Evidence for Ventilation through Collective Respiratory Movements in Giant Honeybee (Apis dorsata) Nests

The Asian giant honeybees (Apis dorsata) build single-comb nests in the open, which makes this species particularly susceptible to environmental strains. Long-term infrared (IR) records documented cool nest regions (CNR) at the bee curtain (nCNR = 207, nnests > 20) distinguished by marked negative gradients (ΔTCNR/d < -3°C / 5 cm) at their margins. CNRs develop and recede within minutes, predominantly at higher ambient temperatures in the early afternoon. The differential size (ΔACNR) and temperature (ΔTCNR) values per time unit correlated mostly positively (RAT > 0) displaying the Venturi effect, which evidences funnel properties of CNRs. The air flows inwards through CNRs, which is verified by the negative spatial gradient ΔTCNR/d, by the positive grading of TCNR with Tamb and lastly by fanners which have directed their abdomens towards CNRs. Rare cases of RAT < 0 (< 3%) document closing processes (for ΔACNR/Δt < -0.4 cm2/s) but also suggest ventilation of the bee curtain (for ΔACNR/Δt > +0.4 cm2/s) displaying “inhalation” and “exhalation” cycling. “Inhalation” could be boosted by bees at the inner curtain layers, which stretch their extremities against the comb enlarging the inner nest lumen and thus causing a pressure fall which drives ambient air inwards through CNR funnels. The relaxing of the formerly “activated” bees could then trigger the “exhalation” process, which brings the bee curtain, passively by gravity, close to the comb again. That way, warm, CO2-enriched nest-borne air is pressed outwards through the leaking mesh of the bee curtain. This ventilation hypothesis is supported by IR imaging and laser vibrometry depicting CNRs in at least four aspects as low-resistance convection funnels for maintaining thermoregulation and restoring fresh air in the nest.

For example, (a) the preference for southward nest orientation maximizes sun irradiation at one of the nest sides but leaves the other side in the shade [6][7][8][9][10][11]. (b) The performance of the bee curtain changes regularly, compacting under cooler conditions (quite similar to winter clustering of A. mellifera [21][22][23][24][25][26]) and widening up under warmer conditions (forming a wider meshed, sometimes beard-like structure; additionally, curtain bees may roam over cooler structures, e.g. alongside the upper nest parts [6][7][8]). (c) The nest also transforms into a looser formation in defence mode, in particular in preparation for the mass release of flying guards [5-8, 12, 34]. (d) Regularly, periodic mass flight activity [35][36] dramatically affects the interior nest milieu, when a good part of colony members set off to defecate, which is discussed to serve for dumping excessive heat [13][14]37].
Long-term infrared recording of A. dorsata nests [39] brought evidence of a further, so far unknown potential for thermoregulation and ventilation in honeybees: Regularly, cool nest regions (CNRs) emerge on the bee curtain within minutes and fade away minutes or hours later (S1 Movie). We stipulate here the funnel hypothesis assuming that CNRs are gates through which ambient air flows into the nest interior. The further-going ventilation hypothesis proposes that colonies open transitory pathways such as CNR funnels to constitute and maintain the appropriate milieu inside the bee curtain, adaptive for brood incubation. Two prerequisites of CNRs are here mandatory to verify both hypotheses: first, CNRs should preferentially occur under higher ambient temperatures when the need of thermo-ventilation rises, and not incidentally without any relation to environmental conditions; and second, they should facilitate cycling airflows to establish the proper interior nest milieu regarding temperature, humidity and fresh air.
This paper substantiates both hypotheses by quantitative data, describing for the first time the functional properties of CNR funnels in A. dorsata nests regarding their occurrence, their physical properties, and their significance in fanning-supported ventilation.

Ethics Statement
The office of the Rector of the Centre for International Relations of the Tribhuvan University (Kathmandu, Nepal) supported the research expeditions 2009 and 2010 entitled ''Study on the behaviour of the giant honeybees: Observations and Recording of behaviours at the nesting site" in the Chitwan district of Nepal.

Recording and image analysis
The experimental nests (e.g. Fig 1) were filmed through 200 h of observation time from a distance of 1.5 m with a high-definition (HD) camera (Panasonic HVX 200) and in parallel, with an infrared (IR) camera (Flir A320; resolution: 640 x 560 pixel; 9 Hz). The color-coded (rainbow-900 palette) IR images were transferred from the IMG-format (providing adjustable temperature scales when operated by Flir-Researcher 2.9) into the fixed-scale BMP-format, which was further analysed by the Image-Pro software (MediaCybernetics 7.0). In total, > 30 000 frames were selected for the final evaluation representing 120 min recording time. Selected images from both HD and IR films were processed by the ThermaCAM Reporter 9.1 Professional (Flir) and Image-Pro and superposed by triangulation to the view of the IR camera. This allowed the identification of the temperature values of bee bodies and of the cavities between.
Data loggers (HOBO U12) were mounted one meter in front and behind the nest and registered ambient humidity, irradiation and ambient temperature (T amb ), which latter was also used to calibrate the IR camera.
Spatial and thermal properties of cooler regions on the nest surface Giant honeybee nests occasionally display cool nest regions (CNRs), which are distinguished by a distinct spatial temperature gradient, and they are variable in size and position ( [39], Figs 2-4; S1 Fig; S1 Movie). For evaluation, selected CNRs were enveloped by a rectangular area A env (as illustrated by the white frame in Fig 5, panel A), adjusted automated or manually every  frames that the total number of pixel areas associated to the sink of CNR (n px_sink ) was lower than 80% of the enveloped area A env . Subsequently, the RGB coded pixel areas of the BMP images were re-calibrated as temperature (T) values in°C by the luminance values of the associated IR scales using Image Pro software. The pixel areas (a px ) inside A env were processed horizontally (i px_H = 1. n px_H ) and vertically (i px_V = 1. n px_V ) along line profiles, with the total number of n px_env [A env ] = n px_H x n px_V . The frame-specific position of the gravity point of the sink region (X sink , Y sink ; Eq 1) regards to the positions of only those pixel areas which can be allocated up to 1°C above the minimum temperature T min .
For further evaluation of the sink characteristics of a CNR, the 80% of pixel areas sorted as the lower temperature part were defined as the frame-specific reference area with A ref = n px_env [A env ] x 0.80. The pixel areas allocated to this lower temperature part of A env were sorted along i px_50% = 1 to n px_50% from T min (represented by the pixel area a ipx_50% at i px_50% = 1 with the lowest temperature) upwards to T mid (represented by the pixel area a ipx50% , which revealed the mid temperature T npx_50% at i px_50% = n px_50% ). The frame-specific temperature of the CNR was then characterized by the area A mid , the sum of the 50% of the lower temperature pixels The experimental Apis dorsata nest in a bay at the shaded rear side of the second floor of a hotel in Chitwan (Nepal); built at a traditional nesting site, which can be discerned by the wax traces from previous years. In front of the nest on the unsecured balcony the recording devices were placed: IR, infrared camera; HD, high definition camera; chr1 & chr2, two additional high resolution cameras for other purposes [28][29][30][31]; LDV, laser Doppler vibrometer [30]. The yellow arrow marks the spot of the red LDV light reflected at the end plane of a rod, which had been stuck through the comb (see also schematics in S3 Fig). a ipx_50% (with i px_50% = 1 to n px_50% ) of A ref (Eq 2). This algorithm was important to exclude rim-related noise in CNRs and to allocate the representative sink value of CNRs defined as Ts ink (Eq 3) and as the area A CNR scaled in cm 2 (Eq 2) to the position calculated as the gravity point with the coordinates X sink and Y sink (Eq 1).
with x ipx and y ipx as the horizontal and vertical coordinates of those pixel areas (with 1 < i px < n px_sink ) which were sorted according to their temperature values T ipx from i px = 1 (with T 1 T min ) up to i px = n px_sink (with T npx_sink T min + 1°C).
with F c = 27.5625 px / cm 2 as calibration factor for the main experiment in the BMP-formatted IR image to determine the real-world sizes of CNRs.
with T Ipx = 1 equals T min and T np_50% equals the temperature of the pixel area a npx_50% which is sorted at the lower half temperature part of A ref according to n px_50% = n px_env [A env ] Ã 0.80 /2. The frame-specific relative median temperature value of the CNR (ΔTC NR ) was defined according to with Ts urr as the median of the temperature values of those pixel areas collected along surrounding lines of the enveloping rectangle of A env outside the respective CNR. These definitions allowed an automated evaluation of the temperature-dependent, positional and areal structure of CNRs over time.

Monitoring of fanning bees
The HD documents were manually checked to confirm that the assemblage of the bee curtain remained unaltered during the emergence of CNRs and to identify fanning bees on the nest. Generally, fanning bees (Fig 3, panel A; S2 Movie) clung with their extremities to other surface bees, typically pointing away with their heads from the nest while their abdomens and thus, the  air streams provoked by them were directed towards the nest. The total number of IR frames with simultaneous HD records was n ff > 24 000 amounting to 76.63% images under fanning conditions ("fanners were identified at CNRs") and to 23.38% images under non-fanning conditions ("no active fanners were identified at CNRs").

Laser vibrometry
A laser Doppler vibrometer (abbreviated further as "LDV"; Polytec PDV 100) was positioned on the experimental (further termed as "ipsilateral") side of the nest (Fig 1). A wooden rod with round diameter (8 x 100 mm; 1.28 g) was stuck into the comb at a central position [30], whereby the ipsilateral end protruded slightly over the surface of the bee curtain. A piece of white paper was glued to this plane end serving as a reflector for the laser beam of the LDV. The firm connection of the rod with the comb allowed the measurement of the directional z-component of the comb movement (ΔZ comb /Δt) utilizing the Doppler phase shift between emission and reflection of the LDV signal. By definition, the direction of these dislocations of  Ventilation in Giant Honeybee Nests the comb can be discerned simply by the sign of the shifts (ΔZ comb /Δt < 0: "towards", and ΔZ comb /Δt > 0: " away from"the ipsilateral LDV position). The raw LDV data with a resolution of <0.05 μm/s and sampled at intervals of 20 μs were further processed by MATLAB through a low-pass Butterworth IIR filter with a cut-off frequency of 250 Hz and displayed in data streams, frequency spectrograms and single-sided Fourier spectra. Finally, the raw Butterworth-filtered LDV-data streams were offset-corrected, weighted due to an insufficiency of a high-pass operation of LDV, by assigning an attenuation factor estimated at f att = 0.667 (Table 3, Pos 2), and were lastly scaled as z-velocities in mm/s or integrated as z-dislocations in mm.

Occurrence of Cool Nest Regions (CNRs)
At the nesting sites giant honeybees have to cope with the exposure to predators, but also with rain, wind and sun irradiation, which latter may lead to even excessively high temperatures. One of the most peculiar examples were nests under the hot tin roof of a college building in Assam, which heated up in the subtropical sun above 50°C (S1 Fig, panels A-B), with the risk of wax melting [60] and loosing the nest fixing., which affects the thermal properties of the cell building material. In contrast to Meliponines or Bombines, honeybees are unique among the social insects in using essentially unmodified wax for nest construction [60]. It is not known whether A. dorsata, nevertheless, mixes additives at extremely heat-exposed spots to increase the onset of wax melting.
Anyway, the colonies managed to cope with this critical situation by keeping the thermal effusivity [60][61] at the attachment of the comb extremely low; at least, as documented, the temperature at the nest surface was kept below 30°C, and therefore, they also succeeded to maintain the temperature milieu in the nest interior within acceptable limits [25][26]55]. However, these conditions implicated the occurrence of a series of cool nest regions (CNRs) all over the bee curtain, which emerged and faded off in terms of minutes. To the contrary, even at the same daytime, honeybee nests in the cooler canopy of a 40 m high tree hardly showed any CNRs (S1 Fig, panel E).
For this study, CNRs have been detected on various nests (n CNR = 207, n nests > 20, n days = 11) under different environmental conditions (Fig 2; S1 Movie). Although they occurred more often under higher ambient temperature (T amb ), particularly in the afternoon, they were also observed under much lower T amb in the early morning hours and during night-time (Figs 2-4). In the main experiment, their average numbers remained constant from the late morning up to 14.00 h, but then they markedly increased for two hours (Fig 4, panel B), proportional to ambient temperature (  Pooled data from "nest 02" assessed in steps of 30 min (n = 209 measurements; n exp = 11 experiments; Nov. 2010, Chitwan, Nepal); grey line, regression of arithmetical means: R 2 = 0.9785. (B-C) Occurrence of CNRs (total N CNR = 208) per 30 min over daytime (panel B: R 2 = 0.9631) and T amb (panel C: R 2 = 0.9754). Stars give significant differences between adjacent pairs of data (*, P < 0.05; **, P < 0.01; ***, P < 0.001; t-test). Full circles, means; vertical bars, mean errors. The background colours symbolize the temperature gradient from cool (blue) to warm (red). (D-G) IR images at different T amb and day times (see white text insets); scale bar (inset D), temperature range in°C.

Fanners at CNRs
In most cases when CNRs were monitored jointly in IR and HD from the first notice until their disappearance (n CNR < 40; n nests = 9) fanning bees were identified as positioned close to the CNRs (n fb > 100). For example, in Fig 6, panels A-B and in S2 Movie the fanning bee was identified at the left rim of the CNR, while she characteristically kept the head away from the nest and the abdomen towards the nest surface, producing an air stream directed obviously towards the centre of this selected CNR.
The functional properties of CNRs were described frame wise by mid-based parameters (see Eqs 1-4) of temperature measures (T mid , Ts ink , ΔTC NR ), gravity positions (X sink , Y sink ) and size cm; r POS hor , r POS vert : frame-specific relative positional data (cf. Eq 1) of the selected CNR (absolute values of partition 1 were set zero at the starting position, at 15:32 h); see panels C-D for the time courses of the relative r POS hor and r POS vert data. (E) The relative size ( r A) of the six partitions over rel time in min; the ordinate value r A = 1.0 refers to the double size of A CNR (see Eq 2) at the start of observation, calculated by 2 x A CNR = A env x 0.8 = 11.57 cm 2 ; the frame wise sum of the relative sizes of the six partitions was r A = 1.0. (F-G) The time course of the median values TC NR of the six partitions and of the ambient temperature (T amb   In this example, the fanner bee was active throughout the presence of the CNR, explicitly also during opening and closing, but did not affect temperature nor size of the CNR. Therefore, it can be supposed that the dynamics of CNRs are controlled primarily by a collective of curtain bees located around CNRs rather than by fanners. Identification of the sources making up the temperature patterns in the nest surface of A. dorsata A single bee is capable of heating up the thoracic muscles to temperatures much above T amb [25][26][48][49][50][51][52][53][54][55][56]. This is illustrated in A. dorsata from dancers and their followers during waggle dance (S1 Fig, panel C), or from water foragers prior to taking off (S1 Fig, panel D). The closeup image of the dancer's episode (S1 Fig, panel C) also shows quiescent bees of the surface layer with uniquely cool body temperatures, whereas the cavities between these surface bees point to the warmer nest interior. This temperature gradient within the bee curtain can also be demonstrated when the nest surface was depleted exposing the sub-surface layer of quiescent bees below (e.g. by treatment with lavender oil: S1 Fig, panels F-G).
The spatial pattern of surface temperature was assessed along transect lines through CNRs and their warmer surroundings (Fig 7) in synchronously recorded HD and IR images, which allows to identify abdomens of the bees of the surface layer as cooler than the interstices between them. This example demonstrates how surface bees loop up the lower temperature from the ambience with the consequence that even in the centre of a CNR the bee bodies were slightly cooler at the surface than in the subsurface layer (Fig 7, panel D).
Consequently, there are two surmises to be made: (1) Together with the finding that T CNR correlates with T amb (Fig 5, panel H) evidence is strong that CNRs function as funnels through which ambient air flows into the nest, representing low-resistance gates for bundling in-going air streams. (2) Without any airflow and at a given thickness of the multi-layered bee curtain, the interstices around a CNR are supposed to be affected more by the cooler ambience than by the warmer nest interior. Nevertheless, in all IR images these interstices were much warmer than expected (e.g. Fig 7; S1 Movie). Therefore, it is plausible to assume that these interstitial temperatures are caused by airflows by which warm, nest-borne air comes out, widely dispersed, through the mesh of the bee curtain around CNRs. Both surmises allow postulating the existence of a driven convection supporting respiration of the nest, by generating a cool airstream flowing inwards through CNRs and an outward nest-warm airflow through the mesh of curtain bees in the periphery of CNRs.
Tracing a respiratory mechanism by the assessment of size and temperature of CNRs The entire data set of the selected experimental nests (n = 9) comprised 334 synchronized sequences of IR and HD images. For the in-depth analysis described in this chapter only the dataset "09/nest 02"was used; it comprised a session over 13 days, from 9 am to 6 pm recording time each and delivered the highest abundance of CNRs compared to all other experiments. The differential data (ΔA CNR /Δt, ΔTs ink /Δt) are plotted in Fig 8 and referred to time intervals of Δt = 21.16 s (corresponding to a sequence of 100 IR frames). Under both conditions, with and without fanning bees, the A CNR data (Fig 8, panel A) were uniformly distributed (between 20 and 80 cm 2 ), but their differential data (ΔA CNR /Δt, Fig 8, panel B) were gauss distributed (between +1.0 and -1.0 cm 2 /s). Under the presence of fanning bees the selected data sets (Fig 8,  panels A-B) were five times larger than under non-fanning conditions. The majority of data, concerning e.g. 97.20% for fanning conditions (n ff = 24 359 inter-frame intervals; Fig 8, panel C), referred to the central zone of the ΔA CNR plots (detailed below as "scenario 1") while the complimentary minority was positioned at the periphery of both, positive and negative abscissa branches of ΔA CNR data ("scenario 2").
Scenario 1: Positive correlation between changes in CNR size and temperature. Under fanning condition (Fig 8, panel C, blue symbols) a smooth positive gradient was displayed centrally [-1.20 > ΔA CNR /Δt > +0.60 cm 2 /s]. It means that increasing CNR temperature (+ΔTs ink ) correlates with increasing CNR size (+ΔA CNR ), which is, however, the same to say that a decrease in CNR aperture is associated with a cooling effect; e.g., for ΔA CNR /Δt = -1.0 cm 2 /s the temperature decreased by ΔTs ink /Δt = -0.0111°C/s. In physics, this effect is known as Venturi effect; it is the consequence of the Bernoulli equation [61][62] that the temperature in an ideal gas decreases with increasing flow speed. With other words: if there exists a current flow through an aperture, any restriction of this aperture would increase the speed of the flowing medium and decrease its temperature.
In the case of CNRs, however, this Venturi effect is practically ineffective for any cooling effect of the nest interior, essentially because of the small magnitudes, but it still evidences the existence of a dynamically controlled air stream and therefore, once again, the funnel property Scenario 2: Negative correlation between changes in CNR size and temperature. Theoretically, a negative correlation between differential data of size (ΔA CNR ) and temperature (ΔTs ink ) can be explained by at least four different aspects: by an adiabatic process, by evaporation, by closing funnels, and by opening funnels.
(a) In adiabatic processes, a medium flowing through a physical tube is cooled by opening it and warmed up by constricting it. In nature this typically happens under foehn conditions by which air pressed over mountain ridges [63][64] is cooled down to its adiabatic dew point when rising through orographic lifting up, and is warmed up by adiabatic pressure on the leeward side of the ridge. Adiabatic processes are also utilized technically, e.g. in snow guns where water and pressurized air are forced through a narrow tube to be emitted into the open, which transforms liquid water into snow [65]. CNR funnels would, however, hardly comply with data were uniformly distributed, and ΔA CNR data were gauss distributed. (C) Regression functions (a: blue-coded, "fanning" state with R 2 = 0.9353; b: red coded, "non-fanning" state with R 2 = 0.0617) concern the central region of both correlations. One-sided arrows on the left side of correlation symbolize "closing" reactions (data for fanning state are here outside the scope); double-sided arrows on the right side give "inhalation" activities (see Discussion for ventilation hypothesis). Vertical blue and red bars in panel C give the range of data within ± standard error. doi:10.1371/journal.pone.0157882.g008 Ventilation in Giant Honeybee Nests adiabatic cooling processes, as they would require extremely high energy levels concerning airflows and abruptly opening gates.
(b) In evaporation, cooling effort grades negatively with the size of a humid area. To support the evaporation hypothesis for CNRs, water must be delivered to drive evaporation. Water could be brought to the CNRs, e.g. by water foragers, to suspend droplets of water. Rapid evaporation could be established by gobbetting behaviour of such water carriers, by which they repeatedly extend and contract their probosces, eventually pressing drops of water from the mouths into a thin film [25], and re-ingest them after evaporative cooling. Theoretically, curtain bees may also contribute in such cooling at CNRs, if they collectively regurgitate watery honey [25], but they could also speed up this evaporation as fanners by producing air streams towards the CNRs. Fact is, however, no water carriers had been observed at CNRs up-to-date, and even more important, the size changes (ΔA CNR ) correlate negatively with temperature changes (ΔTs ink ) independently from the visible presence of fanning bees (at least for ΔA CNR > +0.40 cm 2 /s; Fig 8, panel C).
(c) The negative correlation in the changes of CNR size and temperature on the left-side branch of Fig 8, panel C (with ΔA CNR /Δt < 0) refers to abrupt increases of Ts ink , possibly up to Ts urr , while the size A CNR may have diminished to zero (Fig 8, panel C). This constellation is nothing else than the closing of CNR funnels, which, astonishingly, occurred under non-fanning conditions at smaller |ΔA CNR |/Δt values than under fanning conditions (which were in Their repetitive occurrence can be plausibly explained with the assumption that CNRs operate as convection funnels in nest ventilation. Combined with an "inhalation-exhalation cycling" (IEC) activity of the bee curtain, the opening of CNRs leads to a rapid "inhalation" of cooler ambient air and thus to a negative correlation between ΔTs ink and ΔA CNR .
Tracing potential "respiration" movements in the bee curtain The performance of such hypothetical CNR-based ventilation in an A. dorsata nest is determined by the assumed funnel properties of CNRs and by a proposed IEC process. In the "inhalation" phase, the lumen between comb and inner surface of the bee curtain must be widened out, which can be only generated by muscle force. As potential candidates, curtain bees in the nest interior positioned around CNRs may synchronously stretch the extremities pushing the bodies away from the comb. Such local increments of the interior lumen would cause minute, but assessable dislocations of the comb (ΔZ comb << 1 mm) and of the bee curtain on both sides of the comb from the direction of gravity. Hereby, the comb and the contralateral part of the bee curtain would be shifted away from the stationary LDV, while the ipsilateral part of the bee curtain would be driven towards the LDV (see the schematics in S3 Fig, panel B). In the "exhalation" phase, the relaxation of the "stretcher" bees could reposition the comb and both parts of the bee curtain to the direction of gravity, to the original quiescent, "non-ventilatory" state (S3 Fig, panel A), narrowing again the inner lumen of the affected, ipsilateral nest side.
The efficiency of such hypothetical ventilation depends on the rhythmicity of the respiratory movements (at the frequency z IEC ) and by the magnitude of the air filling per cycle (ΔV IEC /Δt). Both values can be estimated on the basis of LDV data (Fig 9) together with the definition of nest parameters (Tables 1-3; Eq 5), such as the properties of the comb (mass of the comb per dm 2 , the density of cells, the mass of a single larva) and the arrangement of the bee curtain (the mass of a single bee, density of bees, number of bee layers on each side of the nest).
Assessment of the rhythmicity of respiratory (IEC) movements. In the experiment, the LDV records reveal dislocations of the comb (ΔZ comb ) in two phases (n LDV = 23; Fig 9, panels A-B; [30]): (a) during the presentation of a dummy wasp [28][29][30][31] provoking shimmering waves (sh), and (b) under quiescent conditions, i.e. without the presentation of the dummy wasp. Comb dislocations as caused by the shimmering activity can be identified at periods of < 1s (Fig 9, panel F: FFT peak marked by the p sh arrow). The marked dislocations at much lower frequencies as disclosed by the FFT peak at p IEC = 109.96 ± 0.55 s (Fig 9, panel C; considering the frequency band of 0.0025-0.1 Hz) do not represent any systemic LDV drift (which has already been corrected in the pre-assessment phase [30]), nor were they caused by external air convection (the nest was protected by linen curtains in the hotel bay, see S1 Fig). The only possibly explanation for these low frequency comb movements is to assume cycling respiratory movements due to nest ventilation. This view is supported by the IR data (S2 Fig, subpanels b) that most of the CNRs exhibited rhythmic openings and closings, alike the LDV records, in periods of minutes.
Volume changes affected by the hypothetical ventilation. Any dislocation of the nest triggered by external or internal forces concerns the comb and both sides of the bee curtain. In detail, if the ipsilateral side of the bee curtain with the mass m 1 = M bc_ipsi is dislocated from the comb (as a physical pendulum against gravity), also the opponent, conjoined masses of the comb plus the non-affected (contralateral) part of the bee curtain (m 2 = M comb + M bc_contra ; S3 Fig; Table 2, Pos 4) are dislocated from the line of gravity at the same time. The resulting dislocation of the affected part of the bee curtain (ΔZ bc_ipsi ) can be calculated considering the dislocation of the comb ΔZ comb as assessed by LDV and both mass components (m 1 , m 2 ) by applying the principle of the conservation of momentum and kinetic energy in coupled physical pendulums [66] (Eq 5).
The mean dislocation of the comb at the cycling period p IEC was estimated on the basis of the LDV records at the maximum of average dislocation values (ΔZ comb = 58.58 ± 5.73 μm; n LDV = 23; cf. Table 3, Pos 1-4). Under normative nest conditions (defined in Tables 1-3) the mass of the bee curtain at one side was 70.71 g / dm 2 and the mass of the comb was 134.29 / dm 2 resulting in a mass relation of m 2 / m 1 = 205.00 g / 70.71 g = 2.8992 (Table 2; Eq 5; see S3  Fig for schematic representation). Therefore, the real dislocation at the affected comb side  [30], scaled in mm/s; see Methods and S3 Fig). Black curves, unfiltered data; white superposed curves give low-frequency components defined as moving average values (±50 frames with interframe intervals of Δt ff = 20 ms); yellow background marks the first 60 s of observation, in which shimmering waves had been provoked by dummy wasp presentation [30]. (C) FFT-diagram: abscissa, the periods of partial frequency components of comb dislocations p {Z comb } in s; ordinate, the relative amplitude of these frequency components rA f {Z comb }. The period of the main low-frequency component presumably caused by "inhalation / exhalation cycling" (IEC) was assessed at p f {Z comb } = p IEC = 109.96 s (marked by the black arrow in panel C), as compared to p sh , the period of oscillation provoked by shimmering (cf. [30]); (D-F) Mathematical model estimating the hourly change in volume of gas exchange affected by IEC according to the ventilation hypothesis (ordinate: ΔV IEC [dm 3 h -1 ]). In this model, the size of the nest area affected by ventilation was chosen as 1 000 cm 2 corresponding to an area with a radius of 17.85 cm around the respective CNR funnel. The volume of gas exchange is dependent on three mass parameters of the bee curtain (number of bee layers N layers : panel D; individual weight of a honeybee W bee in mg: panel E) and of the comb (the relative weight of the comb area rW comb : panel F). Red curves, mean values; black curves, range of mean errors; n LDV = 23 LDV episodes. Normative base data (see Tables 1-3): density of bees in the bee curtain = 1 bee per cm 3 ; density of cells at both comb sides = 787 / dm 2 [72]; mass of the wax = 24.11 g dm -2 [72]; this adds up to a mass of W comb = 134.29 g /dm 2 comb area with larvae-containing cells (corresponding with rW comb = 1.0 in panel F). doi:10.1371/journal.pone.0157882.g009 Ventilation in Giant Honeybee Nests during the "inhalation" phase can be estimated by ΔZ bc_ipsi = 169.84 μm (Table 3, Pos 4), which corresponds well with the hypothetical range, the bees activated at the inner surface of the bee curtain could stretch their extremities.
On the basis of this dislocation value (ΔZ bc_ipsi ), applied to an affected area of 1 000 cm 2 around a CNR (r = 17.85 cm), the support of fresh air from the ambience would amount to an hourly volume of 571.23 ± 55.91 cm 3 (n LDV = 23; Table 3, Pos 8). However, CNRs can here only run as potential "breathe-in" gates if the airway resistance inside the funnel (R CNR ) is much lower than that of the neighbouring mesh of the bee curtain (R mesh ). In detail, the IR images document just this: CNRs behave in such a hypothetical "inhalation" period like nostrils in mammals (with R CNR << R mesh ). In the consecutive"exhalation" phase, the relaxation of the affected curtain bees brings then, simply by gravity, all dislocated masses (m 1, m 2 ) back into the vertical direction, pressing nest-borne air outwards through the diffuse mesh of the bee curtain (illustrated in Fig 7, panels C-D and in S1 Movie). Therefore, CNRs may operate here likewise as one-way valves giving access for inbound airflow rather than representing a homogenous, leaking part of the bee curtain.

Fanning at CNRs
At most CNRs, solitary fanning bees were detected (n CNR = 60) in a characteristic body alignment, by pointing their heads away from the nest and producing air streams, which were directed towards the centre of CNRs (Fig 6, panel A; S2 Movie). Fanning in A. dorsata can generally be observed in various contexts: it assists in evaporation of water droplets delivered by water foragers and pushes away raindrops from the nest surface [6], but it also occurs, though in a confined way, during shimmering [7][8][27][28][29][30][31][32][33].
In A. mellifera nests, ventilation is conjoined with pumping out nest-borne air through the entrance hole [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Fanners of the Indian honeybee A. cerana, however, align their bodies with the heads away from the nest [57][58], which presses air into the nest entrance. Most likely this is the evolutionarily older way to drive ventilation in honeybees, which is utilized even by cavity nesting species (provided the nest borne air can flow out under this pressure from outside through leaking hive structures). This could explain why also the fanners of the also evolutionary older, open-nesting giant honeybees direct their air streams towards the bee curtain (Fig 7, panel A; S2 Movie). As we have observed, this fanning in A. dorsata was definitely not escorted by Nasonov scenting and was also not linked to any evaporative process, neither mediated by water foragers nor by curtain bees as potential honey storers. Moreover, it is physically impossible that airflows initiated by such fanners towards the nest surface could effectively ventilate the interior of A. dorsata nests through CNRs.

Funnel and ventilation hypotheses
The occurrence of CNRs correlates with ambient conditions (Fig 4), whereby CNRs, nevertheless, possess autonomy in their spatial dynamics (Figs 5 and 6). The data bring reliable evidence that CNRs do not effectuate evaporative cooling but do have funnel functions (Fig 5, panel H;  Fig 8, panel C). The performance of CNR funnels is obviously supported by fanning bees (Fig  6, panel A), they are likely to enlarge the operational "Venturi" range [61][62] by stimulating the initiation and maintenance of CNRs (Fig 8, panel C) when pushing air from the cooler ambience towards CNRs.
Here, the formation of CNR funnels prompts the questions how the air streams through CNRs are directed inwards, how they are generated and how they ventilate the nest. The findings of this paper (Figs 6-8) definitely exclude fanning activity as the main motor for ventilation without any primary role in opening and closing of CNRs (Fig 6; Fig 8, panel C). They support the view, however, that A. dorsata colonies have obviously found a more forceful solution to safeguard aeration of the nest interior than pushing ambient air into the nest by fanning. The most plausible explanation is in support of the ventilation hypothesis, which presumes the existence of "inhalation-exhalation" cycling (IEC). Ventilation may happen here quite analogous to the abdominal respiration in mammals [69], where the muscular force of the diaphragm rhythmically enlarges the lung volume, which leads to a pressure fall in the lungs and instils an airflow inwards through the nostrils.
In A. dorsata nests an analogous process could suck fresh air from the ambiance into the nest, promoted by CNR funnels as low-resistance gates for air streams. The pumping mechanism behind this "breathe-in" probably is due to transient and synchronously forced actions of a collective of curtain bees around CNRs. According to this surmise, such bees could stretch their extremities against the comb to arch the bee curtain slightly outwards, which enlarges the nest lumen at the comb site, causing a fall of pressure herein. In the consecutive "exhalation" phase, the same bees, previously active in pushing themselves from the comb by muscle force, would relax. This would drive the bee curtain back to the comb by gravity, pressing the warm, residual, nest-borne and CO 2 -enriched air outwards through the diffuse leaking mesh structure of the bee curtain. Such transient ventilation should occur rhythmically, and should be not necessarily coupled with the presence of active fanners.
These surmises of the ventilation hypothesis are verified by a series of quantitative observations: (a) Funnel functions are substantiated for CNRs by the Venturi principle [61][62] (Fig 8,  panel C; S2 Fig). (b) The inwards direction of the airflows through CNRs is inferred from the body alignment of the fanners at CNRs (Fig 6, panel A) and by the strong influence of the temperature profile of the CNRs with ambient temperature (Fig 5, panel H). (c) IR imaging evidences CNR funnels as "inhalation" tubes (through which air flows inwards, analogously to the mammal nostrils in the "cool" phase) rather than as "exhalation" outlets (Figs 6 and 7). (d) Cooling by opening happened at CNRs in the presence of fanners but also without them (ΔA CNR > +0.40 cm 2 /s; Fig 8; S2 Fig). (e) Fanning stimulates the nest for voluminous "breathe-ins", which is documented by the expansion of the "cooling" range by dilating CNR funnels under fanning. (f) Rhythmicity of ventilation is documented by two different methods of data assessment, both revealing cycling in periods of 1-2 min: in IR imaging, by the mostly pulsating time courses of the CNR apertures (e.g. in the A CNR data of S2 Fig, subpanels c), and in the LDV signals, by the low-frequency rhythm of comb dislocations at the period length of p IEC (Fig 9, panel C). (g) The hypothetical "exhalation" process leads to a leaking out of warm air through the mesh of the bee curtain, which is factually traced in the sequences of IR images (Fig 7; S1 Movie). Considering that the interstices between bees at the nest surface are practically exposed to ambience, these cavities, which allow the view on the subsurface layer of the bee curtain, are much warmer than expected without any outward flow of nest borne air.
Lastly, the mathematical model (Fig 9, panels D-F) allows to estimate the capacity of such a hypothesized IEC process in nest ventilation: at normative conditions (see Tables 1-3 for definition), the hourly aeration of the nest through CNR funnels amounts at least to more than 0.5 dm 3 fresh air per 1 000 cm 2 nest area ( Table 3, Pos 5), in which the lumen between bee curtain and comb is rhythmically expanded. An A. dorsata colony may raise this hourly volume of gas exchange simply by increasing the number of CNRs in the nest to meet the needs even under the higher ambient temperatures of a subtropical mid afternoon (e.g. Figs 2 and 3; S1 Movie).

Conclusive remarks
The bee curtain of an A. dorsata nest possesses five to seven layers of bees and thus provides a relatively dense and insulating cover for the protection of the brood against environmental curtailing, but keeps off venting it without additional strain. The CNR funnels, so far as known up-to-date, are the only way to provide the brood under undisturbed conditions with both homoeothermy and ventilation with fresh air.
Hereby, the need of ventilation in honeybee nests is considerably high: even quiescent honeybees consume due to their high metabolism rate notable amounts of oxygen (e.g. A. mellifera at 35°C: 5.55 μl O 2 min -1 per individual [70][71]), even linearly increasing at falling ambient temperature, and produce hereby a considerable amount of CO 2 [71]. Honeybees are also highly susceptible to CO 2 gradients [70]: this is shown in A. mellifera colonies, which intensify fanning inside and outside the nest with increasing partial pressure of CO 2 in the nest [71]. And it is also observed in A. dorsata nests, in context with the occurrence of CNRs, which emerge not only under higher ambient temperatures in the early afternoon but also in morning and evening hours when the ambience is much cooler (e.g. during November in Chitwan with T amb = 23°-24°C; Fig 2, panel C; Fig 3). Evidence is therefore strong that CNRs depict low-resistance convection funnels not only for maintaining inner nest homoeothermy but also for restoring fresh air in the nest. (C) Close-up views from the surface of an experimental nest revealing a dancing forager bee and her followers with hot thoraces and cool abdomens, whereas neighbouring quiescent surface bees had uniquely cooler bodies at ambient temperature; the yellowish areas around some surface bees regard to interstices and allow the view at the warmer, deeper layers of the curtain. (D) A single water forager, some seconds before taking off from the water place with the characteristic heated-up thorax. (E) Nests in the canopy region of a big tree without any CNRs (Assam, 1998). (F-G) Experimental nest before (F) and during (G) manual treatment with lavender oil which depleted the surface layer; the bees of the surface layer were urged to walk aside. The higher temperature of this lower exposed layer comes from the nest interior (Chitwan, Nepal 2010). Insets give the temperature scales of the images. and comb (ΔZ comb ) during the hypothetical IEC in a giant honeybee nest. A, quiescent, "non-ventilatory" phase; B, "inhalation" phase. Red areas symbolize the bee curtain, the grey areas the comb; thin black horizontal lines show that the bees of the inner surface of the bee curtain contact the comb with their extremities; longer lines refer to stretched extremities; horizontal orange bar is a wooden rod which was stuck through the comb and the ipsi-and contralateral parts of the bee curtain (bc_ipsi, bc_contra). The LDV ray was reflected on the ipsilateral plane end of the rod. Black vertical arrows give the direction of gravity (d g ). The dislocation of the comb (ΔZ comb ) from the direction of gravity was measured with LDV and the dislocation of the ipsilateral bee curtain (ΔZ bc_ipsi ), locally around the convection funnel, was calculated according to Eq 5. (TIF) S1 Movie. Occurrence of CNRs. IR monitoring of experimental "nest 02" (cf. Fig 1) through 33 min at 3.9427 Hz. The temperature scale on the right is fixed between 26°and 40°C, whereby the range of the actual temperature pixels is displayed by the small bar between the scale partition and the rainbow-900 palette. The black bar at the bottom displays the relative time of the image noted in minutes. The blue-green areas represent CNRs while the tiny red spots regard to the interstices between the bees of the surface layer; according to the ventilation hypothesis they document the "exhalation" phase when nest-warm air is pressed out through the diffuse mesh of the curtain (cf. Fig 7). (MP4) S2 Movie. Fanning bee at a CNR. In the quiescent region of the bee curtain, peripheral to the mouth zone [6][7][8]12], most of the bees are positioned in a vertical body alignment, with heads up and abdomens down. However, some bees display postures with the head pointing away from the vertical surface of the nest. These bees are potential fanners, most of them were identified near or at CNRs. This bee displayed in the mid of the image was fanning throughout nearly the entire observation session (cf. Fig 6, panel A). (MP4)