Figure 1.
Experimental Giant honeybee nest.
Chitwan (Nepal) in January 2009. (A) View of the whole nest; the green line gives the quiescent zone, where the bees are positioned with their heads upwards and the abdomens downwards; outside of this zone are the rim areas (left side and bottom), the attachment zone (top), and the mouth zone (right) marked with the yellow line; the green and yellow rectangles show nest areas which are displayed at a bigger scale in (B, quiescent area) and (C, mouth zone); white circles show the near neighbourhood (r<40 mm) and the far neighbourhood (r<100 mm) of the selected focus bee, which is positioned in the centre of the circles. The outer black circle within the white size marker (bottom left of the nest) is 6 cm in diameter. (B) Area of the quiescent zone; the white dot shows the position of the thorax of the selected focus bee, defining the centre of the white open circle (r = 40 mm) of the near neighbourhood and of the white square which indicates the detection area (60 x 60 px) of the selected bee to assess the relXYmov values (see Methods). Note the differences in orientation of the surface bees between quiescent zone (B) and mouth zone (C).
Figure 2.
Schematic of bucket bridging during shimmering and the aspects of linearity and continuity in propagation.
(A) Linear and continuous transmittance: Information is transferred (symbolized by red arrows) from one agent bee to the next member of the chain. (B) Linear but discontinuous transmittance: one agent bee in the chain fails to act as transmitter but information is by-passed to the next agent in the chain. (C) Schema of a sample wave which spreads from left to right (dirWAV = fromLtoR) explaining the complex situation of the bee curtain of A. dorsata during shimmering, with non-linearity and discontinuity of transmittance; three types of agent bees are noted: red, strong transmittance corresponding to wave strength levels of cws>2; light red, weak transmittance corresponding to wave strength levels of 1≥cws≤2; grey, no transmittance corresponding to a wave strength level of cws = 0 (these bees were detected as agent bees but not further considered in the evaluation). The arrows signify that information is transmitted from any abdomen-flipping agent bee into all eight neighbourhood sectors (for definition of dir Nh, see sketch at the bottom right, see Table 1 for definitions of angular sectors).
Figure 3.
Schematic of the evaluation process to analyse properties of the propagation process in shimmering.
The light-grey flow charts (A–G) address the single-agent analysis from image acquisition, stereoscopic imaging of individuals, wave incident detection, to the synchronization, categorization, and pooling of wave incidents. The black arrows and dashed lines on the right side symbolize that the stereoscopic analysis produced further data for hundreds of agent bees simultaneously. (A) The experimental nest was captured by two frame-locked video cameras positioned at an angle of 30° two meters in front of the nest. A single recording session lasted 15 s and included up to two shimmering waves which spread across the nest surface. Shimmering was elicited by a dummy wasp. (B) In the offline data assessment phase the acquired images were processed as follows: Segmentation distinguished single agent bees in the densely packed clusters of bees on the surface of the nest in each of the paired images, stereo matching identified corresponding agent bees in both paired images. These two processes enabled stereo tracking of the agents in subsequent frames throughout whole film scenes and the triangulation of their thoracic positions regarding the three dimensions of space (x,y,z) [14]. (C) The stereoscopic analysis delivered identities of agent bees in subsequent image sequences. The arrival of the wave front at an individual agent was recognized by a movement detection algorithm (see Fig.1B, white square). The grey arrow on the right with the stop bar symbolizes that a minority of identified agents did not participate in shimmering and was not evaluated further. (D) The detection of active participation in the wave allowed synchronization of wave incidents of individual agent bees at different positions of the nest. (E,F) Four categorizations of participating agents were discerned to define single focus bees: the wave direction dirWAV (F1); the wave strength level (cWS) as a measure of the response strength, which refers to the maximal relXYmov values of a wave incident (F2); the trigger direction dirTRIG gives the angle of the triggering neighbour in the near neighbourhood (F3); the oval area with its displacement from the centre shows the direction of the maximum activity of neighbours in the far neighbourhood (F4); in (F5), the paradigm of direct-sector and opposite-sector analysis was introduced. (G) Pooling of synchronized and categorized 3D data (Δx, Δy, Δz) and wave strength values relXYmov. (H-J) Using the parameters defined in F1–5, three criteria of bucket bridging were assessed (dark-grey flow charts H,I: linearity, continuity, graduality) and the respective hypotheses (directed-trigger-, active-neighbours- and gradual-transfer-) were tested (J1–3). The panels in D, F and I illustrate the results of the processes given in the grey or black boxes (see referenced figures and movies for details).
Table 1.
Definitions of categories of directions (dir) and sectors around a focus bee.
Figure 4.
The time courses of wave strength of focus bees and their triggering neighbours.
(A) Details about the assessment of the image-based relXYmov values (see Methods); yellow square gives the 60×60 px region of interest (ROI) around the selected focus bee; the red circle defines the near neighbourhood (r < 40 mm); the white lines in the background show the eight sectors of neighbourhood (dirNh = 1–8). (B) Time courses of the relXYmov values of focus bees at different wave strength levels (dirWAV = fromBtoT; cws = 1-6; n = 2908 wave incidents). The contours of the green areas show arithmetic means, vertical grey bars show mean errors. Black lines are means of relXYmov values of the triggering neighbours (radiusNh<40 m) regarding the paired, focus bee-related wave incidents; mean errors are not displayed here. Red vertical bars signify the time points t0 defined by the rapid onset of shimmering activity (quantified by the ordinate relXYmov values) of the focus bees. (C) How long does it take that information of shimmering is transferred from the neighbours in the far neighbourhood (radiusNh<100 mm) to the focus bees? Estimation exemplified for dirWAV = fromRtoL; abscissa, wave strength level; ordinate, time interval in ms in which information has been transferred, with means (red dots) ± SE (black vertical bars), n = 14 threshold levels (relXYmov = 1.0–2.3 in steps of 0.1) for the neighbourhood activity; ordinate values are calculated by weighted interpolation and cross correlation of the time courses between focus bees (fb) and their trigger neighbours (nb) of the same wave strength level (Nfb = 2824; Nnb = 29237).
Figure 5.
Correspondence of trigger direction and wave direction in individual focus bees addressing linearity of wave spreading in shimmering.
The ordinates show the rate of wave incidents assessed at individual focus bees (relnfb) and normalized for the maximum number of incidents per wave direction (relnfb = 1 for MAX nfb [dirWAV]). (A) Distribution of wave incidents regarding the four wave directions (dirWAV = 1–4). The focus bees were distinguished according to their individual wave strength levels (cws = 1–6) in different colours; for evaluation, only those focus bees were selected that had been triggered by an immediate neighbour in the near neighbourhood (radiusNh<40 mm); red, from Right to Left (fromRtoL), n = 2825 wave incidents; green, from Bottom to Top (fromBtoT), n = 2908; orange, from Left to Right (fromLtoR), n = 2433; blue, from Top to Bottom (fromTtoB), n = 1256. (B-C) distributions of wave events regarding the trigger directions of individual focus bees (dirTRIG = 1–8; for definition, see Table 1). Angular sector lines in (B) and abscissa in (C) show the trigger angle αTRIG. (C) The curves show the regression polynomials (for specification see Table 2); the grey vertical bars refer to the main wave directions coded by the median as αWAV (dark grey) and the tolerances of ± 45° (bright grey).
Figure 6.
Proof of linearity and continuity in wave spreading of shimmering as documented by neighbour-bee related analysis.
(A) Arithmetic means (curves) and SE (vertical bars) of the relative numbers of shimmering neighbours (relnNh) in the far neighbourhood (radiusNh<100 mm) around the focus bees regarding to the wave strength levels cws = 1-5; abscissa: ΔαTRIG | Nh, the deviation from the trigger angle in degrees at which the focus bees were activated to participate in shimmering, therefore ΔαTRIG | Nh = 0 refers to the trigger angle (trigger direction). Four data sets representing different spreading directions of shimmering waves (for colour codes, see Fig. 5): fromRtoL, nnb = 138190 neighbours; fromBtoT, 105356; fromLtoR, 159417; fromTtoB, 93199; (B) arithmetic means (curves) of the relative numbers of shimmering neighbours in the far neighbourhood (relnNh), considering four classes of wave strength levels were considered: darkest grey lines, cws = 4-5; brightest grey lines, cws = 1–2. The curves show the respective regression functions of the means (see Table S2); SEs are not shown. (C) Angular diagrams of relative numbers of shimmering neighbours (relnNh ) of only those focus bees selected for mid-level wave strength activation (cws = 3): fromRtoL, nnb = 4652 neighbours; fromBtoT, 4458; fromLtoR, 7182; fromTtoB, 2295; background sectors give the trigger angles αTRIG of the focus bees (C1) focus bees which were triggered in the direction where the wave had come from (equation 1a); (C2) focus bees which were triggered in the direction opposite to that under C1 (equation 1b).
Figure 7.
Proof of graduality in the wave strength between focus bees and their neighbours.
Abscissa, wave strength levels of the focus bee (cws [fb] = 1–6). (A) How are the focus bees influenced from their neighbours in the far neighbourhood? Ordinate, the regression coefficients resulting from the comparison of wave strength values (relXYmov) of focus bees (fb) and those of their nest mates (nb) in the far neighbourhood (r<100 mm); the data were pooled from all sets of wave directions (dirWAV = 1–4); white columns refer to direct-sector analysis, black columns refer to opposite-sector analysis (for further definition, see text and equations 4a–d); the white curve refers to the distribution of direct-sector data (polynomial: a2 = 0.0324, a1 = -0.1763, a0 = 0.2379, R2 = 0.975; n = 5 | cws [fb] = 1–5). (B) How are focus bees influenced from their immediate triggering neighbours? Ordinate, regression coefficients resulting from the comparison of relXYmov values of focus bees (fb) and those of their triggering neighbours (tn) in the near neighbourhood (r<40 mm), considering all wave incidences separately per wave direction (dirWAV = 1 to 4); polynomial: a4 = −0.0037, a3 = 0.0668, a2 = −0.3926, a1 = 0.896, a0 = 0,5691, R2 = 0.9994; n = 6 | cws [fb] = 1–6); means (full circles) and SE (bars). (C) Numbers of wave incidences selected for B.