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Changing Resonator Geometry to Boost Sound Power Decouples Size And Changing resonator geometry to boost sound power PNAS PLUS decouples size and song frequency in a small insect Natasha Mhatrea,1, Fernando Montealegre-Za, Rohini Balakrishnanb, and Daniel Roberta aSchool of Biological Sciences, Woodland Road, University of Bristol, Bristol BS8 1UG, United Kingdom; and bCentre for Ecological Sciences, Indian Institute of Science, Bangalore 560012, India Edited by A. J. Hudspeth, Howard Hughes Medical Institute, New York, NY, and approved March 28, 2012 (received for review January 6, 2012) Despite their small size, some insects, such as crickets, can produce by the pallets allows the gear to move forward only once every high amplitude mating songs by rubbing their wings together. By oscillation by mechanically blocking its motion at other times. exploiting structural resonance for sound radiation, crickets broad- Hence, the frequency at which the gear tooth engages and im- cast species-specific songs at a sharply tuned frequency. Such songs parts force back to the pendulum is set by the pendulum itself enhance the range of signal transmission, contain information (8). Cricket wings play the same role as the pendulum by deter- about the signaler’s quality, and allow mate choice. The production mining the dominant or carrier frequency (CF) of the cricket’s of pure tones requires elaborate structural mechanisms that con- song (5, 6), and the file and plectrum are the analogs of the gear trol and sustain resonance at the species-specific frequency. Tree and pallets parts of the escapement mechanism prompting the crickets differ sharply from this scheme. Although they use a reso- term “clockwork cricket” (5, 7). In the absence of such an esca- nant system to produce sound, tree crickets can produce high am- pement mechanism, the CF of a cricket song would be variable, plitude songs at different frequencies, varying by as much as an and their wings would be much less efficient at producing high octave. Based on an investigation of the driving mechanism and amplitude mate attraction signals (2). the resonant system, using laser Doppler vibrometry and finite ele- Crickets are poikilothermic animals, and their physiology is ment modeling, we show that it is the distinctive geometry of the greatly affected by changes in ambient temperature as is their crickets’ forewings (the resonant system) that is responsible for song (10–13). In field crickets, where the escapement system is their capacity to vary frequency. The long, enlarged wings enable best studied, the song CF changes very little with temperature BIOPHYSICS AND the production of high amplitude songs; however, as a mechanical (6). As the resonant frequency of the wings does not change with consequence of the high aspect ratio, the resonant structures have temperature, it was proposed that the plectrum cannot proceed COMPUTATIONAL BIOLOGY multiple resonant modes that are similar in frequency. The drive along the file any faster despite the overall change in the speed of produced by the singing apparatus cannot, therefore, be locked the wing-stroke (5, 6). As a result, the song CF does not change, to a single frequency, and different resonant modes can easily be and crickets can produce high amplitude, pure-tone signals re- engaged, allowing individual males to vary the carrier frequency of gardless of ambient temperature (6). their songs. Such flexibility in sound production, decoupling body Another implication of this deterministic mechanical model of size and song frequency, has important implications for conven- sound production is that there is an inflexible relationship be- tional views of mate choice, and offers inspiration for the design tween body size and song CF within a species of cricket (4, 14, of miniature, multifrequency, resonant acoustic radiators. 15); hence, CF is an obligatorily honest signal of an individual’s size. Moreover, all insects that use similar sound production me- bioacoustics ∣ biological modelling ∣ biomechanics ∣ finite element analysis chanisms such as katydids (tettigoniids) and field crickets (gryl- lids), were expected to follow this pattern (4). Earlier research showed that females prefer males broadcasting lower CF songs; ale crickets produce high amplitude calling songs to attract – Mconspecific females (1, 2). The sounds are produced by stri- hence, females choose larger and potentially fitter males (16 18). dulation, a rapid and controlled rubbing of forewings against each The generality of this mechanism for female choice has been other. The plectrum, a sclerotized portion on the anal edge of one challenged in birds and mammals (19, 20) but not in insects. Ex- wing, is drawn across the file, a series of teeth on the underside of amples of uncoupling CF from size is rare in insects; yet, a notable a vein, on the other wing (reviewed in ref. 3). The stridulatory exception are the Oecanthines, or tree-crickets, whose calling apparatus acts as a mechanical frequency-multiplying system, song CF varies greatly with temperature (10, 21, 22). converting the slow wing-stroke rate (ca 30 Hz) of the insect into Tree crickets (Oecanthinae, Gryllinae, Orthoptera) are distin- guished by beautiful, transparent wings that are conspicuously en- a sound of much higher frequency (e.g., 4.5 kHz in the field crick- – et Gryllus bimaculatus) (3, 4). Stridulation sets the wing into larged with respect to their body size (22 25). Little is known, vibration, and if the frequency produced by the plectrum-file in- however, about the relationship between temperature, the stridu- teraction (the tooth strike rate) matches the resonance frequency latory mechanism, and wing resonances in Oecathines (23, 26). of the wings a higher amplitude pure-tone sound can be produced Even less is known about the evolutionary reasons for their re- (2). The exact biophysical mechanisms enabling such sound ra- markable wings and the consequences of having sound radiators diation using soft structures many times smaller than the sound that are so different from those of the previously studied field crickets (27, 28) and katydids (29, 30). wavelength remain elusive. The key outstanding question pertains to the mechanism that The mechanism that crickets use to match stridulatory fre- enables the production of variable frequency songs that are high quency to resonant frequency is similar to a clockwork-like esca- amplitude and tonal. We dissect the relationship between the pement system (5–7). In the field of horology, escapement mechanisms display different degrees of sophistication (8), one is even called the grasshopper escapement (9). The fundamental Author contributions: N.M., F.M.-Z., R.B., and D.R. designed research; N.M. and F.M.-Z. principle of an escapement can, however, be illustrated by the performed research; N.M. and F.M.-Z. analyzed data; and N.M. wrote the paper. simple deadbeat escapement. In a deadbeat escapement, the re- The authors declare no conflict of interest. sonant system is a pendulum that acts as a regulator and sets the This article is a PNAS Direct Submission. speed at which the mechanism oscillates. The force comes from a 1To whom correspondence should be addressed. E-mail: [email protected]. rotating gear whose teeth engage and apply force to pallets at- This article contains supporting information online at www.pnas.org/lookup/suppl/ tached to the pendulum. The sequential release of the gear teeth doi:10.1073/pnas.1200192109/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1200192109 PNAS Early Edition ∣ 1of9 Downloaded by guest on September 25, 2021 forces generated by the stridulatory mechanism, and the resonant changes over time (7). Alternatively, if the two envelopes corre- behavior, size and shape of the acoustic radiators. The results re- spond exactly, it is expected that the HF elements are a product of veal that the ability to produce variable frequencies is determined harmonic distortion and not produced by the stridulatory appa- by morphological geometry; i.e., the high aspect ratio of the re- ratus. We found that the envelope of the HF ticking sound was sonator. The results also suggest that the evolution of this wing different from that of the CF sound as can be observed in the time morphology is driven by the need to produce higher amplitude resolved gain between the unfiltered and filtered syllables over a mate attraction songs, and the variable frequency is an inevitable range of temperatures (Fig. 1). Remarkably, the temporal dy- outcome. In biophysical terms, the results uncover a remarkably namics of instantaneous frequency and HF components change simple method to design efficient resonators with variable fre- with temperature (Fig. 1). quency output. The other interesting outcome vis a vis sexual se- lection is that it negates the idea that insects are obliged to signal Modeling the Stridulatory Apparatus. Having found evidence for an their body size honestly as a result of their inflexible sound pro- escapement mechanism in O. henryi songs, the next step was to duction mechanism. probe the nature of the mechanical drive imparted to the wings. Three models of the forces that developed during the closing Results stroke of stridulation were generated. Each model had a different The “Ticking” in Tree-Cricket Song. It has been suggested that if stri- force regime: a sinusoidal drive, an impulsive drive, and a “catch dulation relies on an escapement mechanism, the plectrum will and release “drive (Fig. 2A). The latter two have been the domi- make a high frequency ‘ticking’ sound as it engages each tooth of nant models in describing an escapement system in field cricket the file (7). The ticking that is produced is soft; yet, it is expected stridulatory behavior (6, 31). to produce small irregularities in the acoustic waveform. Close With all three models, because there is a net positive force on examination of song recordings made in the field from the South each wing through time, a net forward movement of the plectrum Indian tree cricket Oecanthus henryi (22) reveals the presence of along the file will be produced (Fig.
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