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1 Introduction

More than 60 years ago, Karl von Frisch interpreted the dances of honey bees, and since then the missing link in our understanding of this communication system has been how the follower bees obtain information about direction and distance from the movements of the dancer. Von Frisch [13] suggested that the followers might touch the dancer, and that vibrations in the wax comb caused by the 12–15 Hz wagging motion and/or the 250–300 Hz wing vibrations might be perceived by the follower bees. He also argued that vision was not involved, since the follower bees can obtain the specific information in the darkness of the hive (this view has recently been questioned, see [3]). Other strategies may be possible, since oscillatory motions like wagging and wing vibrations may generate sounds as well as oscillatory air flows and jet air flows.

Honey bees are probably deaf to sound pressures, but they can sense oscillatory air flows and vibrations of the substrate [5, 6]. However, the vibrations seem only to attract followers rather than to transmit information about the direction and distance to food [11], and a transfer of specific information is possible from a robot dancer, which does not touch the comb [8]. Studies using high speed video have shown that follower bees have a chance of touching the dancer with one or both antennae during each waggle movement [10], but the most obvious information to be obtained from touching is whether the follower bee is facing the dancer’s abdomen laterally or from behind. This information is probably not sufficient for allowing the follower bee to determine the direction of the waggle run.

2 The Dance Sounds

Fifty years ago, Wenner [14] and Esch [1] reported that waggle dances were associated with brief (about 4 ms) sound pulses repeated ca. 30 times per second. Esch found that the sounds had a frequency of ca. 250 Hz and pressures up to 1.3 microbar (ca. 76 dB SPL) at a distance of 1 cm dorsal to the dancer. Lower values were measured behind the dancer and lateral to the dancer. Esch suggested that the follower bees might sense the vibrations with their antennae, but Wenner referred to a general agreement in the literature that “there is a lack of response by bees to airborne sounds of normal intensity, but evidence for response to substrate sounds”. Shortly after these studies, Esch [2] reported that silent dances occurred, and that the silent dancers were not successful in the recruitment of nest mates.

After these pioneering studies, the case rested for 20 years until Donald R. Griffin investigated the effect of the dancer’s wagging on the amplitude of the sounds received by a pair of mechanically coupled microphones positioned lateral and symmetric to the dancer. Griffin (in [9]) confirmed the observation by Esch that the sound pressure was much smaller behind and lateral to the dancer than above the dancer, but he also observed that, although the sounds measured by the two microphones were generally in phase, they were often out of phase. The bee sounds thus appeared to be quite directional, which is not what one would expect from a simple sound emitter at low frequencies. In addition, the sounds seemed to be inherently variable.

The reason for this confusion was that the sound source (the vibrating wings) is not a monopole source, but a dipole source. At a certain time, the entire sound radiating surface of a monopole “agrees” on producing a surplus pressure and a little later a rarefaction. In contrast, in dipoles and higher order radiators some parts of the surface produce a surplus pressure while other parts produce a rarefaction, and the two components tend to cancel. In the case of a vibrating wing, there will be an almost perfect cancellation in the plane of the wing (thus the small sound pressures lateral to and behind the dancer). In contrast, the sound pressures will be at maximum above and below the wings. Because most of the generated sound is cancelled by sound of opposite phase, the radiation of sound energy from the dancer is small.

In order to investigate the sound field of dancing bees, we used a pair of mechanically coupled probe microphones with the tips 1.5 or 2 mm apart [9]. The results were used to calculate the air flows driven by the differences in pressure. The up and down vibrations of the wings were found to cause pressures above and below the wings of ca. 1 Pa (Pascal  =  94 dB SPL), that is almost 10 times larger than the value measured by Esch [1]. The pressures at the two surfaces of the wings are totally out of phase, and a pressure gradient of ca. 2 Pa thus exists at the edge of a wing. This causes the air to oscillate with a peak velocity of ca. 0.5 m/s. The pressure gradient and air velocity decrease with the third power of the distance from the dancer. (In contrast, the sound pressure from a monopole source decreases with only the second power of distance). At a distance of one bee length, the amplitude of the 250–300 Hz oscillatory air flows has decreased to less than 1% of the value close to the dancer (Fig. 2.2.1). The 12–15 Hz wagging motion also causes air flows, but the much smaller sound emission means that neither the driving force nor the air flows can be estimated with the microphone technique.

Fig. 2.2.1
figure 1_6

Average maximum pressure amplitudes (given in Pa) of the dance sounds measured in two directions radially away from the dancer. Note that the pressure difference (∆ p), which is proportional to the velocity of the air, decreases rapidly with distance (From [9])

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3 Experiments with a Robot Dancer

The measurements of sound pressures generated by dancing bees led to the hypo­thesis that the follower bees could obtain the specific information about direction and distance by perceiving the oscillating air flows around the dancer that are caused by the wing vibrations and the wagging motion. In order to test this hypothesis, we decided to build a robot dancer, which could perform the figure-of-eight dance and was surrounded by air flows similar to those of live dancers [8].

In brief, the robot was made of brass covered with a thin layer of beeswax. It was the same length (13 mm) as a worker honey bee, but somewhat broader (5 mm). The wings (a single piece of razorblade) was vibrated by an electromagnetic driver and caused a 280 Hz acoustic near-field around the robot similar to that around live dancers. A step motor rotated the robot during the figure-of-eight path and also caused the robot to waggle during the waggle run. The robot was also moved in a figure-of-eight path. All motors were controlled by a computer. The software made it possible to vary the individual dance components independently and to create dances other than the normal waggle dance. The robot was located on the dance floor in an observation hive, and observers in the field noted the number of bees visiting baits at various locations.

In experiments with normal dances the majority of the bees were noted in the direction indicated by the dance, but some bees were noted in other directions – very similar to the result of experiments with live dancers. The main difference is that the number of bees recruited by a live dancer is 5–10 times larger. That live dancers are more efficient than metal models was not a surprise. The results of some manipulated dances were more informative. For example, the waggle run could be displaced from the centre of the figure eight to one of the return runs, so that the bees received conflicting information about direction. The bees followed the instructions given by the waggle run and ignored the information given by the dance figure. That the wagging run is the “master parameter” for the transfer of information was also found in experiments on the coding of the distance to the target, where the robot was running fast during the waggle run, but slowly during the return run (or vice versa). The bees followed the information about distance given by the waggle run and ignored the information given by the return run. The follower bees thus obtain information about both distance and direction to the food mainly by “observing” the waggle run.

4 Doubts

The robot dancer was made in such a manner that it simulated both the movements and the oscillating air flows that were known at the time of its construction. The experiments showed that its signals were understood. It was therefore logical to conclude that the oscillating air flows were playing a major role in the transfer of information, but after some time I began to doubt whether this explanation really was true. Although the air flows perpendicular to the wings are well above the perception thresholds determined by Kirchner et al. [6], these air flows do not contain any information about the direction of the waggle run. In contrast, the air flows parallel or normal to the dancer’s body, which are the likely carriers of directional information, had not received much attention.

In the middle 1990s we investigated the air flows with two new laser instruments. Neither of them could be used for measurements in the hive, but they allowed us to map the air flows around models of bees that were caused to waggle and perform wing vibrations by various drivers. A laser anemometer allowed us to study the flows in a small volume of air as a function of time. Very accurate maps of air flows close to models of dancing bees were made with Particle Image Velocimetry (PIV). This method exploits a standard trick in fluid mechanics: a thin sheet of laser light is photographed twice with a very brief time interval by a digital camera mounted normal to the sheet. The changes in the positions of a large number of smoke particles from the first to the second digital photograph are then used for computing a map of the flows.

When the PIV technique was used for mapping the air flows around a wagging bee (a metal model or a real bee made robust by being stuffed with plastic) it became obvious that our ideas about the air flows during wagging had been very naïve. We had imagined that the air was just moved to and from by the wagging body. In reality, a thin (1–2 mm) boundary layer follows the movement of the body exactly, whereas other flows are lagging somewhat behind the body motion. The other flows are therefore not sufficient to fill the volume left by the body or remove the air from the space to be occupied by the body, and they have to be supplemented by short-circuit air flows opposite to the body motion (Fig. 2.2.2b). The flows often collide and lead to the formation of short-lived eddies (Fig. 2.2.2a). The life times of eddies are below one half of an oscillation period, so the air flows are basically laminar. Nevertheless, the complicated flow pattern must make it difficult for the follower bees to monitor the air flows due to the wagging motion with their antennae.

Fig. 2.2.2
figure 2_6

Air flows caused by the body wagging with an amplitude of ±15° (rotating around a point about 1 mm in front of the head). Bars for velocity vectors (middle right for (a), lower right for (b)) 100 mm/s. Measurements taken using particle image velocimetry. (a) The bee seen from above when moving towards the left and illuminated by a 0.6 mm thick sheet of laser light parallel to the comb and 1–2 mm below the dorsal surface of the bee. Simple laminar flows occur in the air next to the thorax and most of the abdomen, but a collision with displaced air from the left side of the abdomen creates an eddy (e) close to the abdominal tip. (b) The bee seen from behind. A thin sheet of laser light (normal to the comb) hits the middle of the abdomen and a part of the left wing. Displaced air flows to the left close to the left part of the abdomen, then upwards and to the right over the back of the bee. Above the back, the air close to the body flows towards the left, whereas the air further away flows towards the right

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The most prominent component of the air flows oscillating with the frequency of the wing vibration is the short-circuiting flow around the edges of the wings. The measured air velocity (between 400 and 500 mm/s, peak) is very close to that predicted from the values obtained with the probe microphones. As predicted, the magnitude decreases rapidly with distance. Another component, which had not been predicted from the probe measurements, consists of flows in and out of the space between the wing and the abdomen. Again, it must be difficult for follower bees to obtain useful information about the direction of the waggle run by monitoring these flows with their antennae.

5 The Jet Air Flow

To our big surprise, the up and down movements of the wing of our bee models generated not only oscillating air flows, but also a non-oscillating jet air flow behind the tip of the wings. In contrast to the oscillatory air flows, where the masses of air are flowing to and from, the air flows in only one direction in the jet (away from the dancer). The generation and propagation of such jet flows cannot be detected by measuring local sound pressures.

The jet shown in Fig. 2.2.3 was generated by continuous wing vibration in a bee model that did not waggle. The jet is broad in the dancer’s dorso-ventral direction, but quite narrow in the direction normal to the plane of the photograph. The width of the jet increases linearly with distance from about 1 mm close to the wing tip to 11 mm at a distance of 5 cm. When the jet propagates away from the wing tip, it recruits air from its surroundings, increases in width, and slows down.

Fig. 2.2.3
figure 3_6

Jet air flow caused by continuous wing vibration in a non-wagging metal model. Lateral view of a part of the abdomen when the wing was moving up. Bar for velocity vectors (lower right): 100 mm/s

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A more complicated pattern was seen with discontinuous wing vibration similar to that of live dancers. The velocity profiles in the PIV recordings now varied with the phases of the cycle of vibrations and pause. That air puffs produced ­during each series of wing vibrations travel away was verified with laser anemometry of the air flows in small volumes of air in the direction away from the wing tip. The build-up and decay of the air puffs take some time, however, and the flow amplitude does not decrease to zero during pauses in the wing vibration similar to those of live dancers.

The PIV apparatus is very large and certainly not suited for measurements in a bee hive. In addition, the bees do not like smoke. Obviously, a more suitable instrument is needed for measurements in the hive. The hot wire anemometer is the classical method for measuring air flows, but in standard hot wire anemometers the noise in the output signal is too large to allow measurements of the bees’ air flows. In addition, the bees are hostile towards the very hot wires (typically 300°C). By reducing the wire temperature to about 30°C above the ambient temperature we reduced the noise and made the wire acceptable to the bees. The disadvantage is that the output voltage now varies with the ambient temperature, so that a careful calibration of the nonlinear relationship between air flow velocity and output voltage is necessary. During our initial measurements, the hot wire probe was held by hand close to the dancing bees in an open observation hive. The direction of the hot wire was perpendicular to the surface of the wax comb. Much to our surprise, the 3 mm long hot wire is surprisingly robust and generally survives being hit by dancing bees.

Measurements with the hot wire anemometer showed that jet air flows are also generated by live dancers. Figure 2.2.4 shows the output signal from an anemometer when the hot wire is held stationary behind the dancer at an extreme lateral position within the angle of wagging (position a in Fig. 2.2.5). The velocity signal recorded by the probe reflects the 14 Hz wagging frequency. The maximum values occur when the dancer’s abdomen points directly at the probe (indicated by arrows). The shape of the signal shows that the wire has been hit very briefly by the maximum air ­velocity. In other words, the jet must have been quite narrow. As already discussed, consecutive peaks may show much variation in amplitude, because the wing vibration occurs in bursts of 3–4 vibrations about 30 times per second.

Fig. 2.2.4
figure 4_6

Air flows measured by a hot wire anemometer at an extreme lateral position within the angle of wagging behind a dancing bee. The arrows indicate the times when the dancer’s abdomen pointed towards the hot wire (From [7])

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Fig. 2.2.5
figure 5_6

Predicted time patterns for reception of a jet emitted by a wagging dancer at positions a, b, and c behind a bee. The predicted time patterns have been observed in recordings with hot wire anemometers behind live dancers. With a 13 Hz wagging, the time between consecutive receptions of the jet would be about 77 ms in a and 38 ms in b (From [7])

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6 A Hypothesis for the Transfer of Directional Information

Assuming that the antennae are the air flow receivers of honey bees, we can predict the time patterns with which an antenna of a follower bee is maximally activated (Fig. 2.2.5). The time pattern is a simple function of the angular position of the follower relative to the axis of the waggle run. I suggest that the follower bees exploit this to obtain fairly precise information about the direction to the target reported in the dance. I further suggest that the brain of the bee compares the timing of the two antennal signals in order to judge whether she is located to the left or to the right of the axis of the waggle run.

One can now imagine a strategy for the transfer of information about direction: when bees are attracted to a dancer, they align themselves perpendicularly to the body contours of the dancer [10]. Perhaps the bees perceive the oscillating wing air flows with their antennae and exploit them for the alignment. From their positions in this typical alignment, the followers may then be able to use the antennal contact pattern to determine their approximate position relative to the dancer and finally reach a position behind the dancer within the angle of wagging.

One can imagine two possible strategies for the followers located behind the dancer within the angle of wagging. The followers may try to find the middle position (in line with the waggle run, position c in Fig. 2.2.5) by searching for the corresponding temporal pattern, or they may use the temporal pattern for estimating their angular position relative to the axis of the waggle run. In both cases, touching and/or perception of the direction of the air flow may serve to align the body of the follower with the body of the wagging dancer during the periods of contact. Judd [4] found two examples of followers, which were aligned with the axis of the waggle run (and which found the target after having followed just two waggle runs each) and four examples of followers that had located the target after having followed waggle runs within the angle of wagging, but far away from the middle position. This may suggest that the bees are able to use both strategies.

In three independent studies ([4, 10], a study by Martin Lindauer and our group) it was found that the specific information about the location of the food is available only to the follower bees that have spent some time behind the dancer within the angle of the wagging motion.

7 The Variable Jets

During the laboratory studies with the PIV technique and model bees we always observed a jet air flow of the shape already described, and we saw no difference between the jets made by a metal wing and real bee wings. The generation of jets by live dancers is more variable. Most of the jets start from a velocity of ∼1 cm/s, which seems to be the background level of air flows in the hive (Fig. 2.2.4). In other recordings, the jets were accompanied by a broad flow of air with a velocity of about 8–15 cm/s (Fig. 2.2.6). With this broad flow the dancer displaces at least 10 ml of air per second.

Fig. 2.2.6
figure 6_6

Simultaneous recordings (during the last second of a waggle run lasting 2.2 s) of the distance between the tips of the wings (in mm, above), of sound generated by the vibrating wings (middle), and of the velocity in cm/s of air flowing away from the dancer about 5 mm behind the tip of the abdomen. The sound recording shows that the dancer vibrated its wings during the entire record, but it only produced a jet air flow during the 0.5 s when the distance between the tips of the wings had increased by 2–3 mm. Arrows indicate the times of wing opening and closure (From [7])

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A further complication is the observation that live dancers may switch the jet air flows and the broad air flow on and off (Fig. 2.2.6). From the high speed films it can be seen that the distance between the tips of the wings (which are held over the abdomen during the dances) increases when the jets and broad flow are switched on (and decreases when they are switched off). In the high speed films it is not possible to see whether the wings are rotating around their length axis (like during flight). One may speculate that the broad jet air flow serves to mark the zone behind the dancer, where the follower bees can obtain specific information, and/or to mark periods of particularly stable dancing (perhaps by means of an odor?). It remains to be learned how and why the dancers control the generation of the two kinds of air flow.

The honey bee waggle dances have, until recently, been considered a very stereotype behavior, where the main variation was the duration and direction of the waggle run, although the duration of dancing and the tendency to vibrate the wings were known to depend on the motivation of the dancer [2]. We now know that the duration of the return run (between consecutive waggle runs) varies with the profitability of the food source. A similar flexibility is found in the dance following. The patterns of following dances are related to the foraging experiences of the follower bees and to the presence, on the dance floor, of dancers announcing other targets. Finally, the patterns of moving with the dancer also show much flexibility.

8 Outlook

These findings raise a number of questions, which call for additional research. Do bees have the neural circuits necessary for handling the temporal information obtained when the jets hit the antennae? Are the waggle dance scents [12] released through the broad flow of air pumped by the dancer? If yes, why are the dancers not always making the broad air flows? Are the jets the reliable channel of information for the follower bees? If yes, is it possible to provide the bees with the necessary information for finding the target by means of a new robot, which only produces jets with a suitable time pattern, but does not dance? And so on. It seems fair to conclude that the dance language will keep the investigators busy for many years to come.