Moving objects are often occluded by neighboring objects. In order for the eye to smoothly pursue a moving object that is transiently occluded, a prediction of its trajectory is necessary. For targets moving on a linear path, predictive eye velocity can be regulated on the basis of target motion before and after the occlusions. However, objects in a more dynamic environment move along more complex trajectories. In this condition, a dynamic internal representation of target motion is required. Yet, the nature of such an internal representation has never been investigated. Similarly, the impact of predictive saccades on the predictive smooth pursuit response has never been considered. Therefore, we investigated the predictive smooth pursuit and saccadic responses during the occlusion of a target moving along a circular path. We found that the predictive smooth pursuit was driven by an internal representation of target motion that evolved with time. In addition, we demonstrated that in two dimensions, the predictive smooth pursuit system does influence the amplitude of predictive saccades but not vice versa. In conclusion, in the absence of retinal inputs, the smooth pursuit system is driven by the output of a short-term velocity memory that contains the dynamic representation of target motion.

*θ*

_{0}) was chosen at random on the circular path for each trial.

^{2}and were labeled predictive if their onset occurred at least 170 ms after the start of the occlusion period. The first visually guided saccades after the end of the occlusion period were selected if their onset occurred within a time interval ranging from 75 to 400 ms after the end of the occlusion. Measures of position error or heading direction were taken 25 ms before and after each saccade. To evaluate the smooth pursuit response, we analyzed both the vectorial eye velocity profile and the pursuit heading direction. The vectorial velocity corresponds to the square root of the sum of the squared horizontal and vertical components. The heading direction of the smooth pursuit response was computed as the direction of the tangent to the smooth eye position trace. The time courses for the eye and the target heading direction during the occlusion periods were measured relative to the heading of the target at the start of the occlusion. Finally, it is worth mentioning that the vectorial eye velocity (

*V*) is a good approximation of the angular eye velocity (

*ω*) as

*V*=

*R**

*ω*. Since

*R*remains approximately constant during the occlusions (vectorial eye position is equal to or larger than 95% of the radius of the circular trajectory 400 ms after the start of the occlusion and at its end), the angular eye velocity is directly proportional to the vectorial eye velocity.

*g,*the eye velocity gain at the start of the occlusion;

*T,*the time at the start of the eye velocity decay;

*G,*the value of the eye velocity gain after the exponential decay; and

*τ,*the time constant of the negative exponential. The constants were the following:

*R,*the radius of the circular path;

*ω,*the angular velocity of the target; and

*ϕ,*the angular target phase at the start of the occlusion. The non-linear regression was performed on the average velocity profiles using a least-square approximation (lsqcurvefit in Matlab). The same non-linear functions were used to fit vectorial eye velocity profiles.

*T*-test) were performed using Statistica (Statsoft, Tulsa, OK, USA). 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).

*deg*

_{ p}. This is in contrast to the degree unit of visual angle, noted

*deg*. The three frequencies (0.15, 0.2, and 0.25 Hz) of the target led to angular velocities of 54, 72, and 90 deg

_{p}/s, respectively.

*p*< 0.001). Surprisingly, this gain did not depend on the duration of the occlusion period for four of the six subjects (ANOVA,

*p*> 0.05 in at least 7 out of the 9 target conditions). The last two subjects showed a significant decrease in their gain relative to occlusion duration in the majority of the target conditions (7 and 8 of the 9 conditions). In addition, for all subjects, the gain was independent of the number of occlusion (first, second, or third occlusion within the trial, Tukey Post-Hoc tests,

*p*> 0.05). This demonstrates that half a revolution was sufficient in our paradigm to build an accurate dynamic representation of target motion.

*SE*) for the time of velocity decay (152 ± 4 ms) and for the time constant of the exponential (107 ± 8 ms) matched the values found in the literature (Becker & Fuchs, 1985). Similar results were obtained when the fits were performed for each subject separately (time of velocity decay: 153 ± 2 ms; time constant of the exponential: 126 ± 5 ms).

*α*in Figure 6C). This prediction is due to the fact that the pursuit heading direction before and after the saccade should be parallel to the target heading direction before and after the saccade, respectively. In contrast, if the position dependence hypothesis was true, changes in the pursuit heading direction elicited by saccades should be equal to changes in the angular eye position during these saccades (

*β*in Figure 6C). Indeed, according to the position dependence hypothesis ( Figure 6B), before the saccade (resp. after the saccade), the pursuit heading direction should be perpendicular to the radius of the circle connecting the center of the circular path to the current eye position at saccade onset (resp. at saccade offset). Therefore, according to the position dependence hypothesis, geometric rules imply that the change in pursuit heading direction should be equal to the change in angular eye position during saccades (

*β*in Figure 6C).

_{p}ahead of the target (30% of the first predictive saccades), yielding a significant difference between

*α*and

*β*. Indeed, for the selected saccades, the mean

*α*was equal to 10.4 deg

_{p}, whereas the mean

*β*was equal to 22.1 deg

_{p}(across all subjects and conditions, Figure 6D). Interestingly, the actual average change in pursuit heading direction during the saccades was equal to 8.5 deg

_{p}( Figure 6D), which supports the position independence hypothesis, i.e., the pursuit heading direction is independent of current eye position. This hypothesis was confirmed by statistical comparisons for each of the conditions separately (3 target frequencies × 3 target radii × 5 subjects). For all conditions, the change in heading direction predicted by the position dependence hypothesis was significantly larger than the observed value (

*T*-tests,

*p*< 0.05), which was confirmed by the multiple comparison procedure. In contrast, the predictions of the heading change during the selected saccades by the position independence hypothesis were not significantly different in 35 of the 45 conditions (

*T*-test,

*p*> 0.05), when compared to the actual change. The prediction from the position independence hypothesis overestimated the actual change in the remaining 10 conditions (

*T*-tests,

*p*< 0.05). However, the significance of these 10 comparisons was rejected by the multiple comparison procedure. The same results were found when the heading was measured 50 ms after saccade offset rather than immediately at saccade offset. In sum, even around the time of predictive saccades, the pursuit heading direction was parallel to the actual target heading direction and supported a dynamic internal representation of target motion.

_{p}and 78 deg

_{p}, for an angular target displacement of approximately 85 deg

_{p}. Interestingly, predictive saccades compensated for the difference between the angular smooth eye displacement and the angular target displacement (i.e., the smooth angular error). Indeed, for these four trials, the sum of the angular saccadic amplitudes (i.e., the total saccadic displacement) was negatively correlated with the angular smooth eye displacement ( Figure 7B). In other words, the smaller the smooth eye displacement, the larger the total saccadic displacement. This indicates that the smooth angular error was accounted for by the predictive saccades. We confirmed this result by demonstrating that for the whole population of occlusions, the total angular saccadic displacement was correlated with the smooth angular error, i.e., the difference between the angular target displacement and the angular smooth eye displacement during the occlusion ( Figure 7C,

*r*= 0.55,

*p*< 10

^{−4}, target velocity = 25 deg/s, with all subjects pooled together). This correlation was significant for each target condition when all subjects were pooled together and the correlation coefficient was between 0.21 and 0.55 (all

*p*< 10

^{−4}). Overall, there was significance in 34 of the 45 conditions (5 subjects × 3 frequencies × 3 radii).