Temporal structure in zebra finch song: implications for motor coding

Abstract

Adult zebra finch songs consist of stereotyped sequences of syllables. Although some behavioral and physiological data suggest that songs are structured hierarchically, there is also evidence that they are driven by nonhierarchical, clock-like bursting in the premotor nucleus HVC (used as a proper name). In this study, we developed a semiautomated template-matching algorithm to identify repeated sequences of syllables and a modified dynamic time-warping algorithm to make fine-grained measurements of the temporal structure of song. We find that changes in song length are expressed across the song as a whole rather than resulting from an accumulation of independent variance during singing. Song length changes systematically over the course of a day and is related to the general level of bird activity as well as the presence of a female. The data also show patterns of variability that suggest distinct mechanisms underlying syllable and gap lengths: as tempo varies, syllables stretch and compress proportionally less than gaps, whereas syllable-syllable and gap-gap correlations are significantly stronger than syllable-gap correlations. There is also increased temporal variability at motif boundaries and especially strong positive correlations between the same syllables sung in different motifs. Finally, we find evidence that syllable onsets may have a special role in aligning syllables with global song structure. Generally, the timing data support a hierarchical view in which song is composed of smaller syllable-based units and provide a rich set of constraints for interpreting the results of physiological recordings.

Figure 1.

The song system. The premotor pathway consists of HVC to RA to brainstem nuclei RAm (retroambigualis), PAm (parambigualis), and RVL (ventrolateral nucleus of the rostral medulla), which project to respiratory motor neurons, and nXIIts (nervi hypoglossi, pars tracheosyringealis), which projects to the syrinx. RA can influence respiratory brainstem nuclei via alternative circuitry passing through the midbrain nucleus DM (dorsomedial intercollicular). DM is also involved in an ascending pathway that extends to Uva (nucleus uvaeformis), NIf (interfacial nucleus of the nidopallium), and back to HVC. HVC–RA activity is modulated by two pathways: (1) the descending anterior forebrain pathway (AFP), which consists of area X, DLM (dorsolateral nucleus of the medial thalamus), and LMAN, and (2) an ascending pathway from DMP (dorsomedialis posterior thalami) to MMAN (medial magnocellular nucleus of the anterior nidopallium).

Figure 2.

Zebra finch song. Spectrograms from the shortest (top) and longest (bottom) songs in the sequences recorded from bird 10. Arrowheads indicate the onset and offset of each syllable measured by an automated algorithm. The algorithm marks syllable boundaries according to reliable peaks in the amplitude derivative, so that less reliable, small amplitude parts of some syllables fall outside these boundaries (see Materials and Methods).

Figure 3.

Qualitative analysis of interval length deviations. Each line indicates cumulative deviations from the mean for a single sequence. Markers indicate syllable onsets and offsets. The x-axis indicates the mean time from the beginning of the sequence for each onset and offset. The y-axis represents cumulative deviation from mean timing up to that point in the sequence. Sequences shown are at the fifth, 15,..., 85, and 95 percentiles of the distributions of sequence length (thus, individual interval deviations do not necessarily reflect percentiles because they do not perfectly correlate with sequence length).A, Simulated sequences in which interval deviations are independent. B, Simulation sequences in which deviations are positively correlated. C, Experimentally measured sequences from bird 10.

Figure 4.

Behavioral factors and song tempo. A, C, E, Means and SEs across birds. B, D, F, Pearson's coefficients by bird for each relationship indicated directly to the left. Pearson's marked * are significant with p < 0.05. A, Song tempo by time of day in hourly bins. B, Strength of tendency for songs to speed up in the first 4 h after lights on (white bars) and slow down between hours 5 and 11 (black bars). C, Acoustic activity by hour of day. D, Tendency for activity to decrease over the afternoon beginning at hour 6. Acoustic activity was defined as the number of recordings per min in a 30 min window centered on each song. E, F, The relationship between sequence length deviation and acoustic activity binned in integers. Song tempo changes systematically during the course of the day and may be influenced by factors correlated with overall arousal.

Figure 5.

Elasticity by interval type. The elasticity coefficient measures the fractional change in interval length relative to the changes in sequence length. Syllables (black) are significantly less elastic than gaps (white). This violates the proportional scaling predicted by a simple music box model of song production.

Figure 6.

Elasticity by bird. Titles indicate bird, gross covariance (g), sample size, and mean sequence length. Plots are sorted by g. Error bars show 95% confidence intervals for the sequence length regression. Coefficients are spaced along the x-axis according to mean interval lengths and onset times (syllables are demarcated with black bars).

Figure 7.

Elasticity for intervals at motif boundaries.A, Distributions of elasticity coefficients for syllables that start a song motif (syllable A; white) and other syllables (black). B, Distributions for gaps falling between motifs (white) and other gaps (black). Intervals at motif boundaries are more elastic.

Figure 8.

Pairwise correlations among and between syllables and gaps. Distributions of the correlation coefficient for all pairs containing two syllables (A), two gaps (B), or a syllable and a gap(C). To remove the effects of song tempo, correlations were calculated between the residual values of regression of interval length versus total sequence length. Directly adjacent syl–gap pairs were omitted because measurement jitter in the boundary between the pair will induce negative correlations. Stronger within-type versus between-type correlations suggest shared neural mechanisms in addition to the differential dependence on song tempo shown in Figure 5.

Figure 9.

Intervals of the same identity are linked. Distributions of pairwise differences between elasticity coefficients (A, C) and pairwise Pearson's coefficients (B, D) for syllables (A, B) and gaps (C, D). Black, Pairs containing intervals of the same identity (i.d.) (e.g., syllable D in motifs 1 and 3, gap between B and C in motifs 2 and 3). White, Pairs containing intervals of the same type (syl–syl or gap–gap) but different identity.

Figure 10.

Tradeoffs in elasticity coefficients for different syllable–gap pairings. The summed length of a syllable (s) and a gap (g) has elasticity given by β_s+g = c_sβ_s + c_gβ_g, where c_s and c_g are relative lengths of each interval in the pair (see Materials and Methods). Plots show gap (c_gβ_g) and syllable (c_sβ_s) components along x- and y-axes, respectively. A, Inter-onset pairs (gap and preceding syllable). B, Inter-offset pair (gap and after syllable). C, Gaps paired with random syllable. Tighter clustering around the β_s+g = 1 line (dashed) for the inter-onset pairings suggests that elasticity in a syllable comes at the expense of the subsequent gap, i.e., syllable onsets are more closely tied to tempo than syllable offsets. The negative slope for random pairings is attributable to the fact that c_s + c_g = 1.

Figure 11.

Functional elements possibly contributing to temporal structure. “Tempo” represents a pattern generator that drives song, either continuously across the entire song or at particular points such as syllable onsets (thicker arrows). “Syllable” and “Gap” boxes represent mechanisms that control the temporal structure of the corresponding units of song. Superscripts indicate participation of these mechanisms in three basic models of song production. MB, Music box model. A clock-like drum triggers the production of acoustic output on a fine time-scale. The song is not decomposed into syllable or gap-based units. CH, Chaining model. Temporal structure results from a chaining of syllables and gaps. Song length is a consequence of the combined action of the syllable and gap mechanisms. TS, Tempo and syllable model. A tempo mechanism determines the overall rate of song production and triggers the action of a mechanism that produces syllables as units of song. Gaps are simply the intervals left over between syllables.