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First published online February 15, 2008
Journal of Experimental Biology 211, 686-698 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.013938
The sound field generated by tethered stingless bees (Melipona scutellaris): inferences on its potential as a recruitment mechanism inside the hive
1 Department of Biology, University of São Paulo, FFCLRP, Av.
Bandeirantes 3900, 14040-901 Ribeirão Preto, SP, Brazil
2 Department of Neurobiology and Cognition Research, University of Vienna,
Althanstrasse 14, A-1090 Vienna, Austria
* Author for correspondence (e-mail: michael.hrncir{at}gmx.at)
Accepted 17 December 2007
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5 mm). Almost 80% of the hive bees attending trophallactic
food transfers stayed within a range of 5 mm from the vibrating foragers. It
remains to be shown, however, whether air particle velocity alone is strong
enough to be detected by Johnston's organ of the bee antenna. Taking the
physiological properties of the honey bee's Johnston's organ as the reference,
M. scutellaris hive bees are able to detect the forager vibrations
through particle movements at distances of up to 2 cm.
Key words: stingless bees, thorax vibration, airborne sound, airflow, particle velocity, signal transmission, recruitment communication
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INTRODUCTION |
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). There
are three potential pathways for the transmission of this information to
prospective recruits: (i) direct contact during trophallaxis
(Hrncir et al., 2006b), (ii)
substrate vibrations (Lindauer and Kerr,
1958), and (iii) airborne sounds
(Esch, 1967;
Nieh, 1998;
Nieh et al., 2003). So far,
only pathways (i) and (ii) have been investigated in some detail in
Melipona bees (Hrncir et al.,
2000; Hrncir et al.,
2006b; Hrncir,
2003; Morawetz,
2007; Morawetz et al.,
2007).
Current knowledge of the transformation of thoracic vibrations to airborne
sound is based on a few studies in honey bees
(Esch, 1961;
Wenner, 1962;
Michelsen et al., 1986;
Michelsen et al., 1987;
Michelsen, 2003) and in bumble
bees (Schneider, 1975). In
honey bees, wing oscillations going along with the thoracic vibrations
transform these into airborne sound (Esch,
1961; Wenner,
1962; Michelsen et al.,
1987). In bumble bees, on the other hand, wing oscillations are
not significantly involved in the emission of airborne sound
(Schneider, 1975). The defence
sounds of bumble bee queens (sound pressure), which could be recorded behind,
laterally and in front of the bees, remained largely unaffected by the partial
or even the complete ablation of the wings
(Schneider, 1975).
The physical parameter of airborne sound relevant as input to Johnston's
organ in the pedicellus of the bees' antenna, the mechanoreceptor potentially
involved in its perception, is air particle movement
(Dreller and Kirchner, 1993;
Michelsen, 1993). Close to the
abdomen of dancing honey bees, strong air particle oscillations with velocity
amplitudes of up to 70 cm s–1 (peak to peak, p-p) were
measured. This value decreased rapidly with distance from the bee
(Michelsen et al., 1987). In
addition to these particle oscillations, honeybees generate a unidirectional
`jet airflow' during their dance, but only when the wingtips of the dancer are
apart by more than 7 mm (Michelsen,
2003). The study of a mechanical bee model suggested that this
airflow, directed away from the abdomen, is formed by the air emanating from
the space between the wings and the abdomen. In contrast to the air particle
oscillations, the amplitude of the jet airflow decreased only slowly and
linearly with distance to the bee
(Michelsen, 2003).
In stingless bees, nothing is known so far about the transformation of
thoracic vibrations to airborne sound, even though airborne sound has been
considered important as a carrier of information
(Esch, 1967;
Nieh, 1998;
Nieh et al., 2003). In the
present study, we therefore asked the following questions. (1) How strong is
the airborne sound (particle velocity and sound pressure) generated by
vibrating stingless bees? (2) Is airborne sound limited to the abdominal
region of the vibrating bee, as is the case in honey bees? (3) How important
are the wings for the transformation of thorax vibrations to airborne sound?
(4) Do vibrating stingless bees generate `jet airflows' like honey bees? (5)
Do hive bees stay close enough to a forager to detect with their antennae the
particle velocity resulting from the forager's thoracic vibrations?
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MATERIALS AND METHODS |
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).
Although annoyance buzzing differed significantly with respect to both the
main frequency component and the velocity amplitude from forager vibrations,
the mechanism of generation is similar in these two types of vibrations. Most
importantly for their putative transformation into airborne sounds
(Michelsen et al., 1987), both
vibration types resulted in oscillations of the wings to a similar degree
(average velocity amplitude measured at the wingtips: annoyance buzzing, 688
mm s–1; forager vibrations, 660 mm s–1;
average gain between thorax and wingtips: annoyance buzzing, 16.2 dB; forager
vibrations, 17.9 dB) (Hrncir et al.,
2008). The way that thoracic vibrations are transformed into
airborne sounds, therefore, is very similar in these two types of vibrations.
The study of annoyance buzzing has the great advantage over the study of
forager vibrations that the first type of vibrations is generated in a
controllable environment and sensors can be easily positioned around the bees.
However, differences in the absolute values of particle velocity and sound
pressure due to differences in the velocity amplitude and the main frequency
component between the two vibration types must be taken into account.
In the present study we examined bees of the species Melipona
scutellaris Latreille 1811, which are similar in size to M.
seminigra, and reliably emit annoyance buzzing when sling-tethered as
well (M.H., unpublished). Two colonies were housed in wooden nest-boxes inside
a laboratory building on the campus of the University of São Paulo in
Ribeirão Preto, Brazil. For video recordings of trophallactic
interactions between foragers and hive bees we installed an acrylic,
glass-covered observation box (10x5x4 cm3) between the
nest and the entrance/exit tube through the wall. In most of the cases the
returning foragers distributed their nectar or sugar water among nestmates
inside this observation box (see Hrncir et
al., 2004b; Hrncir et al.,
2006b). The recordings described in the present study were made
between December 2005 and April 2006.
Sound field generated by vibrating bees
We measured the air particle velocity (amplitude p-p) and the sound
pressure (pressure amplitude p-p) induced by the thoracic vibrations of
sling-tethered bees. Sound pressure is not of immediate importance here
because no pressure receivers are known in bees. Yet, sound pressure
measurements enabled us to compare our results with those of the existing
literature. Both air particle velocity and sound pressure were recorded using
a MicroflownTM USP-probe (UT0406-5, Microflown Technologies, Arnhem, The
Netherlands) which combines three particle velocity sensors (sensitivity: 15
mV/[mm s–1]) and a pressure microphone (sensitivity: 14
mV/Pa). At frequencies relevant for the present study [main frequency range of
stingless bee thorax vibrations: 200–600 Hz
(Hrncir et al., 2006a)],
particle velocities measured with the USP-probe showed an average deviation of
12.7% (range: 8–18%) from particle velocities measured under the same
experimental conditions in our Vienna laboratory by means of particle image
velocimetry (DPIV system: 2 New wave Mercury Nd:YAG lasers and an IDT
iNanoSense TR camera, Dantec Dynamics, Skorlunde, Denmark). Hence, an average
measurement error of ±1.07 dB relative to the DPIV measurements has to
be taken into consideration for the particle velocities recorded in the
present study.
To record the sound field around sling-tethered individuals
(Ntotal=47), bees were placed on a plane acrylic substrate
(15x15 cm2). Particle velocity was measured both above and
around the vibrating bees (Fig.
1). The sensor positions were at distances of 5, 10, 15 and 20 mm
from the bee (Fig. 1). Due to
slight, inevitable movements of the bees during the recordings, the accuracy
of these measurement distances was ±1 mm. Above the bees
(N=11), we measured the particle velocity oriented perpendicularly to
the substrate above the head, above the thorax and above the wings close to
the wingtips (Fig. 1B, inset).
In the plane around the bee (5 mm above the substrate), two components of
particle velocity were investigated: (i) the particle velocity oriented
perpendicularly to the substrate (vertically oriented particle velocity;
N=12), and (ii) the particle velocity oriented parallel to the
substrate and towards/away from the vibrating bee (horizontally oriented
particle velocity, N=12) (ii)
(Fig. 1). In addition to the
particle velocity caused by the vibrating bee itself, part of the vertically
oriented particle velocity originated from sound reflected by the substrate.
During foraging, collecting bees generate their thoracic vibrations
predominantly close to the nest entrance on particular structures made of
stiff batumen (Hrncir et al.,
2006b; Morawetz,
2007; Morawetz et al.,
2007). These often tubular `entrance structures' certainly also
reflect the airborne sounds produced by foragers. Due to the irregular form of
the entrance structures, however, and due to the variability in the materials
used, sound reflections in the natural situation are expected to be more
complex than those from the flat acrylic surface used in the present study.
Nevertheless, similarities in the way reflected sound effects the air particle
velocity can be expected between the natural situation and the situation used
in the present study. Assuming no differences between the sound fields on the
left and right side of a bee, we measured on one side only. Sound pressure was
picked up in the horizontal plane around the bees (N=12) at the same
measurement points as the particle velocity
(Fig. 1B). The sling-tethered
bees showed slight intra-individual variations in the generation of thoracic
vibrations during an experiment (average variation: velocity amplitude,
±12.5%; main frequency component, ±3.7%; duration of single
pulses, ±12.5%; pulse sequence, ±14.1%). We therefore took the
measurements (12 different measurement points above the bees or 24 different
measurement points in the horizontal plane around the bees) in an arbitrary
sequence to reduce any bias caused by potential differences in signalling due
to increasing exhaustion of the bees along with the duration of a recording.
Sling-tethered bees generated annoyance buzzing for about 10 min
(Hrncir et al., 2008). In the
present study, the recordings covered time periods between 3 and 5 min per
investigated bee.
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To judge the significance of the wings for the transformation of thorax vibrations into particle velocity and sound pressure we clipped the wings close to their base. Immediately after wing ablation, the respective aspect of the sound field was measured again with the sensor at the same positions as before. At all measurement points, the respective sound field was thus measured twice for each individual.
The closest possible distance between the USP-probe and the vibrating bee was 5 mm, which prevented the tethered individuals from getting hold of the sensors and damaging them. The amplitudes of air particle velocity at still closer distances (1, 2, 3 and 4 mm) were extrapolated using a hyperbolic decay function (Regression wizard, SigmaPlot 2001, SPSS Inc., Chicago, IL, USA; see Appendix 1). Extrapolations were only applied to particle velocities because sound pressure is not immediately relevant for any known sensory organ of bees.
Preservation of signal pattern
In order to see the extent to which the temporal pattern of the pulsed
thorax vibrations is preserved in airborne signals, we simultaneously recorded
the thorax vibrations and the particle velocity generated by sling-tethered
bees (N=12 bees). Thorax vibrations were recorded as velocities using
a portable Laser Doppler Vibrometer (PDV-100, Polytec, Waldbronn, Germany).
The measurement point of the laser vibrometer was on the bee's scutum. The
particle velocity was measured at 5 mm and 10 mm behind the vibrating bee,
lateral to its thorax and in front of its head. The following parameters were
analysed: the duration of single pulses (PD), their main frequency
component (MF), and the pulse sequence (PS), which is the
time from the onset of one pulse to the onset of the following pulse
(Fig. 2).
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1.2mV/[mm s–1]) 5 mm
behind a total of six sling-tethered bees (where the jet should occur), and 5
mm laterally of its thorax (where the jet seemed unlikely). Simultaneously,
the thorax vibrations of the bees were picked up with a laser vibrometer. The
anemometer was placed both behind the bee and laterally to it, for about one
minute each. We reduced the influence of ambient air currents within the
laboratory by performing the measurements inside a cardboard arena
(20x20x10 cm2). However, sound reflections from the
cardboard box, air currents caused by the cooling systems of our equipment
(laser vibrometer, notebook), and electrical noise originating from the
current supply could not be fully avoided and resulted in background noise
equivalent to about 2 mm s–1. Yet, jet airflows if present
should still have been detected, as they were reported to reach velocity
amplitudes of 150 mm s–1 at a distance of 5 mm behind
vibrating honey bees (Michelsen,
2003).
Distribution of hive bees around vibrating foragers
To see whether hive bees stay within a range around vibrating foragers
allowing signal transmission through airborne sound, we videotaped 20
trophallactic interactions of six different foragers (digital video-camera:
Panasonic, NV-GS400GE; 30 frames s–1). For these recordings,
the foragers (one individual per recording day) had been trained to collect
sugar solution (50% cane sugar w/w) at an artificial food source 15 m away
from the nest entrance. The video-caption showed the vibrating forager and a
ca. 2 cm range around it during trophallaxis. This caption size allowed both a
good view of the distribution of the hive bees around the forager, and exact
distance measurements. The recordings were analysed using the software
VideoPoint 2.5 (Lenox Softworks Inc., Lenox, MA, USA). Due to their movement
and the resulting blurred video-image, it was impossible to identify the exact
position of the antennae. Instead, we took the midpoint of the hive bees'
heads as a reference to measure their position. We analysed the closest
distance to the vibrating forager for those hive bees that were not involved
in the food transfer during the respective trophallactic interaction. We only
took those hive bees into account that `showed an interest' in the forager
without getting involved into trophallactic food transfer. As a measure for
`being interested' we took the approach towards the forager in a roughly
straight line. Several hive bees that just passed by, moved out of the
caption, or did not clearly change position during the recording were excluded
from the analysis. Because the caption size of the camera had a radius of only
about 2 cm, we could not determine at which points the bees decided to move
towards the forager. However, our emphasis was to determine whether those hive
bees that moved towards the forager do get close enough to the vibrating bee
to detect any particle velocity generated by its thoracic vibrations.
Analysis and statistics
The output signals of the USP-probe, the hot-wire anemometer and the laser
vibrometer were fed into a notebook (Pentium IV, 2.4 GHz) using a 24-bit
stereo soundcard (PSC 805, Philips, Amsterdam, The Netherlands) and the
software Soundforge 7.0 (Sony Digital Inc., Madison, WI, USA) at a sampling
rate of 44.1 kHz. For the analysis of thorax vibrations and airborne sound we
used the softwares SpectraPro 3.32 (Sound Technology Inc., Campbell, CA, USA),
SigmaPlot 2001 (SPSS Inc., Chicago, IL, USA) and SigmaStat 3.10 (Systat
Software Inc., San Jose, CA, USA).
For each individual, the mean values of sound pressure or air particle
velocity at each measurement point were calculated from 15–30 vibratory
pulses. The statistical tests were performed with these representative mean
values. Because the data were normally distributed in all cases
(Kolmogorov–Smirnov test, P>0.05) and showed equal variance
(Levene median test, P>0.05), we applied parametric tests. The
Paired t-test was used to compare the amplitudes of airborne sounds
at each measurement point before and after clipping the wings. One-way
repeated-measures ANOVA (post-hoc pairwise comparison: Tukey test)
indicated possible significant differences between amplitudes measured at the
same distance but in different horizontal directions to the vibrating bee.
Spearman rank correlation was applied to test the relationship between signal
parameters (PD, pulse duration; PS, pulse sequence;
MF, main frequency component; VA, velocity amplitude) of
thorax vibrations and air particle oscillations. The correlation coefficient
(rS) indicates the degree of association between them
(rS=1, high association; rS=0, no
association). Throughout the text, values are presented as mean ±1 s.d.
N refers to the number of different individuals tested, and
n to the number of single pulses evaluated. The level of significance
of differences was taken as P0.05. A Bonferroni correction for
the level of significance was performed
(Pcorr.0.05/number of comparisons)
(Sokal and Rohlf, 1995) when
data sets were used for more than one statistical comparison.
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0.025; Tables
1,
2). The highest particle
velocity was measured 5 mm above the plane of the wings (16.0±4.76 mm
s–1). Here, the velocity amplitude of the air particle
oscillations was significantly larger than the highest values measured in the
horizontal plane around the bee (vertically oriented oscillations, 5 mm behind
the wingtips: 6.0±2.08 mm s–1; horizontally oriented
oscillations, 5 mm in front of the head: 8.6±2.95 mm
s–1; one-way ANOVA, F2,32=26.60,
P<0.001) (compare Table
1 with Table 2).
Above the bee, the vertically oriented particle velocity steadily decreased
between the measurement points above the wings and the measurement points
above the head (Fig. 4,
Table 1). In the plane around
the bee, vertically oriented particle velocity was strongest behind the bee's
wingtips and weakest in front of its head at distances 5 mm (values
extrapolated from the exponential decay functions given in
Appendix 2)
(Fig. 5,
Table 2). At distances beyond 5
mm, the field of vertical particle velocities was largely homogeneous around
the vibrating bee (one-way repeated measures ANOVA: no significant differences
between directions; Fig. 5,
Table 2). Horizontally oriented
particle velocity around the bee was largest in front of the bee's head, and
lowest lateral to the bee's thorax at distances 
5 mm
(Fig. 6,
Table 2). Closer to the
vibrating bee, at distances <5 mm (values extrapolated from the exponential
decay functions given in Appendix
2), the field of horizontally oriented particle oscillations was
highly polarised, showing highest velocity amplitudes in front of the bee's
head and lowest values behind its wings (direction v;
Fig. 6,
Table 2). Thus, the
polarization of the field of horizontally oriented particle velocity decreased
with increasing distance to the vibrating bee, becoming insignificant
(P>0.05) at a distance of 20 mm.
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Sound pressure
Similar to horizontally oriented particle velocity, sound pressure in the
plane around the bee was generally highest in front of the bee's head and
lowest behind its wingtips (directions v and vi)
(Fig. 7,
Table 3). The highest sound
pressure recorded was at 5 mm in front of the bee's head (323.0±85.6
mPa). Differences between the fields of sound pressure and horizontally
oriented particle velocity (compare Table
2 with Table 3;
e.g. at a distance of 15 mm to the vibrating bee, the highest sound pressure
was recorded laterally of the bee's thorax, and the highest horizontal
particle velocity in front of its head) might originate from slight
differences in the distance between the vibrating bee and the sensor between
different recordings (±1 mm accuracy: see Materials and methods).
Alternatively, or in addition, they point to the fact that close to a
vibrating bee sound pressure and particle velocity might not be related to
each other in a simple way.
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The significance of the wings for the generation of the sound field
By removing the bee's wings, we determined their significance for the
transformation of thorax vibrations into airborne sounds. According to a
comparison of air particle velocity and sound pressure before and after wing
removal neither the amplitude of the horizontally oriented particle velocity
nor the sound pressure were significantly influenced (paired t-test:
Pcorr.>0.025; Figs
6 and
7). Yet, removing the wings
reduced the amplitude of vertically oriented particle velocity above and
behind the abdomen. However, this effect was statistically significant only at
a distance of 5 mm from the vibrating individuals (paired t-test:
Pcorr.<0.025; Figs
4 and
5).
To determine which portion of the particle velocity is generated solely by the oscillating wings, we subtracted each bee's mean particle velocity generated after wing removal from its `intact' value. Again, an exponential decay function was applied to extrapolate particle velocity values close to the bees. As shown in Figs 4 and 5, the significance of the wings for vertical particle oscillations (above and around a bee) was restricted to the immediate neighbourhood of the wings, and the abdomen, respectively. The oscillating wings were responsible for a part of the horizontal particle oscillations measured laterally to the bee and in front of it (Fig. 6). Compared to the effect on vertically oriented particle oscillations, however, this effect was very small.
Preservation of temporal signal patterns
According to previous studies (Hrncir
et al., 2006a), the potential signal value of air movement (sound)
should depend on the extent to which the temporal pattern of the thorax
vibrations is preserved after its transformation into particle velocity. At
all measurement points around a vibrating bee (directions i, iii and vi, at
both 5 and at 10 mm distance from the individual) the temporal pattern of the
air particle oscillations highly correlated with that of the thorax vibrations
(5 mm, Spearman rank correlation, i:
rS,PD=0.96,
rS,PS=1.00,
rS,MF=0.98, N=12,
n=156; iii: rS,PD=0.97,
rS,PS=1.00,
rS,MF=0.98, N=12,
n=155; vi: rS,PD=0.96,
rS,PS=1.00,
rS,MF=0.91; N=12,
n=183; 10 mm, Spearman rank correlation, i:
rS,PD=0.96,
rS,PS=1.00,
rS,MF=0.94, N=12,
n=142; iii: rS,PD=0.93,
rS,PS=1.00,
rS,MF=0.95, N=12,
n=153; vi: rS,PD=0.95,
rS,PS=1.00,
rS,MF=0.96; N=12,
n=152).
Vibrating stingless bees do not generate jet airflows
The possible existence of jet airflows generated by vibrating stingless
bees was tested by measuring the air particle movement behind the wingtips
(direction vi) and laterally of the thorax (direction iii) at a distance of 5
mm. In honey bees, the wing movements going along with the thorax vibrations
during the waggle dance were found responsible for the generation of an air
jet with velocity amplitudes of up to 150 mm s–1 behind the
wingtips (Michelsen, 2003). In
M. scutellaris, no obvious differences existed between the position
behind the vibrating bee and the lateral position
(Fig. 8). Despite the strong
background noise in our recordings (Fig.
8), a strong, unidirectional jet airflow would have been detected
if present. However, the recordings made behind and laterally to the bees did
not differ.
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) the
structure responsible for the generation of airborne sounds is predominantly
the vibrating thorax itself.
A simple comparison of the distribution of sound pressures produced by a
vibrating stingless bee (M. scutellaris) and a honey bee (Apis
mellifera), already suggests a difference in the respective generation of
the sound fields. In the dancing honey bee, sound pressure was as high as
P=156 mPa 10 mm behind its abdomen, and as high as P=127 mPa
lateral to its wings (Esch,
1961). No sounds could be heard in recordings made in front of the
head, which was taken to indicate that airborne sounds are generated by the
oscillating wings (Esch, 1961;
Wenner, 1962). This is
supported by findings of Michelsen et al.
(Michelsen et al., 1987).
After removing the wings from one body side, the sound pressure measured
laterally on the winged side was 3–4 times higher than that on the
wingless side. With all four wings removed, the amplitude of the sound
decreased to values below the sensitivity of the pressure microphone located 2
mm above the bee's abdomen (Michelsen et
al., 1987).
In M. scutellaris, the sound pressure behind the wingtips of
vibrating sling-tethered individuals was very similar to that measured in
honey bees (direction vi, 10 mm distance to wingtips: P=151 mPa,
Table 3). However, different
from honey bees, sound pressure could be measured all around an individual and
even reached its maximum in front of its heads
(Fig. 7,
Table 3). Clipping the wings
did not affect sound pressure (Fig.
7). Apparently, in M. scutellaris the wings do not play a
significant role in the transformation of thoracic vibrations into sound
pressure. Similarly, in bumble bee queens emitting a pulsed defence buzzing
when tethered (Schneider,
1975), sound pressure could be recorded behind, laterally and in
front of the vibrating individuals. Unfortunately, sound pressure values for
the different positions around the bee are not provided in this publication
(Schneider, 1975). However,
similar to our findings, the sound pressure did not change in general in
amplitude following the removal of the wings
(Schneider, 1975).
Air particle movement
The physical parameter most relevant for the sensory perception of airborne
sound by bees is air particle movement. In dancing honey bees, two different
forms of air particle movement have been described. First, the oscillating
wings create intense air particle oscillations close to their edges
(Michelsen et al., 1987).
Second, air that moves out from the space between the wings and the abdomen
during wing vibrations creates an air jet moving away from the bee's abdomen
(Michelsen, 2003). Both these
forms of air particle movement in the honey bee depend on the wing
oscillations that go along with the thoracic vibrations. In M.
scutellaris, particle velocity, similar to sound pressure, was
predominantly generated by the thoracic oscillations. As expected,
oscillations of the wings significantly affected the vertically oriented
particle velocity close to the abdomen only (Figs
4,
5,
6).
The differing importance of the wings for the generation of the sound field
in A. mellifera and M. scutellaris, respectively, is thought
to be due to a difference in wing position. Whereas honey bees generate sounds
with splayed wings during their dance movements, with the wing tips 5–9
mm apart (Michelsen, 2003),
stingless bees generate thorax vibrations during both forager vibrations and
annoyance buzzing with their wings closely folded over the abdomen
(Lindauer and Kerr, 1958;
Hrncir et al., 2006a;
Hrncir et al., 2006b;
Hrncir et al., 2008). Due to
the folding of the wings, these are uncoupled from the indirect flight
mechanism and, thus, their oscillation amplitude during `buzzing' is strongly
reduced compared to that during flight
(Heinrich, 1993;
King et al., 1996). A
spreading of the wings increases the effective wing area
(Schneider, 1975) which, in
turn, increases the amount of air between the wings and the abdomen which is
moved by every wing stroke. Wing position probably also influences the way how
the air is expelled from this space as indicated by the observation that the
splaying of the wings is essential for the generation of the honey bee's jet
airflow. A unidirectional airflow behind a dancing honey bee could only be
measured when the dancer's wingtips had a distance of at least 2.5 mm from
each other (Michelsen, 2003).
In accordance with this, no jet airflow could be measured behind vibrating
M. scutellaris (Fig.
8), which generates sound with its wings completely folded over
the abdomen.
Use of airborne sounds for information transfer
In Melipona bees, the temporal pattern of the forager's thoracic
vibrations predominantly depends on the sugar concentration of the collected
food (Hrncir et al., 2006a).
The airborne sound going along with the thoracic vibrations was repeatedly
assumed to transmit information to the nestmates although particle velocity
had not been measured in these studies
(Esch, 1967;
Nieh et al., 2003). Whereas
the temporal pattern of the thorax vibrations (pulse duration, pulse sequence
and main frequency component) is indeed well preserved in the airborne sounds
[sound pressure (Hrncir et al.,
2004a); air particle oscillations, present study] the crucial
question whether the air particle velocity close to a vibrating bee is strong
enough to be detected by the hive bees is still not answered yet.
The candidate mechanosensory organ able to detect particle velocity is
Johnston's organ in the antennal pedicel, which is stimulated by the
deflection of the flagellum (Snodgrass,
1956; Heran, 1959;
Tsujiuchi et al., 2007). To
date, neither the physiological nor the mechanical properties of this
mechanoreceptor are known in stingless bees. A comparison with data available
for the honey bee may be helpful, nevertheless. It has only recently been
demonstrated (Tsujiuchi et al.,
2007) that the minimum displacement amplitude of the honey bee's
flagellar tip necessary to elicit a neural response of Johnston's organ is 20
nm, achieved by a free-field air particle displacement of 60 nm. The magnitude
of the sound-evoked compound potentials of Johnston's organ linearly increased
with antennal tip displacements up to 100 nm. At a flagellar tip displacement
above 200 nm, corresponding to a free-field air particle displacement
amplitude larger than 5 µm, the magnitude of the neural response reached a
saturation level (Tsujiuchi et al.,
2007).
Adopting these findings for the recruitment communication of M.
scutellaris, we conclude that stingless bees in the nest should be able
to detect the particle velocities generated by foragers with their antennal
mechanoreceptors. Taking the honey bee values, the minimum free-field particle
velocities that can be detected by the bees are between 0.13 mm
s–1 at a frequency of 350 Hz and 0.21 mm s–1
at 550 Hz [frequency range of M. scutellaris forager vibrations
(Hrncir et al., 2000)],
corresponding to a particle displacement of 60 nm (free-field) at these
frequencies. Saturation of Johnston's organ is reached at free-field particle
velocities between 11.0 mm s–1 (350 Hz) and 17.2 mm
s–1 (550 Hz), corresponding to a particle displacement of 5
µm at these frequencies.
Due to the difficulties in accurately positioning sensors around vibrating
foragers during their trophallactic interactions with hive bees, it is an
almost impossible task to properly measure particle velocities induced by
forager vibrations close to the receiver bee. Forager vibrations, however, are
very similar in terms of the mechanism of their generation to annoyance
buzzing. Both types of thoracic vibrations result to a similar degree in
oscillations of the legs and of the wingtips
(Hrncir et al., 2008).
Therefore, the study of annoyance buzzing can give an insight into signals
generated during forager vibrations. Yet, the velocity amplitudes of thoracic
vibrations by foragers are about 55% of those during annoyance buzzing
(Hrncir et al., 2008). Since
the particle velocity depends on the velocity amplitude of the sound source
(Appendix 1), we must take into account that the particle velocities generated
by vibrating foragers might be only about half of the values recorded in the
present study. Even so, and despite the complexities of the physics of sound
generation close to a structure like a vibrating thorax, hive bees of M.
scutellaris should be able to detect forager generated particle
velocities within a range of at least 2 cm from the vibrating bee (smallest
measured particle velocity at 2 cm from a sling-tethered bee: 1.04 mm
s–1 
0.52 mm s–1 induced through
forager vibrations). At distances smaller than 5 mm from the vibrating bee,
the particle velocity generated by foragers will even result in the maximum
response of Johnston's organ neurons. The maximum particle velocities found in
the present study were 25.5 mm s–1 (first standard deviation:
±8.7 mm s–1) at 1 mm behind the vibrating bee
(12.8 mm s–1 in behind the forager), 43.2 mm
s–1 (±15.6 mm s–1) at 1 mm above the
thorax (21.6 mm s–1 above the forager's thorax), and
61.5 mm/s (±18.5 mm s–1) at 1 mm above the wings
(30.8 mm s–1 above the forager's wings). Hive bees that
attended trophallactic events stayed predominantly within <5 mm from the
vibrating forager (Fig. 9) and
their splayed antennae were close to or indeed touching the forager
(Fig. 9A). Similarly, in M.
panamica the antennal tips of hive bees were within a distance of at most
2 mm from the vibrating forager's body during trophallaxis, and in about 30%
of the cases the antennal tips were above the wings or the thorax of the
forager (Nieh, 1998). In the
case of physical contact between the hive bees' antennae and the body of a
forager, the thoracic vibrations will be directly transmitted. The thoracic
vibrations will then be a stronger stimulus for Johnston's organ than the air
particle velocity around the bees (see Appendix 1).
In addition to using the temporal pattern of the airborne sounds (which
highly correlates with the temporal pattern of the forager's thoracic
vibrations) as information on the profitability of the food source
(Hrncir et al., 2004a), hive
bees could use any air particle movements to detect an active forager in the
darkness of the hive. This information is important for both nectar processing
bees and inactive foragers (Biesmeijer et
al., 1998; Anderson and
Ratnieks, 1999). Thus, airborne sound may transmit different kinds
of information. Electrophysiological studies of the responses of the
appropriate mechanoreceptors in stingless bees are needed to answer this
question.
|
APPENDIX 1 |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIX 1References |
|---|
;
Jacobsen et al., 2007) might
help to get more quantitative understanding of the air particle velocities
very close to the bees, where measurements were not possible. The models that
come closest to a vibrating thorax are a monopole (pulsating sphere), and a
dipole (sphere vibrating along polar axis).
Radiation of sound from monopole sources
The simplest sort of outgoing sound wave is from a uniformly expanding and
contracting sphere of radius a. The particle velocity u at
distance r from the center of the sphere
(r=a+d) at the frequency v is
(Jacobsen et al., 2007):
 | (A1) |
v/c;
r, distance from the center of the sphere; u, air particle
velocity; v, oscillation frequency).
Knowing the velocity amplitude at the surface of the sphere (r=a)
for a given frequency
(U0(v)), we can
determine Q(v):
 | (A2) |
From the combination of the Eqn
A1 and
A2 results:
 | (A3) |
 | (A4) |
MF/c;
MF, main frequency component).
Because:
 | (A5) |
 | (A6) |
Radiation from dipole sources
If the center of a sphere oscillated along the polar axis with a velocity
of
U0e–2ivt,
the radial velocity of the surface of the sphere is
U0cos
e–2ivt,
where is the angle from the polar axis. Close to the source, if
r0, the particle velocity u at the distance r
from the center of the sphere (r=a+d) at the
frequency v is (Morse,
1981):
 | (A7) |
, angle from the polar axis; 
, density of air).
If the radius (a) of the sphere is small compared to the
wavelength (which is the case with the thorax of bees), the constant
K(v) can be approximated as
(Morse, 1981):
 | (A8) |
):
 | (A9) |
 | (A10) |
Comparison between calculated and measured particle velocity
For calculations of the particle velocity radiated from monopole
(Eqn A6) and dipole sources
(Eqn A10), the radius of the
sound source, its vibration velocity, and the main frequency component of the
vibrations are required. From the laser-vibrometer recordings in M.
scutellaris, we can determine these two vibration parameters only for the
dorsal surface of the thoracic scutum. We assumed the thorax of the bee to be
a sphere with the radius a=1.7 mm (mean ± 1 s.d. from 17
bees=1.70± 0.07 mm; vertical thoracic diameter divided by two). The
velocity amplitude p-p of the thoracic oscillations was
VATx=188 mm s–1 (mean ± 1
s.d.=187.8± 95.2 mm s–1; N=15,
n=120). When comparing the measured particle velocity values to the
theoretical values, the difficulties to describe the vibrating bee as a simple
sound source become obvious (Fig.
A1). Considering the bee's thorax as simple monopole source
overestimates the measured values, and considering it as simple dipole source
underestimates them.
|
 | (A11) |
 | (A12) |
The function variables (x, y), calculated by the regression analysis, should therefore represent the velocity amplitude of the thorax (VATx) and the radius a of the sound source. For the hyperbolic decay function 1 (Eqn A11), the variables were: x=556 (=VATx) and y=0.09 (=a). For the hyperbolic decay function 2 (Eqn A12) the variables were: x=63 (=VATx) and y=6.26 (=a). As can be seen from these values, decay function 1 demands a thoracic vibration velocity almost three times stronger than the actual value measured (and a source radius about 20 times smaller), and decay function 2 one that is three times weaker (sound source 4x bigger). Therefore, even if both applied regression functions fit well to the measured particle velocity at distances >5 mm from the vibrating bee (regression coefficients: R2=70% and 78%), they not necessarily result in reasonable values at distances closer than 5 mm.
|
1 mm). In the present study we, therefore,
used the hyperbolic decay 1 (which is mathematically similar to the decay
around a monopole source) to calculate vertical particle velocities at
distances between 1 and 4 mm from the vibrating bee, and hyperbolic decay 2
(mathematically similar to the decay around a dipole source) to calculate the
horizontal particle velocities at these distances. However, since it is
impossible to describe air particle velocities very close to a vibrating
thorax with simple mathematical functions, particle velocities for distances
<1 mm from the vibrating bee were not calculated. |
Acknowledgments |
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|
References |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIX 1References |
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  M. Hrncir, A.-I. Gravel, D. L. P. Schorkopf, V. M. Schmidt, R. Zucchi, and F. G. Barth Thoracic vibrations in stingless bees (Melipona seminigra): resonances of the thorax influence vibrations associated with flight but not those associated with sound production J. Exp. Biol., March 1, 2008; 211(5): 678 - 685. [Abstract] [Full Text] [PDF]
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