Follow the flower: approach-flight behaviour of bumblebees landing on a moving target Open Access

Foraging pollinators, like honeybees and bumblebees, have to land on flowers many times per day. For example, bumblebees can land on more than one thousand flowers per hour during a foraging trip (Heinrich, 1979). Since they have to make many landings per day, foraging efficiency will be improved if a bee lands swiftly and successfully in one try. Yet, while landing, bees often need to deal with environmental challenges. Windy conditions can, for example, cause both regular and unpredictable flower movements. Here, we determined how flower movement affects the landing performance of bumblebees, and how bumblebees use their visual–motor control system to land on a moving flower. Studying these aspects of the landing behaviour of bees will provide a better understanding of the way bees land on flowers in nature.

To make a successful landing on a moving flower, two flight characteristics are important. Firstly, the bees have to end their landing manoeuvre at the position of the flower. To do this, they need to aim towards the flower during landing. Secondly, bees need to securely grip the flower when they touch it during landing (Alcorn et al., 2012). When the difference between the velocity of the bee and the velocity of the flower is high during landing, the forces on the legs of the bee may become too high for the bee to be able to hold on to the flower. To prevent this, we expect bees will align their movement velocity with the movement velocity of the flower during landing. For example, when landing on a stationary flower, the bee will decrease both its sideways and its perpendicular approach speed towards zero before landing (Goyal et al., 2021, 2023). And when landing on a flower that is moving sideways, we expect the bee to decrease its approach speed towards zero and match its sideways movement to that of the flower.

As in most insects, bees presumably do not see depth while approaching a flower (Lehrer, 1996). To estimate their flight speed and their distance to objects in their environment, bees use optic flow and optic expansion information (Baird et al., 2010, 2013; Egelhaaf, 2023; Goyal et al., 2021; Lehrer, 1996). The optic flow is the speed at which an object or the surroundings move within the visual field of view, while the optic expansion is the rate at which an object gets larger in the visual field of view, for example while approaching it. Honeybees and bumblebees use the global optic flow of their surrounding environment to control their flight speed (Baird et al., 2005, 2010; Linander et al., 2015). Nearby walls or objects have a higher translational optic flow than objects that are further away. Bees use this information to decrease their flight speed when flying close to a wall, or in a cluttered environment. Honeybees and bumblebees use a similar technique to slow down when landing on a vertical platform like a flower, but in this case, they use the optic expansion of the flower (Baird et al., 2013; Goyal et al., 2021, 2022, 2023, 2024). Since the optic expansion of a flower scales with the ratio of approach speed and distance, bees automatically slow down when keeping a constant optic expansion during their approach. The approach dynamics of bees have been found to be slightly more complicated than just keeping a constant optic expansion. Depending only on this strategy while landing can lead to instability close to the landing target (De Croon, 2016). During their approach of a landing target, bees usually change the setpoint of the optic expansion a few times, to land faster than with a fixed setpoint (Goyal et al., 2021, 2022, 2023, 2024). Additionally, the optic expansion of the bees depends on the visual conditions, such as light intensity and the visual pattern of the landing target, during their approach (Goyal et al., 2021). In lower light intensity levels, bees keep on average, a lower optic expansion.

Several studies investigated the landing dynamics of bees on stationary landing targets (Baird et al., 2013, 2015; Chang et al., 2016; De Vries et al., 2020; Evangelista et al., 2010; Goyal et al., 2021, 2022, 2023; Lehrer and Srinivasan, 1993; Reber et al., 2016a,b). So far, these studies mainly looked into the longitudinal movements of the bees: the movement in the direction of the landing target. While approaching a landing target, bees usually first slow down by alternating deceleration phases with acceleration phases. During the deceleration phases, the bees keep a constant optic expansion (Baird et al., 2013; Goyal et al., 2021, 2022, 2023). When getting closer to the landing target, bees often show one or multiple hovering phases. During a hovering phase, the bee drastically decreases its speed, and for about 50–120 ms, flies at a very low speed in front of the landing target. This often happens around the time when the bee extends its legs. At a distance of about 8 mm (bumblebees) or 16 mm (honeybees) from a vertically oriented flower, the bee will extend its legs, to be able to land on the flower (Evangelista et al., 2010; Reber et al., 2016a). The approach dynamics of a bee flying towards a landing target can depend on the visual appearance of the landing target, its orientation, light conditions and wind conditions (Baird et al., 2013; Chang et al., 2016; Evangelista et al., 2010; Goyal et al., 2021).

These approach behaviours mainly describe the dynamics of the bee in the longitudinal direction, towards the flower. When a flower is standing still, focusing on this axis seems logical. When approaching a moving flower, however, lateral movements are as important as longitudinal movements, to both aim towards and align with the flower movement. Yet, the way bees aim towards and align with moving flowers using lateral movements is not well understood. Most studies determining the interaction between bees and moving flowers focus on aspects other than the landing dynamics (Alcorn et al., 2012; Desai et al., 2024; Hennessy et al., 2020, 2021; Mirwan and Kevan, 2015). Only Zhang et al. (1990) investigated the way honeybees track and fly towards a moving, horizontally placed, flower. To increase our understanding of how bees use their visual–motor control system to land on moving flowers, we here determined the landing dynamics of bumblebees approaching the vertically oriented surface of a moving artificial flower.

To land on a moving flower, bees need to continuously adapt their motor output in response to sensory information. We expect that this visual–motor control system consists of three modules. Firstly, bees use the visual perception of the flower position in their retinal field to steer towards the flower (Zhang et al., 1990). Secondly, they align with the sideways movements of the flower by attempting to bring the optic flow of the flower (the angular rate of change of the position of the flower) in their visual field to zero (Zhang et al., 1990). The first and second control actions enable the bees to align their sideways position and sideways velocity with that of the flower, respectively. Finally, bees keep on average the optic expansion of the approaching flower constant, which will result in a linear decrease of their approach speed and a zero approach speed at touchdown (Baird et al., 2013; Goyal et al., 2021).

To determine the effect of flower movement on the landing performance and landing dynamics of bumblebees, we here conducted standardized bumblebee landing experiments with an artificial flower moving at different frequencies. We predicted that flower movement would affect the landing performance and dynamics of bumblebees. To successfully land on a moving flower, we expected bees would need to aim towards it, align with its movement and slow down while approaching it. We expected them to do this by responding to the position of the flower in their field of view, and to the optic flow and the optic expansion of the retinal image of the flower. Aiming and aligning to a moving flower is likely more complicated than aiming and aligning to a stationary flower. Therefore, we expected a reduced landing performance in moving flower conditions, for example a lower landing success, a lower landing accuracy or a lower approach speed by the bumblebees. To test these predictions, we built an experimental setup containing a sideways moving artificial flower. In this setup, we trained Bombus terrestris bumblebees to land on the flower and filmed the landing manoeuvres. We determined the effect of flower movement on the landing performance of the bees, and we determined how visual input affected the motor output of the bees during the landing manoeuvres.

We used two hives of Bombus terrestris (Linnaeus 1758) bumblebees for the experiments, provided by Koppert Biological Systems (Berkel en Rodenrijs, The Netherlands). The colonies consisted of 20–50 female bumblebees at arrival and grew during the experiments. The bees had access to a 50% sugar water food source, which was used to train them. Additionally, ∼10 g pollen was fed to the bumblebees twice a day inside their hive. While in The Netherlands no licence is required when studying insects, we took care to design the experimental setup and methods in a way to minimize harm to the bumblebees.

The experimental setup consisted of a 1 m³ flight area, a hive and a feeding compartment with a moving artificial flower (Fig. 1A–D, Table S1). The hive was connected to the flight box by a tunnel with a one-way door that was closed outside experiment times. Inside the flight box, the wall opposite of the hive contained a built-in controllable moving artificial flower (Fig. 1C,D). The flower moved at 50 cm height through a horizontal gap in the back wall. Brushes were attached on both sides of the gap over the full length of the wooden wall, to prevent the bumblebees from entering the back compartment via this gap. The flower moved over a distance of 10 cm back and forth in between the brushes. Inside the back compartment, the bumblebees could forage from a sugar water food source (Fig. 1D). They could get back into the flight box via two one-way trapdoors, which they could not use to enter the back compartment. The artificial flower was designed to mimic a real flower (Fig. 1C). It was a round 7.2 cm diameter platform, of which the front was covered with a 7.2 cm diameter white paper. A black 3.0 cm diameter middle part was printed on this paper, and it contained a 1.0 cm hole in the middle. The black-white contrast of the flower stimulated both their chromatic system processing colour information, and their achromatic system processing contrast and motion information (Dyer et al., 2011; Hempel De Ibarra et al., 2015).

One of the side walls and the top wall of the flight box were transparent (clear PMMA, 8 mm thick), so that we could film the bumblebees from the side and from above (Fig. 1B). The opposite side wall, the bottom of the setup, and the wall to which the hive was connected, were white (foamed PVC). The two side walls were resting on 11-cm-high, 100-cm-long transparent panels (clear PMMA, 25 mm thick). These were included to make sure the bees did not escape the setup when a side wall was being removed. The wall to which the hive was connected included four 8-cm-diameter ventilation holes, covered with a fine mesh. The wall containing the moving artificial flower was made of a wooden panel with a black cover (foamed PVC). It was black to decrease the amount of visual information behind the flower, and to provide maximum contrast with the white flower.

Visible light was provided by two 60×60 cm white light LED panels (LedVance PanelLED, 40 W, 4000 K, 3600 lm, 30–42 V dc, 1000 mA) that were attached to the ceiling. The LED panels were used at their maximum light intensity level. During the experiments, the irradiance at 50 cm height in the middle of the flight box was 3.72 W m⁻², as measured by a spectroradiometer (JETI specbos 1211). This was equivalent to 1246 lx. Directly in front of the artificial flower, the measured irradiance was 3.65 W m⁻², which was equivalent to 1228 lx. In addition, the light intensity and temperature in the room were logged every 15 min using an Adafruit TSL 2591 Lux sensor, and a DHT22 sensor, respectively.

Bumblebees were filmed and tracked in real-time with a stereo-camera system, using four Basler acA2000-165umNIR cameras (2048×1088 pixels, enhanced sensor sensitivity in NIR range, binning 2×2, frame rate 90 frames s⁻¹, exposure time 1 ms) with 12 mm lenses (Fujinon HF12XA lenses, f ∼5.6). Two were filming from above the setup, while the other two were filming from the side. The cameras were positioned in a way to cover a large volume of interest, while focusing on the area in front of the moving flower (Fig. S1). Two IR light LED panels (Bosch SuperLED, 850 nm, 10 deg angle, SLED10-8BD) were used to provide light for the camera setup. For a uniform illumination, plastic diffuser sheet (PMMA, 3 mm thick, matt finish, 78% transmission) was placed in front of the IR lights. Infrared pass filters (Hoya R-72, cut-on wavelength 720 nm) were used to filter out the visible light. Up to 20 bumblebees flying inside the setup could automatically be tracked in real-time in 3D with the software Flydra (Straw et al., 2011). When a bumblebee flew into a designated cube (10×10×10 cm), 3 cm offset from the centre position of a still standing flower, this triggered a fifth camera (Basler acA2000-165umNIR with 35–70 mm Nikkor AF lens and infrared pass filter Hoya IR80N cut-on wavelength 800 nm). This fifth camera recorded a close-up view of the bumblebee landings (Fig. 1E). The landings were filmed at 50 frames s⁻¹, recordings contained 200 frames before and 175 frames after the trigger. As the maximum movement frequency of the flower was 0.65 Hz, this frame rate provided us with at least 77 images per flower movement. The recordings of this camera were used in the analysis.

The artificial flower was connected to a cart riding on an aluminium profile (Fig. 1D). The cart was moved by a NEMA23 stepper motor (ACT 23HS8430 1.8 deg 3.0 A) with a 60-tooth timing belt pulley and a 6-mm-wide GT2 timing belt. The stepper motor was powered by a TMC2209 driver, moving in SilentMode at a resolution of 1/8 step. A 24 V, 6.5 A power supply (TDK Lambda LS150-24) provided power to the driver. The driver was controlled by an Arduino microcontroller (Arduino Due, Arduino), which calculated the sinuous movement patterns of the flower and timed the drive steps. During the experiments, we used five different flower movement patterns, which contained four sinusoidal movements moving at four different frequencies and one treatment in which the flower remained stationary in the middle, as a control. For the four sinusoidal movements, the amplitude of the sine function was 5 cm for each of the movements. The four movement frequencies were 0.03 Hz, 0.24 Hz, 0.53 Hz and 0.65 Hz (Fig. 1F). This resulted in maximum flower sideways speeds of 0.9, 7.5, 16.8 and 20.4 cm s⁻¹, and maximum flower sideways accelerations of 0.2, 10, 39 and 50 cm s⁻², respectively. The frequency range we used (0–0.65 Hz) falls within the range of frequencies flowers move at, as the majority (94%) of flower movements investigated in a study focusing on moth–flower interaction was at frequencies between 0.1 and 1.7 Hz, for the largest part below 0.65 Hz (fig. 3C in Sponberg et al., 2015). The flower position was calibrated by reaching an end-stop on one side of the track. At the start of each new treatment, the position of the flower was recalibrated by moving until the end stop was switched on, and then moving to the start position. A temperature sensor (DS18B20) was attached to stop the motor if it should overheat.

The timing of the different setup components was coordinated using ROS (Robotic Operating System, version Kinetic Kame). Additional specifications of the materials used are given in Table S1.

Experiments with the first hive were done between 31 January and 15 February, 2022, while experiments with the second hive were done between 28 March and 29 April, 2022. During the experiments, we tracked and filmed the landings of bumblebees on our artificial flower. This flower either oscillated sideways or stood stationary (control). Experiments ran between 09:00 and 17:00 h. Every 30 min, the flower stood still for 10 min and moved for 20 min, with movement patterns changing every 5 min. The order of the flower movement frequencies during each movement period was randomized with a few limitations to the randomization schedule. During these periods, three different movement frequencies were always used. One randomly determined movement frequency was used twice during the 20 min, but it was never used during two consecutive time periods. Within these limitations, the order of the movement frequencies within the 20 min was randomized (Fig. 1G). The short time span of 5 min was to prevent the bumblebees from getting used to a flower movement frequency. Owing to technical limitations of the moving artificial flower, we were not able to use the 0.65 Hz frequency treatment as often as the other movement frequencies. At this frequency, the mechanical system would sometimes get stuck because the cart drifted, preventing the flower from continuing its movement. Therefore, we were constrained to fewer data points for this frequency.

Before running the experiments, we had trained the bumblebees to land on the moving flower during a training period. The specific appearance of the flower was to make it easier to train the bumblebees to land on the flower, by making it look similar to flowers in nature (Hempel De Ibarra and Vorobyev, 2009; Fig. 1C). The bees were trained to land on our artificial flower and crawl through the middle of the flower to enter the back compartment behind the flight box (Fig. 1A). There, sugar water was provided. They could get back into the flight box via two one-way doors. The training of a bumblebee hive was done by luring the bumblebees slowly toward the flower using a sugar water food source (Fig. 1B). The first step was to entice the bumblebees to go out of the hive by placing a training food source directly in front of the hive entrance inside the flight box. After the bumblebees started foraging there, every few days this food source was moved about 10 cm, to slowly train the bumblebees to fly towards the flower. The next step was to remove the training food source from the flight box, to force the bumblebees to go into the back compartment for foraging. When the bumblebees had learned this, the last step was to let the flower move and start the experimental phase. This was the first time the bees were subjected to flower movement; flower movement was not part of the training phase. The process of training the bumblebees in this way took ∼8 weeks for the first hive, and 5 weeks for the second hive.

We determined the location of the bumblebee and flower in the horizontal plane by tracking the close-up videos using DeepLabCut version 2.3.0 (Mathis et al., 2018; Nath et al., 2019). We tracked the position of the head, tail, and two sides of the bumblebee (Fig. 1E). The head was defined as the most anterior part of the body and the tail as the most posterior part of the body. The sides tracked at the lateral part of the body were black transitioned into yellow. We would have preferred to track the locations where the wings are attached to the body, but this was insufficiently visible on the videos (Fig. 1E). In addition, the two sides of the flower were tracked. We first manually tracked frames to create a sample on which to train the algorithm. The training sample consisted of 340 frames selected by DeepLabCut (17 videos, 20 frames per video). Then, we trained a ResNet-50-based neural network (He et al., 2016; Insafutdinov et al., 2016) for 500,000 training iterations using 95% of the training sample. We used default parameters. Evaluation of the network provided a test error of 5.3 pixels (0.72 mm) and a train error of 4.18 pixels (0.56 mm) (image size 2048×1088 pixels). This was 8–11% of the body width of the bees, as the average body width was 6.8 mm and the average body length was 15.9 mm. Finally, using this trained neural network, we automatically tracked the videos we had made with the close-up camera during the experiments. This gave us the x- and y-positions of the two sides of the flower and of the head, tail and sides of the bumblebees over time, and a P-value for reliability per data point. We filtered for position data with P<0.05. Fig. 1E shows the x- and y-axis as used during the analyses. Movies 1 and 2 are examples of movies in which the neural network automatically tracked the bumblebee and the flower.

We analysed the data using MATLAB version 2021b (The MathWorks Inc.). Scripts that were developed for the data analyses can be obtained by contacting the authors. x- and y-coordinates in pixels were converted to coordinates in cm by using the size of the flower as a reference distance. Sometimes, the neural network tracked a wrong position, for example when a second bumblebee was present in the video. To remove outlier points from the tracks, we filtered the data in two ways. Firstly, we applied a backward difference scheme to the position data and removed data points that had a speed above 200 cm s⁻¹. Secondly, we checked per frame how close together the four points of the bumblebee were, by calculating the standard deviation of the locations of the four points for each frame. When the standard deviation of the four points was higher than 2 cm, we removed the point furthest away from the middle of the four points. We did this procedure three times to remove additional points if needed. However, during the third round we removed both remaining points if the standard deviation was still too high.

After filtering the data this way, we applied a Kalman smoother on the position data of both the bumblebee and the flower, to get slightly smoothed position data (Fig. S2), and the velocities and the accelerations over time. The filter also interpolated missing data points. However, in a follow-up step, we made sure tracks did not contain more than three consecutive missing values estimated by the filter. We used slightly different settings in the Kalman smoother for the four bumblebee points compared with the two flower points. For both the flower and bumblebee points, we set the measurement–noise covariance matrix to identity and the cross product of the error covariance matrices to zero. For the bumblebee points, we set values in the processing noise matrix related to position, velocity and acceleration to 10, 5 and 1, respectively. For the flower points, these values were set to 1, 0.1 and 0.001.

After applying the Kalman smoother on the data, we performed several additional filter steps. We selected the tracks in which a bumblebee lands on the flower, and we extracted the landing manoeuvre part of these tracks from start to touchdown. We applied these steps independently for the head, tail, middle (average between head and tail position) and two sides of the bumblebee. However, we used the location of the middle of the bumblebee during most of the analyses. Only when determining the viewing direction of the bee, the head and tail position were also used. To extract the landing manoeuvre part of the tracks, we first determined the moment of touchdown (t_touchdown) for each track, if present. The moment of touchdown was defined as the first frame of the track that met the requirements we set, and of which two out of the three following frames also met these requirements. To define the requirements, we determined the moment of touchdown visually on some of the videos and checked the position and velocity at this time. This led us to the following requirements. (1) The distance between the middle of the bee and the middle of the flower in the y-axis had to be between −0.1 cm and 1.0 cm, and the distance between the middle of the bee and the middle of the flower in the x-axis between −3.6 cm and 3.6 cm (width of flower). (2) The velocity in the y-direction had to be below 3 cm s⁻¹, and the absolute velocity in the x-direction relative to the velocity of the flower had to be below 4 cm s⁻¹.

Secondly, we determined the start frames of the landing trajectories. The start frame was defined as the first frame in which the bumblebee was flying with a positive y-velocity, and a y-position closer than 5 cm from the video frame edge opposite the flower. We then removed all data points before the starting frame of the track and all data points after the moment of touchdown, to get the landing trajectories from start to touchdown. The landing tracks could include temporary negative y-velocities if a bee temporarily moved backwards during its approach.

Next, we performed a few more filter steps. We removed landing tracks outside experiment times and tracks made when the light intensity was incorrect or uncertain from the dataset. Also, we removed data points with an x- or y-velocity above 200 cm s⁻¹. Finally, we visually inspected all tracks by plotting the x- against y-coordinates, to check for abnormalities in the tracks. For tracks that showed an abnormal behaviour, such as a very quick turn or a large jump, we checked the video images. Based on the videos, we decided whether we needed to remove the track, or part of it. Often the cause for abnormal behaviour in the plots was the presence of a second bumblebee in the video. Tracks where the tracking algorithm switched between bumblebees were removed from the dataset.

After having the bumblebee tracks from start to touchdown, the flower tracks of the left, right and middle of the flower were extracted. The flower tracks were extracted from 50 frames before the start of the bumblebee track, until the moment of touchdown. The bumblebee and flower tracks were then aligned with the moment of touchdown at t=0. We set the [0,0] coordinate at the average position of the middle of the flower when the flower was standing still. This gave us the positions and velocities of the bee in the world-reference frame relative to the average position of a stationary flower: x^w, y^w, v_x^w and v_y^w (Fig. 1E; see ‘List of symbols and abbreviations’). In the rest of this study, we will refer to v^w as the ground velocity of the bees. We determined the position of the bee in the flower reference frame by taking the bee's position relative to the position of the moving flower (x^f and y^f; Fig. 1E). We determined the velocity of the bee in the flower reference frame by taking the bee's velocity relative to the velocity of the moving flower (v_x^f and v_y^f). Using Pythagoras' theorem, we determined the horizontal component of the flight speed of the bee in both the world and flower reference frames (V^w and V^f, respectively).

To estimate the landing performance of the bumblebees, we calculated parameters related to the landing success, duration and accuracy of the bumblebees. Then, we tested our expectation that bumblebees gradually slow down while approaching the flower, aim towards the middle and align with its movement to successfully land. To investigate how bumblebees use their visual–motor control system to do this, we next looked into the related visual information parameters.

The landing performance metrics were used to quantify the landing success, landing duration, and accuracy. We estimated the landing success percentage (S_landing) per flower movement frequency as the number of video clips containing a bumblebee performing a touchdown on the flower (see criteria 1 and 2 from ‘Pre-processing of videography data’), divided by the number of videos containing a flying bumblebee. The landing accuracy of the bees was estimated by determining how close to the middle of the flower the bees landed, on the x-axis. To determine this distance between the bee and the middle of the flower at the moment of touchdown (d_touchdown), x^f was taken at the moment of touchdown (t_touchdown). Landing duration of a bee, Δt_landing, was calculated as the duration of the period starting when a bee was at 10 cm from the middle of the flower (t_D10) (in the horizontal plane), ending at touchdown (t_touchdown).

We determined how well the bees aimed to the moving flower by comparing the distance between the bee and the middle of the flower at the moment of touchdown (d_touchdown) for the different flower movement conditions. In addition, we compared the x-position of the bees in the world reference frame (x^w) with their x-position in the flower reference frame (x^f). Next, we determined how well the bees aligned with the flower movement. Aligning with the movement direction of the flower means the bees and flower have a similar x-velocity. To test whether this was the case, we compared the ground x-velocity of the bees (v_x^w) with their x-velocity relative to the moving flower (v_x^f) in both stationary and moving flower conditions. Average absolute x-velocity in the world-reference frame (⁠⁠) was calculated per bee by first taking the absolute values of v_x^w, and then taking the mean of |v_x|^w during Δt_landing. Average absolute x-velocity in the flower-reference frame (⁠⁠) was calculated per bee by first taking the absolute values of v_x^f, and then taking the mean of |v_x|^f during Δt_landing. Then, we determined the deceleration of the bees towards the flower in different conditions by comparing their y-velocity (v_y) in stationary conditions with v_y in moving flower conditions. Average y-velocity (⁠⁠) was calculated per bee by taking the mean of v_y during Δt_landing.

To provide additional information on the flight kinematics of the bees, we also investigated the total flight speed of the bees (V) in the horizontal plane, and the flight heading of the bees (β), defined as the angular flight direction of the bees relative to the direction of the flower (Fig. 5H). Average flight speed during Δt_landing (⁠⁠) was calculated per bee by taking the mean of all flight speeds (V) during Δt_landing. The flight heading β was calculated as the angle between the velocity vector of the bee and the position vector between the middle of the bee and the middle of the flower (Fig. 5H). The average flight heading was calculated during the period between t_D10 and t_D2, giving. The moment when the bee was closer than 2 cm from the flower for the first time is t_D2.

To investigate how bees use their visual–motor control system to aim and align to the flower and slow down, we estimated three visual information parameters: the viewing angle of the flower (α), the optic flow (OF) and the optic expansion (OE). To calculate these variables, we needed to transform our parameters expressed in the Cartesian coordinate system to a polar coordinate system. By converting x^f, y^f, v_x^f and v_y^f to polar coordinates, we could estimate the straight-line distance between the bee and the flower (d), the ground velocity of the bee towards the flower (U^w), and the velocity of the bee towards the flower relative to the velocity of the flower (U^f). Using these parameters, we determined α in the visual field of the bee, OF and OE. We assumed the viewing direction of the bees was in the direction of the longitudinal axis over the body (extended line through tail and head of bee). The resolution of the videos was not high enough to take head movements into account.

We did the statistical analyses in R version 4.2.1 (r-project.org). By automizing the experiments, we expected we would gather a large enough dataset to ensure adequate statistical power to detect relevant statistical differences. The effect of flower movement frequency on landing success (S_landing) was tested with a generalized linear model using a binomial distribution and a logit link, using the glm function. Subsequently, we did a pairwise post hoc Tukey test to check which treatment groups differed from each other.

We tested the effect of flower movement frequency on other variables using linear regression models, using the function lm. We tested the effect of flower movement on two more performance variables: distance between the bee and the middle of the flower at the moment of touchdown (d_touchdown) and landing duration (Δt_landing). Then, we tested the effect of flower movement on average flight speed (⁠⁠). To investigate the way bees aim towards a flower, align with its movement and slow down while approaching it, other variables related to velocity were tested: ⁠, ⁠, and ⁠. Finally, we looked at the effect of flower movement on two variables related to the visual input the bees experienced: average flower viewing angle (⁠⁠), and average optic flow (⁠⁠).

After running each model, we checked if the residuals behaved randomly and if they were normally distributed. When necessary, we applied a log, a double log, a square root, or a double square root transformation on the data. We included hive number, number of days since the experiment started, and their interaction as additional fixed factors in the starting models. We used backward selection to determine the final models; however, flower movement frequency was always included as this was the variable of interest. The interaction between hive number and number of days since the experiment started was never significant, and therefore excluded from all models. In the model that tested the effect of flower movement frequency on landing location, both hive number and number of days since the experiment started were included in the final model, because they both showed a significant effect. In the model testing the effect of flower movement frequency on optic flow, hive number was included in the final model. In all other models, neither hive number nor number of days since the experiment started were included in the final model, because they were both not significant. We obtained the predicted values by back transforming the predicted values we got from the models. If a model showed a significant effect of flower movement frequency, we did a pairwise post hoc Tukey test to check which treatment groups differed from each other.

During the experiments, we recorded 1760 videos of flying bumblebees during 29 different days, of which 1080 contained a bee that landed on the flower following our criteria. From these data, we determined the landing success per treatment. The landing success percentage during the different flower movement frequencies was 69% (f₀=0 Hz), 65% (f₁=0.03 Hz), 67% (f₂=0.24 Hz), 64% (f₃=0.53) and 47% (f₄=0.65 Hz). Flower frequency had a significant effect on landing success (P<0.001, Chi square deviance=−21.68, d.f.=4,1660). The landing success was significantly lower during the highest frequency (f₄) than during the other movement frequencies (Table S2).

We continued analysing the successful landings, which constituted, after filtering, 728 landing manoeuvres (n_f0=294, n_f1=174, n_f2=125, n_f3=113, n_f4=22). Of these 728 videos, 137 were recorded during the experiments with hive 1, and 591 with hive 2. Fig. 2 gives an overview of these filtered trajectories of landing bumblebees for the different flower frequencies, both in the world reference frame and the flower reference frame. A difference in approach caused by the movement of the flower can be observed when comparing Fig. 2A with Fig. 2B–E. When approaching y=0, the x-positions of the bees covered a larger range when the flower was moving. Additionally, the landing locations of the bees were spread over the total movement range of the flower. However, when the trajectories are placed in the flower reference frame, this difference in approach between bees flying towards a stationary flower and bees flying to a moving flower, is no longer apparent (Fig. 2F–J).

The distance between the bee and the flower decreased in a similar way in the different flower movement treatments during the approach of the bees (Fig. 3A). At touchdown, it was on average ∼1.3 cm. This distance at touchdown was partly caused by the y-distance between the middle of the bee and the middle of the flower at touchdown (Fig. 2) and partly by the x-distance caused by inaccuracy of the bees (Figs 2, 3C). Landing accuracy of the bees (d_touchdown) did not significantly reduce with increasing flower frequency (P=0.28, F=1.26, d.f.=6,721, Table 1, Fig. 3C). The bumblebees landed very close to the middle of the flower (d_touchdown) in all five treatments, with predictions of the linear model below 4 mm for each treatment. The bees did improve their landing accuracy over time, as the number of days since the start of the experiments had a significant effect on the accuracy of the bees (P=0.0085, F=6.96, d.f.=6,721). In addition, flower frequency did not significantly affect landing duration Δt_landing (P=0.85, F=0.34, d.f.=4,723, Table 1, Fig. 3D). The landing duration from 10 cm distance from the flower until touchdown was on average between 0.6 and 0.65 s.

During their approach, the bees reduced their flight speed (Fig. 4A). Just before touchdown, their flight speed in the horizontal plane was on average between 5 cm s⁻¹ (f₀=0 Hz) and 16 cm s⁻¹ (f₄=0.65 Hz). Flower frequency had a significant effect on the average flight speed (⁠⁠) of the bumblebees (P<0.0001, F=19.3, d.f.=4,723; Table 1, Fig. 4A,E). On average, the bees had a higher flight speed (⁠⁠) when approaching a flower moving at 0.53 Hz or 0.65 Hz (Table S2). The predicted average flight speed increased from 17.5 cm s⁻¹ (f₀) to 23.0 cm s⁻¹ (f₄) with increasing flower frequency (Table 1).

To understand why the average flight speed was affected by flower movement frequency, we decomposed flight speed into sideways ground velocity (|v_x|^w), parallel to the flower movement and approach velocity (v_y), perpendicular to the flower movement. The bees decreased their approach velocity in a similar way for the different flower frequencies (Fig. 4B); no significant effect on average approach velocity was found (P=0.56, F=0.72, d.f.=4,723; Table 1, Fig. 4F). The increase in flight speed with increasing flower frequency was caused by an increased sideways ground velocity, especially when getting closer to the moment of touchdown (P<0.0001, F=53.22, d.f.=4,723; Table 1, Table S2, Fig. 4C,G). The predicted average sideways ground velocity (⁠⁠) increased from 8.5 cm s⁻¹ (f₀) to 15.6 cm s⁻¹ (f₄) with increasing flower frequency. This seemed to be caused by bumblebees compensating for the flower movement: when we determined the bumblebee sideways velocity relative to the sideways velocity of the flower (|v_x|^f), flower frequency had no effect on (P=0.58, F=0.72, d.f.=4,723; Table 1, Fig. 4D,H). The predicted sideways velocity relative to the sideways velocity of the flower remained between 8.5 cm s⁻¹ (f₀) and 9.2 cm s⁻¹ (f₃). So, the sideways velocity of the bees matched the sideways velocity of the flower in our study. Our results show that during their approach of a moving flower, the bumblebees increased their sideways ground velocity (parallel to the flower movement) to match the sideways ground velocity of the flower. By doing this, they kept their sideways velocity relative to the velocity of the flower constant while the flower frequency increased. Meanwhile, they did not change their approach velocity.

As the increased flight speed at faster flower movements was caused by an increased sideways ground velocity of the bees, this effect should also be visible in the flight heading of the bees. The absolute flight heading |β| of the bees deviated on average 31 deg (f₀) to 50 deg (f₃) from heading towards the middle of the flower (Table 1, Fig. 5G). The angle remained almost constant while the bees approached a stationary flower (Fig. 5A, Fig. S3A). However, for flowers moving at 0.53–0.65 Hz (f₃, f₄), the flight heading angle increased while the bees approached the flower (Fig. 5D–F, Fig. S3A). This increase could also, to a lesser extent, be observed for flowers moving at 0.24 Hz (Fig. 5C,F, Fig. S3A). Flower movement frequency significantly affected the average absolute flight heading of the bees (P<0.0001, F=13.33, d.f.=4,723; Table 1, Table S2, Fig. 5G).

To be able to land on a moving flower, bees need to use visual information to aim towards it, align with its movement and slow down while approaching it. We expected the bees to aim towards the flower by minimizing the flower viewing angle (α), or in other words, keeping their viewing direction towards the flower. The absolute flower viewing angle (|α|), tells how much the viewing direction of the bumblebees deviated from the direction of the flower. On average, |α| remained rather constant while the bees approached the flower and also when the flower was moving (Fig. 6A–F, Fig. S3B). So, the bees kept aligning their body in the direction of the flower during their approach of a moving flower. They did this so well that we found no significant effect of flower frequency on (P=0.21, F=1.48, d.f.=4,723; Table 1, Fig. 6G). The predicted values for stayed between 12.1 deg (f₁) and 14.3 deg (f₄) for the different flower frequencies (Table 1). The predicted average flower viewing angle was 18 to 35 deg lower than the predicted average flight heading angle of the bees, so the bees aligned their body more towards the flower than towards their flight direction (Table 1, Figs 5G, 6G).

Secondly, we expected the bees would use the optic flow of the flower (OF) to align to the movement of the flower (Fig. 7H). During the first part of the bumblebees' approach, the optic flow stayed rather constant (Fig. 7A–F, Fig. S3C). After the bees were closer than 4 cm from the flower (Fig. 7F), or the retinal size of the flower became larger than 35 deg (Fig. S3C), the optic flow increased more quickly with decreasing distance. The average optic flow (⁠⁠) was similar for flower frequencies of 0, 0.03 and 0.24 Hz (Fig. 7G). It seemed to be slightly higher at 0.53 Hz, and the highest at 0.65 Hz, especially near the flower. The predicted values of the average optic flow ranged from 93 deg s⁻¹ (f₀) to 117 deg s⁻¹ (f₄). However, no significant effect of flower frequency on average optic flow was found (P=0.13, F=1.78, d.f.=5,722; Table 1).

Finally, we expected the bees would use the optic expansion of the flower (OE) to slow down while approaching the moving flower (Baird et al., 2013; Goyal et al., 2021). We estimated the average optic expansion by taking the slope between the relative velocity of the bees towards the flower (U^f), and their distance from the flower (d). While approaching the flower, the bumblebees decreased U^f in a similar way over the distance for the different flower frequencies (Fig. 8A–F, Fig. S3D). The average lines mostly overlap (Fig. 8F, Fig. S3D). Only at 0.65 Hz was the velocity of the bees towards the flower a bit higher when the bees were at a distance of 10 cm from the flower. Because of this, the slope of U^f/d is steeper at 0.65 Hz, indicating a higher optic expansion for the bees when the flower was moving at 0.65 Hz (Fig. 8G). This could, however, also have been caused by the lower number of data points we collected at this flower frequency.

Here, we determined the landing performance and approach behaviour of bumblebees landing on a moving artificial flower. The bumblebees performed well over the range of flower movement frequencies we tested. The percentage landing success decreased significantly only at a frequency of 0.65 Hz (amplitude of 5 cm) and landing accuracy and landing duration remained constant (Fig. 3). A reason for the drop in landing success at the highest frequency could be that the bees managed to find enough grip to the flower less often. Another explanation could be that the bees may have been deterred by the quicker movement of the mechanical flower at this frequency, and therefore more often cancelled their landing attempt prematurely.

To successfully land on the moving flower, we expected the bees would need to aim towards the middle of the flower, and bring their flight velocity relative to the velocity of the moving flower towards zero. Our results show this was indeed the case. The bumblebees aimed towards the middle of the flower regardless the frequency of the flower. Also, they reduced their approach speed towards zero while flying towards the flower and aligned their sideways movement with the sideways movement of the flower. We hypothesized bees use three behavioural modules to be able to land on a moving target, responding to: (1) the viewing angle of the target, (2) its optic flow and (3) its optic expansion. We found support for this in our results.

The bees landed on average at a distance of less than 4 mm from the middle of the flower, for all flower movement frequencies, which is between the sides of the 5 mm radius hole in the middle of the 36 mm radius flower (Fig. 3C). Various factors could have affected the bees landing near the middle of the flower. Firstly, we had provided the bees with a clear motivation to land in the flower centre, as the tunnel towards the food source was in the middle. The data suggest that the bees aimed specifically for the bottom edge of the hole in the flower, presumably to achieve a secure grip. Observations of the video data showed the bees often attached with their front legs to the edge of the hole in the flower during touchdown. This was likely easier than attaching to the paper surface of the flower. As bees have been found to prefer flowers that provide a better grip when the flowers are moving (Alcorn et al., 2012), it is likely they also aim for the part of the flower that provides most grip. Furthermore, we expect that bees are also naturally inclined to land on the middle of flowers. The design of the flower, with the outer ring simulating the flower petals, could have directed the bees towards the middle of the flower (Hempel De Ibarra et al., 2015). As almost all landing locations were within the 15 mm radius black inner ring of the flower (Figs 2, 3C), the bees may have been aiming for this ring. The bees improved their landing accuracy over the course of the experiment, suggesting a possible learning effect. Muijres et al. (2020) also observed a learning effect over time in the landing performance of honeybees. While we expected the bees would have to decrease their landing accuracy with increasing flower frequency, the bees kept up their landing accuracy well. Additionally, the bees followed the position of the moving flower while approaching it. When taking the position of the bee relative to the position of the flower (x^f), the approach tracks towards a moving flower (Fig. 2G–J) are very similar to the approach tracks towards a stationary flower (Fig. 2F).

We expected the bumblebees to aim towards the moving flower by keeping it in the middle of their field of view. Blowflies, houseflies and honeybees also have been found to use this so-called smooth pursuit strategy for aiming towards a moving target (Boeddeker et al., 2003; Land and Collett, 1974; Zhang et al., 1990). The smooth pursuit strategy is the simplest pursuit strategy (Pal, 2015). Our results suggest bumblebees also aim to keep the moving flower in the middle of their view while approaching it. Firstly, we found only a small increase in flower viewing angle during the approach of the bees (Fig. 6A–F, Fig. S3B). When the bees did not actively orient their viewing direction towards the flower, this angle would have increased proportionally to the decrease in distance. Secondly, we found no significant effect of flower movement frequency on the flower viewing angle; the predicted values for the angles were lower than 15 deg in all conditions (Table 1). This suggests the bees align their body and viewing direction towards the direction of the flower while it is moving. And thirdly, the predicted flight heading angle was a lot larger than the flower viewing angle and increased with flower frequency, whereas flower viewing angle did not (Table 1). This indicates that the bees align their body and viewing direction more towards the flower direction than with their flight heading. So, our results support our expectation that bumblebees, like honeybees, aim to keep the flower viewing angle at zero while approaching a moving flower. This suggests that bumblebees may use a smooth pursuit strategy like honeybees do. However, further testing of other pursuit strategies is needed to identify the strategy bumblebees use while tracking a moving target.

Since honeybees have been observed to follow the movement of the flower in their approach of a horizontally placed moving artificial flower (Zhang et al., 1990), we expected the bumblebees in our study to also track the flower movement. Indeed, the bees aligned very well to the flower movement in all frequencies (Fig. 4C,D). We expected to see a decline in the ability of the bees to track the sideways movement of the flower with increasing flower frequency, because of the delay in their motor response to visual information. This delay is likely to be between 20 and 80 ms (Zhang et al., 1990). However, we did not find a decline in their ability to track the flower movement for higher movement frequencies. When looking at the sideways flight speed relative to the flower, the relative speeds of the bees were indistinguishable from the sideways flight speed in all flower frequencies when approaching a stationary flower (Fig. 4D,H). So, at the frequency range we used, bumblebees seemed well able to follow the sideways movement of the flower. The increasingly higher flight heading for increasing flower frequencies (Fig. 5G) can also be explained by the bees not only aiming towards the position of the flower, but also following its sideways movement.

Bumblebees have been found to use optic flow and optic expansion cues to adjust their flight speed and position in response to their environment (Baird et al., 2010, 2013, 2021; Dyhr and Higgins, 2010; Linander et al., 2016). Therefore, we expected they would also use the optic flow cues of the moving flower to enable them to land on it. Several insect species have been found to keep the optic flow, also called angular velocity, at zero while pursuing a target (Boeddeker et al., 2003; Land and Collett, 1974; Pal, 2015). As honeybees show this behaviour as well (Zhang et al., 1990), we expected the bumblebees to also aim to keep the optic flow at zero during their approach. Our results supported this expectation. Firstly, we found an approximately constant optic flow at a distance between ∼10 and 4 cm from the flower, when the retinal size of the flower was smaller than 35 deg (Fig. 7A–F, Fig. S3C). Because the optic flow of a target will naturally increase while approaching the target without compensating for the movement of the target, the constant optic flow in this range suggests the bees indeed aimed to maintain a low optic flow. Secondly, we found no significant effect of flower movement frequency on the optic flow, so the bees kept a low optic flow even if the flower was moving rapidly (Table 1, Fig. 7G). This likely means the bees responded to the optic flow of the flower and actively compensated for it.

The bees reduced their velocity during their approach of the artificial flower in our study. Their approach velocity just before touchdown was on average around 4 cm s⁻¹ (Fig. 4B), which is similar to other studies (Chang et al., 2016; De Vries et al., 2020; Reber et al., 2016a). We expected the bees to decrease their approach velocity with increasing flower frequency. We expected this because bumblebees decrease their flight speed or approach speed towards a target in other challenging conditions, such as a low light intensity level (Goyal et al., 2021; Reber et al., 2015), although some studies found no effect of light conditions on approach flight speed (De Vries et al., 2020; Reber et al., 2016b). However, the bees in our study slowed down in a similar way for all flower movement frequencies; they did not land more slowly at higher flower frequencies. This could mean the bees were not challenged enough in our study. Another explanation could be that the decreased approach velocity at low light intensity levels is a direct response to the slowing down of the visual system (Reber et al., 2015), instead of a response to challenging conditions.

Previous studies showed that bees use the optic expansion of the landing target to slow down while approaching the target (Baird et al., 2013; Goyal et al., 2021, 2022, 2023). They can adapt their setpoint of the optic expansion when faced with challenging conditions, such as a low light intensity. They keep a lower optic expansion, probably to land more carefully (Goyal et al., 2021). Here, we compared the average optic expansion of bumblebees approaching stationary and moving flowers. We expected to find a lower average optic expansion in moving flower conditions, since landing on a moving flower is more challenging than landing on a stationary flower. However, except for the fastest flower movement, the slopes between velocity to the flower and distance to the flower remained similar (Fig. 8G). In line with our observation that bees do not decrease their approach speed while landing on a moving landing target, they also did not decrease their average optic expansion while approaching a moving flower. In contrast to our expectation, the bees even seemed to have a slightly higher optic expansion when flying towards the fastest flower movement of 0.65 Hz. This was caused by a relatively high velocity towards the flower between 8 and 10 cm from the flower (Fig. 8F). A possible explanation could be that at this movement frequency, the bees needed a high approach speed to respond faster to the moving flower. Another explanation could be that bumblebees may track fast moving flowers more easily than slow or stationary flowers, allowing the bees to keep a high optic expansion. A high optic flow possibly improves detection (Desai et al., 2024).

As all bumblebees of a hive were allowed to enter the experimental setup freely for foraging, their behaviour was possibly influenced by other bees present in the experimental setup. Our methods did not allow us to distinguish between individual bumblebees. Therefore, multiple approach flights from the same bee are likely included in the dataset. Additionally, owing to technical limitations, our highest movement frequency group (f₄) contained a very small sample size (n=22) compared with the sample size (n=294) when the flower was stationary (f₀). A larger sample size for this group might have reduced the effect of single outliers, possibly allowing us to detect additional significant effects. Limitations in the frame rate and resolution of the videos prevented us from detecting subtle or high frequency movements of the bees. We could, for example, not take head movements into account when determining the viewing direction of the bees. Furthermore, in our analyses, we focused on the average approach behaviour of the bumblebees. Analyses of individual flight tracks would make it possible to investigate the delay between the movement of the bee and the flower, to analyse which pursuit strategy bumblebees use or investigate whether oscillations occur close to the flower, as De Croon (2016) suggests.

An important study limitation was the range of movements the artificial flower could make. The frequency range we used was within the range of movement frequencies of flowers in nature (Sponberg et al., 2015). However, it may not have challenged the bumblebees, as honeybees have been found to forage from flowers moving at frequencies up to 1.83 Hz (Hennessy et al., 2020). Additionally, the maximum acceleration of the flower (0.5 m s⁻²) was much lower than the maximum lateral accelerations of bumblebees (4 m s⁻²) when they avoid obstacles (Crall et al., 2015). Another factor limiting the scope of this study is the predictability of the flower's movement pattern. Its sinuous movement probably made it easier for the bees to land on the flower. Although we changed the frequency of the artificial flower every 5 min, in natural conditions, flowers will also move unpredictably in the short term. In follow-up research, it would be interesting to determine how bees deal with unpredictable flower movements and to increase the range of frequencies of the moving flower. As flowers in nature move in all directions, it would also be interesting to determine the effect of other movement directions. For example, by letting the flower move both side-ways, and back and forth. This will create a more complicated combination of optic flow and optic expansion cues.

Our results show that bees indeed aim towards the middle of the flower and align with its movement speed and direction to successfully land. In flower movement frequencies up to 0.53 Hz, bumblebees can successfully aim towards a flower and align with its movement without a negative effect on their landing performance. Our results support our expectation that bumblebees use their visual–motor control system to do this: they aim towards a flower by keeping it in the middle of their field of view, align with its movement by minimizing the optic flow and slow down by keeping on average a constant optic expansion. With these findings, we contribute to better understanding the challenges of flying pollinators when flowers move in the wind.

We thank the following people for their useful contributions. Simon Sponberg contributed to the research design, and gave valuable feedback at various points of the research process. Andrew Straw and Antoine Cribellier developed the tracking system, and Pulkit Goyal optimized it for tracking bumblebees. Leonardo Honfi Camilo and Camille le Roy helped with the installation, application and use of DeepLabCut. Mark de Vries contributed to the development of the moving artificial flower setup. Laurens Berends, Pien van der Poll, Steffie van der Peet, Nadine Staal and Niels Gobel contributed to the experimental work. Remco Huvermann of Koppert Biological Systems provided the bumblebee colonies used during the experiments.