Accelerated landing in a stingless bee and its unexpected benefits for traffic congestion

Abstract

To land, flying animals must simultaneously reduce speed and control their path to the target. While the control of approach speed has been studied in many different animals, little is known about the effect of target size on landing, particularly for small targets that require precise trajectory control. To begin to explore this, we recorded the stingless bees Scaptotrigona depilis landing on their natural hive entrance—a narrow wax tube built by the bees themselves. Rather than decelerating before touchdown as most animals do, S. depilis accelerates in preparation for its high precision landings on the narrow tube of wax. A simulation of traffic at the hive suggests that this counterintuitive landing strategy could confer a collective advantage to the colony by minimizing the risk of mid-air collisions and thus of traffic congestion. If the simulated size of the hive entrance increases and if traffic intensity decreases relative to the measured real-world values, ‘accelerated landing' ceases to provide a clear benefit, suggesting that it is only a useful strategy when target cross-section is small and landing traffic is high. We discuss this strategy in the context of S. depilis' ecology and propose that it is an adaptive behaviour that benefits foraging and nest defence.

1. Introduction

All flying animals perform landings—shifting from active flight to touchdown on a surface—and this fundamental behaviour is probably shaped by selection pressure on the control of both momentum and trajectory. Failure to control these variables in flight or at touchdown may lead to mid-air collisions with other flying animals (in the case of crowded landing sites) or to a crash-landing on the target, generating a risk of injury. Unlike with birds and bats [1,2], however, the physical cost of such collisions for insects is relatively low owing to their small body size, and crash-landings in some cases can even be part of their locomotory strategy [3]. Failure to reach the landing target accurately will nonetheless require an insect to repeat the landing manoeuvre or to laboriously crawl towards the goal. This will be expensive with respect to time and energy. In social bees, who routinely perform tens or hundreds of landings on flowers [4] and on their hive entrance, the cost of crashing into an obstacle owing to poor aim while landing or colliding with a conspecific is likely to be particularly high.

For many animals, including honeybees [5,6], bumblebees [7,8], fruit flies [9], birds [10] and bats [11], landing is typically characterized by a reduction in speed to a value close to zero at touchdown and a well-timed leg extension [6–10,12–15]. Animals that fail to decelerate or to extend their legs in time risk crashing into the landing target [9]. To land at a specific location, such as a nest entrance, a branch or a food source, the animal also needs to orient its own body with respect to the orientation of the target [6,8] and to control its trajectory. Studies with tethered animals [16,17] are intrinsically unable to provide information about how animals guide their trajectories towards targets and studies performed on free-flying insects often use flat, artificial targets that are several times larger than the animal's body [8,9,13]. This does not reflect the constraints that animals face when approaching natural targets such as flowers or nest entrances. Targets that are small relative to the animal's wing span require precise control of the landing trajectory if touchdowns are to be executed efficiently, but whether and how animals attain this precision remains unclear.

Scaptotrigona depilis is a Brazilian stingless bee that lands on a narrow tube-like hive entrance (approx. 20 mm in diameter, approx. 20 mm in length) constructed out of wax and propolis [18]. The hive entrance is typically less than double the wing span of an individual bee (approx. 11 mm), necessitating fine control of landing position. Furthermore, landing S. depilis must also contend with the high rate of returning and leaving foragers that occurs at the hive entrance [19]. This restricts the space that they have to land in and presents the additional challenge of having to avoid mid-air collisions with conspecifics. The high traffic flow at the nest also limits the time that each forager may spend landing (to free up landing space at the hive entrance). These constraints make S. depilis not only an interesting model for investigating trajectory control when aiming for small natural targets in an ecologically relevant context but also for exploring the effect of traffic pressure on landing behaviour.

Here, we investigate how S. depilis approach and land on their hive entrance and find that, unlike most animals studied to date, they accelerate prior to touchdown. To better understand this behaviour and how it could mitigate the problem of limited space and/or high traffic intensity, we developed a mathematical simulation of bee traffic at the hive based on our real-world data. This allowed us to manipulate the acceleration profile of landing trajectories, as well as other variables that may affect landing efficiency, such as hive entrance size, and traffic intensity. Our findings suggest that this unusual landing behaviour may represent an adaptation that minimizes traffic congestion in S. depilis under the dual constraints of small target size and high traffic intensity.

2. Methods

(a). Study site and animals

The study was conducted in November–December 2017 in the garden outside the ‘Laboratório de Abelhas' at the University of São Paulo, Brazil. We used two managed colonies of the stingless bee S. depilis [20,21] kept in white wooden hive boxes (200 mm × 200 mm × 300 mm). Before moving the hives to a place suitable for video recordings, we removed the wax/propolis hive entrance constructed by the bees and closed the circular opening into the hive box (diameter = 20 mm). The hives were placed on platforms (approx. 600 mm above the ground), the entrances to the hives were opened and left undisturbed for a minimum of 10 days, allowing the bees to become familiar with the new location and to build a new nest entrance.

(b). Recording protocol

Over a period of 4 h (between 11.00 and 15.00), recordings of bees landing at the hive entrance were made using a pair of synchronized high-speed cameras (MotionBLITZ EoSens®, Mikrotron GmbH, Unterschleissheim, Germany) equipped with a 25 mm f/0.95 lens and filming at 120 frames s⁻¹. The cameras were directed sideways at the hive such that they simultaneously recorded landing bees at touchdown on the hive over a distance of 300 mm from the hive entrance. During the recording period, there was a light breeze, the external temperature was 25°C–27°C and the light intensity in front of the hive entrances varied from 1100 lux to 7500 lux. We limited the recordings to six 13.6 s time windows (comprising 83 complete landing trajectories) to control for the effects of climatic variables on the bees' activity and to minimize the risk of recording multiple landings from the same individual, which was also unlikely owing to the large number of foragers in each hive (estimated to be in the thousands) and the high rate of foragers returning to the hive during the recording period. We thus treated each trajectory as an independent data point in the analysis. When visible in the recorded images, leg extension before touchdown was reported. Collisions with other bees were also noted.

To facilitate the tracking of the bees in the recordings, we attached two white sheets (1000 mm × 2000 mm) on each side of the hive at least 24 h before recording. While initially disturbed by the presence of the sheets, the activity of the bees returned to normal within a few hours. To control for the effect of the sheets on the landing behaviour, we recorded 23 landing trajectories before the sheets were installed (temperature and light intensity: 25°C–26°C, 500 lux-4500 lux).

(c). Trajectory reconstruction and landmarks on the hive entrance

Landing trajectories were reconstructed from the image sequences recorded by each camera with an automated tracking software [22] and reconstructed in three dimensions (3D) using the camera calibration toolbox in Matlab (The MathWorks, Inc.). This process also calibrated for any distortions in the images caused by the lenses. The natural waxy hive entrance that had been built by the bees started at the circular opening in the hive box and ended with an edge that protruded mostly on the lower side (figure 1). The length of this entrance was defined as the distance between its lower edge and the lowest point in the hive box opening (figure 1d, segment EB₂), while its diameter was defined as the distance between the upper and the lower point of the hive opening (figure 1d, segment B₁B₂). The centre of the hive entrance was defined as the centre of the opening in the hive box (figure 1d, point C).

Figure 1.

Recording set-up. (a) Hive 1 with one of the two white sheets used to facilitate tracking. (b) Top-down image of the experimental set-up showing the position of the high-speed cameras in front of hive 2. (c) Close-up view of the entrance of hive 2 before placement of the white sheets (note the guards at the edge of the entrance). The scale in each image is given by the diameter of the hive entrance (hive 1: 21 mm; hive 2: 25 mm). (d) Illustration of the hive entrance as seen from the side and the front (bottom panel). The points E, B₁ and B₂ were used to measure the length and diameter of the hive entrance. The point C at the centre of the base of the entrance represents the origin of the (x, y, z) coordinates.

(d). Trajectory analysis

A custom-made Matlab code was used to analyse the trajectories, which were normalized with respect to the centre of the hive entrance. The frontal plane of each hive box was nearly vertical with respect to gravity, with a marginal error of less than 3°. The vertical y-axis could thus be approximated by the projection of the gravity vector onto the box plane, with the z-axis perpendicular to this plane (figure 1d).

The different spatial components of instantaneous speed were calculated and smoothed using a robust version of the ‘Lowess' method of linear fit over a moving window of 10 frames, which was used because visual inspection of the data indicated that this was sufficient to remove noise generated from minor tracking errors without affecting the overall profile of the trajectory. We defined the start of a landing when a bee's z distance was between 250 mm and 245 mm from the hive plane, and the end of landing when z was between 25 mm and 20 mm from this point.

To accurately identify changes in acceleration, we averaged instantaneous acceleration over a window of 10 frames moving backwards from the end to the beginning of the landing sequence. When this average changed sign, the time with the minimum speed in this moving window was defined as when a ‘switch' in acceleration occurred. Landings in which this switch was more than 10 frames away from both the end and start of the landing sequence (the bees made a deceleration followed by an acceleration) were classified as ‘type 1’. Landings were classified as ‘type 2’ when the switch was within 10 frames of the start of the trajectory (the bees accelerated before touchdown), and of ‘type 0' when the switch was absent or within 10 frames of the end of recording (the bees decelerated before touchdown). The reliability of this method can be assessed visually in the electronic supplementary material, figure S1. At the acceleration switch point, local parameters such as speed V_switch were only calculated when meaningful, that is to say in the case of type 1-2 landings.

In the recorded videos, 25 trajectories of bees flying out of one hive were tracked and the parameters were used to simulate outgoing traffic in the mathematical simulation.

Further analyses were performed in R (R Development Core Team, Vienna, Austria). Speeds at start, switch or end, grouped by hive, were compared using non-parametric Mann–Whitney U tests. The effect of mean acceleration on the final accuracy of the bees was modelled using the Markov chain Monte Carlo (MCMC) sampler for multivariate generalized linear mixed models from the MCMCglmm package with hive as a random variable. Unless otherwise specified, values are given as mean ± s.d., ‘n' represents the number of data points.

(e). Mathematical simulation of landing traffic

(i). Model structure

The framework of the landing traffic model is shown in figure 4a. All simulations were run in Matlab. At each time interval, there is a probability P_start that a new landing bee with the spatial coordinates (x_start, y_start, z_start) starts a landing towards the final point (x_end, y_end, z_end) on the virtual hive entrance (figure 4a,b). Trajectories were simulated as straight lines to reflect the real flight paths of S. depilis, which were on average 29 ± 35% (n = 83) longer than a straight line (electronic supplementary material, figure S7). To be consistent with the real data, z_start and z_end were fixed at 250 mm and 20 mm, respectively. Each simulated trajectory typically started with a uniformly decelerating movement that was determined by three parameters: speed at start V_start, and speed and distance from the hive at acceleration switch: V_switch and D_switch, respectively (figure 4d). Once the switch from deceleration to acceleration was reached, the movement rule was given by three parameters: V_switch, D_switch, V_end. For each iteration, two bees were considered to have collided if they were separated by a distance inferior to the constant collision distance D_collision (further details are given in §2e(ii)). Simulated bees that collided on their way to the hive would attempt a new landing.

Figure 4.

(a) Framework of the traffic simulation. At each iteration, an incoming (resp. outgoing) bee is generated with a probability P_start $(P_{\mathrm{start}}^{\mathrm{OUT}})$ at the coordinates x_start, y_start, z_start ($x_{\mathrm{start}}^{\mathrm{OUT}}$, $y_{\mathrm{start}}^{\mathrm{OUT}}$, $z_{\mathrm{start}}^{\mathrm{OUT}}$). Bees fly along a straight line towards the final coordinates x_end, y_end, z_end ($x_{\mathrm{end}}^{\mathrm{OUT}}$, $y_{\mathrm{end}}^{\mathrm{OUT}}$, $z_{\mathrm{end}}^{\mathrm{OUT}}$). The speed curve is determined by the parameters V_start, V_switch, D_switch and V_end ($V_{\mathrm{start}}^{\mathrm{OUT}}$, $V_{\mathrm{end}}^{\mathrm{OUT}}$). At any iteration, bees collide if they are separated by a distance inferior to D_collision. (b–d) Normalized densities of flight parameters in the observed data (grey fill) and the simulated distributions for a constant-speed (orange line) or an accelerated (grey line) landing (platform size and traffic intensity ratios of 100%). Note that speeds equal to the minimal realistic speed V_min are excluded. (e,f) Results of the traffic simulation. The effect of platform size and incoming traffic intensity on the collision benefit of accelerated landings with (e) or without (f) outgoing traffic. The collision benefit is the mean difference between the percentage of incoming bees that collided before reaching the hive in the constant speed and in the accelerated scenarios (n = 200). Traffic intensity and platform size are expressed as the ratio (in %) between the tested and the real-world values of P_start (respectively, the half-widths of the distributions of x_end, y_end, $x_{\mathrm{end}}^{\mathrm{OUT}}$ and $y_{\mathrm{end}}^{\mathrm{OUT}}$). Significance was tested with one-sided t-tests (blue bars: p < 10⁻², red bars: p > 10⁻²). (Online version in colour.)

Trajectories of outgoing bees were simulated in a way similar to the landing bees described above. Bees were generated with a probability $P_{\mathrm{start}}^{\mathrm{OUT}}$ at the hive with the coordinates $x_{\mathrm{start}}^{\mathrm{OUT}}$, $y_{\mathrm{start}}^{\mathrm{OUT}}$ and $z_{\mathrm{start}}^{\mathrm{OUT}}$ and flew out towards the coordinates $x_{\mathrm{end}}^{\mathrm{OUT}}$, $y_{\mathrm{end}}^{\mathrm{OUT}}$ and $z_{\mathrm{end}}^{\mathrm{OUT}}$(electronic supplementary material, figure S4) at a constantly increasing speed (from $V_{\mathrm{start}}^{\mathrm{OUT}}$ to $V_{\mathrm{end}}^{\mathrm{OUT}}$; figure 4c), which faithfully simulated the real flight kinematics (electronic supplementary material, figure S2). The same collision rules were used for incoming and outgoing individuals, but the latter were removed from the simulation if they collided.

Each simulation of the landing traffic model was run for 8000 iterations with a burn-in of 800 iterations (to ensure that the model had reached a stable state), corresponding to a simulated time of about one minute at a rate of 120 iterations s⁻¹ to mimic the frame rate used in the original recordings. We compared the frequency of mid-air collisions that occur when using an accelerated landing strategy to the number that occur when using a constant speed landing strategy by setting the average of V_end such that $\overline{V_{\mathrm{end}}}\hspace{0.17em}=\hspace{0.17em}\overline{V_{\mathrm{switch}}}$ (constant speed landing), or $\overline{V_{\mathrm{end}}}\hspace{0.17em}=\hspace{0.17em}{1.5}^{\ast }\overline{V_{\mathrm{switch}}}$ (accelerated landing; figure 4d). In this way, we could simulate two average landing strategies while maintaining the same degree of individual variability as we observed in the original data (figure 4a–d; electronic supplementary material, figure S4a–d).

In subsequent simulations, we simultaneously tested the effect of the incoming traffic intensity and the size of the landing platform at the hive entrance on collisions. We manipulated the landing probability P_start (to modify incoming traffic intensity), and the half-width (variance) of the distributions of the coordinates at the hive entrance: x_end - y_end and $x_{\mathrm{start}}^{\mathrm{OUT}}$ - $y_{\mathrm{start}}^{\mathrm{OUT}}$ (to modify platform size). We performed 200 replicates of the simulation for each combination of landing strategy, traffic intensity and platform size.

Finally, we performed a sensitivity analysis of the model by investigating how the simulation result was affected by random changes of one parameter at a time around its baseline value (electronic supplementary material, text S1).

(ii). Modelling of input parameters

The parameters defined above were estimated from the real-world data recorded from hive 1 (electronic supplementary material, table S1). The collision distance D_collision was two times the average length of a bee left wing (5.4 ± 0.29 mm; n = 5), approximating the total wing span. The probability distribution P_start that a bee is generated and starts a landing in an iteration was estimated from the distribution of arrival times at the hive entrance observed in all recordings. All other parameters related to trajectory and speed were specifically assigned to a bee according to their observed distributions and relationship to one another in the real-world dataset, with the exception of V_end, which was the parameter being tested and modified, as described in §2e(i). The distributions of V_start, V_switch and V_end were truncated at V_min = 10 mm s⁻¹ as speeds below this limit are unrealistic for S. depilis.

With the exception of D_collision, P_start and $P_{\mathrm{start}}^{\mathrm{OUT}}$, all parameter distributions were estimated using a Gaussian distribution in the MCMC sampler from the MCMCglmm packages in R. In the second method, the best model was defined as the one with the lowest deviance information criterion (DIC). MCMC simulations were run three times with default priors for 1 100 000 iterations with a burn-in of 100 000 iterations. The traces of the sampled output and density estimates were plotted to check that mixing was sufficient, that is to say that there was little correlation between consecutive iterations. The density estimates for each parameter used in the model were used to generate a unique set of parameters for each bee.

3. Results

(a). Landing characteristics

Scaptotrigona depilis typically build nests in tree trunk cavities, sealing off the internal area and constructing just one small entrance tube made of wax and propolis to access the outside. For the hives used in this study, the entrance started at a circular opening in the hive box and ended with a slightly flared, tilted edge (figure 1a–c). The dimensions of the entrance were similar for the two hives (diameter and length: hive 1: 21 mm and 14 mm; hive 2: 25 mm and 22 mm). Bees returning to the hives landed at high speed either on the edge or directly inside the entrance, at a mean frequency of 1.0 bee s⁻¹ (n = 83, min = 0 bee s⁻¹, max = 5 bee s⁻¹). Figure 2 shows the trajectories of landing bees from different perspectives and the x_end-y_end coordinates of the bees at a horizontal distance of z_end equal to 20 mm from the base of the hive entrance.

Figure 2.

Details of landing in S. depilis. (a) Superimposed frames from a high-speed camera showing a typical accelerated landing in S. depilis (hive 1) with the switch to acceleration (red arrow) and the onset of leg extension (black arrow). Images were resampled to a frame rate of 60 frames s⁻¹ for clarity. (b) Landing trajectories of S. depilis workers with (blue, n = 83) and without sheets (red, n = 23) towards the hive entrance of hive 1 and 2 in the x-z (i) and y-z plane (ii). (c) Distributions of D_{Leg extension} where bees extended the legs with (blue, n = 35) and without (red, n = 14) sheets (Mann–Whitney U test, p < 10⁻²). (d) Final coordinates x_end and y_end of the bees without or with sheets (circles and triangles, respectively). (e) Effect of mean acceleration on the final accuracy of the bees with sheets (orange circles). The black line represents a linear fit with sheets (n = 63) with the credible interval in grey (MCMCglmm with hive as a random variable, intercept: p_MCMC < 10⁻⁴, slope: p_MCMC = 0.021). (Online version in colour.)

(i). Kinematics of landing

Features of the landing kinematics are summarized in figure 3, and the speed profiles of all 83 trajectories are given in the electronic supplementary material, figure S1. The minimum velocity of most trajectories did not occur at touchdown on the entrance (as would be expected if the bees reduce their speed, and hence their momentum, until touchdown), but at a distance D_switch of 150 ± 69 mm from the base of the hive entrance (n = 77; figure 3a,b). Thus, instead of continuously decelerating before touchdown, most bees first decelerated, and then accelerated. The final speed prior to touchdown V_end was 830 ± 170 mm s⁻¹ (n = 53) while at the start of acceleration, V_switch was 500 ± 200 mm s⁻¹ (n = 77). The acceleration was most commonly preceded by a deceleration, with 83% of bees (n = 69) following this pattern (‘type 1', figure 3a)). An analysis of the final acceleration (over the last 10 frames, or 83 ms) as a function of the mean acceleration (figure 3c) revealed alternative types of speed curves. Ten per cent of bees (n = 8) had a high mean acceleration because they accelerated continuously throughout the field of view of the camera (‘type 2', figure 3a). This group may have had a deceleration phase in their trajectories prior to entering the camera view. The remaining 7% (n = 6) had a negative final acceleration because they decelerated in the last phase of landing before touchdown (‘type 0', figure 3a). Even though bees had significantly greater speeds when landing on hive 1 compared to hive 2 (Mann–Whitney U test, p < 10⁻¹⁵), the characteristics and prevalence of accelerated landings were similar in both hives (Fisher's exact test on types of speed profiles, p > 0.09). Accelerating prior to touchdown—hereafter referred to as ‘accelerated landing'—therefore appears to be the most common landing behaviour in S. depilis.

Figure 3.

Analysis of landing trajectories in S. depilis. (a) Examples of smoothed speed profiles of individual bees that performed different landing types: final deceleration (green), ‘type 0'; deceleration followed by acceleration (orange), ‘type 1’; or a sustained acceleration (purple), ‘type 2'. The red arrow indicates the change in acceleration, or ‘switch' point. (b) Flight speeds at the start V_start, the switch V_switch, and the end V_end without or with sheets (circles and triangles, respectively). Boxplots show the first quartile, median value, third quartile, and all jittered speed values. Whiskers show 10%–90% percentiles. The effect of the sheets was tested with Mann–Whitney U tests (p > 0.05; n.s.). (c) Final and mean acceleration without or with sheets (circles and triangles, respectively) separated by types of speed curves (type 0: green; type 1: orange; type 2: purple). (Online version in colour.)

(ii). Accuracy of touchdown and leg extension

Touchdown accuracy—defined as the distance in the x-y plane between the bee and the centre of the hive entrance at touchdown—was 14.0 ± 6.2 mm (n = 83; figure 2e) (the diameter of the two entrances were 21 mm and 25 mm). As the average acceleration during landing increased, touchdown accuracy appeared to decrease (figure 2e; MCMCglmm with hive as a random variable (10⁶ iterations); intercept: p_MCMC < 10⁻⁴; slope: p_MCMC = 0.021). Similar p-values (highly and marginally significant, respectively) were also found when we fitted a linear model using generalized least squares, suggesting that this result is unlikely to be an artefact of the statistical approach used. This result indicates that acceleration during landing might come at the cost of reduced accuracy at touchdown in S. depilis.

For the trajectories where the touchdown was discernible in the recorded images, most bees landed with their legs first (n = 76 out of 83) and extended their legs at D_{Leg extension} = 43 ± 12 mm from the base of the hive entrance (figure 2c; measured from the 35 landings from hive 1 in which this was visible). The distance at which leg extension occurred was not related to the type of landing (Mann–Whitney U test, p > 0.15). The occurrence of leg extension before touchdown in most bees strongly indicates that, despite accelerating during the final stages, landing in S. depilis is well controlled.

(iii). Effect of hive manipulation

Overall, landing sequences (figure 2) and kinematics (figure 3) were strikingly similar in both the absence (n = 23) and presence of white sheets (n = 83) around the hive. The only two notable differences were a larger D_{Leg extension} in the presence of sheets (figure 2c; Mann–Whitney U test, p < 10⁻²), and the absence of type 0 landings without sheets (figure 3c). This indicates that the observed accelerated landings represent a stereotypical, natural behaviour that is not an artefact of the experimental design. On the contrary, our results suggest that the few decelerated landings we observed (type 0) might represent an unnatural behaviour caused by the presence of sheets.

Despite the apparent decrease in accuracy at touchdown, our results show that accelerated landings are typical for S. depilis. Why is this extraordinary behaviour, that seems to come at the cost of reduced accuracy at touchdown, maintained in the population? In addition to making controlled landings on a restricted target, S. depilis must also contend with the high rate of other bees approaching and leaving the hive entrance, which presumably requires them to minimize the time spent landing in order to avoid mid-air collisions with conspecifics. Aerial collisions indeed seem very rare in S. depilis colonies under ecologically relevant conditions, with only two cases being recorded during our experiment: one in which a landing bee collided with a nest-mate at the hive entrance and another in which an incoming bee collided with a departing nest-mate, which disrupted its landing sequence (electronic supplementary material, movie M5, 00:00:02). We propose that accelerated landings have arisen as a strategy that enables S. depilis to minimize the risk of collision with conspecifics when target size is small and traffic intensity is high. To explore this idea, we developed a model that allowed us to simulate the flow of bees and to manipulate different parameters associated with it.

(b). Model of landing traffic in S. depilis

To investigate if the risk of mid-air collisions is affected by landing strategy type (i.e. accelerating, decelerating or maintaining the same speed during landing), we created a model of landing traffic derived from the observed real-world landing behaviour of S. depilis described above. We compared the frequency of mid-air collisions when bees performed accelerated ($\overline{V_{\mathrm{end}}}$ = 854 mm s⁻¹) or constant speed landings ( = 568 mm s⁻¹) in different conditions of incoming bee traffic and landing platform size (figure 4). The ‘collision benefit' is defined here as the difference between the percentage of incoming bees that collided before reaching the hive in the constant speed and in the accelerated landing scenarios (i.e. a positive value indicates a decreased risk of collision with accelerated landings). When bee traffic and landing platform size were the same as in our experiments (100% of the original size), the collision benefit of 1.5% was significantly different from zero (figure 4e; one-sided t-test; n = 120; p < 10⁻²²). Although this benefit seems small, it implies that accelerated landing reduces the percentage of collisions from 7.5% to 6.0%, which represents a relative improvement of 20%. The collision benefit of accelerated landing was highest in a given range of high traffic intensity and small hive entrance (figure 4e), but lower, or even non-significant (red bars) if these constraints were alleviated. When outgoing traffic was not included in the simulation, a similar result was obtained (figure 4f).

We performed a sensitivity analysis to assess the robustness of the simulation, and found that the collision benefit was generally still observed despite the changes in the other model parameters, including the number of simulated iterations and the tortuosity of the trajectories and speed curves (electronic supplementary material, figure S10).

4. Discussion

In the present study, we reconstructed 3D trajectories and speed profiles of the stingless bee S. depilis landing on a natural hive entrance. Landings consistently ended with a 1.7-fold increase in speed over 150 mm. We explored one potential function of the accelerated landing strategy of S. depilis using a mathematical simulation and suggest that this strategy may minimize the risk of mid-air collisions at the busy hive entrance.

Furthermore, our simulations indicate that this benefit could depend on the size of the hive entrance and on traffic intensity. We thus propose that accelerated landing may be an adaptation that reduces traffic congestion in S. depilis.

(a). Scaptotrigona depilis lands at increasing speed

Our analyses show that S. depilis maintain remarkable control during their accelerated landings—aiming with precision at the small hive entrance and extending their legs before making a smooth legs-first touchdown. This accelerated landing strategy is surprising as it is generally assumed that, to ensure a smooth and safe touchdown, animals need to reduce their speed as they approach the landing surface. Indeed, most animals studied to date show that this is exactly what they do [5,6,8–11,13], with the exception of the fly Calliphora vomitoria, which accelerates when landing upside down on a ceiling [23]. Landings without deceleration on vertical surfaces have, to our knowledge, only been reported in two cases. Shackleton [24] recorded accelerated landings in the stingless bee Partamona helleri but, unlike the finely controlled touchdowns of S. depilis recorded here, these flights systematically ended with the bees crashing into the target. In another study, Shen & Sun [14] reported accelerated landings in Drosophila melanogaster, although their findings contradict those of a former study by van Breugel & Dickinson [9] who observed decelerated landings in this species. Shen & Sun [14] suggest that differences in the diameter of the landing target—which was at least seven times narrower in their experiment—explain the discrepancy between the two studies [9]. Together with our finding that S. depilis performs accelerated landings on its narrow hive entrance, the potential effect of landing target size on Drosophila's landing behaviour provides some indication that the size of the landing target may influence landing kinematics and suggests that this parameter should be considered in future studies of landing behaviour.

Interestingly, van Breugel & Dickinson [9] observed that, when Drosophila failed to reduce their approach speed during landing, they crashed into the target. In S. depilis, increasing acceleration also appears to decrease the bees' ability to aim precisely at the centre of the hive entrance. Although some level of imprecision might help to avoid congestion by distributing landing locations across the available space at the hive entrance, poor precision could lead to failed landings when the bees miss the hive entrance. For accelerated landings to be beneficial, individuals may thus have to adjust their level of acceleration in order to trade-off accuracy and collision-avoidance, particularly when traffic flow is high. If and how they do this remains unclear.

(b). Accelerated landing could provide a collective benefit by minimizing traffic congestion

Our simulation of bee traffic suggests that accelerated landing reduces the risk of aerial collisions in comparison to constant speed landing. This is most likely because accelerated landing reduces the density of bees in the vicinity of the hive (electronic supplementary material, figure S9) where most collisions occur (electronic supplementary material, figure S3) because they spend less time landing (electronic supplementary material, figure S8). This means that the landing behaviour of individuals may confer a benefit to the colony as a whole. Such phenomena are common in social insects whose colonies are often the result of self-organization [25], with simple interactions between individuals leading to complex collective behaviours. Accelerated landings in S. depilis could help to prevent traffic congestion at the hive entrance by limiting the number of individuals that fail landing and have to make a new attempt, thus enabling a high traffic intensity. Indeed, aerial collisions seem very rare in S. depilis colonies under ecologically relevant conditions, with only two cases being recorded during our experiment.

(c). Minimizing traffic congestion could favour foraging and defensiveness

Guaranteeing fluid traffic in insect societies is essential for maximizing the resources returned to the nest, which ultimately affects a colony's fitness [26]. For instance, individual behavioural strategies for minimizing traffic congestion have been described in several ant species. When traffic increases to a critical level, ants use priority rules that separate foraging trails [27,28] or that start new trails to alleviate traffic on the original route [29]. Accelerated landings in S. depilis may similarly increase foraging efficiency by ensuring a fluid traffic flow. Another non-exclusive and equally valid hypothesis is that accelerated landings may also be beneficial against predators and robbers, which probably place a strong selection pressure on the behaviour of stingless bees [30]. Fewer bees flying at or near the hive entrance may reduce the likelihood of attracting predators or robbers, as well as facilitate the work of guards that inspect incoming foragers before they fly into the hive [31]. Finally, for bee species with narrow nest entrances that force them to approach one at a time, landing bees are isolated and thus possibly more vulnerable to predators. Accelerating during approach may make it more difficult for visually guided predators to track and catch them. This is consistent with the observation that the presence of a predator at the hive entrance of Partamona helleri may stimulate their accelerated crash-landing behaviour [24].

(d). Why did this strategy evolve in S. depilis?

According to our model, the benefit of accelerated landings for mitigating mid-air collisions, and thus possibly for maintaining foraging efficiency and nest defensiveness is high only within a given range of high incoming traffic intensity and small hive entrance. To summarize this, we can define the ratio R of incoming traffic intensity over relative size of the hive entrance (the area of the hive entrance normalized by the area of the bee head) in the different stingless bee species where these parameters have been measured. A small R means a reduced benefit of accelerated landings. Interestingly, R was highest in S. depilis (R = 3.2 bees min⁻¹) when compared to three related species of Scaptotrigona (R = [1.0, 1.5, 1.6] bees min⁻¹) [19], and even more extreme when compared to the mean value recorded in 22 other stingless bee species (R = 0.8 ± 0.7 bees min⁻¹) [19]. In honeybees, which perform decelerated landings, R is probably even smaller despite their high traffic intensity because they tend to alight on a large area around their nest entrance, and this would be especially extreme in open nests. Accelerated landing in S. depilis may have emerged as an adaptation to particularly intense foraging traffic through a very small nest entrance.

Traffic fluidity may not be the only or even necessarily the main driver of S. depilis' unusual landing behaviour. Couvillon et al. [19] showed that, along with foraging traffic intensity, security is included in a trade-off that determines the size of the species-specific hive entrance constructed by stingless bees. Scaptotrigona sp. are highly defensive with more than six guards usually being present at the small, circular hive entrance. They also have several protective strategies including harassment of intruders, recruitment of new defenders using alarm pheromones, and suicidal biting [19,32], which probably reflects a high pressure from robbers and/or predators, such as spiders that ambush bees at the hive entrance [24]. Accelerated landings, with minimal time spent in front of the nest entrance, may thus also be a way to escape predation.

(e). Other possible explanations for accelerated landing

Instead of being an active strategy, as we propose here, accelerated landing may potentially be a passive phenomenon that emerges from individual interactions between bees. Indeed, the typical deceleration followed by an acceleration of S. depilis resembles a ‘stop and go wave' as referred in engineering studies of traffic [33]. We argue however that the behaviour of S. depilis is very unlikely to be such an emerging phenomenon. First, a traffic intensity of approximately one incoming bee per second is most likely too low to generate stop and go waves, especially when compared with the density of vehicles commonly observed in car traffic problems [34]. Moreover, the presence of bees in front of a landing individual had no notable influence on its speed (V_start, V_switch, V_end) or D_switch (Mann–Whitney U tests, all p > 0.1)).

So far, we have focused on the benefits of accelerated landing for reducing traffic congestion, but this strategy could have other functions, and these may have been the primary drivers of this behaviour. From an aerodynamical point of view, for example, higher flight speeds may make bees less sensitive to wind turbulence [35] and could help to maintain a stable flight path towards the narrow entrance. We cannot, and do not intend to, rule out the possibility that accelerated landing is a behavioural side effect of another adaptive trait that confers a direct benefit to S. depilis. Nonetheless, this study has generated the novel suggestion that accelerated landing is maintained in S. depilis owing to the advantage it confers on traffic fluidity when the landing target is small and traffic flow is high.

5. Conclusion

Here, we show that the stingless bee S. depilis has an atypical strategy to land on the hive entrance: it accelerates before making a well-controlled touchdown on its narrow hive entrance. By reducing the risk of mid-air collisions and thus traffic congestion, this behaviour appears to improve foraging efficiency and potentially also decrease predation of these stingless bees at the nest entrance, two functions that are of high importance for the fitness of S. depilis. This would explain why accelerated landings evolved in this species but appear to be mostly absent in other animals. Further analyses are necessary to explore if such behaviour has also emerged in other stingless bee species with narrow hive entrances and high traffic. Our study thus gives an insight into how ecological factors may drive the evolution of diverse and, in this case, maybe even unexpected landing strategies. In order to fully distinguish the adaptive nature of accelerated landing from the influence of history and chance [36,37], it would be valuable in the future to evaluate the performance of experimentally manipulated landings in comparison to the original behaviour in S. depilis studied here, and to study landing in relation to traffic intensity and predation across the phylogeny of stingless bees.

Ethics

The experiments were performed in accordance with the Brazilian and Swedish guidelines for animal experiments.

Data accessibility

The files and scripts used for trajectory analysis, for traffic simulations, as well as the electronic supplementary movies M1-8 are available on Dryad Digital Repository: https://dx.doi.org/10.5061/dryad.hhmgqnkcj [38].

Authors' contributions

E.B., I.A.S. and P.T. designed the study, P.T. carried out collection and processing of behavioural data, E.B. and P.T. carried out analysis of behavioural data and mathematical simulations, E.B. and P.T. drafted the manuscript, I.A.S. and M.D. critically revised the manuscript.

Competing interests

We declare we have no competing interests.

Funding

This work was supported by the Air Force Office of Scientific Research (FA8655-12-1-2136), the Swedish Research Council (2014-4762), the Lund University Natural Sciences Faculty, Interreg (project LU-011) and the Conselho Nacional de Desenvolvimento Científico e Technológico (309216-2016-8).