State pruning by merging and data normalization. (A) The first principal component of the EODR and activity level (PC1) over time (green trace), and resulting states after the state segregation (red, up-state; blue, down-state). Dashed black line represents the PC1 segregation threshold, and black arrows in the left panel indicate transient up-states (left) to be merged into the down-state (right). (B) Histogram of the down- (blue) and up-state (red) durations before (left) and after (right) the state pruning procedure from the same animal (4 days pooled). Dashed grey lines indicate a threshold for the minimum state duration (1.5 s), which was set at the first local minimum of the up-state duration histogram (left). (C) Normalization of data across multiple days and animals. Survivor functions of the EODR are shown during down- (dashed lines) and up-states (solid lines) before (left) and after (right) the normalization procedure. Each animal is represented by a different colour.

State-dependent sensory sampling activities. (A) Distributions of the EODR showed distinct sensory sampling rates during down- and up-states from a spontaneously behaving animal. Red/blue indicates down/up-states throughout this figure. Dashed black lines indicate shifted log-normal distribution fitting. (B) Mean EOD rates exhibited significant differences between the two states in all four animals; error bars indicate ±1 s.d.; ***P<0.001. (C) Left, distribution of the EOD acceleration (EODA=dEODR/dt) showed wider spread during up-states, indicating greater temporal modulations of the sensory sampling. Right, positive (solid lines) and negative (dashed lines) sides of the EODA distributions were superimposed to depict the asymmetry in the increasing and decreasing phases of the EODR. (D) An example trace of the EODR showed quicker rising (magenta line) and slower falling (cyan line) phases during an up-state. (E) Fano factors of the EOD pulse counts during a down-state (200 s long) followed by an up-state (200 s long); shaded areas indicate 95% bootstrap confidence intervals. All data in A and C–E were obtained from the same animal.

Increase in the sensory sampling rate precedes voluntary movement. (A,B) Pseudo-colour plots of the normalized EODR (A) and the EODA (B) time courses during spontaneous (top) and sound-evoked (middle) transitions. Time 0 indicates the movement onset, and trials are ordered by their EODR up-transition onsets. Bottom, trial-averaged EODR and EODA normalized by the peak; both exhibited striking differences between spontaneous (green traces) and evoked (magenta traces) transitions. (C) Activity level time courses averaged across all trials showed no significant differences between the spontaneous (green) and evoked (magenta) trials (all animals pooled). Dashed grey line indicates the activity threshold (0.2) for the movement-onset detection. (D) No significant increases in the background noise were observed before spontaneous movement onset. ΔSPL, trial-averaged underwater sound pressure level (SPL) after baseline subtraction. (E) Comparisons of the distributions between spontaneous (green shading) and evoked (magenta shading) transitions demonstrate significantly longer EODR transition latencies for spontaneous compared with sound-evoked transitions in all animals tested (Table 2). (F) The probability of initiating movement increased as the duration threshold of the EODR up-state increased in all animals. (G) Comparison of the two trajectories (moved versus aborted) averaged across trials that crossed the EODR up-state threshold (0.4). Dashed horizontal line indicates the movement threshold, and dashed vertical line indicates the EODR threshold. Colours represent the time since the threshold crossing. The error bars or colour shading indicate 95% bootstrap confidence intervals. All data in A, B and G were obtained from the same animal; all tested animals were pooled for C and D. Solid lines and shaded areas indicate the trial-averaged mean ± s.e.m.

Visual confirmation of the EOD-based movement onset detection. (A) Example traces of the EOD-based activity level (blue line) and the image correlation (ImCr) measure (red line) during movement onset. Each image frame is represented by a red dot, and joined together for visual aid. Vertical dashed lines indicate movement onset times determined by the two detection methods, and the horizontal dashed line indicates the EOD-based activity threshold (0.2). (B) Distribution of the time differences (ΔT_move) between the two movement onset detection methods. (C) Cumulative distribution of the absolute time differences (|ΔT_move|). Shaded area indicates 95% bootstrap confidence interval. (D,E) Trial-averaged EODR (D) and EODA (E) time courses computed by the EOD-based (blue) and visual (red) movement onset detection methods agree within ~0.1 s. Shaded areas indicate ±1 s.e.m. (F) Box-plot of the log-speed of the image centroid as a function of the activity level (displaying 5th, 25th, 50th, 75th and 95th percentiles). Medians are indicated by black bars, and outliers are shown as grey crosses. All data in A–F were obtained from animal B.

Increase in the sensory sampling variability precedes voluntary movement. (A) Time-dependent distribution of the EODR during spontaneous transitions (left) exhibited a wider spread than during evoked transitions (right). Colours represent the probability density of the EODR; time 0 indicates the movement or sound onset. (B) EODR time courses from 10 randomly selected trials (grey lines) showed greater deviations from the mean (coloured lines) during spontaneous transitions (left). Green/magenta indicates the spontaneous/evoked conditions throughout this figure. (C) Across-trial s.d. of the EODR reveal greater trial-to-trial variability during spontaneous transitions (left). (D) Comparison of the across-trial s.d. of any given mean EODR confirms greater trial-to-trial variability during spontaneous transitions. Colours represent the time of transition; +, movement onset; x, stimulus onset. All data in A–D were obtained from animal C. (E) In all animals tested, the across-trial s.d. at the transition threshold (dashed grey line in D) exhibited significant differences between the spontaneous and evoked transitions; **P<0.01, ***P<0.001. (F) The coefficient of variation (CV) of the EOD intervals (black lines) declined after stimulus onset, but the mean rate (cyan lines) simultaneously increased (top). The CV was recomputed after applying the time-rescaling procedure (N=98, animal A), which produced a constant mean rate (bottom). IPI, inter-pulse interval. (G) Trial-to-trial variability peaked near the spontaneous movement onset (N=1157, five animals), but declined after stimulus onset (N=291, five animals). All shaded areas indicate 95% bootstrap confidence intervals. The CVs were computed after averaging four successive EOD intervals at 0.1 ms resolution.

Trial-to-trial variability and mean of the EODR for each animal during up-transitions. (A) Across-trial mean (cyan traces) and s.d. (green traces) of the EODR for spontaneous transitions as a function of time before and after movement onset. (B) Same as A for evoked transitions as a function of time before and after stimulus onset. The across-trial s.d. are shown as magenta traces. (C) Across-trial s.d. of the EODR as a function of the trial-averaged EODR during spontaneous (green) and evoked transitions (magenta). Shaded areas represent 95% bootstrap confidence interval. Pseudo-colour indicates time during transition; black cross marks the movement onset. The EODR transition threshold (0.4) is indicated by vertical dashed grey lines.

Spontaneous behavioural transitions follow a random distribution and lack temporal structure. (A,B) Survivor functions (=1–cumulative distribution function) of the log-intervals between two successive up-transitions (A), and log-durations of up- and down-states (B) showed downward linear trends for all four animals. The symbols for each animal are consistent throughout this figure. (C) Distribution of the up-transition intervals from the same animal (solid black line) were well fitted by a log-normal distribution (dashed black line). Shaded areas indicate 99% bootstrap confidence intervals. (D) Power spectral density (PSD) of the up-transition events in the log-frequency domain exhibited approximately equal power at all frequencies, suggesting no characteristic time-scale. (E) No significant temporal correlation exists between two successive log-intervals between spontaneous up-transitions from the same animal. (F) Temporal correlations (Pearson) between successive spontaneous transitions were mostly absent or statistically insignificant; *P<0.01. Up–up intervals, two successive intervals between Up-transitions; Down–up dur., durations of a down-state and a following up-state; Latency–down dur., transition latency and duration of a preceding down-state; Latency–up dur., transition latency and duration of a following up-state. (G) Fano factors for the up-transition counts showed linearly increasing trends on a log–log scale in all four animals. (H) The original Fano factors do not significantly differ from 10 randomly shuffled controls from the same animal (grey lines), indicating lack of temporal structure. Errors bars represent 95% bootstrap confidence interval.

Distributions of the intervals between spontaneous up-transitions for each animal. (A) Distributions of the up-transition intervals. Shaded areas indicate 99% bootstrap confidence intervals, and dashed black lines indicate log-normal distribution fitting. (B) Kolmogorov–Smirnov (KS) plots of the empirical versus ΔCDF (=empirical CDF–theoretical CDF, where CDF is cumulative distribution function). Shaded areas indicate 99% confidence interval for the paired KS test between the empirical and theoretical CDF (log-normal distribution). (C,D) Log–log plots of the Fano (C) and Allan factors (D) of the up-transition counts. Shaded areas indicate 95% bootstrap confidence intervals, and grey traces indicate 10 randomly shuffled controls.