Biomechanical properties of non-flight vibrations produced by bees Free

Vibrations are key components of the behavioural repertoire of bees and have a fundamental effect on their survival and interactions with other organisms. Bees produce vibrations when powering wingbeat during flight, during intra-specific communication, to ward-off potential predators (defence vibrations) and during pollen collection in certain types of flowers (Buchmann, 1985; Conrad and Ayasse, 2015; De Luca and Vallejo-Marin, 2013; Larsen et al., 1986). However, the biomechanical properties of these vibrations have been poorly studied beyond the context of flight (Dudley, 2000) and only in a few bee taxa (e.g. Arroyo-Correa et al., 2019; Conrad and Ayasse, 2015; Hrncir et al., 2008; Jankauski et al., 2022; King et al., 1996; King and Lengoc, 1993). Given the enormous taxonomic diversity of bees (20,000 species; Almeida et al., 2023), and wide-ranging ecological, functional, morphological and size diversity (Danforth et al., 2019), establishing how variation in bee form permits and constrains the types of vibrations they produce is an important biological question.

Both flight and non-flight vibrations are produced by rapid contraction of the indirect flight muscles that occupy most of the thorax capsule of bees and flies (Dickinson and Tu, 1997; Snodgrass, 1935, 1942; Vallejo-Marin, 2022). In non-flight vibrations, although the thorax vibrates rapidly, the wings remain mostly undeployed. A type of thoracic vibration that appears to be common in bees and some flies, such as hoverflies (Syrphidae), is elicited when an individual is captured or manipulated, presumably as a mechanism to deter or startle potential predators (Moore and Hassall, 2016). This type of vibration is often referred to as defence, annoyance or alarm vibration (De Luca et al., 2014; Hrncir et al., 2008). In larger insects, defence vibrations have a clearly audible component and can be perceived as high-pitched buzzes. In bumblebees, the entire nest engages in ‘hissing’ when disturbed, and this aposematic signal can deter potential predators such as mice (Kirchner and Röschard, 1999). The biomechanical characteristics of non-flight vibrations have been studied very little (e.g. Hrncir et al., 2005; Jankauski et al., 2022; King and Buchmann, 1996; King and Lengoc, 1993; Pritchard and Vallejo-Marin, 2020), but it is likely that these depend on both physiological and morphological characteristics of the insects that produce them.

In the present study, we conducted a survey of non-flight, defence vibrations by bees sampled in the field across three continents (North America, Europe and Australia) to characterise the biomechanical properties of these vibrations in bees with diverse sizes and morphologies. We focused on defence vibrations because they can be induced experimentally and provide a common currency to compare among taxa. However, it is important to keep in mind that different types of non-flight vibrations (defence, mating, pollination) probably differ in their mechanical properties, despite sharing a common form of production (Vallejo-Marin, 2022; Vallejo-Marin and Russell, 2024). In one of the few studies where different non-flight vibrations have been directly compared, Pritchard and Vallejo-Marin (2020) found that defence vibrations have a lower amplitude and frequency than floral vibrations in Bombus terrestris. Thus, defence vibrations could serve as a conservative estimate of non-flight pollination vibrations.

Here, we specifically addressed the question of how variation in thorax size affects the acceleration amplitude, duration and frequency of defence buzzes. We evaluated three hypotheses. (1) Vibration amplitude and thorax size. Assuming that thorax size reflects the cross-sectional area of indirect flight muscles (Clemente and Dick, 2023), and if muscle strain is scale invariant, the displacement amplitude of defence vibrations should scale with thorax size. Furthermore, if the frequency of defence vibrations is relatively scale invariant (which appears to be the case for pollination buzzes; De Luca et al., 2019; Vallejo-Marin, 2022), then we expect that acceleration amplitude should likewise increase with thorax size. (2) Buzz duration and thorax size. We hypothesise that the duration of defence buzzes should be positively related to thorax size as larger bees have a lower mass-specific metabolism and presumably can continue buzzing for longer than smaller bees, all else being equal. While empirical measurement of the duration of pollination buzzes in bumblebees suggests that larger individuals produce shorter buzzes (Barbosa et al., 2023; De Luca et al., 2014), this does not necessarily imply that larger bees are incapable of producing longer buzzes, and instead could simply reflect that a larger bee can extract more pollen with a short buzz than can a smaller bee. In fact, larger bees may be able to buzz longer than smaller bees, as they have a lower mass-specific metabolic rate than smaller bees (Darveau et al., 2005), and longer buzzes may be advantageous when used in a defence context. Thus, the relationship between bee size and buzz duration may be contingent on the behavioural context in which they are deployed. (3) Vibration frequency and thorax size. While studies of wingbeat frequency show that, across species, there is a negative relationship between body size (e.g. mass) and wingbeat frequency (Dudley, 2000), analyses of non-flight buzzes produced during buzz pollination (i.e. the pollination of flowers by bees using substrate-borne vibrations) suggest no relationship between bee size, measured as inter-tegular distance, and buzz frequency (De Luca et al., 2014, 2019). It has been suggested that maximising buzz frequency (to the physiological maximum) during pollination might be advantageous because this would increase the vibration's velocity amplitude for a given maximum displacement that the bee can achieve, and therefore dislodge pollen from anthers at higher rates (Vallejo-Marin, 2022). The functional consequences of buzz frequency on other non-flight vibrations in bees, such as defence buzzes, is unknown. We hypothesise that to the extent that defence buzzes resemble pollination buzzes, any variation in the vibration frequency of defence buzzes should be independent of thorax size. Our overarching goal in this study is to contribute to characterising the properties of non-flight vibrations across a wide sample of bee species.

We conducted two new field expeditions to sample bee vibrations, one to western Mexico (Jalisco and Colima states; 20 May–5 June 2022) and one to Australia (Western Australia and Queensland; 10 September–3 October 2022). In addition, we use an identical experimental procedure to re-analyse raw vibration data from bees that were sampled in Scotland (including the Outer Hebrides and Orkney) in May–August 2020. A subset of the Scottish vibration dataset has been previously published in a study comparing thoracic vibrations of bees and hoverflies (Vallejo-Marín and Vallejo, 2020) but here we re-analysed the whole bee dataset in order to maximise the taxonomic and geographic coverage of our study. In each of these three geographic regions, we sampled bees visiting flowers, flying or in surrounding vegetation, using insect nets. Bees were placed individually in a plastic vial and stored in a cooler with ice packs. Bees were immediately transported to a field lab for measurement, and vibration data were acquired within 10 min to 3 h after collecting the bees. In Australia, we used a camper van as a mobile lab to minimise the time between sampling and data acquisition.

In Mexico and Australia, bees were photographed with an SLR camera and a macro lens (100 mm f/2.8L, Canon, Tokyo, Japan), and the high-definition digital images were used to determine thorax width size using ImageJ (Abramoff et al., 2004). In Scotland, the thorax width was measured with digital callipers (0.01 mm precision; CD-6-CSX, Mitutoyo Inc., Kanagawa, Japan). Thorax width was measured at the widest point of the thorax from a top view, usually at the height or just above the base of the forewing (tegulae). Linear measurements of the thorax, such as inter-tegular distance, are closely associated with other estimates of body size, including fresh and dry mass (Cane, 1987; Kendall et al., 2019) (Fig. S1). For identification and sexing, voucher specimens were pinned and determined with the aid of entomological keys (G.C.V. and M.V.-M. in Scotland; R.A.B. in Mexico; and K. Prendergast and T. Houston in Australia). Voucher specimens have been deposited in the National Museum of Scotland and the Queensland Museum, Australia.

We used a miniature uniaxial piezoelectric accelerometer (0.2 g; 352C23, PCB Piezotronics, Hückelhoven, Germany) to measure vibrations produced by the bee's thorax. The accelerometer was mounted at the end of a split bamboo stick (3.7 mm diameter×200 mm length) with 30 mm of connecting electrical cable (1 mm diameter, PCB Piezotronics) between the end of the stick and the accelerometer. The stick was affixed to a plastic box through two small holes. The natural resonance of the system was empirically measured to be approximately 17 Hz (Vallejo-Marín and Vallejo, 2020). While the mass of the accelerometer is smaller than that of the largest bees measured, we note that it is much larger than that of the smallest bees. However, for defence buzzes, wing locking is expected to increase the bees' resonance frequencies by approximately an order of magnitude compared with their flapping frequencies, so we expect the defence buzzes to be well below resonance, and thus in a regime dominated by the bees' stiffness and damping, rather than inertia. In this regime, the added mass of the accelerometer would have only a small effect on the system dynamics. Future work will investigate this in more detail. To acquire the accelerometer signal, we used a C-Series Sound and Vibration module (9250; NI, Newbury, UK) on a Compact DAQ chassis (cDAQ-9171, NI) connected to a portable computer. Accelerometer data were sampled at a rate of 10,240 Hz using custom software written in LabView NXG 5.0 (NI), stored as TDMS files (high throughput data format from NI) in the computer, and then converted to tab-separated text files for downstream analysis.

Bees were cold-anaesthetised using icepacks or by briefly putting them in a −20°C freezer for 1–3 min until they became inactive. Each bee was then tethered using a nylon loop (0.18 mm diameter) placed at the end of a blunt metal syringe needle (Pritchard and Vallejo-Marin, 2020; Vallejo-Marín and Vallejo, 2020). The bee was then allowed to return to room temperature and, once it had fully recovered, we pressed the dorsal surface of the thorax gently but firmly against the accelerometer so that the dorso-ventral axis of the thorax was aligned to the axis of vibration measurement of the accelerometer. This method induced most bees to produce defence vibrations (see Results). Note that failure to elicit a defence buzz in our experiment should not be taken as evidence that an individual or species is incapable of producing defence vibrations in a different situation. We aimed to acquire vibrations for each bee for a period of at least 45 s but the duration varied among individuals.

Vibration data analyses were done in R v.4.3.1 (http://www.R-project.org/) using the packages seewave (Sueur, 2018) and tuneR (https://CRAN.R-project.org/package=tuneR). To analyse vibration data, we first applied a high-pass frequency filter (20 Hz, window length=512) to remove background noise, and removed the offset by subtracting mean amplitude from each data file. We then used an automatic algorithm (seewave:timer) to identify all individual buzzes in a file with a detection threshold of 8% and a minimum duration of 100 ms. For some bees, the minimum duration was reduced to 50–60 ms to capture very short buzzes. The values of these parameters were chosen as they allowed us to capture the range of buzzes observed across species. Oscillograms and spectrograms of all the identified buzzes were examined by eye to remove spurious identifications caused by electrical noise or by accidentally knocking the accelerometer during bee manipulation. A full list of all buzzes identified, including those removed from downstream analysis, and their start and stop times relative to the start of the recording is available from Dryad (https://doi.org/10.5061/dryad.4tmpg4fkg)

For each identified buzz, we calculated the fundamental frequency using the seewave:fund function with a window length of 512 samples, overlap of 50% and a maximum frequency of 1000 Hz, and then obtained the median frequency for each buzz (hereafter referred to as frequency). For calculating vibration amplitude, we obtained the absolute amplitude envelope of the time series with a smoothing function window of two samples and overlap of 75% (seewave:env), and then calculated both peak and root mean square (RMS) amplitude values for each buzz.

To incorporate phylogenetic relationships in our analysis, we used a genus-level phylogeny containing all the taxa studied here (see tree 1 of Hedtke et al., 2013). We chose a genus-level phylogeny as no equivalent species-level phylogeny exists for all studied species here, some of which are undescribed. Species were added to this phylogeny backbone as polytomies with a branch length of zero. We also classified genera as either buzz pollinating or non-buzz pollinating using published information (Cardinal et al., 2018) and an unpublished list of buzz-pollinating taxa (A. Russell, Missouri State University, personal communication). A genus was considered to be capable of buzz pollination if at least one species in that genus has been reported to be buzz pollinating, which is currently the best estimate that we have, as there is no species-level information on the capacity to buzz pollinate for most bees included in our study­.

We used linear mixed effects models using R v.4.3.1 (http://www.R-project.org/) to investigate the relationship between vibration properties and bee size. We ran separate models for duration, fundamental frequency and amplitude acceleration of buzzes. Thorax width was the explanatory variable and individual bee was used as a random effect. For buzz duration, we excluded buzzes shorter than 100 ms (n=81 out of 150,000 buzzes) as this was the minimum buzz duration used for most individuals and prevents false positives when running the automated classification. We used natural log transformation (ln) of duration, fundamental frequency, amplitude and thorax width to facilitate allometric comparisons across a wide range of values and improve statistical fitting. The taxonomic and phylogenetic relationships among the taxa studied here were incorporated into the statistical analysis as follows. We used a Markov Chain Monte Carlo (MCMC) sampler for generalised linear mixed models that includes correlated random effects from a phylogeny, as implemented in the package MCMCglmm (Hadfield, 2010). In this model, we included species and individual as random effects, and phylogeny as the correlated random effects (pedigree). Sex was not included in the analyses as few species had both male and female individuals sampled (see Results). We ran 23,000 MCMC iterations with 3000 discarded as burn-in and thinned every 10 iterations.

We sampled 356 bees (81% females, 19% males), 202 in Scotland, 80 in Mexico and 74 in Australia. The 356 sampled bees belonged to 70 bee taxa in six families: Andrenidae (4% individuals), Apidae (74%), Colletidae (10%), Halicitdae (8%), Megachilidae (2%) and Stenotitridae (1%) (Fig. 1). Our sample included mostly females, probably because in most species, males fly for shorter periods than females and are shorter lived. Of these sampled bees, 50 did not produce defence vibrations during our experiment (Table S1). Non-buzzing bees included Tetragonula carbonaria and Trigona fulviventris, in which no individual was observed buzzing (n>8 individuals per species), and Apis mellifera, of which only a third of the sampled individuals produced a defence buzz (4/12). A full list of buzzing and non-buzzing individuals is provided in Table S1. In total, we extracted buzz data from 306 individual bees (80% females and 20% males), in 65 taxa from six bee families (Table S1). The thorax width of buzzing bees ranged from 0.84 to 9.6 mm (mean±s.d. 4.2±1.6 mm). For bees in which both thorax width and inter-tegular distance were measured, the correlation coefficient was very high (Pearson's ρ=0.985, P<0.001; Fig. S1). Most buzzing bees were sampled in Scotland (60% of individuals), with the remaining nearly equally split between Mexico and Australia (21% versus 19%, respectively).

We recorded 15,000 individual buzzes, with an average of 49 buzzes per bee (median 35 buzzes, range 2–319). The average duration of a defence buzz was 0.76 s (range 0.05–43 s, median 0.29 s), and the average fundamental frequency was 205 Hz (range 40–488 Hz, median 193 Hz). The peak acceleration amplitude of defence buzzes ranged from 2 to 1473 m s⁻², with an average of 112 m s⁻² (approximately 11.4 g-force equivalents; median 82.7 m s⁻²). Peak amplitude acceleration was strongly correlated with RMS amplitude acceleration (Pearson's ρ=0.854, P<0.001; Fig. S1).

We found that thorax width was positively associated with peak acceleration amplitude, as assessed in the MCMC model incorporating the phylogenetic structure of the data at the genus level, and both species and individual identity as random effects (Fig. 2, Table 1). This model also indicated a statistically significant difference between buzz-pollinating and non-buzz-pollinating taxa, with bees belonging to genera that are not known to buzz pollinate producing lower acceleration amplitude buzzes (Fig. 2, Table 1A). In contrast, the fundamental frequency of non-flight buzzes was not associated with thorax width and did not differ between buzz-pollinating and non-buzz-pollinating taxa (Fig. 2B, Table 1). For buzz duration, we found a statistically significant effect of body size, with larger bees producing longer buzzes (Fig. 2, Table 1). Whether a bee belongs to a buzz-pollinating genus or not had no effect on buzz duration.

As expected, a main determinant of defence vibration amplitude is the size of the bee's thorax; specifically, the width of the mesosoma. A similar relationship between thorax size and vibration amplitude acceleration also holds for defence buzzes produced by hoverflies (Vallejo-Marín and Vallejo, 2020). This thorax width–amplitude relationship is probably related to an increase in the volume and cross-sectional area of the indirect flight muscles, but this hypothesis remains to be further explored. Thorax width should scale positively with the cross-sectional area of the dorso-ventral and dorsal longitudinal muscles (indirect flight muscles), which power bee buzzes across all behaviour contexts (Dickinson et al., 1998; Vallejo-Marin, 2022). If the proportion of muscles to body is scale invariant, then the thorax width would be approximately proportional to the square root of the muscle cross-sectional area. We do not expect the characteristics of muscle tissue to vary too widely among different species of bees because they do not vary across asynchronous flight muscles of distantly related insect lineages (Marden, 2000). Therefore, we conjecture that the positive relationship detected here between thorax width and vibration amplitude reflects the increased power of larger indirect flight muscles in larger bees. In particular, if the muscle contraction is limited by some scale-invariant strain, the muscle deformation amplitude would scale linearly with thorax width, and, given the observed scale-invariant buzzing frequency, this would result in the acceleration amplitude also scaling linearly with thorax width, which is very close to the measured data. Additionally, if the muscle properties, proportion of muscles to body size, and body shape are scale invariant, then we would expect muscle stiffness to scale linearly with thorax width, and the muscle force to scale with the square of thorax width, which would also result in a linear scaling of amplitude with thorax width, for operation in a stiffness-dominated regime. While these hypotheses are consistent with our measured data, they remain to be further explored. It is unknown whether higher amplitude defence vibrations are more effective at deterring potential bee predators such as birds or mammals. However, vibration amplitude directly affects the amount of pollen removed from flowers during buzz pollination. Although further work should compare defence and pollination buzzes across a wider range of bee taxa, our results suggest that, all else being equal, a larger bee should be able to remove more pollen per time spent buzzing than a smaller bee. In addition, we found that bee size is positively correlated with buzz duration, which could mean that larger bees might be able to produce both longer and higher amplitude buzzes. This does not mean that smaller bees are at a disadvantage in terms of total pollen removal, as the behaviour of the bee on the flower will affect how these vibrations are applied to the flower and the amount of pollen removed, and small bees might adjust how they manipulate and interact with flowers to maximise pollen removal (Barbosa et al., 2023; Delgado et al., 2023).

While all bees reported to buzz pollinate produced defence vibrations, five out of 13 bee species not reported to buzz pollinate in the literature did not produce defence buzzes in our experiment. Why some bee species buzz pollinate and others do not, or whether this is related to the capacity of producing other non-flight buzzes is unclear and a topic of interest for further work (Vallejo-Marin and Russell, 2024). When considering only bee species that produce defence buzzes, bees belonging to buzz-pollinated genera produced higher amplitude vibrations than those not in buzz-pollinated genera. If a bee is unable to produce vibrations of sufficient amplitude to dislodge pollen, this could explain why some bees do not buzz pollinate (e.g. Apis mellifera) (King and Buchmann, 2003). However, the vibration amplitude of defence buzzes in buzz-pollinating and non-buzz-pollinating bees shows considerable overlap, and it is unclear whether the statistical difference detected here has any functional effect on the amount of pollen removed from flowers. Indeed, this biomechanical limitation hypothesis does not seem to be a general explanation of why some insects do not buzz pollinate, as hoverflies (Diptera: Syrphidae), which are not generally known to buzz pollinate, are capable of producing vibration amplitudes equivalent to those of similarly sized buzz-pollinating bees (Vallejo-Marín and Vallejo, 2020). Additional work is thus required to establish whether limits on the vibration amplitude that a bee can reach explain why some bees do not buzz pollinate.

The frequency of non-flight defence buzzes was not related to bee size. This is consistent with previous analyses of pollination buzzes (another type of non-flight thoracic vibration). Acoustic surveys of pollination buzzes among North American (De Luca et al., 2019) and neotropical bees (Burkart et al., 2011) found no statistical association between intertegular distance and buzz frequency, in contrast to the frequency of flight buzzes, which scales negatively with size. In contrast to flight, defensive and floral buzzing allows the mechanics of the thoracic muscles to be uncoupled from both the aerodynamic properties and the size of the wings (Hickey et al., 2022), removing the frequency limitations enforced during flight. Frequency variation between buzzes produced by the same individual can also be mediated by bee behaviour. Bees may be able to alter the resonant properties of the thorax by using axillary muscles and altering thorax stiffness, as in the case of dipteran indirect synchronous muscles that regulate wing stroke frequency and amplitude (Dickinson et al., 1998). In addition, it is possible that the thorax could be driven at frequencies different to their resonant frequency, and there is some evidence that this is the case in the alarm and communication buzzes produced by Melipona seminigra (Hrncir et al., 2008), providing an additional mechanism to dynamically alter the frequency of thoracic vibrations (Vallejo-Marin, 2022). Together with previous work, our results suggest that across a wide diversity of bees, the frequency of non-flight buzzes, including pollination and defence buzzes, is not strongly constrained by bee size (Burkart et al., 2011; De Luca et al., 2019). Therefore, bees appear to be relatively free to exploit different buzz frequencies regardless of their size, although we still do not fully know the functional consequences of frequency variation in the different behavioural contexts.

We observed a large amount of variation in the properties of buzzes of bees of similar size, and even within individuals. Similarly to vibration frequency, vibration amplitude is also partially under neural control of the bee, and the bee might have the capacity not only to turn the indirect flight muscles on and off but also to modulate their amplitude similarly to the modulation of wing stroke amplitude in flies (Dickinson et al., 1998). The ability to control both amplitude and frequency of thoracic vibrations should help the bee to regulate energy expenditure, as the thoracic power muscles are capable of producing significant power (>100 W kg⁻¹; Josephson, 1997) but are very energetically demanding. These potential mechanisms of regulating the timing, frequency and amplitude of thoracic vibrations as well as the observed variation in buzz properties within individuals and between individuals and species of similar size, suggests that there is considerable flexibility in any potential constraints of morphology on vibration production (Switzer et al., 2019). This flexibility in producing vibrations of different mechanical properties should be ecologically advantageous, as thoracic vibrations are deployed in very different contexts from flight to pollination to defence to mating (Conrad and Ayasse, 2015; King and Buchmann, 1996; Kirchner and Röschard, 1999; Larsen et al., 1986; Russell et al., 2017).

Despite the behavioural control of vibration properties, ultimately, the limits of these properties are set by biomechanical and physiological constraints. The next step in understanding the capacity of a bee to produce non-flight buzzes should be to compare the architecture of the indirect flight muscles across species. Do buzz-pollinating taxa have larger muscles? How do different castes differ in their indirect flight muscle anatomies? Do buzzes differ between male and female bees? Such questions offer a rich avenue for interdisciplinary research in bee phylogenetics, form, function and biomechanics.

We thank M. Saunders, M. Hall, M. Whitehead, F. Montealegre and G. Martin-Ordas for their support in the development of the project and for their contribution in securing funding for fieldwork. Estación Biológica de Chamela-UNAM and Estacion Cientifica Las Joyas kindly provided access and support during fieldwork. We thank José Rubén Pérez Ishiwara for logistic support, and K. Prendergast and T. Houston for their assistance in identifying Australian bees. We thank the editor and three anonymous reviewers for their helpful suggestions.