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Article  |   June 2019
Vertical and horizontal meridian modulations suggest areas with quadrantic representations as neural locus of the attentional repulsion effect
Author Affiliations
  • Denise Baumeler
    Faculté de Psychologie et des Sciences de l'Éducation, Université de Genève, Switzerland
    denise.baumeler@unige.ch
  • Sabine Born
    Faculté de Psychologie et des Sciences de l'Éducation, Université de Genève, Switzerland
Journal of Vision June 2019, Vol.19, 15. doi:10.1167/19.6.15
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      Denise Baumeler, Sabine Born; Vertical and horizontal meridian modulations suggest areas with quadrantic representations as neural locus of the attentional repulsion effect. Journal of Vision 2019;19(6):15. doi: 10.1167/19.6.15.

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Abstract

The attentional repulsion effect (ARE) is a perceptual bias attributed to a covert shift of attention toward a peripheral cue, which, in turn, repulses the perceived position of a subsequently presented probe (Suzuki & Cavanagh, 1997). So far, probes were mainly presented around the vertical meridian. Other studies of perceptual biases reported disruptions when stimuli were presented across the vertical meridian. These disruptions were explained by separate representations of the left and right visual hemifields, projecting to opposite anatomical hemispheres. As the ARE is typically examined through two-alternative, forced-choice tasks in which the estimation of the probe's position is based on the cue's effectiveness to repulse the probe across the vertical meridian, no such asymmetry has been reported. To test for similar meridian disruptions in the ARE, we collected absolute estimations (computer mouse responses) of the perceived probe positions (Experiment 1a). As absolute estimations of memorized positions are associated with overestimated distances in reproduction, results had to be compared to a no-cue baseline condition (Experiment 1b). Through this new methodological approach, we found the ARE to be strongest when the attentional capturing cue and the subsequently presented probe were displayed in the same hemifield (Experiment 2a). In a further experiment (Experiment 2b), we observed that the ARE is not only disrupted at the vertical, but also at the horizontal meridian. These disruptions at both meridians suggest the involvement of visual neural areas with quadrantic representations, such as V2 and/or V3 in the generation of the ARE.

Introduction
Attention is regarded as a filter for selecting relevant incoming sensory information (for a review, see Carrasco, 2011). A sudden appearance of a cue automatically captures visual attention (reviewed in Mulckhuyse & Theeuwes, 2010; Yantis & Jonides, 1984). This change in the focus of attention toward the cued location has been associated with faster and more accurate detection of targets appearing in the attended region and worse performance for targets appearing outside the focus of attention (Henderson, 1991; Jonides, 1980; Posner, 1980; Posner & Cohen, 1984). However, attentional shifts may not only affect detection and identification of objects. For instance, Suzuki and Cavanagh (1997) described the attentional repulsion effect (ARE) in which an involuntary attentional shift to a briefly presented peripheral cue biases the perceived spatial position of a subsequently presented probe. In their task, peripheral visual cues consisted of one circle flashed in a randomly chosen quadrant or two circles flashed in either of the two diagonal pairs of quadrants (top left/lower right or top right/lower left). These were presented prior to a Vernier probe, consisting of two vertical lines positioned above and below the center of the screen (see Figure 1). Observers were then asked to judge the horizontal offset of the two vertical lines, either clockwise or counterclockwise. They found that observers systematically misperceived the location of the Vernier lines as shifted or “repelled” away from the cues. That is to say perfectly aligned lines were perceived with a horizontal offset with the direction of offset depending on where the cue(s) had been presented. 
Figure 1
 
Trial sequence in Experiment 1a. Note that only top-left cue presentation is displayed although top-right cue presentation was equally likely from trial to trial. During probe presentation, Vernier lines were presented above and below fixation. The top Vernier line was equally likely to appear at nine different positions: −0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5°; the lower line was always centered (0°). ISI = interstimulus interval.
Figure 1
 
Trial sequence in Experiment 1a. Note that only top-left cue presentation is displayed although top-right cue presentation was equally likely from trial to trial. During probe presentation, Vernier lines were presented above and below fixation. The top Vernier line was equally likely to appear at nine different positions: −0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5°; the lower line was always centered (0°). ISI = interstimulus interval.
One interesting aspect of the attentional repulsion paradigm is that the Vernier probe is primarily presented around the vertical midline (e.g., Pratt & Arnott, 2008; Pratt & Turk-Browne, 2003; Suzuki & Cavanagh, 1997). Visual hemifields are represented in contralateral hemispheres; that is, the cortical representation of visual space is divided by the vertical meridian (for a review, see Wandell, Dumoulin, & Brewer, 2007). Thus, stimuli presented very close to each other but on either side of the vertical midline are represented very far from each other in cortical space. Accordingly, disruptions of attentional and perceptual effects when stimuli are presented close to or straddling the vertical meridian have been reported in a number of studies. For instance, T. Liu, Jiang, Sun, and He (2009) observed that crowding by a single distractor was less pronounced when target and distractor were presented on opposite sides of the vertical meridian compared to when they were presented in the same hemifield. Pillow and Rubin (2002) showed that discrimination of shapes induced by illusory contours (Kanizsa figures) was impaired when the relevant inducers appeared in separate hemifields. Further, in a recently published paper, S. Liu, Tse, and Cavanagh (2018) found that the double-drift illusion, a change in the perceived path of a moving Gabor patch induced by internal drift, was reduced at the vertical meridian when the illusory path would cross or be driven toward it. Moreover, increased reaction times have been described in a cueing paradigm when cue and target were presented in different hemifields (Rizzolatti, Riggio, Dascola, & Umiltá, 1987). Finally, multiple object tracking studies demonstrated higher tracking capacity and less interference when the moving stimuli were separated by the vertical meridian (Alvarez & Cavanagh, 2005; Carlson, Alvarez, & Cavanagh, 2007). In a similar vein, an attention-capturing cue should provoke the largest ARE when presented in the same hemifield as the subsequently presented Vernier stimulus. Surprisingly, such an asymmetry has never been reported. Quite to the contrary, the ARE has been observed to be strongest at the central position when the Vernier lines are presented perfectly aligned and to diminish when the test line is presented slightly away from the midline (DiGiacomo & Pratt, 2012; Pratt & Turk-Browne, 2003). 
In many cases, however, the reduced ARE with increasing eccentricity from the midline is a direct consequence of the used methods. The ARE has mainly been tested by two-alternative, forced-choice (2AFC) estimations of the top Vernier line in relation to the centrally presented lower Vernier line (e.g., Arnott & Goodale, 2006; DiGiacomo & Pratt, 2012; Pratt & Arnott, 2008). This relative measure has the disadvantage that conclusions are based on the cue's effectiveness to repulse the Vernier line across the vertical meridian. For example, a cue presented to the left may still strongly repel a probe likewise presented to the left of the midline; however, the effect is only apparent when the repulsion effect is larger than the probe's physical offset from the midline (i.e., when participants respond to have seen it right of the midline). Thus, repulsion of Vernier lines with a slight offset from the midline may be underestimated. 
To test for repulsion effects independent of the vertical meridian, measurements need to be adapted to collect absolute perceived Vernier line positions. Therefore, in the current study, we asked participants to indicate the perceived Vernier line position by pointing it out with a computer mouse cursor (Experiment 1a; see also Pratt & Turk-Browne, 2003). As is shown, a critical aspect is to assess not only absolute position, but to compare the absolute reports to position estimates from a no-cue control condition (Experiment 1b). This procedure indeed revealed that the ARE is strongest when cue and Vernier are presented in the same hemifield (Experiment 2a). In a last experiment (Experiment 2b), we examined whether the ARE is not only disrupted by the vertical, but also by the horizontal meridian. This was indeed the case. These findings point to areas with quadrantic representations, such as V2 and/or V3, as the neural locus of the ARE (Carlson et al., 2007; T. Liu et al., 2009). 
Experiment 1a
To get an idea of how results from computer mouse pointing compare to a classic 2AFC task, we first performed a within-subject comparison of those two response modes. These measurements of the ARE have already been compared by Pratt and Turk-Browne (2003), revealing an effect of similar magnitude. One advantage of computer mouse responses is that they give absolute values for the perceived location of the probe. Additionally, we also wanted to investigate the impact of the lower Vernier line on the ARE by introducing a “half” Vernier condition, that is, a single line shown above fixation. Results of this manipulation can be found in Supplementary File S1. Findings suggest that measuring the ARE with half Vernier lines could be noisier and potentially produce smaller effects than the classic “full” Vernier condition. It is possible that the lower Vernier line serves as a visual reference that facilitates the precision of responses but may also introduce a larger bias. As the role of the lower Vernier line remained somewhat unclear and is not the focus of the current study, we chose to use only full Vernier lines for the following experiments, which is in accordance with previous studies. 
Methods
Participants
In Experiment 1a, 24 undergraduate students from the University of Geneva, Switzerland, participated in exchange for course credit. After exclusion of four participants (see below), 20 participants remained for analysis (13 women, Mage = 20.9 years, age range: 18–27). For all experiments, students had normal or corrected-to-normal vision, were naïve to the hypotheses of the experiment, and gave written informed consent prior to participating. The procedures were approved by the ethics committee of the Faculty of Psychology and Educational Sciences, Geneva, and followed the principles laid down in the Code of Ethics of the World Medical Association (Declaration of Helsinki). 
Apparatus
Experiments were conducted in a dimly lit room. For the majority of participants (n = 15), stimuli were presented on a Viewpixx monitor (VPixx Technologies Inc., Saint-Bruno, Canada) running at 100 Hz with a screen resolution of 1,920 × 1,200 pixels. For the remaining participants (n = 5), stimuli were presented on a 21-in. CRT monitor (NEC MultiSync FE2111SB) with a screen resolution of 1,280 × 1,024 pixels running at 85 Hz. To assure a stable viewing distance of 55 cm, a chin and headrest was used. 
The experimental program was written in MATLAB (MathWorks, Natick, MA) using the Psychophysics and Eyelink Toolbox extensions (Brainard, 1997; Cornelissen, Peters, & Palmer, 2002). Eye movements were monitored using an EyeLink1000 desk-mounted eye tracker (SR-Research Ltd., Ottawa, Canada) at a sampling rate of 1,000 Hz. 
Stimuli, procedure, and design
Stimuli appeared in black (0 cd/m2) against a gray (30 cd/m2) background. The trial sequence is illustrated in Figure 1. Trials started with the presentation of a central fixation point (0.1° in diameter) for a variable duration of 500–800 ms. Then, a lateralized cue (filled circle of 1° in diameter) was shown, either top left or top right at a horizontal eccentricity of ±3.5° and 3.5° above fixation (eccentricities are reported with respect to the center of the circle). Following the removal of the cue after 30 ms, there was a blank interval of 170 ms, resulting in a total stimulus onset asynchrony of 200 ms. Previous research has found the ARE to be strongest when the probe was presented around 200 ms after cue onset (e.g., Kosovicheva, Fortenbaugh, & Robertson, 2010; Ono & Watanabe, 2011; Suzuki & Cavanagh, 1997). The subsequent Vernier probe, consisting of two vertical lines, 1° long and 0.1° wide, was displayed for 100 ms. The lower Vernier line always appeared −2.5° center-to-center below the fixation point without offset from the vertical midline (0°). The top Vernier was shown 2.5° above the fixation point at one of nine horizontal locations: −0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5° (negative = left of fixation). Vernier probe presentation was followed by a 250-ms full-screen pattern mask (gray squares of randomized luminance with 0.7° side length) and a successive response display. Response modes differed across blocks of trials: Participants were either asked to determine whether the top Vernier line was left or right relative to the fixation point by pressing the corresponding arrow key on a keyboard (2AFC) or were asked to indicate the absolute perceived position of the top Vernier line with a computer mouse cursor (crosshair, 0.3° × 0.3°). For each trial, the initial cursor position was placed at a vertical distance of 2.5° above fixation with a randomly assigned horizontal eccentricity between ±3°. After each response, there was an 800-ms intertrial interval before the fixation point reappeared to indicate the start of the next trial. 
In total, each participant completed 720 trials separated into four blocks (two blocks in 2AFC, two blocks in mouse response mode) after an individual number of practice trials. The order of the four blocks was randomized for each participant. Over the course of a block of trials, the nine top Vernier positions and the two cue sides were randomized. Participants were instructed to keep fixation throughout the entire trial (until the response display appeared). Feedback regarding breaks of fixation (gaze coordinates outside of ±1.5°) or blinks was provided after the response was given. 
Results
For all experiments, we adopt an alpha level of p = 0.050 (two-sided) to determine statistical significance and report Greenhouse–Geisser corrected values if the assumption of sphericity is violated. Post hoc t tests and the inferential 95% confidence intervals were corrected for multiple comparison using Holm–Bonferroni adjusted alpha levels (Holm, 1979; Ludbrook, 2000). 
Exclusions
Two participants were excluded due to misunderstanding of the task instructions (cue positions were indicated instead of probe positions) and two participants were excluded because of high proportions of breaks of fixation and blinks (>35%). For the remaining 20 participants, trials with breaks of fixation and blinks (10.33%) were excluded from further analyses. 
Psychometric functions
The proportion of “right” responses (i.e., the top Vernier line was perceived to the right of the fixation point) were calculated for both cue sides (left or right) at each of the nine top Vernier positions (−0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5°), separate for the two response modes (2AFC as well as mouse responses) as seen in Figure 2A. To this end, absolute values of the mouse responses were recoded into binary 2AFC responses (i.e., mouse click either left or right of fixation). An ARE is present in the data if we find a higher proportion of “right” responses when the cue preceding the Vernier was presented to the left than when the cue was presented to the right. Indeed, Figure 2A suggests that this was the case. To summarize the data across different Vernier line positions into one single index of the ARE, we fit logistic psychometric functions (maximum likelihood estimate) to the data of each participant and determined the point of subjective verticality (PSV) for both cue sides. Figure 2B shows the proportion or right responses of one representative participant in the different conditions and its corresponding fits. The PSV is the top Vernier position for which the participants would be equally likely to respond with a key press left or right. If the lateralized cues introduced a bias (i.e., ARE), the PSV should be slightly shifted toward the side of the cue: If the cue repulses the Vernier line away from it, it must be presented with a slight offset toward the cue's side to be perceived right above fixation. Figure 2C illustrates the average PSV values across all participants. The PSVs were analyzed with a 2 (cue side: left or right) × 2 (response mode: 2AFC or recoded mouse responses) repeated-measures ANOVA. We obtained a significant main effect of the factor cue side, F(1, 19) = 20.09, p < 0.001, ηp2 = 0.51, confirming an ARE: Overall, if a cue was presented on the left side, the PSV was more negative than when the cue was presented on the right side (Mleft: −0.02°, Mright: 0.04°). The main effect of the factor response mode, F(1, 19) = 3.27, p = 0.086, ηp2 = 0.15, as well as the two-way interaction, F(1, 19) = 1.11, p = 0.304, ηp2 = 0.06, did not reach significance. 
Figure 2
 
Results of Experiment 1a: Psychometric functions (2AFC and recoded data for mouse-response mode). (A) Proportion of “right” responses as a function of top Vernier positions averaged across all 20 participants. (B) Proportion of “right” responses of one representative participant (subject 25). The curves show the psychometric functions' fit to the data. (C) Average PSVs and (D) slopes (higher values denote steeper slopes) of the psychometric functions, cue sides, and response modes. In all cases, error bars represent 95% confidence interval of comparison cue left versus cue right (orange vs. blue) for a given response mode: If error bars do not overlap, the difference is significant.
Figure 2
 
Results of Experiment 1a: Psychometric functions (2AFC and recoded data for mouse-response mode). (A) Proportion of “right” responses as a function of top Vernier positions averaged across all 20 participants. (B) Proportion of “right” responses of one representative participant (subject 25). The curves show the psychometric functions' fit to the data. (C) Average PSVs and (D) slopes (higher values denote steeper slopes) of the psychometric functions, cue sides, and response modes. In all cases, error bars represent 95% confidence interval of comparison cue left versus cue right (orange vs. blue) for a given response mode: If error bars do not overlap, the difference is significant.
A respective ANOVA on the slope values (see Figure 2D) revealed no significant main effects or interactions, all Fs(1, 19) < 0.84, all ps > 0.371, all ηp2s < 0.04, suggesting that the left/right discrimination was of equal difficulty for the two response modes. 
Absolute localization judgments for each top Vernier position
To test for the absolute perceived location in the mouse response condition, the reported top Vernier positions were averaged for each participant per cue side and actual location. Then the resulting perceived locations were plotted against the actual positions of the displayed top Vernier line (Figure 3A). Note that more negative values represent a leftward bias in the perceived location of the line. The ARE at every top Vernier position was analyzed in a 2 (cue side: left or right) × 9 (top Vernier position: −0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5°) repeated-measures ANOVA. A significant main effect of the factor cue side, F(1, 19) = 8.76, p = 0.008, ηp2 = 0.32, was found, confirming an ARE: Top Vernier lines presented after a left cue were perceived more to the right than top Vernier lines presented after a right cue (Mleft: 0.01°, Mright: −0.07°). Furthermore, the main effect of the factor top Vernier position was significant, F(2.07, 39.32) = 602.54, p < 0.001, ηp2 = 0.97, indicating that participants were able to discriminate between the nine top Vernier positions. 
Figure 3
 
Results of Experiment 1a: Absolute values. (A) Average perceived position of top Vernier lines against actual positions averaged across all 20 participants. The gray dotted line represents a regression line with a slope b1 = 1 (actual = perceived location). (B) Difference between cue left and cue right induced repulsion as a parameter for the ARE at each top Vernier line position. Error bars represent 95% confidence intervals of the difference cue left versus cue right: If error bars do not overlap (A) or cross the zero line (B), the difference is significant. Significant findings of the post hoc analyses are additionally indicated by asterisks in panel B.
Figure 3
 
Results of Experiment 1a: Absolute values. (A) Average perceived position of top Vernier lines against actual positions averaged across all 20 participants. The gray dotted line represents a regression line with a slope b1 = 1 (actual = perceived location). (B) Difference between cue left and cue right induced repulsion as a parameter for the ARE at each top Vernier line position. Error bars represent 95% confidence intervals of the difference cue left versus cue right: If error bars do not overlap (A) or cross the zero line (B), the difference is significant. Significant findings of the post hoc analyses are additionally indicated by asterisks in panel B.
These main effects were qualified by a significant two-way interaction between cue side and top Vernier position, F(5.29, 100.51) = 5.82, p < 0.001, ηp2 = 0.23, revealing that the size of the bias induced by the cues differed across top Vernier positions. To follow up on the two-way interaction, we conducted post hoc tests of the difference between cue left and right conditions as a measure of the ARE across top Vernier positions. A significant difference emerged at the following top Vernier positions (see Figure 3B): −0.1°, Diff = 0.11°, t(19) = 3.00, p < 0.007; 0°, Diff = 0.12°, t(19) = 4.00, p < 0.006; 0.1°, Diff = 0.14°, t(19) = 4.22, p < 0.006, no other difference reached significance, ts(19) < 2.55, ps > 0.009, using a Holm–Bonferroni alpha level correction. In other words, no ARE was present for the outer Vernier positions (more specifically, for the −0.5°, −0.3°, −0.2°, 0.2°, 0.3°, and 0.5° positions). 
Horizontal eccentricity
As in the study of Pratt and Turk-Browne (2003), another interesting pattern emerged in the mouse-pointing condition: In general, the horizontal eccentricity of the stimuli was overestimated. For instance, test lines presented 0.2° away from the midline were reported further out, around 0.4° from the midline (see Figure 3A). To quantify this overestimation, we fitted linear regressions separately to the data of the cue left and cue right conditions. To statistically test for overestimations, one-sample t tests were conducted in which the slope values of the fitted regression lines were tested against a slope of b1 = 1 (actual = perceived location). Both slopes were significantly larger than one, bs > 1.78, ts(19) > 13.14, ps < 0.001. 
Summary and discussion
Experiment 1a was mainly a replication of results observed by Pratt and Turk-Browne (2003), albeit using a within-subject comparison and more elaborate analysis. Comparing 2AFC with recoded mouse-pointing responses, an ARE, as indexed by the difference in the PSV, was observed with both response modes. Further, when quantifying the ARE as the difference between cue left and cue right localization responses, results of Experiment 1a confirmed that the ARE seems to be biggest within ±0.1° of the vertical meridian and to drop at larger eccentricities. These findings are in line with previously documented results (DiGiacomo & Pratt, 2012; Pratt & Turk-Browne, 2003) although, as was mentioned in the Introduction, results from 2AFC tasks are difficult to interpret in this context as repulsion needs to be stronger than the horizontal offset of the stimulus to be noticeable as repulsion. With mouse responses, the difference between cue left and cue right localization was fairly stable within ±0.3° of eccentricity (see Figure 3B). Across those eccentricities that produced a significant result, the difference was around Diff ≈ 0.10°, which was bigger than the estimate of the difference in the PSV (Diff = 0.06°). The mouse pointing also revealed a horizontal overestimation in the perceived eccentricity of the Vernier stimuli. Pratt and Turk-Browne already reported this pattern for computer mouse responses. A discussion of the possible origins of this effect is deferred to the General discussion. However, this general bias suitably emphasizes the difficulty in judging the relative strength of repulsion from left and right cues for Vernier lines with a slight offset from the midline: Take the example of the Vernier presented slightly left of fixation at −0.1°, which was localized at around −0.15° in the cue left condition and at around −0.25° in the cue right condition. Does this mean that the Vernier was actually attracted by 0.05° by the left cue and repulsed by 0.15° by the right cue? We cannot know unless we have an unbiased reference point. 
Experiment 1b
To test for their feasibility in providing an unbiased reference for mouse localization responses, we examined cue absent and bilateral cue conditions in Experiment 1b. One critical question is whether the overestimation of horizontal eccentricity observed in Experiment 1a is still evident even when no ARE is elicited. 
Methods
Participants
Twenty-six newly recruited undergraduate students from the University of Geneva, Switzerland, participated in Experiment 1b in exchange for course credits. After exclusion of three participants, 23 remained for analysis (16 women, Mage = 20.7, age range: 20–32). 
Apparatus
The apparatus was identical to Experiment 1a with the exception that, this time, for all participants, stimuli were presented on a 21-in. CRT monitor (NEC MultiSync FE2111SB) with a screen resolution of 1,280 × 1,024 pixels running at 85 Hz. 
Stimuli, procedure, and design
Stimuli, procedure, and design were similar to Experiment 1a except that cues were either presented bilaterally (i.e., simultaneously at both top-left and top-right positions), or no cues were presented. Only computer mouse responses were collected. In total, each participant completed 720 trials separated into four blocks after an individual number of practice trials. 
Results
Exclusions
Three participants were excluded because of high proportions of breaks of fixation and blinks (>35%). For the remaining participants, trials with eye movements and blinks (10.93%) were excluded from further analyses. 
Absolute localization judgments for each top Vernier position
The averaged perceived top Vernier positions plotted against each actual position are shown in Figure 4A. Responses were analyzed with a 2 (cue side: bilateral or absent) × 9 (top Vernier position: −0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5°) repeated-measures ANOVA. The main effect of the factor top Vernier position was significant, F(1.39, 30.70) = 394.05, p < 0.001, ηp2 = 0.95, indicating that participants were able to discriminate between the nine top Vernier positions. As expected, all other main effects and interactions did not reach significance, Fs(3.78, 83.19) < 1.82, ps > 0.136, ηp2s < 0.08. 
Figure 4
 
Results of Experiment 1b: Absolute values. (A) Average perceived positions of top Vernier lines against actual locations averaged across all 23 participants. The gray dotted line represents a regression line with a slope b1 = 1. Error bars represent 95% confidence intervals of comparison cue bilateral versus cue absent. (B) Between-subject comparison of absolute values from Figures 3A and 4A. Error bars represent 95% confidence intervals of the mean of each data point. (C) Repulsion at each top Vernier position with relative contribution of cue left and cue right.
Figure 4
 
Results of Experiment 1b: Absolute values. (A) Average perceived positions of top Vernier lines against actual locations averaged across all 23 participants. The gray dotted line represents a regression line with a slope b1 = 1. Error bars represent 95% confidence intervals of comparison cue bilateral versus cue absent. (B) Between-subject comparison of absolute values from Figures 3A and 4A. Error bars represent 95% confidence intervals of the mean of each data point. (C) Repulsion at each top Vernier position with relative contribution of cue left and cue right.
Horizontal eccentricity
An overestimation of horizontal eccentricity was also observed in Experiment 1b (see Figure 4A). This was confirmed by one-sample t tests, checking whether the slopes of the linear regressions fitted to the data (not shown in the figure) differed from b1 = 1. Both tests revealed a significant difference, bs > 1.94, ts(22) > 10.38, ps < 0.001. These results suggest that the overestimation of the horizontal eccentricity is independent of the ARE as it occurs for bilateral, unilateral, and no-cue conditions. 
Contribution of each cue to the ARE: Comparing Experiment 1a to Experiment 1b
As a first estimate to quantify the distribution of repulsion induced by left and right cues, we compared the results of the cue-absent condition to the results of Experiment 1a (see Figure 4B). The corresponding differences (cue left − cue absent vs. cue absent − cue right: for both, positive values of the difference indicate a repulsion from the cue) are illustrated in Figure 4C. Although data are from two different groups of participants, when referenced to a no-cue condition, cues seemed to trigger a greater repulsion of the subsequently presented probes when the two stimuli were presented in the same hemifield. 
Summary and discussion
Results of Experiment 1b confirmed that an overestimation of the horizontal eccentricity of a similar magnitude occurred with bilateral cues and when no cue was presented. In contrast to studies with a stronger emphasis on spatial memory (e.g., Diedrichsen, Werner, Schmidt, & Trommershäuser, 2004), the mere presence of cues in the sense of visual landmarks did not affect localization judgments in the current paradigm. Thus, comparing mouse-pointing responses of unilateral cue conditions (i.e., typical ARE paradigm) to a no-cue baseline condition seems a feasible method to estimate the contribution of left and right cues to the overall ARE at different top Vernier positions. Indeed, a first screening comparing data from Experiment 1a and 1b suggests that top Vernier lines presented in the cued hemifield are exposed to a stronger repulsion compared to top Vernier lines that are presented in the uncued hemifield (see Figure 4B). To corroborate this, Experiment 2a compared repulsion induced by left and right cues in relation to an unbiased reference from a no-cue condition in a within-subject design. 
Experiment 2a
Experiment 2a addresses our main question whether the magnitude of the ARE is dependent on stimuli being presented within the same visual hemifield. We determined the absolute perceived top Vernier positions in conditions in which the cue was either presented on the left side of the vertical meridian, the right side of the vertical meridian, or was absent in a within-subject design. Subtracting estimates of the uncued condition and the cued conditions, we extracted the absolute repulsion triggered by either cue left or cue right at a given top Vernier location. Furthermore, we wanted to assure that the obtained spatial profiles of the ARE are not simply reflecting changes with cue–Vernier distance. Kosovicheva et al. (2010) demonstrated that the ARE depends on cue–Vernier distance. The relationship can be characterized by an inverted U-shaped function: The amount of perceived repulsion was attenuated below 2° and above 8° of cue–Vernier distance in their study. Therefore, we also varied cue–Vernier distances, presenting the cues at three possible eccentricities ±9°, ±3.5°, and ±1° and examined whether the spatial profile of the ARE varied across those conditions. In accordance with the findings of Kosovicheva et al. that the magnitude of the ARE is dependent on the distance to the cue's center of mass (as opposed to its edges), eccentricities refer to the cue circle's center. 
Methods
Participants
For Experiment 2a, 33 newly recruited undergraduate students from the University of Geneva, Switzerland, participated in exchange for course credit. After exclusion of four participants, 29 students remained for analysis (26 women, Mage = 21.3 years, age range: 17–50). 
Apparatus, stimuli, procedure, and design
The apparatus, stimuli, procedure, and experimental design were the same as in Experiment 1b. However, in Experiment 2a, cues were equally likely to appear top left or top right at a vertical eccentricity of 3.5° with a horizontal eccentricity of ±9°, ±3.5°, ±1° to the cue's center or not at all (absent). In total, each participant completed 756 trials separated into four blocks after an individual number of practice trials. 
Results
Exclusions
Four participants were excluded because of high proportions of breaks of fixation and blinks (>35%). For the remaining participants, trials with eye movements and blinks (15.58%) were eliminated for further analyses. 
Absolute localization judgments for each top Vernier position
As in the two previous experiments, the perceived top Vernier positions were averaged for each participant's data, separate for each of the three cue eccentricities (±9°, ±3.5°, ±1°; see Figure 5A). To statistically analyze the perceived positions, we computed absolute localization without the eccentricity bias by subtracting the overestimations of the no-cue condition from the estimates of the unilateral conditions (see Figure 5B). These means were then analyzed with a 3 (cue eccentricity: ±9°, ±3.5°, or ±1°) × 2 (cue side: left or right) × 9 (top Vernier position: −0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5°) three-way, repeated-measures ANOVA. A significant main effect of the factor cue side, F(1, 28) = 48.54, p < 0.001, ηp2 = 0.63, was found with left cues leading to estimates biased to the right and right cues to estimates biased to the left (Mleft: 0.08°, Mright: −0.08°). Moreover, the main effect of the factor top Vernier position was significant, F(5.50, 153.93) = 17.38, p < 0.001, ηp2 = 0.86, revealing that participants were able to discriminate between the nine top Vernier positions. 
Figure 5
 
Results of Experiment 2a: Absolute values, vertical meridian. Evaluations are displayed separately for each cue eccentricity (±9°, ±3.5°, ±1°) as well as averaged across all three eccentricities. (A) Average perceived positions of top Vernier lines against actual locations for the three cue conditions (left, right, absent), averaged across all 29 participants. The gray dotted line represents a regression line with b1 = 1. Error bars represent 95% confidence intervals of the data points. (B) Perceived position of top Vernier lines plotted against the actual top Vernier positions when the overestimation of the no-cue condition is subtracted from the estimates of the unilateral conditions. Error bars represent 95% confidence intervals of the data points. (C) Repulsion at each top Vernier position with relative contribution of cue left and cue right. Error bars represent 95% confidence intervals of the cue-induced repulsion effect: If error bars do not cross the zero line, repulsion is significant. Significant findings of the across eccentricities post hoc analyses are additionally indicated by asterisks.
Figure 5
 
Results of Experiment 2a: Absolute values, vertical meridian. Evaluations are displayed separately for each cue eccentricity (±9°, ±3.5°, ±1°) as well as averaged across all three eccentricities. (A) Average perceived positions of top Vernier lines against actual locations for the three cue conditions (left, right, absent), averaged across all 29 participants. The gray dotted line represents a regression line with b1 = 1. Error bars represent 95% confidence intervals of the data points. (B) Perceived position of top Vernier lines plotted against the actual top Vernier positions when the overestimation of the no-cue condition is subtracted from the estimates of the unilateral conditions. Error bars represent 95% confidence intervals of the data points. (C) Repulsion at each top Vernier position with relative contribution of cue left and cue right. Error bars represent 95% confidence intervals of the cue-induced repulsion effect: If error bars do not cross the zero line, repulsion is significant. Significant findings of the across eccentricities post hoc analyses are additionally indicated by asterisks.
These main effects were qualified by a significant two-way interaction between the factor cue side and the factor top Vernier position, F(5.49, 153.83) = 17.22, p < 0.001, ηp2 = 0.38. To follow up on this two-way interaction, we once more computed absolute repulsion values by subtracting estimates of the unilateral conditions and the no-cue condition. This time, to keep a positive sign for repulsion, we subtracted as follows for cue left: cue left − no cue; for cue right: no cue − cue right (see Figure 5C). Post hoc t tests of these differences tested against zero showed that there was a significant repulsion for cue left at the following top Vernier positions: −0.5°, Diff = 0.09°, t(28) = 2.95, p < 0.013; −0.3°, Diff = 0.10°, t(28) = 4.83, p < 0.006; −0.2°, Diff = 0.11°, t(28) = 3.83, p < 0.008; −0.1°, Diff = 0.16°, t(28) = 6.19, p < 0.006; 0°, Diff = 0.13°, t(28) = 4.44, p < 0.007; and 0.1°, Diff = 0.08°, t(28) = 3.40, p < 0.010. Top Vernier line positions 0.2°, 0.3°, and 0.5° did not reach significance, ts(28) < 1.47, ps > 0.017. For cue right, a significant repulsion was reached at the following top Vernier positions: −0.2°, Diff = 0.05°, t(28) = 2.70, p < 0.013; −0.1°, Diff = 0.08°, t(28) = 3.71, p < 0.007; 0°, Diff = 0.11°, t(28) = 3.19, p < 0.010; 0.1°, Diff = 0.16°, t(28) = 5.72, p < 0.006; 0.2°, Diff = 0.15°, t(28) = 6.63, p < 0.006; and 0.3°, Diff = 0.07°, t(28) = 3.27, p < 0.008. Top Vernier line positions −0.5°, −0.3°, and 0.5° did not reach significance, ts(28) < 1.53, ps > 0.017, using a Holm–Bonferroni alpha level correction. These results demonstrate that a cue presented in the same hemifield as the Vernier stimulus elicited a stronger repulsion compared to conditions in which the cue and the Vernier were presented in separate hemifields. 
Moreover, a significant two-way interaction between the factor cue eccentricity and the factor cue side emerged, F(1.68, 46.89) = 13.50, p < 0.001, ηp2 = 0.33. Post hoc pairwise comparisons showed that the differences between the cue sides (i.e., the ARE in general) was overall slightly larger for the smaller cue–Vernier distances but was significant at each of the three cue positions: ±9°, Diff = 0.10°, t(28) = 5.07, p < 0.050; ±3.5°, Diff = 0.17°, t(28) = 5.43, p < 0.025; ±1°, Diff = 0.19°, t(28) = 8.64, p < 0.017. 
Importantly, the three-way interaction was not significant, F(8.44, 236.28) = 1.26, p = 0.264, ηp2 = 0.04. This can also be seen in Figure 5C: The general pattern of asymmetry with larger repulsion in the same hemifield is preserved for all three cue distances. Also no other main effect or interaction reached significance, Fs(9.56, 267.60) < 1.18, ps > 0.309, ηp2s < 0.04. 
Horizontal eccentricity
As before, one-sample t tests were computed to test whether the slopes of the fitted linear regressions for each of the three cue conditions at each eccentricity (i.e., based on the data as shown in Figure 5A) differed from b1 = 1, which was the case, bs > 1.75, ts(28) > 9.65, ps < 0.001. 
Summary and discussion
To summarize the findings of Experiment 2a, we found strongest repulsion when the Vernier probe was slightly offset from the vertical meridian in the direction of the cue. The repulsion effect diminished remarkably when the attention-capturing cue and the subsequently presented probe were displayed across the vertical meridian. This pattern is in line with the spatial organization of cortical visual representation in which visual hemifields project to separate hemispheres. Moreover, Figure 5C suggests that results from other methods for which the largest AREs were observed with Vernier lines presented on the meridian (see also Experiment 1a) may be easily explained: Usually the difference between the two cue conditions is taken as the ARE. When adding up repulsion from the left and right cues, a similar pattern would emerge in the current experiment. In general, our results suggest that the cue–Vernier distances seem to influence the robustness of the ARE with stronger ARE for smaller cue–Vernier distances. In our experiment, the ARE was most pronounced at the smallest cue distance of 1°. In contrast, Kosovicheva et al. (2010) found an inverted U-shaped function with diminishing repulsion for cue–Vernier distances smaller than 2° and larger than 8°. Interestingly, Kosovicheva et al. reported considerable interindividual differences in the shape of the function and some variations across experiments. Thus, we do not think our results invalidate the assumption that the ARE should diminish at some point for very small cue–Vernier distances. Importantly, even though there were slight alterations in the magnitude of the ARE dependent on cue–Vernier distances, it seems that these distances do not account for the hemifield-specific spatial distribution of the ARE revealed in Experiment 2a. To further confine the possible neural locus of the ARE, our last experiment examines whether the ARE is also disrupted across the horizontal meridian. 
Experiment 2b
To further confine the possible locus of origin, we investigated the disruption of the ARE at the horizontal meridian. Therefore, stimuli were rotated by ±90°. As a consequence, the cue and the test Vernier line were now presented within one hemifield. This time, we were interested in the separation of the visual field by the horizontal meridian (i.e., lower and upper visual field). If the ARE is disrupted when the cue and the Vernier line are presented across the horizontal meridian, this would indicate that the neural origin of the ARE is most likely located in V2 and/or V3, which have quadrant-specific representations of visual space (S. Liu et al., 2018; T. Liu et al., 2009). 
Methods
Participants
For Experiment 2b, 33 newly recruited undergraduate students from the University of Geneva, Switzerland, participated in exchange for course credit. After exclusion of three participants, 30 students remained for analysis (26 women, Mage = 21.1 years, age range: 17–48). Participants were randomly assigned to two groups (G1: test stimuli left, G2: test stimuli right) of 15 participants each. Even though the main effect of the factor group was significant, F(1, 28) = 4.81, p = 0.037, ηp2 = 0.15, when performing the later described ANOVA, including an additional between-subjects factor group, none of the interactions involving the factor group reached significance, Fs(8.97, 251.21) < 1.82, ps > 0.065, ηp2s < 0.06. Based on these findings, the two data sets were collapsed. 
Apparatus, stimuli, procedure, and design
The apparatus, stimuli, procedure, and experimental design were the same as in Experiment 2a. However, in Experiment 2b, stimuli were rotated either by −90° in group 1 or by +90° in group 2. Hence, cues appeared at a horizontal eccentricity of −3.5° in group 1 and 3.5° in group 2. In both groups, cues were presented at a vertical eccentricity of ±9°, ±3.5°, ±1°, or not at all (absent). The test Vernier line, comparable to the previously described top Vernier line, was presented −2.5° left of the fixation point in group 1 and 2.5° right of the fixation point in group 2. For both groups, the test Vernier line was presented horizontally at one of nine vertical locations: −0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5° (negative = below fixation). 
Results
Exclusions
The first three participants were excluded due to unclear task instructions. Trials with eye movements and blinks (9.41%) were excluded from further analyses. 
Absolute localization judgments for each test Vernier position
As in the previous experiment, the perceived test Vernier positions, this time presented either left or right of fixation, were averaged for each participant's data, separate for each of the three cue eccentricities (±9°, ±3.5°, ±1°; see Figure 6A). As in Experiment 2a the (vertical) eccentricity overestimations of the no-cue condition were subtracted from the estimates of the unilateral cue conditions (see Figure 6B). These means were then analyzed with a 3 (cue eccentricity: ±9°, ±3.5°, or ±1°) × 2 (cue side: below or above) × 9 (test Vernier position: −0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5°) three-way, repeated-measures ANOVA. A significant main effect of the factor cue side, F(1, 29) = 29.53, p < 0.001, ηp2 = 0.50, was found with below cues leading to estimates biased upward and above cues leading to estimates biased downward (Mbelow: 0.05°, Mabove: −0.04°). Moreover, the main effect of the factor test Vernier position was significant, F(5.47, 158.68) = 260.07, p < 0.001, ηp2 = 0.90, indicating that participants were able to discriminate between the nine test Vernier positions. 
Figure 6
 
Results of Experiment 2b: Absolute values, horizontal meridian. Evaluations are displayed separately for each cue eccentricity (±9°, ±3.5°, ±1°) as well as averaged across all three cue eccentricities. (A) Average perceived positions of test Vernier lines against actual locations for the three cue conditions (below, above, absent) averaged across all 30 participants. The gray dotted line represents a regression line with b1 = 1. Error bars represent 95% confidence intervals of the data points. (B) Perceived position of test Vernier lines plotted against the actual test Vernier positions when the overestimation of the no-cue condition is subtracted from the estimates of the unilateral conditions. Error bars represent 95% confidence intervals of the cue-induced repulsion effect: If error bars do not cross the zero line, repulsion is significant. Significant findings of the across eccentricities post hoc analyses are additionally indicated by asterisks.
Figure 6
 
Results of Experiment 2b: Absolute values, horizontal meridian. Evaluations are displayed separately for each cue eccentricity (±9°, ±3.5°, ±1°) as well as averaged across all three cue eccentricities. (A) Average perceived positions of test Vernier lines against actual locations for the three cue conditions (below, above, absent) averaged across all 30 participants. The gray dotted line represents a regression line with b1 = 1. Error bars represent 95% confidence intervals of the data points. (B) Perceived position of test Vernier lines plotted against the actual test Vernier positions when the overestimation of the no-cue condition is subtracted from the estimates of the unilateral conditions. Error bars represent 95% confidence intervals of the cue-induced repulsion effect: If error bars do not cross the zero line, repulsion is significant. Significant findings of the across eccentricities post hoc analyses are additionally indicated by asterisks.
Importantly, the main effects were qualified by a significant two-way interaction between the factor cue side and the factor test Vernier position, F(4.28, 124.02) = 18.30, p < 0.001, ηp2 = 0.39. To follow up on this two-way interaction, we once again computed absolute repulsion values by subtracting estimates of the unilateral conditions and the no-cue condition (see Figure 5C). Post hoc t tests of these differences tested against zero showed that there was significant repulsion for below cues at the following test Vernier positions: −0.3°, Diff = 0.06°, t(29) = 2.77, p < 0.010; −0.2°, Diff = 0.08°, t(29) = 2.97, p < 0.007; −0.1°, Diff = 0.13°, t(29) = 4.42, p < 0.006; 0°, Diff = 0.06°, t(29) = 3.05, p < 0.006; and 0.1°, Diff = 0.08°, t(29) = 2.87, p < 0.008. Test Vernier line positions −0.5, 0.2°, 0.3°, and 0.5° did not reach significance, ts(29) < 2.04, ps > 0.013. For above cues, a significant repulsion was reached at the following test Vernier positions: −0.2°, Diff = 0.07°, t(29) = 2.94, p < 0.008; 0°, Diff = 0.09°, t(29) = 3.44 p < 0.006; 0.1°, Diff = 0.08°, t(29) = 3.32, p < 0.007; and 0.2°, Diff = 0.11°, t(29) = 4.71, p < 0.006. Test Vernier line positions −0.5°, −0.3°, −0.1°, 0.3°, and 0.5° did not reach significance, ts(29) < 1.38, ps > 0.010. These results underline that a cue presented on the same side of the horizontal meridian as the Vernier stimulus elicited a stronger repulsion compared to conditions in which the cue and the Vernier were presented on separate sides of the horizontal meridian. 
Furthermore, a significant two-way interaction was found for the factor cue eccentricity and the factor test Vernier position, F(9.46, 274.51) = 3.07, p = 0.001, ηp2 = 0.10. Figure 6B suggests no evident explanation for why this interaction reached significance. 
Moreover, the interaction of the factor cue eccentricity and cue side was significant, F(1.84, 53.40) = 8.85, p = 0.001, ηp2 = 0.23. Post hoc pairwise comparisons showed that the differences between the cue sides (i.e., the ARE in general) were overall larger for smaller cue–Vernier distances, but was significant at each of the three cue positions: ±9°, Diff = 0.05°, t(29) = 4.19, p < 0.050; ±3.5°, Diff = 0.09°, t(29) = 4.60, p < 0.025; ±1°, Diff = 0.12°, t(29) = 5.48, p < 0.017. 
As shown in Figure 6C, the general pattern of asymmetry when stimuli are presented on the same side of the horizontal meridian is preserved for all three cue distances; this is also confirmed by the three-way interaction not reaching significance, F(8.87, 257.12) = 1.39, p = 0.192, ηp2 = 0.05. Moreover, the main effect of the factor cue eccentricity did not reach significance, F(1.96, 56.77) < 1.26, ps > 0.292, ηp2s < 0.04. 
Vertical eccentricity
Again, the slopes of the fitted linear regressions for each of the three cue conditions at each eccentricity differed from b1 = 1, bs > 1.52, ts(29) > 8.97, ps < 0.001. 
Summary and discussion
Results of Experiment 2b indicate that the ARE is indeed disrupted when straddling the horizontal meridian. Together with the findings of Experiment 2a, this suggests that the attentional capturing cue induces a greater distortion on the spatial representation of the test Vernier line when the two stimuli are presented within the same visual quadrant. This may be taken to indicate that the effect originates in a neural area with a quadrantic representation of the visual field, such as V2 and/or V3 (S. Liu et al., 2018; T. Liu et al., 2009). 
General discussion
In the current study, we examined the hemifield and quadrant dependence of the ARE, an effect first reported by Suzuki and Cavanagh (1997) in which a covert attentional shift to a briefly presented cue horizontally repulses the perceived location of a subsequently presented probe. From previous research, it seemed as if the ARE was strongest when the probe was presented on the vertical midline. We used computer mouse responses to measure the spatial distribution of the ARE as those having the benefit of giving absolute perceived positions of the Vernier probes. 
Experiment 1a assessed whether computer mouse responses elicit an ARE of a similar magnitude than the previously prevalent 2AFC tasks. Even though Experiment 1a showed that computer mouse responses revealed a repulsion of a slightly greater magnitude, they also seemed to have the disadvantage of overestimating the horizontal (or vertical) eccentricity of the Vernier's position as previously reported by Pratt and Turk-Browne (2003). The authors' explanation for the overestimation in computer mouse localization tasks is that not only the perceived side of the probe has to be held in memory but also the exact positions of the test Vernier lines. Actions to memorized positions have previously been associated with both overestimated (e.g., Gentilucci & Negrotti, 1994) and underestimated (e.g., Mateeff & Gourevich, 1983; Sheth & Shimojo, 2001) eccentricities during visual reproduction. Nevertheless, Experiment 1b demonstrated an overestimation that was independent of the cue, allowing us to estimate the contribution of left and right cues to the overall ARE at different test positions. 
In Experiment 2a, we found that repulsion was stronger when the cue and the top Vernier line were presented in the same hemifield with a peak repulsion for lines with a slight offset from the vertical meridian toward the cued location. When crossing the vertical meridian, the repulsion effect diminished. This was independent of cue–Vernier distances in the range of 1° to 9.5°. Disruptions in perception or attention have been reported in a number of studies when stimuli were presented across the vertical meridian (Alvarez & Cavanagh, 2005; Carlson et al., 2007; S. Liu et al., 2018; T. Liu et al., 2009; Pillow & Rubin, 2002; Rizzolatti et al., 1987). Vertical meridian effects are supposed to reflect the anatomical separation of left and right visual hemifield representations in different hemispheres. 
In Experiment 2b, we further investigated whether the ARE was likewise disrupted by the horizontal meridian. We found a similar pattern of stronger repulsion if the cue and the test Vernier line were presented in the same visual quadrant. Again, a peak repulsion for lines with a slight offset from the horizontal meridian toward the cued location was revealed. Together, findings of Experiment 2a and 2b indicate that the processes involved in the ARE are located most likely in higher visual areas, such as V2 and/or V3, which have an anatomical gap at both the vertical and the horizontal meridian: Even though the lower and the upper visual quadrants are represented in the same hemisphere, stimuli of the upper visual quadrants are represented in ventral projections in V2 and V3 and stimuli of the lower visual quadrants are represented in dorsal projections in V2 and V3 (T. Liu et al., 2009). 
One rather surprising aspect of Experiment 2a and 2b is that the ARE does not only decrease across meridians; it also seems to decrease with increasing probe eccentricity on the cued side and that for all cue eccentricities. In other words, the ARE may be strongest on the ipsilateral side of the quadrant borders. Potentially this may be related to another particularity in the neural representation of the meridians. Previous research documented a nasotemporal overlap of receptive fields in the central retina. That is, ganglion cells within approximately 1°–1.5° of the vertical midline project to both hemispheres (Blakemore, 1969; Fendrich, Wessinger, & Gazzaniga, 1996). Although overlapping, the ipsilateral projection is nevertheless stronger (Fendrich et al., 1996), which could explain why we found stronger repulsion on the ipsilateral side of the vertical meridian. Similarly, the horizontal meridian is represented in both the ventral as well as the dorsal part of V2, which represent the upper and lower visual field, respectively (Gattass, Gross, & Sandell, 1981). Further, within the dorsal projections in which receptive fields in the lower visual field prevail, some receptive fields have been located up to 1° above the horizontal meridian (Van Essen & Zeki, 1978). With these anatomical characteristics in mind, our results could imply that the ARE is specific to the meridians, at which dual representations of stimuli are possible. Firm conclusions based on our results are difficult to draw, though. Fendrich et al. (1996) note that effects of the nasotemporal overlap on behavioral measures may remain elusive when stimuli are briefly flashed (<200 ms), which was the case in our experiments. Decreasing repulsion with higher eccentricity in the cued quadrant might also be related to a decreasing influence of the lower/nontest Vernier line as visual reference for the ARE (see Supplementary File S1) or might be caused by a range effect (Poulton, 1975). To investigate whether the ARE is quadrant-specific or even restricted to a small region around the meridians, future experiments could test for repulsion effects with cue and probe presented within the same quadrant but far from the meridians. Ongoing experiments from our own lab also examine the potential influence of microsaccades and exact gaze direction at the time of probe onset on the ARE. 
Previous studies already touched on the subject of the neural locus of the ARE. For instance, Pratt and Turk-Browne (2003) found the ARE in both perceptual and motor-action tasks, concluding that the effect originates prior to the separation of the “object-action” and “object-perception” pathways. Moreover, DiGiacomo and Pratt (2012) found that, when presenting the stimuli in an interocular condition (in which the cue was presented to one eye and the Vernier to the other eye), no ARE was elicited. They argued that this pattern of results suggests that the ARE originates at the level of monocular processing from structures early in the visual hierarchy (i.e., in the lateral geniculate nucleus or in primary visual cortex, V1), which is in contradiction to our findings. However, more recently, Menceloglu, Grabowecky, and Suzuki (2018) reexamined the interocular transfer of the ARE by using a mirror-based stereoscope and measuring the ARE with both vertically and horizontally configured Vernier lines. They were able to demonstrate an almost complete interocular transfer in the ARE. Moreover, they displayed a stronger ARE when Vernier lines were presented horizontally. They speculated that the ARE might only be hemifield-specific and not quadrant-specific: The assumed interruption of the effect at the vertical but not the horizontal meridian should lead to the overall larger effects around the horizontal meridian. In contrast, we even found a more robust ARE when the Vernier lines were presented around the vertical instead of the horizontal meridian. One could speculate that the degree of attentional capture is reduced when stimuli are presented in a predictive hemifield. Whereas we consistently presented the stimuli in the same hemifield, Menceloglu et al. presented their stimuli in a random hemifield. Consequently, the reduced repulsion we found around the horizontal meridian could be due to our unilateral and, therefore, predictable stimuli presentation within one hemifield. Yet, overall, it is evident that the pattern of asymmetry with larger repulsion when stimuli are presented on the same side of the corresponding meridian is apparent at both the vertical and the horizontal meridian. 
Acknowledgment
This research was supported by the Swiss National Science Foundation: PZ00P1_161224. 
Commercial relationships: none. 
Corresponding author: Denise Baumeler. 
Address: Faculté de Psychologie et des Sciences de l'Éducation, Université de Genève, Switzerland. 
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Figure 1
 
Trial sequence in Experiment 1a. Note that only top-left cue presentation is displayed although top-right cue presentation was equally likely from trial to trial. During probe presentation, Vernier lines were presented above and below fixation. The top Vernier line was equally likely to appear at nine different positions: −0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5°; the lower line was always centered (0°). ISI = interstimulus interval.
Figure 1
 
Trial sequence in Experiment 1a. Note that only top-left cue presentation is displayed although top-right cue presentation was equally likely from trial to trial. During probe presentation, Vernier lines were presented above and below fixation. The top Vernier line was equally likely to appear at nine different positions: −0.5°, −0.3°, −0.2°, −0.1°, 0°, 0.1°, 0.2°, 0.3°, or 0.5°; the lower line was always centered (0°). ISI = interstimulus interval.
Figure 2
 
Results of Experiment 1a: Psychometric functions (2AFC and recoded data for mouse-response mode). (A) Proportion of “right” responses as a function of top Vernier positions averaged across all 20 participants. (B) Proportion of “right” responses of one representative participant (subject 25). The curves show the psychometric functions' fit to the data. (C) Average PSVs and (D) slopes (higher values denote steeper slopes) of the psychometric functions, cue sides, and response modes. In all cases, error bars represent 95% confidence interval of comparison cue left versus cue right (orange vs. blue) for a given response mode: If error bars do not overlap, the difference is significant.
Figure 2
 
Results of Experiment 1a: Psychometric functions (2AFC and recoded data for mouse-response mode). (A) Proportion of “right” responses as a function of top Vernier positions averaged across all 20 participants. (B) Proportion of “right” responses of one representative participant (subject 25). The curves show the psychometric functions' fit to the data. (C) Average PSVs and (D) slopes (higher values denote steeper slopes) of the psychometric functions, cue sides, and response modes. In all cases, error bars represent 95% confidence interval of comparison cue left versus cue right (orange vs. blue) for a given response mode: If error bars do not overlap, the difference is significant.
Figure 3
 
Results of Experiment 1a: Absolute values. (A) Average perceived position of top Vernier lines against actual positions averaged across all 20 participants. The gray dotted line represents a regression line with a slope b1 = 1 (actual = perceived location). (B) Difference between cue left and cue right induced repulsion as a parameter for the ARE at each top Vernier line position. Error bars represent 95% confidence intervals of the difference cue left versus cue right: If error bars do not overlap (A) or cross the zero line (B), the difference is significant. Significant findings of the post hoc analyses are additionally indicated by asterisks in panel B.
Figure 3
 
Results of Experiment 1a: Absolute values. (A) Average perceived position of top Vernier lines against actual positions averaged across all 20 participants. The gray dotted line represents a regression line with a slope b1 = 1 (actual = perceived location). (B) Difference between cue left and cue right induced repulsion as a parameter for the ARE at each top Vernier line position. Error bars represent 95% confidence intervals of the difference cue left versus cue right: If error bars do not overlap (A) or cross the zero line (B), the difference is significant. Significant findings of the post hoc analyses are additionally indicated by asterisks in panel B.
Figure 4
 
Results of Experiment 1b: Absolute values. (A) Average perceived positions of top Vernier lines against actual locations averaged across all 23 participants. The gray dotted line represents a regression line with a slope b1 = 1. Error bars represent 95% confidence intervals of comparison cue bilateral versus cue absent. (B) Between-subject comparison of absolute values from Figures 3A and 4A. Error bars represent 95% confidence intervals of the mean of each data point. (C) Repulsion at each top Vernier position with relative contribution of cue left and cue right.
Figure 4
 
Results of Experiment 1b: Absolute values. (A) Average perceived positions of top Vernier lines against actual locations averaged across all 23 participants. The gray dotted line represents a regression line with a slope b1 = 1. Error bars represent 95% confidence intervals of comparison cue bilateral versus cue absent. (B) Between-subject comparison of absolute values from Figures 3A and 4A. Error bars represent 95% confidence intervals of the mean of each data point. (C) Repulsion at each top Vernier position with relative contribution of cue left and cue right.
Figure 5
 
Results of Experiment 2a: Absolute values, vertical meridian. Evaluations are displayed separately for each cue eccentricity (±9°, ±3.5°, ±1°) as well as averaged across all three eccentricities. (A) Average perceived positions of top Vernier lines against actual locations for the three cue conditions (left, right, absent), averaged across all 29 participants. The gray dotted line represents a regression line with b1 = 1. Error bars represent 95% confidence intervals of the data points. (B) Perceived position of top Vernier lines plotted against the actual top Vernier positions when the overestimation of the no-cue condition is subtracted from the estimates of the unilateral conditions. Error bars represent 95% confidence intervals of the data points. (C) Repulsion at each top Vernier position with relative contribution of cue left and cue right. Error bars represent 95% confidence intervals of the cue-induced repulsion effect: If error bars do not cross the zero line, repulsion is significant. Significant findings of the across eccentricities post hoc analyses are additionally indicated by asterisks.
Figure 5
 
Results of Experiment 2a: Absolute values, vertical meridian. Evaluations are displayed separately for each cue eccentricity (±9°, ±3.5°, ±1°) as well as averaged across all three eccentricities. (A) Average perceived positions of top Vernier lines against actual locations for the three cue conditions (left, right, absent), averaged across all 29 participants. The gray dotted line represents a regression line with b1 = 1. Error bars represent 95% confidence intervals of the data points. (B) Perceived position of top Vernier lines plotted against the actual top Vernier positions when the overestimation of the no-cue condition is subtracted from the estimates of the unilateral conditions. Error bars represent 95% confidence intervals of the data points. (C) Repulsion at each top Vernier position with relative contribution of cue left and cue right. Error bars represent 95% confidence intervals of the cue-induced repulsion effect: If error bars do not cross the zero line, repulsion is significant. Significant findings of the across eccentricities post hoc analyses are additionally indicated by asterisks.
Figure 6
 
Results of Experiment 2b: Absolute values, horizontal meridian. Evaluations are displayed separately for each cue eccentricity (±9°, ±3.5°, ±1°) as well as averaged across all three cue eccentricities. (A) Average perceived positions of test Vernier lines against actual locations for the three cue conditions (below, above, absent) averaged across all 30 participants. The gray dotted line represents a regression line with b1 = 1. Error bars represent 95% confidence intervals of the data points. (B) Perceived position of test Vernier lines plotted against the actual test Vernier positions when the overestimation of the no-cue condition is subtracted from the estimates of the unilateral conditions. Error bars represent 95% confidence intervals of the cue-induced repulsion effect: If error bars do not cross the zero line, repulsion is significant. Significant findings of the across eccentricities post hoc analyses are additionally indicated by asterisks.
Figure 6
 
Results of Experiment 2b: Absolute values, horizontal meridian. Evaluations are displayed separately for each cue eccentricity (±9°, ±3.5°, ±1°) as well as averaged across all three cue eccentricities. (A) Average perceived positions of test Vernier lines against actual locations for the three cue conditions (below, above, absent) averaged across all 30 participants. The gray dotted line represents a regression line with b1 = 1. Error bars represent 95% confidence intervals of the data points. (B) Perceived position of test Vernier lines plotted against the actual test Vernier positions when the overestimation of the no-cue condition is subtracted from the estimates of the unilateral conditions. Error bars represent 95% confidence intervals of the cue-induced repulsion effect: If error bars do not cross the zero line, repulsion is significant. Significant findings of the across eccentricities post hoc analyses are additionally indicated by asterisks.
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