Rapid spatial oculomotor updating across saccades is malleable

The oculomotor system uses a sophisticated updating mechanism to adjust for large retinal displacements which occur with every saccade. Previous studies have shown that updating operates rapidly and starts before saccade is initiated. Here we used saccade adaptation to alter life-long expectations about how a saccade changes the location of an object on the retina. Participants made a sequence of one horizontal and one vertical saccade and ignored an irrelevant distractor. The time-course of oculomotor updating was estimated using saccade curvature of the vertical saccade, relative to the distractor. During the first saccade both saccade targets were shifted on 80% of trials, which induced saccade adaptation (Experiment 1). Critically, since the distractor was left stationary, successful saccade adaptation (e.g., saccade becoming shorter) meant that after the first saccade the distractor appeared in a different hemifield than without adaptation. After adaptation, second saccades curved away only from the newly learned distractor location starting at 80 ms after the first saccade. When on the minority of trials (20%) the targets were not shifted, saccades again first curved away from the newly learned (now empty) location, but then quickly switched to curving away from the life-long learned, visible location. When on some trials the distractor was removed during the first saccade, saccades curved away only from the newly learned (but empty) location (Experiment 2). The results show that updating of locations across saccades is not only fast, but is highly malleable, relying on recently learned sensorimotor contingencies.


Introduction
Humans experience and interact with a vivid and rich visual world. This is remarkable since in order to explore the world in high resolution we need to make fast ballistic eye movements (saccades) that radically change visual input on the retina. Despite constantly changing visual input, we do not become disoriented every time we make a saccade. One of the mechanisms thought to underlie this remarkable feat, is the ability of the visual system to make and use predictions about objects and their locations (Duhamel, Colby, & Goldberg, 1992;Helmholtz, 1896). The predictions about how the world will look after a saccade concern both perception and action (Bays & Husain, 2007). For perception, it is important to anticipate what an object will look like after a saccade and where it will be located. For action, it is important to anticipate where an object will be located, so that appropriate motor action (eye or hand movement) can be planned. In the present study we investigated whether predictions made by the oculomotor system can be modified by learning.
There is a long-standing controversy regarding whether perceptual predictions about objects' features and locations are integrated with information available after a saccade. While initial results supported this idea (Jonides, Irwin, & Yantis, 1982), later research demonstrated that people are unable to combine the pre-and post-saccadic visual information into a single visual percept, suggesting that the pre-saccadic information is discarded (O'Regan & Noë, 2001;Rayner & Pollatsek, 1983). Consistent with this idea, the phenomenon of saccade suppression of displacement (SSD) illustrated that even large object displacements occurring during saccade are often not perceived (Deubel, Bridgeman, & Schneider, 1998;Deubel, Schneider, & Bridgeman, 1996, 2002McConkie & Currie, 1996). Interestingly, introducing a brief blank after the saccade, rendered object displacement during saccade visible, suggesting that pre-saccadic prediction was available after the saccade, but was typically overridden by post-saccadic input. Recent studies have provided further evidence for integration of location information, as well as integration of low-level features, such as color and orientation across saccade, based on their relative reliability (Niemeier, Crawford, & Tweed, 2003;Wijdenes, Marshall, & Bays, 2015). Finally, it has been suggested that spatial attention can also be allocated in a predictive fashion across saccades (Rolfs, Jonikaitis, Deubel, & Cavanagh, 2011; but see Arkesteijn, Belopolsky, Smeets, & Donk, 2019). Taken together, the current state-of-the-art suggests that limited predictions for perception are available, but are not always used.
On the other hand, it appears that predictions formed by the oculomotor system are quite accurate and are available very rapidly (Deubel, Schneider, & Bridgeman, 2002;Bridgeman, Hendry, & Stark, 1975;Deubel et al., 1998Deubel et al., , 1996Jonikaitis & Belopolsky, 2014; van Leeuwen & Belopolsky, 2018. For instance, Deubel, Wolf, and Hauske (1986) showed that when a saccade target was slightly displaced during a saccade, participants were unable to report target displacement even though they made accurate and rapid corrective saccades to the new target location. Recent studies have used saccadic curvature, which is considered a proxy for the oculomotor competition in the superior colliculus (McPeek, 2003), to further demonstrate that the oculomotor system relies on pre-saccadic predictions (Jonikaitis & Belopolsky, 2014; van Leeuwen & Belopolsky, 2018. Using a double-step task, Jonikaitis and Belopolsky (2014) showed that when participants made two saccades, one horizontal saccade followed by a vertical saccade and where presented with a task-irrelevant distractor, which induced oculomotor competition and was flashed before the first saccade, the second saccade curved away from the empty spatial location of the flashed distractor. The oculomotor system has also been shown to rapidly, within 80 ms after the first saccade, detect small displacements of irrelevant distractors that occurred during the first saccade ( van Leeuwen & Belopolsky, 2018. These results show that the oculomotor system makes accurate predictions, which are rapidly available for efficient interaction with the environment. The goal of the present study was to investigate whether predictions made by the oculomotor system are malleable. It is plausible that the ability to rapidly form predictions in the oculomotor system emerges from years of experience of making eye movements. But it is also wellknown that when one consistently displaces saccade target in the same direction on a sequence of trials, the oculomotor system quickly adapts by adjusting saccade amplitude so that the eyes land on the target (Bahcall & Kowler, 1999;Collins, Rolfs, Deubel, & Cavanagh, 2009;Deubel et al., 1986;Hopp & Fuchs, 2004). Therefore, it is possible that predictions in the oculomotor system are flexible and can be modified through saccade adaptation.
To determine whether the oculomotor system is able to accurately keep track of objects when adapted, we combined the double-step curvature paradigm (van Leeuwen & Belopolsky, 2018 with saccade adaptation paradigm (see Fig. 1). In order to induce saccade adaptation, we displaced the two saccade targets on 80% of the trials, while keeping the distractor location stationary across saccade. Successful saccade adaptation meant that after the first saccade distractor appeared in a different hemifield than without adaptation. If updating in the oculomotor system is not flexible, the eyes would curve away from the "old" pre-saccadic location early in the intersaccadic interval and away from the post-saccadic location later in the intersaccadic interval (as in van Leeuwen & Belopolsky, 2018. Alternatively, if the oculomotor system learns that after adaptation the distractor appears in a different hemifield than suggested by the pre-saccadic information, the eyes would always curve away from the "new" learned distractor location.

Experiment 1
The goal of the present experiment was to determine whether the oculomotor system is able to accurately keep track of locations of stationary distractors after saccade adaptation. Similar to van Leeuwen and Belopolsky (2019), participants made a sequence of horizontal and vertical saccades while ignoring an irrelevant distractor. The curvature of the second saccade away from a stationary distractor was then used to estimate the time-course of oculomotor updating. During the first saccade both saccade targets were displaced on 80% of the trials to induce saccade adaptation. When saccades were adapted to the displaced target position, the distractor appeared in a different hemifield than suggested by the pre-saccadic information (Fig. 1). If the oculomotor system learned to keep track of distractor locations, then the second saccade should show sustained curvature away from the "new" distractor location. When on a small subset of trials (20%) the targets are not displaced, the second saccade should again curve away from the "new" (but now empty) distractor location early in the intersaccadic interval, but then curve away from the post-saccadic distractor location Fig. 1. The trial structure for Experiments 1 and 2. A) An example trial, showing the Displacement condition. B) The difference between the conditions. The left column reflects the position of the distractor dot before the onset of the first saccade. The second column reflects the position of the distractor dot after the first saccade. All the target position displacements happened during the initial saccade. The displays in the right column were displayed until the completion of the second saccade. Each of the conditions were presented in one of four saccade direction configurations. With saccades starting on the left or right going to the center of the screen, then up or down. The figure only illustrates the left to up configuration. The white and black arrows indicate saccade directions. Note that the figure is not drawn to scale. Colors are used for illustration purposes only; in the experiment all stimuli had the same color (black targets, white distractor). later in the intersaccadic interval. Alternatively, if the oculomotor system did not learn to keep track of distractor locations, we expected the exact opposite effects for the two conditions. Specifically, we expected a flip in the direction of saccade curvature when the targets were displaced and sustained curvature away when the targets remained stationary (as in van Leeuwen & Belopolsky, 2018. The methods, procedure and analysis for both Experiment 1 and Experiment 2 largely overlap with our previous studies, van Leeuwen and Belopolsky (2018), van Leeuwen & Belopolsky (2019) and therefore the descriptions of the current methods share a high degree of similarity to the methods in our previous studies.

Setup and calibration
The experiment consisted of two sessions. Both sessions were conducted in the same, dimly lit, room. The stimuli were presented on a 21 ′′ LCD monitor (Samsung 2233RZ) with a resolution of 1680 × 1050 with refresh rate of 120 Hz. Participants viewed the screen from a distance of 70 cm. A chin and forehead rest ensured that the correct head position was maintained during the experiment. Left eye gaze position was recorded with the Eyelink 1000 (SR Research), sampling at 1000 Hz. A nine-point automatic calibration was used and repeated until the max validation offset was less than 1 • and the average validation offset was less than 0.5 • . The participant was alone in the room during the calibration. The calibration and experiment backgrounds were always gray (40 cd/m 2 ). The calibration and experiment target dots were always black (0 cd/m 2 ).

Participants
31 Naïve participants took part in the experiment. Two participants were excluded due to bad data quality (more than 45% data exclusion) and twelve participants were either unable to pass the screening (see stimuli, design and procedure) or were unable to maintain a stable calibration. Seventeen participants, fifteen females (mean age: 21) and two males (mean age: 25) were included in the experiment. Participants received either money (8€ per hour) or credits (60 credits per hour) as compensation for their time. All participants had normal or corrected to normal vision, the details of the experiment were explained and they gave their informed consent prior to participating. The experiment was conducted with approval of the local ethics committee of the Vrije Universiteit Amsterdam and all rules, regulations and guidelines were followed.

Stimuli, design and procedure
The experiment was almost identical to the experiment in van Leeuwen and Belopolsky (2018), but was reprogrammed in Python (Analytics, 2016). The stimuli consisted of one fixation dot, two saccade target dots and a distractor dot. The fixation and target dots were black, had a radius of 0.15 • . The fixation dot was presented 10 • to the left or right of the screen center. The first saccade target was always in the center of the screen. The second saccade target was presented 10 • above or below the first saccade target (Fig. 1). The distractor was a white dot (122 cd/m 2 ) with a radius of 0.375 • . The vertical distance between the distractor dot and the first saccade target dot was 5 • . The horizontal distance between the distractor dot and the first saccade target was ±0.75 • . In the displacement condition both target dots were displaced 1.5 • during the initial saccade (see Fig. 1).
We used a 2 (target displacement: Displacement vs. No-Displacement) × 4 (saccade configuration) × 2 (Displacement direction: With saccade direction, Against saccade direction) design, manipulated orthogonally within-subjects in each block (except for Displacement direction, this was changed across sessions to induce adaptation). In 80% of the trials the target dots were displaced. The participants were instructed to make a sequence of a horizontal and vertical saccades (see Fig. 1). They were told that a white distractor dot would appear and were instructed to ignore it. In each session, to accelerate saccade adaptation, the participants first performed a practice block (40 trials) in which the targets were always displaced, followed by 7 experimental blocks, in which the targets were displaced on 80% of the trials. To induce adaptation and to measure saccade curvature, the direction of target displacement was consistent within a session, but different across the two sessions. In one session the targets were displaced in the direction of the first saccade, while the other session the targets were displaced in the direction that was opposite to the direction of the first saccade. The session order was changed across participants. All blocks were identical and consisted of 160 trials (the last block consisted of 80 trials). Each of the sessions lasted approximately 1 h and were done on separate days.
Each trial started with participants fixating the dot on either the left or the right side of the screen. The trial started when fixation was detected. The start of fixation was defined as the first gaze sample in a trial which was less than 3 • of Euclidian distance from the fixation dot. After fixating the dot for 1000 ms a white distractor dot was presented. 50 -150 ms after the presentation of the distractor the first and second saccade target dots were presented simultaneously. The participants were instructed to keep fixating the fixation dot until the target dots were presented, then to look at the first and second saccade targets as fast and accurate as possible. The target displacement was triggered if the distance between gaze position and fixation dot was greater than 3 • and the distance between gaze position and the first saccade target was less than 7.5 • . This was done to ensure that the targets' displacement only happened during a saccade towards the first target. If the first saccade was directed towards the distractor at the moment the target dots were displaced, the trial was aborted. The trial ended when gaze was within 3 • of the second saccade target or until trial timeout (2000 ms after onset of saccade targets). Both conditions were identical except for the following: 1: In the Displacement condition the target dots were displaced during the first saccade. 2: In the No-Displacement condition all dots remained in the same location across saccades. 80% of the trials were target displacement trials (see Fig. 1a for trial layout and Fig. 1b for the difference between the conditions).
A saccade was considered correct if the gaze position at any time after targets' onset was within 3 • of the target dot. If the trial was too slow (more than 2 s) or one of the saccades was incorrect the trial was logged as incorrect. After each trial participants received feedback about saccade accuracy, e.g., if they made correct saccades the saccade targets turned green (79 cd/m 2 ), if they were incorrect they turned red (31 cd/ m 2 ). If the trial was correct, but the second saccade landed more than 200 ms after the onset of the saccade targets, auditory feedback was played immediately after the saccade landing. The feedback was a sine wave at 2000 Hz with a decay time of 5 ms and duration of 300 ms. After each block participants received feedback on their performance (accuracy and saccade latency) in the preceding block. If the number of correct trials was lower than 90% or the average intersaccadic interval (time from the first saccade offset to the second saccade onset) of the correct trials was slower than 220 ms, the participants were prompted to do better. The first session was also used as a screening session. Fourteen participants were excluded after the first session because they had less than 80% correct trials, their average duration between target onset and second saccade was more than 210 ms or they were unable to maintain a stable calibration.

Data pre-processing
Saccades where defined using an acceleration threshold of 9500 • /s 2 , a velocity threshold of 35 • /s and were automatically detected by the Eyelink system. Using custom code, all relevant events and data were extracted for each trial. The first saccade was defined as the first saccade which started after the targets were displayed. The second saccade was defined as the first saccade which started at the first target and ended at the second target (any corrective saccades after the first saccade were ignored if they started and ended within 3 • of the first target dot).
The data from the 4 different saccade sequences were transformed to fit into the same reference frame (first saccade from left, second saccade upwards) and analyzed separately before collapsing the data.
Twelve criteria for rejecting trials were used. Combined over all included participants there were a total of 36,720 experimental trials in the experiment of which a total of 29.9% were rejected, resulting in 25,742 included trials (see Supplementary Table 1 for a detailed list of rejection criteria and the percentage of trials rejected for each criterion).

Saccade curvature calculation
Saccade curvature was calculated as the median angle between each sample point in a saccade and an imaginary line between the start and end point of the saccade (see Fig. 2B). All points within 0.5 • of the saccade start and endpoint were discarded before calculating saccade curvature. The curvature values were analyzed separately for each of the conditions described in the design, target displacement, saccade configuration and displacement direction. Each saccade has intrinsic curvature, which is independent of experimental manipulations. To show the influence of distractor position on saccade curvature, curvature difference between conditions has to be computed. Curvature difference was defined as the difference between the curvature on the trials where the displacement direction was against the saccade direction and the curvature on the trials where the displacement direction was with the saccade direction (see Fig. 2A). Note that saccade curvature difference is usually too small to be observed on individual trials. After calculating the difference for each saccade configuration, the curvature difference was collapsed for each configuration by using a weighted mean. A negative curvature difference value reflects curvature away from the "new" learned distractor location (see Fig. 2A). Note that all statistics and results are plots done using the curvature difference and is referred to as degrees of curvature.

Gaussian smoothing
Since we were interested in how the direction of saccade curvature changes depending on second saccade latency, trials with similar second saccade latencies had to be compared across conditions. In order to get a precise estimate of the time-course of oculomotor competition we smoothed the curvature over time using the SMART method ( van Leeuwen, Smeets, & Belopolsky, 2019). It has been demonstrated that the SMART method provides more precise temporal estimates than conventional binning techniques. The saccade curvature was smoothed as a function of intersaccadic interval using a moving Gaussian window between 50 and 300 ms of intersaccadic interval (step size 1 ms and σ = 20 ms). A smoothed curvature time-series was made for the trials in each of the target Displacement direction sessions (with saccade and against saccade direction) saccade configurations, separately for each individual participant. The smoothed time-series were collapsed over saccade configurations using a weighted mean and then collapsed over participants using a weighted mean. This resulted in an averaged smoothed curvature time-series for each condition. 95% confidence intervals were calculated for each condition. Subsequently, cluster-based permutation testing was used to determine when the curvature time-series differed significantly between the two conditions as well as when the curvature time-series differed significantly from baseline (zero curvature). The pvalue for each of the clusters in the observed data is the proportion of clusters in the permutation distribution with equal or larger sum of tvalues than the clusters in observed data (see van Leeuwen et al. (2019) for a detailed description of the SMART-method).

Saccade adaptation
For each participant the saccade adaptation was calculated as the difference between the landing position and the first target position (before displacement), this was done separately for both adaptation session (against and with saccade direction). A within-subjects t-test was . Besides a significant group effect of adaptation session, each individual participant also showed qualitative saccade adaptation in the expected direction when comparing saccade amplitudes for the against and with saccade direction adaptation sessions (see Fig. 3, top right panel). This means that the target displacement during the first saccade was successful in inducing saccade adaptation in both sessions (see Fig. 3).

Saccade curvature
The between-conditions SMART-method was used to determine if and when the two conditions differed significantly as a function of intersaccadic interval (van Leeuwen et al., 2019). The betweenconditions (Displacement vs. No-Displacement) analysis resulted in one statistically significant cluster which showed differences in saccade curvature between the two conditions from 111 ms to 300 ms, p < 0.001 (Fig. 4). The mean difference between the two conditions was 5.2 degrees of curvature (SD = 1.7).
Subsequently, the against-baseline SMART-method was used to determine if and when the two conditions (Displacement and No-Displacement) showed significant curvature away from zero as a function of intersaccadic interval (van Leeuwen et al., 2019). For the Displacement condition the against-baseline analysis resulted in one statistically significant cluster from 88 ms to 300 ms (p < 0.001). The average saccade curvature in the cluster was − 3.2 degrees of curvature (SD = 1.15), with saccades curving away from the "new" learned distractor location (see Fig. 2A, upper panel for the Displacement condition).
For the No-Displacement condition the against-baseline analysis showed two statistically significant clusters (see Fig. 4). The first cluster ranged from 50 ms to 101 ms (p = 0.006), with the average saccade curvature in the cluster being − 2.2 • (SD = 0.68) and with saccades curving away from the "new" learned but empty distractor location (see Fig. 2A, lower panel for the No-Displacement condition). The direction of saccade curvature changed for the second cluster, ranging from 132 ms to 271 ms (p < 0.001). The average saccade curvature in the cluster was 2.3 • (SD = 0.45), with saccades now curving away from the postsaccadic distractor location (see Fig. 2A, upper panel for the No-Displacement condition).

Discussion
The results of Experiment 1 clearly show that saccade adaptation was successful and had a profound influence on the direction of saccade curvature. After successful adaptation of the first (horizontal) saccade, the second (vertical) saccade showed sustained curvature away from the "new" learned distractor location when the targets were displaced. The oculomotor system quickly learned that, for example, when the distractor appeared to the right of the first target based on the pre-saccadic information, it would be to the left of the first target after the adapted saccade landed.
When on a subset of trials, the targets were not displaced, the second saccade again curved away from the "new", learned, but now empty distractor location when the intersaccadic interval was short. However, for the intersaccadic intervals longer than approximately 130 ms, the second saccade started to curve away from the post-saccadic (visible) distractor location. These results suggest that the oculomotor system is able to learn to accurately update the spatial location of a distractor even though the saccade amplitude is adapted. Alternatively, one could argue that, as the distractor stays on the screen throughout the whole trial, the sustained curvature away in the Displacement condition could be merely driven by the post-saccadic distractor, and not by the pre-saccadic prediction. Note that the switch in curvature in the No-Displacement condition already argues against such proposition. Nevertheless, Experiment 2 was designed to refute this alternative explanation and to provide further evidence for rapid learning of predictions about object locations in the oculomotor system.

Experiment 2
The goal of the present experiment was to show that sustained saccade curvature away from the "new" learned distractor location found in the Displacement condition of Experiment 1, was not driven by the mere visible presence of the post-saccadic distractor. To that end, in Experiment 2, the targets were always displaced, but on half of the trials the distractor was not present after the first saccade. If sustained curvature was driven merely by the presence of the post-saccadic distractor, then it should not be present when distractor is not present after the saccade. However, if sustained curvature is still observed even when the post-saccadic distractor is absent, this would demonstrate that it is driven by the learned prediction about where the distractor should be located after the saccade. The methods and analysis used in Experiment 2 were identical to those used in Experiment 1 unless explicitly stated.

Participants
23 naïve participants took part in the experiment. Three participants were excluded due to bad data quality (more than 45% data exclusion) and two participants were either unable to pass the screening (see stimuli, design and procedure) or were unable to maintain a stable calibration. Eighteen participants, thirteen females (mean age: 20) and five males (mean age: 20) were included in the experiment. Participants received either money (8€ per hour) or credits (60 credits per hour) as compensation for their time. All participants had normal or corrected to normal vision, the details of the experiment were explained and they gave their informed consent prior to participating. The experiment was conducted with approval of the local ethics committee of the Vrije Universiteit Amsterdam and all rules, regulations and guidelines were followed.

Design
The experiment was identical to Experiment 1, except for the following: 1. The targets where displaced on 100% of the trials. 2. On 50% of the trials the distractor was removed during the initial saccade (see Figs. 1 and 2).

Data pre-processing
Twelve criteria for rejecting trials were used. Combined over all included participants there were a total of 38,880 experimental trials in the experiment of which a total of 30.5% were rejected, resulting in 27,020 included trials (see Supplementary Table 1 for a detailed list of rejection criteria and the percentage of trials rejected for each criterion).

Saccade adaptation
For each participant the saccade adaptation was calculated as the difference between the landing position and the first target position (before displacement), this was done separately for both adaptation sessions (against and with saccade direction). A within-subjects t-test was then performed to test for differences in saccade adaption between the two adaptation sessions. There was a significant effect of adaptation session, t (20) Fig. 3 bottom right panel). This means that the target displacement during the first saccade was successful in inducing saccade adaptation in both sessions (see Fig. 3).

Saccade curvature
The analysis was similar to the one performed for Experiment 1. The between-conditions SMART-method was used to determine if and when the two conditions differed significantly as a function of intersaccadic interval (van Leeuwen et al., 2019). The between-conditions (Distractor Present and Distractor Absent) analysis showed that the two conditions did not differ significantly from each other between the intersaccadic interval of 50 ms and 300 ms (see Fig. 5, upper panels). Again, the against-baseline SMART-method was used to determine if and when the two conditions (Distractor Present and Distractor Absent) showed significant curvature away from zero as a function of intersaccadic interval (van Leeuwen et al., 2019). For the Distractor Present condition the against-baseline analysis showed one statistically significant cluster from 50 ms to 236 ms (p < 0.001). The average saccade curvature in the cluster was − 3.05 • (SD = 0.54), with saccades curving away from the "new" learned distractor location (see Fig. 5, lower panels). In the Distractor Absent condition one statistically significant cluster from 50 ms to 257 ms was observed (p < 0.001, see Fig. 5, lower panels). The average saccade curvature in the cluster was − 3.02 degrees of curvature (SD = 0.48), with saccades curving away from the "new" learned (but empty) distractor location (see Fig. 2A, upper panel for the Distractor Absent condition).

Discussion
The results of Experiment 2 replicate the results of Experiment 1 and furthermore clearly show that sustained curvature away from the "new" learned distractor location was observed even when the post-saccadic distractor was absent. This demonstrates that in both experiments the learned predictions about where the distractor should be located after the saccade were driving the representation in the oculomotor system.

Experiment 3
One may wonder whether the context of saccadic adaptation is critical or necessary for learning how distractor location changes with a saccade. Perhaps, as similar result could be observed without saccade adaptation, but by simply shifting distractor during a saccade in a predictable fashion. To test this idea, we conducted a control experiment in which the saccade targets remained stationary, but the distractor predictably changed its location during saccade on 80% of trials. If the results of Experiment 1 and 2 were driven primarily by visual prediction, the same pattern of results would be observed here. However, if the context of saccadic adaptation was critical for observing learning of new sensorimotor contingencies, then a different pattern of results should emerge.

Participants
26 naïve participants took part in the experiment. Five participants were excluded due to bad data quality (more than 45% data exclusion) and seven participants were either unable to pass the screening (see stimuli, design and procedure) or were unable to maintain a stable calibration. Fourteen participants, eleven females (mean age: 22) and three males (mean age: 23) were included in the experiment. Participants received either money (8€ per hour) or credits (60 credits per hour) as compensation for their time. All participants had normal or corrected to normal vision, the details of the experiment were explained and they gave their informed consent prior to participating. The experiment was conducted with approval of the local ethics committee of the Vrije Universiteit Amsterdam and all rules, regulations and guidelines were followed.

Design
The experiment was identical to Experiment 1, except for the following: 1. The targets always stationary and it was the distractor which was displaced in the displacement condition (see Fig. 1), in one session it was displaced in the saccade direction and in the other session it was displaced against the saccade direction. 2. No saccade adaptation was measured as saccade amplitudes were not changed.

Data pre-processing
Twelve criteria for rejecting trials were used. Combined over all included participants there were a total of 30,240 experimental trials in the experiment of which a total of 31.3% were rejected, resulting in 20,776 included trials (see Supplementary Table 1 for a detailed list of rejection criteria and the percentage of trials rejected for each criterion).

Saccade curvature
The between-conditions SMART-method was used to determine if and when the two conditions differed significantly as a function of intersaccadic interval (van Leeuwen et al., 2019). The between-conditions (Displacement vs. No-Displacement) analysis resulted in one statistically significant cluster which showed differences in saccade curvature between the two conditions from 73 ms to 161 ms, p = 0.004 (Fig. 6). The mean difference between the two conditions was 0.77 degrees of curvature (SD = 0.22).

Discussion
The results do not show the same pattern of learning sensorimotor contingencies as with saccade adaptation (Fig. 6 vs Fig. 4). While there was a significant difference between Displacement and No-Displacement conditions from 73 ms to 161 ms, it did not follow the same time-course as in Experiment 1 and there was no switch in saccade curvature direction later in time to reflect the post-saccade competition of the distractor, as was also observed in Experiment 1. Nevertheless, making distractor displacement predictable, changed the way oculomotor competition was updated across saccade, as the observed time-course was very different from the time-course observed in our previous studies, in which the probability of distractor displacement was 50% ( van Leeuwen & Belopolsky, 2018.

General discussion
The current study provides clear evidence that rapid spatial oculomotor updating across saccades is malleable. In Experiments 1 and 2 we have demonstrated that successful adaptation of the first (horizontal) saccade changed how the location of the stationary distractor was updated. Specifically, saccade adaptation led to a change in prediction where the stationary distractor would appear after the first saccade. For example, if based on the pre-saccadic information, distractor appeared to the right of the first target, the oculomotor system learned to expect it to be located to the left of the first target after the adapted saccade landed. Learning this contingency was evident in the direction of saccade curvature of the second (vertical) saccade, reflecting the spatial locus of target-distractor competition in the oculomotor system. In both Experiments 1 and 2 the second saccade curved away from the new learned distractor location and the onset of curvature was evident very early in time, already for the second saccades with a latency of around 100 ms. Such rapid onset of the oculomotor updating was similar to the previous studies using a similar paradigm (van Leeuwen & Belopolsky, 2018.
In addition, both Experiments 1 and 2 showed that the new learned representation is based on a forward prediction and is not driven by the presence of the post-saccadic distractor. In fact, the physical presence of the distractor after the first saccade was not necessary to elicit the oculomotor competition for the second saccade. In Experiment 1 this was evident from the switch in the direction of the saccade curvature on a subset of trials on which the targets were not displaced. On these trials, the curvature of the second saccade reflected the competition from the new learned location early in the intersaccadic interval, but then, around 130 ms, switched to reflect the competition from the visible postsaccadic distractor. In Experiment 2, on the adapted trials, where the post-saccadic distractor was absent altogether, the updated oculomotor competition was not different from the trials where the distractor remained visible. This clearly suggests that new forward prediction is responsible for rapid updating of the learned representations in the oculomotor system.
It is remarkable that only a few adaptation trials were necessary to change the forward model of where the pre-saccadic distractor would appear after the saccade. In fact, saccade adaptation was able to completely reverse the pattern of oculomotor updating demonstrated in previous studies using a similar paradigm (Boon, Zeni, Theeuwes, & Belopolsky, 2018;Jonikaitis & Belopolsky, 2014; van Leeuwen & Belopolsky, 2018. The most direct comparison can be made to the studies in which the targets always remained stationary while the distractor was occasionally displaced to a different hemifield during the first saccade ( van Leeuwen & Belopolsky, 2018. The results showed that when distractor was displaced, the oculomotor system was driven by the pre-saccadic prediction up to 180 ms after the first saccade, and only after that, the eyes started to curve away from the new post-saccadic location. On trials in which distractor and target remained stationary, saccades showed sustained curvature away from the distractor location. In contrast, in Experiment 1 in the present study, we demonstrated that saccade adaptation can produce a switch in the direction of the saccade curvature on trials where all stimuli unexpectedly remained stationary. At the same time, trials on which the adaptation changed the hemifield of the distractor, showed sustained curvature away from the post-saccadic location of the distractor. Importantly, Experiment 3 demonstrated that saccadic adaptation was critical for observing rapid malleable spatial oculomotor updating. Keeping the saccade targets stable and only displacing distractor in a predictable way did have an effect on the time-course of updating, but did not produce the same time-course of distractor competition across saccade as with saccade adaptation. This speaks in favor of the proposal that learning sensorimotor contingencies is anchored to saccade targets and that the positions of distractors are coded and updated relatively to the positions of saccade targets, and not as independent vectors. Previous research has shown that saccade adaptation is a complex phenomenon. It can occur either locally (Mclaughlin, 1967), with saccades being adapted to a specific vector and amplitude, or globally (Rolfs, Knapen, & Cavanagh, 2010), to all directions. Furthermore, inward (gain-decreasing) adaptation is typically thought to be implemented in the motor system (Frens & van Opstal, 1994), while outward (gain-increasing) adaptation is thought to be implemented in the visual system (Garaas & Pomplun, 2011). Zimmermann, Burr, and Morrone (2011) have demonstrated that outward (but not inward) saccade adaptation occurs primarily in spatiotopic coordinates. They showed that when participants had to make a memory-guided saccade to the adapted target, the adaptation persisted even when saccade originated from a location different from the one used during adaptation. They concluded that visual spatiotopic map is used to guide eye movements and this map can be modified by saccade adaptation.
The present results also demonstrated that saccade adaptation is even more flexible than previously thought. In our study saccades were adapted to two different directions, and we used both inward and outward saccade adaptation. Importantly, we have demonstrated that eye movement system can learn to perform separate updates to several positions across the eye movement. While saccade gain was adapted to decrease or increase, the gain of the distractor update remained the same. Since we have demonstrated that such updating occurs only when saccadic adaptation is involved, this indicates that updating distractor positions is most likely coded relatively to the positions of saccade targets, and not as independent vectors. Previous research showed that saccade adaptation induced perceived motion of stationary targets if they were not displaced in an expected manner, suggesting that the efference copy was used for perceptually predicting the post-saccadic locations of objects (Bahcall & Kowler, 1999;Collins et al., 2009). In contrast, here we showed that the oculomotor system was able to learn to simultaneously adapt to both moving targets and stationary distractors. This shows that the oculomotor system can adapt to predictable The observed flexibility of the oculomotor system can be understood from the perspective of the sensorimotor contingency framework (O'Regan & Noë, 2001). According to this framework, there is no need to update the entire visual world every time we make a saccade. Instead, we can use the world as external and stable memory and just store a pointer to where the information is located. This does imply a mechanism for updating pointers to relevant information with every movement (e.g., Cavanagh, Hunt, Afraz, & Rolfs, 2010), based on learning the perceptual consequences of one's actions. One striking example of such learned flexibility is the phenomenon of prism adaption, when people learn to successfully interact with the world while wearing glasses that dramatically distort visual input (Kohler, 1963;Stratton, 1897, but see Linden, Kallenbach, Heinecke, Singer, & Goebel, 1999). Recent studies have extended this view by showing that perception of pre-saccadic stimuli can also be changed by systematically changing visual features during saccades on the preceding trials (Herwig & Schneider, 2014, 2015. Together with our results, this illustrates a great flexibility of predictions made for both perception and action before each saccade.
To conclude, in the present study we demonstrated that predictions made by the oculomotor system can be modified by learning. A brief intervention was enough to change the forward model about where a distractor was going to be after a saccade. Furthermore, updating of the oculomotor representations was just as rapid as in the previous studies. This suggests that despite high predictability of the external world and extensive experience of interacting with it, the oculomotor predictions are constantly updated based on the preceding sensorimotor contingencies. Such a flexible system allows to anticipate where an object will be located after each saccade, so that appropriate motor action can be executed rapidly and accurately. Overall, we conclude that visual spatiotopic map that is used to guide eye movements is not set in stone, but is a flexible system, heavily influenced by how previous saccades have changed the locations of objects on the retina.