Dynamical origin of spectrally rich vocalizations in birdsong

J. D. Sitt, A. Amador, F. Goller, and G. B. Mindlin

Phys. Rev. E 78, 011905 – Published 11 July 2008

Abstract

Birdsong is a model system for learned vocal behavior with remarkable parallels to human vocal development and sound production mechanisms. Upper vocal tract filtering plays an important role in human speech, and its importance has recently also been recognized in birdsong. However, the mechanisms of how the avian sound source might contribute to spectral richness are largely unknown. Here we show in the most widely studied songbird, the zebra finch (Taeniopygia guttata), that the broad range of upper harmonic content in different low-frequency song elements is the fingerprint of the dynamics displayed by its vocal apparatus, which can be captured by a two-dimensional dynamical model. As in human speech and singing, the varying harmonic content of birdsong is not only the result of vocal tract filtering but of a varying degree of tonality emerging from the sound source. The spectral content carries a strong signature of the intrinsic dynamics of the sound source.

Received 30 April 2008

DOI:https://doi.org/10.1103/PhysRevE.78.011905

Authors & Affiliations

J. D. Sitt¹, A. Amador¹, F. Goller², and G. B. Mindlin¹

¹Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I (1428), Buenos Aires, Argentina
²Department of Biology, University of Utah, Salt Lake City, Utah 84112, USA

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Vol. 78, Iss. 1 — July 2008

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Images

Figure 1
Example of a zebra finch song, shown spectrographically (a). In the lower panels, examples of different sound types [indicated by the bars in (a) are analyzed: rich harmonic content sounds $(B)$ and tonal sounds $(C)$ ]. (b). Low fundamental frequency sound wave (left panel) extracted from the bout displayed in (a), and its corresponding spectrum (right panel). (c) High fundamental frequency sound waves (left) are more sinusoidal and their spectra are less rich (right). In both right panels, the first peak corresponds to the fundamental frequency of the sound fragment: $560 Hz$ for (b) and $5940 Hz$ for (c).Reuse & Permissions
Figure 2
(Color online) The spectral content of the syllables and sound frequency are correlated. We show the analysis for 172 sound segments uttered by six zebra finches. For each syllable we compute the spectral content index (SCI) and the average fundamental frequency (AFF) (see Methods). Each syllable analyzed is represented by a point. Different point types correspond to different birds. The dotted line is obtained through a numerical experiment where only $p_{s}$ (air sac pressure), was changed generating sounds of frequency smaller than $1.5 kHz$ and then filtered with a tube of length $20 mm$ and reflection coefficient $α = 0.95$ . The solid line was computed changing the parameters $p_{s}$ (air sac pressure) and $g_{0}$ (dorsal muscle activity) from ( $2004 Pa$ , $- 0.04 dyn$ ) to ( $2004 Pa$ , $- 0.0328 dyn$ ) linearly and then filtered with the same tube.Reuse & Permissions
Figure 3
The physical model can exhibit a saddle-node in a limit cycle (SNILC) bifurcation. We sketch the dynamics of the midpoint position of the labia in a region of the parameter $p_{s}$ (parameter $g_{0} = - 0.0399 dyn$ ), which is divided in two regions by a bifurcation line. For low values of the air sac pressure $(p_{s})$ , there are three fixed points where the stationary state is stable and no oscillations occur (see $A$ ). As $p_{s}$ is increased, and crosses the bifurcation line, an oscillation of zero frequency is born, with finite amplitude and a pulselike time trace (see $B_{1}$ ). As the pressure is further increased and the system moves away from the bifurcation line, the frequency of the solution increases, and the time trace becomes tonal (see $B_{2}$ ).Reuse & Permissions
Figure 4
Scheme of the syrinx-filter model. $p_{s}$ stands for the subsiringeal pressure, $x$ the midpoint displacement of the labia, $a_{01}$ and $a_{02}$ the half separations at the rest (nonoscillating) state, $L$ the tube length, and $α$ the reflection coefficient at the end of the trachea.Reuse & Permissions
Figure 5
(Color online) Optimization of the difference between the experimental values and their theoretical counterparts $(χ^{2})$ as a function the tube parameters of $α$ and $L$ . The contour is drawn at the base of the surface (a). In the lower panel we show the relationship of $χ^{2}$ and $L$ given a fixed $α = 0.95$ for the Hopf (solid line) and SNILC (dotted line) models.Reuse & Permissions
Figure 6
(Color online) Experimental and synthetic sounds of one bird. The simultaneous measurement of sound and air sac pressure $(p_{s})$ while a zebra finch is spontaneously singing allows us to analyze the relationship between fundamental frequency of the sound and air sac pressure. Different point types correspond to different syllables. Note that in the low-frequency range [dotted rectangle in (a)] there are four different syllables. We can replicate all the different sounds with the physical model varying just $p_{s}$ for low fundamental frequencies, and varying simultaneously $p_{s}$ and $g_{0}$ (which represent the activity of the dorsal syringeal muscles) for high values of fundamental frequencies (b). The paths in the parameter space $(p_{s}, g_{0})$ to generate the synthetic syllables with high fundamental frequency are as follows: for squares from ( $2000.8 Pa$ , $- 0.0.384 dyn$ ) to ( $2001.4 Pa$ , $- 0.0384 dyn$ ); for down triangles from ( $2001.6 Pa$ , $- 0.0356 dyn$ ) to ( $2000.8 Pa$ , $- 0.0356 dyn$ ); for circles from ( $2001.2 Pa$ , $- 0.0399 dyn$ ) to ( $2001.4 Pa$ , $- 0.0359 dyn$ ); for up triangles from ( $2001.2 Pa$ , $- 0.0396 dyn$ ) to ( $2001.3 Pa$ , $- 0.0359.8 dyn$ )Reuse & Permissions

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