Simultaneous measurement of metabolic and acoustic power and the efficiency of sound production in two mole cricket species (Orthoptera: Gryllotalpidae)
Department of Biology, College of the Holy Cross, Worcester, MA 01610, USA
* Author for correspondence (e-mail: kprestwich{at}holycross.edu)
Accepted 21 February 2005
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Summary |
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Acoustic power was on average sevenfold greater in S. borellii (21.2 vs 2.9 µW) and was more variable within individuals and across species than the metabolic rate. The efficiency of sound production was significantly higher in S. borellii (0.23 vs 0.03%). These values are below published estimates for other insects even though these mole crickets construct acoustic burrows that have the potential to increase efficiency. The cricket/burrow system in both species have an apparent Qln decrement of about 6, indicative of significant internal damping caused by the airspaces in the sand that forms the burrow's walls. Damping is therefore an important cause of the low sound production efficiency. In field conditions where burrow walls are saturated with water and there is less internal damping, calls are louder and sound production efficiency is likely higher.
File tooth depths and file tooth-to-tooth distances correlated with interspecific differences in metabolism and acoustic power much better than with wing stroke rates and plectrum-to-file tooth strike rates. To further investigate these correlations, we constructed two models of energy input to the tegminal oscillator. A model based on transfer of kinetic energy based on differences in tegminal velocity and file tooth spacing showed the most promise. Related calculations suggest that if there are no elastic savings, the power costs to accelerate and decelerate the tegmina are greater than the predicted power input to the tegminal oscillator, and that they are similar in the two species even though S. vicinus has a nearly threefold higher wing stroke rate.
Key words: mole cricket, Gryllotalpidae, Scapteriscus borellii, Scapteriscus vicinus, acoustics, bioacoustics, energetics, respirometry, stridulation, morphology, efficiency
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Introduction |
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Trilling calls, where a large number of sound pulses are produced without
extended pauses, are supported by high rates of metabolism
(Prestwich and Walker, 1981;
Kavanagh, 1987
;
Lee and Loher, 1993
). Given
the importance of loud signals, we expect that natural selection should favour
mechanisms that efficiently convert energy stores into sound. However, we know
very little about sound production efficiency (E) in insects.
Moreover, the few estimates that exist
(MacNally and Young, 1981
;
Kavanagh, 1987
;
Prestwich, 1988
;
Forrest, 1991
;
Bailey et al., 1993
) were
obtained by dividing each species' average value for acoustic power
(Pac) by the species' average metabolic power for calling,
Pcall. These measures are useful in establishing general
relationships but they do not permit rigorous tests of hypotheses relating to
inter- and intraspecific differences in E. Another problem with
previous studies is that all involved calculation of E using
measurements of Pcall and Pac taken at
different times. The use of respirometry (simultaneous determination of
O2 consumption and CO2 production) to obtain accurate
measurement of a cricket's Pcall requires small
respirometry chambers if there is to be good time resolution. However, these
same vessels are unsuitable for the measurement of acoustic power
(Prestwich et al., 1989
;
Prestwich, 1994
).
Our purpose was to measure the energetics of calling, the sound production,
and the E of sound production in two sibling species of mole crickets
(Orthoptera: Gryllotalpidae) that produce songs with different
fWS and fC. As with most mole
crickets, these species employ specially constructed calling burrows
(Fig. 1) that should allow them
to produce loud calls at a lower fC than would be expected
for insects of their size (Bennet-Clark,
1970,
1987
;
Daws et al., 1996
;
Nickerson et al., 1979
). We
devised a technique that allowed for the concurrent determination of
Pcall and Pac. These data allowed us
to test for intra- and inter-specific differences and to relate these results
to factors associated with the cricket's burrows and the morphology of their
stridulatory structures. We used these data to construct and evaluate two
models designed to predict the energy input into the tegminal
oscillator/acoustic radiators and to estimate the maximum costs associated
with overcoming inertia during the opening and closing movements of the
tegmina.
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Materials and methods |
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Analysis of acoustic features of calls
We collected representative calls from inside a low reverberation room at
25°C. Recordings were made using a Sennheiser (Wedemark, Germany) shotgun
microphone (model ME 66 back electret type capsule in conjunction with a K6
powering module) and Marantz (D&M Professional, Itasca, IL, USA) PMD 201
portable analog cassette tape recorder and type II high bias tape. Calls were
digitized using a 16-bit National Instruments (Austin, TX, USA) A-2100 A/D
board resident in a Macintosh (Cupertino, CA, USA) IIci computer. The A-2100
board was equipped with an antialiasing filter and sampled at 44.2 kHz. Except
as noted, we analyzed calls using Canary© 1.2.4 software (Cornell
Laboratory of Ornithology, Ithaca, NY, USA).
We estimated the period of a tegminal cycle as the mean time between the
start of two successive sound pulses (Fig.
2); the inverse of these values gave the fWS.
Several 1 s waveform samples were analyzed for each individual. We measured
the fC in two ways. Cycle-to-cycle fC
was determined by a custom-made program developed using National Instrument's
LabView. The program uses the zero-crossing (ZC) method to find each cycle's
period and frequency (Simmons and Ritchie,
1996; Bennet-Clark,
1999
). It is freely available from author K.N.P.
(http://www.holycross.edu/departments/biology/kprestwi/ZC).
Average fC was estimated as the peak frequency of a Canary
fast Fourier transform (FFT) spectrogram obtained from 1 s of normal calling.
FFT estimates are weighted towards the most energetic frequencies in the
analyzed pulse while averages of ZC measurements ignore amplitude.
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Driven cycles and cycles to peak power
Driven cycles are sound cycles where sustaining energy is added
via the stridulatory system to the tegmina's acoustic
oscillator/radiator (the harp and file; see
Bennet-Clark, 2003). We
estimated the number of driven cycles per pulse as those from the start to the
time when the sound pulse amplitude began to decay exponentially. This type of
decay is indicative of an undriven oscillator
(Fletcher, 1992
). We emphasize
that it is possible to miss the beginning of the undriven phase of a pulse by
perhaps one or two cycles. Our data for S vicinus are more prone to
error because their pulses are briefer than in S. borellii (see Figs
2 and
3). The number of tooth strikes
needed to reach peak amplitude is the number of driven cycles from the start
of a pulse to when peak amplitude is reached.
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The quality factor, Q
This parameter measures a resonant system's internal to external damping
and also the rate at which such a system reaches maximum amplitude or decays
(Bennet-Clark, 1999).
Q is given as:
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Ideally, Q is determined by exciting a resonant structure with a
high-amplitude acoustic source. When the driving sound is abruptly stopped,
the undriven decaying sound from the subject is recorded and Q is
calculated from the ln(decrement) of successive peaks (Bennet-Clark
1989,
1999
). We needed to know the
Q of the cricket-burrow system. This system consists of two coupled
resonances: the insect's tegmina and the burrow (Bennet-Clark,
1970
,
1987
). However, we could not
find a satisfactory way to mount the tegmina in the normal singing position
within a burrow and then perform the measurements. This forced us to use the
decay of the sound at the end of cricket-produced sound pulses. The main
pitfall to this approach is the inclusion of amplitude values that, although
found during the decaying portion of the call, nevertheless were driven by
tooth-plectrum impacts. Fig. 2
shows that towards the end of a sound pulse, the amplitude decreases over a
number of cycles. Initially the decay is non-exponential and is likely due to
lower energy input to the vibrating system. The exact transition between this
and a true exponential decay is difficult to identify by inspection and so we
calculated `Q-like' values from the each successive pair of peaks
during the pulse decay. Partially driven waves have large `false-Q
values' because their decay is less than what is seen with undriven waves.
When the tegmina are finally no longer being mechanically driven, the
calculated Q values stabilize around a lower, true Q value.
For a given sound pulse, we averaged the cycle-to-cycle Q values for
the true exponential decrease phase. We then replicated the measurement four
times for each individual, calculated individual's means and then used these
to find species averages. The point identified as the start of exponential
decay usually coincides with an abrupt frequency shift
(Bennet-Clark and Bailey,
2002
).
Morphometric measurements
We froze males of both species, removed and weighed the tegmina, and
measured the triangular-shaped harp along its two principal axes using the
inside margins of the veins as boundaries. Then, we measured the pronotum
medially and dissected out, blotted and weighed the tegminal musculature. Mass
was measured using a Mettler (Columbus, OH, USA) Model AC100 balance that
reads to 0.1 mg. Likely sources of errors include possible inclusion of
connective tissue in addition to the muscle and a ±0.1 mg variance in
weight found by repeatedly weighing the same sample. Dr Thomas J. Walker
provided some of these data to us.
Scanning electron microscopy of stridulatory files
We dissected right and left files from the tegmina of dried males of both
species, glued them to stubs, sputter-coated them using an Anatech
(Alexandria, VA, USA) Hummer VI-A and examined them using a JEOL (Peabody, MA,
USA) Model JEM-5400 Scanning Electron Microscope (SEM). Each specimen was
rotated to ensure a side view that allowed for the accurate determination of
file tooth depth. Typical magnification was 1000x or 1500x. Once
we had obtained a complete set of images for each file, we measured the depth
of each tooth as illustrated in Fig.
4 and the tooth-to-tooth distance (referred to as the `pitch' by
Bennet-Clark, 1970,
1987
).
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To estimate measurement variation, all specimens were placed in the SEM and photographed on at least two different days. Measurements of tooth depth from the photographs were done twice and were blind the person doing the measuring did not know the sample number. Repeat measurements were always within 10% (and usually much less) of each other.
Respirometry
Respirometry consisted of simultaneous measurements of CO2
production and O2 consumption. We used two airstreams, one from the
cricket's burrow or a respiratory chamber (for resting rates) and the other
from the room. The samples were first pulled through a Drierite column to
remove water and then passed through a CO2 analyzer (LI-COR
LI-6251, Lincoln, NE, USA) or Anarad AR 50 (Carrollton, TX, USA). Upon
emerging from the CO2 analyzer, both air streams were scrubbed free
of CO2 and water by soda lime and Drierite. Both samples then
passed through a dual channel O2 analyzer operated in the
differential mode (Sable Systems Model 1 FC-2 `Oxzilla', Las Vegas, NV, USA or
Ametek Applied Electrochemistry S-3A/II with N-37M sensor, Paoli, PA, USA). An
Ametek Applied Electrochemistry R-2 pump was upstream from the O2
analyser and the two flow rates were set to equal values using either two
Sierra Instruments mass flow control values (150 ml min1
capacity; Monterey, CA, USA) operated by a Sable Systems controller or by two
Cole-Parmer Manostat Riteflow® 150mm Flowmeters (Vernon Hills, IL, USA).
Flow rates were 6075 ml min1. We read gas fraction
data from the O2 and CO2 analyzer analog outputs using a
16-bit resolution National Instruments NB MIO16X A/D board in the Mac
computer. The A/D process was controlled by a custom program developed using
National Instruments LabView® software. The program recorded data points
that were the average of 100 readings taken over a 0.1 s period, each with a
theoretical resolution of 76 µV. A new round of measurements was made every
2 s. The averaging procedure corrected for small, short-period, random
fluctuations in the instrument and A/D converter outputs. At the conclusion of
an experiment, the software saved the data in a spreadsheet format for later
analysis.
There were a number of potential sources of error in our respirometry. The experimenter's presence and position in the room will change FO2 and FCO2 in the ambient air. To avoid this, whenever the observer (K.N.P.) was in the room, he breathed through an Otis valve that routed his expired breath into a Douglas bag. A more difficult set of problems related to the conflict between gas sampling that gave good time resolution and the capabilities of the gas analyzers, especially the O2 analyzers, to register consistent differences. Obtaining high precision oxygen fractions (FO2) is difficult because at sampling flow rates that give good time resolution, the differences in FO2 caused by the cricket are relatively small compared to the background concentration of O2. Additionally, O2 analyzers are sensitive to changes in airflow rate such as occurs when sand from calling burrows entered the sampling tube. Finally, O2 analyzers are also prone to significant drift. This problem is made worse by the fact that the two O2 detectors in the instruments we used tended to drift independently of each other (although the FC-2 was considerably more stable).
To minimize error from these sources, we (i) selected flow rates that
provided the desired time resolution yet that are low enough so that the
animal creates a reliably detectable difference in partial pressure between
the sample and reference streams; (ii) used short measurement periods (seldom
longer than 15 min), always followed by re-standardization of the two
airstreams; (iii) carefully monitored air flow rates (see below); and (iv)
performed many replications. The volumes of the acoustic burrows were
1015 ml (Bennet-Clark,
1987) and we found that 6075 ml min1 flow
rates were high enough to give good temporal resolution, low enough to give
values of FO2 that were distinguishable from environmental
and instrumental fluctuations, and were low enough that sand was usually not
aspirated into the system. A mathematical model that used burrow volume, flow,
estimated metabolic rates, and initial gas concentrations, predicted that,
under expected conditions, less than 3 min would be required to reach a steady
state once sampling began. In order to err towards caution, we sampled air
from the burrow of continuously calling crickets for at least 4 min before
using the gas fractions in metabolism calculations. To evaluate the success of
these procedures, we compared the magnitude of typical changes in
FO2 associated with calling metabolism to the largest
fluctuations in FO2 observed when monitoring room air over
the same time interval. Changes in FO2 in going from rest
to calling were minimally 8 times this standard. We note that drift was never
a problem with CO2 readings. Changes in FCO2
during calling were greater than 10% of the analyzer's full span and more than
twice the background FCO2.
Calculations of the rates of oxygen consumption
(O2) and carbon dioxide
production (
CO2) were
according to Withers (1977
):
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To facilitate comparison with previous studies, we calculated metabolic rates on both whole animal and mass-specific bases. Crickets were weighed when first placed in their sand-filled bucket and about every 10 days thereafter. The reason for not weighing more frequently was to avoid disruption of the burrow system. Typically crickets did not call for several days after extensive burrow disruption. Nevertheless, mass changes were small (about ±5% of total initial mass) and their direction was unpredictable.
All evidence suggests that calling crickets are completely aerobic
(Prestwich, 1994).
Accordingly, we found metabolic power (mW) from
CO2 by finding the
respiratory quotient
(RQ=
CO2/
O2)
and then using this to find energy equivalence of a volume of CO2
from a standard conversion table.
Sampling air from the calling burrow
Several hours before `lab sunset', we sprinkled water on the soil of each
cricket's container. This packed the sand and increased the likelihood that
the crickets would build or reopen an acoustic burrow and sing. Individuals
began tuning their burrows shortly after the lab sunset. Calling began within
half an hour and continued for up to 2 h.
We sampled gas from the bulb portion of the burrow (Fig. 1) using a Tygon tube (3 mm o.d., 2.5 mm i.d.). To place the sampling tube, we guessed the location of the bulb from the shape of the burrow opening and then gently punched through the overburden with a 3 mm diameter dowel (using a swirling motion that tended to pack sand into the burrow walls). Resistance to pushing the dowel decreased when the bulb was breached. We then gradually widened the hole to a final diameter of 45 mm. Finally, we inserted the sampling tube to a depth slightly greater than the sampling hole and then sealed the sampling tube in place by tamping moist soil around the tube and by adding small amounts of water with an eyedropper. As a result, air was drawn into the burrow opening, past the cricket and then to the sampling tube. The burrow became the functional equivalent of a mask.
The problems with this method are that (i) sand can enter the sampling tube, and (ii) air from sources besides the burrow entrance might be able to enter the sample air stream. Entry of sand resulted in increased resistance to airflow as compared to when the gas analyzers were standardized. Increased resistance leads to decreased air stream pressure, which results in spuriously lowered O2 partial pressures and erroneously inflated metabolic rates. Fortunately, sand was easy to detect after the run by inspection and/or during a run by decreases in flow rate and FO2. Any time more than a few grains were present in the tube (about 30% of all measurements), the data were discarded.
We believe that contamination of the sampling air stream by gases not from the calling burrow (e.g. from the main burrow) was a minor problem. Although we knew that air from the main burrow and soil interstitial air contained more CO2 and less O2 than air entering the burrow, we also knew that both of these were high-resistance pathways. To ensure that their resistance remained high, we watered and packed the surface as mentioned previously and made certain that the exponential horn (Fig. 1) was the only opening to the animal's burrow. We also ascertained that burrow and interstitial gases did not cause noticeable errors with the following procedure. Typically, when mole crickets stop calling, they fill the exponential horn with sand. During the day when the mole crickets were typically deep in the soil, we unplugged the horn and set up the sampling and recording apparatus as described above. However, we covered the opening of the horn with a cut-off top of a plastic soft drink bottle. The cut ends were buried in the soil and the bottle's top was connected via a tube to a Douglas bag filled with essentially pure N2. We sampled O2 and CO2 from the covered burrow as if there were an animal calling and found that during the first 30 s to 1 min, FCO2 was slightly elevated and thereafter it dropped to zero (as did O2). These data indicated that some CO2 (most likely from the calling burrow and the main tunnel) was sampled at the start of the measurement interval. However, the calling burrow gas was quickly replaced with N2 and, by 3 min equilibrium, with the main burrow gas. Since our experimental measurements all relied on steady-state FO2 and FCO2 values taken over a 510 min interval, this transition period was not a problem.
There was no measurable effect on sound pressure level, fC or fWS as a result of inserting the sampling tube. We concluded that the energetics of calling was not altered by our sampling procedure.
Resting metabolic rates
We measured resting CO2
and
O2 by putting crickets
in 25 ml flow-through respirometry chambers with a flow rate of 25 ml
min1. Each chamber contained a folded, moistened piece of
paper towel that simulated wet sand and allowed the animals to hide.
Measurement periods typically lasted 30 min, during which time the crickets
remained inactive. These are not standard metabolic rates because the animals
had access to food up to the time of the measurements. It is unlikely that
S. borellii and S. vicinus ever undergo periods of food
deprivation and we wished our data to be as comparable as possible to natural
conditions.
Acoustic power
We measured sound pressure levels (SPL) at the same time we measured the
cricket's calling metabolism. We used a Larson-Davis (Provo, UT, USA) Model
812 sound pressure level meter (re: 20 µPa) set to the slow r.m.s. (0.5 s
timeconstant) and `C' scale settings
(Peterson, 1980). The SPL
meter was calibrated at least once a week, although it rarely required
adjustment. Since both species' songs are continuous trills of nearly
identical sound pulses, a true r.m.s. (average) SPL can be obtained by taking
2 s or more of continuous readings
(Prestwich et al., 1989
). The
experimenter held the SPL meter's detachable microphone at a series of defined
positions in the far field, 0.25 m from the burrow while using a thin metal
rod and wire hemisphere as a distance gauges.
Forrest (1991) reported
that the sound fields in both species are essentially hemispherical. We
confirmed this by determining sound fields for four individuals of each
species by measuring SPL at 33 regularly spaced points on a 0.25 m hemisphere
(Prestwich et al., 1989
;
Forrest, 1991
). SPL readings
were usually within ±1 dB of the average SPL with occasional values up
to 3 dB different from average (usually those taken near ground level). The
fact that the sound fields were approximately hemispherical made us confident
that we could determine the acoustic power output accurately and rapidly by
using five positions (vertical, and 45° above ground level on lines
running through the long axis of the burrow opening and its perpendicular). We
repeated these measurements 34 times for each individual during the 10
min interval when respiration was also being measured. Each SPL value was then
converted to intensity I using the equation:
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Since we knew that the sound fields are not exact hemispheres, we attempted
to estimate the error inherent in our method. Accordingly, we measured ten
33-point sound fields and calculated their surface areas using a custom-made
computer Excel spreadsheet that summed the areas of a surface determined by
triangles whose vertices included all measurement points (see
Forrest, 1991). We then took a
five-point subset of the 33 values using the points that corresponded to those
used in our sound field measurements. From this, we determined the average
distance to the isobar as used with the 33-point set, and calculated the
surface area of a hemisphere of that radius. The largest discrepancy between
these methods was nearly 11%, but overall it averaged ca. ±3%.
Statistical analyses
Unless otherwise reported, all tests of significance used a two-tailed
t-test that assumed unequal variance or one-way analyses of variance
(ANOVA). Efficiency and other measures calculated from ratios were transformed
by taking the arcsine of the square root of the data expressed prior to
statistical analysis (Sokal and Rohlf,
1981, p. 427). In this paper, we consider the result of any
statistical test where the chance of a null hypothesis being correct,
P, was <0.05 as significant: P<0.01, was considered
highly significant. We do not believe in following these cutoffs blindly and
so we do discuss some cases where 0.15<H0>0.05. In
all other cases we simply term the results non-significant.
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Results |
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Table 1 summarizes species
averages for call parameters related to energetics. The
fWS is nearly threefold greater in S. vicinus and
its mean fC is about 20% higher, as reported previously by
Ulagaraj (1976). The
percentage of the tegminal cycle when there is contact between the
stridulatory surfaces is significantly greater in S. borellii (64%
vs 52%). Moreover, S. borellii strikes significantly more
teeth per wing stroke (30.4 vs 10.7), and a significantly greater
number of teeth before maximum sound amplitude is reached (about 16
vs 7) than S. vicinus. There were no significant differences
in the numbers of teeth struck per second, about 1600 in both species at
25°C. The Q values of the cricket-burrow systems were about
67. These Q values lie between Bennet-Clark's measurements for
the burrows and tegmina in S. borellii
(Bennet-Clark, 1987
).
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There were highly significant interspecific differences in
Pac. Table
1 shows that on average S. borellii produced about 7
times (8.6 dB) more acoustic energy than did typical S. vicinus.
There was no overlap in Pac values between the species.
Among S. vicinus there was an 18-fold difference in individuals' mean
Pac, and there were statistically significant differences
in Pac (P=0.02). By contrast,
Pac in S. borellii varied by only a factor of
three among individuals and this difference was not statistically significant.
We note that Forrest (1991
)
measured SPL and Pac for both species as individuals
called from containers identical to the ones we used. Our analysis of
Forrest's published data does not reveal significant differences in
Pac between the two species (P=0.25, 20 d.f.,
t-test). The means we report for each species
(Table 1) fall within the
ranges of Pac reported by Forrest, but the mean
Pac we measured for S. borellii is about 3.1-fold
or 5 dB greater (P=0.001, 20 d.f., t-test) than that
obtained by Forrest (1991
). On
the other hand, the mean Pac that we measured for S
vicinus is about one-third the value measured by Forrest
(1991
). This is a significant
difference (P=0.04).
The differences between our data and published Pac
values led us to re-measure Pac on 3 subsequent years
using the same conditions as in the original experiments. Later results agreed
with our earlier measurements. We also took field measurements on unconfined
individuals. These showed that S. borellii was louder (typically
23 dB SPL) than its congener and that both species had
approximately the same shape sound field as we measured in the laboratory and
as was found by Forrest
(1991
). The reasons for the
discrepancies remain unclear. In any case, our results reinforce earlier
measurements showing that the amount of acoustic energy that leaves the burrow
of these species is highly variable and that S. borellii usually
produces more sound (Ulagaraj,
1976
; Forrest,
1991
).
File morphology
The length of the file is similar in both species
(Table 2). In S.
vicinus, tooth spacing was approximately constant along the lengths of
both the left and right files (Fig.
5). By contrast, in S. borellii there was marked
variation in tooth-to-tooth distance along both the left and right files.
Fig. 5 shows that, moving from
the plectrum, tooth spacing begins to increase at about tooth number 5 and
reaches a maximum spacing between numbers 25 to 30. Thereafter, the spacing
gradually decreases.
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Besides differences in the pattern of tooth spacing, there are 30% more
teeth per file in S. vicinus and the teeth are 50% more densely
packed (Table 2). Part of the
difference in tooth density is explained by the 1.2-fold greater average
distance between file teeth in S. borellii, especially mid-file
(Fig. 5). Moreover, in the
region of the file most likely used for stridulation (tooth numbers
545) the inter-tooth distances average about 1.5-fold greater in S.
borellii (maximum of about 1.7-fold difference). All of these ratios are
highly significant statistically, as are the ratios for left side files. We
note that our measurements of tooth-to-tooth distance are twofold greater than
those reported by Bennet-Clark
(1987) for S.
borellii. We believe that his measurements (of what he called the file
pitch) are of the `tooth interval' the distance between the end of one
tooth and start of the next, instead of the distance between tooth `peaks'
that we used (see Fig. 4). If
we use this definition, we find distances similar to Bennet-Clark's.
The average tegminal closing velocity is greater in S. borellii, even though it has the lower fC. The tooth strike rate equals the fC, and so teeth are hit about 1.2 times as frequently in S. vicinus (Table 1). However, the average distance between teeth in the sections of the file likely used for stridulation average are 1.5 times greater in S. borellii.
Each species' file teeth have similar shapes
(Fig. 4) but the teeth are
decidedly larger in S. borellii. For right tegmina, the S.
borellii to S. vicinus ratio of tooth depth is 1.33
(Fig. 6) and for the left it is
1.24. In S. borellii, the right file teeth were deeper than the left,
a highly significant difference, although this traced entirely to the first 20
teeth, which tended to be shallower on the left tegmen
(P<<0.001 for all comparisons; t-tests). By contrast,
we found no significant difference in left and right side tooth depths for
S. vicinus (P=0.12, 156 d.f.; t-test). We note that
our measurements of file tooth depth for S. borellii average 30% less
than those reported by Bennet-Clark
(1987). We believe the
difference is explained by the fact we were able to obtain higher
magnification images.
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Tegminal and thoracic morphology
Morphometric measurements of the tegmina and associated musculature for
similarly sized individuals of both species are given on
Table 3. Correlations between
pronotal length and tegminal muscle masses, although all positive, were not
statistically significant. The lack of significance may trace to the small
size range of the crickets we measured. Although S. borellii is
louder than S. vicinus (Table
1), we found no significant differences in their tegminal muscle
masses, an observation that seems inconsistent with our measurements of a
higher mass-specific calling metabolism (see below). Nor were the apparent
left vs right side asymmetries in muscle mass statistically
significant. Lack of statistical significance is not the same thing as
identity and we view these results with caution, given the difficulty of
repeatably excising small muscles.
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Table 3 also presents
average dimensions of the harps for the right side tegmina. Note that these
measurements are for different insects than those given in
Table 2. Regressions of
pronotal lengths with harp's linear dimensions and areas (not given) were
highly significant in both species: larger animals generally possessed larger
harps. Harp area is about 7.5% greater for S. vicinus. The orthodox
view is that the acoustic inertance of the harp should vary directly with
area, especially in closely related species
(Nocke, 1971). If we assume
that the spring constant of the tegminal acoustic resonance is the same in
both species and is independent of harp area and body size, then we predict
the fC to be about 3.5% lower in S. vicinus, when
in fact it averages 20% higher (Table
1). This suggests that either harp area does not strictly predict
inertance or/and that harp stiffness is greater in S. vicinus.
Bennet-Clark (2003
) showed that
in Teleogryllus, the most important resonant structure is the file.
If this were the case in Scapteriscus, harp area would not
necessarily be a good predictor of fC.
Metabolism
Figs 7,
8,
9 show
CO2 and/or
O2 during calling in S.
borellii. Results for S. vicinus were similar.
Fig. 7 is typical of 60% of our
records. This individual called continuously except for brief 1224 s
stops at time =5 and 7 min. Otherwise,
CO2 and
O2 were approximately
constant, consistent with a constant Pac. This
individual's respiratory quotient (RQ) was steady at about 0.89, similar to
the values for all individuals of both species
(Table 4) and indicative of
mixed fat/carbohydrate metabolism.
|
|
|
|
In contrast to Fig. 7, about
40% of our measurements of metabolism during continuous calling showed that
the metabolic rate gradually decreased between 5 and 20%.
Fig. 8 is the record for a
cricket that called continuously for 6 min. Its metabolic rate increased and
then slowly dropped by nearly 20% while maintaining a constant value RQ.
Fig. 9 shows
CO2 for another S.
borellii over an 18.5 min period, containing seven distinct calling bouts
ranging in duration from 90 s to nearly 5 min. Peak and average
CO2 differs between many of
the calling periods.
We suspected that decreases in metabolism during continuous trilling were artifacts due, for example, to a lack of equilibration of the burrow air with the cricket's expired respiratory gases (see Materials and methods). Yet Fig. 9 depicts a result where the burrow was sampled continuously and where the highest metabolic rates were measured during the shorter calling bouts. If crickets had a constant calling metabolic rate, then short calling bouts would have the greatest chance to produce underestimates. Nor could the decreases be explained as the metabolic reflection of decreased body movements; unlike many other crickets, mole crickets do not move about when calling. During four long calling bouts in two individual S. borellii, we observed Pac decreases of 1015% (about 0.4 to 0.7 dB) over a time when respiratory rates decreased by an average 15%. Although detectable using a SPL meter, this decrease in Pac is difficult for human observers to discern. Recently, one of us (K.N.P.) obtained similar results in a gryllid (Anurogryllus arboreus) under highly controlled conditions. We conclude that an individual's calling metabolic rate can vary although the mechanism is not clear.
Table 4 makes several
interspecific comparisons of metabolic rates. At rest, there were no
significant interspecific differences in either whole-animal or mass-specific
measures of respiration and the RQ values suggested carbohydrate metabolism.
All individuals used for resting rates were approximately the same size. By
contrast, the interpretation of the data for calling individuals was
complicated by size biases. Although similar variation in body size and mass
is seen in field collections, the mass of S. borellii that called in
our study averaged over 20% less, with smaller pronota, than the S.
vicinus used in the calling study. Given this difference, we preferred to
use mass-specific CO2 for
interspecific comparisons of calling costs. By this measure, S.
borellii averaged 40% higher metabolic rate. On the other hand,
whole-cricket metabolic rates during calling were not significantly
different.
We note an apparent conflict between results in Tables 3 and 4. Table 3 suggests that similarly sized individuals of the two species have nearly identical tegminal muscle mass. Assuming that calling metabolism mostly reflects the activity of tegminal muscles and since we expect smaller muscles in smaller individuals, then we expected lower whole-animal rates of metabolism in the smaller S. borellii. Yet their calling metabolic rates were nearly the same as the larger S. vicinus. In retrospect, it would be far more useful to have obtained muscle masses and tegminal measurements for the same crickets used in the metabolism study. Nevertheless, the discrepancy illustrates the dangers inherent in comparisons involving related but different measures on different individuals.
We found intraspecific differences in whole-animal Pcall in S. vicinus. In S. borellii, differences were suggested but were not statistically significant (one-way ANOVA, P=0.12; 6,36 d.f.). Regressions of Pcall on mass were not statistically significant for either species. However, the sample sizes were small, as were the ranges of mass. Moreover, although mass is the most commonly used measure of size when normalizing metabolism, perhaps there are better indices less susceptible to recent feeding, drinking or evacuation. The usefulness of other size metrics needs to be investigated in more tractable and better-known species.
We obtained three measurements of the energetics of refurbishing and tuning
burrows in S. borellii (for a detailed discussion of burrow building,
see Bennet-Clark, 1987). Loose
sand used to plug the burrow was moved about mostly in the first half of this
period. Later, less sand was moved, although the animal continued moving about
steadily except when it made brief (<5 s) calls to check on the progress of
tuning its burrow. We were not able to separate satisfactorily the cost of
digging from the cost of these brief calls. On average, a 0.83 g S.
borellii needed about 14 min to complete the process, at a cost of
between about 2.2 and 3.4 J. Average power consumption was slightly less than
4.0 mW, approximately 2.5 times resting but only 40% of the typical
Pcall (Table
4). For comparison, the net cost of calling in S.
borellii for 14 min is about 7.7 J and calling bouts commonly last 2 h
for a total calling cost of about 65 J.
Covariation of acoustic and metabolic power and the efficiency of sound production
We found little evidence for relationships between
Pcall and Pac. Although individual's
metabolic rates and loudness varied on different evenings, only one of six
S. borellii and one out of four S. vicinus had statistically
significant regressions of Pac on
Pcall. Within these individuals, Pac
was generally more variable than Pcall. Values often
differed from the individual's mean by more than ±50%. Likewise, we did
not find statistically significant linear regressions between individuals'
mean Pac vs their mean Pcall
(see Fig. 10, S. borellii,
r2=0.37, P=0.19, ANOVA, 1,5 d.f.; for S. vicinus,
r2=0.32, P=0.27; 1,3 d.f.). Thus, with our samples,
Pac is not a reliable indicator of a signaler's metabolic
power. We caution that this conclusion is based on a small sample size with a
small range of body sizes when compared to what can be found in the field.
|
Efficiency of sound production E is defined as the ratio of acoustic (output) to metabolic (input) power. Table 4 gives species averages and error terms computed using both total metabolism and net metabolism for calling. Our data are unique for animal sound production measurements because they allowed us not only to estimate E for individuals, but also to obtain error terms and test for differences. Calculated values of E based on total metabolism averaged 0.23% in S. borellii (N=7) and 0.03% in S. vicinus (N=5), an approximately eightfold difference. The difference between species averages was statistically highly significant. Means and error terms for individuals are shown in Fig. 11. For S. borellii, coefficients of variation for E average 64% (range: 10131%) and there were no statistically significant differences among individuals. By contrast, individuals' coefficients of variation for E were less in S. vicinus (mean 41%, range 2578%) and there were statistically highly significant individual differences (P=0.002; 3, 21 d.f.; ANOVA).
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Discussion |
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Metabolism and calling
If a signal's energy attributes provide accurate information about the
condition of the signaler, then we expect to see individual differences in
whole-animal Pcall. Moreover, call parameters that
determine Pac should reliably correlate with
Pcall. The causes of differences in
Pcall may be classified as size-dependent (larger crickets
are expected to have larger muscles) and size-independent (general condition
or calling strategy without respect to size). We found significant differences
in Pcall among individual S. vicinus, and our
data suggest the same in S. borellii using samples consisting of
similarly sized individuals (all masses within 15% of the species' sample
mean). This supports the presence of size-independent differences in
Pcall in both species. This conclusion is also supported
by evening-to-evening variation in some individuals'
Pcall. The average coefficient of variation (s.d./mean) in
CO2 within individuals of
both species over time was about 10% (maximum=15%), and our controls suggest
that <20% of this variation was experimental artifact. Although we did not
demonstrate them, we believe it likely that size-dependent differences in
Pcall will be found with a sample that incorporated the
full range of body masses seen in the field (mass varies in both species by a
factor of 23).
Pcall, Pac, E and calling
parameters in crickets that trill are compared in
Table 5. In comparison to the
other species, both Scapteriscus species have low mass-specific
Pcall. The most relevant comparison is with an Australian
mole cricket Gryllotalpa australis, which has a value of
Pcall about 2.6-fold greater than S. borellii.
Prestwich and Walker (1981)
proposed that fWS might be of paramount importance in
determining Pcall. However, the data on
Table 5 refute this hypothesis,
at least as far as its being strongly determinative in all species. For
instance, G. australis is roughly the same size and has a value for
fWS that is about half that of S. vicinus. Yet
G. australis' cost of calling is 2.6-fold higher. The same holds when
S. borellii and S. vicinus are compared: S. vicinus
has the higher fWS and the lower mass-specific
Pcall. Nor are the differences in
Pcall shown in Table
5 fully explainable by differences in calling effort. In crickets,
calling effort is closely related to the total number of plectrum-to-tooth
strikes per unit time. Using Scapteriscus as an example, the total
number of teeth struck per second is the same in both species although there
are significant interspecific differences in mass-specific
Pcall (Tables
1 and
4).
|
The data in Table 5 suggest
call amplitude as a central correlate with Pcall. G.
australis has a greater SPL
(Kavanagh, 1987) than either
of the Scapteriscus (Table
1) and a higher mass-specific Pcall.
Anurogryllus muticus has a Pcall about 2.5-fold
greater than its congener, A. arboreus and a small data set (K.N.P.,
unpublished data) suggests that its average SPL is several dB greater.
However, any correlation is complicated because fWS in
A. muticus is about twice that of A. arboreus
(Table 5). Moreover, we found
that Pac in S. borellii was about sevenfold
greater than S. vicinus even though its mass-specific
Pcall was only 30% greater.
In summary, it is evident and not surprising that energy is partitioned
differently between fWS, calling effort and signal
amplitude in different species. The relationships between these variables need
to be more systematically and rigorously investigated than in the past
(Prestwich and Walker, 1981;
Prestwich, 1994
). It is
especially important that individual differences in these parameters should be
documented when they exist.
The acoustic burrow and the efficiency of sound production
In mole crickets, E is determined by (i) the characteristics of
the acoustic burrow and (ii) the biochemical and mechanical processes that
operate as energy is transferred from fuel molecules to the cricket's
immediate acoustic environment (Bennet-Clark,
1970,
1989
,
1995
;
Prestwich, 1994
).
The burrow's effect on E is determined by its construction, the
animal's calling position, and the porosity of the burrow walls (Bennet-Clark,
1970,
1987
;
Daws et al., 1996
). If the
soil is porous and filled with air, sound will penetrate the burrow walls and
dissipate (Daws et al., 1996
).
This increases internal damping and lowers the Q (Eq. 1) of the
cricket-burrow system (Bennet-Clark,
1989
; Fletcher,
1992
). The Q values we measured for individuals of both
species calling within burrows are generally less than one-half those of
isolated tegmina or crickets calling in the open (Nocke, 1970; Bennet-Clark,
1970
,
1975
,
1987
,
2003
;
Prestwich et al., 2000
).
Others have reported that mole cricket calls issuing from wetter burrows
are louder (Scapteriscus;
Ulagaraj, 1976; Forrest,
1979
,
1983
,
1989
, 1999;
Gryllotalpa; Bennet-Clark,
1970
). In our study, two S. borellii whose singing
burrows were located at the edges of ponds produced songs with mean SPL re: 20
µPa of 8285 dB at 0.25 m, corresponding to Pac
of 62124 µW. These values were three- to sixfold larger than we
typically measured in the laboratory (Table
1). Several nights after capture, these same individuals called in
the laboratory from moist (but not saturated) burrows and their SPL re: 20
µPa had decreased to approximately 75 dB at 0.25 m
(Pac
12 µW). Heavy watering of the soil in the
cricket's buckets on subsequent days was accompanied by an increase in
loudness of several dB without any consistent change in
Pcall. Regrettably, we failed to measure the
burrow/cricket Q as a function of watering. Nevertheless, day-to-day
differences within individuals' Pac were greater in both
species than was the variation in Pcall. As has been
suspected since the earliest field studies, reversible changes in
Pac are due to changes in burrow damping and therefore in
E. Variation in Pcall plays a comparatively minor
role.
The E for both Scapteriscus species are several-fold
lower than other trilling crickets, at least with the soil conditions
prevailing during our measurements. Bennet-Clark
(1970,
1987
) and Daws et al.
(1996
) have shown that mole
cricket burrows have the potential to confer exceptionally high E:
certainly greater than 1% and perhaps much higher. In Gryllotalpa
australis, E is about 1% (Kavanagh,
1987
). Our data suggest that in S. borellii and perhaps
its congener, E might be as high as 0.61.3% if the burrow
walls are saturated with water. We predict similarly high E in
species that live in non-porous, clay soils. However, in Florida few burrows
are built in conditions where the walls are consistently saturated and we
believe that E is commonly low if there has not been a recent rain.
Bennet-Clark (1987
,
1989
) suggested that an
important function of the acoustic burrow is to allow production of reasonably
loud sounds at a lower fC than could be radiated
efficiently without the burrow. In many environments, lower frequencies
attenuate less rapidly (Marten and Marler,
1977
). Thus, for a given initial signal intensity, a lower
fC increases the potential number of females that might be
attracted to a calling male (Bennet-Clark,
1987
,
1989
;
Forrest, 1979
;
Forrest and Raspet, 1994
).
However, since intensity varies with soil conditions, the usefulness of the
signal to conspecific females would seem restricted to species identity,
caller location and habitat quality
(Forrest, 1989
;
Forrest and Raspet, 1994
),
although it remains possible that information about the signaller's condition
might be encoded in fC and/or frequency stability
(Simmons and Ritchie, 1996
) or
pulse duration.
Efficiency of sound production and the operation of the stridulatory apparatus
Discussions and analyses of energy transfers have centered on estimating
E for the entire process and/or have focused on the coupling of the
radiator to acoustic environment (Bennet-Clark,
1970,
1975
,
1987
,
1989
,
1995
;
Kavanagh, 1987
;
Prestwich, 1994
;
Forrest, 1991
;
Bailey et al., 1993
). What
follows is our attempt to provide quantitative analyses of the energetics of
stridulation proper. By this, we mean the power associated with: (i) contact
between stridulatory surfaces that ultimately drive the vibrations of the
tegminal oscillator; and (ii) accelerating and decelerating the tegmina when
the stridulatory surfaces are not engaged (the entire opening stroke plus the
closing stroke's initial and final accelerations). We first present two models
of power transfer to the tegminal oscillator. They differ in how they
calculate the energy transferred from the closing tegmina to the vibrating
wing surface during each tooth strike.
The spring model
This model centers on finding the energy required to bend the file enough
so that the plectrum disengages and moves on to the next tooth. The model
assumes that the minimum bending required to unlock the file and plectrum
would equal the file tooth depth. For both tegmina:
![]() | ((5) |
The kinetic energy (KE) transfer model
Bennet-Clark (1970,
1987
) found that the peak
amplitude of each cycle during a sound pulse was directly related to the
`tooth pitch' (tooth-to-tooth distance) profile of the midsection of the files
in Gryllotalpa vineae and in S. borellii. Although
Bennet-Clark did not write it, the implication of this relationship is that
tooth spacing helps to determine the relative velocities of the tegmina at
plectrumtooth impact. Assuming a constant applied muscular force, a
greater inter-tooth distance results in a greater tegminal velocity at
toothplectrum contact since the time required to skip from one tooth to
the next is constant due to the operation of an escapement-like mechanism
(Nocke, 1971
;
Elliott and Koch, 1985
;
Koch et al., 1988
).
The energy transfer that occurs while the plectrum is captured by the file
may be conceived as having two immediate sources. The closing muscles are
continuously active and therefore, when the stridulatory surfaces are engaged,
energy that would otherwise accelerate the tegmina is directly transferred to
the tegminal oscillator. The tegmina also lose velocity and therefore some of
their kinetic energy (KE) to the oscillator. When the plectrum is released,
the tegmina again accelerate and gain KE that will be lost on the next tooth
capture. We assume that the amounts of energy transferred by these two
pathways, taken as an average over all capture and release cycles, are
approximately equal. We base this assumption on what is known of the
stridulatory mechanics of Gryllus campestris
(Elliott and Koch, 1985;
Koch et al., 1988
). In this
species, accelerations that are consistent with an approximately constant
applied force occur when teeth are removed from the file. Moreover, EMG data
suggest constant muscle fiber activation during much of the closing
stroke.
Thus, the power input is twice that associated with KE changes that occur
during fileplectrum capture and release. Remembering this, then using
the familiar equation for KE and finally incorporating variables for the tooth
strike rate, we can write the power transfer for both tegmina as:
![]() | (6) |
![]() | (7) |
Comparison of models
The predictions of the two models are compared in
Table 6. The KE transfer model
predicts a sevenfold greater energy transfer in both species than does the
spring model. Crucially, when the calculated energy transfers are compared to
measured Pac for each species, the spring model fails to
predict enough energy to account for the sound produced in S.
borellii and although it does predict sufficient energy in S.
vicinus, it implies an extraordinarily high E. Nevertheless, we
are inclined to believe that Eq. 5 is correct and its inability to give
reasonable values traces from two factors. First, there is considerable
uncertainty associated with the spring constant's value. Second, using file
tooth depth, the bending value is almost certainly an underestimate.
Bennet-Clark and Bailey (2002)
suggest that when relatively high amplitude vibrations occur, usually mid-way
through a sound pulse, the Cu2 veins bend much more than the file tooth
depth.
|
The KE transfer model yields predictions that are more consistent with our
energetics measurements. It suggests that about 0.4% (S. vicinus) and
0.5% (S. borellii) of net mass-specific Pcall
(Table 4) is used to drive the
tegminal oscillator. The majority of the energy would be lost in metabolism,
in the contractile fibers, and in the elastic and skeletal systems
(Bennet-Clark, 1995). The KE
model also predicts that 11% (S. vicinus) and 43% (S.
borellii) of the energy inputted to the oscillator is ultimately radiated
as sound from the burrow. Although these numbers seem reasonable, when this
calculation is repeated using the highest Pac observed for
S. borellii in the field, 125250% of the energy input to the
oscillator is predicted to convert into sound! Thus, energy inputs to the
tegminal oscillator must be larger than calculated on
Table 6. The suspect variables
are vC and vR, which were estimated
(see Eq. 7), not measured.
Efficiency and the inertial costs of stridulation
Stridulation requires the tegmina to be accelerated and decelerated during
both halves of the tegminal cycle. In the absence of elastic storage
mechanisms, inertial losses might be high, especially in species with high
fWS. However, Table
7 presents the results of calculations that suggest both
Scapteriscus potentially require similar amounts of power to overcome
inertia, even though S. vicinus has a wing stroke rate that is nearly
threefold greater than S. borellii. This surprising prediction traces
to S. vicinus' lower opening and closing tegminal velocities (related
to the smaller file teeth and the shorter length of the file that is
stridulated). Table 7
alsopredicts that, in the absence of thoracic resonance, (i) power
requirements to overcome inertia are much greater in the opening than closing
stroke due to higher velocities, and (ii) overcoming inertia is predicted to
be a greater power sink than is the input to the tegminal oscillators (using
the KE model; Table 6).
|
We want to emphasize the tentative nature of the predictions on Tables 6 and 7. These models are built on assumptions about thoracic skeletal/muscular resonance, file stiffness and bending, and tegminal velocities that may not be correct. Nevertheless, we include them as a first step in a more quantitative analysis of the energetics of stridulation in the hope that they will suggest future areas of investigation.
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List of symbols and abbreviations |
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Acknowledgments |
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