Biomechanics of the Peacock’s Display: How Feather Structure and Resonance Influence Multimodal Signaling

The train-rattling display attracts the peahen's visual attention.

“This “train-rattling” display attracts the peahen’s visual attention [15]”

• cites [15] JL Yorzinski, 2013, Through their eyes: selective attention in peahens during courtship, Journal of Experimental Biology sourceSupported

Different feathers within the train should have resonant frequencies that vary by more than an order of magnitude because eyespot feathers vary in length by an order of magnitude.

“The eyespot feathers in the train also vary in length by an order of magnitude, so cantilever beam theory predicts that different feathers within the train should have resonant frequencies that vary by more than an order of magnitude [21, 25].”

• cites [21] WF Smith, 2010Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [25] MA Neimark, 2003, Vibrissa resonance as a transduction mechanism for tactile encoding, Journal of Neuroscience sourcePartly supported

  The 'Model of the vibrissa as a thin elastic beam' section gives a resonance-frequency model that scales with base radius divided by length squared; 'Prediction 3' reports that this relationship fit rat vibrissae. This supports the length-based reasoning, but the paper does not examine eyespot feathers or establish that their resonant frequencies vary by more than an order of magnitude. Its model also depends on properties besides length. (LLM, conf=0.85)

  Experimental — accuracy not yet measured

Train-rattling always precedes copulation.

“and always precedes copulation [14].”

• Also stated in: § 4. Discussion · plain

  “Given that train-rattling always precedes copulation, and attracts a peahen’s gaze [15]”

• cites [14] R Dakin, 2009, Peacocks orient their courtship displays towards the sun, Behavioral Ecology and Sociobiology sourceNot checked — no full text of the source
• cites [15] JL Yorzinski, 2013, Through their eyes: selective attention in peahens during courtship, Journal of Experimental Biology sourcePartly supported

  The Introduction (page unavailable) describes train-rattling as part of the courtship sequence and says females may then choose to mate. It does not establish that train-rattling always precedes copulation; the Results and Discussion (page unavailable) report copulations but do not link every one to a preceding rattle. (LLM, conf=0.82)

  Experimental — accuracy not yet measured

The vibration frequency of other behaviors such as shivering and shaking dry scales negatively with body mass across species.

“The vibration frequency of other behaviors, such as shivering and shaking dry, scales negatively with body mass across species [17–20].”

• cites [17] AK Dickerson, 2012, Wet mammals shake at tuned frequencies to dry, Journal of the Royal Society Interface sourceSupported
• cites [18] D Kleinebeckel, 1990, Thermoregulation: physiology and biochemistryNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [19] VM Ortega-Jimenez, 2012, Aerial shaking performance of wet Anna's hummingbirds, Journal of the Royal Society Interface sourcePartly supported

  The Introduction reports that wet-shaking frequency varies inversely with shoulder width across terrestrial mammals, supporting the direction of the shaking-dry relationship. It does not establish scaling with body mass or address shivering frequency. (LLM, conf=0.87)

  Experimental — accuracy not yet measured
• cites [20] T Iwata, 2013, Detection of grooming behaviours with an acceleration data logger in a captive northern fur seal, Aquatic Mammals sourceNot checked — no full text of the source

SEM imaging revealed barbule ultrastructures that lock together the eyespot barbs, similar to those found on flight primaries and contour feathers in other bird species.

“SEM imaging also revealed barbule ultrastructures that lock together the eyespot barbs (Fig 8F and 8G), similar to those found on flight primaries and contour feathers in other bird species [44].”

• cites [44] A Kovalev, 2014, Unzipping bird feathers, Journal of the Royal Society Interface sourcePartly supported

  The Introduction describes SEM-visible hooklets on barbules of typical contour feathers in most birds and explains how they anchor neighbouring barbs. This supports the comparison to interlocking structures in other birds, but our copy does not specifically identify flight primaries. The eyespot observation is the citing authors’ own finding, not a finding attributed to this source. (LLM, conf=0.86)

  Experimental — accuracy not yet measured

Train-rattling attracts a peahen's gaze.

“Given that train-rattling always precedes copulation, and attracts a peahen’s gaze [15]”

• cites [15] JL Yorzinski, 2013, Through their eyes: selective attention in peahens during courtship, Journal of Experimental Biology sourceSupported

Peahens should be able to visually resolve the iridescence of the loose barbs moving at 20-30 Hz, given that all bird species studied to date can resolve flicker at much higher rates.

“peahens should be able to visually resolve the iridescence of the loose barbs moving at 20–30 Hz, given that all bird species studied to date can resolve flicker at much higher rates [45].”

• cites [45] K Healy, 2013, Metabolic rate and body size are linked with perception of temporal information, Animal Behaviour sourcePartly supported

  The Methods (Data Collection; page unavailable) describe flicker-fusion measurements in birds, including behavioural tests in domestic chickens, so the paper supports the general premise that avian temporal resolution has been studied. The retrieved passages do not establish that every bird species studied resolves flicker well above 20–30 Hz, or that peahens can resolve the iridescence of moving barbs. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

The feathers that manakins use to sonate have Q > 10.

“whereas the feathers that manakins (family Pipridae) use to sonate have Q > 10 [27].”

• cites [27] KS Bostwick, 2010, Resonating feathers produce courtship song, Proceedings of the Royal Society B-Biological Sciences sourceSupported

The position dependence of bending stiffness in the lateral direction for the eyespot feathers is similar to that found for flight and tail feathers in other bird species.

“The position dependence of bending stiffness in the lateral direction for the eyespot feathers (as shown by I in Fig 8D) is similar to that found for flight and tail feathers in other bird species [38, 43].”

• cites [38] T Bachmann, 2012, Flexural stiffness of feather shafts: geometry rules over material properties, Journal of Experimental Biology sourceNot checked — no full text of the source
• cites [43] A Schmitz, 2015, Morphological properties of the last primaries, the tail feathers, and the alulae of <italic>Accipiter nisus</italic>, <italic>Columba livia</italic>, <italic>Falco peregrinus</italic>, and <italic>Falco tinnunculus</italic>, Journal of Morphology sourceSupported

The motion of feathers during train-rattling is just as expected for feathers shaking near resonance.

“and the motion of feathers is just as expected for feathers shaking near resonance.”

• AssumptionRests on an assumption: Feathers obtained from commercial sources and zoos are representative of feathers used by wild displaying peacocks.
• AssumptionRests on an assumption: Low-amplitude horizontal vibrations in the lateral plane adequately mimic the feather vibrations during train-rattling.

The mechanical structure of the train feathers affects the peacock's visual display by allowing the colorful iridescent eyespots to remain nearly stationary against a dynamic iridescent background.

“Finally, we demonstrate how the mechanical structure of the train feathers affects the peacock’s visual display by allowing the colorful iridescent eyespots–which strongly influence female mate choice–to remain nearly stationary against a dynamic iridescent background.”

• AssumptionRests on an assumption: Feathers obtained from commercial sources and zoos are representative of feathers used by wild displaying peacocks.
• AssumptionRests on an assumption: Low-amplitude horizontal vibrations in the lateral plane adequately mimic the feather vibrations during train-rattling.

The train-rattling and train-shivering vibrations of interest occur in the plane of the eyespot and loose barbs.

“the train-rattling and train-shivering vibrations of interest occur in the plane of the eyespot and loose barbs.”

• AssumptionRests on an assumption: The feral peafowl population in Arcadia, California is representative of Indian peafowl for train-rattling biomechanics.

Arrays of peacock tail and train feathers have a broad resonant peak in their vibrational spectra at the range of frequencies used for train-rattling during the display.

“Laboratory measurements demonstrate that arrays of peacock tail and train feathers have a broad resonant peak in their vibrational spectra at the range of frequencies used for train-rattling during the display”

• AssumptionRests on an assumption: Feathers obtained from commercial sources and zoos are representative of feathers used by wild displaying peacocks.
• AssumptionRests on an assumption: Low-amplitude horizontal vibrations in the lateral plane adequately mimic the feather vibrations during train-rattling.

At the beginning of the display, train-rattling frequency increases exponentially to a maximum with an initial rate of 43 Hz s-1 ± 10 Hz s-1 and a time constant of 0.8 s (95% CI 0.4, 1.2).

“These frequency sweep parameters were chosen based on analysis of data from field videos indicating that at the beginning of the display the train-rattling frequency increases exponentially to a maximum (initial rate = 43 Hz s-1 ± 10 Hz s-1 measurement precision; time constant = 0.8 s [95% CI: 0.4, 1.2]).”

• AssumptionRests on an assumption: The feral peafowl population in Arcadia, California is representative of Indian peafowl for train-rattling biomechanics.

Peacocks with longer trains use slightly higher vibration frequencies on average.

“Using our field data, we show that peacocks with longer trains use slightly higher vibration frequencies on average”

• AssumptionRests on an assumption: The feral peafowl population in Arcadia, California is representative of Indian peafowl for train-rattling biomechanics.

In field videos, train and tail feathers were observed to vibrate primarily in the lateral plane parallel to the barbs.

“In the field videos, train and tail feathers were observed to vibrate primarily in the lateral plane (parallel to the barbs)”

• AssumptionRests on an assumption: The feral peafowl population in Arcadia, California is representative of Indian peafowl for train-rattling biomechanics.

The rattle sound repetition rate is the same as the average feather vibration frequency measured in field videos.

“the same as the average feather vibration frequency measured in the field videos.”

Spectral peaks for single feathers were well approximated by the Lorentzian functional forms predicted for elongated structures oscillating in a single plane.

“Spectral peaks for single feathers were well approximated by the Lorentzian functional forms predicted for elongated structures oscillating in a single plane”

Adding mass at the end of a long eyespot feather did not affect its resonant frequencies.

“but did not affect its resonant frequencies.”

The rattle sounds recorded in the field during the train-rattling display consist of short, broadband pulses.

“The rattle sounds recorded in the field during the train-rattling display consist of short, broadband pulses (Fig 4A)”

Higher order vibrational modes of the rectrix array were substantially damped.

“Higher order vibrational modes of the rectrix array were also substantially damped.”

Audio recordings made when the rectrix array was shaken at 25.6 Hz in the laboratory produced spectrograms with broadband frequency ranges and pulse durations similar to those of actual train-rattling spectrograms recorded in the field.

“Second, audio recordings made when the rectrix array was shaken at 25.6 Hz in the laboratory (Fig 4B) produced spectrograms with broadband frequency ranges and pulse durations that were similar to those of actual train-rattling spectrograms recorded in the field.”

When single eyespot feathers were shaken at their k = 1 normal mode frequency, the eyespots moved freely.

“When single eyespot feathers were shaken at their k = 1 normal mode frequency, the eyespots moved freely”

All but the shortest feathers in the train array had a k = 1 peak at 1.2 Hz.

“All but the shortest feathers in the train array had the same peaks in their vibrational spectra: a k = 1 peak at 1.2 Hz”

The scaling with length predicted by Eq 3 agrees well with that of measured resonant frequencies for eyespot feathers with LR ≥ 66 to 80 cm.

“The scaling with length predicted by Eq 3 (Fig 6B) agrees well with that of measured resonant frequencies for eyespot feathers with LR ≥ 66 to 80 cm.”

A male's train-rattling vibration frequency decreased after it reached peak amplitude during a train-rattling bout.

“A male’s train-rattling vibration frequency decreased slightly with advancing date during the mating season, increased later in the day, and decreased after it reached peak amplitude during a train-rattling bout (Table 2; Fig 3B).”

Each resonant peak in the single feather spectrum was replaced by a slightly wider compound peak in the corresponding feather array spectrum.

“Each resonant peak in the single feather spectrum was replaced by a slightly wider compound peak in the corresponding feather array spectrum (Fig 5A and 5B).”

For eyespot feathers, the k = 1 to 4 normal modes had mean Qk ranging from 3.6-4.5 (± 0.4 SE).

“For the eyespot feathers, the k = 1 to 4 normal modes had mean Qk ranging from 3.6–4.5 (± 0.4 SE)”

The shape of the rachis in eyespot feathers varies with feather length, with LR/Davg ranging from 95 for LR = 14 cm to 293 for LR = 112 cm.

“the shape of the rachis in eyespot feathers varies with feather length such that LR/Davg ranges from 95 (LR = 14 cm) to 293 (LR = 112 cm)”

In each of 9 males performing train-shivering and train-rattling at a steady frequency, the feather motions corresponded to normal modes.

“we used the methods described in section 2.3 to determine the spatial pattern of vibrations for 9 males performing train-shivering and train-rattling at a steady frequency. In each case we determined that the feather motions corresponded to normal modes.”

Audio recordings had the highest amplitude directly behind the tail.

“First, audio recordings had the highest amplitude directly behind the tail (S3 Text).”

When peacocks performed train-shivering behavior, the rectrices oscillated in a pattern consistent with the k = 1 normal mode for all but a few of the longest feathers, which oscillated in the k = 2 mode.

“When peacocks performed train-shivering behavior (S3 Movie), the rectrices oscillated in a pattern consistent with the k = 1 normal mode for all but a few of the longest feathers, which oscillated in the k = 2 mode”

• Also stated in: § 3.6 Feather Vibrational Resonance · hedged

  “Again, this is consistent with our observations from the field videos.”

Train feathers also oscillated in normal modes during train-rattling.

“we were able to track the motion of antinodes and determined that train feathers also oscillated in normal modes during train-rattling.”

A male's train-rattling vibration frequency decreased slightly with advancing date during the mating season.

“A male’s train-rattling vibration frequency decreased slightly with advancing date during the mating season, increased later in the day, and decreased after it reached peak amplitude during a train-rattling bout (Table 2; Fig 3B).”

When single eyespot feathers were shaken at 25.6 Hz, the eyespots barely moved (≤ 6-9% of eyespot diameter).

“but when they were shaken at 25.6 Hz, the eyespots barely moved (≤ 6–9% of eyespot diameter; S4 Movie)”

For rectrices, the relation between fk and LR agreed with a power law (fk ∝ LR−b) where b = 1.7 [1.5, 1.9] for k = 2.

“For rectrices, the relation between fk and LR agreed with a power law (fk ∝ LR−b) where b = 2.2 [1.9, 2.5], 1.7 [1.5, 1.9], and 3.0 [2.8, 3.2] for k = 1, 2, and 3, respectively (Fig 6A; R2 > 0.99, 0.98, and 0.99; n = 8, 8, and 4 feathers, respectively).”

Adult peacocks with longer trains shook their feathers at slightly higher frequencies on average, such that a 43 cm difference in train length (116 to 159 cm) resulted in an increase of only 1.7 Hz [0.5, 2.8].

“Adult peacocks with longer trains shook their feathers at slightly higher frequencies on average (Table 2), such that a 43 cm difference in train length (116 to 159 cm) resulted in an increase of only 1.7 Hz [0.5, 2.8] (Fig 3B).”

The broad resonant peak at 21.9 Hz also agrees with the broad k = 3 spectral peak for the train array at ~27 Hz.

“and that also agrees with the broad k = 3 spectral peak for the train array at ~27 Hz (Fig 5E).”

For the rectrix array and the female tail covert array, the resonant frequencies of the k = 1 and 2 normal modes were similar to those of single feathers of the same length and type.

“For the rectrix array and the female tail covert array, the resonant frequencies of the k = 1 and 2 normal modes were similar to those of single feathers of the same length and type.”

The rattle sounds are repeated at a rate of 25.6 Hz [24.7, 26.5] (grand mean [95% CI], n = 30 recordings of 10 adult peacocks).

“repeated at a rate of 25.6 Hz [24.7, 26.5] (grand mean [95% CI], n = 30 recordings of 10 adult peacocks)”

During train-rattling displays, peacocks courted peahens by shaking their rectrices laterally against the erect train at a mean frequency of 25.6 Hz.

“During train-rattling displays, peacocks courted peahens by shaking their rectrices laterally (i.e., side to side) against the erect train at a mean frequency of 25.6 Hz (n = 14 displays by 14 adult peacocks; Table 1).”

For adult males, most (60%) of the variation in peak vibration frequency was due to differences among individuals.

“For adult males, most (60%) of the variation in peak vibration frequency was due to differences among individuals.”

Eyespots on the longest feathers at the sides of the train had a maximum lateral displacement of 1.1 mm [0.9, 1.3] during train-rattling.

“and the eyespots on the longest feathers at the sides of the train had a maximum lateral displacement of 1.1 mm [0.9, 1.3] (grand means [95% CI], n = 18 eyespots from 6 males for each location).”

For eyespot feathers, each resonant frequency, fk, depended only weakly on feather length.

“By contrast, for eyespot feathers, each resonant frequency, fk, depended only weakly on feather length (Fig 6B).”

Adding mass at the end of a long eyespot feather reduced its motion.

“Fig 5F shows that adding mass at the end of a long eyespot feather reduced its motion”

From Fig 6A, the train-rattling frequency is closest to the resonant frequency for the k = 1, 2 and 3 modes of the shortest, medium and longest rectrices, respectively.

“From Fig 6A, we see that the train-rattling frequency is closest to the resonant frequency for the k = 1, 2 and 3 modes of the shortest, medium and longest rectrices, respectively.”

• AssumptionRests on an assumption: For a given feather length and vibration frequency, the closest resonant frequency fk determines which normal mode pattern (k) is excited by the vibration.

The second peak frequency in each model spectrum decreased with increasing tail length (slope -1.0 Hz cm-1 [-1.4, -0.6]).

“The first and second peak frequencies in each model spectrum decreased with increasing tail length (slopes of –0.32 Hz cm-1 [–0.39, –0.25] and –1.0 Hz cm-1 [–1.4, –0.6], respectively).”

The train array has its k = 1 peak at about 1.3-1.6 Hz.

“because the train array has its k = 1 peak at about 1.3–1.6 Hz; Fig 5E”

The eyespot is denser than the proximal parts of the feather for all but the shortest feathers.

“The eyespot is denser than the proximal parts of the feather for all but the shortest feathers.”

A male's train-rattling vibration frequency increased later in the day.

“A male’s train-rattling vibration frequency decreased slightly with advancing date during the mating season, increased later in the day, and decreased after it reached peak amplitude during a train-rattling bout (Table 2; Fig 3B).”

For rectrices, the relation between fk and LR agreed with a power law (fk ∝ LR−b) where b = 3.0 [2.8, 3.2] for k = 3.

“For rectrices, the relation between fk and LR agreed with a power law (fk ∝ LR−b) where b = 2.2 [1.9, 2.5], 1.7 [1.5, 1.9], and 3.0 [2.8, 3.2] for k = 1, 2, and 3, respectively (Fig 6A; R2 > 0.99, 0.98, and 0.99; n = 8, 8, and 4 feathers, respectively).”

During train-shivering, the longest train feathers oscillated in either the k = 3 or 4 normal modes.

“whereas the longest train feathers oscillated in either the k = 3 or 4 normal modes (e.g., Fig 1F).”

None of the model spectra for the tail had a peak below ~5 Hz.

“Finally, none of the model spectra for the tail had a peak below ~5 Hz (Fig 7)”

All but the shortest feathers in the train array had a broad k = 2 peak centered at ~6 Hz that extended into the frequency range of train-shivering (10.4 Hz).

“a broad k = 2 peak centered at ~6 Hz that extended into the frequency range of train-shivering (10.4 Hz)”

Other individual tail morphologies gave similar model spectra (n = 12 model power spectra, each based on tail morphology data from a different peacock).

“(note other individual tail morphologies gave similar model spectra; n = 12 model power spectra, each based tail morphology data from a different peacock).”

When linear density profiles and second moment of area of eyespot feather rachises are scaled to one at u = 0, rachises of different feather lengths have similar functional forms.

“they have similar functional forms for all feather lengths when the linear density profiles and the second moment of area of the rachis are scaled to have a value of one at u = 0 (Fig 8E).”

During train-rattling, a constant frequency is reached within 2.4 s [1.2, 3.6] of onset.

“with a constant frequency reached within 2.4 s [1.2, 3.6] of onset (n = 6 displays by 6 adult males).”

Eyespots near the center of the train moved during train-rattling with a maximum displacement of 1.7 mm [1.3, 2.1] in the lateral plane.

“The eyespots near the center of the train moved during train-rattling with a maximum displacement of 1.7 mm [1.3, 2.1] in the lateral plane”

Peacock wing-shaking and train-shivering frequencies are within the range of predicted values for an animal the mass of a peacock shaking dry.

“On the other hand, peacock wing-shaking and train-shivering frequencies (Table 1) are within the range of predicted values for an animal the mass of a peacock shaking dry (Fig 2).”

The nearby loose barbs are widely spaced and free to move as independent cantilevers.

“By contrast, the nearby loose barbs are widely spaced and free to move as independent cantilevers.”

During train-rattling, the shortest, medium, and longest rectrices oscillated in a pattern consistent with the k = 1, 2, and 3 normal modes, respectively.

“During train-rattling, the shortest, medium, and longest rectrices oscillated in a pattern consistent with the k = 1, 2, and 3 normal modes, respectively (Fig 1E).”

• Also stated in: § 3.6 Feather Vibrational Resonance · plain

  “This is indeed the pattern of normal modes that we observed for those rectrices in the field videos (section 3.5, Fig 1E).”

The first peak frequency in each model spectrum decreased with increasing tail length (slope -0.32 Hz cm-1 [-0.39, -0.25]).

“The first and second peak frequencies in each model spectrum decreased with increasing tail length (slopes of –0.32 Hz cm-1 [–0.39, –0.25] and –1.0 Hz cm-1 [–1.4, –0.6], respectively).”

When single rectrices were shaken in the laboratory at 25.6 Hz, they oscillated in the same modes as those observed during train-rattling in the field.

“When single rectrices were shaken in the laboratory at 25.6 Hz, they oscillated in the same modes as those observed during train-rattling in the field.”

All but the shortest feathers in the train array had a broad peak centered at ~20-30 Hz that includes the train-rattling frequency (25.6 Hz).

“and a broad peak centered at ~20–30 Hz that includes the train-rattling frequency (25.6 Hz).”

For rectrices, the relation between fk and LR agreed with a power law (fk ∝ LR−b) where b = 2.2 [1.9, 2.5] for k = 1.

“For rectrices, the relation between fk and LR agreed with a power law (fk ∝ LR−b) where b = 2.2 [1.9, 2.5], 1.7 [1.5, 1.9], and 3.0 [2.8, 3.2] for k = 1, 2, and 3, respectively (Fig 6A; R2 > 0.99, 0.98, and 0.99; n = 8, 8, and 4 feathers, respectively).”

Iridescent loose barbs near those eyespots had a maximum lateral displacement due to train-rattling of 9.6 mm [3.9, 15.3].

“By contrast, the iridescent loose barbs near those eyespots had a maximum lateral displacement due to train-rattling of 9.6 mm [3.9, 15.3] (n = 13 barbs from 5 males).”

The resonant frequencies of eyespot feathers depend only weakly on feather length.

“the resonant frequencies of these feathers depend only weakly on feather length (Fig 6B).”

The frequencies used during train-rattling are well-matched to a peak in the resonant response of the peacock's tail.

“the frequencies used during train-rattling are well-matched to a peak in the resonant response of the peacock’s tail (Fig 7).”

The magnitude of the second moment of area, I, for short eyespot feathers is only 28% of that of owl and pigeon flight feathers of similar length.

“the magnitude of the second moment of area, I, for short eyespot feathers is only 28% of that of owl and pigeon flight feathers of similar length [38].”

• cites [38] T Bachmann, 2012, Flexural stiffness of feather shafts: geometry rules over material properties, Journal of Experimental Biology sourceNot checked — no full text of the source

Courting peacocks perform the train-rattling display using a relatively narrow range of feather vibration frequencies between 22 and 28 Hz.

“Courting peacocks perform the train-rattling display using a relatively narrow range of feather vibration frequencies between 22 and 28 Hz (Fig 3)”

Eyespot feathers have Q ≤ 6 at the train-rattling vibration frequency.

“Eyespot feathers have Q ≤ 6 at the train-rattling vibration frequency”

The low amplitude of eyespot motion is not solely the result of interactions between feathers, because their motion was similar even when feathers were shaken individually at 20-30 Hz in the laboratory.

“The low amplitude of eyespot motion is not solely the result of interactions between feathers, because their motion was similar even when feathers were shaken individually at 20–30 Hz in the laboratory (S4 Movie).”

The computed values of critical stress for local buckling were greater than those for Euler buckling along almost the entire length of the rachis for all eyespot feathers, with the lowest values near the proximal end.

“The computed values of critical stress for local buckling were greater than those for Euler buckling along almost the entire length of the rachis for all eyespot feathers, with the lowest values near the proximal end.”

The rapid motion of the loose barbs at this frequency of feather shaking creates a dynamic iridescent background around each eyespot.

“The rapid motion of the loose barbs at this frequency of feather shaking creates a dynamic iridescent background around each eyespot (S1 Movie).”

The colorful eyespots remain steady during the peacock's train-rattling display.

“the colorful eyespots–which influence peahen mate preferences [12]–remain so steady during the peacock’s train-rattling display (S1 Movie).”

Peacocks were often video-recorded train-rattling for more than 25 minutes.

“We often video-recorded peacocks train-rattling for > 25 minutes”

Adult peacocks with longer trains shook their trains at slightly higher frequencies on average.

“adult peacocks with longer trains shook their trains at slightly higher frequencies on average (Fig 3B).”

Arrays of peacock eyespot feathers are also in resonance at the train-rattling frequency.

“arrays of peacock eyespot feathers are also in resonance at the train-rattling frequency.”

The range of frequencies used by peacocks performing the train-rattling display lies well above the scaling relationships with body mass for other types of shaking behaviors.

“We also found that the range of frequencies used by peacocks performing the train-rattling display lies well above the scaling relationships with body mass for other types of shaking behaviors (Fig 2).”

The volume of air displaced by the feather vibrating in the lateral plane is less than or equal to that of the nearby feather.

“We also estimated that the volume of air displaced by the feather vibrating in the lateral plane is less than or equal to that of the nearby feather [37].”

• cites [37] MC Potter, 2002Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Within the 22-28 Hz range, different individual peacocks use relatively consistent vibration frequencies.

“within that range we found that different individuals use relatively consistent vibration frequencies.”

For a given shaking amplitude, the peacock should be able to use the least muscular power if it shakes the train at a resonant frequency.

“This means that for a given shaking amplitude, the peacock should be able to use the least muscular power if it shakes the train at a resonant frequency.”

The shapes of the normal modes and their frequencies are determined by mechanical parameters of the feather-elasticity, inertia, geometry, and size-as well as any constraints on its motion.

“The shapes of the normal modes (Fig 1D) and their frequencies are determined by mechanical parameters of the feather–elasticity, inertia, geometry, and size–as well as any constraints on its motion.”

Train length is highly correlated with train mass.

“train length varies considerably among peacocks–and this trait is highly correlated with train mass [24]”

• cites [24] M Petrie, 1996, Variation in the train morphology of peacocks (<italic>Pavo cristatus</italic>), Journal of Zoology sourceNot checked — no full text of the source

Peacocks that display eyespots with greater iridescence obtain more matings.

“peacocks that display eyespots with greater iridescence obtain more matings [11, 12]”

• cites [11] A Loyau, 2007, Iridescent structurally based coloration of eyespots correlates with mating success in the peacock, Behavioral Ecology sourceNot checked — no full text of the source
• cites [12] R Dakin, 2013, Eye for an eyespot: how iridescent plumage ocelli influence peacock mating success, Behavioral Ecology sourceNot checked — no full text of the source

As a complex system with many degrees of freedom, the train should have multiple resonant frequencies at which mechanical power is most efficiently transferred from the drive source.

“As a complex system with many degrees of freedom, the train should have multiple resonant frequencies at which mechanical power is most efficiently transferred from the drive source [21].”

• cites [21] WF Smith, 2010Not checked — no full text of the source

Systems with high damping have the ability to vibrate efficiently over a wider range of frequencies.

“In contrast, systems with high damping have the ability to vibrate efficiently over a wider range of frequencies.”

Peacocks are able to modulate the feather vibration frequency of their displays.

“enabling them to modulate the feather vibration frequency of their displays.”

• AssumptionRests on an assumption: Feathers obtained from commercial sources and zoos are representative of feathers used by wild displaying peacocks.
• AssumptionRests on an assumption: Low-amplitude horizontal vibrations in the lateral plane adequately mimic the feather vibrations during train-rattling.

Cantilever beam theory predicts that each normal mode's resonant frequency should decrease rapidly with increasing feather length.

“Cantilever beam theory predicts that each normal mode’s resonant frequency should decrease rapidly with increasing feather length, L [21].”

• cites [21] WF Smith, 2010Not checked — no full text of the source

Like any elastic mechanical system, the peacock's train should have its greatest vibrational amplitude when driven near a resonant frequency of oscillation.

“Like any elastic mechanical system, the peacock’s train should have its greatest vibrational amplitude when driven near a resonant frequency of oscillation [22].”

• cites [22] NH Fletcher, 1992 sourceNot checked — no full text of the source

Outer loose barb motion obscures the lateral motion of the rachis and eyespots, making it difficult to probe lateral vibrations of these features with scanning laser vibrometry.

“This geometry causes the outer loose barb motion to obscure the lateral motion of the rachis and eyespots, making it difficult to probe lateral vibrations of these features with this technology.”

Minimal out-of-plane motions occurred during laboratory measurements of feather vibrations.

“we confirmed that minimal out-of-plane motions occurred during these measurements.”

FFT magnitudes were not reproducible above approximately 40-60 Hz because broadband noise due to discretization of the motion tracked on video exceeded the amplitude of the shaker drive.

“FFT magnitudes were not reproducible above ~40–60 Hz because at high frequencies the broadband noise due to discretization of the motion tracked on the video exceeded the amplitude of the shaker drive.”

Peacocks are able to drive feather vibrations energetically efficiently over a relatively broad range of frequencies.

“This indicates that peacocks are able to drive feather vibrations energetically efficiently over a relatively broad range of frequencies”

• AssumptionRests on an assumption: Feathers obtained from commercial sources and zoos are representative of feathers used by wild displaying peacocks.
• AssumptionRests on an assumption: Low-amplitude horizontal vibrations in the lateral plane adequately mimic the feather vibrations during train-rattling.

The gel mount had minimal effect on shaking spectra below 36-40 Hz.

“The gel mount had minimal effect on shaking spectra below 36–40 Hz (S5 Text).”

For a thick cantilever, Kk2 takes on non-integer values such that the frequencies of the higher order normal modes are not integer multiples of the fundamental frequency.

“For a thick cantilever, Kk2 takes on non-integer values such that the frequencies of the higher order normal modes are not integer multiples of the fundamental (k = 1) frequency.”

Systems with low damping are in resonance only over a narrow range of frequencies.

“Systems with low damping are in resonance only over a narrow range of frequencies.”

The train-rattling motion starts with the tail and spreads to the train via frictional coupling.

“The motion starts with the tail and spreads to the train via frictional coupling (S1 Movie)”

The breadth of this peak in the model suggests that peacocks can efficiently excite their tails to drive the train vibrations at a range of frequencies from 22-27 Hz.

“The breadth of this peak in the model suggests that peacocks can efficiently excite their tails to drive the train vibrations at a range of frequencies from 22–27 Hz (Fig 7).”

The absence of a model spectral peak below ~5 Hz may explain why the k = 1 mode is not seen excited in the peacock's train in field videos.

“which may explain why we do not see the k = 1 mode excited in the peacock’s train in our field videos (because the train array has its k = 1 peak at about 1.3–1.6 Hz; Fig 5E).”

For a peahen located in the typical position during the display, the eyespots would appear to be almost stationary relative to the oscillating loose barbs, even at their peak amplitude of vibration.

“Thus, for a peahen located in the typical position during the display, the eyespots would appear to be almost stationary relative to the oscillating loose barbs, even at their peak amplitude of vibration.”

The frequencies for the k = 1 and 2 normal modes scale with rectrix length as predicted for uniform cantilevers (i.e., b = 2).

“This indicates that the frequencies for the k = 1 and 2 normal modes scale with rectrix length as predicted for uniform cantilevers (i.e., b = 2) [21].”

• cites [21] WF Smith, 2010Not checked — no full text of the source

Each tail and eyespot feather has relatively broad resonant peaks due to air drag and internal energy dissipation.

“These values imply that each tail and eyespot feather has relatively broad resonant peaks due to air drag and internal energy dissipation.”

Variation in the internal structure of the rachis must compensate for variation in its shape along its length.

“This indicates that variation in the internal structure of the rachis must compensate for the variation in its shape along its length.”

The relative lack of eyespot motion is consistent with the train feathers oscillating in a normal mode pattern with the eyespot very close to a node.

“The relative lack of eyespot motion is also consistent with the train feathers oscillating in a normal mode pattern with the eyespot very close to a node.”

• AssumptionRests on an assumption: For a given feather length and vibration frequency, the closest resonant frequency fk determines which normal mode pattern (k) is excited by the vibration.

The limited motion of the eyespot is due to its mass and the compact structure of its interlocking barbules, and not only the properties of the feather rachis.

“These results suggest that the limited motion of the eyespot is due to its mass and the compact structure of its interlocking barbules, and not only the properties of the feather rachis.”

Peacock rectrices interact only weakly with each other, based on their similar vibrational spectra and normal modes when shaken either singly, in the rectrix array, and during natural train-rattling displays.

“Our results indicate that peacock rectrices interact only weakly with each other, based on their similar vibrational spectra and normal modes when shaken either singly, in the rectrix array, and during natural train-rattling displays.”

• AssumptionThe authors state this as an assumption: Interactions between the feathers are weak.

During train-shivering, when the train feathers are much more widely spaced, eyespot feathers with LR ~100 cm should oscillate in the k = 3 normal mode.

“However, during train-shivering, when the train feathers are much more widely spaced, eyespot feathers with LR ~100 cm should oscillate in the k = 3 normal mode (Fig 6B).”

• AssumptionRests on an assumption: For a given feather length and vibration frequency, the closest resonant frequency fk determines which normal mode pattern (k) is excited by the vibration.

The lack of length-dependence for resonant peaks in the train array indicates that the interactions among train feathers coordinate their motion such that they respond as a unit.

“The lack of length-dependence for resonant peaks in the train array indicates that the interactions among train feathers coordinate their motion such that they respond as a unit.”

Transfer functions were reproducible below 40-60 Hz.

“functions were reproducible below 40–60 Hz.”

The densely intermeshed barbules and microhooks explain how the eyespot can move as a single mass.

“thus explaining how the eyespot can move as a single mass.”

The tail should be able to efficiently drive train vibrations at both the train-rattling and train-shivering frequencies.

“These results indicate that the tail should be able to efficiently drive train vibrations at both the train-rattling and train-shivering frequencies.”

The rectrices may produce a substantial component of the train-rattling sound via stridulation.

“Two results suggest that the rectrices may produce a substantial component of the train-rattling sound via stridulation.”

Peafowl have been shown to perceive playbacks of even the very low frequency (≤ 20 Hz) components of train-rattling.

“Peafowl have been shown to perceive playbacks of even the very low frequency (≤ 20 Hz) components of train-rattling [13].”

• cites [13] AR Freeman, 2015, Infrasound in mating displays: a peacock&apos;s tale, Animal Behaviour sourceNot checked — no full text of the source

The agreement in resonant frequency between the tail and the array of train feathers reduces the power required to drive vibrations.

“This agreement in resonant frequency between the tail and the array of train feathers reduces the power required to drive vibrations.”

When a peacock displays, it moves the mass of the train (0.3 kg) as well as that of supporting muscular, connective, and dermal tissue.

“When a peacock displays, it moves the mass of the train (0.3 kg; [24]) as well as that of supporting muscular, connective, and dermal tissue.”

• cites [24] M Petrie, 1996, Variation in the train morphology of peacocks (<italic>Pavo cristatus</italic>), Journal of Zoology sourceNot checked — no full text of the source

The elastic modulus for long eyespot feathers exceeds that predicted by their individual components due to reinforcing interactions between the cortex and pith.

“the elastic modulus for long eyespot feathers exceeds that predicted by their individual components due to reinforcing interactions between the cortex and pith [30].”

• cites [30] ZQ Liu, 2015, Structure and mechanical properties of naturally occurring lightweight foam-filled cylinder–The peacock’s tail coverts shaft and its components, Acta Biomaterialia sourceNot checked — no full text of the source

The higher damping of peacock feathers broadens the resonant peaks of their train and tail, helping to explain how a single vibrational frequency can be used to move such a large array of feathers relatively efficiently.

“The higher damping of peacock feathers broadens the resonant peaks of their train and tail, helping to explain how a single vibrational frequency can be used to move such a large array of feathers relatively efficiently.”

When multiple eyespot feathers of different lengths are combined into an array, this weak length-dependence promotes their ability to oscillate at similar resonant frequencies.

“When multiple eyespot feathers of different lengths are combined into an array, as they are in the peacock’s train, this weak length-dependence promotes their ability to oscillate at similar resonant frequencies (Fig 5E).”

The greater flexibility of the eyespot feathers facilitates vibrations at large amplitudes during displays.

“This greater flexibility of the eyespot feathers also facilitates vibrations at large amplitudes during displays.”

Displaying peacocks shake their tails at or near resonance when they excite train vibrations during this display.

“This means that displaying peacocks shake their tails at or near resonance when they excite train vibrations during this display.”

Sexual selection via female choice may have shaped both the biomechanical design of the eyespot feathers and the behaviors that produce visual and audio cues.

“our results suggest the possibility that sexual selection (via female choice) has shaped both the biomechanical design of the eyespot feathers and the behaviors that produce visual and audio cues.”

The effect of added air mass on the resonant frequency is negligible.

“we conclude that the effect of the added air mass is negligible.”

• AssumptionRests on an assumption: The density of air is less than 1% of that of the entire feather, including the air gaps between the loose barbs.

Train mass is highly correlated with train length.

“Given that train mass is highly correlated with train length [24]”

• cites [24] M Petrie, 1996, Variation in the train morphology of peacocks (<italic>Pavo cristatus</italic>), Journal of Zoology sourceNot checked — no full text of the source

This level of critical stress ensures that the eyespot feathers bend appreciably before developing unrecoverable kinks.

“This level of critical stress ensures that the eyespot feathers bend appreciably before developing unrecoverable kinks.”

The higher damping of peacock feathers has the advantage of quickly damping out oscillations caused by external sources such as wind.

“This also has the advantage of quickly damping out oscillations caused by external sources (e.g., wind).”

The frequency range of the broadband rattle notes produced by train-rattling lies within the range of peafowl auditory response curves predicted from their inner ear morphology.

“the frequency range of the broadband rattle notes produced by train-rattling lies within the range of peafowl auditory response curves predicted from their inner ear morphology [48].”

• cites [48] JR Corfield, 2013, A quantitative morphological analysis of the inner ear of galliform birds, Hearing Research sourceNot checked — no full text of the source

Train length is positively correlated with fat reserves.

“it is positively correlated with fat reserves [24]”

• cites [24] M Petrie, 1996, Variation in the train morphology of peacocks (<italic>Pavo cristatus</italic>), Journal of Zoology sourceNot checked — no full text of the source

The muscles used to spread and fan the train and tail during displays are sexually dimorphic.

“The muscles used to spread and fan the train and tail during displays are also sexually dimorphic [40]”

• cites [40] GN Pachori, 1970, Mechanism of the tail-fan of the peacock, <italic>Pavo cristatus Linn</italic>, Annals of ZoologyNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Having a larger train does not constrain peacocks to perform vibrations at lower frequencies.

“This indicates that having a larger train does not constrain peacocks to perform vibrations at lower frequencies.”

The ratio of added air mass to feather mass is less than or equal to the ratio of their densities.

“This implies that the ratio of added air mass to feather mass is less than or equal to the ratio of their densities.”

Train-rattling may pose a considerable challenge to metabolic stores and short-term muscle power output.

“suggesting that this behavior may pose a considerable challenge to metabolic stores and short-term muscle power output.”