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

Abstract

Courtship displays may serve as signals of the quality of motor performance, but little is known about the underlying biomechanics that determines both their signal content and costs. Peacocks (Pavo cristatus) perform a complex, multimodal "train-rattling" display in which they court females by vibrating the iridescent feathers in their elaborate train ornament. Here we study how feather biomechanics influences the performance of this display using a combination of field recordings and laboratory experiments. Using high-speed video, we find that train-rattling peacocks stridulate their tail feathers against the train at 25.6 Hz, on average, generating a broadband, pulsating mechanical sound at that frequency. 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, and the motion of feathers is just as expected for feathers shaking near resonance. This indicates that peacocks are able to drive feather vibrations energetically efficiently over a relatively broad range of frequencies, enabling them to modulate the feather vibration frequency of their displays. Using our field data, we show that peacocks with longer trains use slightly higher vibration frequencies on average, even though longer train feathers are heavier and have lower resonant frequencies. Based on these results, we propose hypotheses for future studies of the function and energetics of this display that ask why its dynamic elements might attract and maintain female attention. 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.

Fig 1. Peafowl displays and feather anatomy.

(A) Photos (left to right) show an adult male, a subadult male, and a female performing train-rattling (males) or covert-rattling (female) displays. Feather anatomy and measurements taken from (B) a typical adult peacock rectrix (tail feather) and (C) an eyespot train feather. The length of the rachis outside the body (i.e., excluding the calamus), L_R, is used to characterize the mechanics of vibrations. The position along the rachis, x, is measured from the insertion point into the skin (top of the calamus) as shown. (D) Examples of normal modes of oscillation for a cantilever with a fixed tip, indexed by the integer k, where k = 1 corresponds to the lowest resonant frequency. For a given pattern of vibration corresponding to a normal mode, the value of k can be determined by counting the number of nodes (i.e., points of zero motion, indicated with arrows). (E) Motion of tail feathers viewed from behind a peacock during the train-rattling display. A video showing 10 cycles of oscillation during train-rattling was converted to high-contrast grayscale and then the individual frames were superimposed to show the entire range of motion of the rachises during vibrations. The resulting image illustrates the similarity between the cantilever normal modes shown in D and the patterns of feather rachis vibrations. For example, the centermost tail feather (rectrix) has two nodes (arrows) and is thus oscillating in the k = 3 normal mode. (F) Similar image to E illustrating the motion of train feather rachises viewed from the rear during train-shivering. Arrows indicate that the locations of two nodes in one of the "fishtail" train feathers.

Fig 2. The average feather-shaking frequency of the peacock’s train-rattling display is above the predictions for an animal the mass of a peacock shivering and shaking dry, respecitvely.

The mean values for peafowl behaviors are denoted with stars. Lines indicate fitted power law models derived in allometric studies of other shaking behaviors (Kleinebeckel and Klugmann 1990) (Dickerson, Mills and Hu 2012) with shaded 95% confidence intervals for the predicted values. For shivering, log₁₀(frequency) = 1.335–1.86 log₁₀(body mass), and for shaking dry, log₁₀(frequency) = 1.063–0.215 log₁₀(body mass). Circles are data from mammals used to calculate the scaling relationships for shivering and shaking dry. Black triangles are mean frequencies for hummingbirds (triangle pointing left) and seals (triangle pointing down) shaking dry. Orange and purple symbols are mean frequencies for courtship displays of other bird species (note that “S-t grouse” is the sharp-tailed grouse). Data sources are listed in S2 Text.

Fig 3

Peafowl feather vibration frequencies during displays in relation to (A) sex, age, and (B) other factors that predict feather vibration frequencies in adult males. (A) Displaying peafowl vibrate their feathers at frequencies ranging from ~22–30 Hz, with broad overlap in the ranges of frequencies used by different sex and age classes. Horizontal lines in A are grand means. Dashed lines in B are fits from the linear mixed effects models described in section 3.3.

Fig 4. Train-rattling produces a broadband, pulsating sound.

Each white box highlights a single rattle note. (A) Relative waveform amplitude (in arbitrary units) and spectrogram of the mechanical sound produced when a peacock performs the train-rattling display. The variation in intensity from 0 to 1 s is due to the peacock modulating the amplitude of his feather vibrations. (B) An array of tail feathers shaken at the train-rattling frequency in the laboratory produced a mechanical sound similar to that shown in A.

Fig 5. Feather vibrational responses calculated from laboratory feather shaking experiments.

Vibrational spectra are plotted as drive transfer functions (i.e., the ratio of feather to shaker Fourier magnitudes) vs frequency. Gray shaded regions indicate the range of individual mean shaking frequencies for peahen covert-rattling (25.2–27.1 Hz) in A and adult peacock train-shivering (9.8–10.7 Hz) and train-rattling (23.9–27.1 Hz) in B-F (see Table 1 for details). Sample spectra are shown for (A) one peahen tail covert feather and an array of peahen tail coverts, (B) one peacock rectrix and an array of peacock rectrices, (C) four peacock rectrices of different rachis lengths (L_R) shaken singly, (D) four eyespot feathers of different rachis lengths shaken singly, (E) four eyespot feathers of different rachis lengths shaken in an array of train feathers. (F) Vibrational spectra measured to determine the effect of altering the mass at the distal top of an eyespot feather: a single eyespot feather (L_R = 111 cm) unaltered (Control), with added mass (Taped), and with the eyespot removed (Cut). Note that in F data were omitted below 5 Hz to emphasize changes for frequencies close to peacock shaking behaviors. All lengths are the rachis length, L_R.

Fig 6. Resonant frequency of single peacock feathers as a function of length.

Values of resonant frequency f_k for several normal modes of vibration measured in the laboratory for (A) rectrices (black symbols, solid lines) and (B) eyespot feathers (blue symbols, dashed lines). Horizontal gray bands indicate the range of mean frequencies for train-rattling displays (grand mean = 25.6 Hz) and train-shivering behavior (grand mean = 10.4 Hz) performed by adult males (see Table 1 for details). Solid black lines in A show power law scaling relationships for the rectrices calculated from the resonant frequency data. In B the blue dashed lines connect the mean values for each of the five eyespot feather lengths studied. Note that the resonant frequencies of the eyespot feathers in B have a much weaker length-dependence than the rectrices in A. Red symbols and dot-dashed lines in B show the theoretical predictions for the eyespot feathers as described in the text (Eq 3).

Fig 7. Predicted power spectrum for a peacock’s tail as a function of the vibrational frequency.

These values were computed from laboratory data and the distribution of feather lengths in an individual peacock’s tail, using the mathematical model described in S8 Text. Note that “tail” refers to the array of rectrices, not the elaborate train. This model predicts that the tail has two broad resonant peaks near the average train-shivering and train-rattling frequencies that also agree with resonant peaks in the vibrational spectral response of the train array (Fig 5E). Gray shaded regions indicate the range of individual mean frequencies for shaking behaviors (Table 1).

Fig 8. Morphometrics, mechanical parameters, and ultrastructure of eyespot feathers.

Plots A-D show how feather morphology (n = 4 feathers of each length) varies with position along the rachis, x, rescaled to be a fraction of rachis length, u = x/L_R: (A) rachis diameter, D₁, in the lateral plane (parallel to the barbs), (B) linear density of the rachis, μ_R, (C) linear density of the entire feather, μ_F, and (D) second moment of area for the rachis in the lateral direction, I, computed from the diameter and linear density data. Linear density of the eyespots, μ_E, is shown to the right of the rachis data in B. To compare the functional forms for μ_R and I for different length feathers, the plots in E show the average values of I and μ_R rescaled for each feather to have a value of one at u = 0. SEM images show that peacock eyespots have (F) intermeshed barbules and (G) microhooks that help the eyespot move as a single unit. Insets indicate the approximate locations of the barbules shown in the SEM images with white rectangles.