Habitat-dependent transmission of male advertisement calls in bladder grasshoppers (Orthoptera; Pneumoridae)
Department of Biological Sciences, and JP Scott Center for Neuroscience, Mind and Behavior, Bowling Green State University, Bowling Green, OH 43403, USA
* Author for correspondence (e-mail: vanessa{at}caspar.bgsu.edu)
Accepted 18 May 2004
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Summary |
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Key words: acoustic communication, advertisement call, habitat, bladder grasshopper, Pneumoridae, sound transmission, spectrographic cross correlation
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Introduction |
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The rate of acoustic signal degradation, and subsequently the range at
which sounds can be used effectively for communication purposes, is dependent
upon numerous factors. These include spectral and temporal properties of the
signal itself (Wiley and Richards,
1978), behavioural modifications of the animal during signalling,
such as calling from preferential heights and locations
(Bennet-Clark, 1987
;
Keuper et al., 1986
), and
external properties of the local environment, incorporating vegetation type
(Lang, 2000
), meteorological
conditions (Garstang et al.,
1995
), and acoustic interference from other organisms
(Wollerman, 1999
).
The acoustic adaptation hypothesis emanated largely from the work of Morton
(1975) and Hansen
(1979
) and was conceived as a
means of means of investigating the relationship between animal vocalizations
and ecological factors. This hypothesis was based on the observation that
environmental factors may heavily influence the evolution of long-range
acoustic signals by imposing selection pressures that act to modify the sound
properties of signals in order to maximize their broadcast range and the
number of potential receivers (Endler,
1992
; Forrest,
1994
; Morton,
1975
). This could lead to a matching between signal and
environment, such that signals transmit optimally in native habitats and,
conversely, perform poorly when broadcast through non-native habitats.
Studies concerning the propagation of long-range acoustic signals in
relation to the environment in which they are transmitted have yielded mixed
results. The acoustic adaptation hypothesis for enhanced transmission
efficiency in native habitats has garnered support primarily from studies on
avian and primate taxa. Birds inhabiting different environments produce
vocalizations with characteristics suited to enhancing transmission in their
native habitats (e.g. Bertelli and Tubaro,
2002; Bowman, 1979
;
Cosens and Falls, 1984
;
Gish and Morton, 1981
;
Handford, 1981
;
Morton, 1975
;
Wiley, 1991
). Moreover, calls
broadcast in different environments exhibit differential rates of excess
attenuation and/or distortion in both birds (e.g.
Dabelsteen et al., 1993
;
Shy and Morton, 1986
) and
primates (e.g. Brown et al.,
1995
; Waser and Brown,
1986
; Waser and Waser,
1977
). In contrast, the influence of the environment on the
evolution of signal characteristics has been more difficult to establish in
anurans. Most studies have failed to find a significant correlation between
habitat acoustics and either signal characteristics
(Zimmerman, 1983
) or signal
propagation (Castellano et al.,
2003
; Kime et al.,
2000
; Penna and Solís,
1998
; but see Ryan et al.,
1990
). Variability in detecting the effects of habitat selection
are likely to be due to the multiplicity of additional factors that affect the
evolution of signals. Mismatches between signal and environment, which would
potentially mask the effects of habitat selection, could arise from predator
avoidance, competition avoidance, sexual selection, phylogenetic history, and
variation in the relative strengths of competing selection pressures. Here we
test the acoustic adaptation hypothesis for bladder grasshoppers (Orthoptera,
Pneumoridae) through an examination of acoustic signal transmission of
species-specific male mating calls in different habitat types. This is the
first detailed examination of the relationship between the environment and
sound propagation in an invertebrate group specialized for long-distance
signalling. We focus exclusively on habitat effects, since constraints imposed
by acoustic characteristics of the habitat provide the framework within which
other selection pressures must operate. We thus anticipate an effect that is
detectable, though perhaps not strong.
Bladder grasshoppers comprise a small family of up to 17 species
(Dirsh, 1965), with behaviour
and morphology uniquely suited for pair-formation via acoustic
duetting over distances of at least 50 m
(van Staaden and Römer,
1997
). With the aid of an air-filled, inflated abdomen functioning
as an acoustic resonator, males produce a nocturnal advertisement call that is
both extremely loud (98 dB SPL at 1 m) and relatively low in
frequency (1.43.2 kHz) for an insect only 50 mm in length. Together
with six pairs of highly sensitive abdominal hearing organs
(van Staaden and Römer,
1998
), this enables male signals to attain a viable transmission
distance of up to 1.9 km at night (van
Staaden and Römer, 1997
). Male signalling functions as the
primary basis for pair formation, with non-flighted receptive females
producing a softer response, enabling flighted males to locate them. The male
advertisement calls of pneumorids possess a high degree of species
specificity, displaying substantial variation in both temporal and structural
properties among species. However, despite these broad interspecific
differences in the male signal, courtship and mating follow a stereotyped
sequence in all species, and female calls are virtually indistinguishable.
Here we focus our attention on male signals, due to both the lack of
discernable differences in the female signal and the shorter transmission
distances thereof.
Pneumorids are endemic to the coastal regions of southern Africa, where
they are found in four distinct vegetation biomes: forest, savanna, fynbos
(`fine bush') and succulent karoo
(Rutherford, 1997). These four
habitat types represent a wide range of environmental conditions, varying in
extremes from dense, humid, forested areas to open, arid, semi-desert areas.
The forest biome is confined mostly to the wetter eastern seaboard, where it
is extremely patchy in distribution and comprises a very small total land
area. Forest vegetation at the site of transmission experiments comprised a
closed canopy of woody vegetation up to 25 m tall and was dominated by
Leucosidea sericea and Ficus thonningi, with trunk diameters
reaching 1 m, and an understory of Maytenus acuminata, Hypericum and
Helichrysum spp. The subtropical savanna biome, by far the largest
biome in southern Africa, consists of grasses interspersed with taller woody
vegetation. The area where experiments were conducted fell under the class of
broad-leaved savanna. This is a typical C4 grassland with Themeda,
Tristachya, Trachypogon and Aristida spp. being the most
prominent components, and average grass height reaching approximately 0.5 m.
The fynbos biome occupies the most southern and south-western regions of
southern Africa and is characterized by evergreen, fine-leaved shrubs of
intermediate height. Fynbos vegetation is renowned for its unparalleled
species diversity and is characterized by the presence of three distinctive
elements viz. restioids and ericoid shrubs, both ranging in height
from 0.5 m to 2 m, and overstory proteoid shrubs reaching a maximum height of
5 m (Cowling et al., 1997
). The
sparsely vegetated succulent karoo biome derives its name from the low-lying
leaf-succulent plants that dominate this biome. It is located along the
western coast of southern Africa and represents an intermediate state between
the less arid fynbos to the south and true desert to the north. Succulent
karoo vegetation, although similar to fynbos in some respects, has a
relatively higher proportion of bulbous plants, and the vegetation is lower
growing, sparser, and comprises more succulents than fynbos.
Our primary objective was to evaluate the relative importance of the environment in shaping signal evolution by comparing signal degradation across the four habitat types for seven species of bladder grasshopper. Of these, one species (Pneumora inanis Fabricius) was classified as being native to the forest, three (Bullacris intermedia Péringuey, B. membracioides Walker, B. serrata Thunberg) native to the savanna, two (B. obliqua Thunberg, Physemacris variolosus L.) native to the fynbos, and one (B. unicolor L.) native to the succulent karoo. With one exception, all species have geographic ranges that fall exclusively into one biome. However, B. unicolor, which is predominantly a succulent karoo species, extends slightly into the fynbos along the edges of its geographic distribution. In concordance with the acoustic adaptation hypothesis, we test the prediction that the transmission efficiency of long-distance signals is greater in native habitats relative to that in non-native habitats, specifically with respect to (i) transmission distance and (ii) signal fidelity.
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Materials and methods |
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Test sounds
Sound recordings of male advertisement calls used in the transmission
experiments (i.e. test sounds) were exemplars selected from a previously
recorded sound library. These songs were recorded in the laboratory using a
sound level meter (Bruel & Kjaer, model 2009; Naerum, Denmark) and a
microphone (1/2" condenser, type 2540, Larson & Davis, Provo, UT,
USA; A weighting, RMS fast) placed 1 m dorsal to a calling male in a wire mesh
cage. Songs were sampled at 44.1 kHz on an Apple Macintosh Powerbook
via the built-in 16-bit A/D soundboard and subsequently edited with
SoundEditTM16 (San Francisco, CA, USA). Male call characteristics,
including length, frequency and temporal patterning, vary substantially among
species (Table 1,
Fig. 2). Background noise was
generally low in the laboratory setting, thus test sounds had equivalent low
levels of background noise for each species. For each species, a single
exemplar was selected, based on average call characteristics for the species.
For ease of comparison, all calls were amplified to a uniform peak amplitude
value (amplification range: 0.819.1 dB). The order of signal
presentation was randomized and inter-song pauses of 3 s for repetitions of
the same call and 5 s fordifferent calls minimized the risk of
forward-masking. In other words, this time window was sufficient to prevent
reverberations of the previous call overlapping with the next signal.
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Transmission experiments
Experiments were carried out in which advertisement signals of seven
pneumorid species were broadcast and rerecorded along a transect at various
distances and heights from the sound source. An identical protocol was
followed in each of four habitat biomes. All sound transmission experiments
were conducted when wind speed was less than 1 m s1 and
ambient noise levels relatively low. A single speaker elevation (1.5 m) and
three microphone heights (0.2 m, 1 m, 2 m) were selected as representative
caller heights and receiver locations, respectively. Signal propagation was
assessed for three different receiver elevations, since female restriction to
their specific host plants determines the most likely transmission channel.
Males of most bladder grasshopper species call at the intermediate height of
1.5 m (M. J. van Staaden, personal observation), corresponding with the
maximum vegetation height in most habitats. The only notable exception is the
forest-dwelling P. inanis, which has a propensity to call at higher
elevations. Test sounds were broadcast from an Apple G4 laptop computer
running SoundEditTM16, and passed through a Pioneer GM-X252 amplifier
connected to a Jensen 6944 loudspeaker at the origin of the transect. The
broadcast signal was adjusted to a maximum intensity level of 95 dB
SPL (re 20 µPa) at a distance of 1 m, as measured with a
Larson-Davis DSP83 sound level meter. This value was selected based on the
known value for B. membracioides, the only species for which natural
sound intensity levels have been reliably recorded. While the values for
B. membracioides are believed to be similar to the natural calling
intensity levels of the other species, the possibility exists that some
species may call at intensities either higher or lower than the chosen
broadcast intensity. Within B. membracioides, males always call at
the maximal recorded intensity level to advertise their presence, and only
reduce the amplitude of their calls when in close proximity to a responding
female.
In each of the four field sites, a 100 m straight line transect was marked
out along a flat stretch of land bearing representative vegetation. This
distance corresponds to the maximum transmission distance at the behavioural
response threshold of female B. membracioides (van Staaden and
Römer, 1997,
1998
). The broadcast sounds
were re-recorded along the transect at six distances (1 m, 5 m, 10 m, 25 m, 50
m, 100 m) from the sound source using a Marantz PMD 430 (Setagaya, Japan)
audio cassette recorder connected via a 6 m cable to a wind-shielded,
unidirectional microphone (Sennheiser MZW 66; Wedemark, Germany). The
horizontally positioned microphone was shock mounted (Audio-Technica AT 8415,
Tokyo, Japan) on a 2 m extendible rod, and aligned with the loudspeaker by
eye. Recordings at a distance of 1 m were taken at a height of 1.5 m only,
level with the speaker. Under these circumstances, the sounds had suffered
negligible habitat-induced degradation, and served both as a control for any
sound distortion caused by the recording system and as calibration signals
with which to compare recordings taken at greater distances. Six repetitions
of each call were recorded at each distance and height over two consecutive
nights, in order to better represent the natural variability present under
field conditions.
Data analysis
All control (recorded at a distance of 1 m) and observation (recorded at
distances greater than 1 m) sounds were digitized onto an Apple MacIntosh G4
computer via the built-in sound-board (44.1 kHz sampling rate; 16 bit
sample size) and filtered with Canary 1.2 (Canary: the Cornell
Bioacoustics Workstation, Version 1.2. Cornell Laboratory of Ornithology,
Ithaca, NY, USA; 1995) to remove frequencies below 500 Hz and above 12 kHz.
This filtering did not compromise any components of the test signal itself.
Through auditory and sonogram inspection, we selected as a control sound one
of the three repetitions of each test signal recorded at 1 m that was not
superimposed by transient noise fluctuations. Data analysis involved
comparisons between filtered, degraded observation sounds, and their
respective species-specific, undegraded control sounds. Quality of signal
transmission was assessed via two measurements. Overall signal
amplitude was used as a measure of attenuation over distance and
spectrographic cross correlation (described below) served as a measure of
distortion over distance.
Spectrograms were created for each of the signals using a transform length of 256 points and cross correlation analysis performed on these. Control and observation signals were aligned at the start, the two signals slid past each other, and a correlation coefficient calculated for each point in time based on both temporal and amplitude differences between the two calls. The maximum cross correlation coefficient obtained from each comparison was plotted against recording distance for each species in each habitat type and height. A curve was then fitted to each of these 84 plots and the values of the slopes of the curves used in subsequent analyses. Because data were normally distributed, three-way analysis of variance (ANOVA) was used to test for differences in signal transmission, with broadcast habitat, native habitat and recording height as independent variables.
Signal attenuation was analyzed by measuring the average intensity for each signal and then plotting this value against recording distance in a similar manner to that described above. The slopes of the curves were again used to evaluate differences in signal transmission.
In addition, ANOVAs were used to analyze both cross correlation coefficients and amplitude at the maximum recording distance of 100 m, to assess differences among species within each vegetation biome. Due to the logarithmic nature of the dB scale, amplitude values in dB were converted into sound pressure values for the analysis and then converted back into dB.
Standard deviations (S.D.) of both cross correlation and intensity data were used to assess consistency of signal transmission. No significant differences in consistency (S.D.) were detected among any species for either cross correlation or intensity, and data from all species were therefore pooled to examine differences among habitats, using ANOVAs.
Environmental noise was estimated separately in each habitat by compiling 10 s of uncorrupted background noise from the silence between consecutive test sounds. From these, power spectra were derived representing background noise along the entire transect throughout the experimental session.
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Results |
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Distortion of transmitted grasshopper calls
There was a significant interaction between native habitat (the resident
habitat of the pneumorid producing the call) and broadcast habitat (the
habitat in which the call was broadcast) in the three-way ANOVA of
spectrographic cross correlation, indicating that calls distort differently
when broadcast in native versus non-native habitats
(Table 2). In addition, there
were marginally non-significant differences in broadcast habitat, recording
height and the interaction between these two factors
(Table 2). This suggests that
call distortion varies independently according to both the habitat through
which it is being transmitted and the height at which it is being transmitted,
and that calls may transmit differently at given heights in different
habitats.
|
Comparisons of cross correlation coefficients at a distance of 100 m revealed that the native forest species performed significantly better than all other species in the forest habitat at heights of both 1 m and 2 m, and significantly better than all except the succulent karoo species at a height of 0.2 m(Fig. 3A). In the fynbos (Fig. 3B), inhabitant species had significantly higher correlation coefficients than all other species at recording heights of 1 m and 2 m, although there were no significant differences at a height of 0.2 m. In their native habitat, savanna species outperformed the succulent karoo species at 0.2 m and 1 m heights, but fared significantly worse than fynbos species at 0.2 m and 2 m heights (Fig. 3C). Finally, in the succulent karoo, the indigenous species had significantly lower correlation coefficients than fynbos species at 0.2 m and 2 m, and than fynbos and savanna species at 1 m (Fig. 3D).
|
Attenuation of transmitted grasshopper calls
The habitat in which signals were broadcast, the native habitat of the
grasshoppers, and the height at which signals were recorded all had a strongly
significant effect on the amplitude of transmitted signals
(Table 3). Height also had a
significant interaction with broadcast habitat, indicating that calls
attenuate differently in different habitats at similar heights.
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Comparisons of amplitude measures at a maximum recording distance of 100 m are shown in Fig. 4. The call of the forest species attenuated significantly less in its native habitat than all other species at a height of 0.2 m, less than savanna and succulent karoo species at a height of 2 m, and less than savanna and succulent karoo species, but more than fynbos species, at a height of 1 m (Fig. 4A). Fynbos species had significantly higher amplitudes in the fynbos habitat than savanna and succulent karoo species at each of the three heights (Fig. 4B). Native species in the savanna had significantly lower amplitudes than forest and fynbos species at all three heights and significantly higher amplitudes than the succulent karoo species at 0.2 m and 1 m heights only (Fig. 4C). In the succulent karoo, the inhabitant species had significantly greater attenuation than forest and fynbos species at a height of 2 m, but showed no significant differences at both 0.2 m and 1 m heights (Fig. 4D).
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Consistency of grasshopper calls
Consistency of signal distortion differed significantly among habitats
(F3,417=38.351; P<0.001; Tukey multiple
comparison tests), with least variable distortion in forest and succulent
karoo habitats, followed by the savanna and then by the fynbos
(Fig. 5). Variation in sound
distortion increased with distance from the speaker and as height above ground
decreased. Consistency of signal attenuation also varied significantly among
habitats (F3,417=63.133; P<0.001; Tukey
multiple comparison tests), with the highest consistency exhibited in the
forest and the lowest in the fynbos (Fig.
6). Savanna and succulent karoo habitats were intermediate between
these two and did not differ from each other. As expected, variation in
attenuation was extremely low in the forest, and changed with neither
recording distance nor height. In the other three habitats, consistency
increased noticeably with distance at elevations of 1 m and 2 m.However, at
0.2 m recording height there was little or no relationship between standard
deviation and distance.
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Environmental noise
Levels of ambient background noise varied appreciably among localities
(Fig. 7). Background noise in
the forest was higher than in any other habitat and consisted mainly of the
sounds of water running in nearby streams and of calling frogs. The savanna
was also relatively noisy and was predominated by the songs of crickets and
other insects. Both the fynbos and the succulent karoo appeared to have less
background noise than the other two habitats. The fynbos was mostly
characterized by a few calling frogs and night birds, and the succulent karoo
by the calls of insects. In addition, background noise in the forest was
continuous, whereas in the other habitats it was intermittent.
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Discussion |
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The pattern of performance of species' signals in the forest was distinctly
different to that in the other three habitats, which all produced similar
results. Although transmission in the savanna, fynbos and succulent karoo
habitats yielded different levels of signal degradation, the relative
relationship among species remained comparable. This may be explained in part
by structural differences in the type of vegetation among the four habitats.
Whereas the forest represents a closed habitat dominated by 525 m high
trees and several understory layers, the other habitats are all more open with
predominately low-lying vegetation (<1 m), sparsely interspersed with
taller (12 m) shrubs. Moreover, while structural features are likely to
be of greater import than floristic ones, it is notable that fynbos and
succulent karoo biomes share 55% of their species diversity
(Rutherford, 1997). It is
therefore not surprising that at this level, our observations conform to
expectations, with species performing similarly in the savanna, fynbos and
succulent karoo, particularly at higher elevations, and performance in the
forest differing significantly from that of the open habitats.
Recent studies have stressed the importance of broadcast variability as a
critical consideration in the evolution of signals, perhaps even more so than
broadcast quality (Brown and Handford,
2000,
2003
). Although we found no
differences in transmission variation among species, we did identify
substantial differences among habitats. Interestingly, signal degradation in
the fynbos was far more variable than in any other habitat and may provide an
explanation as to why the calls of the native fynbos species performed
admirably in all habitats. Selection pressure to maximize the reliability of
information transfer in the signals of fynbos species potentially derives from
two sources, viz. inherent characteristics of the transmission
channel and inter-specific acoustic competition. The acoustic signals of
native fynbos species are characterized by either relatively low-frequency
calls, or very brief, high-frequency calls
(Fig. 2), design features that
could compensate for the lack of transmission reliability in their native
habitat. In addition, pneumorid species diversity and sympatry achieve their
highest levels in the fynbos habitat. The two fynbos species considered here
are sympatric in at least part of their range, as well as with other pneumorid
species not considered here (Dirsh,
1965
). This temporal and spatial overlap means that males of
several species may frequently call together in the same area, placing further
selection pressure on the transmission channel to produce calls that can be
clearly distinguished from those of heterospecifics. In light of this
distribution overlap, fynbos species may have increased the transmission
quality, rather than the consistency of their signals, and these features
cannot simultaneously be maximized in open habitats
(Brown and Handford, 2000
).
Height above ground level is an essential consideration in the transmission
of sounds (Dabelsteen et al.,
1993; Marten and Marler,
1977
; Mathevon et al.,
1996
; Waser and Waser,
1977
). We found cross correlation coefficients to be similar at
all three heights, indicating that, in contrast to the situation with birds
(Holland et al., 1998
),
elevation did not play a large role in signal distortion. Elevation did,
however, have considerable impact on signal attenuation, which was much more
pronounced closer to the ground. Consistency in signal propagation was also
found to vary in accordance with height. Degradation was more variable at
lower elevations and variation increased with distance at all three heights.
Variation in attenuation tended to remain static at 0.2 m, but increased with
distance at higher elevations. It should be noted that in our experimental
design, the speaker was always kept at a constant height above the ground and
only the position of the microphone was varied. It is likely that elevation
would have had a much more pronounced effect had the broadcast height been
adjusted in accordance with the receiver height.
The frequency dependency of the pattern of excess attenuation accumulation
with transmission distance has been widely documented
(Lang, 2000;
Marten and Marler, 1977
;
Morton, 1975
;
Naguib, 1995
). However, we
found no significant correlation between call frequency and transmission in
bladder grasshoppers. This lack of correlation was mostly due to the anomaly
of P. variolosus emitting a comparatively high frequency signal, yet
being one of the species with the highest transmission performances. Indeed,
if P. variolosus is removed from the analysis, the relationship
between call frequency and degradation becomes significant in the predicted
direction. Furthermore, carrier frequency and call length are strongly
negatively correlated in the species under examination here (Spearman
Rho=0.9643; P<0.001) and this relationship with call length
may well be masking the effect of frequency on call transmission, particularly
in P. variolosus, which has an exceptionally short advertisement
call. Reducing the duration of high frequency signals appears to be an
effective adaptive mechanism to counteract degradation, irrespective of
habitat type.
Ambient environmental noise is a form of acoustic interference that can
mask signals in the same frequency range, and noise levels have previously
been implicated in song divergence among populations within a species
(Slabbekoorn and Smith, 2002).
It is possible that environmental noise is placing selection pressure on
bladder grasshoppers to avoid calling in the same frequency range as either
other animals or abiotic factors in their local environment. Indeed, virtually
all species tested here produced calls with peak frequencies mismatched to the
dominant frequencies of ambient noise, from both biotic and abiotic sources,
in their native habitats. The only exception was B. unicolor in the
succulent karoo, which calls at a peak frequency that corresponds closely
(within 200 Hz) with the most dominant frequency of background noise in its
indigenous habitat. The precise source of this intermittent call is, as yet,
unidentified, but the acoustic challenge the species presents for B.
unicolor may constitute a telling exception to the apparent facility of
bladder grasshoppers for maintaining a private communication channel.
Only thirteen species of bladder grasshopper have males displaying the
primary morph of an inflated abdomen
(Dirsh, 1965) and thus have
the potential to produce long-distance mating signals. The seven species
included in this study were those for which quality sound recordings are
available, and represented the four vegetation types in unequal numbers of
between one and three species per biome. This inequality and the lack of
multiple representations of native species in two habitats are unfortunate,
but unavoidable. Pneumorids are notoriously difficult to find in the field and
the calls of six species have not yet been recorded. While a comprehensive
picture of the effects of habitat acoustics on the evolution of male
advertisement signals in this particular taxon would indubitably benefit by
including some of the currently more elusive species, the present study
demonstrates that signal structure varies among species in ways that reflect
acoustically relevant differences in the environment. Different environments
favour qualitatively different traits, thus supporting long-term evolutionary
effects of habitat acoustics on signals and signalling behaviour (sensory
drive; Endler, 1993
).
The results presented here provide support in an invertebrate group for the acoustic adaptation hypothesis of covariance of acoustic signals and habitat characteristics in a manner that maximizes communication range. Moreover, they provide a bridge between the evolutionary history of the group and the ecological drive on the sensory system. A striking feature of the results is that while environmental selection explains some of the observed signal diversity of bladder grasshoppers, the effects of selection on species-specific advertisement calls are rather uneven. This discrepancy may be attributable in part to variation in selection pressure; those species inhabiting environments less conducive to sound propagation over extended distances likely face stronger selection pressures to modify their signal characteristics in accordance with environmental properties. Furthermore, additional factors not considered here, such as female choice, malemale competition, density and variety of predators, and phylogenetic constraints, may all have had far-reaching impacts on signal evolution. The simultaneous coupling of these factors with environmental factors may account for the complex observed patterns of signal transmission.
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Acknowledgments |
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