Extended Data Fig. 9: A neural frequency axis in AAC state space.

a, Pitches (white lines on top) were estimated from vocalizations with harmonic indices that exceeded the median of the distribution (shaded region). b, Distribution of estimated pitches for each individual budgerigar. c, Schematic of the calculation of the neural frequency axis. The axis was computed as the vector between the mean neural responses to low and high pitches in half of the data. The other half of the data was then used to calculate the relationship between pitch and projection onto the axis (see Methods). d, Slope of the relationship between pitch and projections onto the neural frequency axis for each budgerigar. Black vertical lines denote slope from data; gray distributions indicate slopes from pitch-shuffled data. Exact p-values displayed in each plot are derived from one-sided permutation tests (n = 5,000 permutations). e, Population neural responses at different time windows relative to vocalizations were mapped to a two-dimensional state space using PCA. Colored dots represent neural states underlying vocalizations with frequency estimated (color indicates pitch), and gray dots are associated with less harmonic vocalizations whose pitch was difficult to estimate. f, Performance of a linear model in predicting pitch values using scores of the first two PCs for neural responses calculated within a motor time window (−30 to −5 ms), compared to two other time windows with large temporal shifts (−125 to −100 ms and 100 to 125 ms). P-values displayed within the plot are from two-sided Wilcoxon rank-sum tests (n = 14,566 neural states) with Bonferroni correction. Boxplot elements: center line, median; box limits, upper and lower quartiles; whiskers, minimum and maximum values excluding outliers. g, Population-level pitch representation (Fig. 4c) displayed separately for calls and warble syllables. Colored dots denote neural states associated with pitches in calls (left) or warble syllables (right). Gray dots represent neural states for other vocalizations.