Geometry of elytra opening and closing in some beetles (Coleoptera, Polyphaga)
1 Schmalhausen-Institute of Zoology, 15 B. Khmelnitsky Str., Kiev 30, 01601,
Ukraine
2 Nanjing University of Aeronautics and Astronautics, 29 Yudao Street,
Nanjing, Jiangsu 210016, China
* Author for correspondence (e-mail: leopup{at}izan.kiev.ua)
Accepted 14 June 2005
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Summary |
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Broad opening and closing was video recorded in beetles, tethered by the mesothorax, and has been analyzed frame by frame. For tracing, small dots or straw arms were glued to the elytra. Opening and closing traces coincided. The trace of the elytron apex was a flat circular arc about the axis of abductionadduction (AAA). The rising hemiaxis pointed contralaterad. The AAA was tilted forwards in Melolontha hippocastani, Allomyrina dichotoma and Prionus coriarius but backwards in Chalcophora mariana. In Cetonia aurata, the AAA had a low elevation and a strong backward orientation. If another elytra-fixed point was traced in addition to the apex (in M. hippocastani and P. coriarius), then secondary rotation about the sutural edge (supination on opening) occurred. Modeling of abductionadduction revealed that the elytron rose on opening if the AAA pointed contralaterad. The more the AAA was tilted forward, the more negative was the attack angle of the open elytra. The negative attack angle was partly compensated by positive body pitch and, more effectively, by supination of the costal edge about the sutural edge.
The initial stage of opening included elevation of closed elytra (by 1012°) and partition to the sides, combined with an inward turn (<23°). Axis of rotation at this stage presumably coincided with the AAA. Movement of one elytron with respect to the opposite one at the beginning of opening followed the shallow arc convex down. The geometry of this relative movement describes the initial partition of the elytra and release of the sutural lock.
Key words: biomechanics, coadapted structure, Coleoptera, Polyphaga, elytra, elytral lock, insect flight
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Introduction |
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The elytra in beetles are the forewings, modified for a protective function. The rigid elytra reliably seal the wings and abdominal spiracles inside the subelytral space. This adaptation allows beetles to penetrate soil, bark, wood and water, an enriched diversity of ecological niches, and facilitates enormous adaptive radiation. Sealing is provided by many locks between the perimeter of the elytra and the body, between the elytra and the underlying wings and between the two elytra themselves (down their anal edges) or by the suture (see details and references in Discussion).
Physiological study of elytral movement is hindered by the covert position of the mesothorax in beetles: for example, of the whole mesotergite, only the scutellum is exposed. Suggestions on the role of mesothoracical muscles were derived from anatomical observations on separate muscles, without understanding their action in concert.
Mobility of the elytra is simple compared with that of the hind wings.
Indirect fibrillar muscles, which drive the wings, are absent from the
mesothorax. If elytra do beat in synchrony with wings during flight, they do
so passively due to mechanical coupling between the meta- and mesothorax
(Schneider and Meurer, 1975).
Autonomous movements of elytra only occur during transitory opening and
closing, driven by a limited set of direct and indirect elytral muscles.
There exist several anatomical descriptions of how the elytra open and
close (see details in Discussion), and these descriptions are sometimes
contradictory. Previous cine recordings of elytra, together with wings, during
flight (Schneider, 1986,
1987
;
Schneider and Hermes, 1976
;
Schneider and Krämer,
1974
) did not include the transient opening and closing. The first
goal of our study was to film this transient process and to derive a
quantitative three-dimensional (3-D) description of opening and closing
relative to the elytra-bearing segment, the mesothorax. We aimed to answer the
following questions: (1) are there distinct stages during opening (closing);
(2) how diverse are the movements of the elytra and (3) how is the axis (or
axes) of elytra rotation directed? The 3-D description gives a basis for
further quantitative understanding of the complicated kinematics of
elytra-to-body articulation.
Our final goal was to elucidate the relative partition of the two elytra on opening (or the reverse on closing). This problem is regarded with respect to the sutural lock: this lock is released by the simultaneous motion of two elytra relative to each other, while all other locks are released by movement of the given elytron relative to the body. Relative motion of two rotating bodies creates peculiar geometry. For example, elaborate shapes of the teeth in gear wheels have been constructed taking into account similar relative movement of wheels. If parts of a lock are pulled in a particular direction on opening, then the lock must provide easy partition in this very direction but must block other imposed forces. Our question is whether the shape of the relative partition on opening influences the shape of the sutural lock.
We present data on 3-D measurements of opening and closing of the elytra in
large beetles that belong to Schneider's Cantharis and
Oryctes types (Schneider,
1978).
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Materials and methods |
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Videorecordings
In preliminary observations, beetles were tethered from above at the
pronotum. Later, they were tethered from below at the meso- and metasternum to
a wire holder (2 mm diameter) with cyanoacrylate glue. Cock-chafers,
Melolontha, were tethered at the lateral surface of the meso- and
metapleura. Legs were clipped, to prevent grasping. The beetle was mounted
straightly, at an approximately horizontal body orientation, or tilted head up
by 2040°. A mirror, inclined by 45°, was placed above the
beetle. Beetles were stimulated to fly by blowing an air stream from a
fan.
Small paper marks with black dots were glued onto the tips of the elytra. In other experiments, we prepared light tripods of three 15 mm pieces of thin straw, glued together at right angles. Each tripod weighed 2834 mg. One tripod was glued to each elytron. Black dots or tips of tripods are referred to below as `landmarks'. A tilted body orientation was used in order to obtain better views of the landmarks both in the real and mirror fields. The insect was viewed using a video camera from behind as a real image and from above as a mirror image. Scales of the real and mirror images were calibrated. The set-up was illuminated with a 300 W projector lamp.
A digital video camera recorder (Panasonic NV-A3EN, Matsushita Electric Industrial Co., Japan) was used for recordings at a frame rate of 25 frames s1. This rate was evidently below the wing stroke frequency. Due to bright illumination and a short exposure of 2 ms, we obtained sharp images of the elytra in various positions in repetitive episodes of opening and closing, enough to trace the trajectory of the landmark on the elytron. A series of episodes at the same body orientation comprised one film series. Selected episodes were digitized with the aid of a videocard ATI Rage Pro Furi Viva (ATI Technologies, Inc.) and the program ATI Video In 6.3 (ATI Technologies, Inc.), with further compression into the format DivX MPEG4 Fast motion.
Data processing
To track the motion of the elytra, we needed to obtain the 3-D positions of
landmarks, which were obtained from the geometric position of marker points
from each image in both real and mirror fields through frame-by-frame
analysis. Two programs, AVIEdit (AM Software, Moscow, Russia) and Sigma Scan
Pro (SPSS Inc., Chicago, IL, USA), were launched in parallel windows. Numbered
frames, displayed by AVIEdit, were copied into the Sigma Scan image window,
where relevant points were indicated and their pixel coordinates were saved as
an Excel 5.0 (Microsoft Corporation, Redmond, WA, USA) table.
We used several coordinate systems for 3-D measurements and spatial transformations: the global system was fixed to the video camera or video frame, the second, body-fixed system was fixed to the beetle's mesothorax, and the third system, determined by the landmark, was fixed to the moving elytron. By modeling the movement of a flat elytron, we introduced the fourth system, fixed to this flat elytron. Definition of axes in the images, as well as definitions of other coordinate systems, are given in Table 1.
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The frame contains the real and mirror images of the beetle. Each image is a projection of the beetle on two global axes (Fig. 1). In each image, we indicated either the apex of the scutellum and two marks on the elytra, or the scutellum and the arms of the tripod. The apex of the scutellum was adopted as the origin of the global coordinate system. After proper scaling of the real and mirror images, coordinates of relevant points were measured with respect to the scutellum. The real image provided us with coordinates down the x and y axes, while the mirror image provided x and z coordinates.
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Further data processing for 3-D data presentation, analysis and modeling used Excel 2000, MatLab 6.5 (MathWorks, Inc., Natick, MA, USA) and custom programs written in Turbo Basic 1.3. The custom programs provided convenient tools for geometrical constructions in 3-D space. Graphic facilities were provided by Adobe Photoshop 5.5 (Adobe Systems, Inc., San Jose, CA, USA) and Corel Draw 5.0 (Corel Corp., Ottawa, Ontario, Canada).
Eleven film series were selected for digitization. They contained 139 episodes of opening and closing, totaling over 1850 frames. For each film, 316 dots were indicated in two images.
The error of localization of a certain dot in one image was 12 pixels (0.20.4 mm). The error accumulated during multiple spatial transformations. To assess the resultant error in the body-fixed reference frame, we measured the Euclidian distance, D, between tips of two arms in a tripod in four film series (445 frames). The standard deviation for D was in the range of ±0.35 to ±0.96 mm. We compared D with the coordinate of the longitudinal tripod arm tip down the axis of the camera lens. In three out of four records, regression of D on p (or z at tilted body orientation) was non-significant, meaning negligible perspective distortion.
The prime goal in data processing was to reveal planar rotation of the landmark. Hence, we neglected corrections for perspective and spherical distortions, because the plane transforms again into the plane after perspective transformations or in a skew coordinate system.
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Results |
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We shall denote the broad spread of the elytra to the side, forwards and upwards as abduction on opening, and the reverse motion as adduction on closing. Additional rotation of the moving elytron about the sutural edge, the costal edge turning dorsad, is referred to below as supination, and the reverse rotation is pronation.
A definition of coordinate systems used in this study is given in Table 1. Localization of the landmarks is measured and illustrated directly from the frames in the global coordinate system (x, y, z) relative to the scutellum. This localization is recalculated into the body-fixed system (q, p, v), where we compute the position of the axis of abductionadduction (AAA). Additional supination of the abducting elytron (or reverse pronation on adduction) is revealed with the aid of the tripod landmarks in the landmark-fixed system.
The direction of the rotation axis, as well as of any vector, was expressed as a triplet of cosine directions (projections of the unit vector onto coordinate axes) or, more explicitly, as a pair of angles: `elevation' is the angle between the vector and the horizontal plane (external or body-fixed), positive upwards; `azimuth' is the angle (positive homolaterad) between the longitudinal axis p and projection of the vector onto the horizontal plane. Cosine directions were used in all vector computations.
Flexibility of the beetle's body and firm tethering
Preliminary filming revealed that a stag beetle, Serrognathus
titanus, tethered at the pronotum, was able to flex and extend its head
and the mesothorax (together with posterior body parts), with respect to the
prothorax, by 50° and 40°, respectively. The mesothorax, metathorax
and abdomen bent down on opening and rose on closing. The same behavior, with
a lower angular span, has been recorded in the dung beetle, Catharsius
molossus, and in the rose chaffer, Liocola brevitarsis. The
prothorax is not a reliable place for taking measurements of elytron position
with respect to the articulation site, the mesothorax. We decided to fix the
beetle to a holder at the metasternum, which is firmly fused with the
mesosternum, or at the meso- and metapleura.
The mesothorax itself is not a solid structure: the tergite is compressed down or rises with respect to the pleura during flight, and the pleura are able to shift laterad or mesad. The range of movements is small, even in large beetles, compared with the size of the whole elytron. Thus, we assume below that the elytron has a fixed articulation point.
First approximation: broad abductionadduction
Opening of elytra in the tethered beetle lasted 5060 ms in
Chalcophora mariana, 40150 ms in Prionus coriarius,
150190 ms in Allomyrina dichotoma and 200450 ms in
Melolontha hippocastani. Closing lasted longer: 6080 ms,
120200 ms, 400600 ms and 300600 ms, respectively. The
specimen of P. coriarius with tripods opened and closed its elytra in
80120 ms, and the specimen of M. hippocastani with tripods in
300450 ms, which is within the range of beetles with unloaded elytra.
Three specimens of Cetonia aurata (all with tripods) opened and
closed elytra in 60170 ms and80150 ms, respectively.
Traces of the dot landmark in the external reference system (x, y, z) during opening and closing of the elytra are illustrated for three species in Figs 2, 3, 4. The shape of the trace depends on the pitch of the beetle: for example, traces are seen as arcs in the jewel-beetle, C. mariana, tethered at a skew (Fig. 2). The trace in the sagittal plane was reconstructed and appeared to be least informative. The traces of opening and closing overlay each other almost perfectly, especially at the smaller angles of turn. If two curves coincide in two projections, they coincide in 3-D space. Below, we process both traces together.
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In a cock-chafer, M. hippocastani (Fig. 3), and a long-horn beetle, P. coriarius (Fig. 4), both mounted at a skew, we observed traces that looked like straight segments in the projective plane xy. In the jewel-beetle, on the other hand, the straight trace in this projection was seen at the straight body orientation of the insect. It is possible to rotate traces in 3-D space so as to see one of them stretched down a straight line or to see both as arcs (Fig. 5).
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The radius-vector from the articulation point to the landmark is obviously constant. During arbitrary rotations of the elytron, this radius-vector, as the generatrix of a cone, circumscribes a conical surface. The trace of the end-point is the `base' of the cone in 3-D space, but is not necessary flat. If a trace has a straight projection at a certain view, then this trace lies within a plane. Hence, the flat base of the cone with the generatrix of constant length is the flat arc of a circle.
Fitting of a circle to the random cloud of 3-D dots is a puzzle, because five parameters are unknown: the three coordinates of the center and the two angles, which characterize the tilt of the base plane. Having only a short arc of the circle, we applied an heuristic solution: mark three dots at the beginning, in the middle and at the end of the arc and construct a plane and then a circle across these dots in 3-D space. Computation returns the position of the center, the radius, the arc of the turn and the direction of the normal to the plane of the circle. The direction of the normal coincides with the direction of the rotation axis. We conventionally call this the `axis of abduction-adduction' (AAA). Below, we apply the name `radius-vector' only to the line between the center of the circle (not coinciding with the articulation point!) and the dot landmark. The quality of this approximation is verified in the section below on relative multiple rotations.
We applied the same procedure to the tip of the longitudinal tripod arm as the landmark for the wing apex. In two film series, we constructed circles by three selected frames in separate episodes, with further averaging of axial vectors.
For the insects mounted straight, the direction of the AAA in the external and body-fixed reference systems coincides. For insects filmed at tilted body orientation, we used the coordinate transformation according to the body pitch. Then we changed the sign of the q-component for the left elytron and averaged the axis directions for both elytra as 3-D unit vectors. Mean direction refers to the right side. All data are pooled together in Table 2.
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Despite the large scatter of data, due to the difficulty of controlling the symmetry of mounting and landmarking, pixelization errors, cumulated errors of spatial transformations, the rough method of circle construction, and the eventual asymmetry in elytra performance, we noticed some general features in the organization of the AAA.
The rising half of the AAA always pointed contralaterad (positive v-component, negative q-component). In M. hippocastani, A. dichotoma and P. coriarius, the AAA was tilted forwards (positive p-component). Indeed, we have observed straight traces of the landmark, when the beetles had positive pitch and the AAA occurred in the image plane. By tilting the beetle head down to zero pitch, we tilt the AAA forward. The AAA pointed backwards in the jewel-beetle, C. mariana. The angle between the right and left AAA was assessed in the approximate range of 40110°, while the angle of turn about the AAA was assessed in the range of 75100°.
The main conclusion is that the apex of the elytron rotates flatly during opening and closing. The method of construction of the AAA is explained in the Appendix.
Initial stage of opening
Opening is preceded by a downward movement of the abdomen (probably
together with the metathorax) and elevation of the still closed elytra. The
inverse process has been observed at the end of closing. The trajectory of
elevation-depression in P. coriarius, traced for the dot landmark, is
illustrated in Fig. 4 (dots
enclosed inside a box). Assessing the amplitude of elevation-depression as
34 mm and the distance from the articulation to the landmark as 18 mm,
we derive the angle of elevation-depression to be 0.2 rad
(1012°). Elevation-depression of a similar angular range was
recorded in M. hippocastani. The axis of elevation-depression lay in
parallel to the transverse body axis q.
At the very beginning of opening, a narrow slit appeared between the
elytra. This partition might persist without further broad opening. The angle
between the elytra was estimated as 23°. As is shown in the section
below on modeling of elytra opening, the width of the sutural lock is
0.10.3 mm at a distance of 1020 mm from the base of the
wing in large beetles. That means that the angular partition of elytra
released from the sutural lock is much less than 1°.
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In some experiments, we glued two orthogonal tripods on the elytra. They moved together with the elytron. The beetles with and without tripods are compared in Fig. 7. The size, mass and, obviously, moment of inertia of the elytron are comparable to or less than those of the tripod. The mass/length ratio of the elytra is 10 mg/12 mm in C. aurata, 10 mg/17 mm in M. hippocastani and 26 mg/30 mm in P. coriarius. Nevertheless, tripods do not affect the flight position of the elytra (Fig. 7) or the time of abductionadduction.
One tripod arm (arm P) was aligned with the suture and approximately with the body-fixed axis p. The transverse arm (arm Q) pointed to the side and slightly downwards, and the third arm (arm V) pointed approximately upwards and a bit laterad, following the slope of the elytron. Arms are additionally described as L for the left elytron and R for the right elytron.
We selected two film series of M. hippocastani and P. coriarius for detailed analysis. In these series, tripods on opening did not touch the mirror and did not collide with the opposite tripod. Only two arms were traced for each elytron, because the third arm was obscured by the elytron in some frames. The tilted body orientation was better for recordings with tripods, because it provided more space for the elytra below the mirror. We describe frames recorded at the tilted orientation in the global coordinate system.
Tracing of arm P gave essentially the same results as tracing of the apical landmark; when the beetle was viewed from behind, straight traces were seen (Figs 8, 9B, traces LP and RP). This arm tip rotated flatly about the AAA. The direction of the AAA and localization of the rotation center (which did not coincide with the articulation point!) were derived from three arbitrarily selected points on the trace, as before. Parameters for the two elytra are stated in Table 3.
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To check the quality of our reconstruction, we projected each point of the trace onto the axis of rotation and plotted the distance of the projection point from the center versus the angle of turn (Fig. 10). During flat rotation, this distance must be zero. We obtained the distances of 0.31±1.58 mm (mean ± S.D.) for the arm RP and 0.73±1.60 mm for the arm LP in P. coriarius and 0.44±0.88 mm for the arm RP and 0.62±0.96 mm for the arm LP in M. hippocastani. The displacement from zero and the scatter of points were small enough for reliable comparison with traces obtained in other arms.
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Relative multiple rotations
We defined the spatial position of the elytron by the articulation point
and two landmarks. One may argue that our landmarks were placed arbitrarily.
Even the apex is an arbitrary point, convenient for tracing. Tripod arms
increase the radius of rotation and facilitate measurements.
Hence, the direction of the elytral rotation may be defined only with respect to the elytron-fixed landmark. In general, any landmark on the elytron might be set for description of the primary, body-fixed movement. In order to investigate this problem, we analyzed movement of the left elytron in M. hippocastani, because it showed the best unbiased coordinate transform (S.D. of the interarm distance was ±0.35 mm; correlation between the interarm distance and the distance from the camera was 0.14).
For both landmarks, P and V, we constructed circles of their body-fixed flat rotations. Now, we introduce a new reference frame: fixed to the landmark (Table 1). Three axes, a, w and b, comprise a local basis of the elytron, which in turn moves in the body-fixed space. If we select the landmark P as the primary one, then projection of this landmark on the axis a is scattered about zero (Table 4). Projection on the axis w is scattered about the mean radius of rotation, with small standard deviations. Projection on the binormal axis (b) equals zero. By contrast, the trace of the other landmark, V, within the arm P-fixed system, shows great scatter in projections on the three mentioned axes.
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We obtain similar results by selecting arm V as the primary landmark and checking the quality of construction of the body-fixed circle of rotation. Precision is worse here due to the smaller radius; however, standard deviations are of the order of 1 mm. Another landmark, now P, shows larger scatter. The axis of rotation of the landmark V is tilted backwards (negative p-component) in the body-fixed system and lies close to the body vertical (Table 3). Angles between two axes one for the longitudinal arm landmark and the other for the side arm lie in the range of 5768° in both beetle species.
By computing traces of two arms in two arm-fixed systems (Fig. 11), we observed less dot scatter for the primary landmark about the position of the radius and more-or-less broad arcs for the secondary landmark. This feature was better reconstructed for the arm P-fixed system. The trace of side arm V, viewed from the tip of the arm P, rotated clockwise about the longitudinal wing axis on opening; that means supination of the costal edge for the left elytron. The direction of the 3-D turn of arm P in the V-fixed system was hard to interpret in anatomically reasonable terms.
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Opening and closing in rose-chafers
Elytra movements in Cetoniinae are of small amplitude. Therefore, it was
impossible to trace elytra-fixed points reliably in the short course of their
rotations. At the first approximation, we applied the model of flat rotation
of the whole elytron. We filmed the insect at straight mount, head to the
camera, with the tripod on each elytron. We compared orientations of tripod
arms (with respect to the apex of the tripod) for the elytron in its open and
closed positions. Four films of opening and closing were analyzed, and a total
of 288 dots was pixelized in 16 frames (including the scutellum). The check
angle between the tripod arms was estimated as 90.26±2.35°, and arm
length as 15.5±0.49 mm (mean ± S.D.). The
distance between tripod tips diminished on opening by 0.74±0.09 mm
(mean ± mean error), which is significantly different from zero
according to the Student's t-test (P0<0.1).
That meant some perspective distortion.
For each of eight episodes of opening or closing, we fitted three unknown parameters (azimuth and elevation of the rotation axis and arc of turn) with the aid of an interactive iterative program, which started from the open position of the tripod and compared the mean-squared Euclidian distance between the computed and observed localization of the three arm tips at the closed position for each combination of parameters (least square approach). The criterion of quality was the minimal value of the mean-squared distance per one arm (referred to as `error' in Table 5). This error contained some systemic component because the longitudinal arm tip was partly obscured in open position, especially in the left tripod. Results of fitting are reported in Table 5.
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The scatter of fitted values was rather tight for each tripod. The difference between the left and right tripods was due to the imperfect (non-symmetrical) mounting of the animal. Mean values are included in Table 2. A peculiar feature in Cetonia is the lowest elevation and strong backward pointing of the rotation axis, in addition to a small arc of rotation.
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The width of the dorsal ridge in temporary locks increased with the distance from the base of the elytron. At a distance of 1520 mm from the scutellum, the depth of the groove did not exceed 0.20.3 mm.
Modeling of elytra opening
We modeled only flat elytra and typically limited their turns to 90°.
We varied the orientation of the AAA to see how the orientation affected the
final position. Fig.
13AC illustrates the rotation of the elytron (horizontal at
the start) versus the changing tilt of the AAA. Raising of the
elytron is possible only if the AAA points contralaterad. The larger the
azimuth, the steeper the rise of the elytron. If the AAA is tilted back
(azimuth less than 135°), the attack angle after a turn by 90°
may be positive, especially at high elevation of the rotation axis. If the AAA
is tilted forwards (azimuth greater than 135°), the attack angle is
negative. At an elevation of 45° and an azimuth of 135° or
90°, inclination of the elytron against the airstream is 8° or
45°, respectively, with a negative attack angle. At an azimuth of more
than 90°, the final position of the elytron is even less
streamlined.
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The model of secondary rotation about the straight sutural edge of the flat elytron is illustrated in Fig. 13DF. The model allowed us to either supinate the elytral plane about the immobile sutural edge or to combine abduction and supination. It was possible to find, by iteration, the amount of supination that ensured horizontal placement of the elytron, i.e. minimal drag. Supination, consequently, improves the streamlined position against the airstream.
We also modeled the relative movement of the left elytron with respect to the right one at the beginning of opening. This model was computed in the right-elytron-fixed coordinate system (Table 1, final system). We computed abduction by 10° and also, hypothetically, rotation about the same AAA by 10° through crossed elytra, keeping in mind that the blade of the sutural lock penetrates into the opposite elytron. The trace of a point at the left suture relative to the right elytron is a shallow arc with positive curvature (convex down, the center of curvature is above the right elytron). This is illustrated in the insets in Fig. 13. Curvature is larger (or arcs are more convex) in models with additional supination. It is important to note that the curvature of the vault of the closed elytra is negative, opposite to the trace of divergence. Unlocking of the sutural lock must follow the surface of relative rotation.
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Discussion |
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Movements of the elytra on opening and closing were examined long ago.
Straus-Duerkheim (1828) named
muscles in the cock-chafer, Melolontha melolontha L., according to
their function. In particular, he discerned the direct flexor and extensor of
the elytron (M35 and M42; sensu
Larsén, 1966
), the
direct adductors (M36a, M36b) and the indirect adductor (M33). Further
investigators described, not univocally, the turn of elytra on opening as a
process of several stages. Functions of separate muscles will not be
comprehensively discussed here.
Stellwaag (1914)
distinguished unlocking, turn forward and then elevation in Lucanus
cervus (Lucanidae). According to Herbst
(1944
,
1952
), elytra in
Melolonthinae, Rutelinae are initially opened slightly to the sides, and this
is followed by the powerful elevation and outward motion. The elytra return
(down) to their original position, driven by gravity and the elasticity of the
mesonotum, whereas contraction of M36a closes them. According to the
observations of Schneider and Meurer
(1975
) on Oryctes
boas Fabr. (Scarabaeidae, Dynastinae), the elytra at the start flap
forward, but only after release from their locks. The latter is possible if
the elytra first rise at the sides. The forward turn is on a slant, because
contraction of the direct M42 pulls the axilliary chain down and backwards.
Belkaceme (1991
) stated that
the indirect M29 and M33 open the elytra by turning the scutellum forwards in
Noterus laevis Sturm. (Noteridae). Reviewing the existing works,
Matsuda (1970
) concluded that
elytra are extended simultaneously with elevation of the mesoscutellum by
cooperative contraction of M29 (t12) and M33 (t-p3), whereas M47 (t-tr1),
which is lacking in scarabs, elevates the elytron. We conclude therefore that
unlocking from manifold locks with the rest of the body is the generally
accepted first stage, but further movements have only been conjectured. Some
authors accept the notion of combined rotation on opening.
These earlier descriptions are far from the quantitative analysis that is
required to gain a clear understanding of how the thoracical sclerites, direct
and indirect muscles, multiple axilliary plates of complicated shape, and the
blade of the elytron interact during opening and closing. Only Heberdey
(1938) proposed a simple
geometrical model of the rotation axis, which lay in the transverse body-fixed
plane. Assuming that the transverse cross-section was an ellipse, the rotation
axis connected the homolateral tip of the long, horizontal axis of the ellipse
to the dorsal tip of the short axis. Hence, the rotation axis in Heberdey's
model pointed contralaterad.
We have confirmed that elytra rotate about different axes during the initial elevation (final depression) of linked elytra, broad abductionadduction and wing flaps. Such versatility is possible if the elytral articulation possesses three rotatory degrees of freedom.
Our measurements revealed that it is possible to describe the trajectory of the apex of the elytron on opening and closing as a flat rotation. Its axis lies at a skew and points contralaterad. Modeling of elytra opening confirmed that elevation of the elytron is possible only if the axis of rotation points contralaterad. This conclusion agrees with Heberdey's model, with the difference that the AAA, in general, is tilted forwards or backwards, in some taxa rather markedly (Cetoniinae).
Inspection of our model revealed that, after initially rising, the costal edge moves down. At least, after a turn of 90° or more, the elytron comes to the flight position with the negative attack angle, which may provide substantial drag. The situation is most marked in the case of forward inclination of the rotation axis, for example in the cock-chafer M. hippocastani, the rhinoceros beetle A. dichotoma and the long-horn beetle P. coriarius.
We found, further, that the positive body pitch partially compensated for
the negative inclination of the elytra. Indeed, many beetles fly with positive
pitch of the body. In particular, pitch was assessed in a cock-chafer by
Nachtigall (1964). He
calculated that passive lift of a dry specimen with `naturally' opened elytra
in the wind tunnel was maximal at a pitch of 27.5°. Brodsky (1988) cited
even higher values for large beetles: 30° for a long-horn beetle
(Megopis sp.), 40° for a rhinoceros beetle (Strategus
sp.) and 60° for a jewel-beetle (Julodis variolaris).
Additional rotation is necessary in order to put the elytral plane in parallel to the opposite airstream. In our model, it was provided by supination of the elytral plane about the apical radius-vector. Indeed, the tripod technics revealed additional rotation of the moving elytron about the sutural edge, supinationpronation. Supination (pronation) is evenly distributed throughout the phase of abduction (adduction). We have demonstrated that both these rotations have only relative sense, with respect to the traced landmarks.
The standard and even abductionsupination on opening (or adductionpronation on closing) suggests that the elytron moves as a mechanism with one degree of freedom and with one common drive. We believe that future studies will compare the 3-D organization of movements with the 3-D organization of pivots and hubs in the complex forewing articulation.
The diversity of beetles with respect to the geometry of the elytra, shapes
of articulatory elements, set of driving muscles and flight posture must be
taken into account. Observations of flying beetles revealed variability in
open elytra positions among different species
(Schneider, 1978),
predominantly at a skew with respect to the vertical body axis. The extreme
cases were almost horizontal orientation, in Dytiscus marginatus
(Schneider, 1978
) and
histerids (Prasse, 1960
;
Frantsevich, 1981
), and
vertical placement, reported by Schneider
(1978
) in Necrophorus
humator and N. vespilloides (Silphidae).
Locks to the body and unlocking
Breed and Ball (1909) first
discovered the junction between the elytron and the rest of the body down the
entire perimeter of the elytron. Stellwaag
(1914
) counted 14 kinds of
locks, which we can classify as clamps, clicks and fields of microtrichia
(VelcroTM-type locks). Further investigations added several new locks to
this list (Heberdey, 1938
;
Nachtigall, 1974
;
Nikolaev, 1987
), especially
when scanning electron microscopy resolved the variety in the fields of
microtrichia underneath the elytron and thus contributed not only to
understanding of their function (Gorb,
1998
) but also to taxonomical differentiation
(Baehr, 1980
;
Samuelson, 1996
).
The strongest two locks are: (1) the clamp at the base of the elytron by
the hind edge of the pronotum and (2) the subsutural click with the ridge on
the metascutellum. These locks are released by the forward movement of the
pronotum and depression of the metathorax (together with the abdomen) with
respect to the mesothorax. Downward bending of the head, prothorax and abdomen
was filmed during the unrestrained take-off of a leaf beetle, Chalicoides
aurata (Chrysomelidae), by Brackenbury and Wang
(1995). In Pachnoda
marginata (Scarabaeidae, Cetoniinae), preparing for flight, the elytra
and abdomen were separated by 5°. Elevation of the still-closed elytra
before take-off was recorded also in a scarab, Sisyphus schaefferi
(Prasse, 1960
). These
observations are completely confirmed by our own recordings on preliminary
bending of the prothorax and the hind body with respect to the mesothorax and
on elevation of the closed elytra before partition by 1012°.
The inverse depression appears on closing, being complicated by the
participation of vertical movements of the almost-closed elytra in order to
fold the hind wings (Schneider,
1978; Haas and Beutel,
2001
).
The sutural lock and unlocking
The sutural lock was noticed by early observers, Straus-Duerkheim
(1828) and Lacordaire
(1834
), described in more
detail by Allaud (1902
) and
first depicted by Breed and Ball
(1909
). The lock is built by a
kind of malefemale plug. It is a matter of pure chance which ventral
ridge right or left becomes the male component on eclosion
(Pisano, 1982
). Components of
the sutural lock bear fasting areas, covered by short microtrichia or scales
(Heberdey, 1938
).
Any temporary lock performs two alternative tasks: to keep both components
in tight contact against external disturbances and to release voluntarily with
minimal effort. These contradictory demands are satisfied by anisotropy of the
lock resistance to the applied force. This idea was clear to all early
investigators. Lacordaire
(1834) first noticed multiple
teeth (fastening microtrichia) within the sutural lock in a leaf-beetle,
Chlamys, while Heberdey
(1938
) demonstrated
co-adaptation of hair directions in these and other fastening hairy fields.
Nachtigall (1974
) confirmed
this observation in a diving beetle, Cnemidotus caesus. However,
there exist no dynamometric measurements on linked elytra subjected to
partition in various directions. Only Nachtigall
(1974
) noticed that the linked
elytra resist vertically applied forces but slide apart sideways without
resistance. The principle has been proven quantitatively in the insects of
another order, the Heteroptera (Perez
Goodwyn and Gorb, 2003
). Features of natural relative partition of
elytra must be taken into account when we consider disengagement or engagement
of the sutural lock.
Release from the sutural lock and initial partition of the elytra are enough to notice but too small to measure against the background of broad wing spreading. The necessary angular partition of elytra is below 1°. It is not unexpected that such a tiny movement was treated only hypothetically.
Heberdey (1938) postulated
that either the ventral sutural ridge of one elytron must press downwards onto
the groove in the opposite elytron, in order to unclip hairy fields at the
ridges, or that the opposite elytron must rise, or that both movements were
simultaneous. In any case, asymmetric motion of the elytra was necessary. Even
vibration of elytra was assumed. After release, elytra had to part
horizontally.
Judging by the noticeable inward tilt of elytra at partition, we suggest that the axis of this initial rotation does not differ significantly from the AAA. We emphasize that unlocking the suture is caused by the simultaneous movement of both elytra. The geometry of this relative movement is described in the elytron-fixed coordinate system.
Fiori (fig. 2 in Fiori,
1975) proposed a model of co-adaptation of two symmetrical sutural
profiles in opposite elytra, at the formation of the sutural lock, which
obviously supported a quite different direction of locking and unlocking.
According to Fiori, elytra come to engagement from below, repeating the shape
of the vault. We propose that elytra part dorsad and engage from above
(Fig. 14). Our suggestion is
that the profile of the male component of the lock may conform to the
divergence trace or divergence surface.
|
We have seen an upwardly curved dorsal ridge only in rose-chafers (Cetoniinae), with their extremely low and backwardly oriented rotation axis. In many beetles, the curvature of the partition surface had negligible affect on the shape of the male component, whose orientation was close to the tangent to the vault of elytra. Probably, curvature of the arc of partition is not noticeable at the very short initial opening of less than 1°.
Conclusions
Complicated movement of the elytra during broad opening or closing may be
quantitatively described with respect to certain reference points on the
elytron. The trajectory of the apex is a flat circular arc, hence the apex
rotates about the mesothorax-fixed axis. This axis comes across the
elytra-to-body articulation and points contralaterad and upwards. It is tilted
forward in Melolontha hippocastani, Allomyrina dichotoma and
Prionus coriarius and backwards in Chalcophora mariana; in
Cetonia aurata, the rotation axis is tilted extremely low and
backwards.
Turning flatly by 90° on opening, the elytron comes to a flight position with a negative attack angle. The latter is partly compensated for by the positive pitch of the body, but even more effectively by supination of the abducting elytron about the sutural edge. Supination was demonstrated in M. hippocastani and P. coriarius. In these two species, the open elytra flap during flight across the plane of abductionadduction. Before opening, linked elytra elevate by 1012° about the common horizontal body-fixed axis. This movement disengages the elytron-to-body locks. At the very beginning of opening, the elytra part a little. This movement disengages the sutural lock. The axis of partition probably coincides with the axis of abduction. Reverse closing movements mimic the trajectories of opening.
By releasing the sutural lock, the elytra move relative to one another. The trace of the relative partition is a shallow arc, convex down, opposite to the vault of linked elytra. The profile of the linking ridge in the suture in some beetles conforms to such a curved convex-down shape.
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Appendix. Construction of the axis of abductionadduction |
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Acknowledgments |
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References |
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Allaud, C. (1902). Note sur la conformation de la suture des élytres les Coléoptères. Bull. Soc. Entomol. 5,176 -178.
Baehr, M. (1980). Zur Funktionsmorphologie und Evolutiven Bedeutung der Elytralen Sperrmechanismen der Scaritini (Coleoptera: Carabidae). Entomol. Gen. 6, 311-333.
Belkaceme, T. (1991). Skelett und Muskulatur des Kopfes und Thorax von Noterus laevis Sturm. Stuttgarter Beitr. Naturkunde Ser. A 462, 1-94.
Brackenbury, J. and Wang, R. (1995). Ballistics and visual targetting in flea-beetles, J. Exp. Biol. 198,1931 -1942.[Medline]
Breed, R. S. and Ball, E. F. (1909). The interlocking mechanisms which are found in connection with the elytra of Coleoptera. Biol. Bull. 61,289 -303.
Brodsky, A. K. (1994). The Evolution of the Insect Flight. Oxford: Oxford University Press.
Fiori, G. (1975). La `sutura' elitrale dei coleotteri. In Atti del Congresso Nazionale Italiano di Entomologia 10,91 -111.
Frantsevich, L. I. (1981). The jump of the black-beetle (Coleoptera, Histeridae). Zool. Jb. Anat. 106,333 -348.
Gorb, S. N. (1998). Frictional surfaces of the elytra-to-body arresting mechanism in tenebrionid beetles (Coleoptera: Tenebrionidae): design of co-opted fields of microtrichia and cuticle ultrastructure. Int. J. Insect Morphol. 27,205 -225.[CrossRef]
Haas, F. and Beutel, R. G. (2001). Wing folding and the functional morphology of the wing base in Coleoptera. Zoology 104,123 -141.
Heberdey, R. F. (1938). Beiträge zum Bau des Subelytralraumes und zur Atmung der Coleopteren. Z. Morphol. Ökol. Tiere 33,667 -734.[CrossRef]
Herbst, H. G. (1944). Studien über, die Flügeldecken der Rutelinen und, Cetoniinen, (Coleoptera Scarabaeidae). Das Elytralgelenk. Z. Morphol. Ökol. Tiere 40, 1-66.
Herbst, H. G. (1952). Studien über, die Flügeldecken der Rutelinen und, Cetoniinen, (Coleoptera Scarabaeidae). Das Elytralgelenk. Zool. Jb. Anat. 72, 1-66.
Lacordaire, T. (1834). Introduction à l'Entomologie. Paris 1,383 .
Larsén, O. (1966). On the morphology and function of locomotor organs of the Gyrinidae and other Coleoptera. Opuscula Entomologica 30, 1-241.
Matsuda, R. (1970). Morphology and evolution of the insect thorax. Mem. Entomol. Soc. Can. 76, 1-431.
Nachtigall, W. (1964). Zur Aerodynamik des Coleopteren-Fluges: wirken die Elytren als Tragflächen? Verh. Dtsch. Zool. Ges. Suppl. 27,319 -326.
Nachtigall, W. (1974). Biological Mechanisms of Attachment. Berlin: Springer.
Nikolaev, G. V. (1987). Lamellicornian beetles (Coleoptera, Scarabaeidae) of the Kazakhstan and Middle Asia. (In Russian.) Alma-Ata: Nauka.
Perez Goodwyn, P. J. and Gorb, S. N. (2003). Attachment forces of the hemelytra-locking mechanisms in aquatic bugs (Heteroptera: Belostomatidae). J. Insect Physiol. 49,753 -764.[CrossRef][Medline]
Pisano, P. (1982). Frequenze `destrorsa' e `sinistrora' del cosiddetto `maschio' della sutura elitrale in una popolazione sarda di Ocys harpaloides Serv. (Coleoptera Carabidae).Rendiconti del Seminario della Facolta di Scienze dell'Universita di Cagliari 52,147 -152.
Prasse, J. (1960). Über Start und Flug des Sisyphus schaefferi L. Beitr. Entomol. 10,168 -183.
Samuelson, G. A. (1996). Binding sites: elytron-to-body meshing structures of possible significance in the higher classification of Chrysomeloidea. In Chrysomelidae Biology: The Classification, Phylogeny and Genetics, vol.1 (ed. P. H. A. Jolivet and M. L. Cox), pp.267 -290. Amsterdam, The Netherlands: SPB Academic Publishing.
Schneider, P. (1978). Die Flug- und Faltungstypen der Käfer (Coleoptera). Zool. Jb. Anat. 99,174 -210.
Schneider, P. (1986). Studies about the flight of Dytiscus marginalis. 1. (Coleoptera, Dytiscidae). Entomologica Basiliensia 11,451 -460.
Schneider, P. (1987). Mechanik des Auf- und Abschlages der Hinterflügel bei Käfern (Coleoptera). Zool. Anzeiger 218,25 -32.
Schneider, P. and Hermes, M. (1976). Die Bedeutung der Elytren bei Vertretern des Melolontha-Flugtyps (Coleoptera). J. Comp. Physiol. 106,39 -49.[CrossRef]
Schneider, P. and Krämer, B. (1974). Die Steuerung des Fluges beim Sandlaufkäfer (Cicindela) und beim Maikäfer (Melolontha). J. Comp. Physiol. 91,377 -386.[CrossRef]
Schneider, P. and Meurer, J. (1975). Die mittelbar-indirekte Bewegung der Elytren beim Nashornkäfer Oryctes boas Fabr. (Coleoptera). Zool. Jb. Physiol. 79,297 -310.
Stellwaag, F. (1914). Der Flugapparat der Lamellicornier. Z. Wiss. Zool. 108,359 -429.
Straus-Duerkheim, H. E. (1828).Considérations générales sur l'anatomie comparée des animaux articulees . Paris.