Speeding Up Social Waves. Propagation Mechanisms of Shimmering in Giant Honeybees

<div><p>Shimmering is a defence behaviour in giant honeybees (<i>Apis dorsata</i>), whereby bees on the nest surface flip their abdomen upwards in a Mexican wave-like process. However, information spreads faster than can be ascribed to bucket bridging, which is the transfer of information from one individual to an adjacent one. We identified a saltatoric process that speeds up shimmering by the generation of daughter waves, which subsequently merge with the parental wave, producing a new wave front. Motion patterns of individual “focus” bees (n = 10,894) and their shimmering-active neighbours (n = 459,558) were measured with high-resolution video recording and stereoscopic imaging. Three types of shimmering-active surface bees were distinguished by their communication status, termed “agents”: “Bucket-bridging” agents comprised 74.98% of all agents, affected 88.17% of their neighbours, and transferred information at a velocity of v = 0.317±0.015 m/s. “Chain-tail” agents comprised 9.20% of the agents, were activated by 6.35% of their neighbours, but did not motivate others to participate in the wave. “Generator agents” comprised 15.82% of agents, showed abdominal flipping before the arrival of the main wave front, and initiated daughter waves. They affected 6.75% of their neighbourhood and speeded up the compound shimmering process compared to bucket bridging alone by 41.5% to v = 0.514±0.019 m/s. The main direction of shimmering was reinforced by 35.82% of agents, whereas the contribution of the complementing agents was fuzzy. We discuss that the saltatoric process could enable the bees to instantly recruit larger cohorts to participate in shimmering and to respond rapidly to changes in flight direction of preying wasps. A third, non-exclusive explanation is that at a distance of up to three metres from the nest the acceleration of shimmering could notably contribute to the startle response in mammals and birds.</p></div

Definition of three communication statuses of surface bees (shown for the wave direction

<p><b>).</b> Sketches of activity plots for distinguishing the <i>statuses</i> (<i>I,II,III</i>) of <i>focus bees</i>. (A_1–3) <i>Focus bees</i> are marked by red full rectangles at ; abscissa, time in frames (fps = 60 Hz) in relation to [] when the <i>focus bee</i> started her flipping; ordinate, distance of neighbours from the <i>focus bee</i> in mm; grey thin horizontal lines symbolize the <i>quiescent</i> state of the sample agents; small full rectangles with numbers mark the onset of their abdominal flips; orange coding refers to positions of the neighbours within the <i>near neighbourhood</i> (<40 mm) with flipping activities within the critical time window of ±10 ff; black coding refers to complimentary attributes (>40 mm; >|±10 ff|). Thick horizontal lines (black, orange, red) symbolize that abdomen flipping is still going on. (B_1–3) The panels <i>Pre t₀</i> and <i>Post t₀</i> display the <i>near neighbourhood</i> of a <i>focus bee</i> which is marked black when quiescent and marked red when she flips her abdomen. The numbers and colour codes of shimmering-active neighbours are the same as in the panels A_1–3; arrows of the central panels (regarding the time ) explain the directions of information transfer: <i>status I</i> (<i>bucket-bridging</i>) agents in the <i>pre</i>-<i>stroke</i> (<i>Pre t₀</i>) phase receive mechanical information (full orange arrows) predominantly from the side from where the wave came, in the <i>post</i>--<i>stroke</i> (<i>Post t₀</i>) phase information is transmitted predominantly to the side where the wave is spreading to (open red arrows); s<i>tatus II</i> (<i>chain-tail</i>) agents receive and emit mechanical information but fail to recruit other neighbours as transmitters; <i>status III</i> (<i>generator</i>) agents utilize predominantly visual information from the threatening cues, but not from shimmering-active agents in their <i>near neighbourhood</i>. They are leaders in emitting mechanical information and generate <i>parental</i> or <i>daughter</i> waves.</p

Experimental nest of Apis dorsata.

<p>(<b>A</b>) High resolution photo of <i>nest B</i>; grey open squares refer to the boundaries of the images of the panels B and C; the four yellow points mark the corners of the image part in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315.s002" target="_blank">Movies S1</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315.s004" target="_blank">S3</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315.s006" target="_blank">S5</a>. In the mouth zone the surface bees are randomly oriented (which is visible at the right side and below the white curve); peripheral to the mouth zone the surface bees are mostly vertically oriented, with their heads upwards and abdomens downwards. (B–C) Differential images (see image analysis in Methods, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315-Kastberger3" target="_blank">[7]</a>) from high resolution video recordings (fps = 60 Hz) of nest part specified in the panel A (real-world measures of panels: B/43×34 cm; C/14×10 cm); large capital numbers show the panel count, small numbers give the relative count of frames during the propagation of the shimmering process which took place from left to right () in the image. The rectangle in panel B indicates the boundaries of panel C. The time difference between the images of B₁ and B₂ was 317 ms [≡19 ff]. Pseudo colours (panels B_1,2 and C₁) visualize 8-bit <i>v</i>alues of <i>motion strength</i> pixelwise in the rainbow palette with <i>blue</i> = 0, <i>red</i> =  (see scale in B₁ and Methods). (C₂) The same image as in panel C₁ but in black-and-white and inverted for better discrimination of the abdomens; at the crossing points of the both marker lines an <i>agent bee</i> was selected which was moving solitarily ahead the shimmering front which was proceeding from the left to right; the schematic on the right gives the angular sectors of the <i>near neighbourhood</i> of this <i>focus bee</i> (with the directional categories; <40 mm).</p

Propagation of a shimmering wave across the nest surface (survey view).

<p>This example refers to a wave that spread from left to right () in the image. Capital letters in the right corners (1–6) show the panel count, small numbers give the relative count of selected frames (ff 01–22), comparable to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone-0086315-g001" target="_blank">Figs. 1</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone-0086315-g002" target="_blank">2</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone-0086315-g004" target="_blank">4</a> (for distance measures, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone-0086315-g001" target="_blank">Fig. 1B</a>). The pseudo colour bar in panel 3 shows the scale for the relative motion strength (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone-0086315-g002" target="_blank">Fig. 2</a>). For better comparison, the thick grey line fl 01 gives the <i>front line</i> of the (<i>parental</i>) wave manually drawn in panel 1 (at f 01), and the line fl 22 shows the front line of the same wave 384 ms later (at ff 22); red points marked with red arrows show the thorax of the <i>focus bee</i> selected in this wave, which flipped her abdomen at f 02 and generated a <i>daughter</i> wave that subsequently merged with the <i>parental</i> wave at f 12. The circles around the <i>focus bee</i> indicate the range of the <i>near neighbourhood</i> (<40 mm).</p

Mathematical model of the velocities in mixed-strategy wave propagation.

<p>(A) Lookup table for estimating the effect of the <i>saltatoric</i> process (sp) in shimmering in a mixed strategy with <i>bucket bridging</i> (bb): the proportion (abscissa) gives the impact of the <i>saltatoric</i> process on shimmering velocity (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315.e182" target="_blank">Equations 3a</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315.e183" target="_blank">b</a>) with as ordinate and with ( = 0.8 m/s) and ( = var [0.10–0.45 m/s]) as parameters. For the benchmark values ( = 0.8 m/s;  = 0.317 m/s;  = 0.517 m/s) the impact of the <i>saltatoric</i> process on shimmering velocity is calculated as  = 41.50%. (B) Ordinate, the impact of the <i>saltatoric</i> process on the empirical value of shimmering velocity ( = 0.517 m/s) in dependence of <i>bucket bridging</i> (abscissa: ) with the regression function: ( = −97.57,  = 61.04;  = 0.8 m/s). (C) Lookup table to estimate the <i>decision interval</i> (abscissa: [ms]) of an agent bee in which she can decide to join a shimmering wave or not. is calculated as the time interval in which a wave front spreads from an emitter (E) bee to a receiver (R) bee; ordinate, shimmering velocity in m/s; the parameter gives the distance between a <i>focus bee</i> and her adjacent neighbour ( = 20 to 45 mm). For a typical distance ( = 25 mm) the bee would have a time interval of  = 48.33 ms to “decide” to join the wave (for  = 0.517 m/s, green arrows); for the benchmark value of <i>bucket bridging</i> ( = 0.317 m/s, blue arrows) this time interval would be longer ( = 78.86 ms). (D) Pseudo coloured differential images (rel motion strength; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone-0086315-g001" target="_blank">Figs. 1</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone-0086315-g002" target="_blank">2</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone-0086315-g004" target="_blank">4</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone-0086315-g005" target="_blank">5</a>) to explain the principle of <i>bucket bridging</i> and of the <i>saltatoric</i> process.</p

Definition of a shimmering incident and of the three phases of a shimmering wave.

<p>(A) Typical time course of the motion of an individual <i>focus bee</i> during abdominal flipping (termed <i>shimmering incident</i>): ordinate: relative motion strength assessed by (for definitions, see Methods). Abscissa, observation time in ms; , start time of the <i>shimmering incident</i> of the agent, and start time of the <i>stroke</i> phase, synonymous to the <i>post-[</i><i>]</i>-<i>stroke</i> phase; Grey shaded zone, the time window of ±167 ms (≡±10 ff) for categorizing the communication <i>status</i> of agents (see text). (B) The three phases (<i>ascending</i>, <i>climax</i>, <i>descending</i>) of a shimmering wave can be categorized by the course of recruitment of agents participating in a wave, quantified by the relative number of <i>shimmering incidents</i> which were traced per image at the relative observation time with [per wave] and  = 10,894 (see Methods; n = 25 episodes of 2 min duration). Full circles, arithmetical, vertical bars, SEMs; n = 40 waves. The time gives the time point of the <i>climax</i> when the maximum number of <i>shimmering incidents</i> () occurred simultaneously. Red colour marks the <i>ascending</i> phase (<) of the shimmering waves, yellow colour marks the <i>descending</i> phase (>).</p

The time courses of wave strength of <i>focus bees</i> and their triggering neighbours.

<p>(A) Details about the assessment of the image-based _relXYmov values (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036736#s2" target="_blank">Methods</a>); yellow square gives the 60×60 px region of interest (ROI) around the selected <i>focus bee</i>; the red circle defines the <i>near neighbourhood</i> (r < 40 mm); the white lines in the background show the eight sectors of neighbourhood (dir_Nh = 1–8). (B) Time courses of the _relXYmov values of <i>focus bees</i> at different wave strength levels (dir_WAV = _fromB_toT; c_ws = 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 (radius_Nh<40 m) regarding the paired, <i>focus bee</i>-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 <i>focus bees</i>. (C) How long does it take that information of shimmering is transferred from the neighbours in the <i>far neighbourhood</i> (radius_Nh<100 mm) to the <i>focus bees</i>? Estimation exemplified for dir_WAV = _fromR_toL; 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 <i>focus bees</i> (<i>fb</i>) and their trigger neighbours (<i>nb</i>) of the same wave strength level (N_fb = 2824; N_nb = 29237).</p

Two examples of bucket-bridging in the signal propagation of shimmering of A. dorsata.

<p>(A_1–4) Information transfer from left to right () in the images, displayed over six frames (from f 74 to f 79≡100 ms) from the <i>focus bee</i> (whose thoracic position was marked with a white cross throughout the frames) to one of her neighbours (whose thoracic position was marked with a white cross in a white circle); differential images represent luminance [] patterns according to the rainbow scale displayed in panel A₁ (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone-0086315-g001" target="_blank">Fig. 1</a> and Methods), the grey open rectangles signify the extension of the receiver agent, the numbers at the bottom of the rectangles refer to the relative activation level of the <i>shimmering incident</i> (whereby the pixel-by-pixel luminance differences were scaled on the rainbow palette with ; for the estimation of the momentary expression of motion strength, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315.e096" target="_blank">Equations 2a</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315.e097" target="_blank">b</a> for retrograde and prograde extrapolation in Methods under “Benchmarking <i>bucket-bridging</i>”). (B_1–7) Information transfer from a <i>focus bee</i> (thoracic position marked with a white cross) over a chain of four neighbours to a target agent; the thoracic positions of intermediate neighbours were marked by closed white circles, that of the target agent with a white cross inserted in a white circle; this target bee was passively moved from B₄–B₆, and flipped her abdomen in B₇); the white open rectangles signify the range of the respective agent along the selected chain, the numbers inside the rectangles give the respective activation levels.</p

Properties of status I–III agents.

<p>(A_1–3) Rates of <i>status I–III</i> agents () regarding the four directions of wave propagation (grey background, panel A₁,  = 13,678) and regarding the wave direction (pink background, panel A₂,  = 4,025); panel A₃, rates of shimmering-active neighbours () of <i>status I–III</i> agents (,  = 29,248) in the respective <i>pre-stroke</i> (pre) and <i>post-stroke</i> (post) phases; see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315.s008" target="_blank">Table S1</a>. (B_1–3) Rates of <i>status I–III</i> agents () in dependence of the length of the discrimination window (abscissa in [ff], fps = 60 Hz). (C_1–4) Numbers of shimmering-active neighbours () of <i>status I–III</i> agents depending on the length of the discrimination window (abscissa scaled as ±ff); ff<0 refers to <i>pre-stroke</i> phase (yellow coding), ff>0 to <i>post</i>--<i>stroke</i> phase (red coding). Columns (A) and full circles (B–C), arithmetical means; vertical bars, SEMs.</p

Relationship between status I–III agents and their neighbours.

<p>(A) The number of <i>status I</i> agents in dependence of the ratio of their shimmering–active neighbours in the <i>pre-stroke</i> and <i>post-stroke</i> phase (); abscissa, 57 classes of in steps of 0.1; ordinate, rate of <i>focus bees</i> whereby the value  = 1.0 refers to the maximum number of cases per data set; red symbols: (n = 7 data sets); black symbols: (n = 25 data sets); for regressions, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315.s008" target="_blank">Table S1</a>. (B,C) The rate of <i>focus bees</i> () of <i>status II</i> & <i>III</i> in dependence of the numbers of their shimmering-active neighbours (); regressions of the mean values are shown into two parts: panel B: <5; >5; panel C: : <6, >5; : <5, >4); for regressions, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086315#pone.0086315.s008" target="_blank">Table S1</a>. Full circles and mid positions of vertical bars, arithmetical means; vertical bars, SEMs.</p