Target localization across saccades and at fixation: Nontargets both facilitate and bias responses

The image on our retina changes every time we make an eye movement. To maintain visual stability across saccades, specifically to locate visual targets, we may use nontarget objects as “landmarks”. In the current study, we compared how the presence of nontargets affects target localization across saccades and during sustained fixation. Participants fixated a target object, which either maintained its location on the screen (sustained-fixation trials), or displaced to trigger a saccade (saccade trials). After the target disappeared, participants reported the most recent target location with a mouse click. We found that the presence of nontargets decreased response error magnitude and variability. However, this nontarget facilitation effect was not larger for saccade trials than sustained-fixation trials, indicating that nontarget facilitation might be a general effect for target localization, rather than of particular importance to saccadic stability. Additionally, participants’ responses were biased towards the nontarget locations, particularly when the nontarget-target relationships were preserved in relative coordinates across the saccade. This nontarget bias interacted with biases from other spatial references, e.g. eye movement paths, possibly in a way that emphasized non-redundant information. In summary, the presence of nontargets is one of several sources of reference that combine to influence (both facilitate and bias) target localization.

156 perform a target localization task by indicating target location with a mouse click (similar to 157 [13]). Moreover, the more robust free-report task (compared to a two-alternative forced choice) 158 allows us to measure with the response distribution not only whether target localization is 159 facilitated or impaired under different nontarget conditions, but also whether and how much the  Participants. An independent set of sixteen subjects participated in each of the three

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On some trials, nontarget objects (white empty circles of 0.2° radius) were also presented 239 during the trial: trials were equally distributed among 0, 1, or 2 NTs. Participants were told that 240 they should complete the task on the target cross, and that the circles were irrelevant to their task.

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In all three experiments, we designed the NT location conditions to be either to the left or 249 right of the target's final position, and thus either on the same side or opposite side as the initial 250 fixation on saccade trials ( Fig 1C). The actual NT locations were randomized for each trial 251 within an imaginary vertical rectangle zone of 1°× 2°, centered 2° to the left or right of the target.
252 This means that on trials with 2 NTs, these two NTs were both presented on the same side of the 253 target. In the Baseline experiment, NTs were presented when the target appeared in its final 254 position, centered 2° to the left or right of that final target location. In the Relative experiment, 255 the NTs first appeared centered 2° to the left or right of the initial target location, and moved 256 with the target to remain in the same relative location. Note that because the NTs moved with the 257 target instead of the eyes, we call this condition "relative" instead of "retinotopic". In the

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The conditions we analyzed included saccade presence (no-saccade and saccade), NT 284 number (0, 1 and 2 NTs), and NT location (same and opposite side relative to initial fixation 285 location). Each of these conditions was tested within each experiment (within-subjects), and 286 compared across experiments (between-subjects), which varied reference frame.

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Our primary goal was to assess how the above factors influence target localization 288 performance; thus, the analyses primarily focus on the participants' mouse responses (though we 289 include some additional analyses of eye-tracking data in the supplementary materials). We first 290 investigated how making saccades influences target localization by comparing saccade versus 291 no-saccade trials; then how NTs influence target localization by comparing trials with zero, one 292 and two NTs; and finally, if/how these saccade and NT influences interact by analyzing saccade 293 trials with NTs. We used three measurements to quantify target localization outcomes: 1) how 294 accurate participants' responses were, by calculating the mean error magnitude as the distance 295 (i.e., absolute value) between the reported and correct target location; 2) how variable 298 the mean directional error vector along the horizontal axis along which saccades and NT 299 locations were manipulated.

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Specifically, RMSD was calculated using the formula: where for each subject each condition, ( , ) is the response coordinates for trial i, 303 centered around the actual target location; ( , ) is the average coordinates of all responses in 304 that condition; n is the number of trials, and the denominator (n-1) is the degree of freedom to 305 get an unbiased estimate.

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All of the above three measurements were calculated in units of visual angle. We used 307 ANOVAs and t-tests for statistical analyses; effect sizes were calculated using η p 2 and Cohen's 308 d. Greenhouse-Geisser correction for violations of sphericity and Holm-Bonferroni correction 309 for multiple comparisons were used when necessary.

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Our research question focused on how saccades and nontargets influence target 313 localization independently and interactively.

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A descriptive plot of participants' responses is depicted in Fig 2,  332 333 Accuracy of target localization 334 We first looked at the effects of saccades and NTs on overall target localization accuracy, 335 measured by the mean magnitude of error (distance) between the correct and reported locations.

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The results showed a significant main effect of saccade presence , F(1,45) 378 We next examined another important measurement of target localization performance, 379 the variability of the responses, quantified using RMSD.

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We did similar analyses as above, using a 2 (saccade presence: 0, 1)  3 (NT number: 0, 381 1, 2)  3 (experiment: 1, 2, 3) mixed-design ANOVA, and found similar patterns. There was a  In the current study, we tested how the presence of nontargets influences target 521 localization across saccades and during sustained fixation. Unsurprisingly, we found that target 522 localization performance was generally worse on saccade than no-saccade trials (in terms of 523 mean error magnitude and response variability), and the presence of nontargets improved target 524 localization performance. The presence of nontargets exerted comparable facilitation effects on 525 saccade trials and no-saccade trials, suggesting that the facilitation effect is a more general visual 526 effect rather than of particular importance to saccadic stability. We also measured response bias 527 (directional error), finding that participants' responses were biased towards both the initial 528 fixation location (saccade-related bias) and the NT locations. These two sources of bias 529 interacted in an interesting way: When both sources fell on the same side of the target they were 530 not additive, but when they fell on opposite sides of the target, the NT bias counteracted the 531 saccade-related bias. For both facilitation and bias effects, the influence of nontargets was 532 stronger when there were 2 NTs than 1 NT, and was weaker in the absolute than relative and 533 baseline experiments. Below we discuss the implications of each of these findings. 562 however, participants were not simply clicking on the location that they looked at.

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Our result is consistent with a number of previous studies demonstrating a response bias 564 towards the current and/or initial fixation locations [13,36,47]. Sheth and Shimojo found that 565 visual memory of peripheral spatial locations can be biased towards the current fixation (i.e., 566 "foveal bias") over time, independent of saccade preparation or saccade execution. They 567 proposed that this bias likely happens during encoding period when the eccentricity of the target 568 might be underestimated [13]. A response bias towards the initial fixation location has also been 569 found across saccades, when participants retained spatial memory of a peripheral target [36]. It 570 should be noted that our design differed from these previous studies in that instead of a 572 the saccade-related bias in our result likely happened in a similar way as the studies mentioned 573 above. When the saccade target location was presented on the screen while participants were still 574 fixating on the initial fixation, the saccade target was indeed in the periphery at that time point.
575 Due to the underestimated eccentricity during the encoding process, a biased representation of 576 space was likely created and maintained across the saccade. Therefore, we still found "foveal 577 bias" -bias towards the initial fixation, after the saccade was completed. Indeed, the magnitude 578 of saccade-related bias we found (0.05°) is much smaller than the foveal bias in [13] (about 1°), 579 and this is likely due to the acuity difference between processing foveal and peripheral targets.

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Our results reflect the idea that nontargets perform as anchors or landmarks, so that the 604 target localization could be done with them as relative references in space, consistent with 605 previous literature (e.g., [10]; see later discussion on the effect of reference frame). Note that in 606 our experiments, we did not explicitly instruct participants to use nontargets, which means that 607 nontarget information might be processed and used by default, instead of only triggered by 608 instruction. Our results showed that two nontargets facilitated slightly more than one, but the 609 second nontarget did not double the facilitation. A possible reason is that in our design, the two 610 nontargets always appeared inside one rectangle region: they were always on the same side of 611 the target, and their distance to the target was similar (within 1.5° and 2.5° to the target location 612 on the horizontal axis). Thus, the two NT objects might have been grouped together as a single 613 landmark, or simply provided similar information, and therefore, the second nontarget might not 614 have provided much additional reference beyond the first one. We also found that when the 615 initial fixation location and nontargets were on the same side of the target, the presence of