End-Point Variability Is Not Noise in Saccade Adaptation

When each of many saccades is made to overshoot its target, amplitude gradually decreases in a form of motor learning called saccade adaptation. Overshoot is induced experimentally by a secondary, backwards intrasaccadic target step (ISS) triggered by the primary saccade. Surprisingly, however, no study has compared the effectiveness of different sizes of ISS in driving adaptation by systematically varying ISS amplitude across different sessions. Additionally, very few studies have examined the feasibility of adaptation with relatively small ISSs. In order to best understand saccade adaptation at a fundamental level, we addressed these two points in an experiment using a range of small, fixed ISS values (from 0° to 1° after a 10° primary target step). We found that significant adaptation occurred across subjects with an ISS as small as 0.25°. Interestingly, though only adaptation in response to 0.25° ISSs appeared to be complete (the magnitude of change in saccade amplitude was comparable to size of the ISS), further analysis revealed that a comparable proportion of the ISS was compensated for across conditions. Finally, we found that ISS size alone was sufficient to explain the magnitude of adaptation we observed; additional factors did not significantly improve explanatory power. Overall, our findings suggest that current assumptions regarding the computation of saccadic error may need to be revisited

Gain adaptation and recovery.

<p>A. Raw data from an example subject. Primary saccade gains (black dots) are plotted versus trial numbers for each ISS condition, with 0.0-ISS at top, down to 0.1 at bottom. Red dashed lines indicate the final target position, and purple traces are robust lowess smooths, this color indicates the example subject’s data, also in purple, at right (subject 5), in B and C. Gray shaded regions indicate those used to calculate adaptation and recovery magnitudes plotted in B, and C. For the details of this procedure, see Methods. Briefly, adaptation was calculated by the difference between the means of the final 50 trials of baseline and adapt phase using the Tukey-Kramer method after an ANOVA. B. Magnitude of adaptation across and within subjects. Gray boxes and dark gray line segments in background represent across-subjects adaptation, while colored boxes and white line-segments represent individual subject adaptation (mean ±95% CI: Confidence Interval; box colors correspond to subjects as indicated in legend). Dashed grey line represents 0 adaptation, and may be used to determine significance by comparison with group or individual CIs (non-overlapping meaning significant adaptation). Red dashed lines represent ISS values (in gain units), and grey italic text above axis indicates mean across-subjects adaptation magnitude. We have also indicated those cases in which the ISS value was greater than the subject’s baseline variability (σ_b) in that session. C. Magnitude of recovery across and within subjects. Conventions as in B, except red dashed line-segments now indicate (sign-reversed) adaptation magnitude as calculated above (in A) and grey italic text above axis now indicates the magnitude of recovery across subjects. Black dashed line represents 0 recovery, and may again be used to determine significance by comparison with a CI of interest.</p

Rate of adaptation and ISS proportion learned.

<p>A. Single exponential fits to adapt-phase gains (y) as a function of trial number (x). We show fits to individual subject gains (dashed lines) as well as to gains pooled by condition (solid lines; shaded areas are 95% prediction bounds). To fit pooled data, we first additively aligned individual subject gains: setting each subject’s final 50 baseline trials to a mean across subjects. Individual conditions are colored as in B, C, and D. B. Fit rate parameter (“b”) estimates by condition (ISS). Colored dots are individual subjects, dark line segments and grey boxes are across-subject means and 95% CIs; dashed black line indicates a rate of 0. The small scale of these parameter values reflects the choice of gain and trial number as units for fitting. Asterisks indicate significant differences across subjects in ANOVA post-hoc tests at α = 0.05. C. Estimates of scale parameter (“a”) by condition; conventions as in B. D. Magnitude of adaptation expressed as a proportion of the ISS used. Colored dots again represent individual subjects while dark line segments and grey boxes means and standard errors. Dashed and dashed-dotted black lines indicate proportions of 0 and 1, respectively. Grey italic text above axis indicate mean proportion of adaptation ±95% CI across subjects.</p

Regression analysis.

<p>In all panels, one data point (colored dots) for each subject in each condition (colors as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059731#pone-0059731-g002" target="_blank">Figures 2</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059731#pone-0059731-g004" target="_blank">4</a>); dashed lines are linear least-squares fits by subject; solid black line and shaded area are linear least-squares fits across subjects and 95% prediction bounds, corresponding R² values are inset; solid gray lines are x and y = 0, respectively; vertical axis is the mean amount of adaptation (for details of this calculation, see Methods). A. Mean error was calculated using the first 25 trials of adaptation, since error will be most distinct for a given condition in this initial portion of the adaptation phase; see text for clarification. B. Similarly, mean corrective saccade amplitude was calculated only in the first 25 adapt-phase trials. C. The difference between “inherent hypometria” (IH) and baseline end-point variability (σ_b). IH was calculated as the mean undershoot during the final 50 trials of the baseline phase, the same trials were used to calculate baseline σ_b. D. The difference between ISS and IH. E. The difference between “mean error” and IH. F. Intrasaccadic Step Size in degrees. Note that in this figure, we have chosen to use degrees of visual angle for the abscissa and gain-units for the ordinate.</p

Methods.

<p>A. Single-Trial Temporal & Spatial Structure. Red: pre-saccade target; black: right-eye gaze; violet: 0.0 (no) ISS; blue: 0.01; light blue: 0.025; green: 0.05; orange: 0.075; yellow: 0.1. ISSs and primary target step are not drawn to scale. Gray scale boxes and italic text above indicate trial temporal windows. Fixation: pre-target-step fixation period; Latency: delay (ms) between primary target step and primary saccade onset; ISS: intrasaccadic target step and subsequent corrective saccade period. B. Experimental session phase structure. Phases are depicted as gray scale boxes with phase names above (italic). White numerals in each box indicate phase-length in trials. Absolute trial number is indicated on the axis.</p

End-point variability and smallest effective ISS.

<p>We define baseline end-point variability (σ_b) as: the standard deviation of primary saccade gain during the final 50 trials of the baseline phase. Colored dots are σ_b calculated for each subject in each condition; dark line segments and grey boxes are across-condition estimates and bootstrapped 95% CIs for each subject (see Methods for details). The smallest effective ISS is the minimum ISS size for which a particular subject showed a significant adaptive decrease in gain (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059731#pone-0059731-g002" target="_blank">Figure 2A</a>). Colors and subject numbers as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059731#pone-0059731-g002" target="_blank">Figure 2</a>.</p