it is accompanied by a proportionately equivalent elongation of the Region I-II boundary lever arm.
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Appendix II |
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A key difference in the equations describing mechanical advantage is that
palate widths differ among juveniles and adults so that:
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Acknowledgments |
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References |
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