Smooth ocular pursuit during the transient disappearance of an accelerating visual target: the role of reflexive and voluntary control

The effect of different depth planes during a manual tracking task in three-dimensional virtual reality space

Unlike ballistic arm movements such as reaching, the contribution of depth information to the performance of manual tracking movements is unclear. Thus, to understand how the brain handles information, we investigated how a required movement along the depth axis would affect behavioral tracking performance, postulating that it would be affected by the amount of depth movement. We designed a visually guided planar tracking task that requires movement on three planes with different depths: a fronto-parallel plane called ROT (0), a sagittal plane called ROT (90), and a plane rotated by 45° with respect to the sagittal plane called ROT (45). Fifteen participants performed a circular manual tracking task under binocular and monocular visions in a three-dimensional (3D) virtual reality space. As a result, under binocular vision, ROT (90), which required the largest depth movement among the tasks, showed the greatest error in 3D. Similarly, the errors (deviation from the target path) on the depth axis revealed significant differences among the tasks. Under monocular vision, significant differences in errors were observed only on the lateral axis. Moreover, we observed that the errors in the lateral and depth axes were proportional to the required movement on these axes under binocular vision and confirmed that the required depth movement under binocular vision determined depth error independent of the other axes. This finding implies that the brain may independently process binocular vision information on each axis. Meanwhile, the required depth movement under monocular vision was independent of performance along the depth axis, indicating an intractable behavior. Our findings highlight the importance of handling depth movement, especially when a virtual reality situation, involving tracking tasks, is generated.

Watching the Effects of Gravity. Vestibular Cortex and the Neural Representation of "Visual" Gravity

Gravity is a physical constraint all terrestrial species have adapted to through evolution. Indeed, gravity effects are taken into account in many forms of interaction with the environment, from the seemingly simple task of maintaining balance to the complex motor skills performed by athletes and dancers. Graviceptors, primarily located in the vestibular otolith organs, feed the Central Nervous System with information related to the gravity acceleration vector. This information is integrated with signals from semicircular canals, vision, and proprioception in an ensemble of interconnected brain areas, including the vestibular nuclei, cerebellum, thalamus, insula, retroinsula, parietal operculum, and temporo-parietal junction, in the so-called vestibular network. Classical views consider this stage of multisensory integration as instrumental to sort out conflicting and/or ambiguous information from the incoming sensory signals. However, there is compelling evidence that it also contributes to an internal representation of gravity effects based on prior experience with the environment. This a priori knowledge could be engaged by various types of information, including sensory signals like the visual ones, which lack a direct correspondence with physical gravity. Indeed, the retinal accelerations elicited by gravitational motion in a visual scene are not invariant, but scale with viewing distance. Moreover, the "visual" gravity vector may not be aligned with physical gravity, as when we watch a scene on a tilted monitor or in weightlessness. This review will discuss experimental evidence from behavioral, neuroimaging (connectomics, fMRI, TMS), and patients' studies, supporting the idea that the internal model estimating the effects of gravity on visual objects is constructed by transforming the vestibular estimates of physical gravity, which are computed in the brainstem and cerebellum, into internalized estimates of virtual gravity, stored in the vestibular cortex. The integration of the internal model of gravity with visual and non-visual signals would take place at multiple levels in the cortex and might involve recurrent connections between early visual areas engaged in the analysis of spatio-temporal features of the visual stimuli and higher visual areas in temporo-parietal-insular regions.

Investigation into the dynamic visual acuity of skilled cricketers using a continuous motion task

BACKGROUND

Great demands are imposed upon the perceptual-motor system when undertaking ball-throwing and -hitting tasks including cricket. That is, performers must detect and resolve object details while on the move - something referred to as dynamic visual acuity (DVA). The present study aimed to investigate DVA in skilled cricketers and non-cricketers using a more immediate or real-time assessment.

METHODS

Skilled cricketers and non-cricketers had to detect the presence of the gap within a Landolt-C ring as it moved horizontally or vertically, while progressively increasing the size until the participants registered a response. Measures were taken as the mean (dynamic) minimum angle of resolution of the object size at the moment that participants correctly responded to the gap. Objects would move at either a high, medium or low velocity.

RESULTS

There was greater dynamic visual acuity in the skilled cricketers compared to non-cricketers (P<0.05). There was a reduced negative influence of object velocity on dynamic visual acuity in the skilled cricketers compared to non-cricketers (P<0.05).

CONCLUSIONS

We suggest these findings contribute to the growing evidence surrounding DVA within ball-throwing and -hitting sports, while making some assertions as to the implications for the cricket performance setting.

Mechanisms of smooth pursuit eye movements in schizotypy

Several studies suggest that highly schizotypal individuals display a deficit in smooth pursuit eye movements (SPEM), which are considered an important biomarker of schizophrenia. In schizophrenia, abnormal SPEM is thought to be driven by impairments in motion perception. In schizotypy, the processes underlying reduced SPEM performance have not been examined so far, and there are no studies on motion perception deficits in schizotypy. Thus, in this registered report, we aimed to investigate whether motion perception is impaired in highly schizotypal individuals, and how it contributes to SPEM performance. On an exploratory basis, we were interested in the association between schizotypy and prediction, another mechanism underlying SPEM. To address this issue, participants with high total scores of the Oxford-Liverpool Inventory of Feelings and Experiences (O-LIFE short form) and control participants with low scores (N = 86 in each group) performed a standard sinusoidal SPEM task, random dot kinematograms to measure motion perception, and a blanking SPEM task to assess prediction abilities. Group comparisons as well as mediator analyses were carried out to identify whether motion perception or prediction are responsible for SPEM performance in schizotypy. We found reduced blanking SPEM performance in schizotypes compared to controls, but no group differences regarding sinusoidal SPEM and motion perception. Although no significant mediators were identified for SPEM performance in schizotypes, an exploratory analysis revealed an association between motion perception and SPEM gain in high, but not in low schizotypy. Our findings imply that despite the schizotypy-related impairment in prediction, motion perception seems to be a more important predictor of SPEM performance in schizotypes. A deficit in prediction that does not relate to SPEM performance suggests that protective factors (e.g., other cognitive processes) might operate in schizotypal individuals to maintain SPEM performance on a healthy level.

Ocular tracking of occluded ballistic trajectories: Effects of visual context and of target law of motion

In tracking a moving target, the visual context may provide cues for an observer to interpret the causal nature of the target motion and extract features to which the visual system is weakly sensitive, such as target acceleration. This information could be critical when vision of the target is temporarily impeded, requiring visual motion extrapolation processes. Here we investigated how visual context influences ocular tracking of motion either congruent or not with natural gravity. To this end, 28 subjects tracked computer-simulated ballistic trajectories either perturbed in the descending segment with altered gravity effects (0g/2g) or retaining natural-like motion (1g). Shortly after the perturbation (550 ms), targets disappeared for either 450 or 650 ms and became visible again until landing. Target motion occurred with either quasi-realistic pictorial cues or a uniform background, presented in counterbalanced order. We analyzed saccadic and pursuit movements after 0g and 2g target-motion perturbations and for corresponding intervals of unperturbed 1g trajectories, as well as after corresponding occlusions. Moreover, we considered the eye-to-target distance at target reappearance. Tracking parameters differed significantly between scenarios: With a neutral background, eye movements did not depend consistently on target motion, whereas with pictorial background they showed significant dependence, denoting better tracking of accelerated targets. These results suggest that oculomotor control is tuned to realistic properties of the visual scene.

Eye Tracking of Occluded Self-Moved Targets: Role of Haptic Feedback and Hand-Target Dynamics

Previous studies on smooth pursuit eye movements have shown that humans can continue to track the position of their hand, or a target controlled by the hand, after it is occluded, thereby demonstrating that arm motor commands contribute to the prediction of target motion driving pursuit eye movements. Here, we investigated this predictive mechanism by manipulating both the complexity of the hand-target mapping and the provision of haptic feedback. Two hand-target mappings were used, either a rigid (simple) one in which hand and target motion matched perfectly or a nonrigid (complex) one in which the target behaved as a mass attached to the hand by means of a spring. Target animation was obtained by asking participants to oscillate a lightweight robotic device that provided (or not) haptic feedback consistent with the target dynamics. Results showed that as long as 7 s after target occlusion, smooth pursuit continued to be the main contributor to total eye displacement (∼60%). However, the accuracy of eye-tracking varied substantially across experimental conditions. In general, eye-tracking was less accurate under the nonrigid mapping, as reflected by higher positional and velocity errors. Interestingly, haptic feedback helped to reduce the detrimental effects of target occlusion when participants used the nonrigid mapping, but not when they used the rigid one. Overall, we conclude that the ability to maintain smooth pursuit in the absence of visual information can extend to complex hand-target mappings, but the provision of haptic feedback is critical for the maintenance of accurate eye-tracking performance.

Smooth pursuit eye movements in patients with macular degeneration

Currently, there are no quantitative studies of smooth pursuit, a behavior attributed to the fovea, in individuals with macular degeneration (MD). We hypothesize that pursuit in MD patients depends on the relative positions of the scotoma and target trajectory. We tested this hypothesis with a scanning laser ophthalmoscope (SLO), which allows for direct visualization of the target on the damaged retina. Monocular microperimetry and eye movements were assessed in eleven individuals with differing degrees of MD. Observers were asked to visually track a 1.7° target that moved in one of eight radial directions at 5°/s–6°/s. Consistent with our hypothesis, pursuit metrics depended on whether the target moved into or out of scotoma. Pursuit gains decreased with increasing scotoma extent in the target's heading direction (p = 0.017). Latencies were higher when the scotoma was present along the target trajectory (in either starting or heading directions, p < 0.001). Furthermore, an analysis of retinal position shows that targets fell on the fixational locus nearly 50% of the time. The results suggest that MD patients are capable of smooth pursuit eye movements, but are limited by target trajectory and scotoma characteristics.

Spatial Estimation of Accelerated Stimuli Is Based on a Linear Extrapolation of First-Order Information

Abstract. We examined spatial estimation of accelerating objects (−8, −4, 0, +4, or +8 deg/s2) during occlusion (600, 1,000 ms) in a spatial prediction motion task. Multiple logistic regression indicated spatial estimation was influenced by these factors such that participants estimated objects with positive acceleration to reappear behind less often than those with negative acceleration, and particularly after the longer occlusion. Individual-participant logistic regressions indicated spatial estimation was better predicted by a first-order extrapolation of the occluded object motion based on pre-occlusion velocity rather than a second-order extrapolation that took account of object acceleration. We suggest a general principle of extrapolation is involved in prediction motion tasks whereby there is a contraction of the variable of interest (i.e., displacement in spatial prediction motion and time in temporal prediction motion). Such an approach to extrapolation could be advantageous as it would offer participants better opportunity to correct for an initial estimation error.

Hand interception of occluded motion in humans: a test of model-based vs. on-line control

Two control schemes have been hypothesized for the manual interception of fast visual targets. In the model-free on-line control, extrapolation of target motion is based on continuous visual information, without resorting to physical models. In the model-based control, instead, a prior model of target motion predicts the future spatiotemporal trajectory. To distinguish between the two hypotheses in the case of projectile motion, we asked participants to hit a ball that rolled down an incline at 0.2 g and then fell in air at 1 g along a parabola. By varying starting position, ball velocity and trajectory differed between trials. Motion on the incline was always visible, whereas parabolic motion was either visible or occluded. We found that participants were equally successful at hitting the falling ball in both visible and occluded conditions. Moreover, in different trials the intersection points were distributed along the parabolic trajectories of the ball, indicating that subjects were able to extrapolate an extended segment of the target trajectory. Remarkably, this trend was observed even at the very first repetition of movements. These results are consistent with the hypothesis of model-based control, but not with on-line control. Indeed, ball path and speed during the occlusion could not be extrapolated solely from the kinematic information obtained during the preceding visible phase. The only way to extrapolate ball motion correctly during the occlusion was to assume that the ball would fall under gravity and air drag when hidden from view. Such an assumption had to be derived from prior experience.

Filling gaps in visual motion for target capture

A remarkable challenge our brain must face constantly when interacting with the environment is represented by ambiguous and, at times, even missing sensory information. This is particularly compelling for visual information, being the main sensory system we rely upon to gather cues about the external world. It is not uncommon, for example, that objects catching our attention may disappear temporarily from view, occluded by visual obstacles in the foreground. Nevertheless, we are often able to keep our gaze on them throughout the occlusion or even catch them on the fly in the face of the transient lack of visual motion information. This implies that the brain can fill the gaps of missing sensory information by extrapolating the object motion through the occlusion. In recent years, much experimental evidence has been accumulated that both perceptual and motor processes exploit visual motion extrapolation mechanisms. Moreover, neurophysiological and neuroimaging studies have identified brain regions potentially involved in the predictive representation of the occluded target motion. Within this framework, ocular pursuit and manual interceptive behavior have proven to be useful experimental models for investigating visual extrapolation mechanisms. Studies in these fields have pointed out that visual motion extrapolation processes depend on manifold information related to short-term memory representations of the target motion before the occlusion, as well as to longer term representations derived from previous experience with the environment. We will review recent oculomotor and manual interception literature to provide up-to-date views on the neurophysiological underpinnings of visual motion extrapolation.

Kalman filtering naturally accounts for visually guided and predictive smooth pursuit dynamics

The brain makes use of noisy sensory inputs to produce eye, head, or arm motion. In most instances, the brain combines this sensory information with predictions about future events. Here, we propose that Kalman filtering can account for the dynamics of both visually guided and predictive motor behaviors within one simple unifying mechanism. Our model relies on two Kalman filters: (1) one processing visual information about retinal input; and (2) one maintaining a dynamic internal memory of target motion. The outputs of both Kalman filters are then combined in a statistically optimal manner, i.e., weighted with respect to their reliability. The model was tested on data from several smooth pursuit experiments and reproduced all major characteristics of visually guided and predictive smooth pursuit. This contrasts with the common belief that anticipatory pursuit, pursuit maintenance during target blanking, and zero-lag pursuit of sinusoidally moving targets all result from different control systems. This is the first instance of a model integrating all aspects of pursuit dynamics within one coherent and simple model and without switching between different parallel mechanisms. Our model suggests that the brain circuitry generating a pursuit command might be simpler than previously believed and only implement the functional equivalents of two Kalman filters whose outputs are optimally combined. It provides a general framework of how the brain can combine continuous sensory information with a dynamic internal memory and transform it into motor commands.

Is acceleration used for ocular pursuit and spatial estimation during prediction motion?

Here we examined ocular pursuit and spatial estimation in a linear prediction motion task that emphasized extrapolation of occluded accelerative object motion. Results from the ocular response up to occlusion showed that there was evidence in the eye position, velocity and acceleration data that participants were attempting to pursue the moving object in accord with the veridical motion properties. They then attempted to maintain ocular pursuit of the randomly-ordered accelerative object motion during occlusion but this was not ideal, and resulted in undershoot of eye position and velocity at the moment of object reappearance. In spatial estimation there was a general bias, with participants less likely to report object reappearance being behind than ahead of the expected position. In addition, participants’ spatial estimation did not take into account the effects of object acceleration. Logistic regression indicated that spatial estimation was best predicted for the majority of participants by the difference between actual object reappearance position and an extrapolation based on pre-occlusion velocity. In combination, and in light of previous work, we interpret these findings as showing that eye movements are scaled in accord with the effects of object acceleration but do not directly specify information for accurate spatial estimation in prediction motion.

Keep your eyes on the ball: smooth pursuit eye movements enhance prediction of visual motion

Success of motor behavior often depends on the ability to predict the path of moving objects. Here we asked whether tracking a visual object with smooth pursuit eye movements helps to predict its motion direction. We developed a paradigm, “eye soccer,” in which observers had to either track or fixate a visual target (ball) and judge whether it would have hit or missed a stationary vertical line segment (goal). Ball and goal were presented briefly for 100–500 ms and disappeared from the screen together before the perceptual judgment was prompted. In pursuit conditions, the ball moved towards the goal; in fixation conditions, the goal moved towards the stationary ball, resulting in similar retinal stimulation during pursuit and fixation. We also tested the condition in which the goal was fixated and the ball moved. Motion direction prediction was significantly better in pursuit than in fixation trials, regardless of whether ball or goal served as fixation target. In both fixation and pursuit trials, prediction performance was better when eye movements were accurate. Performance also increased with shorter ball-goal distance and longer presentation duration. A longer trajectory did not affect performance. During pursuit, an efference copy signal might provide additional motion information, leading to the advantage in motion prediction.

Extraction of visual motion information for the control of eye and head movement during head-free pursuit

We investigated how effectively briefly presented visual motion could be assimilated and used to track future target motion with head and eyes during target disappearance. Without vision, continuation of eye and head movement is controlled by internal (extra-retinal) mechanisms, but head movement stimulates compensatory vestibulo-ocular reflex (VOR) responses that must be countermanded for gaze to remain in the direction of target motion. We used target exposures of 50–200 ms at the start of randomised step-ramp stimuli, followed by >400 ms of target disappearance, to investigate the ability to sample target velocity and subsequently generate internally controlled responses. Subjects could appropriately grade gaze velocity to different target velocities without visual feedback, but responses were fully developed only when exposure was >100 ms. Gaze velocities were sustained or even increased during target disappearance, especially when there was expectation of target reappearance, but they were always less than for controls, where the target was continuously visible. Gaze velocity remained in the direction of target motion throughout target extinction, implying that compensatory (VOR) responses were suppressed by internal drive mechanisms. Regression analysis revealed that the underlying compensatory response remained active, but with gain slightly less than unity (0.85), resulting in head-free gaze responses that were very similar to, but slightly greater than, head-fixed. The sampled velocity information was also used to grade head velocity, but in contrast to gaze, head velocity was similar whether the target was briefly or continuously presented, suggesting that head motion was controlled by internal mechanisms alone, without direct influence of visual feedback.

Oculomotor prediction of accelerative target motion during occlusion: long-term and short-term effects

The present study examined the influence of long-term (i.e., between-trial) and short-term (i.e., within-trial) predictive mechanisms on ocular pursuit during transient occlusion. To this end, we compared ocular pursuit of accelerative and decelerative target motion in trials that were presented in random or blocked-order. Catch trials in which target acceleration was unexpectedly modified were randomly interleaved in blocked-order trials. Irrespective of trial order, eye velocity decayed following target occlusion and then recovered towards the different levels of target velocity at reappearance. However, the recovery was better scaled in blocked-order trials than random-order trials. In blocked-order trials only, the reduced gain of smooth pursuit during occlusion was compensated by a change in saccade amplitude and resulted in total eye displacement (TED) that was well matched to target displacement. Subsidiary analysis indicated that three repeats of blocked-order trials was sufficient for participants to modify eye displacement compared to that exhibited in random-order trials, although more trials were required before end-occlusion eye velocity was better scaled. Finally, we found that participants exhibited evidence of a scaled response to an unexpected change in target acceleration (i.e., catch trials), although there were also transfer effects from the preceding blocked-order trials. These findings are consistent with the suggestion that on-the-fly prediction (short-term effect) is combined with memorized information from previous trials (long-term effect) to generate a persistent and veridical prediction of occluded target motion.

Predictive disjunctive pursuit of virtual images perceived to move in depth

Human and nonhuman primates predictively use smooth pursuit and saccades to track visual targets that move in a fronto-parallel plane. This behaviour is believed to be facilitated by short-term memory of the target motion and/or an efference copy of the subject's motor effort. Subjects in our experiments tracked dichoptically viewed targets that appeared to move vertically, right or left and towards the subject. The virtual image of the target was tracked using disjunctive smooth pursuit and saccades. To reveal predictive tracking, targets were blanked 100 ms after the onset of motion for intervals of 800 ms. During the blanked interval, subjects initiated pursuit and predictively tracked the unseen virtual image using memory guided eye movements. Our data are consistent with recent electrophysiological studies that describe cells that encode target or eye movements in depth when a target is briefly blanked but pursuit is maintained. However, predictive pursuit of a virtual target with disjunctive eye movements poses a challenge for understanding how a short-term memory store might encode the desired eye movement, its coordinate frame, and how it is transformed into motor commands.

Evidence for a link between the extra-retinal component of random-onset pursuit and the anticipatory pursuit of predictable object motion

During pursuit of moving targets that temporarily disappear, residual smooth eye movements represent the internal (extra-retinal) component of pursuit. However, this response is dependent on expectation of target reappearance. By comparing responses with and without such expectation during early random-onset pursuit, we examined the temporal development of the extra-retinal component and compared it with anticipatory pursuit, another form of internally driven response. In an initial task (mid-ramp extinction), a moving, random-velocity target was initially visible for 100 or 150 ms but then extinguished for 600 ms before reappearing and continuing to move. Responses comprised an initial visually driven rapid rise in eye velocity, followed by a secondary slower increase during extinction. In a second task (short ramp), with identical initial target presentation but no expectation of target reappearance, the initial rapid rise in eye velocity was followed by decay toward zero. The expectation-dependent difference between responses to these tasks increased in velocity during extinction much more slowly than the initial, visually driven component. In a third task (initial extinction), the moving target was extinguished at motion onset but reappeared 600 ms later. Repetition of identical stimuli evoked anticipatory pursuit triggered by initial target offset. Temporal development and scaling of this anticipatory response, which was based on remembered velocity from prior stimuli, was remarkably similar to and covaried with the difference between mid-ramp extinction and short ramp tasks. Results suggest a common mechanism is responsible for anticipatory pursuit and the extra-retinal component of random-onset pursuit, a finding that is consistent with a previously developed model of pursuit.

The Influence of Briefly Presented Randomized Target Motion on the Extraretinal Component of Ocular Pursuit

We assessed the ability to extract velocity information from brief exposure of a moving target and sought evidence that this information could be used to modulate the extraretinal component of ocular pursuit. A step-ramp target motion was initially visible for a brief randomized period of 50, 100, 150, or 200 ms, but then extinguished for a randomized period of 400 or 600 ms before reappearing and continuing along its trajectory. Target speed (5–20°/s), direction (left/right), and intertrial interval (2.7–3.7 s) were also randomized. Smooth eye movements were initiated after about 130 ms and comprised an initial visually dependent component, which reached a peak velocity that increased with target velocity and initial exposure duration, followed by a sustained secondary component that actually increased throughout extinction for 50- and 100-ms initial exposures. End-extinction eye velocity, reflecting extraretinal drive, increased with initial exposure from 50 to 100 ms but remained similar for longer exposures; it was significantly scaled to target velocity for 150- and 200-ms exposures. The results suggest that extraretinal drive is based on a sample of target velocity, mostly acquired during the first 150 ms, that is stored and forms a goal for generating appropriately scaled eye movements during absence of visual input. End-extinction eye velocity was significantly higher when target reappearance was expected than when it was not, confirming the importance of expectation in generating sustained smooth movement. However, end-extinction eye displacement remained similar irrespective of expectation, suggesting that the ability to use sampled velocity information to predict future target displacement operates independently of the control of smooth eye movement.

Target Acceleration Can Be Extracted and Represented Within the Predictive Drive to Ocular Pursuit

Given sufficient exposure to stimulus presentation, the oculomotor system generates a representation of the stimulus characteristics, which is then used to predict the upcoming target motion. In addition to compensating for the perceptual-motor delay, these predictive processes perpetuate eye motion during a transient occlusion and compensate for the loss of visual input. At present, however, it is not well understood whether and how the oculomotor system extracts and represents target acceleration for subsequent predictive control. To this end, we used a target occlusion paradigm where both position and velocity of the target during the occlusion and at reappearance could not be predicted without extracting target acceleration before target disappearance. We found that the oculomotor response during the blanking period was not influenced by target acceleration when the initial exposure was 200 ms. However, smooth and saccadic eye movements did discriminate between the different levels of acceleration after an initial 500- or 800-ms exposure. In the event that the smooth response during the occlusion did not match well the target trajectory and thus eliminate a developing displacement error, there was an increased saccadic displacement. Still, the combined response during the blanking period did not eliminate retinal slip and position error at target reappearance. These results indicate that information on target acceleration can be extracted on-line, during pursuit of a visible ramp, and then used to drive a predictive oculomotor response in the absence of visual input.

Velocity scaling of cue-induced smooth pursuit acceleration obeys constraints of natural motion

Information about the future trajectory of a visual target is contained not only in the history of target motion but also in static visual cues, e.g., the street provides information about the car's future trajectory. For most natural moving targets, this information imposes strong constraints on the relation between velocity and acceleration which can be exploited by predictive smooth pursuit mechanisms. We questioned how cue-induced predictive changes in pursuit direction depend on target speed and how cue- and target-induced pursuit interact. Subjects pursued a target entering a +/-90 degrees curve and moving on either a homogeneous background or on a low contrast static band indicating the future trajectory. The cue induced a predictive change of pursuit direction, which occurred before curve onset of the target. The predictive velocity component orthogonal to the initial pursuit direction started later and became faster with increasing target velocity. The predictive eye acceleration increased quadratically with target velocity and was independent of the initial target direction. After curve onset, cue- and target-induced pursuit velocity components were not linearly superimposed. The quadratic increase of eye acceleration with target velocity is consistent with the natural velocity scaling implied by the two-thirds power law, which is a characteristic of biological controlled movements. Comparison with linear pursuit models reveals that the ratio between eye acceleration and actual or expected retinal slip cannot be considered a constant gain factor. To obey a natural velocity scaling, this acceleration gain must linearly increase with target or pursuit velocity. We suggest that gain control mechanisms, which affect target-induced changes of pursuit velocity, act similarly on predictive changes of pursuit induced by static visual cues.