Transmission of bee-like vibrations in buzz-pollinated plants with different stamen architectures

In buzz-pollinated plants, bees apply thoracic vibrations to the flower, causing pollen release from anthers, often through apical pores. Bees grasp one or more anthers with their mandibles, and vibrations are transmitted to this focal anther(s), adjacent anthers, and the whole flower. Pollen release depends on anther vibration, and thus it should be affected by vibration transmission through flowers with distinct morphologies, as found among buzz-pollinated taxa. We compare vibration transmission between focal and non-focal anthers in four species with contrasting stamen architectures: Cyclamen persicum, Exacum affine, Solanum dulcamara and S. houstonii. We used a mechanical transducer to apply bee-like vibrations to focal anthers, measuring the vibration frequency and displacement amplitude at focal and non-focal anther tips simultaneously using high-speed video analysis (6000 frames per second). In flowers in which anthers are tightly arranged (C. persicum and S. dulcamara), vibrations in focal and non-focal anthers are indistinguishable in both frequency and displacement amplitude. In contrast, flowers with loosely arranged anthers (E. affine) including those with differentiated stamens (heterantherous S. houstonii), show the same frequency but higher displacement amplitude in non-focal anthers compared to focal anthers. We suggest that stamen architecture modulates vibration transmission, potentially affecting pollen release and bee behaviour.

Overall, in this experiment, we used 18 flowers, 9 of each species. In the second experiment we generated signals as above with constant relative amplitude (0 dB) but with different individual frequencies (150, 200, 250, 300, 350, 400, 450, and 500 Hz). The frequency values we used reflect the range of frequencies recorded from bees vibrating on buzz-pollinated flowers 19,20,42 . For each frequency, we conducted 3-4 playback replicates for each of the four species studied, depending on flower availability. Overall, in this experiment, we used 104 flowers, 26 of each of the four species. We played back each vibration signal using a Zoom H2 audio recorder (Zoom Corporation; Tokyo, Japan) connected to a vibration speaker (Adin S8BT 26 W). The output volume of the Zoom H2 and vibration speaker was kept constant, except as noted in the "Results" section. The vibration speaker was modified as described in Brito et al. 43 to transduce the vibrations to the flower by fixing a metal rod to the vibrating plate of the speaker and attaching a pair of very fine tipped forceps (Fine Science Tools, Dumont #5 Biology Tip Inox Forceps) to the end of the rod. The forceps were used to hold 1-2 anthers (the short anthers in the case of Solanum houstonii) (see Fig. 1A for setup). Individual flowers were placed in floral water tubes, with the stamen's long axis parallel to the ground, i.e., flowers were kept horizontal to the ground as they would be perceived by a pollinator directly approaching the centre of the flower. The movement of the forceps was thus perpendicular to the anthers. The forceps were clamped at approximately the same position (1/4 of the anther length from the connection with the filament) on the anthers for each trial. In trials on C. persicum, one petal was cut away to allow visualisation of the anthers. A fresh flower was used for each replicate such that each flower was vibrated only once and we collected data sequentially for each amplitude level or frequency before moving to the next set of replicates to control for effects of time of day on vibration characteristics.
High speed digital imaging. To analyse the vibration of different parts of the flower simultaneously, we used high-speed digital imaging, which allowed us to simultaneously track the movement of captured objects along two dimensions at different locations of the image frame. We recorded the vibrating flowers at 6000 frames per second (fps; 1280 × 512 pixels) against a black background using a FASTCAM SA-8 camera (Photron, San  www.nature.com/scientificreports/ Diego, California USA) and halogen bulbs for illumination. Recording started before the vibration playback began and captured the whole 1 s vibration. An entomological pin (size 1) was kept in shot for videos, to enable size calibration and consistency in video tracking output across different videos (Fig. 1).

Digitising video files and time-series analysis. All video footage was analysed in two dimensions
using the DLTdv7 digitising tool 44 in MATLAB 9.6 (R2019a; MathWorks Inc). Recordings were 730 ms long on average. This digitising tool allows point tracking in high-speed video footage 45 , and we used it to generate a time series of x-y coordinates for each tracked point. For each video, we simultaneously tracked three points through time to extract vibrational information measured as displacement: (1) The tip of the forceps, hereafter control. This allowed us to empirically obtain frequency and displacement amplitude of the input vibrations transduced to the flowers, and to account for variation in volume playback introduced during the experiment. (2) The tip of the anther held by the forceps, hereafter the focal anther.
(3) The tip of the anther furthest away from the focal anther, hereafter the non-focal anther. In a few cases, it was not possible to track all three points for each sample due to obstruction of the control point by other parts of the flower or due to low light. All three points were reliably tracked in 87 out of 122 samples. The x-y time series data was analysed using the seewave package 46 in R ver. 4.0.2 (R Core Development Team, 2020). Displacement values (calibrated to mm, using the insect pin described previously as a reference for size) were calculated for x-and y-axes, by zero-centring the data. These x-y displacements were used to obtain an overall measure of displacement magnitude defined as (x-displacement 2 + y-displacement 2 ) 1/2 . We used a high pass filter of 80 Hz using the fir function (Hanning window, window length = 512 samples). For each digitised recording, a section of 100 ms in the middle of each time series was selected, where the vibration was more stable (approximately from 0.3 to 0.4 s for every sample). Twelve digitised samples which were too short were removed from the dataset, leaving 75 samples remaining as the final total sample size. From these 100 ms sections (sampled at 44,100 samples per second), we computed the frequency spectra using the function spec (using power spectral density) and calculated the dominant frequency using the function fpeaks (nmax = 1). We also estimated peak displacement amplitude (D P ), peak-to-peak displacement (D P-P ), and Root Mean Squared displacement (D RMS ) using the functions max (on absolute values), max -min, and rms, respectively. These are commonly used parameters describing vibration properties in buzz pollination (Vallejo-Marín 2019). For example, the dominant frequency is the frequency of the sinusoidal component with the highest relative amplitude, while D RMS reflects the overall energy content of a vibration (Sueur 2018).

Statistical analysis.
We evaluated the correlation between the different measurements of displacement amplitude (D P , D P-P , D RMS ), and between displacement in the x-, y-axis and v-vector using Pearson moment correlations. We assessed the association between the characteristics of the input vibrations applied by the forceps (dominant frequency and D RMS ) and those measured at the anther tips using linear models fitted with the function lm. In these models, vibration dominant frequency or D RMS were used as the response variable, and input vibration (at the forceps tip), anther type (non-focal and focal anthers) and species as the explanatory variables. For each model, diagnostics were produced using the package DHARMa 47 . For those which showed significant outliers, models were re-created without these data points. The statistical significance of effects remained similar and therefore we kept the full data set for the final analysis. Statistical significance of the main effects and their interactions were assessed using Type III sums of squares using the package car 48 . Model predictions were plotted using plot_model (type = pred) in the package sjPlot 49 . All statistical analysis was performed in R 4.0.2 (R Core Development Team 2020).
Ethics. All plant collection and material used in this study adheres to current state and federal US legislation.

Results
Frequency of anther vibrations. The dominant frequencies measured in the x-and y-axis were highly correlated across all samples. (Pearson's correlation r: 0.98, df: 266, p < 0.001) ( Fig. 2A). Dominant frequency across anthers and plant species ranged from 150 to 529 Hz (Fig. S3). Forceps dominant frequency was the only significant predictor of anther dominant frequency in our linear model (p < 0.001, Table 1A) and we found no effect of either anther type or plant species (i.e., anther arrangement) on the dominant frequency of vibrations measured at the tips of anthers (p > 0.05, Table 1A). In other words, the dominant frequency did not change as vibrations were transmitted through the flowers from the forceps. The overall frequency spectra were also similar between species and anther types, with very few harmonics in any of the vibrations (Fig. 3).
Amplitude of anther vibrations. All three measures of displacement amplitude differed slightly between the x-and y-axis across all samples, including in the forceps ( Table 2). The average amplitude was higher in the y-axis, particularly in D P and D P-P (Table 2). Axes were nonetheless strongly correlated for all measures of amplitude: D P (r: 0.81, df: 266, p < 0.001); D P-P (r: 0.82, df: 266, p < 0.001); D RMS (r: 0.79, df: 266, p < 0.001) (Fig. 2B for D RMS correlations). Therefore, we used the vector magnitude (see "Materials and methods" section for details) for downstream analysis on amplitude, to capture variation in displacement in both x and y axes.
We extracted three measures of displacement amplitude: D P, D P-P, and D RMS . D P across anther types and species ranged from 16.4 µm to 1030 µm (mean 195), D P-P ranges from 39.3 to 1840 µm (mean 353), D RMS ranged from 6.94 to 363 µm (mean 77.8). The highest displacements for all measures were from vibrations in the non-focal anther of S. houstonii (heterantherous and loosely arranged stamens), and the lowest were from the non-focal anther of C. persicum (stamens fused in a cone). All three measures of displacements were strongly correlated www.nature.com/scientificreports/ across all trials: D P and D P-P (r: 1, df: 179, p < 0.001); D P and D RMS (r: 0.98, df: 179, p < 0.001); D P-P and D RMS (r: 0.99, df: 179, p < 0.001). D RMS was used for all further amplitude analysis. We found a significant interaction between anther type and input D RMS (measured at the forceps) on anther displacement (vector D RMS ), with displacement in non-focal anthers generally increasing more rapidly with input amplitude than in focal anthers (Table 1B, Fig. 4). We also found a significant interaction effect between anther type and plant species on the displacement amplitude (vector D RMS ) of vibrations (p < 0.001, Table 1B, Fig. 4), with higher displacements in the non-focal anthers of E. affine (coefficient = 42.87) and S. houstonii (coefficient = 46.11) (both species have loosely arranged stamens), compared to focal anthers of C. persicum, which has a fused stamen cone (Table 1B, Fig. 4). Separate analyses of the x-and y-axes both showed significant interactions between anther type and plant species (p < 0.005) (Figs. S5, S6, Tables S1, S2). When we calculated the disparity in D RMS (vector) between the forceps and the anther, the mean difference across both anther types in C. persicum and S. dulcamara (both with fused stamen cones) was close to zero (Table 3). In contrast, the mean differences (disparity in D RMS between the forceps and anther) for the non-focal anthers of E. affine and S. houstonii were 36.6 µm and 55.1 µm respectively, and for the focal anther of S. houstonii it was 13.8 µm (Table 3).

Discussion
Our study suggests that the arrangement of poricidal anthers affects the transmission of vibrations between anthers. We found that vibrations are transmitted similarly, in both frequency and amplitude, across focal and non-focal anthers in species with stamens partially or totally fused to form a cone (S. dulcamara and C. persicum).
In contrast, species in which individual stamens can move freely (E. affine and S. houstonii) showed identical frequency but higher vibration amplitudes at the tip of non-focal anthers compared to the focal anthers where vibrations were applied. Overall, the highest displacements occurred in the long anthers of the heterantherous S. houstonii. Our work shows that floral architecture, including the functional fusion of stamens into an anther cone, affects the transmission of vibrations applied to a subset of anthers. Because buzz-pollinating bees often grasp with their mandibles and contact with their thorax or abdomen only one or few anthers during buzz pollination, and because pollen release is a function of vibration amplitude, our results suggest that stamen architecture is an important determinant of the functional consequences of the applied vibrations.
The dominant frequency of artificial vibrations did not change as they were transmitted through flowers, regardless of flower type or vibration characteristics. This result aligns with Brito et al. 43 who also found that artificial vibration dominant frequency is conserved throughout the heterantherous flowers of S. rostratum Dunal, both at anther tips and petals. Although some plant substrates such as stems can act as frequency filters 4 , differentially attenuating vibrations components depending on their frequency, frequency is not altered over the short distances involved in vibration transmission during buzz-pollination interactions 20 . Although the natural frequency of anthers is affected by their morphology and organisation within the flower 31 , the frequency of vibrations has limited effects on pollen release in buzz-pollinated flowers, suggesting that resonance plays a minor role within the range of frequencies produced by most bees (100 to 400 Hz) 17,20,31 .
In contrast, we found that the amplitudes of artificial vibrations were differentially altered as they travelled through the two types of buzz-pollinated flowers. In the flowers with more loosely arranged androecia, E. affine and S. houstonii, vibrations at the tip of the non-focal anther had generally higher displacement amplitude, i.e. moved further, than those observed in the tip of anthers being vibrated. This effect was strongest in the heterantherous S. houstonii where, in some cases, displacement was doubled between input and the longer, non-focal pollinating anther. In S. rostratum, velocity amplitude from the vibration source to the anther tips of  Table 2. Summary statistics across all samples of three measures of displacement amplitude (µm) of both focal and non-focal anthers combined. The axis of measurement indicates whether the displacement was measured in the x-axis, the y-axes, or the resulting vector calculated from the combined x-y displacement (see "Materials and methods" section). D P peak displacement amplitude, D P-P peak-to-peak displacement amplitude, D RMS root mean square displacement amplitude. www.nature.com/scientificreports/ both feeding and pollinating anthers increases up to four-fold when vibrations were applied at the base of the flower 43 . Stamens can be thought of as a complex cantilever beam, a structure with one fixed end and one free end 50 . Vibration displacement amplitude at the tip of the stamen should be partly a function of the stamen's length, second moment of area, Young's modulus of elasticity, and mass 51 . Based on cantilever theory, we expect longer stamens to show generally higher displacements at the tip than shorter stamens. Stamen length differences may help explain the difference in vibration amplitude between the short anthers of E. affine and the long pollinating anthers of S. houstonii. However, stamen material properties, morphology and architecture are likely to affect important parameters determining their vibrational properties, including their second moment of area and Young's modulus (stiffness) 51 , and predictions based on length alone might not capture the behaviour of real stamens 51 . Previous empirical work shows that amplitude has a significant, positive effect on pollen release 10,16,18 , with increased anther acceleration causing pollen grains to gain in energy and escape through the pores at a higher rate 52 . Clearly more work in this area is needed, including both empirical and modelling studies of the vibrational properties of stamens incorporating the complexity of the forms and material properties of stamens. Unlike the heterogenous vibration amplitude observed between focal and non-focal anthers of species with loosely held stamens, species in which anthers are held together forming tight, connivent, anther cones (C. persicum and S. dulcamara) showed vibrations of the same, uniform amplitude between focal and non-focal anthers. The functionally cohesive androecium in these species appears to homogeneously transmit vibrations across the anther cone. The uniformity of the amplitude and frequency of vibrations across all anthers of species with fully or partly fused (connate or connivent) anther cones might have implications for patterns of pollen  Table 3. Difference in displacement amplitude in µm (Anther D RMS -Forceps D RMS ) between forceps and anther for each anther type and species across samples. Values for the vector are calculated from the x-and y-axes (see "Materials and methods" section for details). N number of flowers. www.nature.com/scientificreports/ release during buzz pollination. Species with connivent anther cones may show a more uniform rate of pollen release from each anther when vibrated, compared to the more heterogenous range of vibrations experienced by individual anthers of species in which anthers move more freely. Anther cones have evolved in a variety of taxa with buzz-pollinated flowers including species in the families Ericaceae, Gesneriaceae, Melastomataceae, Primulaceae, Rubiaceae, and Solanaceae 10,24,36,53 , providing excellent opportunities to compare the functional significance of convergent floral morphologies. The same putative uniform pollen release may also occur when non-poricidal anthers are enclosed in a corolla and flowers are buzz-pollinated, as seen in some Pedicularis species 11,54 . Our study did not investigate pollen release patterns in different types of flowers and further work quantifying vibratory pollen release in flowers with disparate morphologies across taxonomic groups could help establish the functional consequences, if any, of different androecium architectures. We suggest that the differences in vibration transmission we see in this study are largely due to differences in stamen architecture in our chosen flower types. However, other morphological differences between the four species are also likely to be important in determining vibration transmission. Studies on other types of insect vibrations have shown that flexible plant stems attenuate vibrations more than stiff stems, as do thick leaves compared with thin leaves 4,5 . In buzz-pollinated flowers, traits affecting vibration properties might include anther curvature (e.g. S. houstonii), stamen stiffness and length 31 . Similarly, the size of the anther locules (where the pollen is located before release) and thickness of the anther walls may affect vibration transmission. Few studies have examined the effect of specific morphological traits on vibration transmission in buzz-pollinated flowers, but closely-related species of Solanum with similar morphologies can differ in their vibration transmission properties 35 . Moreover, partial removal of stamen structures, such as the connective appendages in Huberia bradeana (Melastomataceae), can affect the relative amplitude of vibrations 55 . Although the species studied here differed in anther architecture and the transmission of vibrations through the androecium, all of them have stamens positioned relatively closely together, more or less forming a cone. Other buzz-pollinated species can have stamens more widely separated and not forming a cone, such as those found in several species of Melastomataceae 56 . Given the wide range of morphologies of buzz pollinated flowers 6,20,57 , we expect that a greater difference in vibration transmission could be found in species with more disparate morphologies than those studied here.

Species
We hypothesise that differences in the transmission of vibrations observed here among species with "tight cone" vs. "loose cone" stamen architectures have functional implications for the interaction with buzz pollinators and for patterns of pollen release. If stamen architecture type affects vibration transmission and pollen release patterns, bee pollinators may display different behavioural strategies to buzz these different flowers and maximize pollen removal, for example, by changing the manipulation of anthers during visitation. For instance, we predict that bees on flowers with loose anther arrangements might learn to simultaneously manipulate and buzz multiple anthers if this resulted in more efficient vibration transmission and thus a higher rate of pollen collection 58 . In contrast, bees visiting flowers with anthers that form a tight cone may be able to extract pollen from all anthers regardless of which and how many anthers are manipulated.
From the plant perspective, the uniform vs. heterogenous transmission of vibrations from focal to non-focal anthers in species with cone vs. loose stamens could also have fitness consequences. On the one hand, efficient transmission of vibrations from focal to non-focal anthers could increase pollen deposited on pollinators during single visits, potentially increasing pollen export to other flowers. On the other hand, although not observed here, vibration damping from focal to non-focal anthers could limit the amount of pollen removed from the flower during single visits and increase the release of pollen over multiple visits (pollen dispensing) 18 . The fitness consequences of these patterns of pollen release may also depend on the relative size of the interacting flower and pollinator. Bees that are small relative to the flower are often unable to buzz all anthers at once. To the extent that the visitor is too small to be a legitimate pollinator 59 , reducing pollen release in non-focal anthers (for example by limiting the vibration amplitude of non-focal anthers) may limit pollen loss during visitation by floral larcenists. Both the different stamen arrangements in cone vs. loose stamens and the associated changes in floral handling by visiting pollinators might also influence the precision of pollen placement on bees' bodies 24 , the placement of pollen of "safe sites", and thus the efficiency of pollen transfer to stigmas 28,60 . Further studies of how vibrations are applied to flowers with different stamen architectures and their effect on pollen release, including their placement on pollinators' bodies, in both laboratory and field settings, will help ascertain the functional consequences of the enormous morphological diversity observed in buzz-pollinated flowers.