Biomechanics of the peafowl’s crest reveals frequencies tuned to social displays

Feathers act as vibrotactile sensors that can detect mechanical stimuli during avian flight and tactile navigation, suggesting that they may also detect stimuli during social displays. In this study, we present the first measurements of the biomechanical properties of the feather crests found on the heads of birds, with an emphasis on those from the Indian peafowl (Pavo cristatus). We show that in peafowl these crest feathers are coupled to filoplumes, small feathers known to function as mechanosensors. We also determined that airborne stimuli with the frequencies used during peafowl courtship and social displays couple efficiently via resonance to the vibrational response of their feather crests. Specifically, vibrational measurements showed that although different types of feathers have a wide range of fundamental resonant frequencies, peafowl crests are driven near-optimally by the shaking frequencies used by peacocks performing train-rattling displays. Peafowl crests were also driven to vibrate near resonance in a playback experiment that mimicked the effect of these mechanical sounds in the acoustic very near-field, reproducing the way peafowl displays are experienced at distances ≤ 1.5m in vivo. When peacock wing-shaking courtship behaviour was simulated in the laboratory, the resulting airflow excited measurable vibrations of crest feathers. These results demonstrate that peafowl crests have mechanical properties that allow them to respond to airborne stimuli at the frequencies typical of this species’ social displays. This suggests a new hypothesis that mechanosensory stimuli could complement acoustic and visual perception and/or proprioception of social displays in peafowl and other bird species. We suggest behavioral studies to explore these ideas and their functional implications.


Introduction
Bird feathers are known to act as mechanosensors that allow birds to detect and respond to a variety of mechanical stimuli [1][2][3]. For example, flight, contour, and facial bristle feathers can 42 act as sensors that provide important information during flight and prey capture [4,5,3,6,7].
Indeed, feathers have been suggested to have evolved originally to serve sensory functions, 44 because even isolated protofeathers could have played a sensory role before the evolution of specialized arrays of feathers that enabled flight or thermoregulation [8]. Feather head crests 46 have been found in fossils of some dinosaurs and early birds as well as a wide variety of living species of birds [9,10]. While feather crests have usually been studied for their roles as possible 48 visual signals [11-13, see also 14 for a review], recent behavioral studies of two auklet species have shown that their erect head crest feathers can play a mechanosensory role during tactile 50 navigation similar to that of mammalian whiskers and arthropod antennae [14,15]. These findings suggest that feather crests in other birds also might play a previously unrecognized 52 mechanosensory functional role. Crest feathers and other types of feathers found on the heads of birds have received little attention in the literature, especially in comparison to the significant 54 body of literature on the morphology and mechanical properties of wing, tail and train covert feathers [16]. In addition, no research has considered whether birds, like some arthropods, might 56 detect air-borne stimuli generated during social displays via mechanoreception, or what influence this may have on their social interactions. 58 Here we report on the first biomechanical study of bird crest feathers, with an emphasis on 60 understanding how their physical properties might relate to their various possible functions. This work focused on the large crest of the Indian Peafowl (Pavo cristatus), which is found on both 62 6 (P1-P4) are outlined in Box 1 below. A large body of research in mammals and arthropods has 108 found that antennae and sensory hairs play important mechanosensory roles in sound detection; this function is also known to be influenced by their vibrational response and mechanical 110 structures [27,28]. For example, in order for a feather crest to sense environmental airflows, it would need to bend sufficiently to activate mechanosensory nerve cells (P1-P4; Box 1), as has 112 been shown for pigeon covert feathers [2], arthropod sensory hairs, pinniped whiskers, bat sensory hairs, fish lateral line organs [29], and rat whiskers [30,30]. Thus, one would expect 114 crest feathers to be compliant enough to deflect when stimulated by salient airflow stimuli.
Sound consist of oscillations of the surrounding medium in both pressure and particle velocity. 116 Animals can detect pressure oscillations using ears and tympanal organs, whereas particle velocity oscillations can be detected in a variety of ways, including using sensory hairs and 118 antennae that have mechanosensors at their bases [31,32]. Feathers of all types in birds of all orders have at their bases specialized short mechanosensitive feathers called filoplumes that 120 couple to motions of their associated feather's shaft [33,34]; thus, we expect this to also be true for crest feathers (prediction P1; Box 1). Like many sensory hairs and antennae, the plumose 122 structure of feathers enables effective mechanical coupling to air motions via drag forces [2,35] and elongated, tapering shafts well-suited for bending and transmitting force to an enervated 124 base. Both contour feathers and filoplumes have been shown empirically to detect bending and vibrations via mechanoreceptive Herbst corpuscles at their bases [36,2,3,37]. 126 Because the peafowl's region of most acute vision is oriented laterally [38], when a peahen gazes 128 at a displaying male, the maximum area of her crest feathers also points toward the peacock's moving feathers (Fig 1A). This results in an optimal orientation for intercepting airborne 130 7 vibrations generated by display behaviors; these medium oscillations should tend to drive feather crests to oscillate in the "out-of-plane" orientation (i.e., normal to the plane of the crest as shown 132 in Fig 1D). The displaying peacock shakes its body laterally during such behaviors, so any corresponding vibrations of its own crest should also occur in the out-of-plane direction. The 134 design of the crest also provides a mechanical advantage, enabling it to transmit a magnified version of the forces applied to its distal end to its base, because the flag is wider than the tapered 136 base and because each feather shaft acts as a lever arm coupling the flag to the base. Another important consideration is the frequency-tuning between sensory structures and their 148 stimuli (prediction P2; Box 1), as this can provide several advantages including filtering out background noise and other irrelevant stimuli [31]. In fact, a variety of arthropods use receivers 150 with a response that is frequency-matched to the stimulus source, including antennae and sensory hairs used by various insect species to detect wingbeat signals of near-by conspecifics, 152 trichobotheria used by some arachnids to sense prey wingbeats [39][40][41][42][43], and frequency-tuned PREPRINT VERSION 8 eardrums used by cicadas and crickets to detect conspecific songs [44,45]. Such mechanical 154 frequency tuning can be accomplished readily via resonance, the phenomenon whereby an object responds with maximum amplitude to a driving force that oscillates near one of its natural 156 frequencies of vibration [31]. Resonant frequency matching enables a mechanoreceptor to respond with optimal sensitivity to low amplitude airborne stimuli, at the expense of frequency 158 discrimination (by contrast, human eardrums and microphones have broadly-tuned resonance responses that allow efficient detection of natural stimuli over a wide range of frequencies). 160 Therefore, given that peafowl displays take place at well-defined shaking frequencies, we predict 162 that their feather crests might have a resonant frequency response with a peak and width matched to the display, as found for the arthropods cited above. If this frequency tuning is indeed present, 164 the crest might enable peafowl to detect airborne stimuli generated by a conspecific individual's shaking motions by undergoing sympathetic vibrations (i.e., undergoing oscillations driven by 166 coupling through drag forces to air particle velocity oscillations). Feather crests optimized to vibrate at the shaking frequency could also provide proprioceptive feedback to the individual 168 performing the display [46, 47,31].

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Some arthropods have the additional ability to use mechanosensory hairs to sense separate airflow pulses generated by abrupt, repetitive motions. The resulting impulsive forces cause the 172 mechanosensors to oscillate only briefly at their natural frequency before their motion is damped out. For example, the cerci sensory hairs of female African crickets (Phaeophilacris spectrum) 174 function in this way to detect air vortices produced by males performing wing flicks [48][49][50].
These motions are similar to those performed during peacock wing-shaking displays. Detecting 176 9 airflow impulses via transient oscillations requires the right level of damping and natural frequency to allow a high amplitude response while also enabling detection of the airflow 178 impulse repetition rate (prediction P3). Consequently, feather crests would also need this specific combination of vibrational response parameters in order to respond efficiently to 180 impulsive airflows generated by wing motions.

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In other animals, vibrotactile sensors detect sound particle velocity oscillations in the acoustic near-field, a region close enough to the source that particle velocity can couple efficiently to 184 mechanoreceptors via drag forces [31]. For example, in arthropods, many species use filiform hairs to detect near-field particle velocity for predator or prey detection and for intraspecies 186 signaling [51 -53]. Near-field communication has been studied in a wide variety of invertebrate terrestrial taxa [54,51] and in fish [55]. By contrast, it is often assumed that only the acoustic far-188 field is relevant for sound reception by birds. In the far-field, sound predominantly consists of pressure waves detectable by vertebrate ears, insect tympanal organs and similar receptors. 190 Because the particle velocity magnitude falls off more rapidly with distance than the pressure wave component, particle velocity stimuli are greater than those due to pressure waves only for 192 distances R < 0.16 to 0.22 λ (where λ = wavelength) for monopole sources (e.g., loudspeakers) and dipole sources (e.g., moving wings, tails and trains), respectively [56, 31,57]. Consequently, 194 this wavelength-dependent distance is often used to distinguish the acoustic far-and near-fields.
However, the relevant criterion for efficient mechanosensation is the absolute magnitude of 196 particle velocity, not the relative value of particle velocity compared to the pressure wave [58].
Thus, the regime relevant for vibrotactile sensing is the flow (reactive) near-field: the region near 198 the sound source where the particle velocity has its greatest magnitude because the air acts as a PREPRINT VERSION layer of effectively incompressible fluid that moves with the source [32,59]. The extent of the 200 flow near-field depends on source size, A, not wavelength (see e.g., Fig 2 in [59]). For R ≤ 0.16 A (the "very near-field"), the particle velocity is approximately constant. As R increases, 202 particle velocity becomes negligible for mechanosensing at approximately R ≈ A [31,59,35].
The lateral extent of the flow near-field also depends on A. In addition, the overall magnitude of 204 the particle velocity increases as A 2 for a monopole and A 3 for a dipole. In summary, increasing source size, A, increases the spatial extent of the flow near-field regime in which 206 mechanoreception can take place, as well as the magnitude of particle velocity stimuli [56].

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During the peacock's display, typical female-male distances, R = 1.0 to 1.5 m, are equal to the typical peacock train radius, which plays the role of source size A. Female therefore experience 210 train-rattling sound in the acoustic flow near-field [18,60], satisfying a prerequisite for vibrotactile sensing. The criterion R = 1 to 1.5 m < 0.22 λ corresponds to frequencies < 50 to 75 212 Hz at this distance; therefore, the mechanical sound generated by the peacock's display has appreciable pressure wave magnitude as well for most frequencies in the human audible range. 214 Spectrograms from earlier studies of peacock train-rattling indicate that these mechanical sounds consist of broadband impulsive rattles with spectral density primarily in the human audible 216 range, emitted at a repetition rate of approximately 26 Hz; they are neither low frequency pure tones, nor are they sound with spectral density predominantly in the low frequency or infrasound 218 regime [19,20]. As a result, a consideration of the sound fields of peacock train-rattling displays indicates that rattling sounds might be detectable as particle velocity or pressure wave stimuli, or 220 both, at typical display distances.

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In this study, we compare the mechanical properties of peafowl crests with those predicted for mechanosensation (predictions P1-3; Box 1), and we furthermore test whether stimuli from 224 peacock displays induce a vibrational response in the crest (prediction P4). We also wished to determine whether any agreement between social display frequencies and crest resonant 226 frequencies was generic or specific to this system. Therefore, we sought to understand how the peafowl crest's resonant properties relate to those of other types of peafowl feathers as well as 228 crest feathers from other species. This work was designed to serve as a first step to determine whether the head crests of birds might serve a variety of mechanosensory functions, including 230 the detection of body self-motion and various airborne stimuli. Assiniboine Park Zoo (Winnipeg, Manitoba, Canada) and Siskiyou Aviary (Ashland, OR USA) (see S1

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Microscope Pro (Celestron, Torrance, CA USA) was used to examine the base of peafowl crest 246 feathers to determine whether filoplumes were present, using the structural criteria employed in previous studies of this feather type (i.e., short feathers with a long, bare shaft with a tuft of short 248 barbs on the distal end, located near the base of a longer feather but not growing from the same follicle [61,33,62,64,63,65]; see micrographs in [33, 36,65]. Crest length and width 250 measurements were made by hand and from digital photographs of the crest samples and highresolution scans (0.02 mm/pixel) of single feathers with a ruler included in the sample plane. We 252 used these measurements to compare the morphology of dried crest samples with that found for crests on live peafowl in a previous study [17], including length, width and number of feathers. 254 Because some peafowl, especially females, have non-uniform crest feather lengths [17], we also measured the lengths of individual feathers within the dried crest samples to compare with the 256 previous study. If the crest feathers were closely clustered, the attached skin was first softened in water and the crest was spread to approximate its natural configuration. 258 Following earlier studies of feather vibrational properties [20,66,67], we mounted crest feathers 260 by gluing the crest skin to a rigid sample holder (a 2.5 cm cube of balsa wood) ( Fig 1D). This method is justified because the resonant frequency of a flexible shaft secured at one end by a stiff 262 clamp is not expected to be affected by the clamp's mechanical properties [31]. In an earlier study, we had verified that this is true for peafowl tail and train feathers [20]: i.e., there was 264 minimal shift (< a few percent) in feather resonant frequencies in the frequency range considered in this study when samples were mounted on rigid wooden blocks vs. embedded in a compliant 266 gel to mimic the shaft's native soft tissue environment. Further supporting this method, we found good agreement between train-rattling display shaking frequencies and the value predicted 268 PREPRINT VERSION 13 from a model of the peacock tail's resonant frequency based on laboratory measurements [20]; in addition, an earlier study of manakin feather resonance that used similar mounting methods 270 found good agreement between the frequencies of feather vibrational resonance measured in the laboratory and sonations recorded in the field [66]. 272 Because interactions between feathers can influence their resonant frequency and damping 274 [66,68], we compared the biomechanics of whole crests to that of isolated crest feathers. To study individual, isolated crest feathers, we removed all but three to five feathers (on the outer 276 edges and in the middle) from two male crests and one female crest and analyzed the characteristics of those remaining feathers. Note that because this procedure was necessarily 278 destructive, it precluded any further whole-crest analyses on those samples, we limited it to only the three crests. Isolated body and crest feathers were inserted into a close-fitting hole in the 280 wood base using polyvinyl acetate glue. For measurements on other peafowl feathers and crest feathers from other species, all but two feather samples in S1 Table were inserted up to the top of 282 their calamus (the part of the shaft inserted into the skin). The Victoria crowned pigeon crest feathers had been trimmed just above the calamus, so they were mounted such that 3 mm of the 284 exposed feather shaft (3% of its length) was inserted into the wooden base.

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To ensure further that the feathers had the same mechanical properties as those found on live birds, we stored and tested all samples using environmental conditions similar to those measured in the field at a median temperature of 19.4ºC and a median relative humidity of 60.7% [20], with over half of the displays occurring within ±2.2ºC and ±14% of the average laboratory 294 temperature and relative humidity, respectively. Moreover, a re-analysis of previous published data on 35 peacock displays performed by 12 males in the field [20] shows that there is no 296 significant association between display vibration frequency and relative humidity (p > 0. 45) when accounting for the date and time of the displays. This analysis and the associated data are 298 provided in the data repository for this study [70]. As an additional check, we also measured the audio playback response with crest samples held at 35% relative humidity and 22 Cº for 1 min to 300 10 min and found no measurable change in the natural frequency over this time.

Ethics statement
All research procedures were approved by the Haverford College Institutional Animal Care and 304 Use Committee (protocol #sak_050916).

Vibrational dynamics measurements
To determine the vibrational resonant frequency of each feather sample, and its relationship to 308 possible driving mechanisms during displays, we applied a sinusoidal force to the sample while measuring its resulting vibrational amplitude as a function of the driving force's frequency. The This apparatus applied sinusoidal forces with a linearly varying frequency ("frequency sweeps") while high-speed video was used to measure the 316 amplitude and frequency of vibration of both the driving mechanism and the feather sample (details on the frequency sweep parameters and video methods are discussed below). The 318 driving force was applied in two orthogonal directions ( Fig 1D): 1) "out-of-plane" (oriented normal to the plane of the crest), corresponding to the geometry when a peafowl views a display 320 with its laterally-oriented visual field, or drives its own crest into vibrations by performing a train-or tail-rattling display [20]; and 2) "in-plane" (oriented parallel to the plane of the crest, in 322 the posterior-anterior axis of the head), corresponding to the geometry when the front of the head is oriented towards the display. 324 The resulting vibrational response spectra of the crests were measured using three linear 326 frequency sweeps. One of these sweeps used the frequency range (0-80 Hz) to include all peaks in the spectral response found for peacock tail and trail feathers in an earlier study [20]; the rate 328 of frequency increase (1.33 Hz/s) was chosen to be less than the values measured at the start of peafowl displays in the same study. These conditions were used to test the vibrational response 330 in the out-of-plane direction for each of the 15 peafowl crests, as well as three of the crests that had been trimmed down to have only three to five isolated crest feathers remaining (n = 3 trials 332 for each sample); this allowed us to compare the vibrational response of intact crests with that of isolated crest feathers. We ran the following additional trials to make sure that this combination 334 of frequency range and sweep rate above did not miss any spectra peaks or affect the shapes of the resonant peaks: six crests out-of-plane at 10-120 Hz (1.83 Hz/s; n = 18 trials), six crests out-336 of-plane at 0-15 Hz (0.25 Hz/s, n = 6 trials), five crests in-plane at the 0-80 Hz range (1.33 Hz/s; PREPRINT VERSION 16 n = 14 trials), and two crests in-plane at 10-120 Hz (1.83 Hz/s; n = 2 trials). For one crest, we 338 determined that varying the amplitude of shaking by a factor of four resulted in the same resonant response within measurement error. 340 We also measured the resonant vibrational response of crest feathers for several other types of 342 short peacock feathers (three lengths of peacock mantle feathers, the shortest length of train eyespot feather, and four different body contour feathers), and for one or more crest feathers 344 from four other bird species: two additional species from order Galliformes, the Himalayan monal (Lophophorus impejanus) and the golden pheasant (Chrysolophus pictus); the Victoria 346 crowned pigeon (Goura Victoria) from the order Columbiformes, and the yellow-crested cockatoo (Cacatua sulphurea) from the order Psittaciformes; see S1 Table and  The resonant response for each of these feathers was measured for driving forces in the out-ofplane direction for n = 3 trials for each feather at each of two frequency sweep rates (2.0 Hz/s, 0 350 to 120 Hz; 1.33 Hz/s, 0 to 80 Hz); the Himalayan monal sample was also studied using a sweep rate of 0.5 Hz/s over 0 to 30 Hz because it had a lower frequency response. to reproduce this analysis are available with the data repository for this study [70]. The Nyquist frequency, which gives the upper bound on measurable frequencies [79], was 120 Hz (half the 362 frame capture rate) (> 4× typical biological vibration frequencies used during peafowl displays).
Images were first corrected for lens distortion using the MATLAB Camera Calibration tool. All magnitude, Ad, at each drive frequency, fd , and smoothed the ratio over a 1.3 Hz window using a cubic Savitzky-Golay filter to give the drive transfer function, H(fd) = A/Ad [71,66]. Nonlinear 376 least squares fitting using Origin 8.6 (Originlab, Northampton MA USA) was used to fit each peak in the transfer function, to a Lorentzian spectral response: 378 where the fit parameters are fr , the resonant frequency, and Δf , the full-width-half-maximum of 380 the spectral power; this yielded mean and s.e.m. estimates for the fit parameters as well as the quality factor, Q = fr /Δf , a measure of how sharply the transfer function is peaked about the 382

Force impulse experiments
A second standard method for determining the vibrational response of a system involves 386 applying a transient impulsive force and then measuring the system's subsequent vibrational response to measure its natural frequency of vibration, fo, and the exponential decay in time of its 388 vibrational amplitude [71,82,72,75,76]; this is analogous to striking a bell and recording how it rings at a well-defined frequency as its sound intensity decays in time. This method is also 390 relevant for determining the response of the crest to impulsive airflows due to each flap of the wing during wing-shaking. Thirdly, it also serves as a check on the validity of the vibrational 392 response frequency sweep methods described above, because the natural and resonant frequency should be related as [79]: 394 This prediction can be tested by comparing the natural frequency measured directly from the 396 force impulse method with the value computed from the vibrational response's transfer function using Eq 1 and 2. 398 To determine the peafowl crests' response to impulsive airflows, we impacted crests with single widest cross-section facing the source at 0.5 m from the point of creation. As explained above, because we expected such impulses to result in the crest feathers oscillating at their natural 408 frequency, this provided an additional check on our resonant frequency values. This also provides a model for understanding how crest feathers would respond to impulsive airflows 410 generated by other sources (e.g., displays, wind, etc.).

Audio playback experiments and analysis
To determine if peafowl crests can vibrate detectably due to peacock train-rattling, we filmed 414 high-speed video of peahen crest samples placed in the flow near-field of a loudspeaker playing back train-rattling sounds. Note that because peacock train-rattling consists of broad-band rattles 416 at low repetition rates, not pure tones, we used audio equipment rated for frequencies 20 Hz to 20 kHz rather than equipment designed for infrasound, similar to how one would treat the sound 418 of hands clapping or birds calling at a repetition rate of a few Hz. To generate audio playback sequences, we used audio field recordings (24-bit, 44.1 kHz, no filtering) of peacock train-420 rattling displays made using a PMD661 recorder (±1 dB: 20 Hz to 24 kHz; Marantz, New York, NY, USA) and a ME-62 omnidirectional microphone (±2.5 dB: 20 Hz to 20 kHz; Sennheiser, 422 Wedemark, Germany), as described in a previous study [20]. Three playback sequences were used (each using sound from a different peacock), with mean rattle repetition rates of 26.7 ± 0.5 424 Hz; 25.3 ± 0.5 Hz; and 24.6 ± 0.5 Hz. Recordings of train-rattling in the field indicated that rattles are in-phase (i.e., temporally coherent) over bouts approximately 1.2 s duration that are 426 repeated for several minutes during displays [18,20]. We spliced together bouts with an integer number of rattling periods to form a longer audio playback file with a total duration of 428 approximately 5 min.

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All sound files were played back on a Lenovo Thinkpad T460S computer connected to a 402-VLZ4 mixer (Mackie; preamplifier; < 0.0007% distortion 20 Hz to 50 kHz) and a ROKIT 10-3 432 G3 10" powered studio monitor (KRK Systems, Fort Lauderdale, Florida, USA; ± 2.5 dB over to 40 Hz to 20kHz, -10 dB at 25 Hz relative to ≥ 40 Hz) with a 25.4 cm diameter subwoofer (A = 434 12.7 cm). Following [83], we examined re-recordings of the playback stimuli made with the same microphone and recorder used for the original field audio recordings, and found that the 436 resulting waveforms and spectrograms (e.g., S2 Fig) had the same temporal features ("rattle" notes) as the original field recordings of train-rattling (e.g., Fig 4A in [20]). 438 As a control, we played back a Gaussian white noise file generated using MATLAB's imnoise 440 command (5 min. duration, 24-bit, 44100 Hz, FFT amplitude flat from < 1 Hz to 22,000 Hz computed using a rectangular window to preserve Fourier amplitudes). The white noise 442 playback assessed whether the crest samples could be driven to vibrate measurably by a broadband signal similar to the train-rattles, but lacking the low-frequency amplitude modulation 444 of the train-rattling recording at the "rattle" repetition rate. The root-mean-squared (rms) amplitudes of all playback recordings and the white noise control were scaled to the same value 446 while also ensuring that no clipping occurred at high amplitude.

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For playback experiments, the preamplifier volume controls of the mixer were adjusted so that the mean playback SPL was 88 ± 1 dB at 3 m as measured by a Type 2 model R8050 sound level 450 meter (accuracy ±1.4 dB, C-weighting, 30-100 dB, slow 1.0 s setting; Reed Instruments, Wilmington, NC USA). For comparison, previously-reported values for peacock train-rattling 452 mechanical sounds corrected for background noise were given as 67 to 77 dB at R = 3 m (unweighted SPL) [19], similar to audible bird wingbeat SPL summarized in S2 Table. Based on 454 the frequency response specifications for our microphone and playback system, we estimated their combined response at 26 Hz to be reduced by 12.5 dB compared to the audible range; the 456 increase in playback SPL relative to the reported values accommodates for this attenuation.
During playbacks, the background noise with no audio was 58 ± 1 dB SPL. 458 Another consequence of the broadband nature of train-rattling is that rapid intensity variations 460 due to interference at small R (the "interference near-field") should not be relevant for this display, because this effect depends on the superposition of sound waves with a well-defined 462 frequency emitted by different parts of an extended source. The predicted interference near-field regime is = 0.7 cm for 26 Hz [32]. Consistent with this expectation, we found no 464 variation due to interference when we measured SPL at nine different positions across the subwoofer speaker between the center and edges, at distances perpendicular to the speaker 466 between 12.7 cm to 0.5 m. High-speed videos from a previous study were used to determine the frequency and amplitude of wing motions during the peacock's wing-shaking display [20]. We used four videos filmed with 494 the wingtip motion closely aligned with the image plane (see S1 Movie) that also showed tail feathers with known lengths. The amplitude of wing-shaking motion was defined by the mean 496 diameter of motion circumscribed by the tips of the partly-unfurled wings during this display, which we estimated to be 7.6 cm on average (range 5.5 to 10 cm). To simulate the wing motions 498 observed in displaying peacocks and the resulting air motions, we used a robotic mechanism that caused an entire peacock wing to flap with the wing plane held in a fixed vertical orientation 500 while the wingtip circumscribed a circle (S1 Movie and S3 Fig). The peacock wing was mounted on a carbon fiber rod using a balsa wood base that was attached to the wing via 502 adhesive at the shoulder; this rod pivoted about a clevis joint, which allowed the wing axis to move in a vertical circle while the wingspan remained in the vertical plane. At the end opposite 504 the wing, the rod was attached to a circular crank by a universal joint. The crank and attached wing assembly was driven at 4.95 ± 0.05 Hz by a DC motor. To account for the fact that actual 506 wing-shaking involves motion of two wings toward each other, which presumably displaces more air than a single wing, this apparatus used a single flapping wing moving in a slightly 508 larger diameter (14 cm) circle at the wingtips. feather crest samples (Crests 08, 12, and 13) were positioned using a tripod at the vertical midline of the wing located at various distances from the wing-tips. The resulting motion of the 520 crests was then filmed using high-speed video as described above in "Video analysis" to quantify PREPRINT VERSION 24 the vibrational response of the three peahen crests. To verify that substrate vibrations did not 522 drive the crest motion, we also performed a control by inserting a 3 x 4 ft foamboard in between the crest and wing to block the airflow from the wing motion; this reduced the root-mean-524 squared crest motion to 14% of its value with wing motion-induced airflow present. For comparison with the wing-shaking frequency during displays, flapping frequencies during 526 ascending and level flight were also measured for 9 peacocks from 6 online videos (S3 Table).

Force measurements
Peacock feather keratin, like other biopolymers, can have a nonlinear elastic response to external 530 stresses [86]. Because the stimuli in the mechanical shaker, audio playback and wing-shaking experiments each exerted different forces and these forces may have had greater magnitudes than 532 those encountered in the field, we wanted to understand how to extrapolate from our laboratory experiments to a lower force regime that is potentially more biologically relevant. Consequently, 534 we measured the elastic mechanical response of peafowl crests to an external bending force applied to the flags of the crest. We studied the static mechanical response of peafowl crests in 536 the single cantilever bending geometry by measuring the relationship between flag displacement and restoring force of the crest in the out-of-plane orientation (Fig 1D). . We first verified that trial order and frequency sweep rate, two aspects of the experimental design, did not have significant effects on either fr or Q (all p > 0.28). 558 The next step was to evaluate the potential effects of morphological traits that could influence crest resonance (some of which could be weakly correlated in a much larger study; see [17]). 560 Because our sample size was only 15 crests, but we had five morphological traits, our statistical power was only sufficient to consider models with only one morphological trait predictor at a 562 time: length, width, number of feathers, percent of unaligned feathers, and percent of short feathers. These morphological traits were fitted as fixed effect predictors. All models also 564 included fixed effects of sex as well as the vibration orientation (either in-plane, or out-of-plane).
We used AICc to select the best-fit model [89] and evaluated significance of the fixed effects 566 using Wald tests. We report R 2 LMM(m) as a measure of the total variance explained by the fixed PREPRINT VERSION 26 effects [90,89]. We also used the variance components of the best-fit model to calculate the 568 adjusted repeatability, defined as the variance attributed to differences among crests after adjusting for variation explained by the fixed effects [91]. Inspection of the data and model 570 residuals revealed that variance in fr differed among crests, so when modelling fr, we fit a heteroskedastic model that had its standard errors adjusted to account for the appropriate within-572 group error variance, by using the varIdent option in the weights argument in nlme [87].

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A microscopic examination of peafowl crest feathers reveals that their shafts have associated feathers with the structure of filoplumes at the base (Fig 1E) that agree in location and 578 morphology with those shown in micrographs of filoplumes cited earlier in the Methods. These were structurally distinct from immature crest feathers, which also retained a sheath until they 580 had grown to a length much greater than that of the filoplumes. female crests, and 6.1 [5.3, 6.9] cm for the male crests. These width values were approximately 20% (female) to 27% (male) smaller than those found on live birds (Fig 2). This difference 588 could be due to the crest ornament being spread 1-2 cm more in the sagittal plane by muscle PREPRINT VERSION 27 action in the live bird, as observed for erectile crest plumage in many other species [13], in 590 addition to the effect of skin drying. samples had all feathers oriented in the same plane within ±5º; five of the crests had 7-11% of the feathers unaligned, and two male crests had 22% and 50% unaligned feathers, respectively. 608 We also studied the morphology of individual peafowl crest feathers to understand their unusual 610 structure (Fig 1C). The average rachis tapered evenly over its 39.90 [38.89, 40. Lorentzian (mean adjusted-R 2 = 0.97; range [0.91, 0.998]) (Eq 1) predicted for a cantilever [92], indicating that the system responded in the linear regime for our shaker amplitudes and 622 frequency sweep rates (Fig 3A). The value of fr ± Δf /2 defines the approximate range of drive frequencies over which power is efficiently coupled into the oscillator. Fig 3B shows that  624 shaking frequencies measured in the field for displaying male and female peafowl [20] lay within fr ± Δf/2 of the crest resonant frequency for both sexes (n = 8 female crests and 7 male crests). 626 When the shaking force was oriented out-of-plane, the mean crest resonant frequency, fr, was 28  vibrations in the out-of-plane orientation for peafowl crest and non-crest feathers with similar lengths and crest feathers from four non-peafowl species described in S1 Table and S1 Fig.  646 Means for male and female peafowl crests are both plotted. The y-axis of (C) is aligned with that of (B) for comparison. (D) The mean quality factor, Q, was also influenced by the 648 vibrational orientation, and was associated with the sex of the bird and the area of pennaceous flags. The average 95% CI for each mean Q estimate spanned 0.233. Black horizontal lines in 650 (B) and (D) are grand means.

652
The repeatability of fr for whole crests was very high at 92% (95% confidence interval, 87-94%), demonstrating strong and consistent differences among individual crests (Fig 3B). Analysis of 654 the sources of variation in fr indicated that 28% of the total variation in fr could be explained by sex, crest orientation, and the total area of the pennaceous flags (Fig 3B; see S5 Table for the 656 best-fit model). The effect of crest orientation was strong and significant, such that out-of-plane vibrations have fr values approximately 2.4 Hz higher on average (p < 0.0001), whereas the sex 658 difference was not significant (p = 0.86) and crests with reduced flag area have a slight but nonsignificant tendency to have higher fr values (p = 0.10). Crest length, width, number of feathers, 660 and the percent of unaligned and short feathers did not explain variation among crests in the value of fr. The frequency response of individual crest feathers was generally consistent with 662 that of the whole/intact crests, as the resonant frequencies of these feathers in the out-of-plane orientation ranged from 19.2 Hz to 32.4 Hz (Fig 3B). when the dependence of frequency on rachis length is taken into account.

678
The repeatability of Q was estimated at 47% (95% confidence interval, 17-55%), indicating moderate differences among crests in Q. Approximately 49% of the variation in crest Q could be 680 explained by sex, crest orientation, and the total area of the pennaceous flags (Fig 3D, Table). Male crests were significantly more sharply-tuned than those of females (p < 0.005), 682 and crests that had less flag area tended to be more sharply-tuned (p = 0.04). Peafowl crests also have more sharply-tuned resonance when they are vibrated out-of-plane (p < 0.0001) as 684 compared to the in-plane orientation.

686
Note that the complete analysis of vibration data can be reproduced using data and code available at: https://doi.org/10.6084/m9.figshare.5451379.v5 [70]. 688 agreed to ≤ ± 0.4 Δf of the value of fo predicted by Eq 2 using values of resonant frequency, fr, and Q measured using sinusoidal forces and frequency sweeps (Fig 4B). Thus, vortices cause 696 the feather crest to vibrate at its natural frequency, with a decrease in amplitude of 13% after 0.2 s, the approximate period of peafowl wing-shaking displays. 698 for the vibrational response of a peahen crest sample during audio playback is shown in Fig 5B. For train-rattling audio playback experiments in which the peahen crest samples were located in 712 the flow near-field of the speaker, the vibrational power spectra of the samples had a peak well above noise near the playback train-rattling repetition rate (the effective drive frequency). 714

Force impulse experiments
However, when the white noise recording was played back, the spectral power near the drive frequency was < 4.3% of that found during playbacks. The peak frequency of crest vibrations 716 agreed with the playback train-rattling repetition rate to within 95% CI for all measurements but one, for which it lay within 2.5 s.e.m. Measurements of crest vibrations made with an acoustic 718 foam tile between the speaker and sample had < 11 % of the FFT spectral power at the drive frequency compared to measurements made without the foam; this value placed an upper bound 720 on the contribution of background sources (e.g., room reverberations, substrate vibrations, etc.) that were not associated with particle-velocity oscillations from the playback stimulus. 722

746
The average peacock wing-flapping frequency during ascending and level flight was 5.5 [5.0, 6.1] Hz (S3 Table). This frequency agrees with the average frequency of 5.4 Hz (range of 748 individual bird means = 4.5-6.8 Hz) found for wing-shaking display frequencies measured in the field [20].

Discussion
The fundamental vibrational resonant frequencies of peafowl crests were found to agree closely 762 with the frequencies used during male train-rattling and female tail-rattling displays in Fig 3B. By contrast, these display frequencies do not agree with the resonant frequencies found for 764 feathers of similar length from other parts of the peafowl's body, or with those found for the crest feathers of four other bird species in Fig 3C, which collectively span a frequency range that 766 is nearly seven times that of the observed range of rattling displays. This means that the close frequency match between peafowl displays and crest resonance is not due simply to species, type 768 of feather (i.e., crest vs. tail), or rachis length. This finding agrees with prediction P2 (Box 1) that crest feathers with a mechanosensory function would have a frequency response tuned to 770 match stimuli with a well-defined frequency.

35
Our results also indicate that both the resonant frequency and the Q factor of the peafowl crest's vibrational response should agree with those of the array of tail and train feathers that produce 774 the shaking display, which have been previously characterized in [20]. This implies that the peafowl's crest would be well-matched to the train's mechanical sound, but not to environmental 776 sources of noise [31]. In agreement with prediction P4 (Box 1), we also found that exposing peahen crest samples to the near-field of audio playbacks of train-rattling sounds caused the 778 crests to vibrate detectably on video at their resonant frequency (Fig 5B). By contrast, exposing crest samples to white noise resulted in no measurable vibrations above background noise levels. 780 We therefore hypothesize that this match of vibrational resonant properties might have functional significance during multimodal courtship displays that generate mechanical sound. 782 As found for live birds [17], the peafowl crest samples had relatively uniform lengths and 784 numbers of feathers (Fig 2). While our crest samples had slightly lower flag area than fully spread crests of living birds, we found that individual crest feathers had similar vibrational 786 responses to those of entire crests, indicating that interactions between crest feathers is not the main determinant of resonant frequency. This indicates that the results of our vibrational 788 dynamics experiments are also applicable to crests in vivo, on the live bird.

790
Peafowl crests do not have a resonant frequency near the 5.4 Hz rate of wing-shaking displays.
However, we still found that peafowl crests vibrated detectably in response to impulsive airflows 792 similar to those produced during wing-shaking (prediction P3; Box 1). By measuring the deflection of peafowl crests when they were struck by individual air ring vortices (Fig 4), we 794 found that each impulsive stimulus generated a distinct crest response in which the crest feathers briefly vibrated at their natural frequency, before decaying to zero in a time comparable to that of 796 the wing-shaking period. This result provided independent validation of the resonant frequency of crests, measured from the spectral responses in Fig 3. It also means that periodic but isolated 798 force impulses generated by the wing-shaking display are effectively experienced as distinct stimuli that cause the crest to oscillate only briefly near resonance, akin to an infrequently struck 800 bell. Further confirming this interpretation, we found that airflows due to simulated wingshaking at distances from the crest £ 90 cm drove measurable transient crest deflections (Fig 6), 802 similar to the minimum male-female distances in the field during such displays. The linearity of the measured elastic response also suggests that this result can be extrapolated to greater 804 distances. These findings imply that the airflow impulses generated by in vivo wing-shaking displays could stimulate the feather crests of nearby female by producing a series of distinct 806 vibrational responses.

808
Our measurements of vibrational responses during audio playback were limited to relatively large amplitudes and small distances compared to the very small thresholds found for other 810 mechanoreceptors in vivo, and consequently to relatively small source-receiver distances.
However, the low thresholds found for mechanosensation in vivo suggest that the actual 812 detection range could be much greater than our in vitro limits. For example, pigeons can detect submicron threshold vibrational amplitudes applied to flight feathers [93,94], mammalian hair 814 cells are sensitive to sub-nanometer displacements and 0.01 deg rotations [95], tactile receptors in human skin are sensitive to submicron vibrational amplitudes [96], and insect filiform hairs 816 are sensitive to airspeeds as low as 0.03 mm s −1 [97]. This idea also is supported by our measured linear elastic response of feather crests to bending (S4 Fig), which indicates that our 818 37 results can be extrapolated linearly to lower magnitude stimuli corresponding to larger sourcesample separation than those measured here during the audio playback experiments. Our 820 microscopy results confirmed that peafowl crest feathers have feathers at their bases with the morphology expected for filoplumes (prediction P1; Box 1). However, further histological and 822 electrophysiological studies of the receptors at the base of avian crest feathers and their associated filoplumes are needed to determine whether these crests can in fact function as 824 sensors that are sensitive to airborne stimuli like the ones studied here.

826
Given that feathers are known to function as airflow sensors during flight, it is easy to imagine how they also could be adapted to function as sensors during social signaling. For example, 828 during social displays, many birds flap or vibrate their wings or tails [66,67,98,99,20], producing dynamic visual stimuli as well as mechanical sound and periodic air flow stimuli. Thus, these 830 multimodal displays have the potential to stimulate multiple senses, including vision, hearing, and vibrotactile perception. Several non-exclusive scenarios could provide a functional benefit 832 of such a close frequency match. For example, we can hypothesize that air-borne stimuli generated by train-or tail vibrating or shaking displays provide females with an indication of 834 male muscle power and endurance, or that stimuli generated by wing-shaking displays serve as signals of flight muscle performance [99]. Another hypothesis is that male displays have been 836 selected to match and stimulate pre-existing mechanosensory properties of the female crest, without any benefits to females of this close match. Yet another hypothesis is that both males 838 and females experience crest vibrations driven by body oscillations due to their own train-and tail-rattling displays as a form of proprioception. Conversely, our measurements do not support 840 a visual display function for peafowl feather crest vibrations because the resulting amplitudes of a few mm at most are unresolvable given limitations due to the peafowl's visual acuity [20]. 842 Although we have demonstrated here that peafowl crest feathers are effectively stimulated by 844 airborne stimuli during social displays, we do not yet know whether this has behavioral or social significance. Testing this hypothesis requires in vivo behavioral experiments. Crest vibrations 846 are challenging to measure directly, given that both sexes move frequently during displays and are viewed against complex visual backgrounds. Instead, a first step in peafowl could be to 848 blindfold females and test whether airborne stimuli at the socially salient frequencies elicit a behavioral response. Further experiments could test the function of the crest during male 850 courtship displays by removing or altering the female crest and then examining how females respond to male displays. One way to do this would be to apply a thin coat of clear varnish to 852 the rachis of the crest feathers; this would stiffen the rachis and increase resonant frequency without affecting the crest's visual appearance (i.e., size or flag iridescence). Similar 854 manipulations could also test whether peacocks use proprioception from the crest to modulate their own vibration displays. The movement of females during displays could also be examined 856 in relation to the airflow patterns generated by wing-shaking peacocks, to test whether female movements are correlated with specific airflows generated by the males. These correlative 858 results could then be tested experimentally by measuring the behavioral response of peahens to oscillatory air flows modulated at frequencies close to and distinct from their crest resonance, to

872
Thus far, the elaborate shape, size and color of many bird feather crests has led to an emphasis on their visual appearance [14]. However, many avian courtship displays also involve wing-874 shaking, tail-fanning and mechanical sound production that may be detected by nearby females in the vibrotactile channel. For example, we have compiled a list of at least 35 species 876 distributed in 10 avian orders that have crests and perform these types of displays (S6 Table).
Given the growing interest in multisensory signaling, it seems worth pursuing behavioral studies 878 to investigate whether mechanosensory stimulation enhances the reception of visual and acoustic cues during this multimodal display. The close match between the resonant frequencies found 880 here for peafowl crests and this species' social displays suggest that it is time to explore the hypothesis that birds receive and respond to vibrotactile cues in a wider variety of scenarios. Crests (n = 8 female, n = 7 male) measured in vivo (means shown to the right of each data column) had similar morphology to the dried samples, except that the crests on live birds tended to be wider. Dried sample dimensions were measured to the nearest 0.1 cm. Each crest sample is indicated by a unique symbol-color combination consistent with other figures (see S4 Table for details). The mean resonant frequencies, fr, of the crest are a close match for the range of vibrational frequencies used during peafowl social displays. As an indication of measurement error, the average 95% CI for each mean fr estimate spans 0.072 Hz. The gray shaded area is the range of vibrational frequencies of the train-rattling display, with dotted lines showing the means for displays performed by peacocks (blue) and peahens (green) [20]. Variation in fr was influenced by the vibrational orientation and was also associated with the sex of the bird, but there was no significant association with the area of pennaceous flags at the top of the crest. The first panel in (B) also shows how a small sample of single crest feathers (n = 3 from male Crest 03, n = 5 from male Crest 05, and n = 3 from female Crest 10) had a similar range of resonant frequencies as the whole crests vibrated in the same out-of-plane orientation. (C) Fundamental frequency for vibrations in the out-of-plane orientation for peafowl crest and non-crest feathers with similar lengths and crest feathers from four non-peafowl species described in S1 Table and S1 Fig. Means for male and female peafowl crests are both plotted. The y-axis of (C) is aligned with that of (B) for comparison. (D) The mean quality factor, Q, was also influenced by the vibrational orientation, and was associated with the sex of the bird and the area of pennaceous flags. The average 95% CI for each mean Q estimate spanned 0.233. Black horizontal lines in (B) and (D) are grand means. When peafowl crests were impacted by such air ring vortices, they deflected measurably, oscillating at their resonant frequency with an amplitude that decayed to a few percent of the initial value over the period of the peacock's wing-shaking display. (B) Mean resonant frequencies (fr) and mean vortex response frequencies (± 95% CI) for three crests in the vortex experiment. Vibrational response of a female peahen crest (Crest 13) exposed to airflow from a robot that simulated 5.0 Hz peacock wing-shaking displays at a distance 50 cm from the moving wingtip (see also S3 Fig). Note that the FFT spectral power (y-axis) is plotted on a linear scale.