Biomechanical determinants of bite force dimorphism in Cyclommatus metallifer stag beetles

Abstract

In the stag beetle family (Lucanidae), males have diverged from females by sexual selection. The males fight each other for mating opportunities with their enlarged mandibles. It is known that owners of larger fighting apparatuses are favoured to win the male-male fights, but it was unclear whether male stag beetles also need to produce high bite forces while grabbing and lifting opponents in fights. We show that male Cyclommatus metallifer stag beetles bite three times as forcefully as females. This is not entirely unexpected given the spectacular nature of the fights, but all the more impressive given the difficulty of achieving this with their long mandibles (long levers). Our results suggest no increase in male intrinsic muscle strength to accomplish this. However, morphological analyses show that the long mandibular output levers in males are compensated by elongated input levers (and thus a wider anterior side of the head). The surplus of male bite force capability is realized by enlargement of the closer muscles of the mandibles, while overall muscle force direction remained optimal. To enable the forceful bites required to ensure male reproductive success, male head size and shape are adapted for long input levers and large muscles. Therefore, the entire head should be regarded as an integral part of male armature.

Full text

The Journal of Experimental Biology
© 2014. Published by The Company of Biologists Ltd | The Journal of Experimental Biology (2014) 217, 1065-1071 doi:10.1242/jeb.091744
1065
ABSTRACT
In the stag beetle family (Lucanidae), males have diverged from
females by sexual selection. The males fight each other for mating
opportunities with their enlarged mandibles. It is known that owners
of larger fighting apparatuses are favoured to win the male–male
fights, but it was unclear whether male stag beetles also need to
produce high bite forces while grabbing and lifting opponents in
fights. We show that male Cyclommatus metallifer stag beetles bite
three times as forcefully as females. This is not entirely unexpected
given the spectacular nature of the fights, but all the more impressive
given the difficulty of achieving this with their long mandibles (long
levers). Our results suggest no increase in male intrinsic muscle
strength to accomplish this. However, morphological analyses show
that the long mandibular output levers in males are compensated by
elongated input levers (and thus a wider anterior side of the head).
The surplus of male bite force capability is realized by enlargement
of the closer muscles of the mandibles, while overall muscle force
direction remained optimal. To enable the forceful bites required to
ensure male reproductive success, male head size and shape are
adapted for long input levers and large muscles. Therefore, the entire
head should be regarded as an integral part of male armature.
KEY WORDS: Lucanidae, Sexual dimorphism, Bite force,
Functional morphology
INTRODUCTION
Insect mandibles are often adapted into tools for various tasks: e.g.
fighting, digging, leaf-cutting, grooming and transporting liquids in
ants; penetrating the soft tissues of snails and attaching to amphibian
skin in ground beetles; cutting mature tree leaves and tearing and
shredding young tree leaves in saturniids (Bernays, 1998; Bernays
and Janzen, 1988; Ober et al., 2011; Paul, 2001; Wizen and Gasith,
2011). Male stag beetles (Lucanidae) are widely known for their
extraordinary mandibles: a conspicuous sexual dimorphism where
males can have mandibles in a variety of shapes that can be almost
as long as their own body, while female mandibles are small and
indistinct (Kawano, 2006). The small female mandibles are used to
dig in rotten wood (for oviposition) and in soil (when emerging from
their cocoon and to hide from predators), and possibly to pierce tree
bark to feed from sap runs (Percy, 1998; Tanahashi et al., 2009;
Tanahashi et al., 2010). Male stag beetles, however, fight each other
with their enlarged mandibles to gain access to females (Emlen,
RESEARCH ARTICLE
1University of Antwer p, Laboratory of Functional Mor phology, Universiteitsplein 1,
B-2610 Antwerp, Belgium. 2University of Antwerp, Laboratory of BioMedical
Physics, Groenenborgerlaan 171, B-2020 Antwerp, Belgium. 3Ghent University,
UGCT-Department of Physics and Astronomy, Faculty of Sciences, Proeftuinstraat
86, 9000 Ghent, Belgium. 4Ghent University, Department of Movement and Sport
Sciences, Watersportlaan 2, 9000 Ghent, Belgium.
*Author for correspondence (jana.goyens@uantwerpn.ac.be)
Received 5 June 2013; Accepted 5 December 2013
2008; Inoue and Hasegawa, 2013; Kawano, 2006; Shiokawa and
Iwahashi, 2000; Tatsuta et al., 2001). During such fights, opponents
try to grip each other and the winner will lift the other male and
throw it backwards (Shiokawa and Iwahashi, 2000) (authors’
personal observations; see supplementary material Movie 1). Male
stag beetles with larger mandibles have been shown to win these
male–male fights more often (Emlen et al., 2005; Hosoya and
Araya, 2005; Tatsuta et al., 2001).
Most research on bite performance and sexual dimorphism has
been performed on lizards. As in stag beetles, male lizards often
have larger body and head sizes (Herrel et al., 1995; Herrel et al.,
2007), the latter being correlated with higher male bite forces
(Herrel et al., 1999; Herrel et al., 2001; Herrel et al., 2007;
Verwaijen et al., 2002). It has been suggested that this sexual
dimorphism arose by sexual selection on male bite force and natural
selection on diet [prey size and toughness (Herrel et al., 1995; Herrel
et al., 1999; Vanhooydonck et al., 2010)]. The large male stag beetle
head may suggest a similar system, leading to higher bite force in
males compared with females. However, it remains unexplored
whether bite force, as such, determines fight outcome [such as
already observed, for instance, in several lizard species, field
crickets and fanged frogs (e.g. Emerson and Voris, 1992; Hall et al.,
2010; Husak et al., 2006; Huyghe et al., 2005; Lailvaux et al.,
2004)]. Indeed, fighting success in male stag beetles may rely
equally well on firm interlocking between the ornamented jaws and
the exoskeleton of the opponent without the need for a forceful
pinch [comparable to the interlocking of antlers in fighting red deer
stags (Clutton-Brock et al., 1979; Lincoln, 1972)]. If, however,
forceful biting should prove to be important in stag beetle contests,
male stag beetles face an additional problem: strongly elongated
mandibles mean long output levers that reduce the force
transmission from the closer muscles to the mandibular bite points.
In this case, other compensatory adaptations for the enlarged output
lever should be present in male stag beetles.
In this paper, we investigate the sexual dimorphism of the
mandibular apparatus and the bite force in Cyclommatus metallifer
Boisduval 1835 stag beetles. This Indonesian species belongs to the
genus Cyclommatus, which includes (together with the genus
Prosopocoilus) stag beetle species with the most oversized male
mandibles (Gotoh et al., 2012; Kawano, 2006). In order to assess the
effects of male sexual dimorphism on function and performance, one
should, ideally, compare with non-dimorphic conspecific males. In
(stag) beetles, comparison with properly scaled females (see Materials
and methods) can be used as a proxy for such a hypothetical non-
dimorphic male, as for species without sexual dimorphism (except for
the reproductive organs), males and females can hardly (if at all) be
discerned from each other (Hosoya and Araya, 2005; Kawano, 2006).
We hypothesize that males show an increased bite force
performance compared with females. Okada and Hasegawa (Okada
and Hasegawa, 2005) suggested that the stag beetle mating system
is not based on female choice. Therefore, it seems likely that the
Biomechanical determinants of bite force dimorphism in
Cyclommatus metallifer stag beetles
Jana Goyens1,2,*, Joris Dirckx2, Manuel Dierick3, Luc Van Hoorebeke3and Peter Aerts1,4

The Journal of Experimental Biology
1066
mandibular system is optimized for fight performance. As
mentioned, this should be accompanied by further adaptations of the
mandibular system, e.g. as observed for the cheliceral system in
camel spiders (van der Meijden et al., 2012). In this regard, the
specific working hypotheses that we tested are: (1) males have
prolonged input levers to compensate for their long output levers,
(2) male mandibular muscles are geometrically advantageous
compared with those of females (in terms of size and working
direction), and (3) these muscles are intrinsically stronger than
female muscles.
RESULTS
Bite performance and length tension relationship
Fig. 1 shows a representative example of the bite measurements, and
illustrates the high repeatability of the bite tests. During the 30 s
intervals, successive bursts of activity occur.
Maximal recorded bite force (over all mandible positions) is
higher for males than for females (6.9±2.0 and 1.1±0.4 N,
respectively). Normalized bite force (dimensionless) is also
significantly higher for males than for females (849±164 and
285±81, respectively; Wilcoxon rank sum test: P<0.001).
To investigate the influence of muscle length on tension, male
mandibular angles were converted into muscle lengths. Over the
working range of mandible positions, a linear relationship between
mandibular angle and muscle length exists: muscle length (mm) =
3.8 rad + 7.1 mm (linear regression: P<0.001).
Fig. 2 shows the relationship between muscle length (obtained
with the above equation) and maximal bite force. A negative
relationship between force and muscle length exists: males produce
the highest forces with their mandibles almost closed (see Fig. 2).
Video analysis of male–male fights shows that they bite most
frequently with 4.1±2.0 mm between their bite points. Within the
corresponding range of normalized muscle lengths, the highest bite
forces are measured (see Fig. 2, shaded area).
Morphology and morphometrics
Micro-CT reconstructions give us an insight into the interior of the
head (see Fig. 3). The general anatomy of the head is similar to that
of other beetles (Gorb and Beutel, 2000; Li et al., 2011). The
mandibles articulate by a hinge axis, formed by a pair of condyles.
The closer muscle is cone shaped and is distinctly larger than the
opener muscle: it almost completely fills the head capsule.
Table 1 provides the input and output lever lengths as well as the
lever ratios. In absolute terms, as well as expressed relative to the
width of the posterior part of the body [mesothorax + metathorax +
abdomen (MMA); see Fig. 5], the males have longer levers than the
females. The lever ratio is not significantly different between males
and females, as shown by the nonparametric Wilcoxon rank sum test
(P=0.051). Given the low P-value and the low statistical power of
the test, this indicates that the long input levers compensate for the
long male output levers, albeit probably not completely.
Muscle geometry
Male as well as female mandible closer muscles almost fill the entire
head (see Morphology and morphometrics, above). However,
because head shape and relative size differ, the normalized
physiological cross-sectional area (PCSA) of the male closer muscle
is almost 2.5 times larger (see Table 1).
The force components of the closer muscle in the x-, y- and z-
directions are given in Table 2, averaged over the range of in vivo
used mandible positions (see Fig. 4). The absolute value of the y-
component lies very close to 1 for both males and females,
indicating that the muscle force vector is well aligned with the y-
axis, which is the optimal direction. This holds true in the entire
working range of mandible position (i.e. small standard deviation).
Comparison of measured and predicted bite forces
The theoretical ratio of male and female bite force can be predicted
(according to Eqn 3) using the geometrical properties of the two CT-
scanned individuals. The weight-normalized values of PCSA are used:
This is close to the ratio of maximal measured bite force for these
two individuals (also normalized to MMA weight):
Muscle stress
We measured maximal bite forces of 6.5 and 1.6 N for the male and
female individuals, respectively, that were used for micro-CT
scanning. This corresponds to (maximal) muscles forces of 9.9 and
=××=
F
F
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2557
0.96
0.95
0.28
0.34 2.03. (1)
bite,predicted,male
bite,predicted,female
==
F
F
7.9
3.9 2.06 . (2)
bite,measured,male
bite,measured,female
RESEARCH ARTICLE The Journal of Experimental Biology (2014) doi:10.1242/jeb.091744
List of symbols and abbreviations
Fbite,measured measured bite force, tangent to the orbit of the bite point
Fbite,predicted calculated bite force
Fmuscle calculated muscle force
Fpmeasured bite force, perpendicular to the bite plates
Fpforce perpendicular to the bite plates
MI muscle insertion point on mandible
MMA posterior body part, mesothorax + metathorax + abdomen
PCSA physiological cross-sectional area
riinput lever vector
rooutput lever vector
riinput lever length
rooutput lever length
αmandibular angle
β3D angle between Fbite,measured and ro
γ3D angle between Fmuscle and ri
Fig. 1. Example of force measurements in Cyclommatus
metallifer.Three trails from the same male individual,
obtained at a bite plate distance of 5 mm. The arrow
indicates the overall maximum of 7.22 N.

The Journal of Experimental Biology
2.4 N. Divided by attachment area, this gives almost equal
(maximal) muscle stresses of 18 N cm−2for the male and 17 N cm−2
for the female specimen.
DISCUSSION
Similar to how red deer stags grow large antlers to defend harems
of females, male stag beetles bear heavy and long mandibles to fight
for mating opportunities (Emlen et al., 2005; Inoue and Hasegawa,
2013; Kawano, 2006; Kruuk et al., 2002; Shiokawa and Iwahashi,
2000; Tatsuta et al., 2001). The longer the mandibles, the higher the
chances of winning (Emlen et al., 2005; Tatsuta et al., 2001). The
same was observed for male dung beetles, who try to probe and
dislodge intruder males with their horns in narrow burrows (Emlen,
2008). It is likely that both stag beetles and dung beetles take
advantage of longer mandibles or horns by extending their reach
towards opponents. However, this mandibular elongation could
come at a cost if high bite forces are required, because of a
disadvantageously long output lever. Because our study species, C.
metallifer, belongs to one of the genera with the relatively longest
male mandibles (Gotoh et al., 2012; Kawano, 2006), it is most prone
to a reduced force output. Therefore, we expect distinct adaptations
if high bite forces are generated.
Our bite force measurements show that male C. metallifer
individuals indeed bite more forcefully than female specimens. Even
when normalized to size, a threefold intersexual difference in
maximal bite force exists. So males have, indeed, stepped up their
bite force performance, which indicates that forceful biting is
important for male beetles. This is further supported by the finding
that males use their mandible muscles during fights at optimal or
close to optimal fiber lengths (see Fig. 2). As with lizards, they
probably need the increased bite force in the first place for
male–male combat. Males may also benefit from high bite forces
during the mating itself, by preventing females from escaping. The
same has also been suggested for lizards (Herrel et al., 1995). In
lizards, sexual bite force dimorphism is known to be caused by
natural selection as well, through selection for niche divergence to
lower intersexual competition (Herrel et al., 1995; Vanhooydonck et
al., 2010). This is most probably not the case for stag beetles,
because males do not use their mandibles for feeding (Tanahashi et
al., 2009; Tanahashi et al., 2010). Interestingly, the muscle force
males exert depends on the used bite point: males use less muscle
force when biting at the very tips of the mandibles (J.G., J. Soons,
P.A. and J.D., unpublished data). Whether this has a behavioral or a
mechanical (material failure) cause will be the subject of future
research.
To investigate the adaptations enabling such high bite forces, we
micro-CT-scanned a specimen of each sex. The bite force ratio of
these individuals equals 2.06. When we calculate the same ratio
using geometrical data, we arrive at an almost identical value of
2.03. As it seems very unlikely that both sexes perform at the same
relative submaximal level in the in vivo experiments, we assume that
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RESEARCH ARTICLE The Journal of Experimental Biology (2014) doi:10.1242/jeb.091744
5.5 6
6.5 7
7.5 8
11
10
9
8
7
6
5
4
3
Male bite force, measured (N)
Muscle length (mm)
Fig. 2. Male bite force as a function of muscle length. Mean ± s.d. of nine
specimens are shown. The shaded area indicates the range of most
frequently used muscle lengths in fights (with 4.1±2.0 mm biting point
distance).
Fig. 3. Micro-CT renderings of Cyclommatus metallifer stag beetle
heads. For a male (A) and a female (B) specimen, a mandible (1), cone
shaped mandible closer muscle (2), condyle of mandible rotation hinge (3)
and muscle insertion on the mandible (4) are indicated.
Tab le 1. Absolute and normalized values of lever length, lever ratio and physiological cross-sectional area (PCSA) of the closer muscle in
the stag beetle Cyclommatus metallifer
Absolute value Normalized value (dimensionless)
Male Female Male Female
Input lever length (mm) 3.4±0.4 1.0±0.12 36.8±2.6 14.0±1.7
Output lever length (mm) 12.9±3.2 3.1±0.20 140.6±1 41.7±2.8
Lever ratio 0.28±0.07 0.34±0.04
PCSA (mm2) 54.71 13.95 6220 2557
Lever lengths are normalized to MMA mass1/3 and PCSA to MMA mass2/3, where MMA is the mesothorax + metathorax + abdomen. The lever lengths and
lever ratios are averaged for nine males and 10 females; data are means ± s.d.

The Journal of Experimental Biology
1068
the in vivo performance reflects maximal performance. Also, the
estimates for maximal muscle stress in males and females are almost
identical (18 and 17 N cm−2, respectively) and lie well within the
range of calculated and measured stresses of (synchronous) insect
muscle (2 to 80 N cm−2) (Bennet-Clark, 1975; Ellington, 1985; Full
and Ahn, 1995; Usherwood, 1962; Wheater and Evans, 1989). All
of these arguments not only support the followed procedure to
estimate PCSA, but also suggest that there is no intersexual
difference in the physiology of the jaw closers of stag beetles, and
that the characteristics of these closer muscles are not specialized
compared with other (synchronous) insect muscles. Hence, other
factors are required to explain the size-normalized male/female ratio
in biting force.
The accordance of measured and geometrically predicted force
ratios shows that sexual selection altered the geometry and
dimensions of not only the male mandibles, but also the entire male
head. First, the length of the input levers has increased to
compensate for the elongated output levers, keeping the lever ratio
close to that of females. Functional adaptations of the input lever
have previously been observed for other beetle species: larvae of
detritus-grinding and snail-cracking species were shown to have
larger input levers than larvae of a liquid-feeding species (Gorb and
Beutel, 2000). And in camel spider chelicerae, the lever system is
adapted to their function (digging in compact soil versus crushing
hard prey) (van der Meijden et al., 2012). Second, males have larger
closer muscles than females. The morphology of the posterior part
of the insect head capsule (where the closer muscles attach) is
known to be closely related to (or even ontologically caused by) the
size and shape of the mandible closer muscle (Gorb and Beutel,
2000; Li et al., 2011; Paul, 2001). Our observations of broad male
stag beetle heads led us to hypothesize that males have relatively
larger muscles than females. PCSA calculations confirm this: male
attachment surfaces are more than twice as large as those of females,
theoretically enabling more than twice as much force production.
This is comparable to the finding of enlarged jaw adductor
musculature in Anolis and Podarcis lizards, causing elevated bite
force performance (Herrel et al., 1995; Herrel et al., 2007; Huyghe
et al., 2009). Despite the hypertrophy of the male stag beetle
adductor muscles, they remain well aligned with the optimal
direction. This indicates that the male head shape changed in such a
way that the same percentage of the total muscle force remained
useful.
In order to reproduce, a male stag beetle needs large mandibles and
forceful bites. We showed that no physiological adaptations of the
mandible closer muscles are necessary to arrive at the observed
intersexual bite force dimorphism. The large and well-aligned male
muscles combined with increased input levers to compensate for the
elongated output levers offer a sufficient explanation. This, however,
required substantial geometrical differentiation of the male head.
Therefore, the entire male stag beetle head (and not only the male
mandibles) should be seen as part of male weaponry, as suggested by
Shiokawa and Iwahashi (Shiokawa and Iwahashi, 2000). When
assessing the effects of this sexual dimorphism on other important
ecological functions (such as locomotion), head size and morphology
might become even more important than jaw size and morphology.
MATERIALS AND METHODS
Animals
Adult C. metallifer individuals were obtained from a commercial dealer
(Kingdom of Beetle, Taipei, Taiwan). The animals were individually housed
in plastic containers (39×28×14 cm, length × width × height), at a
temperature of between 20 and 25°C. They were fed beetle jelly and water
ad libitum.
Bite force measurements
Bite forces were obtained from nine male (1.36±0.28 g) and 10 female
(0.55±0.10 g) beetles with an isometric Kistler force transducer (type 9203,
Kistler Inc., Winterthur, Switzerland) connected to a Kistler charge amplifier
(type 5058A). The force transducer was mounted in a setup with two small
plates that were grasped by the mandibles, thus enabling us to measure bite
forces. Spacing between the bite plates could be adjusted [for a detailed
description of the experimental setup, see Herrel et al. (Herrel et al., 1999)].
The analog signals were A/D converted (USB-6009, 14-bit, National
Instruments, Austin, TX, USA) and recorded at a sample frequency of
200 Hz using a purpose-written LabVIEW routine (LabVIEW 9.0.1f2, 32-
bit version, National Instruments). When a defensive response was
provoked, males bit the bite plates with the large protrusions positioned
halfway along the mandibles (P; see Fig. 5). In real fights, males also
regularly (but not exclusively) use the mandibular protrusions. These were
selected as the experimental bite point because: (1) they provide point
contact with the bite plates, (2) they guarantee standardized experimental
conditions within and between individuals (i.e. similar location of force
application) and (3) males were eager to bite with them. Females bit with
the tip of their mandibles, the only possibility given their jaw size and
morphology. The minimal distance between the bite plates (imposed by the
constraints of the setup) was 3 mm for both sexes. The maximal possible
bite plate distance (behaviorally imposed: when the spacing became too
large, specimens refused to bite) was 5 mm for females and 12 mm for
males. We varied the distance between the bite plates between these
boundaries with intervals of 1 mm. The sequence was determined randomly.
For every plate distance (and hence mandibular angle) three recordings of
30 s were made, and the highest force observed in these 90 s recording was
retained as the maximal bite force for that individual.
RESEARCH ARTICLE The Journal of Experimental Biology (2014) doi:10.1242/jeb.091744
Table 2. x-, y- and z-components of the global force direction of the
closer muscle of the mandible of one male and one female
Cyclommatus metallifer
Male Female
x-component 0.27±0.04 0.28±0.14
y-component 0.96±0.01 0.95±0.05
z-component 0.21±0.02 0.09±0.02
Means and standard deviations over the range of possible mandible
positions are given.
Fig. 4. Micro-CT segmentations of male Cyclommatus metallifer stag
beetle mandibles. (A) Male mandible and the associated closer (cm) and
opener muscles (om). The mandible is shown in the CT-scanned position (g)
and with 3, 6, 9 and 12 mm between the bite points (f, e, d and c). The
muscle force vectors associated with these mandible positions are also
shown. (B) Enlargement of A, with designation of the muscle force vectors.
The x- and y-axes are shown for mandible position c. The location of the
rotation hinge (H) is the same for all mandible positions.

The Journal of Experimental Biology
The degree of mandibular abduction (imposed by the bite plate spacing)
was taken into account, as effects of muscle length according the
length–tension relationships could be expected. We defined the mandibular
angle as the angle between the long axis of the body and the line from the
rotation axis of the mandible to the bite point (α, see Fig. 5). This angle was
determined on high-resolution digital photographs using GIMP (GNU Image
Manipulation Program 2.6.11; open source software; average precision
males: 30 μm pixel–1; average precision females: 20 μm pixel–1). The force
transducer only measures force components perpendicular to the bite plates
(Fp; see Fig. 5). The real bite force, tangent to the orbit of the biting point
(Fbite,measured, see Fig. 5), was derived by dividing Fpby the cosine of the
mandibular angle α. For male–female comparisons, normalization was
necessary because of the large size difference between the sexes. Given the
strong sexual dimorphism of the anterior part of the body, bite forces were
normalized to the weight (in N) of the posterior part of the body (MMA),
the size of which can safely be assumed to be entirely independent of the
mandibular apparatus. The MMA was weighed with an analytical
microbalance (Mettler Toledo MT5, Greifensee, Switzerland; precision:
1 μg) after killing the specimens.
Levers
Male and female mandible morphology differ greatly. To enable intersexual
bite force comparison, the lever mechanics have to be taken into account.
The lengths of the input lever (ri, between the mandibular hinge joint and
the muscle insertion point on the mandible MI; see Figs 3, 5) and output
lever (ro, between the mandibular hinge joint and the biting point; see Fig. 5)
were measured from scaled photographs in GIMP. To enable male–female
comparison of the levers, they were normalized to MMA mass (used as
proxy for MMA volume; i.e. identical overall MMA densities are assumed),
raised to the power of 1/3. Lever ratios (mechanical advantage; input lever
divided by output lever) were also calculated.
Micro-CT scans and segmentation
The anterior portion (head + prothorax) of each speciment was fixed in
Bouin’s solution (Sigma-Aldrich, St Louis, MO, USA) for 2 weeks. Then,
they were brought to 100% ethanol (in steps of 70, 80, 90 and 96% ethanol)
and subsequently stained in a 1% iodine solution (I2dissolved in 100%
ethanol; Sigma-Aldrich) for 20 days (adapted from Metscher, 2009). Finally,
the samples were thoroughly washed with and stored in 100% ethanol.
One male and one female specimen were removed from alcohol and
mounted in a falcon tube with cotton wool for micro-CT scanning. A
custom built X-ray micro-CT scanner of medium energy from UGCT, the
Centre for X-ray Tomography of Ghent University, was used (Masschaele
et al., 2007). For the male sample, the X-ray source was operated at
130 kV and 107.7 μA, for the female sample 120 kV and 116.7 μA were
used, both with an aluminum filter of 1 mm thickness. For both samples,
1200 projections with an exposure time of 2 s each were recorded over
360 deg. The section images were reconstructed with the custom-made
software package Octopus (Vlassenbroeck et al., 2007). This resulted in
reconstructed images of 790×805 pixels for the male specimen and
760×750 pixels for the female specimen, and voxel sizes of 38 and 13 μm,
respectively. Three-dimensional renderings were generated using the
commercial package VGStudioMAX (Volume Graphics, Heidelberg,
Germany). Unless otherwise specified, all further calculations were
performed only for these two specimens.
Using the reconstructed slice images, one mandible and the associated
closer (adductor) muscle (craniomandibularis internus; see Fig. 6) of each
sample were segmented in Amira (Amira 5.4.3; 64-bit version; VSG
systems, Mérignac, France). The attachment surface (see Fig. 6) of the closer
muscle at the posterior side of the head was segmented separately, and a
smooth surface model was created.
Muscle size, force direction and muscle stress
The muscle fibers converge from the convex (nearly spherical, see Fig. 6)
head capsule to the MI (see Fig. 3). Therefore, the size of the attachment
surface (see Fig. 6) can be used as a proxy for the PCSA of the muscle and
hence of force production. To assess the area of the attachment surface, its
surface model was converted into a triangulated surface mesh in Geomagic
(Geomagic 10, Morrisville, NY, USA; male specimen: 4894 triangles;
female specimen: 5322 triangles). In MATLAB (MATLAB R2012a,
7.14.0.739, 64-bit version; Natick, MA, USA), we calculated the area of
each triangle using the 3D coordinates of its vertices, to obtain the total area
of the attachment surface in males as well as females. This area was
normalized to MMA mass, raised to the power of 2/3.
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RESEARCH ARTICLE The Journal of Experimental Biology (2014) doi:10.1242/jeb.091744
Fig. 5. Dorsal photographs of Cyclommatus metallifer stag beetles. For
a male (A) and female (B) individual, one mandible is marked (m). Body parts
below the dashed line are the mesothorax, metathorax and abdomen (MMA).
Note that the images are scaled to identical MMA length. For the male, a bite
point (P), input and output levers (riand ro), mandibular angle (α) as well as
the position of the rotation hinge (H) are indicated. The measured bite force
(Fp, perpendicular to the bite plates) and the actual exerted bite force
(Fbite,measured, tangential to the orbit of the bite point) are also shown.
Fig. 6. Micro-CT segmentations of Cyclommatus metallifer stag beetle
heads. For a male (A) and female (B) head, the left mandible, the closer
muscle (c) and its attachment surface (a) are shown, as well as the rotation
hinge (H) and the x- and y-axes used to calculate the direction of the total
muscle force vector. A part of the associated opener muscle is also visible
(orange). The right mandible is depicted transparently.

The Journal of Experimental Biology
1070
For optimal force transmission towards the output lever, the combined
force of all muscle fibers of the closer muscle should be directed
perpendicular to the rotation axis and the input lever (along the y-axis in
Fig. 6; xaligned with the input lever, zpoints downwards, following the
rotation axis, and y=z×x). Muscle force components in the x- or z-direction
have no influence on force output at the biting point, but they do induce
stress on the hinge joint suspension and can, therefore, be expected to be
minimized. We estimated the global muscle force direction by summing the
unit vectors from the MI to every vertex of the triangular mesh of the
attachment surface. The total muscle force vector was divided by its norm
to create a unit vector. This calculation was repeated for the other MI
positions that correspond to the different mandibular abduction angles,
covering the range of mandible positions in the experiments and CT scans
(male: 0.8 to 12 mm between biting points in steps of 1 mm for males; −1.5
to 5 mm in steps of 0.5 mm for females; see Fig. 4).
Using only these geometrical data (muscle attachment area, 3D orientation
of the hinge and lever lengths), it is possible to predict male to female bite
force ratio:
where ymale and yfemale are the y-component muscle force unit vectors for
male and females, respectively, and Rmale and Rfemale are the male and female
lever ratios, respectively.
Besides geometrical differences, male muscle stress could also be
enhanced in order to increase bite performance. Muscle stress is defined as
the muscle force per cross-sectional area of a muscle. Muscle force Fmuscle
was obtained from the moment balance:
where riand roare the 3D input and output lever vectors, 1⁄2Fbite,measured is
the maximal bite force of one mandible of the scanned individuals, and β
and γ are the 3D angles between the force vectors and their respective levers,
calculated from 3D coordinates on the surface model. Assuming that
animals make an effort to bite maximally, the calculated muscle stress
(Fmuscle/PCSA) represents maximal (isometric) stress.
Length–tension relationship
Because force output is influenced by muscle length (Gordon et al., 1966),
we wanted to convert the range of mandibular angles in the male biting
experiments into muscle lengths. Knowing the total muscle force vector
enabled us to calculate the distance between the MI and the point at which
the resultant force vector crosses the attachment surface. This gives the
length of an imaginary muscle fiber with the direction of the global force
vector that could replace the real closer muscle. We repeated this for the
same range of MI positions as for the force direction calculation (see Fig. 4).
The resulting relationship between mandibular angle and muscle length was
used to convert the mandibular angles of all nine males in the biting
experiments into muscle lengths. This enabled us to plot the force
measurements in function of muscle length. Given the limited range of
gaping angles for the females (see above, three bite widths only), their
length–tension relationship could not be determined.
To determine the most frequently used muscle lengths, high-speed
recordings were made of fighting males (combinations of all nine males).
Two beetles were placed in an open-top arena (15×15 cm), with a base
covered with smooth cork for grip. Four mirrors functioned as walls and
were placed at an angle of 45 deg, so five views could be recorded with one
camera (Redlake HR1000; 125 frames s−1). Twenty-three recordings of
males who bit an opponent were obtained.
In each of these recordings, the distance between the medial mandibular
protrusions (the biting points in the force measurements) relative to the
distance between the eyes was determined in GIMP. Absolute distances
between the eyes were measured on scaled digital photographs of the
beetles, which enabled us to infer the absolute distance between the medial
=××
y
y
R
R
F
F
PCSA
PCSA ,(3)
bite,predicted,male
bite,predicted,female
male
female
male
female
male
female
×= ×FrF r
1
2,(4)
muscle i bite,measured o
=⋅⋅ β ⋅ γ
⎡
⎣⎤
⎦
FF r r
1
2sin( ) / sin( ) , (5)
muscle bite,measured o i
mandibular protrusions. These distances were converted into mandibular
angles and subsequently into muscle lengths.
Acknowledgements
We thank Dr Kristiaan D’Août for writing the LabVIEW routine for recording the
force measurements and Josie Meaney for proofreading an earlier version of the
manuscript.
Competing interests
The authors declare no competing financial interests.
Author contributions
J.G. conducted the bite experiments, segmented the micro-CT scans and drafted
the article. J.G., P.A. and J.D. were involved in the analyses and interpretation of
the findings and revised the article. M.D. and L.V.H. executed the micro-CT scans,
CT reconstruction and 3D renderings.
Funding
The present study was funded by BOF grant [ID BOF UA 2011-445-a] of the
Research Council of University of Antwerp.
Supplementary material
Supplementary material available online at
http://jeb.biologists.org/lookup/suppl/doi:10.1242/jeb.091744/-/DC1
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