Greene, Brown and Dauphin ( 6 ) found that during visual search, fixation durations preceding upward eye movements were briefer than fixation durations preceding downward eye movements. This vertical visual field asymmetry in pre-saccadic fixation durations (PSFDs) is similar to the vertical asymmetry reported for saccadic reaction times (SRTs) where SRTs are faster towards upper visual field (UpVF) than lower visual field( LoVF) targets when observers are instructed to make a single saccade as quickly as possible from a fixation point to a peripheral target (e.g., Tzelepi, Laskaris, Amditis, & Kapoula, ( 19 ); see also Greene et al., ( 6 ) for a review). It should be noted that SRTs which are typically influenced by salient cues, are not equivalent to fixation durations, which are heavily influenced by various task demands and endogenous processing (e.g., Henderson, Brockemole, Castelhano, & Mack, ( 7 ).

The vertical visual field asymmetry findings of Greene et al. (2014) suggest that PSFDs and SRTs behave in a manner that is functionally similar with respect to saccade direction. Whereas PSFDs are fixation durations before saccades are executed in a given direction (i.e.,how long the eyes stay before moving in some direction), post saccadic fixation durations (PoSFDs) are fixation durations after saccades land from being executed in a given direction(i.e., how long the eyes stay depending on whence they came). Obviously, PSFDs and PoSFDs are not independent of each other in a multi-fixation visual search task. The same PoSFD after a saccade has been executed in a particular direction serves as the PSFD for the ensuing saccade in the upcoming direction. Despite the lack of independence between PSFDs and PoSFDs, the functional similarity between SRTs and PSFDs suggest that PSFDs may primarily reflect competition between (peripheral) saccade preparation and (foveal) fixation stabilization mechanisms, as has been suggested for SRTs (e.g., Munoz & Fecteau, ( 10 ). Fixation stabilization would have to include the interaction of low-level saccade preparation, and high-level cognitive processing mechanisms. A saccade is executed when the direction-sensitive saccade mechanisms overcome fixation stabilization, in a winner-take-all manner ( 10, 18 ). In contrast to PSFDs, PoSFDs may primarily reflect information accrual (i.e., high-level cognitive processing mechanisms). Justification for this assertion comes from text-reading and scene-viewing studies that have utilized gaze-contingent screen manipulations of peripheral information (see Rayner, ( 15 ) for a review). In these studies, words or target objects which were visible in peripheral vision are changed during, or after a saccade that brought them into foveal processing range. The change imposed on the previewed item before fixation typically leads to an increase in the after-saccade fixation duration. These kinds of findings indicate that PoSFDs are influenced by peripheral preview in text-reading, and scene-viewing. A limitation of the gaze-contingent approach utilized in the text-reading and scene-viewing studies above is that they allowed access only to experimenter-determined elements of interest (i.e., fixation duration on target word or target object). It has been assumed that the findings generalize to all elements in a display.

Visual search may not recruit the same mechanisms as text reading, and scene viewing. During visual search, a simple rejection of a currently-fixated non-target may be sufficient for the eyes to be moved to a different point of interest. Compared to text reading and scene-viewing, during visual search, integration of information from a previous point of interest may be less necessary for successful completion of visual search. In effect, preview benefit may not be utilized as much during visual search. Previous visual search studies have not been designed to contrast PSFDs and PoSFDs. In fact, visual search studies conducted with or without gaze-contingent loss of peripheral information cannot compare PSFD and PoSFD, unless saccade direction information is considered. With concerns almost similar to the focus of the present study (i.e., PSFD and PoSFD with an intervening saccade), Tatler and Vincent ( 17 ) investigated pre- and post-saccade direction effects on fixation duration in a scene-viewing task. Figure 1 contrasts the concern of the present study with the concern of Tatler and Vincent ( 17 ). Tatler and Vincent ( 17 ) found that fixation durations were longer with greater angles of pre- to post-saccade direction change.

While their study is informative, it does not address PSFD/PoSFD issues. Without gaze-contingent manipulations, Tatler and Vincent’s ( 17 ) approach is also not amenable to quantifying peripheral preview effects in visual search (as has been done in text-reading and scene-viewing studies; see Rayner, ( 15 ). When gaze-contingent peripheral screen information manipulations have been utilized in visual search, researchers have speculated and attributed the general increase in fixation durations to a lack of peripheral benefit which led to higher PoSFDs ( 1, 5 ), or competition between fixation stabilizing and saccade preparation mechanisms, which led to higher PSFDs ( 2 ). By considering saccade directions, Greene et al. ( 6 ) revealed an asymmetry in PSFDs. However, the question of PoSFDs was not addressed. In effect, differences between PsFDs and PoSFD have not been well established for visual search. The current state of knowledge inspires two questions that are addressed in the present work. First, do PSFDs and PoSFDs reflect different functional mechanisms? Second, how do competition between saccadic mechanisms and peripheral preview rank in contributing to fixation durations?

Question 1: Do PSFDs and PoSFDs reflect different functional mechanisms?

While a vertical asymmetry is well-established for PSFDs, it is not known, however, how PoSFDs behave as a function of saccade direction. Given our earlier assertion that PoSFDs may primarily reflect information accrual (facilitated by preview benefit), it is reasonable to expect that PoSFDs may be longer after briefer PSFDs. Hence, PoSFDs may exhibit an asymmetry that is opposite to that of PSFDs. It is also possible that such an asymmetry may not be exhibited for visual search, given that preview benefit may not be much utilized during visual search. If PSFDs and PoSFDs demonstrate differences in asymmetry, this would suggest that they are functionally different in their moment-by-moment contributions to conscious vision. A functional difference would call into question, the popular practice of not distinguishing between the two in computational models of fixation duration (e.g. Nuthmann, Smith, Engbert, & Henderson, ( 12 ); Trukenbrod & Engbert, ( 18 ).

Question 2: How do competition between saccadic mechanisms and peripheral preview rank in contributing to fixation durations?

Eye movement visual search is driven primarily by endogenous shifts of attention (e.g., 7 ). As such, the durations of fixations during visual search reflect more than low-level competition between fixation stabilization and saccade preparation mechanisms. Given the assumption that PSFDs primarily reflect low-level competition between fixation stabilization and saccade preparation mechanisms (e.g., 10 ), and that PoSFDs primarily reflect the combination of pre- and post-saccade information accrual mechanisms (e.g., 15 ), it is important to determine relative contributions of both low-level, and information processing mechanisms to fixation durations. It is anticipated that knowledge of the relative contributions of both to fixation durations will contribute to constraining algorithms used to simulate realtime visual search behavior.

To this end, we have devised an approach based on the findings that a gaze-contingent change imposed on previewed items before a saccade, typically leads to an increase in the post-saccade fixation duration ( 5, 15 ). The approach involves quantifying the cost of obstructing one side of the peripheral visual field at a time, in a gaze-contingent manner. Given the difference found in UpVF and LoVF visual field processing during visual search ( 6 ), we blocked the UpVF and LoVF from view. It has been suggested that saccade preparation mechanisms are most active when saccades were directed to visible, locally-defined peripheral targets ( 3, 4 ). Hence, blocking the peripheral visual field should minimize competition from saccade preparation mechanisms, and should thus move the balance of competition towards fixation stabilization (and longer PSFDs). Blocking the peripheral visual field is also expected to minimize peripheral preview, leading to longer PoSFDs (see Rayner, ( 15 ) for a review). If only competition between fixation stabilization and saccade preparation mechanisms are responsible for increased fixation durations, then we expect PSFDs to be longer when ensuing saccades are directed towards the region that was blocked from view. As well, no effect of the visual field would be expected for PoSFDs. If however, only peripheral preview benefit mechanisms are responsible for increased fixation durations, then we expect PoSFDs to be longer if the preceding saccade was directed towards the obstructed visual field. No such increase in PSFDs is expected. Finally, if both types of mechanisms are involved (i.e., competition for dominance, and peripheral preview benefit), then we expect PSFDs and PoSFDs to be longer when saccades are directed towards the obstructed visual field. comparison of the effect sizes would revea which process (competition for dominance, or peripheral preview) is more influential in causing increased fixation duration during obstructed visual search. By inference, we would have quantified the ranking of competition between saccadic competition mechanisms and peripheral preview mechanisms, as they contribute to fixation durations.

The hypotheses of the experiment depend on an influence of visual field obstruction, which was located 2.5 deg above or below eye fixation. As such, it was important to verify that saccades were made beyond the boundary of the obstruction, when it was present. One-sample t tests (comparing mean saccade amplitudes to a parameter of 2.5 deg) indicated that mean saccade amplitudes were significantly greater than 2.5 deg when there was no obstruction (all t(17) > 10.35; all ps < .001), in the Upper Visual Field Obstruction condition (all t(17) > 6.45; all ps < .001), and in the Lower Visual Field Obstruction condition (all t(17) > 4.95; all ps < .001). Indeed, saccades were typically made beyond the boundary of the obstruction. The polar plot in Figure 3 illustrates the amplitudes of saccades relative to upper and lower visual field obstruction.

The primary concern of the experiment was fixation durations made in search of the target. Following Greene ( 5 ), search fixation durations were defined as fixation durations made after the initial saccades but before the final fixations were terminated by key-press responses. Search fixation durations less than 90 ms and greater than 2000 ms were defined as outliers.

Across observers this criterion led to a removal of about 6% of search fixation durations. Each observer was left with between 1800 and 9600 fixation durations (median, 3775). These durations were then classified as PSFD, and PoSFDs, depending on saccade direction. As described earlier, PSFDs are fixation durations before the eyes go to a new location. PoSFDs are fixation durations after the eyes have come from some location in the display. Saccade directions were grouped in 90 deg bins (i.e., up, down, left, right) for statistical analysis. Two separate factorial ANOVAs—one for PSFDs and one for PoSFDs were conducted: 3 Peripheral Obstruction (None, Upper Visual Field Obstruction, and Lower Visual Field Obstruction) X 4 Saccade Direction (Up, Down, Left, Right).

The concern of the present study was the nature of PSFDs and PoSFDs during visual search. PSFDs were defined as fixation durations before the eyes moved in a given direction, and PoSFDs were defined as fixation durations after the eyes landed from the given direction. Given their similarity to SRT patterns, PSFD patterns were assumed to be primarily reflective of low-level competition between saccadic and fixation stability mechanisms, such that a saccade is executed when saccade preparation mechanisms overcome fixation stabilization ( 10 ). Hence, selective minimization of competition from saccade preparation mechanisms was expected to increase selectively, PSFDs. In contrast, PoSFD patterns (which have not been specifically addressed in visual search) were assumed to be reflective of the interaction of pre- and post-saccade information accrual. Selective prevention of preview was expected to increase selectively, PoSFDs.

Novel use of a gaze-contingent moving obstructer paradigm addressed two open questions related to visual search. The first question dealt with functional similarity between PSFDs and PoSFDs. If PSFDs and PoSFDs reflect different mechanisms, it was expected that saccade direction would differentially influence PSFD and PoSFD patterns. Results showed that PSFD patterns exhibited a vertical visual field asymmetry that was weighted towards the LoVF, irrespective of the location of a peripheral obstructer. This was similar to PSFD patterns reported by Greene et al. ( 6 ). However, PoSFD patterns exhibited this LoVF-weighted asymmetry only when the obstructer was in the LoVF.

These findings (summarized in Table 1) support the argument that PSFDs and PoSFDs reflect functionally different mechanisms. The second question of interest was the relative contribution of PSFDs and PoSFDs to visual search fixation duration. Although an obstructer in the UpVF always selectively increased PSFDs and PoSFDs, the increase (i.e., cost) was greater for PoSFDs. The same was true in the opposite direction for an obstructer in the LoVF. Thus, the findings suggest that PoSFDs (which have been assumed to reflect primarily the interaction of pre- and post-saccade information accrual) contribute more to the duration of fixations than PSFDs (which were assumed to reflect saccade competition mechanisms). Together, the results of the present study suggest that it is insufficient to theorize about the control of fixation durations without consideration of differential influences on PSFDs and PoSFDs.

Computational simulations facilitate understanding of biological mechanisms. Many computational models of looking behavior have focused on where saccades are directed (e.g., ( 8, 11, 13, 14, 20 ). Real time simulation of looking behavior can occur only if the control of fixation durations is sufficiently understood. The most relevant model with respect to visual search fixation duration is Trukenbrod & Engbert’s ( 18 ) model (ICAT). ICAT assumes that fixation durations are adjusted both directly (by currently-fixated information) and indirectly (by prior experience with processing demands). While the model accounts for global shifts in fixation duration from processing demands (i.e., indirect influences), and local variations in fixation duration (i.e., direct display influences), simulated distributions of fixations do not take into account PSFD patterns (e.g., ( 6 ) and differences between PSFD and PoSFD patterns, as demonstrated in the present study.

Interestingly, the PSFD asymmetry reported here (and by Greene et al. ( 6) ) is the opposite of the asymmetry observed when observers are instructed to respond manually to the onset of a target in the upper or lower visual field. Manual reaction times (MRTs) tend to be faster for targets in the lower, not upper visual field ( ( 9 ); see also Skrandeis, ( 16 ) for a review). In the present context, MRTs quantify a shift of attention when a target becomes visible. Tzelepi et al., ( 19 ) have speculated on the reason for the dissimilarity in SRT and MRT patterns. In their study, observers were asked either to attend covertly, or make a saccade to stimuli presented in the visual field. As expected, SRTs were faster for saccades towards UpVF than LoVF targets. Beyond this typical finding, magnetoencephalography (MEG) results indicated that frontal lobe areas involved in saccade preparation were accessed earlier and with less cortical activation for saccades about to be directed into the UpVF, than for the saccades about to be directed into the LoVF. The temporal advantage and greater automaticity in frontal processing may both contribute to faster SRTs into the UpVF. In contrast, when observers were instructed to attend covertly (without eye movements), dorsal cortex regions were activated earlier than ventral regions, and cortical activation was lower if attention was directed to LoVF compared to UpVF. This temporal advantage and greater automaticity in response to LoVF targets may contribute to faster MRTs for targets in the LoVF.

Contributions made by research assistants (Ellen Day, Vanessa Osantoski) and by formal and informal reviewers of this work are appreciated. The authors declare that there is no conflict of interest regarding the publication of this paper.