Visually guided catch-up saccades during the pursuit of a moving target are highly influenced by smooth pursuit performance. For example, the decision to execute a saccade and its amplitude is driven by the difference in velocity between the eye and the target. In previous studies, we have demonstrated that the predictive saccades that occur during the blanking of the moving target compensate for the variability of the smooth pursuit response. Therefore, we wondered whether the predictive smooth pursuit response during target blanking influenced the occurrence of predictive saccades, which is the case for visually guided catch-up saccades. To answer this question, we asked subjects to track visually a target moving along a circular path. From time to time, the target was unexpectedly blanked for some randomized durations and disappeared from the screen. Surprisingly, we did not find any differences in smooth pursuit performance between the blanks that did and those that did not contain predictive saccades. In addition, during the blanks, the differences in smooth pursuit performance across the sessions or across the subjects did not correlate with the differences in the number of predictive saccades. Therefore, this study demonstrates that smooth pursuit performance does not influence the occurrence of predictive saccades. We interpret these results in light of the possible minimization of position error at target reappearance, which heavily depends on the saccadic amplitudes but not on their timing.

^{2}. The average number of saccades during the first 170 ms of the blanks was computed by dividing the number of saccades during this interval by the number of blanks for each subject separately. Similarly, the average number of predictive saccades was computed by dividing the number of saccades detected from 170 ms after the start of the blank until its end by the number of trials for each subject.

*p*-value) was computed as the ratio of the K-S tests that did not yield significant results and the number of K-S tests performed (30000). Before fitting a recinormal function to 2/3 of the samples from the population, we smoothed the latency distribution by means of the kernel density estimator technique (François, 2008; Parzen, 1962; Silverman, 1986), such that each data point was replaced by a Gaussian function and the sum of all these Gaussian functions yielded a continuous function (ksdensity function in Matlab). The width of the Gaussian function depended on the standard deviation of the population:

*w*= 1.06 ×

*SD*×

*N*

^{−0.2}, where

*SD*is the standard deviation of the population and

*N*is the number of its elements. The fit was then estimated with the smoothed population.

*t*) was computed by averaging the eye velocity over a 20-ms interval (e.g., from

*t*− 10 ms to

*t*+ 10 ms). Throughout the analyses, we expressed some parameters in polar coordinates, which were noted as deg

_{p}, and others in degree unit of visual angle, which were noted as

*deg*.

*T*-tests,

*F*-tests, and ANOVAs) between different populations using Statistica (Statsoft, Tulsa, OK). Sample means were compared using

*T*-tests. To account for multiple comparisons, the

*p*-values were corrected by means of the false discovery rate procedure (Curran-Everett, 2000). We performed statistical comparisons for each subject and conditions separately and thus performed 54 statistical tests (6 subjects × 3 radii × 3 frequencies).

_{Eucl}, illustrated in Figure 2B) between the eye and the target ( Figure 2C, label “V,”

*T*-test,

*p*< 0.001 for all target velocities). The predictive saccades, however, did not reduce the PE

_{Eucl}. On average, the first predictive saccade increased the PE

_{Eucl}( Figure 2C, label “F,”

*T*-tests,

*p*< 0.0001 for all target velocities), whereas the second predictive saccade did not significantly reduce PE

_{Eucl}( Figure 2C, label “S,”

*p*> 0.15 for all target velocities). This means that the predictive saccades did not correct for the instantaneous position mismatch between the eye and the blanked target as visually guided saccades do.

_{Eucl}. For instance, the first predictive saccade brings the eye toward the center of the circle, whereas the second does not. In addition, after the first predictive saccade, the eye is ahead of the target, i.e., at a position that the target will reach, possibly after it comes out of the blank. Based on these observations, we quantified other parameters such as radial (PE

_{Rad}) and angular (PE

*θ*) position errors. PE

_{Rad}represents the smallest distance between the eye and the circular target path, and PE

*θ*represents the difference in angular position between the eye and the target ( Figure 2B). The analysis of PE

_{Rad}confirmed that, on average, the first predictive saccade during blanks brought the eye toward the center of the circle (

*T*-tests,

*p*< 0.0001). In contrast, the second predictive saccade decreased PE

_{Rad}for two of the five target velocities ( Figure 2D,

*T*-tests

*p*< 0.05). In addition, the predictive saccades reduced the lag, which would lead to the reduction of PE

*θ*after the second saccade (label “S,”

*T*-test,

*p*< 0.01), or even generated a lead, which would lead to a negative PE

*θ*after the first saccade ( Figure 2E, label “F,”

*T*-tests,

*p*< 0.01). The multiple comparison procedure confirmed all of the above results.

*T*-tests,

*p*< 0.05). This result is consistent with the observation that predictive saccades did not correct for the position mismatch between the eye and the target during target blanking but that they tended to minimize the sensory errors at target reappearance.

*SD*= 120 ms), whereas the distribution of the ensuing saccades was more spread with a mean latency of 570 ms (

*SD*= 163 ms). The spread of this distribution was reduced when saccade latency was measured relative to the previous saccade onset (245 ± 130 ms) rather than with respect to the start of the blank.

*r*= 0.99,

*p*< 0.005). Therefore, subjects who exhibited few saccades during steady-state pursuit also executed few saccades during the first 170 ms of the blanks. Surprisingly, the average number of predictive saccades was also highly correlated with the average number of visually guided saccades across our subjects ( Figure 4D,

*r*= 0.885,

*p*< 0.05). This suggests that common mechanisms influence the occurrence of predictive and visually guided saccades.

*p*-values between 0.09 and 0.16. For the ensuing saccades, the

*p*-values were in the same range. The LATER model (Carpenter & Williams, 1995) states that, when an event triggers a saccade, the shape of the saccade latency distribution aligned to the time of this event is recinormal. In our study, the fact that, when the latencies are computed with respect to the time of target disappearance, their distribution has a recinormal shape suggests that the target disappearance triggers the first predictive saccades. In the following section, the putative influence of the smooth pursuit performance on saccade trigger will be systematically investigated.

_{influence}), we separated the population of blanks into two different groups. The first was the “One Sac” group, which included blanks during which a predictive saccade was triggered within a given interval of time, and the second was the “No Sac” group, which included blanks that were free of predictive saccades during this same interval. The vectorial and angular eye velocity measured during the blanks of the “One Sac” group was compared to the same measures taken during the blanks of the “No Sac” group. For the blanks of the “One Sac” group, the vectorial and angular eye velocities were measured around 100 ms before the average latency of the predictive saccade. The measures were taken at the same time points for the “No Sac” group.

_{influence}held, the eye velocity measured during blanks from the “One Sac” group (EV

_{S}) should be smaller than the same measure taken during the blanks of the “No Sac” group (EV

_{NS}). For one subject (S4), we determined the mean EV

_{S}versus mean EV

_{NS}for the nine different target conditions ( Figure 5B). For this subject, the data points were perfectly aligned with the identity line, which was the oblique line at 45 deg

_{p}from the horizontal. This alignment indicates that the mean EV

_{S}and EV

_{NS}did not differ, which was confirmed by the non-significance of the corresponding

*T*-tests (

*p*> 0.05). Therefore, the data from this subject rejected any possible influence of the smooth pursuit performance on the occurrence of the first predictive saccade. This analysis was repeated for each subject separately. Across all subjects, H

_{influence}was rejected in the majority of the cases (48 out of 54,

*T*-tests,

*p*> 0.05), which indicates that the smooth pursuit response did not influence the triggering of the first predictive saccade. In addition, when the

*p*-values were corrected for multiple comparisons (see Methods), the difference between EV

_{S}and EV

_{NS}remained significant in only one single case. The same analysis was performed with the angular velocity rather than the vectorial velocity. Measures of the angular velocity 200 ms after target disappearance did not vary between the “One Sac” and “No Sac” groups in 43 of the 54 cases (

*T*-tests,

*p*> 0.05). In this case, the false discovery rate procedure rejected H

_{influence}in all of the 54 cases. The same analysis was performed on the vectorial velocity taken 100 ms, rather than 200 ms, after the start of the blanks, and it yielded similar results and rejected H

_{influence}. Therefore, this analysis gave the first indication that the smooth pursuit response did not influence the triggering of the first predictive saccade when it occurred during the first 400 ms of the period of blank (rejection of H

_{influence}). The previous analysis focused on the saccades occurring between 200 and 400 ms. In similar analyses (see 1), we considered other time intervals ranging from 170 to 550 ms. Those additional analyses confirm that smooth pursuit performance does not influence the triggering of saccades throughout the whole blanking period. Therefore, these data are consistent with the hypothesis that the first predictive saccade was triggered in response to target disappearance.

_{200}among the four blank groups. Among the 54 ANOVAs (6 subjects × 9 conditions), only five exhibited a significant difference in vectorial eye velocity among the groups of blanks (

*p*< 0.05), i.e., an effect of smooth pursuit performance on the first predictive saccade latencies. In addition, two of them indicated that the saccade latency decreased with increasing EV

_{200}, which is inconsistent with the hypothesis that the predictive saccade latency was influenced by smooth eye velocity. Furthermore, only four ANOVAs (out of the 54) showed a significant main effect when comparing the angular eye velocity rather than the vectorial eye velocity. Again, two of them were inconsistent with the tested hypothesis. Therefore, we did not find any evidence that the smooth pursuit performance at the start of the blank influenced the latency of the first predictive saccade, i.e., that smooth pursuit performance influenced saccade triggering.

Subject | N | Q25 | Q50 | Q75 |
---|---|---|---|---|

S1 | 984 | 0.246 | 0.276 | 0.308 |

S2 | 747 | 0.268 | 0.300 | 0.356 |

S3 | 852 | 0.230 | 0.260 | 0.304 |

S4 | 858 | 0.270 | 0.322 | 0.416 |

S5 | 705 | 0.326 | 0.388 | 0.500 |

S6 | 211 | 0.286 | 0.326 | 0.398 |

*F*-tests,

*p*< 0.05 for each subject, all conditions pooled together). For the majority of the subjects, however, the evolution of the smooth pursuit gain, which was computed 400 ms after target disappearance, did not correspond to the evolution of the proportion of blanks without predictive saccades across sessions ( Figure 6, subject S4). For five subjects, the vectorial eye velocity gain 400 ms after target disappearance increased with the rank of the session (

*F*-test,

*p*< 0.05, all conditions pooled together). For the last subject (S2), there was no significant variation of the mean pursuit gain across sessions. In contrast, the proportion of blanks without any saccade during the first 400 ms did not vary across the different sessions for three subjects (

*F*-test,

*p*> 0.05, subjects S3, S4, and S6). This proportion decreased for two other subjects (

*F*-test,

*p*< 0.05, subjects S2 and S5), and it increased in parallel with the mean pursuit gain for only one subject (

*F*-test,

*p*< 0.05, subject S1). Therefore, inter-session analyses confirmed that the frequency of predictive saccades was not related to the performance of the smooth pursuit response.

_{influence}), then, across subjects, the proportion of blanks without predictive saccades ( Figure 7A) should be correlated with the mean pursuit gain ( Figure 7B), such that the smaller the mean pursuit gain of a subject, the larger the proportion of blanks with predictive saccades. To quantify this correlation under all conditions pooled together, the pursuit gain 200 ms after the start of the blank was measured and compared with the proportion of blanks without any saccade during the first 400 ms. H

_{influence}did not hold among these subjects. In fact, the smooth pursuit performance across the subjects was not significantly correlated with the proportion of trials that were free of saccades (Spearman rank correlation,

*p*= 0.42). We obtained similar results when we tried to correlate, across subjects, the mean pursuit gain measured at 400 ms and the proportion of blanks with at least two saccades in their first 700 ms ( Figure B1; details of the analysis are given in 2).

_{S100}) was measured, and this measure was compared with the measure at the same instant in time (EV

_{NS100}) for the blanks without any predictive saccade (“No Sac,” Figure A1A, top row). For subject S4, this comparison was illustrated by a plot of mean EV

_{S100}versus mean EV

_{NS100}( Figure A1, dark gray points). Each point of this plot was associated with one condition (one radius and frequency). The superposition of the points with the identity line indicates that the means did not differ, and that, for the saccades occurring between 170 and 250 ms after target disappearance, H

_{influence}should be rejected. On the same plot ( Figure A1B, light gray points), eye velocity 400 ms after target disappearance (EV

_{S400}) for a group of blanks during which the first predictive saccade occurred between 450 and 550 ms after target disappearance ( Figure A1, lower row) was compared with eye velocity 400 ms after target disappearance for the same “No Sac” group (EV

_{NS400}). Again, for this subject (S4), all the data points lie along the identity line, which indicates that the means of EV

_{S400}and EV

_{NS400}did not differ ( Figure A1).

_{influence}. Among the 242 tested cases (5 intervals × 9 conditions × 6 subjects minus 28 cases where no saccade was detected in the time window), the vectorial eye velocity did not significantly vary between the “One Sac” and “No Sac” groups in 224 of them (93%;

*T*-tests,

*p*> 0.05). The significant differences did not pass the multiple comparison procedure. Accordingly, for the angular velocity, there was no difference in 220 of the 242 cases (91%). Therefore, this analysis rejected the hypothesis that smooth pursuit influenced the triggering of the first predictive saccade in more than 90% of the cases. Again, the significant differences did not pass the multiple comparison criteria. Therefore, we can conclude that the possible influence of the pursuit performance on the predictive saccade trigger was rejected for the first predictive saccade that occurred during the first 550 ms after the start of the blank, which represents 93% of the first predictive saccade population.

*N*= 2173). The choice of this interval also excluded any second predictive saccades that occurred later than 250 ms after the end of the first predictive saccade, which led to a rejection of 34% of the 827 second predictive saccades.

_{TS}) were compared with the blanks of the “Single Sac” group (EV

_{SS}). The eye velocity was measured 50 ms after the first predictive saccade, as this time corresponded approximately to the average inter-saccadic interval (143 ms) minus 100 ms. This analysis was performed for five of the six subjects, since the last subject (S6) rarely exhibited two predictive saccades for the same blank. Similarly to the technique used in the previous section, the mean EV

_{TS}and EV

_{SS}were compared for each subject and each condition separately. Again, when plotting EV

_{TS}versus EV

_{SS}for all the conditions of subject S4, eight of the nine data points lay on the identity line ( Figure B1B). This superposition on the identity line implied that the mean of EV

_{TS}and EV

_{SS}did not differ for eight out of the nine conditions. The results were similar for the four other subjects. Indeed, in 38 of the 45

*T*-tests performed (5 subjects × 9 conditions), EV

_{TS}and EV

_{SS}did not differ (

*p*> 0.05). When the analysis was performed with the angular eye velocity rather than the vectorial eye velocity, 40 of the 45 statistical comparisons were not significant. Again, the multiple comparison procedure rejected the significance of all but one test.

_{TS}was tested to determine if it differed from the mean EV

_{SS}, such that the level of vectorial eye velocity (respectively, angular) after the first predictive saccade influenced the triggering of a second predictive saccade. Instead, EV

_{TS}and EV

_{SS}were not significantly different in 139 (respectively, 140) of the 153 cases (4 groups × 9 conditions × 5 subjects minus 27 cases where one of the groups was empty). Moreover, three (respectively, seven) of the significant

*T*-tests were inconsistent with the hypothesis that the level of the vectorial (respectively, angular) smooth eye velocity after the first predictive saccade was responsible for the triggering of a second predictive saccade (EV

_{TS}was larger than EV

_{SS}). The multiple comparison procedure rejected all significant differences for the vectorial eye velocity measures and all but one for the angular eye velocity measures.

*T*-tests,

*p*> 0.05). The significant differences failed to pass the multiple comparison procedure.

*p*= 0.14) between the proportion of blanks with several predictive saccades and the mean pursuit gain.

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