Predicted Position Error Triggers Catch-Up Saccades during Sustained Smooth Pursuit

Model illustration of saccade trigger decisions. A representation of the interaction between PE magnitude, uncertainty, and the confidence that the target is outside the fovea. The confidence that the target is to the right of the fovea is represented by the ratio of the AUC to the right of fovea and the left of the fovea (Fig. 2, top panels). Saccades are triggered when the confidence signal rises to threshold (Fig. 2, bottom panel).

Single trial model simulations. A, Target motion that results in a saccade and another that results in smooth pursuit with no saccade. B, C, Noisy PE and RS sensory signals are estimated continuously using a Kalman filter. D, Future PE is continuously estimated using sensory signals. E, A rise to threshold using a log probability ratio or confidence of sensory evidence leads to a trigger or no trigger decision.

Model simulations of trigger time distributions. Model generated saccades trigger time distributions shown made to a clear target (Fig. 4, top panels) and a blurred target (Fig. 4, bottom panels). When the target is moving away from the fovea (T_xt < 0), uncertainty in PE does not significantly change trigger time distributions. For T_xt>0, increasing uncertainty in PE using blurred target increases saccade variability, especially around the smooth zone (0 < T_xt < 400).

Model simulation trends of saccade trial proportions and trigger times. Model simulations of proportion of saccade trials and the trigger times of saccade trials compared to T_xe (-PE/RS) for different VSs. The smooth zone boundaries from de Brouwer et al. (2002b) are marked by vertical dashed lines. The proportion of saccades near the smooth zone increases with increasing target VS. The saccade trigger times decrease with increasing target VS.

Double step-ramp task. A, Representation of the double step ramp task on a screen. Each participant completed ten alternating sessions of clear and blurred target conditions. Each session consisted of 10 blocks of 50 trials each. C, Parameter range for PSs and VSs used to induce catch-up saccade triggering. Large steps were omitted as they resulted in off-screen targets. B, D, Position, velocity-time graphs of the tracking dot for a typical trial. Shown are a positive PS (to the right) and a positive VS (rightward acceleration).

Sensory phase plot and typical saccade trials. For each saccade trial, PE and RS were sampled 100 ms before saccade onset and plotted on a phase plot. Left, Four typical trials for clear and blurred target conditions plotted in pairs on a position-time graph, with saccades in bold. Right, PE and RS phase plots of all trials for clear and blurred target conditions. The colored traces correspond to the evolution of sensory inputs of the typical trials on the left from the target step to 100 ms before saccade onset (represented by black circles). Note that when PE and RS have opposite signs, PE naturally decreases and when PE and RS have the same sign, PE naturally increases in absolute value.

Sensory phase plot and typical smooth trials. For smooth trials where no saccade occurred within 400 ms of target step, PE and RS were sampled continuously and plotted on a phase plot. Left, Typical smooth trial on a position-time graph where eye traces are colored. Trials are considered smooth if no saccades occur within the first 400 ms after target step. Right, Phase plot showing continuous sampling of PE and RS for a subset of trials. Smooth trials tend to begin in the upper left or lower right corners where PE naturally decays as PE and RS are in opposite directions. The colored traces correspond to the typical trials on the left, showing the evolution of PE and RS toward the center where near-perfect tracking is achieved. The red dotted traces represent the smooth zone boundaries from de Brouwer et al. (2002b).

Proportion of saccade trials relative to PE_pred and T_xe. PE_pred, PE, and RS were sampled ∼100 ms before saccade onset for saccadic trials and averaged over the first 400 ms after target step for smooth pursuit trials. A, C, Saccade trial proportions plotted for a given PE_pred from –20° to 20° in bins of 2°. B, D, Saccade trial proportions plotted for a given T_xe from –400 to 600 ms in bins of 50 ms.

Collapsed saccade trigger time for ranges of PE_pred and T_xt. Collapsed trigger time medians were plotted against PE_pred and T_xt for the relevant parameter ranges and increasing VSs. A, C, Collapsed Saccade trigger times as a function of PE_pred for different VSs. B, D, Collapsed saccadic trigger times as a function of T_xt for different VSs showing an increase around values corresponding to the smooth zone. Missing data points for VS0-10 and VS10-20 result from PS being drawn from a uniform discrete distribution.

Saccade trigger time distributions and medians by PE_pred. Saccade trigger times are measured from target step to saccade onset. to make conclusions on how PE_pred contributes to saccade trigger time, PE_pred here was also sampled from target step over 50 ms and averaged, rather than ∼100 ms before saccade onset. Trials were grouped into bins of large negative (A, D), small (B, E), and large positive (C, F) PE_pred. G, Collapsed median trigger times for all subjects for clear and blurred condition. H, Collapsed IQR of all subjects for clear and blurred condition; ** represents a significant difference between groups with a p < 0.001. Each colored dot represents a particular subject’s mean value throughout all six bars.

Saccade trigger time distributions and medians by T_xt. Similarly to Figure 5, at target step, PE and RS can be approximated by PS and RS, and the index T_xt is used to estimate time to contact and directionality. Positive T_xt represents foveopetal motion and negative T_xt represents foveofugal motion. Trials were grouped into bins of negative (A, D) small positive (B, E), and large positive (C, F) T_xt. The bimodalities in B, D, E represent distributions of early and late saccades, which will be addressed later in this paper. G, Collapsed median trigger times for all subjects for clear and blurred condition. H, Collapsed IQR of all subjects for clear and blurred condition; ** represents a significant difference between groups with a p < 0.001. Each colored dot represents a particular subject’s mean value throughout all six bars.

Proportion of early, late, and smooth trials under different PE_pred and T_xt conditions. Trials were classified as early, late, or smooth based on the trigger time cutoffs of 175 and 400 ms, as informed by trigger time distributions from Figures 5. A–D, Variations of trial types by PE_pred bins under foveofugal and foveopetal T_xt. E–H, Variations of trial types by T_xt bins under small and large PE_pred.

Individual trial scatterplot of PE_pred and T_xt. To further illustrate the correlations between PE_pred and T_xt, with saccade trigger times, single trials were plotted and assigned a color corresponding to their trigger time category. A, Early saccades are evenly distributed along the parameter space, whereas smooth trials and late saccades are most evident for positive T_xt and small PE_pred. B, Blurred target conditions disperse late and smooth trial distributions as higher uncertainty reduces the likelihood for a saccade trigger.