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Here, we only present some central, representative results. The entirety of results can be found in our recent publication23. Note that data were mainly analyzed irrespective of the duration of the saccade targets (i.e. transient and continuous cueing conditions were combined for the final analyses). For statistical comparisons, we drew 10,000 bootstrap samples (with replacement) from the distribution of single subject means and derived two-tailed p values from the distribution of differences between the bootstrapped samples.
The detection of saccade onsets and offsets was based on the velocity distribution of the gaze24. We used a moving average over 20 subsequent eye-position samples to determine saccade onsets/offsets whenever the velocity of the eye exceeded/fell below the median of the moving average by 3 SDs for at least 20 ms. Corrective saccades were defined as eye movements executed after the offline selected main saccade sequence and were only included in the respective corrective saccade analysis if they landed between 7° and 13° from the fixation target and were initiated within the first 500 ms following the main saccade sequence as well as before the participant's manual response.
Before proceeding to final data analysis, data were rotated (see 6.2). Consequently, after data rotation, the most counterclockwise saccade target ST1 was always represented at +45°/+15° (in the 90° and 30° conditions, respectively), the location BTW in between the saccade targets at 0° (in both the 90° and 30° conditions), and the most clockwise saccade target ST2 at -45°/-15° (in the 90° and 30° conditions, respectively) relative to the angle 0. Locations other than ST1, ST2, and BTW were considered as control locations (CTRL) in both, the 90° and 30° conditions.
Our protocol allowed us to evaluate saccades in response to oculomotor competition among two saccade targets presented at different angular distances based on the recorded eye data. As expected, the saccade endpoint distributions associated with the 90° (Figure 3A and 3C) and 30° (Figure 3B and 3D) conditions differed substantially. We observed mostly accurate saccades towards one of the saccade targets in the 90 ° condition, where 41.0% ± 1.0% of saccades ended within the sector including the most counterclockwise saccade target ST1 and 41.8% ± 1.9% within the sector including the most clockwise saccade target ST2 (Figure 3C). In the 30° condition, in contrast, participants executed a substantial number of averaging saccades. Here, 33.6% ± 2.4% of the saccades ended within the sector in between the 2 saccade targets BTW, 29.95% ± 1.6% ended within the sector including ST1, and 32.0% ± 1.8% within the sector including ST2 (Figure 3D).
Furthermore, the assessment of visual sensitivity at all 24 locations distributed across the visual field allowed us to analyze the spatial deployment of attention during oculomotor programming in detail. Overall, taking into account saccades of all directions, we observed a selective facilitation of visual sensitivity at the two saccade targets relative to the control locations CTRL (corresponding to the average across all positions except for ST1, ST2, and BTW) in both the 90° (ST1: d' = 2.2 ± 0.3 versus CTRL: d' = 0.3 ± 0.1, p < 0.0001; ST2: d' = 2.2 ± 0.4 versus CTRL, p < 0.0001; ST1 versus ST2, p = 0.8964; Figure 4A) and 30 ° (ST1: d' = 2.2 ± 0.3 versus CTRL: d' = 0.3 ± 0.1, p < 0.0001; ST2: d' = 2.1 ± 0.3 versus CTRL, p < 0.0001; ST1 versus ST2, p = 0.6026; Figure 4B) conditions. While visual sensitivity at the intermediate location was significantly lower than at the saccade target locations (BTW: d' = 0.6 ± 0.2 versus ST1, p < 0.0001; BTW versus ST2, p < 0.0001; Figure 4B), it was, however, slightly increased relative to the control locations in the 30° condition (BTW versus CTRL, p = 0.0010).
In order to disentangle whether visual attention is obligatorily deployed at the endpoint of saccades, we analyzed visual sensitivity at all locations as a function of the saccade landing direction (see step 6.3 in the protocol). Crucially, the specific saccade landing distribution observed in the 30° condition of this protocol made it possible to analyze the deployment of visual attention before saccades associated with spatially distinct endpoints in response to identical visual input. More specifically, by analyzing visual sensitivity before averaging saccades, we could determine whether or not attention shifts towards the endpoint of saccades even when it does not spatially coincide with a saccade goal. We observed that visual sensitivity was significantly enhanced at the endpoint of accurate saccades in both the 90° (ST1+2 saccaded: d' = 3.0 ± 0.4 versus ST1+2 non-saccaded: d' = 1.7 ± 0.4, p < 0.0001; Figure 4E) and the 30° (ST1+2 saccaded: d' = 2.7 ± 0.4 versus ST1+2 non-saccaded: d' = 2.0 ± 0.3, p = 0.0080; Figure 4F) condition. In contrast, before averaging saccades, visual sensitivity was not enhanced at the saccade endpoint but slightly reduced (BTW saccaded: d' = 0.4 ± 0.2 versus BTW non-saccaded: d' = 0.7 ± 0.2, p < 0.0001; Figure 4F). Thus, visual attention was not obligatorily shifted towards the endpoint of the upcoming saccade. Interestingly, averaging saccades were associated with an equal enhancement of visual sensitivity at the two surrounding saccade targets (ST1: d' = 2.2 ± 0.4 versus ST2: d' = 2.2 ± 0.4, p = 0.8402; Figure 4D), suggesting that attentional selection among the saccade targets was not readily resolved before the onset of averaging saccades.
To further evaluate a potential correlate of attentional selection before averaging saccades, data were analyzed as a function of the landing direction of corrective saccades, which can be frequently observed upon the execution of averaging saccades. We did not observe a significant benefit at the endpoint of corrective saccades following an averaging saccade (corrective saccade directed towards ST1+2: d' = 2.8 ± 0.5 versus corrective saccade not directed towards ST1+2: d' = 2.5 ± 0.8, p = 0.68300; Figure 5C), which supports the interpretation that attentional selection was not resolved before averaging saccades.

Figure 1: Instructions as presented to the participants. Visualization of the experimental instructions as presented to the participants at the beginning of each block. Please click here to view a larger version of this figure.

Figure 2: Experimental procedure and normalized saccade landing frequency maps. (A) Stimulus timing and display. Participants prepared a saccade from the fixation target (FT) to one of the two potential saccade targets (ST1 and ST2), presented simultaneously at two randomly chosen stimulus streams with an inter-target angular distance of either 90° (top panels) or 30° (bottom panels). The saccade targets were either shown continuously (cST1+2) or transiently (tST1+2). Stimulus streams could either be distractor streams (DS), composed of alternating vertical Gabors and masks (40 Hz) or discrimination target streams (DTS) which included the presentation of a brief discrimination target (DT, 25 ms), a clockwise or counterclockwise tilted Gabor, shown between 75 and 175 ms after the saccade targets onset. Participants saccaded towards one of the saccade targets and had to report the orientation of the discrimination target, appearing randomly at one of the 24 stimulus stream locations. Note that stimuli are sketched in order to increase their visibility. Actual stimuli match those shown in the stimulus streams depiction. (B) Normalized saccade landing frequency maps averaged across participants (n = 10) for the 90° (top) and 30° (bottom) conditions (collapsed across the transient and continuous ST presentation). This figure has been reprinted from Wollenberg et al. (2018)23. Please click here to view a larger version of this figure.

Figure 3: Saccade metrics. (A-B) Circular plots show the averaged frequency distribution of the saccade landing direction binned in evenly distributed angular sectors of 5°, in the 90° (A) and 30° conditions (B). Stimulus configuration is rotated as to align the two saccade targets symmetrically around the geometrical angle zero (see central insets). (C-D) Bar graphs illustrate averaged frequency of trials as a function of the saccade landing direction binned in 24 evenly distributed angular sectors of 15°. Data are shown for the three positions of interest (ST1, BTW and ST2) in the 90° (C) and 30° conditions (D). (E-H) Averaged saccade latency (E, F) and amplitude (G, H) observed for the same three positions of interest in the 90° (E, G) and 30° conditions (F, H). All data are shown irrespective of the duration (continuously or transiently) of the saccade targets. Light gray areas and error bars represent SEM. Polar plot black lines and corresponding light gray areas show linear interpolation between data points. This figure has been reprinted from Wollenberg et al. (2018)23. Please click here to view a larger version of this figure.

Figure 4: Visual sensitivity. (A-B). Circular plots show averaged visual sensitivity (d') as a function of the DT position in the 90° (A) and 30° conditions (B), irrespective of the duration of the saccade targets and across all saccade directions observed. Bar graphs illustrate visual sensitivity for four positions of interest (ST1, BTW, ST2, CTRL). (C-D) Visual sensitivity as a function of the DT position relative to the saccade landing direction in the 90° (C) and 30° conditions (D), irrespective of the duration of the saccade targets (blue: saccade to ST1; green: saccade to BTW; red: saccade to ST2). For each saccade direction, we took the average sensitivity for each discrimination target location. For example, the blue line plots visual sensitivity when saccades were made towards ST1 and the discrimination target was either at ST1 (+15° on the polar plot), BTW (15° counterclockwise to ST1; 0° on the polar plot) or ST2 (30° counterclockwise to ST1; + 345° on the polar plot), and so on. (E-F) Bar graphs illustrate sensitivity observed for DT shown at the saccaded (purple: e.g., DT at ST1 and saccade to ST1) and the non-saccaded positions (light-purple: e.g. DT at ST1 and saccade to ST2 or BTW) in the 90° (E) and the 30° (F) conditions. Conventions are as in Figure 3. This figure has been reprinted from Wollenberg et al. (2018)23. Please click here to view a larger version of this figure.

Figure 5: Corrective saccades. (A) Circular plot shows averaged frequency distribution of the corrective saccade landing direction following an averaging saccade. (B) The bar graph illustrates averaged frequency of trials as a function of the corrective saccade landing direction following an averaging saccade for three positions of interest (ST1, BTW and ST2). (C) The bar graph illustrates visual sensitivity as a function of the direction of the first corrective saccade for all trials in which an averaging saccade was executed. Purple bars show visual sensitivity for trials in which the corrective saccade was directed towards the location at which the DT appeared (e.g. DT at ST1 and corrective saccade towards ST1). Light purple bars show visual sensitivity for trials in which the corrective saccade was directed towards a different location than the location at which the DT appeared (e.g. DT at ST1 and corrective saccade towards ST2 or BTW). Conventions are as in Figure 3-4. This figure has been reprinted from Wollenberg et al. (2018)23. Please click here to view a larger version of this figure.