Insects display a wide range of acoustic signals used in species recognition and elicitation of courtship and mating [1]. Acoustic signals of several Hymenopterans have been described; perhaps the best characterized being part of the “waggle dance” of honeybees [2], [3], [4], [5], [6]. Parasitic wasps are highly diverse with over 50,000 described species across many families [7], and utilize wing movement or fanning to produce male courtship signals [8]. Wing fanning is hypothesized to draw female pheromones across the male’s body for orientation towards the female and to stimulate production of their courtship song [9]. As demonstrated by wing excision [10], [11], male courtship song in braconid wasps is caused by modulation of wing fanning. The song attenuates rapidly in air but also transmits through the substrate [12], [13], [10]. Acoustic signals have been characterized for the Cotesia flavipes/sesamiae (Cameron) species complex [14] and for a few other braconid wasps, including Glyptapanteles flavicoxis Marsh [15], Aphidius ervi Haliday [11], as well as five species of fruit fly parasitoids in the subfamily Opiinae [12], [16], [17]. Acoustic signals may play a role in reproductive isolation in the Cotesia flavipes/sesamiae species complex [14].

The gregarious endoparasitoid, Cotesia congregata Say (Hymenoptera: Braconidae), parasitizes the tobacco hornworm, Manduca sexta (L.) and other species of sphingid larvae that feed on a diverse array of plant families and species [18], [19]. This parasitoid serves as a component of a model system for host-parasitoid interactions and insect immunology [20], [21], insect learning [22], [23], [24], and tri-trophic interactions [25], [26]. Here we characterized the male courtship song of C. congregata and examined the mechanism of the high-amplitude “boing” component with high-speed videography and synchronized audio recordings. Based on general principles of sound generation [27], we expected that the fundamental frequency would match wing fanning rate, and the maximal sound amplitude would occur during maximal velocity of wing motion. The frequency matched the wing rate, as expected, but surprisingly the boing appears to be generated at the termination of the wing down stroke when displacement is maximal and wing velocity is zero.

The courtship song of Cotesia congregata consists of a two-part signal that begins with a long amplitude-modulated buzz (wing fanning) and concludes with a series of higher amplitude boings, each of which decays into a terminal buzz. The three components differ in amplitude and frequency, which were inversely related; i.e. when amplitude increased, frequency decreased. The higher amplitude boing requires greater wing excursion and therefore wing strokes of longer duration, thereby generating a lower fundamental frequency. The initial fanning may also serve to localize the female pheromone source [9], and the number and amplitude of boings likely reflects an honest signal of male quality for female mate choice. In other parasitic wasps studied, wing fanning produces sound frequencies in harmonic series at multiples of the fundamental frequency, which vary between 122 and 314 Hz across species [15], [12], [16], [11], [17].

Abdomen elevation during high-amplitude components has not been described in the literature for other parasitic wasps. This movement may not be involved directly in sound production because the wings do not strike the abdomen during the downward sweep. Its function is unclear because abdominal muscles are typically separate from thoracic muscles [28], and maximum sound amplitude lags behind abdominal movement (Fig. 5, 7C). Possibly, abdominal elevation could reposition the body for balance or facilitate vibrations transmitted to the substrate, as reported for some species of lacewings [29] and stoneflies [30]. Alternatively, abdomen elevation may be associated with release of a chemical signal. Abdomen elevation is unlikely to provide a visual mating signal because the female typically faces away from the male during courtship.

The sound probe tube microphone was in the near-field for sound radiation, so the sound measurements may be highly sensitive to slight variations in position due to local reflections and reactive sound components. High sensitivity to position for the amplitude and phase measurements of the sound would be indicated by a high variation among the measurements. However the low variation and consistency of the amplitude and phase measurements (Fig. 5) indicates that reactive effects were small. The recordings were aided by experimental conditions that ensured the male maintained a stationary position during boing production. Amplitude indicates that acoustic signals in air would be effective over short distances. Based on spherical spreading, a 64 dB SPL signal recorded at 2–3 mm would be equivalent to a source level of only about 10 dB at 1 m. Using playback from a speaker in air that evoked no measurable substrate vibrations, Danci et al. [15] demonstrated that female parasitic wasps were attracted to the male’s airborne song. This result does not rule out a contribution from leaf vibrations under natural conditions.

Of the 15,000 described species in the Braconidae [31], courtship sounds have been described for eleven other species, representing nine genera in three subfamilies. Compared to other braconids, C. congregata has a relatively complex song that consists of two major parts, the initial buzz and the boings, with each boing followed by a terminal buzz. For example, C. marginiventris, the closest relative to C. congregata [32] for which courtship songs have been described, produces structurally distinct songs with shorter repeated pulses that decay into a warble [12]. Other braconids produce signals that range in structure and complexity: Glyptapanteles flavicoxis utilizes amplitude-modulated wing fanning [15], members of the subfamily Opiinae produce a series of repeating pulses [12], [16], [17], and males of the Cotesia flavipes/sesamiae complex produce separate repeating buzz and pulse components [14].

The wing-beat frequency during courtship displays has been examined photographically [33] and acoustically [17] for the braconid, Psyttalia concolor; however, these studies did not relate wing movement directly to sound generation. For typical wing sound production, including Drosophila spp., acoustic pressure is proportional to velocity [34]. Our finding that the boing sound was generated at maximal wing displacement when velocity is zero was initially surprising, but we believe justified. Sampling theory can be applied to reconstruct the full wing-flap position versus time profile as long as more than two frames are obtained for each wing flap. The high-speed video captured ∼10 frames for each full wing-flap cycle, exceeding the sampling theory requirement. This allows us to correlate the wing position with the sound even though the video and sound sampling rates were different. Note however that camera data are not useful in explaining the waveform of the sound signal, which appears to result from a forced response caused by wing repetition rate (∼210–229 Hz) and wing resonance (∼5 kHz). Because sound cannot be generated by a static structure, we considered several hypotheses to explain sound generation.

The physics of bullwhips, which generate a snap by tip acceleration to supersonic speeds (340 m/s), has received considerable attention from physicists [35] and has been proposed as a possible mechanism of sound generation for the tail tip of sauropod dinosaurs [36] and wing snaps in manakin birds [37]. As in many hymenopterans, the paired wings of C. congregata are hooked together by hamuli and function as a unit; wings never touch the abdomen, the substrate, or the opposite wings ruling out wing collisions as the sound source. The larger forewings are small (2.38 mm long), and veins that support the wing terminate before the wing tip where there is a series of four less-supported folds in the distal wing (Fig. 8) that could be subject to a whip-like motion during rapid wing deceleration. Using values measured in this study, we calculated wing-tip speed with the equation:where v is the peak velocity of the wing tip, R is wing length (2.38e−3 m), θ_pp is wing peak-to-peak angle (2π/3 rad/cycle), and f is wing-beat frequency (230 Hz). Wing velocity would be 32.4 m/s, which is about 10% of the speed of sound. Making the extreme assumption that all energy in the wing is transferred to the posterior terminal wing fold (Fig. 8), about 11.4% of area (measured with grid squares), increases speed to 123 m/s, about 36% of the speed of sound. We therefore reject the whip-snap hypothesis and suggest that it has limited applicability to other biological systems.

Previous work on the directionality of the sounds produced by dancing honeybees indicates that the up and down wing motion has the directionality of a dipole source: a bidirectional sound field that decays rapidly in air [38]. There is no net introduction of fluid by a dipole (cancellation of up and down wing motion), and only net force on a fluid causes energy to be radiated as sound [39]. Equations of pressure of a dipole are typically related to velocity [39]. However, because pressure lags velocity by 90°, it will be in phase with acceleration. The precise timing relationship in the parasitoid wing-sound generation suggests an almost pure dipole source, although we do not rule out an aerodynamic component due to interacting vortices produced by the leaking of higher pressure under the wings to the lower pressure above. Sounds generated from vortices produced by flapping wings have been demonstrated in blowflies [40] and modeled during bumblebee flight [41]. Our measurement of the phase relationship between dipole wing acceleration and sound pressure may be the first demonstration in biological sound generation.

The dipole acceleration model best explains our finding that boing amplitude increases over several cycles as wing displacement decreases. The indirect flight muscles of many insects are excited by a combination of neural input and stretch-induced activation [42], [43]. Toward the end of a large downstroke displacement, when the antagonist elevator muscle is activated, the wings likely slow down, decreasing acceleration at the end of the excursion. Changing direction in midstroke would reverse movement during a faster phase of contraction (higher instantaneous velocity) and therefore increase acceleration and sound amplitude even with a smaller wing stroke because velocity is proportional to Aω and acceleration to Aω², where A is displacement and ω is 2πf. These relationships explain our finding that two fold changes in wing velocity failed to affect sound amplitude in the hysteresis measurements.

In order to understand the relationship of wing beat frequency to sound generation in Cotesia, we calculated the Reynolds number for a 3-dimensional flapping wing, Re_f3, following Shyy et al. [44] using the equation:where 2Rθ_ppf is the mean angular velocity of the wing tip (reference velocity), c_m (1.07e−3 m) is the mean wing chord length (reference length), and ν is the kinematic viscosity of air (1.51e−5 m²/s at 20°C). The Reynolds number is approximately 1000 (959 for 216 Hz and 1020 for 230 Hz wing rate). This compares to ∼100 for Drosophila melanogaster [45] and 18 for the tiny egg parasitoid Encarsia formosa, which has smaller wings [46]. Larger Hymenopterans such as honeybees and bumblebees have Reynolds numbers that range from 1000 to 8800 [46], [41]. As for other small insects with relatively low Reynolds numbers, C. congregata may implement a “clap and fling” mechanism for flight in which the wings come together and then fling apart while the trailing edge remains momentarily in contact [46], [47], [45]. Wing fanning during courtship does not utilize the clap and fling mechanism because the wings do not contact nor do the trailing edges stay together (Video S1). This difference may allow the wasp to remain on the substrate during courtship by not generating enough lift for flight. The low Reynolds number in C. congregata indicates a poor lift to drag ratio, therefore small insects such as parasitic wasps and vinegar flies require a high wing flap rate to generate adequate lift for flight, which predisposes them to produce sound that can later be selected for communication.