Temporal attention and oculomotor effects dissociate distinct types of temporal expectation

Abstract

Temporal expectation—the ability to predict when events occur—relies on probabilistic information within the environment. Two types of temporal expectation—temporal precision, based on the variability of an event's onset, and hazard rate, based on the increasing probability of an event with onset delay—interact with temporal attention (the ability to prioritize specific moments) at the performance level. Attentional benefits increase with precision but diminish with hazard rate. Both temporal expectation and temporal attention improve fixational stability; however, the distinct oculomotor effects of temporal precision and hazard rate, as well as their interactions with temporal attention, remain unknown. Investigating microsaccade dynamics, we found that hazard-based expectations were reflected in the oculomotor responses, whereas precision-based expectations emerged only when temporal attention was deployed. We also found perception–eye movement dissociations for both types of temporal expectation; yet, attentional benefits in performance coincided with microsaccade rate modulations. These findings reveal an interplay among distinct types of temporal expectation and temporal attention in enhancing and recalibrating fixational stability.

Introduction

The world is dynamic and stochastic, yet it possesses predictable elements that enable us to develop expectations. Temporal expectation, the ability to predict when events occur, improves perception in vision (Rohenkohl, Cravo, Wyart, & Nobre, 2012), audition (Bueti & Macaluso, 2010), and touch (Badde, Myers, Yuval-Greenberg, & Carrasco, 2020). It also facilitates actions (Thomaschke & Dreisbach, 2013), alters timing of oculomotor responses (Akdoğan, Balcı, & van Rijn, 2016; Tal-Perry & Yuval-Greenberg, 2022), and modulates neuronal activity at various levels within sensory processing and action pathways (for a review, see Nobre & van Ede, 2023).

Our brain utilizes temporal structures within the environment to develop temporal expectations (Nobre, Correa, & Coull, 2007; Nobre & van Ede, 2018). The passage of time characterizes the hazard rate—the increasing probability of an event, conditional on it not yet having occurred (Coull, 2009; Duyar, Denison, & Carrasco, 2023; Grabenhorst, Maloney, Poeppel, & Michalareas, 2021)—and the variability of the onset of an event within a time window characterizes temporal precision (Rolke & Hofmann, 2007). These two types of temporal structures yield expectations with different temporal scales: The hazard rate is sensitive to immediate changes, whereas temporal precision is computed over longer time scales (e.g., within experimental trials or blocks, respectively).

In the auditory system, hazard rate and temporal precision are partially overlapping and separable at the neural level based on latency, computation, and hierarchical processing stage. The effects of the hazard rate on auditory stimulus–evoked magnetoencephalography (MEG) responses emerge faster and at lower levels of the hierarchical processing than those of temporal precision. Both effects originate in the early auditory regions, but only temporal precision correlates with activity in the inferior parietal cortices (Todorovic & Auksztulewicz, 2021). Such commonalities and differences are unknown at the oculomotor level for microsaccades.

Temporal attention, another fundamental cognitive process, facilitates allocation of the limited resources of the brain across time. In a dynamic environment, visual information changes over time at a given location, and temporal attention enables prioritizing information at specific time points, regardless of predictability (for a review, see Denison, 2024). Given two temporally competing stimuli at the same location, instructive cues can guide observers to attend to the first or the second target occurring at different moments, leading to enhanced visual performance at the expected and attended moments as compared with expected but unattended moments (e.g., Denison, Heeger, & Carrasco, 2017; Denison, Carrasco, & Heeger, 2021; Fernández, Denison, & Carrasco, 2019; Palmieri & Carrasco, 2024). Temporal attention mediates the effects of temporal expectation at the neural level (Todorovic, Schoffelen, van Ede, Maris, & de Lange, 2015; Woldorff, Hackley, & Hillyard, 1991). For example, visual temporal attention modulates anticipatory effects in MEG responses (Denison et al., 2024) and interacts with expectation at the behavioral level. In particular, attentional benefits on performance—the difference in performance in the selective attentional condition relative to the baseline/distributed condition—increase with temporal precision but decrease with hazard rate (Duyar, Ren, & Carrasco, 2024). But, it is unknown whether temporal attention distinctly interacts with these two types of expectation at the oculomotor level.

Microsaccades (MSs), the fastest and largest of fixational eye movements, provide an online metric throughout experimental trials. The MS rate follows a typical temporal profile (Martinez-Conde, Macknik, Troncoso, & Hubel, 2009; Martinez-Conde, Otero-Millan, & Macknik, 2013; Rolfs, 2009). Whereas initially MSs were considered as reflexive eye movements, research by Kowler et al. revealed that they mirror broader aspects of visual perception (for reviews, see Collewijn & Kowler, 2008; Kowler, 2011; Kowler & Collewijn, 2010), including cognitive factors such as prediction (He & Kowler, 1989) and attention (Kowler, 2024). Typically, there are three stages of MS rate within an experimental trial (Figure 1A). First is pre-stimulus endogenous anticipatory inhibition, which occurs before an expected brief visual, auditory, or tactile stimulus (Abeles, Amit, Tal-Perry, Carrasco, & Yuval-Greenberg, 2020; Amit, Abeles, Carrasco, & Yuval-Greenberg, 2019; Badde et al., 2020; Betta & Turatto, 2006; Dankner, Shalev, Carrasco, & Yuval-Greenberg, 2017). This inhibition becomes more pronounced with temporal attention (Denison, Yuval-Greenberg, & Carrasco, 2019; Palmieri, Fernandez, & Carrasco, 2023), but becomes weaker following a delayed visual event (Duyar & Carrasco, 2024; Tal-Perry & Yuval-Greenberg, 2023). Second is post-stimulus reflexive exogenous inhibition (Rolfs, Kliegl, & Engbert, 2008), which indexes conscious perception (White & Rolfs, 2016) and temporal expectation (Badde et al., 2020). Third is rebound to baseline, which depends on endogenous inhibition via expectation (Badde et al., 2020), but effects of temporal attention are lacking (Denison et al., 2019; Palmieri et al., 2023). Precise timing of MSs is modulated not only by stimulus physical characteristics (Bonneh, Adini, & Polat, 2015), but also by task difficulty (Ezzo, Song, Rokers, & Carrasco, 2025) and temporal attention (Denison et al., 2019). Temporal attention shifts the timing of both pre-stimulus and post-stimulus MSs earlier for temporally predictable targets. However, how temporal attention and different types of expectation work together to recalibrate oculomotor dynamics and stabilize gaze under temporal uncertainty is yet to be investigated.

Figure 1.

(A) Typical MS rate profile. (B) Experimental protocol (reported in Duyar et al., 2024). Attention was manipulated via the precue, and expectation was manipulated via the stimulus onset asynchrony (SOA) between the precue and the targets. Observers reported the orientation (clockwise/counterclockwise relative to the reference axis) of the target indicated by the response cue at the end of the trial, with feedback provided based on accuracy. (C) Hazard rate was manipulated via within-trial target delay (early, expected, or late onsets), and temporal precision was manipulated via within-session onset variability (certain, narrow, wide, or uniform).

Although perception and eye movements usually co-occur (Kowler, 2011; Spering & Montagnini, 2011; Vishwanath & Kowler, 2003), perceptual reports and eye movements have been dissociated (e.g., Glasser & Tadin, 2014; Spering & Carrasco, 2012; Spering, Pomplun, & Carrasco, 2010; Vetter, Badde, Phelps, & Carrasco, 2019). Recently, we found that temporal expectations based on the stimulus timing of the preceding trial is reflected in oculomotor dynamics, but it does not affect the specific time when attention benefits performance (Duyar & Carrasco, 2024). To further our understanding of perception–eye movement dissociations (Carrasco & Spering, 2024; Spering & Carrasco, 2015) here we investigated the eye-tracking dataset of a recent study in which we showed that effects of temporal attention on performance (discriminability and reaction speed) interact in an opposite manner with temporal precision and hazard rate (Duyar et al., 2024). Attentional benefits increase with temporal precision, whereas they decrease with hazard rate. Whether these perceptual effects are also reflected in the MS dynamics is unknown.

Previous studies have investigated temporal expectation effects on oculomotor responses by analyzing pupils (Akdoğan et al., 2016), MSs (Abeles et al., 2020; Amit et al., 2019; Badde et al., 2020; Betta & Turatto, 2006; Dankner et al., 2017), and voluntary saccades (Akdoğan et al., 2016; Ameqrane, Pouget, Wattiez, Carpenter, & Missal, 2014; Boutachkourt, Drazyk, & Missal, 2024; Drążyk & Missal, 2023). However, these studies have focused exclusively on temporal expectation—the ability to predict the onset of an event—without considering the concurrent influence of temporal attention—the ability to selectively process a specific moment. The current study addressed this gap by investigating how temporal expectation and temporal attention jointly alter MSs during fixation maintenance, providing the first, to our knowledge, examination of their interactive effects on oculomotor control.

Here, we asked (1) Do hazard rate and temporal precision differentially modulate MSs? (2) Does temporal attention distinctly modulate hazard rate and temporal precision in MS dynamics? (3) Are perceptual effects of attention and expectation reflected in MS dynamics, or is there a perception–eye movement dissociation?

Methods

Dataset

We analyzed the eye-tracking data of a previous study in which we investigated behavioral effects on the interaction between temporal attention and expectation (Duyar et al., 2024). The observers, apparatus, stimuli, and experimental protocol were identical to that study.

Observers

Sixteen observers (10 females, six males; ages 22–34 years; M = 27, SD = 3.445) participated in the study. Two observers were removed from the temporal precision analysis due to corrupted raw eye files for at least one of four conditions; thus, we analyzed the data from the remaining 14 observers (eight females, six males; ages 22–34 years; M = 26.786, SD = 3.599). For the hazard rate analysis, we included all observers because we had eye files for all conditions relevant to that analysis. All observers had normal or corrected-to-normal vision. The research was performed in accordance with the tenets of the Declaration of Helsinki, and the experimental protocol was approved by the New York University Institutional Review Board.

Apparatus

Stimuli were generated using an iMac (3.06 GHz, Intel Core 2 Duo; Apple, Cupertino, CA) and MATLAB 2012b (MathWorks, Natick, MA) using Psychophysics Toolbox (Brainard, 1997; Kleiner, Brainard, & Pelli, 2007), presented on a gamma-corrected cathode-ray tube (CRT) monitor (resolution, 1280 × 960; refresh rate, 100 Hz). The viewing distance was 57 cm, and the observers’ head movements were restrained using a chin and head rest. An infrared eye tracker EyeLink 1000 (SR Research, Ottawa, ON, Canada) was used for recording eye position throughout the experiment. Online eye tracking was implemented to maintain central fixation (1°) throughout the trials. Eye tracking data were recorded at 1000 Hz. Five-point-grid calibration was performed at the beginning of each session and was repeated within the session when necessary. Online monitoring of eye position throughout the trial enabled blink detection, fixation breaks, and data loss during the experimental trials. In case of data loss, a fixation break due to blink, or ≥1° deviation from the center of the screen, the trial was interrupted and repeated at the end of the corresponding experimental block. Observers could blink or make larger saccades during the response window and the intertrial interval. There were no missing eye-position values within the window of analysis.

Stimuli

Stimuli were displayed on a uniform, medium-gray background. A central fixation circle subtended 0.15°, and four black circles (0.2°) were displayed at the corners of a central imaginary square (2.2° side) as placeholders. Two Gaussian-windowed (SD = 0.3°), 100% contrast sinusoidal gratings with a random phase were presented at the center sequentially in each trial. Each grating was tilted clockwise or counterclockwise from the horizontal or vertical axis, independently. The amount of tilt was titrated separately for each target interval for each observer.

The attentional precues were 200 ms auditory tones, presented through speakers. The valid precue was a sinusoidal wave (T1, 800 Hz; T2, 400 Hz), and the neutral precue was a complex waveform that is a combination of a range of frequencies (50–400 Hz). Response cues were identical to the valid precues to instruct the observers to report the first (T1) or the second (T2) target.

Experimental procedure

The experimental protocol was reported in detail in Duyar et al. (2024). The experiment was developed by combining a temporal attention protocol (Denison et al., 2017; Denison et al., 2021) and a temporal expectation protocol (Todorovic & Auksztulewicz, 2021). The experimental protocol is shown in Figure 1B.

Expectation manipulations

Two types of temporal expectation—temporal precision and hazard rate—were manipulated (Figure 1C). For temporal precision via within-session target onset variability, the most expected time point (mean point of each temporal distribution) was kept constant (1400 ms for T1 and 1650 ms for T2 relative to the precue) across precision levels, and the probability of stimulus appearance at the expected moment increased with precision: uniform (33%), wide (42%), narrow (86%), or certain (100%) conditions. Hence, the variability of target onset was systematically decreased as the precision increased. The hazard rate was manipulated via within-trial target onset delay (early-expected-late). Within the low precision experimental sessions, the targets could appear earlier or later than the expected moment. In a trial with low temporal precision, the conditional probability of the appearance of the targets at each time point increased given that they had not appeared yet, resulting in a lower hazard rate at the earlier than expected moments. For hazard rate analysis, we analyzed data from the wide and uniform precision levels, in which there was a comparable number of trials at the expected and unexpected moments.

Attention manipulations

Temporal attention was manipulated via auditory precues. The precue instructed observers which target to attend to and the response cue which target orientation to report. The precue either instructed observers to attend to the first (T1) or the second (T2) target or it was uninformative (neutral/baseline) regarding which targets would be behaviorally relevant. The precues corresponding to T1 or T2 were 100% valid; thus, the response cue was identical to the precue in those trials. In the neutral trials, the response cue indicated either target with 50% probability.

Discrimination task

The task was to report the orientation (clockwise/counterclockwise) of the target that was indicated by the auditory response cue (T1 or T2). The stimuli orientations were independently selected to have a horizontal or vertical reference axis from which they were slightly offset. Visual feedback (green + or red −) was presented after each trial based on whether the observers gave a correct or incorrect response. The average accuracy was presented at the end of each block.

Training and titration procedures

All observers completed a 60-trial training block in the beginning of the first session to familiarize themselves with the attentional precues and the task. In the beginning of each session/day, the observers completed a titration protocol of 128 trials. We used the best PEST procedure (Lieberman & Pentland, 1982), which adjusted the orientation tilt, to attain 75% orientation discrimination accuracy separately for each target in the neutral condition. Neutral performance was monitored throughout the experiment, and, if needed, additional adjustments to the tilt were automatically made after each block. Titration procedure was conducted with constant target timing (temporal precision = certain) (Figure 1C). Observers were explicitly informed regarding the temporal precision of the session.

Eye-tracking data preprocessing and microsaccade detection

Each observer completed 3568 to 4256 trials in total (M = 3689, SD = 245.773). Due to technical problems, the eye data for some blocks were not saved. We recovered ∼90% of the eye-tracking data from 16 people for the hazard rate analysis (M = 3291.44, SD = 425.36) and from 14 people for the precision analysis (M = 3368, SD = 393.470). We used an established velocity-based algorithm to detect MSs within each experimental trial (Engbert & Kliegl, 2003). For each trial, we transformed raw eye position data into a two-dimensional (2D) velocity space. A trial-specific 2D threshold was then determined as an ellipse centered on the median velocity in both horizontal and vertical directions. A MS was detected when the eye movement velocity exceeded this threshold for at least 6 ms. The detected MSs were ≤1° dva. A trial was aborted if the eye position deviated more than 1°; thus, we did not analyze saccades.

MS rate time course

MS rate time courses were calculated for each observer, separately for each attentional precue and expectation condition. For each experimental condition, we averaged the number of MSs per time samples across all trials, multiplied these values by the sampling rate, and then smoothed across time by applying a 50-ms sliding window. We performed a series of nonparametric cluster-based permutation tests to compare MS rate time courses and identify the intervals when they were significantly different (Maris & Oostenveld, 2007). We used two-tailed dependent samples tests (α = 0.05, 2000 permutations) and implemented Bonferroni correction on the identified clusters to account for multiple comparisons. These tests are widely used in MS research and provide useful information regarding when rate time courses differ between two conditions within a time period (e.g., Liu, Nobre & van Ede, 2022; Palmieri et al., 2023).

MS rate rebound inflection points

As a follow-up to the cluster-based permutation tests, we zoomed into the MS rate window to analyze the timing of MS rate rebound. We estimated the inflection point when the MS rates started to increase (rebound onset) and when they stabilized (rebound offset) by doing the following: First, we focused on the MS rate time course between 1500 and 2700 ms after the precue onset for each observer and each experimental condition. Then, we computed the first derivative of the MS rates within this period and identified where it crossed zero. These specific points were considered candidate rebound onsets and offsets. Three independent raters (including one author, AD, and two research assistants) independently identified the inflection points as the start and end points of the MS rate rebounds for each observer and experimental condition. The raters were blind to these conditions, which were presented in a random order.

MS timing around the stimulus onset

Precise timings of the MSs were analyzed to investigate the effects of temporal attention and expectation on the MSs that happened around the stimulus presentation timing. We analyzed the timing of the last MS that occurred before the stimuli presentation (last pre-T1 MS) and the first MS that occurred after the stimuli offset (first post-T1 MS) (Bonneh et al., 2015; Denison et al., 2019). We followed the MS timing analysis in the study by Denison et al. (2019). In short, for each observer, we first converted all of the MS onsets to z-scores and estimated the kernel density for each precue and expectation condition. Density was evaluated using 300 equally spaced points between –5 and +5, and the median of each kernel was computed to perform further statistical analyses.

Statistical analysis and visualization

Repeated-measures analysis of variance (ANOVA) and paired t-tests were performed with R 4.2.3 (R Foundation for Statistical Computing, Vienna, Austria) using the R package ezANOVA, and the nonparametric cluster-based permutation tests were performed using MATLAB. Categorical data were analyzed and visualized using R, whereas time series and kernel densities were investigated using MATLAB. We implemented Bonferroni correction for the cluster-based permutation tests and Holm correction for pairwise t-tests to reduce the likelihood of a Type I errors.

Results

MS rate dynamics

Expectation: Hazard rate versus temporal precision

For hazard rate, we analyzed MS rates from the two lowest temporal precision conditions (uniform and wide), as well as the timing of the rate rebound. For temporal precision, we only analyzed the trials where the targets appeared at the expected moment. These trials had the same target onsets but were embedded in sessions with different levels of temporal precision (as reported in Duyar et al., 2024).

We first compared MS rates in trials in which the stimuli appeared early, expected, or late, regardless of attention (Figure 2A). This analysis enabled us to compare prolonged pre-stimulus inhibition versus stimulus-induced inhibition. The cluster-based permutation tests revealed three significant clusters in the inhibitory period and two during the rebound. In the inhibitory period, observers made less frequent MSs in the early trials compared with the expected trials (1189–1503 ms; p = 0.028); in the early trials compared with the late trials (1239–1639 ms; p = 0.007); and in the expected trials compared with the late trials (1415–1663 ms; p = 0.039). Subsequently, there were modulations in the rebound in which MS rates increased back to baseline level. Observers made less frequent MSs when the stimuli appeared late rather than early (1681–2017 ms; p = 0.003) or expected (1739–2037 ms; p = 0.007). Overall, strength and timing of inhibition and rebound followed hazard rate.

Figure 2.

MS rates compared among temporal expectation conditions, regardless of attention locked to precue onset. (A) MS rate varied with hazard rate. There are three significant clusters in the inhibitory period, where MS rates were higher for delayed stimuli, and two clusters during the rebound, where MS rates were lower with delayed stimuli. Shaded regions indicate early and late onsets, and the vertical lines with circles indicate the expected moment. (B) MS rates were similar among different levels of temporal precision. *p < 0.05; **p < 0.05; ***p < 0.001.

We then compared MS rates among temporal precision levels (Figure 2B). Note that, because precision was blocked, observers had information regarding the uncertainty within each block, and they had information about the expected moment, which could have modulated MS rates. Permutation cluster tests revealed no significant differences among the temporal precision levels. MS rate dynamics were similar regardless of temporal precision; they decreased before the stimulus onset and rebounded after stimulus offset.

We split the data based on attentional precue. For hazard rate in the neutral trials (Figure 3A, top panel), in the inhibitory period observers made less frequent MSs in the early than in the late trials (1069–1611 ms; p = 0.001) or in the expected trials (1191–1480 ms, p = 0.023), or in the expected than in the late trials (1408–1632 ms; p = 0.015). This inhibition was followed by rebound modulations in which observers made less frequent MSs in the late than in the early trials (1675–2005 ms; p = 0.016) or in the expected trials (1729–2011 ms; p = 0.002). When T1 was precued (Figure 3A, middle panel), in the inhibitory period observers made less frequent MSs in the early than in the late trials (1249–1568 ms, p = 0.020), followed by three clusters during the rebound and an extra cluster in the post-rebound. During rebound, MS rates were lower in the expected trials (1619–1862 ms; p = 0.011) and late trials (1649–1985 ms; p < 0.0001) than in the early trials, as well as in the late than in the expected trials (1727–2021 ms; p < 0.0001). And, in the post-rebound, MS rates were lower in the expected than in the late trials (2338–2600 ms, p = 0.012). When T2 was precued (Figure 3A, bottom panel), the MS rates were similar during the inhibitory period, whereas there were clusters after stimulus offset. During rebound, MS rates were lower in the late than in the early trials (1688–2009 ms; p < 0.0001) and in the expected trials (1747–2035 ms; p = 0.001). Subsequently, in the post-rebound, MS rates were lower in the early than in the expected trials (2233–2492 ms; p = 0.002), early than in the late trials (2313–2542 ms; p = 0.021), and in the expected than in the late trials (2390–2600 ms; p = 0.016).

Figure 3.

MS rates compared among temporal expectation conditions, separately for each attentional precue trial (neutral, top panel; T1-precued, middle panel; T2, precued, bottom panel). (A) Darker colors indicate a higher hazard rate within the trial. (B) Darker colors indicate a higher temporal precision.

For temporal precision, there were no significant differences among temporal precision levels, in the neutral trials (Figure 3B, top panel) or T2 trials (Figure 3B, bottom panel). When T1 was precued (Figure 3B, middle panel), two clusters emerged. There were fewer MSs (993–1371 ms; p = 0.033) during the inhibitory period in the uniform trials (33%) than in the narrow trials (86%). Also, after the rebound (2293–2600 ms; p = 0.045), there were fewer MSs in the wide (42%) than in the narrow (86%) conditions.

Temporal attention: Hazard rate versus temporal precision

We compared the attentional conditions by collapsing across hazard rate levels within wide and uniform conditions (Figure 4A). Cluster-based permutation tests revealed significant differences during the inhibitory period. MS rates were lower for T1 trials (251–1508 ms; p < 0.001) or T2 trials (599–1303 ms; p = 0.003) than for neutral trials. There were similar attentional modulations in the inhibitory period within each hazard rate condition (Figure 4B). For early targets (Figure 4B, top panel), MS rates were lower when observers attended to T1 than to neutral trials (627–1453 ms; p = 0.002), which coincides with the T1 onset. For expected targets (Figure 4B, middle panel), MS rates were lower for the T2 trials (604–1036 ms; p = 0.010) and T1 trials (621–1336 ms; p = 0.001) than for neutral trials. For late targets (Figure 4B, bottom panel), MS rates were lower in the T2 trials (970–1264 ms; p = 0.021) and T1 trials (987–1306 ms; p = 0.015) than in the neutral trials. When observers attended to the first target, the modulations coincided with early T1 onsets (1200–1350 ms), but never coincided with any T2 onsets when observers attended to the second target.

Figure 4.

MS rates compared among attentional precue. Blue indicates neutral, and green indicates valid attentional precues (dark green, T1-precued; light green, T2-precued). (A, B) Trials from wide and uniform sessions. (C, D) Trials in which the stimuli occurred at the expected moment. MS rates are collapsed across hazard levels (A), and attentional precue effects are separated by hazard rates (B) (early, top panel; expected, middle panel; late, bottom panel). MS rates are collapsed across precision levels (C), and attentional precue effects are separated by precision (D) (certain, top panel; narrow, second panel; wide, third panel; uniform, bottom panel).

We then compared the attentional conditions by collapsing across temporal precision levels at the expected moment (Figure 4C). There were two practically overlapping clusters identified during the inhibitory period. Observers made less frequent MSs when attending to T1 trials (582–1418 ms; p = 0.002) or T2 trials (630–1370 ms; p = 0.006) than neutral trials. Splitting these data according to temporal precision revealed that similar attentional modulations were present during the inhibitory period within each temporal precision condition (Figure 4D). A cluster was identified in the certain condition (595–886 ms; p = 0.022) in which observers made less frequent MSs for T1 than neutral trials. In the narrow condition, a similar difference emerged between T2 and neutral precue conditions (984–1324 ms, p = 0.009). Two clusters practically overlapped in the wide condition, with lower MS rates in T1 trials (860–1221 ms; p = 0.003) and T2 trials (828–1247 ms; p = 0.006) than in neutral trials. In the uniform condition, a similar cluster emerged when attending to T1 than to T2 trials (994–1330 ms; p = 0.010).

MS rates time-locked to target onset

Similar to analyses in the literature (e.g., Dankner et al., 2017; Román-Caballero, Martín-Arévalo, del Carmen Martín-Sánchez, Lupiáñez, & Capizzi, 2024), for wide and uniform conditions we conducted a target-locked analysis by aligning the MS onsets relative to the T1 onset (between 1000 ms before and after T1) and recalculating the MS rates within this window (Figure 5). First, we compared attention at each hazard rate condition. For early targets (Figure 5A, top panel), MS rates were lower when observers attended to T1 than in neutral trials (between –597 and 258 ms; p = 0.002). A similar modulation was observed for expected targets, with lower MS rates in T1 than neutral trials (between –418 and –38 ms; p = 0.003). For late targets, MS rates in both T1 trials (between –437 and –170 ms; p = 0.016) and T2 trials (between –468 and –198 ms; p = 0.018) were lower than in neutral trials. Then, we compared the hazard rate at each attention. For neutral trials (Figure 5B, top panel), MS rates were lower in late than in early trials (between –932 and 126 ms; p < 0.001) and expected trials (between –811 and –29 ms; p < 0.0001), as well as in expected than in early trials (between –693 and –126 ms; p < 0.001). When attention was deployed to T1 (Figure 5B, middle panel), MS rates were lower in the late than in the early trials (between –889 and –39 ms; p < 0.001) and expected trials (between –621 and –177 ms; p = 0.004), as well as in expected than in early trials (between –665 and –124 ms; p = 0.003). Moreover, during the rebound period, MS rates were lower in early than in expected trials (449–766 ms; p = 0.014). When attention was deployed to T2 trials (Figure 5B, bottom panel), MS rates were lower in late than in early trials (between –840 and –166 ms; p < 0.001) and in expected trials (between –588 and –198 ms; p = 0.004), as well as in expected than in early trials (between –665 and –124 ms; p = 0.003).

Figure 5.

MS rates time-locked to target onset in trials from wide and uniform sessions. (A) Attentional precue effects separated by hazard rate (early, top panel; expected, middle panel; late, bottom panel). (B) Hazard rate effects separated by attentional precue (neutral, top panel; T1, middle panel; T2, bottom panel).

MS rate rebound parameters

We also analyzed the timing and the levels of MS rate rebound. The inter-rater (three) consistency for rebound onset was 91% and for offset was 90% of the trials. In the remaining cases, we included consistently chosen points by two out of three raters. We conducted two-way ANOVAs (precue × hazard rate) on the following parameters: Rebound onset was affected by hazard, F(2, 30) = 35.387, p < 0.0001, η_G² = 0.239 (Figure 6A), but not by precue, F(2, 30) = 2.290, p = 0.119 (Figure 6B), or an interaction between these factors, F(4, 60) = 1.475, p = 0.221. Pairwise comparisons revealed that the rebound onset was delayed with stimulus onset (all p < 0.001; early–expected d = 0.792; early–late d = 1.288; expected–late d = 0.659).

Figure 6.

MS rate rebound parameters for hazard rate, attentional precue, and temporal precision. The left column shows data at different levels of hazard rate (collapsed across attention), and the right column shows data for different levels of attention (collapsed across hazard rate). Error bars represent SEM. (A) Main effect of hazard on MS rebound onset. (B) No significant effect of the attentional precue on MS rebound onset. (C) Main effect of hazard on MS rebound offset. (D) Main effect of attentional precue on MS rebound offset. (E) Main effect of hazard on MS rebound magnitude. (F) Main effect of attentional precue on MS rebound magnitude. (G) No main effect of temporal precision on rebound onset. (H) No main effect of temporal precision on rebound offset. (I) No main effect of temporal precision on rebound magnitude.

Rebound offset was affected by hazard, F(2, 30) = 19.731, p = 0.0001, η_G² = 0.162 (Figure 6C), and precue, F(2, 30) = 11.020, p = 0.0003, η_G² = 0.020 (Figure 6D), but there was no interaction between these factors (F < 1, p > 0.1). Rebound stopped sooner when the stimulus was early rather than expected (p = 0.015, d = 0.284) and when it was expected rather than late (p < 0.001, d = 0.754). Moreover, the rebound stopped sooner in T1 trials (p < 0.001, d = 0.309) or T2 trials (p = 0.001, d = 0.224) than in neutral trials.

Rebound magnitude was affected by hazard, F(2, 30) = 9.095, p = 0.0008, η_G² = 0.006 (Figure 6E), and precue, F(2, 30) = 3.969, p = 0.0295, η_G² = 0.006 (Figure 6F), but there was no interaction between these factors (F < 1, p > 0.1). The rebound was smaller for early than late targets (p = 0.0023, d = 0.186). Moreover, the rebound was larger when observers attended to T1 trials (p = 0.019, d = 0.152) or T2 trials (p = 0.018, d = 0.175) than in the neutral trials.

Rebound slope was affected by hazard, F(2, 30) = 4.036, p = 0.028, η_G² = 0.018, and precue, F(2, 30) = 7.443, p = 0.002, η_G² = 0.012. The slope was steeper at expected than early targets (p = 0.005, d = 0.305) and for T1 trials (p = 0.028, d = 0.189) or T2 trials (p = 0.009, d = 0.249) than in neutral trials. The rebound offset MS rate was affected by hazard rate, F(2, 30) = 4.351, p = 0.018, η_G² = 0.002. The MS rate was lower at the rebound offset for early targets than for late targets (p = 0.043, d = 0.127). Finally, there was no main effect or interaction of precue and hazard rate on MS rate for rebound onset (all F < 1, p > 0.05) or duration, hazard F(2, 30) = 2.112 (all F < 1, all p > 0.1). Additionally, we performed the same analysis for temporal precision at the expected moment. For the corresponding analysis, there was an effect of precue (all p < 0.5), but no effect of precision or their interaction (all F < 1, all p > 0.1) (Figures 6G to 6I).

In sum, with increasing hazard, MS rate inhibition was delayed when collapsing across attentional conditions. This effect was more pronounced in the neutral than in attended trials, with the effect being present in T1 but not in T2 trials. MS rate rebound was delayed and its magnitude increased. However, regardless of hazard rate or temporal precision, attention facilitated MS inhibition and increased the rebound magnitude, steepening its slope and hastening its offset. Rate rebound parameters were not affected by temporal precision.

Microsaccade latency dynamics

To investigate whether the precise timing of the MSs is affected by the interaction between temporal attention and expectation, we analyzed the timing of the MS that occurred around the stimulus onset. We analyzed the timing of the last MSs that occurred before the stimuli (last pre-T1 MSs), and the timing of the first MS that occurred after the stimuli (first post-T1 MSs) (Bonneh et al., 2015; Denison et al., 2019). Analyzing first post-T2 MSs yielded the same results because very few MSs occurred between the T1 and T2 trials.

Hazard rate

Given that target timings varied among trials, we analyzed last pre-T1 and first post-T1 MS latency relative to precue and to the target onset. We performed two-way (3 hazard rates × 3 precues) ANOVAs on the median timings of the estimated kernel densities. Relative to precue onset, ANOVA on the last pre-T1 MS latency revealed main effects of the hazard rate, F(2, 30) = 26.012, p < 0.0001, η_G² = 0.112, and attention, F(2, 30) = 11.875, p = 0.002, η_G² = 0.104, but no interaction, F(4, 60) = 1.284, p = 0.293. Pairwise t-tests showed that the last pre-T1 MSs were sooner for early than expected targets (p < 0.0001, d = 0.478), which in turn were sooner than for late targets (p < 0.001, d = 0.339) (Figure 7A) and when observers attended to T1 trials rather than to T2 trials (p = 0.017, d = 0.216), which in turn were sooner than neutral (p = 0.0001, d = 0.542) (Figure 7B).

Figure 7.

Precise timing of MS that occurred around the stimulus. Diamond icons and the horizontal bars overlaid on the violin plots represent mean and median values, respectively. (A) Main effect of hazard on the last pre-T1 MS timing. (B) Main effect of attentional precue on the last pre-T1 MS timing. (C) Main effect of hazard. (D) Main effect of attentional precue. (E) Main effect of hazard. (F) Main effect of attentional precue. Note that panels (A) to (D) include trials locked to precue onset, and panels (E) and (F) include trials locked to stimulus onset.

ANOVA on the first post-T1 MS rebound locked to the precue yielded main effects of hazard rate, F(2, 30) = 202.788, p < 0.0001, η_G² = 0.513, and attention, F(2, 30) = 4.212, p = 0.024, η_G² = 0.009). Pairwise comparisons revealed that the first post-T1 MSs were delayed with hazard (all p < 0.0001; early–expected d = 1.303; early–late d = 2.596; expected–late d = 1.131) (Figure 7C). Moreover, the first post-T1 MSs were earlier when T1 was precued than in neutral trials (p = 0.008, d = 0.158) (Figure 7D).

Relative to target onset, ANOVA on last pre-T1 MS latency revealed main effects of hazard rate, F(2, 30) = 144.793, p < 0.0001, η_G² = 0.449, and attention, F(2, 30) = 12.026, p = 0.0001, η_G² = 0.103, but no interaction, F(4, 60) = 1.508, p = 0.231. Pairwise t-tests showed that the time window between the last pre-T1 MS and the T1 onset was shorter for early than expected (p < 0.0001, d = 1.022), which in turn was shorter than for late (p < 0.0001, d = 1.052). Similarly, it was shorter when attending to T1 than T2 (p = 0.050, d = 0.147), which in turn was shorter than for neutral trials (p < 0.001, d = 0.423). These findings are in the same direction as the MS timing locked to the precue. A two-way ANOVA on the median first post-T1 MS timing showed a main effect of precue, F(2, 30) = 0.034, p = 0.034, η_G² = 0.006, but not of hazard, F(2, 30) < 1, p > 0.1 (Figure 7E). Post-T1 MSs were sooner when T1 was precued than in neutral trials (p = 0.018, d = 0.201) (Figure 7F).

Temporal precision

We performed two-way (4 precisions × 3 precues) ANOVAs on the median timings of the last pre-T1 and first post-T1 MSs. On both last pre-T1 and first post-T1 MS timings, there was a main effect of attention: last pre-T1, F(2, 26) = 10.111, p < 0.001, η_G² = 0.067 (Figure 8B); first post-T1, F(2, 26) = 7.847, p = 0.002, η_G² = 0.017 (Figure 8D). But there was no main effect of precision (last pre-T1, F < 1, p > 0.1; first post-T1, F < 1, p > 0.1) or their interaction: last pre-T1, F(6, 78) = 1.271, p > 0.1 (Figure 8A); first post-T1, F(6, 78) = 1.563, p > 0.1 (Figure 8C). Post hoc pairwise t-tests showed that the last pre-T1 MSs were earlier in T1 trials (p < 0.001, d = 0.599) and T2 trials (p < 0.001, d = 0.506) than in neutral trials. First post-T1 MSs were earlier when attending to T1 than T2 trials (p = 0.003, d = 0.273) or neutral trials (p = 0.006, d = 0.276).

Figure 8.

Precise timing of MS that occurred around the stimulus. (A) No effect of temporal precision on the last pre-T1 MS timing. (B) Main effect of attentional precue on the last pre-T1 MS timing. (C) No effect of temporal precision on the first post-T1 MS timing. (D) Main effect of attentional precue on the first post-T1 MS timing.

Discussion

Different temporal structures shape temporal expectations, influencing perception, action, and attention through overlapping yet distinct mechanisms, such as modulations in neural signal strength, latency, and synchrony (for a review, see Nobre & van Ede, 2017). The brain forms temporal expectations through distinct neural correlates, which are integrated into behavioral responses based on its temporal structure (Coull, Frith, Büchel, & Nobre, 2000; Grabenhorst et al., 2021; Tal-Perry & Yuval-Greenberg, 2020). Hazard rate (mounting expectations through time passage) and temporal precision (based on probabilistic distributions) differentially influence auditory neural responses (Todorovic & Auksztulewicz, 2021) and interact with temporal attention distinctly when modulating visual performance (Duyar et al., 2024). Here, we explored potential dissociations between perception and eye movements and examined whether they can be distinguished at the oculomotor level.

We focused on the temporal dynamics of the push–pull mechanisms of MS rate signature across three stages: (1) pre-stimulus anticipatory inhibition, (2) post-stimulus reflexive exogenous inhibition, and (3) rebound, which enabled us to disentangle endogenous components driven by anticipatory processes from the exogenous components triggered by external stimuli. The MS rate signature is aligned with the hazard rate but not with precision. We analyzed MS rate signatures across varying hazard rates and across different precision levels. As the stimuli were delayed and the hazard rate increased, pre-stimulus anticipatory inhibition was prolonged, and post-stimulus reflexive exogenous inhibition and the corresponding rebound were delayed. Also, notably, the post-stimulus inhibition was stronger than the anticipatory inhibition, resulting in lower MS rates in early trials than in late trials (Figure 2A). In contrast, MS rate signatures were similar across temporal precision levels (Figure 2B).

Temporal attention modulates hazard rate and temporal precision in an opposite manner during MS rate decrease

We analyzed MS rate signatures across varying hazard rates and across different precision levels as a function of attention. In the neutral condition, MS rates were lower when the target was early during the inhibition, and the corresponding rebound occurred earlier; however, no such effect was observed for temporal precision (Figures 3A and 3B, top panels). When observers attended to T1, pre-stimulus inhibition was stronger, leading to an attenuated reflexive inhibition and resulting in only one cluster during the inhibitory period, highlighting the difference between early and late trials. As a result, the distinctions between the hazard rate levels that were present in neutral trials were diminished when attending to T1 trials and disappeared when attending to T2 trials, when aligned to either cue onset (Figure 3A, middle and bottom panels) or target onset (Figure 5B). In contrast, precision levels were distinct during the pre-stimulus period when observers attended to T1 trials (Figure 3B, middle panel). Specifically, MSs occurred less frequently in the pre-stimulus period under lower (33%) than higher (86%) temporal precision. Because hazard rate depends on stimulus onset, the emergence of attentional interaction in the post-stimulus period is expected. However, the pre-stimulus emergence of the precision effect is notable, especially given its late effect on auditory-evoked MEG responses compared to hazard rate (Todorovic & Auksztulewicz, 2021). Furthermore, our findings indicate that temporal precision information is integrated into eye movement planning primarily during attentional deployment in the anticipatory period. These results suggest that temporal attention plays a gating role: Only when attention is deployed and only when attention is deployed does temporal precision impact MS frequency. The influence of temporal precision is not automatic; instead, it requires attentional allocation in time. The anticipatory integration of temporal precision with attentional deployment suggests enhanced sensitivity of the oculomotor system to temporal precision. Furthermore, this finding also indicates a more precise temporal readout with attentional deployment.

Temporal attention modulates hazard rate and temporal precision similarly after rebound

Notably, we found that post-rebound differences emerged with attention, both for hazard rate (Figure 3A, middle and bottom panels) and for temporal precision (Figure 3B, middle panel). These differences were in the same direction, such that a higher probability of the stimulus onset was associated with a higher MS rate in the post-rebound. This similarity suggests a potential common mechanism for integrating the attended probabilistic temporal information irrespective of the temporal structure from which the probability is derived. Such post-stimulus processing commonality among hazard rate and temporal precision was observed in gain modulation in primary auditory cortex and superior temporal gyrus (Todorovic & Auksztulewicz, 2021).

Perception–eye movement parallelism was observed for the hazard rate but not for temporal precision

Temporal attention facilitates pre-stimulus anticipatory MS inhibition when stimulus timing is predictable (Denison et al., 2019; Palmieri et al., 2023), as well as under low temporal precision (Duyar & Carrasco, 2024). Here, we found that attentional modulation can extend beyond T1 (Figure 4A). Remarkably, this modulation coincides with early stimuli onsets, for which hazard is the lowest (Figures 4B, 5A), within the window with largest attentional benefits on performance (Duyar et al., 2024). Together, these results suggest a parallelism between performance and oculomotor behavior. We did not observe such a parallelism for temporal precision. Attentional modulation occurred earlier for certain trials than for all uncertain trials (Figure 4D).

Temporal attention and hazard rate operated independently during the post-stimulus period

We quantified both rebound temporal shift and magnitude in hazard rate. The MS rate rebound is not merely a reflexive release from prior suppression; it is delayed following an oddball event (Valsecchi, Betta, & Turatto, 2007; Widmann, Engbert, & Schroger, 2014) and with task difficulty due to prolonged sensory evidence accumulation (Ezzo et al., 2025). Its duration also increases as a function of reaction times (Betta & Turatto, 2006), but its magnitude diminishes following an oddball event (Valsecchi & Turatto, 2009). Moreover, the magnitude of the rebound is linked to activity in the frontal eye fields (Fernández, Hanning, & Carrasco, 2023; Hsu, Chen, Tseng, & Wang, 2021). Unlike the effect of interaction between temporal attention and hazard rate on performance, we observed no evidence for an interaction between them on MS rate rebound. In particular, rebound onset was delayed with hazard (Figure 6A), but not with attention (Figure 6B). Rebound offset was also delayed with hazard (Figure 6C), but attention hastened it (Figure 6D), so that post-stimulus MS rate reached baseline level faster with attention. We also found that rebound magnitude increased with both hazard (Figure 6E) and attention (Figure 6F). Overall, these findings suggest that temporal attention and expectation operate independently during the post-stimulus period. The delay in rebound onset and offset with hazard rate primarily indicates a temporal shift locked to stimulus timing, whereas attention hastened rebound offset, expediting a return to baseline rate without affecting its onset. Furthermore, the increase in rebound magnitude with both hazard and attention may reflect their separate contributions to ongoing cognitive control and decision making during the post-stimulus window.

Precise timing of MSs with stimulus onset allows for quantification of oculomotor freezing and the subsequent release, revealing fine-grained temporal dynamics of perceptual and cognitive processes (Bonneh et al., 2015; Yablonski, Polat, Bonneh, & Ben-Shachar, 2017). When the stimulus timing is certain, the last MSs before stimulus onset and the first MSs after stimulus onset occur earlier with temporal attention (Denison et al., 2019).

Perception–eye movement dissociation for the hazard rate

Effects of temporal attention and hazard rate interact on performance (Duyar et al., 2024), but we did not find such an interaction with the precise timing of MSs. The oculomotor freezing onset—indexed by last pre-T1 MS—was delayed with the hazard rate, as the stimulus was delayed (Figure 7A). But, regardless of hazard rate, attention speeded oculomotor freezing (Figure 7B). Correspondingly, release from freezing, indexed by the first post-T1 MSs, was delayed with hazard rate (Figure 7C) and shifted earlier with attention (Figure 7D).

Upcoming MSs are scheduled in advance

To differentiate the effects of MS timing from those of stimulus latency, we analyzed MS timing relative to the stimulus within each trial. This analysis revealed that the release from inhibition was consistent regardless of hazard rate, with the first post-stimulus MSs occurring after a similar duration following stimulus onset (Figure 7E). In comparison, attentional effects on the release from inhibition were still present relative to stimulus onset, such that the release from inhibition occurred earlier in the attended trials as compared to neutral trials (Figure 7F). This finding provides evidence for the preparatory scheduling of MSs in advance (Badde et al., 2020). Hazard rate is stimulus dependent and dynamically updated as the stimulus is delayed; consequently, the release from inhibition cannot be preplanned with respect to hazard rate. The release timing was unaffected by hazard rate, which is inherently tied to immediate, transient changes. In contrast, attentional allocation occurred earlier within the trial, enabling planning of the inhibition release and advance scheduling of MSs. Overall, we conclude that release from inhibition can be governed by endogenous anticipatory rather than transient processes.

Perception–eye movement dissociation for temporal precision

Although temporal attention benefits on visual performance increase with temporal precision (Duyar et al., 2024), we found that precise timing of MS is independently and consistently advanced with attention. Regardless of temporal precision, the oculomotor freezing onset (the last pre-T1 MSs and first post-T1 MSs) were consistent (Figures 8A and 8C), but started (Figure 8B) and released (Figure 8D) earlier with attention.

Target-general and target-specific modulation of MS dynamics with attention

There was a target-general effect of temporal attention on the MS rates. For both targets, they were lower in the pre-stimulus period around similar time windows in comparison with the neutral (Figures 4 and 5A). Furthermore, there was a target-specific effect of temporal attention on the precise timing of the MSs, depending on which particular time point was attended (Figures 7B and 8D). Together, these findings indicate that, whereas MS rate modulations are tied to whether or not temporal attention is deployed, their precise timing can be flexibly shifted depending on which specific moment is attended.

Conclusions

In conclusion, expectations based on hazard rate are represented within the oculomotor system, with probabilistic information through time passage contributing to fixational stability, consistent with previous studies on temporal expectation (Abeles et al., 2020; Akdoğan et al., 2016; Ameqrane et al., 2014; Amit et al., 2019; Badde et al., 2020; Betta & Turatto, 2006; Dankner et al., 2017; Drążyk & Missal, 2023). In addition, in the absence of selective attention, our results reveal that temporal expectation based on precision is not represented in the MS responses. However, when temporal attention is allocated, MS patterns also index precision. Comparing with our perceptual findings (Duyar et al., 2024), on the one hand, we observed perception–eye movement dissociations for both types of expectation on the precise timing of MSs where attention and expectation had independent effects. On the other hand, we found parallel instances in which attentional modulations on MS coincided with performance benefits with increasing hazard rate. Our study provides insights into the endogenous and stimulus-driven components of oculomotor dynamics, revealing how temporal attention and distinct types of expectation work together to enhance fixational stability.