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Singing. Gomphocerinae: Gomphocerus rufus (Linnt, 1758) from Seewiesen, Bavaria; Oedipodinae: Aiolopus strepens. (Latreille, 1804) from a laboratory culture ...
Zoomorphology

Zoomorphology (1990) 109:223-230

© Springer-Verlag1990

Tympana, auditory thresholds, and projection areas of tympanal nerves in singing and silent grasshoppers (Insecta, Acridoidea) K. Riede*, G. K~Jnper**, and I. Hfifler Max-Planck-Institut ffir Verhaltensphysiologie Abteilung Huber, D-8130 Seewiesen, Federal Republic of Germany Received May 11, 1989

Summary. The auditory systems of several species of singing and acoustically communicating grasshoppers, as well as of silent grasshoppers, were compared with respect to the external structure of the tympana, thresholds of the tympanal nerve response and projection areas of tympanal nerves within the metathoracic part of the ventral nerve cord. Extracellular recordings from the tympanal nerves, using suction electrodes, revealed that singing and silent grasshoppers hear within the frequency range tested, from 2 to 40 kHz. However, differences in sensitivity were observed in those silent species with tympana of modified structure. Cobalt-backfills of the tympanal nerves revealed a clearly discernible auditory neuropil in the anterior ring tract of the metathoracic ganglion in all animals. A comparison of the volumes of neuropilar areas calculated from serial sections of the entire ganglion showed a gradation: the volumes were biggest in singing species, slightly smaller in silent species with a well-developed tympanum, and smallest in the species with modified tympana. These findings support several authors who suggested that auditory organs evolved earlier than acoustic communication.

A. Introduction The Acridoidea are characterized by a hearing organ located in the first abdominal segment, the anatomy of which was described by Schwabe (1906). It consists of an outer membrane, the tympanum, a group of sensory cells on its inner surface (Miiller's organ: Graber 1876), and sclerotic support structures. The axons of the sensory cells together with other afferent axons form the tympanal nerve and enter the first abdominal ganglion. Ultrastructure of sensory cells was studied by Gray (1960), their physiology by Michelsen (1971 a), and the biomechanics of the tympanum by Michelsen (1971 b, c), Stephen and Bennet-Clark (1982), and Breckow and Sippel (1985). Projection areas of auditory fibers in the ventral cord were described by Rehbein (1976) and Halex et al. (1988). Comparative studies of acridid communication behavior show that sound production is restricted to the represen* Present address: Institut fiir Biologic I, Albertstrasse 21a, D-7800 Freiburg, Federal Republic of Germany ** Present address: Universit/it Ulm, Abteilung Vergleichende Neurobiologie, Postfach 4066, D-7900 Ulm, Federal Republic of Germany Offprint requests to: K. Riede

tatives of few subfamilies (cf. Otte 1970 for North American, Riede 1987 for South American grasshoppers). The majority of species are mute, but have a well-developed heating-organ. Mason (1968) compared the outer morphology of tympana in 915 genera and found no correlation between sound production and tympanal development. In the present study we examined whether the great range of morphological variation and the different behavioral reactions to sound are reflected in physiological and neuroanatomical properties of tympanal afferents by comparing three groups: species with and without acoustic communication, all with a well-developed tympanum (named "singing" and "silent" in the following), and silent species with a reduced tympanum (" reduced"). B. Materials and methods 1. Species examined Singing. Gomphocerinae: Gomphocerus rufus (Linnt, 1758) from Seewiesen, Bavaria; Oedipodinae: Aiolopus strepens (Latreille, 1804) from a laboratory culture of individuals caught on Gomera, Spain; Locustinae: Locusta migratoria Linn~, 1758 from a laboratory culture; Romaleinae: Xyleus sp. from Iguazfi, Argentina. Silent. Catantopinae: Podisma pedestris (Linnt, 1758) from the Pyrenees, Spain; Leptysminae: Tetrataenia surinama (Linn~, 1758); Melanoplinae: Dichroplus sp. Reduced. Rhytidochrotinae: Galidacris sp.; Ommatolampinae: Psiloscirtus sp. Except for P. pedestris, all animals of groups "silent" and "reduced" were caught in Napo province, Amazonian Ecuador, kept in the semi-natural habitat of a Tropicarium and fed ad libitum. 2. Scanning electron microscopy of tympana Inner and outer structures of the tympanum were examined with a scanning electron microscope (Novascan, Zeiss). Miiller's organ was treated with Hexamethyldisilazane (Bock 1987), air-dried and sputtered with gold. To study the outer structure of the tympana the first abdominal segment was air-dried and sputtered (Fig. 1). 3. Cobalt-backfills of tympanal nerves The metathoracic ganglion was isolated and nerve 6 was cut near the tympanal organ; the proximal nerve stump

224

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225 was dipped into a Plexiglas dish (Eibl 1976) with modified Wilson-Ringer (NaC1 140 m M , KCI 10 m M , CaCI2 7 m M , N a H C O 3 4 m M , MgCL2 1 m M , TES 5 m M , Trehalose 5 m M in distilled water, p H 7.3) and a d r o p o f a 2% solution o f COC12, and left there for 3-4 h at 22o-24 ° C. After silver intensification (Bacon and A l t m a n 1977) the p r e p a r a tion was p h o t o g r a p h e d as a whole m o u n t and drawn. After embedding in Araldite the p r e p a r a t i o n s were sectioned transversally and sagitally (20 Ixm). F o r the terminology o f neuropil and fiber tracts we followed Tyrer and G r e g o r y (1982). 4. Calculation o f the volume o f acoustic neuropil

F o r a quantitative c o m p a r i s o n o f the volume o f acoustic neuropil in different species the outlines o f drawings of sections were fed into a c o m p u t e r (Apple M a c i n t o s h + ) by a video camera and an A / D converter board. Areas and volumes were calculated so that the percentage o f acoustic neuropil in relation to the entire ganglion could be determined. Three-dimensional reconstructions were p r o d u c e d by assembling sections cut from styrofoam plates, 1 cm thick (Fig. 5). 5. Recordings from the tympanal nerve

F o r determination o f hearing threshold animals were fixed on a holder with wax, ventral side up. The metathoracic sternites were removed to expose the nervous system. The t y m p a n a l nerve was cut near the ganglion and the distal stump drawn into a plastic suction electrode. In a soundd a m p e d c h a m b e r tone pulses o f different frequency and intensity (50 ms duration, rise and fall times 5 ms) were generated by a loudspeaker m o u n t e d perpendicularly to the animal's b o d y axis at a distance o f a b o u t 15 cm. Sound intensity was calibrated at the position o f the animal with a Briiel & Kjaer m i c r o p h o n e (Type 4135). S u m m a t e d electrical activity o f the t y m p a n a l nerve was amplified by a differential amplifier, m o n i t o r e d by headphones and recorded with an analog tape recorder (Racal). Relative hearing threshold was defined as the lowest sound intensity that p r o d u c e d a stimulus-correlated signal recognizable in the headphones by the experimenter. Threshold curves obtained by this m e t h o d are a b o u t 15-30 dB above the animals actual hearing threshold (Michelsen 1971 c). W i t h the exception o f Psiloseirtus sp., at least two individuals o f each species were tested. Neuroanatomical abbreviations: Ab l VA C : ventral association center, aRT: anterior p a r t of the ring tract, aVAC: anterior ventral association center, D I T : dorsal intermediate tract, D M T : dorsal median tract, L D T : lateral dorsal tract, M V T : median ventral tract, VIT: ventral intermediate tract, V M T : ventral median tract.

C. Results 1. External morphology o f the tympana

Scanning electronmicrographs o f Miiller's organ reveal a basically similar m o r p h o l o g y in singing a n d silent grasshoppers (Fig. 1 a, b). However, the characteristic thickening in the region o f the d-cells which attach to the pyriform vesicle (pv) is only observed in Aiolopus strepens (singing, Fig. 1 b), and not in Podisma pedestris (silent, Fig. I a). Differences in the external structure o f t y m p a n a are summarized in Table 1. T y m p a n a o f singing species differ from those o f groups " s i l e n t " and " r e d u c e d " by a subtympanal lobe which partially covers the t y m p a n u m ( " c l o s e d " t y m p a n u m , Fig. 1 d). The s u b t y m p a n a l lobe is provided with sensory hairs a b o u t 200 lain in lengths. G r o u p s "sil e n t " and " r e d u c e d " (Fig. 1 c, e) have open tympana. In contrast to Galidacris (" r e d u c e d " , Fig. 1 e), the t y m p a n a l margin o f Tetrataenia (Fig. 1 c) contains sensory hairs. In singing a n d silent species, the t y m p a n a l m e m b r a n e is not homogeneous and is divided into two areas one o f which is sclerotized. In Galidacris it is h o m o g e n e o u s and not separated in all parts from the surrounding cuticular areas. The folded b o d y is reduced, b u t the neighboring groove and a structure p r o b a b l y representing an u n k n o w n sensillum is clearly visible (Fig. 1 f, g). Sensory hairs at the base o f the folded b o d y have been described by Schwabe (1906). The same a u t h o r describes the depression o f the horny process as the attachment site o f a tensor muscle; it is missing in Galidacris. Table l. Comparison of outer structures of the tympanum in representatives of different groups. Abbreviations see Figs. 1, 2 Species

G. rufus T. surinama Galidacr&

Group

A S R

Cuticular structures dp

sul

tm

sm fb

+ +

+ --

+ + + + fused

+ + -

sc

pv

+ + +

+ + -

2. Auditory thresholds

Hearing thresholds (Fig. 2) show that all six species studied are able to hear sound in the tested frequency range 2-40 kHz, even those with reduced tympana. In Gomphocerus, Tetrataenia and Dichroplus threshold curves are similar and fiat with thresholds between 35 and 50 dB sound pressure level. Neither m a x i m a nor minima indicate tuning for special frequency bands. Xyleus is less sensitive a b o v e 15 k H z (for c o m p a r a t i v e d a t a on Locusta, see Michelsen 1971c). N o significant difference could be recognized be-

Fig. 1. Scanning electronmicrographs of different tympana, a Miiller's organ from Podisma pedestris (silent) as seen from inside. It is surrounded by an air sac; the rippled surface is typical for the inner side of its tracheal walls, b Miiller's organ from Aiolopus strepens (singing). e Open tympanum of Tetrataenia surinama (silent) seen from outside; tympanal membrane (tin) and sclerotized region of the membrane (sm) are clearly discernible. The depression of horny process for tensor muscle (dp) is a hollow cuticular structure reaching into the body cavity where it forms the attachment side of a tensor muscle of unknown function, d "Closed" tympanum of Gornphocerus rufus (singing) seen from outside. The subtympanal lobe (sul) partially covers the tympanal membrane (tin), the folded body (fb) is clearly visible, e Galidacris sp. (reduced) has a homogeneous sclerotized tympanal membrane. In contrast to the other species, the depression of horny process for tensor muscle (dp, see e) is missing, f Region of the underdeveloped folded body (fb) of Galidacris sp. The groove neighboring folded body (g), the sclerotic cavity of the sensory structure (sc) and a structure which probably represents a sensillum are clearly visible, g Magnification of the sensillum from f. bp: basal plate of styliform body, d: d-cells, ep: elevated process, pv: pyriform vesicle, s: spiracle

226 100

ic-abdominal ganglionic complex in all groups. However, differences were observed between groups.

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a well-developed tympanal organ have good auditory ability, independent of their use of stridulation for communication (singing: A, silent: S). Of the silent species with reduced hearing organ (R), Psiloscirtus still hears well in the mid-frequency range, Galidacris is relatively insensitive over the whole frequency range

Singing. Gomphocerus rujus is a representative of a soundproducing species with elaborate acoustic communication. Compared with groups " s i l e n t " and " r e d u c e d " , its acoustic neuropil is most densely packed and covers the largest area in the metathoracic ganglion (Figs. 3, 4). Axons of acoustic and non-acoustic sensory neurons run mainly along the VIT and the VMT. They branch in four areas of neuropil: in the first abdominal neuromere in the Abl VAC, dorsally in the same neuromere between the VIT and the median line (an area which corresponds to the a R T of the metathoracic part of the ganglion), in the metathoracic neuromere in the a R T and the aVAC. In the two latter areas fibers with relatively thick branches also project to the contralateral side (Fig. 3 a). It is not k n o w n whether these contralateral arbors are parts of the acoustic nerve fibers or other mechanoreceptors such as chordotonal organs (Hustert 1978). Silent. Tetrataenia surinama and Dichroplus sp. are repre-

tween singing and silent grasshoppers. Within the species with reduced tympana, only Galidacris with its sclerotized t y m p a n u m is 20-30 dB less sensitive over the whole frequency range. In Psiloscirtus thresholds are raised only in the lower (1 l0 kHz) and higher (above 20 kHz) frequency ranges.

3. Comparison of projection areas In accordance with the results of Rehbein (1972) we found a caudal and a frontal acoustic neuropil in the metathorac-

sentatives of silent species with a well-developed tympanum. They show projections similar to Gomphocerus rufus in the abdominal neuromere. Reductions can be observed in the metathoracic neuromere. The density of neuropil in the aRT is less (Fig. 4b) and few branches are visible in the aVAC. This also holds for Locusta (Fig. 4 a), in spite of its stridulatory capacity. Contralateral branches in the a R T were observed in Tetrataenia, in a lesser n u m b e r in Dichroplus but not in Locusta. In the aVAC only a few fibers cross in Dichroplus. Compared with singing species, all three species show a smaller n u m b e r of fibers in the MVT.

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Fig. 3a-c. Transverse sections (20 gm) of the metathoracic

ganglion of Gomphocerus rufus (singing). Planes of sections are marked by lines in the drawing of the whole mount preparation c. In the anterior region of the ganglion a afferents project into the aRT and aVAC; the latter are probably projections from sensory hairs. The posterior section b shows that axons run in the VIT and MVT, leading to the aRT and aVAC projection areas, respectively. Dendrites in the dorsal area belong to stained motoneurons

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Fig. 4 a, b. Transverse sections and drawings of whole mount preparations from representatives of the different groups, a Locusta m~ratoria (singing), b Tetrataenia surinama (silent). Pronounced projections into the contralateral part of the aRT can be recognized, e Galidacris sp. (reduced); the projections are clearly reduced, especially in the median anterior part of the aRT, but stains in the dorsal part of the aVAC are visible. Compared with Gomphocerus rufus (Fig. 3), the acoustic projection area in the ipsilateral aRT is less dense in all these species. It is qualitatively evident that the proportion of acoustic neuropil is smallest in Galidacris sp. Reduced. I n Galidacris and Psiloscirtus, genera with reduced tympana, the branching pattern of tympanal afferents is basically similar to the branching pattern of the species described above (Fig. 4c). However, the volume and density

of arborization are clearly reduced, especially in the aRT. As the stains in the a R T were very clear - even single branches going to the contralateral side were visible - it is unlikely that these reductions are due to artefacts.

228 Table 2. Percentage of acoustic neuropil in metathoracic ganglia

from total volume of the metathoracic-abdominal complex. Means and standard deviation are separated for sexes in G. rufus (M = male, F = female). Double fills in one animal are marked with rn (right neuropil) and In (left neuropil). The greatest proportion can be observed in G. rufus, singing, the smallest in Galidacris sp., reduced. In this species the ganglionic volume (first column) was calculated only once and was the base for the calculations on the other two individuals Species

Volume (103 lama)

Percentage

Metathoracic- Acoustic abdominal neuropil complex Gomphocerus (M) 113 000 rufus 132 000 (singing) 132 000

Locusta rnigratoria (singing)

106 000

1030 In 788 rn 680 800

(F) 134000 167000 130000 130000

690 940 960 870

331000 331000 322 000

In 1 950 rn 2130 2 200

0.92 0.60 0.52 0.76 Mean : 0.70 0.52 0.56 0.74 0.67 Mean: 0.62 Mean M, F: 0.66+0.14 0.59 0.64 0.69 Mean: 0.64

Dichroplus sp. (silent) Tetrataenia surinama (silent) Psiloscirtus sp. (reduced)

126 000 124000 126000

467 361 925

0.37 0.29 0.73

112000 157000 160000

400 430 420

0.36 0.27 0.26 Mean: 0.30

Galidacris sp. (reduced)

92000

70 90 130

0.08 0.10 0.14 Mean : 0.11

In spite o f differences in staining intensity and density o f projections, the stained areas are prominently demarcated in different p r e p a r a t i o n s so that a quantitative comparison of the extension o f the acoustic neuropil in different species is possible. Only the metathoracic neuromere, which is the m a i n projection area o f acoustic fibers (Kalmring 1975; Halex et al. 1988), was considered. The results o f Table 2 show that the p r o p o r t i o n o f neuropil to ganglionic volume reaches m a x i m a l values in singing Gomphocerus ruf u s (0.66%_+0.14%, max. value: 0.92%!). Locusta with 0.64% shows only slightly less. In silent species, Dichroplus shows a clear reduction (0.33%), while the only value from Tetrataenia (0.73%) lies in the range of singing species. A clear reduction is observed in group " r e d u c e d " with 0.3% in Psiloscirtus and 0.11% in Galidaeris. 4. Projections o f the tympanal nerve

The sixth nerve o f the metathoracic ganglion contains not only fibers from the t y m p a n a l organ, but also m o t o n e u r o n s and p r o b a b l y sensory input from mechanoreceptors (e.g.

extra bundle, G r a y 1960). As shown by the 3-D reconstructions o f Fig. 5, the tympanal nerve ramifies into three branches. The motoneurons project into the dorsal part of the ganglion and are easy to differentiate from sensory afferents which lie medially or ventrally. The acoustic neuropil is situated medially (Halex et al. 1988). A further sensory projection area lies more ventrally in the areas of the VAC and the aVAC; on the basis of a comparison o f these latter projections with those described by Pflfiger et al. (1988) in locusts, and taking into account the general topographic organization o f insect ganglia (Murphey et al. 1985), it is suggested that these are projections o f a b d o m i n a l and metathoracic sensory hairs. These latter areas as well as the m o t o n e u r o n s were not seen in all preparations, while the acoustic neuropil was stained in all animals.

D. D i s c u s s i o n

The hearing capacity o f silent grasshoppers, over a frequency range similar to that used by their acoustically communicating relatives, supports the hypothesis that hearing in Acridoidea evolved before singing (Otte 1970; Riede 1987). H a l f a century ago Eggers (1928) interpreted hearing as a p r e a d a p t a t i o n for singing. In the following we c o m p a r e hearing thresholds and n e u r o a n a t o m y of the species studied with the extensive d a t a available on Locusta and Schistocerca and discuss the role of hearing in silent species. 1. Comparison o f hearing thresholds

In Locusta, between 60 and 80 sensory cells are attached to the tympanal membrane by thickened cuticular structures. They can be separated morphologically into four different populations, a-, b-, c- and d-cells (Gray 1960), which correspond to the physiological receptor-cell types 1-4 (Breckow and Sippel 1985). The whole system forms a complex resonance structure in which different receptor groups react to different frequencies by the place principle (Michelsen 1971 a - c ; Stephen and Bennet-Clark 1982). The type-4 or d-cells are the high-frequency units with best frequencies above 10 kHz. In spite o f significant differences in external a n a t o m y o f the tympanum, threshold curves o f all species are qualitatively similar and cover a frequency range from 2 to 40 kHz. A p r o n o u n c e d reduction in sensitivity is observed in group " r e d u c e d " which is p r o b a b l y due to the distinctive external anatomy. However, interspecific comparisons are problematic because even in Locusta Michelsen (1971 b) showed threshold variations up to 20 dB depending on a b d o m i n a l fat content. Furthermore, the directional characteristics o f the different t y m p a n a are still unknown and are most probably affected by the different orientation o f the t y m p a n a l membrane which forms an angle of a b o u t 45 ° to the sagittal plane and is partly covered by the subtympanal lobe in singing species, while open t y m p a n a of groups " s i l e n t " and " r e d u c e d " are oriented parallel to the sagittal plane. A n i m p o r t a n t difference is the presence o f a sclerotized region of the membrane in singing and silent grasshoppers (Fig. l c ) which divides the t y m p a n u m into two areas o f distinct elastic properties, while the t y m p a n u m is almost homogeneous in group " r e d u c e d " (Fig. 1 e). Together with the absence o f the folded body, these anatomical differences should affect the mode of tympanal vibration. A thorough analysis by laser vibrometry is necessary to c o m p a r e the biomechanics o f homogeneous membranes with the well-

229

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Fig. 5. Reconstruction of sensory neuropils made up by back-filling nerve 6 and sectioning the ganglion of Gomphocerus rufus (right) and Galidacris variabilis (left). To facilitate comparison, both structures are separated and embedded into one ganglionic half; the actual sagittal mid-plane for each ganglion is indicated. Especially the supposed mechanosensory projections into the aVAC (pavac) reach far into the contralateral side. For technical reasons, only the most prominent contralateral projections of the frontal neuropil could be reconstructed and the fine branchings of motoneurons into the dorsal part of the ganglion are left out. en: caudal neuropil, fn : frontal neuropil, pavac: projections into the anterior ventral association center known heterogeneous t y m p a n u m of Locusta (Michelsen 1971 b, c; Breckow and Sippel 1985). The tympanal reduction - manifest, for instance, in the absence o f euticular structures such as the pyriform vesicle and folded body - is reminiscent of developmental stages o f the tympanal organ of Loeusta (Michel and Petersen 1982) and therefore of the biogenetic rule - repetition of phylogeny by ontogeny. However, a look at the physiological data reveals a basic difference : individuals with reduced tympana do hear in the high-frequency range while larvae of Locusta do not (Adam and Schwartzkopff 1967; Boyan 1983), because the d-cells differentiate very late during postembryonic development. This indicates that the reduction o f cuticular structures and sensitivity is secondary, without affecting the frequency range. 2. Comparison of projection areas The differences in the proportion of acoustic neuropil between group " r e d u c e d " vs singing and silent groups (Table

2; Figs. 3, 4) could be explained in three ways: (i) size of the acoustic neuropil is determined by the number of auditory cells in Miiller's organ, which implies that there are fewer sensory cells in group "'reduced"; (ii) the number of sensory cells is comparable in different groups, but the terminal arborizations are more extensive in singing and silent species; (iii) a combination of (i) and (ii). The detailed single-fiber analysis by Halex et al. (1988) on Locusta and silent Sehistocerca reveals only slight differences between these two species. This result is consistent with our observations, which indicate that Locusta is more similar to silent species than to the singing Gomphocerus rufus. Pronounced differences should show up when comparing these species with representatives with reduced tympana. There, the attachment site of the d-cells, the pyriform vesicle, is missing completely. However, the hearing capacity above 10 kHz suggests that receptors of population d or a functional equivalent do exist. In Locusta, the c-receptor cells are connected to the folded body. This structure, too, is missing in Galidacris. Its absence may be associated

230 with complete loss of the corresponding receptor group c, which could reduce the relative neuropil volume, especially in the anterior median projection area (Fig. 4c). According to Halex et al. (1988), c-receptor cells project into the anterior median area of the a R T in Locusta. As our results show, Locusta n e u r o a n a t o m y is intermediate between singing and silent species; therefore there is still an urgent need for detailed physiological and morphological studies on good songsters like Gomphocerus rufus.

3. The function o f hearing in silent species The question of the function of hearing in silent grasshopper species is still open. As in other insects, hearing could have a function in predator-prey interactions, especially avoidance behavior against bats (see Yager and Hoy 1989 for m a n t i d hearing physiology and a review of ultrasonic hearing in insects). In Locusta electrophysiological data show acoustic input to c- and m-interneurons which elicit j u m p i n g (Pearson et al. 1980) and others which affect flying (Boyan 1985). However, bat avoidance cannot be important for the wingless but hearing Galidacris and Psiloscirtus. T h o u g h behavioral data that clearly demonstrate the influence of hearing on escape behavior are lacking, this is still the most plausible hypothesis. W i t h o u t doubt, hearing in a n o n - c o m m u n i c a t i v e context was the preadaptation for a functional change in some subfamilies where hearing became involved in communication. U n d e r the selective pressure of conspecific song recognition one would expect an enhancement of frequency discrimination and directionality. Our results and the analysis of Halex et al. (1988) do not suggest any basic neuroanatomical or physiological differences between singing and silent species at the periphery. Differences such as tuning as well as sharpening of directionality have more probably developed at a higher level in the auditory pathway. To test this, electrophysiological records from interneurons, especially in species with reduced tympana, are necessary.

Acknowledgements. We thank Professor Dr. F. Huber, Seewiesen, for generous support and critical reading of the manuscript. Professors Dr. K. Kalmring, Marburg, and Dr. A. Michelsen, Odense, helped with critical comments. Thanks are due to Dr. T. Weber for help with computer-aided volume-calculation, C. Bock for the SEM-photography, and Dr. M. BiedermannoThorson for correction of the manuscript. The 3-D reconstruction was drawn by Mrs. Lisa Tielen-Gfinsslen. This work was financed by the Max-PlanckSociety and by the Deutsche Forschungsgemeinschaft.

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