1 Supplementary data 2 3 The theory of coupling between charged insulators and the calibration of our devices for 4 measuring electric fields. 5 According to Coulomb’s law the force between two charges is directly proportional to the 6 product of these charges and inversely proportional to the square of the distance between them. 7 In the case of two positive charges q1 and q2 at rest, each charge has two roles: firstly, each 8 charge creates an electric field with a field strength E which is inversely proportional to the 9 square of the distance r from its source. 10 q1 generates a field strength of |E1|(r) = k . q1 / r2 11 q2 generates a field strength of |E2|(r) = k . q2 / r2 12 Note that in this case the principle of superposition is not applicable to calculate the resulting 13 fields. 14 Secondly, each of the two charges has a repellent action on the electric field of the other charge. 15 |F1| = q1 . E2(r) = q1 . k . q2 / r2 16 |F2| = q2 . E1(r) = q2 . k . q1 / r2 17 A constant of proportionality k = 1 / 4ε0εr is required to give the strength of the force in 18 newtons (N) when q1 and q2 are in coulombs (C) and r in meters (m). Permittivities ε0εr describe 19 a material’s (or matter’s) ability to transmit (or "permit") an electric field. 20 In the case of multiple charges at rest, the Coulomb forces are calculated separately for each pair 21 of charges as described above. The overall repulsive force along the direct line between each 22 group of charges Q is the vector sum of all Coulomb forces (in this case the principle of 23 superposition applies) (figure S1). Simplifying the complex conditions in the case of wing- 24 flagellum electric field coupling, we assume conditions close to those in a capacitor with a strong 1 25 geometric asymmetry. The strongest coupling effect results from r1 via E1, the orthogonal vector 26 between the two charged insulators, because the distances and the angles increase for other 27 vectors. Thus the repellent force acts predominantly along the direct line between wing and 28 flagellum. Manipulating the size of the wing indicated that only about 10% of the wing surface is 29 required to cause the coupling effect (the surface ratio between a normal wing and the flagellum 30 is about 40 : 1, thus a ratio of 4:1 is effective). During flight, all body parts of the bee are 31 exposed to similar air friction with the wing moving only slightly faster. The polarity and 32 strength of the charges produced differ according to the materials, surface roughness, 33 temperature, strain, and other properties such as the degree of ionization in air. Given enough 34 time, charging will reach a balanced state. If the concentration of positive charge per volume in 35 the air drops, the animal will start to discharge. Overall the surface charge per equal area will be 36 constant. 37 Calibration of the electrometer for measuring the electric charge of the wing beat: 38 As shown in figure 1 in the main text, the sensor of the electrometer is positioned at a defined 39 distance r from the bee body with its moving wings. Assuming an equal distribution of charge Q1 40 to Qn along the surface area elements a1 to an (see the figure S1), the surface potential U can be 41 determined as a function of the distances r1 to rn between coupling areas of the wing and the 42 electrometer electrode. 43 The moving wing with a constant surface potential Ui at a distance r to the sensor of the 44 electrometer will induce an electric displacement current (i) in the sensor. The electrometer can 45 be calibrated for similar distances with known surface potential. The absolute calibration was 46 achieved by measuring relative voltage of a very thin metal plate of the same size and shape as a 47 bee wing connected with a thin flexible wire to a 200 V DC voltage source. This metal plate was 48 vibrated like a bee wing at various distances to the detector. Surface areas of the unshielded parts 49 of the receiving and transmitting electrodes are taken into account following the guide line as 50 described above for the ratio of the effective capacitive coupling between flagellum and wing. 51 The empirical calibration function is given in figure S2. 52 Figure S2 gives the dependence of relative force (or relative surface voltage) on the distance to 53 the charge detector. The DC component shown in figure S2 was calculated and cannot be read by 2 54 the electrometer due to the capacitive coupling of the voltage signal with the sensor. Movement 55 of the wing in the near field (near) induces high modulations of voltage readings and 56 correspondingly high modulations of force. Movements at far distance (far), only low 57 modulations. However, if the dielectric medium has a very high permittivity compared to air e.g. 58 in the case of a bee standing between an emitting bee and a receiving bee even far distant 59 movements will lead to high modulations. The dielectric medium increases the coupling capacity 60 which decreases the surface voltage of the wing. In consequence, the fast moving wing will gain 61 an additional charge by friction (‘dielectric charging’) resulting in an increase of the effective 62 Coulomb forces. A similar effect can be achieved by a conductive medium such as haemolymph. 63 Notice that the distance between wings of a dancing bee and the flagellae of dance-following 64 bees lies in the range of 0.5 to 4 mm. 65 66 67 Electric fields of flying bees 68 The surface potential of bees arriving at the hive entrance was measured with an electrometer 69 array with 8 electrodes at the hive entrance. Figure S3a depicts this measuring device, and figure 70 S3b shows the distribution of the surface potentials of arriving bees. The distribution of the 71 modulated electric signals as induced by wing movement of arriving bees was picked up when 72 the bee was still in flight. After landing the electric field is reduced by up to 5% (not shown). 73 74 Behavioural responses to an electric field 75 Resting bees standing on a Styrofoam ball floating in an air stream respond to an electric field 76 with antennal movement. In the experiment shown in figure S5 the animal was stimulated with 77 the dance pattern (see figure 2) transmitted as an electric field by a copper electrode in front of 78 the animal at a distance of 3 mm to the flagellae. 79 80 3 81 Figure captions 82 Figure S1 Capacitive coupling. (a) Electric coupling of wing and flagellum. Left: The flagellum 83 is glued to the tip of a human hair, which simulates the muscle force and joint flexibility of the 84 flagellum. The wing is mounted to a thin plastic stick driven by a loudspeaker with its sound 85 suppressed and placed at a distance of 3mm from the flagellum. Middle: The wing vibrates at the 86 resonance frequency of the hair to keep the coupling force at a minimum. The wing swing 87 amplitude is 3mm . Right: Discharged flagellum (or wing). The coupling effects from the 88 acoustic force can only be seen at high resolution. This demonstrates that the driving electric 89 force F is proportinal to the product of Qflagellum and Qwing according to Coulomb’s law. When 90 one of the charges Qflagellum or Qwing is zero or neutral, an electric field but no force can be 91 detected between the body parts. (b) Asymmetric capacitor configuration of wing and flagellum. 92 Assuming an equal distribution of charge Q0 to Qn along the surface areas a0 to an , the surface 93 potentials U0 and U1,2 can be calculated as a function of the distances r1 to rn.. Un = Qn / Cn = f(rn) 94 are constant for a0to an. The factor by which wing area and site-specific charge can be increased 95 while still adding to the repulsive force along the direct line between the body parts is 96 empirically determined to be about four. Permittivities ε0εr describe a material's (matter’s) ability 97 to transmit (or "permit") an electric field. 98 Figure S2 Dependence of relative force (or relative surface voltage) on the distance to the charge 99 detector. The ordinate gives the relative voltage nominated as the attenuation coefficient for the 100 oscillation amplitude of the voltage source. The DC component shown was calculated and cannot 101 be read by the electrometer due to the capacitive coupling of the voltage signal with the sensor. 102 The calibration function (green line) was measured for each detector device, and the asymmetry 103 of the signal detected was used to derive the DC potential shown as offset in the figure. The 104 absolute calibration was achieved by measuring relative voltage of a very thin metal plate of the 105 same size and shape as a bee wing connected with a thin flexible wire to a 200 V DC voltage 106 source. This metal plate was vibrated like a bee wing at various distances to the detector. Notice 107 that the received signal is distorted by the non-linear calibration function. This distortion 108 provides us with the information for reconstructing the original signal including the DC offset. 109 By reading the vibration amplitude and distance to the source we can identify the section of the 110 green calibration function which can then be used to reconstruct the original signal. The 4 111 corresponding static relative force for the example ‘near’ is 0.6. In the case of haemolymph 112 between wing and electrode or flagellum both higher electric conductivity and permittivity 113 bridges the containing volume and by this leads to stronger capacitive coupling due to the fact 114 that the distance as given as an example is effectively decreasing from 6.5 to 2 mm. 115 Figure S3 Electric charge of arriving bees at the hive entrance. (a): The electric charge carried 116 by bees arriving at the hive entrance was measured with an electrometer array consisting of eight 117 electrodes. The electrodes picked up the electric field at a distance of 2 - 3 cm both during the 118 last 1-2 cm of flight and after landing. Diameter of the inner landing tube was 2 cm, the outer 119 landing tube which prevented the bees from touching the electrodes was 6 cm. (b): Voltage 120 distribution as induced by the wing beat of arriving foragers at the entrance to the observation 121 hive (n = 436). The experimentally determined curve is close to the theoretically expected 1/r2 122 function. Therefore, the abscissa can be extended to longer distances between voltage source and 123 detector. Notice that each of the eight electrodes was calibrated separately, and capacitively 124 coupled to the amplifier. These data were collected at a temperature of 27° C and 35% relative 125 humidity. 126 Figure S4 Positioning of a bee for laser vibrometric measurements of its antennae. The left 127 figure shows the position of one flagellum, the right figure depicts the vibrating wing in front of 128 the test animal. The red point shows the laser beam. The black square in the background is the 129 sound pressure detector. The images were taken with the calibration camera of the set-up. 130 Figure S5. Antennal responses of a bee standing stationary on a Styrofoam ball floating in an air 131 stream. The animal is stimulated by the electric field dance pattern (see figure 2 in the main text) 132 transmitted by the copper electrode in front at a distance of 3 mm to the flagellae. After several 133 hours of walking on the ball the animal rests, loses its muscle tonus and has its flagellae pointing 134 downwards (idle state, first picture left). The animal raises its flagellae (antennal response, third 135 picture from left) after the stimulus begins (second picture from left) indicated by the illuminated 136 infrared LED in the left background). The fade-out phase lasts up to 50 s for electric field 137 stimulation in the range (20 - 80Vpp). (See movie S1 for more information) 138 5 139 Movie S1: Response of resting bees to electric signals. A bee standing on a Styrofoam ball 140 floating on air is exposed to electric field signals transmitted by the copper electrode in front at a 141 distance of about 5 mm to the flagellae. After several hours of walking on the ball the animal 142 rests, loses its muscle tonus and has its flagellae pointing downwards (idle state). The movie 143 shows ongoing stimulation at intervals of 1 minute with low amplitudes of an electric field in the 144 range of 20 - 80 Vpp at a distance of 5 mm due to our finding that under these conditions the 145 fade-out phase is less than 50 s. The movie begins with a long fade-out phase after stimulation 146 followed by 8 electric field stimulations, i.e. the 700 ms waggle rhythm (see figure 2), of various 147 strengths indicated by the infrared LED which is invisible to the bee’s eye. The bee shows 148 graduated responses with varying delays before the flagellae revert to the resting state. Little 149 spontaneous behaviour is observed, e.g. at 3min 45s. 6