Dynamics behind rough sounds in the song of the Pitangus sulphuratus

The complex vocalizations found in different bird species emerge from the interplay between morphological specializations and neuromuscular control mechanisms. In this work we study the dynamical mechanisms used by a nonlearner bird from the Americas, the suboscine Pitangus sulphuratus, in order to achieve a characteristic timbre of some of its vocalizations. By measuring syringeal muscle activity, air sac pressure, and sound as the bird sings, we are able to show that the birds of this species manage to lock the frequency difference between two sound sources. This provides a precise control of sound amplitude modulations, which gives rise to a distinct timbral property.

Figure 1

Simultaneous measurement of sound and EMG activity of the ovm during three renditions of the song. (a) Sound signal. Numbers indicate the syllable number within a song. (b) Spectrogram of the sound. Notice the spectral richness of the first syllable in each repetition of the song. (c) Simultaneous EMG activity. The most prominent activity is produced during the first syllable, while none is present while the third syllable is uttered.

Figure 2

Comparison of third and first syllables of the song in consecutive renditions. (a) The sound amplitude is modulated during the first syllable of the song. (b) This modulation is observed as a more complex spectrum of the sound. (c) Muscle activity (EMG) consists of a series of peaks at a frequency similar to that of the amplitude modulation and is only present in the first syllable. (d) Detail of the sound and EMG activity during the first syllable.

Figure 3

Sound amplitude modulation frequency is locked to EMG activity frequency. Both frequencies (amplitude modulation and EMG) were calculated as the peaks of their respective Fourier transforms in the range 80–400 Hz. The size of each point is proportional to the amplitude of the modulation, quantified as the amplitude of the Fourier transform at the modulation frequency. The orange line represents the linear fit and the shaded region is the 95% CI of the fit. The slope of the fit ($1.02\pm 0.07$) shows that both frequencies are not only correlated, but highly similar.

Figure 4

Amplitude modulation persists after bilateral denervation, but its amplitude is significantly decreased. (a) Sound and spectrogram of a song from a bird after bilateral denervation. Notice how the third syllable is similar in amplitude to the first syllable of the next song. (b) Amplitude ratio of the first and third syllable before and after bilateral denervation. While before denervation this ratio is about 1.75 [e.g., see Fig. 2], it decreases significantly after denervation.

Figure 5

Plots of $f_1\left(\chi \right)$ (blue line) and $f_2\left(\chi \right)$ (orange line) for three representative sets of parameters. (a) In this case, a high value of air sac pressure (represented by $\mu$) the system has no fixed point and the sources do not lock. (b) Fixed points for $\chi$ (filled dot for stable, empty circle for unstable in the figure) exist when the pressure is decreased. These represent solutions in which the sources are locked (their phase difference remains constant). (c) When pressure is further decreased another pair of fixed points appears. In this regime two stable solutions coexist.

Figure 6

Numerical integrations of the full model for two representative sets of parameters displaying phase drift (top) and locked sources (bottom). (a) $f_1\left(\chi \right)$ (blue line) and $f_2\left(\chi \right)$ (orange line). (b) Results of the numerical integration of the model: $x_1\left(t\right)$ (blue), and $x_2\left(t\right)$ (orange). (c) Sound, computed as ${\dot{x}}_1\left(t\right)+{\dot{x}}_2\left(t\right).$ In the first panel, with parameters in which the sources do not lock, their phase drift causes a slow amplitude modulation in the sound. In the second case, in which the sources are locked, the amplitude of the sound remains constant.

Figure 7

Air sac pressure is greater for the first syllable. (a) A simultaneous measurement of air sac pressure (top) and sound (bottom, represented as a spectrogram). Pressure on the first syllable (in which amplitude modulations occur) is significantly greater than in the third syllable (in which no EMG activity is observed). (b) Pressure ratio between the first and third syllable before and after denervation. In all cases it is significantly greater than 1, indicating that the pressure in the first syllable is greater than that of the third one.

Figure 8

The proposed model reproduces the increase of sound amplitude modulation when forced. Top: $k_A\left(t\right)$ for unforced (left) and forced (right) cases. Bottom: sound (blue) obtained from integration of the model for each case. The full orange line represents the envelope of the sound. Orange dashed lines in the bottom panel indicate the maximum and minimum amplitude for the forced case.

Figure 9

Sound amplitude modulation frequency versus forcing frequency for the model (orange line). The blue dashed line represents the identity. Notice that for a range of frequencies, the modulation frequency locks to the forcing frequency.

Figure 10

A frequency jump observed in a nonmanipulated kiskadee: (a) air sac pressure, (b) recorded sound, and (c) spectrogram. The black arrow indicates the occurrence of the frequency jump.