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Supplementary data
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The theory of coupling between charged insulators and the calibration of our devices for
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measuring electric fields.
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According to Coulomb’s law the force between two charges is directly proportional to the
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product of these charges and inversely proportional to the square of the distance between them.
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In the case of two positive charges q1 and q2 at rest, each charge has two roles: firstly, each
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charge creates an electric field with a field strength E which is inversely proportional to the
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square of the distance r from its source.
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q1 generates a field strength of |E1|(r) = k . q1 / r2
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q2 generates a field strength of |E2|(r) = k . q2 / r2
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Note that in this case the principle of superposition is not applicable to calculate the resulting
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fields.
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Secondly, each of the two charges has a repellent action on the electric field of the other charge.
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|F1| = q1 . E2(r) = q1 . k . q2 / r2
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|F2| = q2 . E1(r) = q2 . k . q1 / r2
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A constant of proportionality k = 1 / 4ε0εr is required to give the strength of the force in
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newtons (N) when q1 and q2 are in coulombs (C) and r in meters (m). Permittivities ε0εr describe
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a material’s (or matter’s) ability to transmit (or "permit") an electric field.
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In the case of multiple charges at rest, the Coulomb forces are calculated separately for each pair
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of charges as described above. The overall repulsive force along the direct line between each
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group of charges Q is the vector sum of all Coulomb forces (in this case the principle of
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superposition applies) (figure S1). Simplifying the complex conditions in the case of wing-
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flagellum electric field coupling, we assume conditions close to those in a capacitor with a strong
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geometric asymmetry. The strongest coupling effect results from r1 via E1, the orthogonal vector
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between the two charged insulators, because the distances and the angles increase for other
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vectors. Thus the repellent force acts predominantly along the direct line between wing and
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flagellum. Manipulating the size of the wing indicated that only about 10% of the wing surface is
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required to cause the coupling effect (the surface ratio between a normal wing and the flagellum
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is about 40 : 1, thus a ratio of 4:1 is effective). During flight, all body parts of the bee are
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exposed to similar air friction with the wing moving only slightly faster. The polarity and
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strength of the charges produced differ according to the materials, surface roughness,
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temperature, strain, and other properties such as the degree of ionization in air. Given enough
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time, charging will reach a balanced state. If the concentration of positive charge per volume in
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the air drops, the animal will start to discharge. Overall the surface charge per equal area will be
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constant.
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Calibration of the electrometer for measuring the electric charge of the wing beat:
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As shown in figure 1 in the main text, the sensor of the electrometer is positioned at a defined
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distance r from the bee body with its moving wings. Assuming an equal distribution of charge Q1
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to Qn along the surface area elements a1 to an (see the figure S1), the surface potential U can be
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determined as a function of the distances r1 to rn between coupling areas of the wing and the
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electrometer electrode.
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The moving wing with a constant surface potential Ui at a distance r to the sensor of the
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electrometer will induce an electric displacement current (i) in the sensor. The electrometer can
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be calibrated for similar distances with known surface potential. The absolute calibration was
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achieved by measuring relative voltage of a very thin metal plate of the same size and shape as a
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bee wing connected with a thin flexible wire to a 200 V DC voltage source. This metal plate was
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vibrated like a bee wing at various distances to the detector. Surface areas of the unshielded parts
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of the receiving and transmitting electrodes are taken into account following the guide line as
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described above for the ratio of the effective capacitive coupling between flagellum and wing.
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The empirical calibration function is given in figure S2.
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Figure S2 gives the dependence of relative force (or relative surface voltage) on the distance to
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the charge detector. The DC component shown in figure S2 was calculated and cannot be read by
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the electrometer due to the capacitive coupling of the voltage signal with the sensor. Movement
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of the wing in the near field (near) induces high modulations of voltage readings and
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correspondingly high modulations of force. Movements at far distance (far), only low
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modulations. However, if the dielectric medium has a very high permittivity compared to air e.g.
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in the case of a bee standing between an emitting bee and a receiving bee even far distant
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movements will lead to high modulations. The dielectric medium increases the coupling capacity
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which decreases the surface voltage of the wing. In consequence, the fast moving wing will gain
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an additional charge by friction (‘dielectric charging’) resulting in an increase of the effective
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Coulomb forces. A similar effect can be achieved by a conductive medium such as haemolymph.
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Notice that the distance between wings of a dancing bee and the flagellae of dance-following
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bees lies in the range of 0.5 to 4 mm.
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Electric fields of flying bees
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The surface potential of bees arriving at the hive entrance was measured with an electrometer
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array with 8 electrodes at the hive entrance. Figure S3a depicts this measuring device, and figure
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S3b shows the distribution of the surface potentials of arriving bees. The distribution of the
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modulated electric signals as induced by wing movement of arriving bees was picked up when
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the bee was still in flight. After landing the electric field is reduced by up to 5% (not shown).
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Behavioural responses to an electric field
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Resting bees standing on a Styrofoam ball floating in an air stream respond to an electric field
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with antennal movement. In the experiment shown in figure S5 the animal was stimulated with
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the dance pattern (see figure 2) transmitted as an electric field by a copper electrode in front of
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the animal at a distance of 3 mm to the flagellae.
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Figure captions
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Figure S1 Capacitive coupling. (a) Electric coupling of wing and flagellum. Left: The flagellum
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is glued to the tip of a human hair, which simulates the muscle force and joint flexibility of the
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flagellum. The wing is mounted to a thin plastic stick driven by a loudspeaker with its sound
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suppressed and placed at a distance of 3mm from the flagellum. Middle: The wing vibrates at the
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resonance frequency of the hair to keep the coupling force at a minimum. The wing swing
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amplitude is 3mm . Right: Discharged flagellum (or wing). The coupling effects from the
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acoustic force can only be seen at high resolution. This demonstrates that the driving electric
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force F is proportinal to the product of Qflagellum and Qwing according to Coulomb’s law. When
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one of the charges Qflagellum or Qwing is zero or neutral, an electric field but no force can be
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detected between the body parts. (b) Asymmetric capacitor configuration of wing and flagellum.
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Assuming an equal distribution of charge Q0 to Qn along the surface areas a0 to an , the surface
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potentials U0 and U1,2 can be calculated as a function of the distances r1 to rn.. Un = Qn / Cn = f(rn)
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are constant for a0to an. The factor by which wing area and site-specific charge can be increased
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while still adding to the repulsive force along the direct line between the body parts is
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empirically determined to be about four. Permittivities ε0εr describe a material's (matter’s) ability
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to transmit (or "permit") an electric field.
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Figure S2 Dependence of relative force (or relative surface voltage) on the distance to the charge
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detector. The ordinate gives the relative voltage nominated as the attenuation coefficient for the
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oscillation amplitude of the voltage source. The DC component shown was calculated and cannot
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be read by the electrometer due to the capacitive coupling of the voltage signal with the sensor.
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The calibration function (green line) was measured for each detector device, and the asymmetry
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of the signal detected was used to derive the DC potential shown as offset in the figure. The
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absolute calibration was achieved by measuring relative voltage of a very thin metal plate of the
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same size and shape as a bee wing connected with a thin flexible wire to a 200 V DC voltage
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source. This metal plate was vibrated like a bee wing at various distances to the detector. Notice
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that the received signal is distorted by the non-linear calibration function. This distortion
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provides us with the information for reconstructing the original signal including the DC offset.
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By reading the vibration amplitude and distance to the source we can identify the section of the
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green calibration function which can then be used to reconstruct the original signal. The
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corresponding static relative force for the example ‘near’ is 0.6. In the case of haemolymph
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between wing and electrode or flagellum both higher electric conductivity and permittivity
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bridges the containing volume and by this leads to stronger capacitive coupling due to the fact
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that the distance as given as an example is effectively decreasing from 6.5 to 2 mm.
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Figure S3 Electric charge of arriving bees at the hive entrance. (a): The electric charge carried
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by bees arriving at the hive entrance was measured with an electrometer array consisting of eight
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electrodes. The electrodes picked up the electric field at a distance of 2 - 3 cm both during the
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last 1-2 cm of flight and after landing. Diameter of the inner landing tube was 2 cm, the outer
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landing tube which prevented the bees from touching the electrodes was 6 cm. (b): Voltage
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distribution as induced by the wing beat of arriving foragers at the entrance to the observation
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hive (n = 436). The experimentally determined curve is close to the theoretically expected 1/r2
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function. Therefore, the abscissa can be extended to longer distances between voltage source and
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detector. Notice that each of the eight electrodes was calibrated separately, and capacitively
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coupled to the amplifier. These data were collected at a temperature of 27° C and 35% relative
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humidity.
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Figure S4 Positioning of a bee for laser vibrometric measurements of its antennae. The left
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figure shows the position of one flagellum, the right figure depicts the vibrating wing in front of
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the test animal. The red point shows the laser beam. The black square in the background is the
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sound pressure detector. The images were taken with the calibration camera of the set-up.
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Figure S5. Antennal responses of a bee standing stationary on a Styrofoam ball floating in an air
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stream. The animal is stimulated by the electric field dance pattern (see figure 2 in the main text)
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transmitted by the copper electrode in front at a distance of 3 mm to the flagellae. After several
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hours of walking on the ball the animal rests, loses its muscle tonus and has its flagellae pointing
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downwards (idle state, first picture left). The animal raises its flagellae (antennal response, third
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picture from left) after the stimulus begins (second picture from left) indicated by the illuminated
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infrared LED in the left background). The fade-out phase lasts up to 50 s for electric field
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stimulation in the range (20 - 80Vpp). (See movie S1 for more information)
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Movie S1: Response of resting bees to electric signals. A bee standing on a Styrofoam ball
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floating on air is exposed to electric field signals transmitted by the copper electrode in front at a
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distance of about 5 mm to the flagellae. After several hours of walking on the ball the animal
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rests, loses its muscle tonus and has its flagellae pointing downwards (idle state). The movie
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shows ongoing stimulation at intervals of 1 minute with low amplitudes of an electric field in the
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range of 20 - 80 Vpp at a distance of 5 mm due to our finding that under these conditions the
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fade-out phase is less than 50 s. The movie begins with a long fade-out phase after stimulation
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followed by 8 electric field stimulations, i.e. the 700 ms waggle rhythm (see figure 2), of various
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strengths indicated by the infrared LED which is invisible to the bee’s eye. The bee shows
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graduated responses with varying delays before the flagellae revert to the resting state. Little
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spontaneous behaviour is observed, e.g. at 3min 45s.
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