Spatiotopic updating facilitates perception immediately after saccades

As the neural representation of visual information is initially coded in retinotopic coordinates, eye movements (saccades) pose a major problem for visual stability. If no visual information were maintained across saccades, retinotopic representations would have to be rebuilt after each saccade. It is currently strongly debated what kind of information (if any at all) is accumulated across saccades, and when this information becomes available after a saccade. Here, we use a motion illusion to examine the accumulation of visual information across saccades. In this illusion, an annulus with a random texture slowly rotates, and is then replaced with a second texture (motion transient). With increasing rotation durations, observers consistently perceive the transient as large rotational jumps in the direction opposite to rotation direction (backward jumps). We first show that accumulated motion information is updated spatiotopically across saccades. Then, we show that this accumulated information is readily available after a saccade, immediately biasing postsaccadic perception. The current findings suggest that presaccadic information is used to facilitate postsaccadic perception and are in support of a forward model of transsaccadic perception, aiming at anticipating the consequences of eye movements and operating within the narrow perisaccadic time window.

another 650-800 ms. Then the auditory beep was played, and 200-300 ms later the inducer was presented. The inducer rotated for 33.3 or 800 ms before transient onset.
2. Spatiotopic -The peripheral annulus started rotating for 650-800 ms. Then the beep was played, and subjects made a saccade towards the rotating annulus. After gaze was detected within a rectangular ROI (1x4° VA) the inducer kept rotating for another 33.3 or 50 ms. A posteriori we determined the actual inducer duration with respect to saccade offset.
3. Purely retinotopic -The annulus around fixation rotated for 650-800 ms. Then the beep was played, and subjects made a saccade towards the rotating annulus. After gaze was detected within a rectangular ROI (1x4° VA) the other annulus, (now around fixation) rotated for 33.3 or 50 ms. The annulus that rotated initially stopped rotating when the other started ( Figure S1). Figure S1. Purely Retinotopic trial. The position of the presaccadic inducer was initially around fixation. After an auditory cue, a saccade was executed and the inducer motion was shifted along with the saccade. After the saccade, the inducer would rotate for another 33.3 ms. Then, the transient was always presented around the last fixation point.

Results
Data preprocessing -After setting transient onset with respect to inducer onset we had on average 20 trials per subject in the spatiotopic condition (range: 17-26) and 20 trials per subject in the retinotopic condition (range: 13-29).
Perceived jump direction -We analyzed the effects of condition in the trials with short inducers (33.3 ms) on the perceived jump direction in a linear mixed effects analysis ( Figure S1). The reported effects are reported in reference to the Full Match condition. Like in the other experiments, 33.3 ms of inducer was sufficient to produce a bias in perceived jump direction (β = -0.92, z = 5.28, p < 0.001), and this bias was stronger when a spatiotopic preview of the inducer was provided (β = -1.15, z = 4.33, p < 0.001). Moreover, like in Experiment 1, the observed bias was also stronger when a retinotopic preview was provided (β = -1.08, z = 4.11, p < 0.001). There was no significant difference between the Spatiotopic and Retinotopic conditions (β = 0.08, z = 0.22, p = 0.83). To test our hypothesis more directly, we also compared both 'saccade'-conditions to the Full Match trials where the inducer rotated for 48 frames. There was a very strong bias in these Full Match trials (β = -3.32, z = 8.89, p < 0.001), that was stronger than the bias in both the Spatiotopic (β = 1.03, z = 3.10, p = 0.002) and the Retinotopic trials (β = 1.13, z = 3.42, p < 0.001). The difference between the Retinotopic trials and the long Full Match trials might be explained by a potential cost of the intervening saccade.

Control analysis -Fixation position
As can be seen in Figure 5a in the main text, there was more variance in the average fixation positions during transient presentation between the different conditions. We used Levene's test to test the differences in horizontal variance of

Figure S3. Fixation parameters in Experiment 1 and 2
Top panels: average fixation variance across subjects (± s.e.m.) for the different conditions in Experiment 1 (left) and Experiment 2 (right). This is a measure of the stability of fixation.
Bottom panels: average fixation error across subjects (± s.e.m.) for the different conditions in Experiment 1 (left) and Experiment 2 (right). This is measure of the retinal mismatch of the annuli around fixation during the presentation of the (pre-saccadic) inducer and during the transient.
Fixation variance and error as random effects -Again, we added the trial by trial fixation variance and fixation error to our original logit linear mixed effects model of Experiment 2. We compared the models with and without (the original model) with a log likelihood test. In contrast to Experiment 1, the additional random effects did improve the fit of the model (χ 2 (5) = 16.28, p = 0.007). However, inferences based on the estimated parameters stay the same as without the random effects (Table S1).  Table S1.
Comparison of fixed effects in the original model (as used in the manuscript) and with the addition of two random effects: fixation variance and fixation error. Although the model with the two additional random effects fits the data better, the inferences on the fixed effects are similar for both models.