The participants underwent EEG while viewing a target through the Gazefinder® infrared eye-tracking system (JVC Kenwood, Kanagawa, Japan). This system is a 19-inch (1280 $\times$ 1024 pixels) monitor fitted with infrared light sources and cameras. The participants were seated with their heads resting on a chin rest, approximately 60 cm from the monitor, which subtended 35.662° (horizontal) and 28.862° (vertical) of their visual field. The X- and Y-coordinates of each participant’s eye position were sampled at 50 Hz. A target (red circle with a radius of 0.38°) appeared and launched from the bottom left corner of the screen and landed in the bottom right half of the visual scene following a parabolic path. In both the PST and SST, the visible and occluded sections had a gray background. In all tasks, the first half of the trajectory was visible, whereas the second half was blocked, so the participant had to guess where it would land. The eye position recording was calibrated using a five-point method, whereby each participant followed the location of a target around the screen before each trial block.

EEG was recorded as previously described [14] using the mobile EEG system, eegoTM sports (ANT Neuro, Enschede, Netherlands), with 32 Ag/AgCl electrodes positioned in accordance with the 10/20 system. The electrode activities at Fz, F3, F4, FC1, FC2, FC5, FC6, Cz, C3, C4, T7, T8, CP1, CP2, CP5, CP6, Pz, P3, P4, P7, P8, POz, Oz, O1, and O2 were analyzed. Frontal electrode activity at Fpz, Fp1, Fp2, F7, and F8 was not analyzed owing to the effect of unwanted eye movements (see Data analysis section, Koshizawa et al. [14], and Makin et al. [29]). During the recording, CPz and AFz served as the reference and ground electrodes, respectively. All EEG data were converted to common average references prior to analysis. The sampling rate was set to 1000 Hz with impedances maintained below 20 k$\mathrm{\Omega }$ [30]. A photosensor (Miyuki Giken, Tokyo, Japan) connected to the EEG system was placed on the monitor to synchronize the EEG with target onset.

The distance between the actual target position of the final arrival point and the eye position when the participant responded by pressing a stick-type button with the thumb to predict that the moving target had reached the final arrival point at the bottom of the display (almost the same height as the starting point) was calculated as “position error (PE) at the response”.

The “response error” was calculated by subtracting 4.6 s (from when the target starts moving until it reaches the final arrival point) from the response time (time from when the target starts moving to when the participant predicts that the target has reached the final arrival point at the bottom of the display and responds by pressing the button).

At each time point (50 Hz) in the period of 4.6 s (from when the target starts moving until it reaches the final arrival point) during which the target moves, the distance between the eye position and the target position at the final arrival point was calculated as “PE at point (0.02–4.60 s)” in the time series data. Likewise, the “eye position of the XY coordinate (0.02–4.60 s)” was defined as the position in the time series data.

The instantaneous log amplitude of the complex analytic signal was calculated in the low beta frequency band (13–15 Hz) according to the Hilbert transform method [16] using EMSE Suite v5.6 (Cortech Solutions, Inc., Wilmington, NC, USA). A rectifier filter was used to obtain the log10 Hilbert envelope output for each channel. Following the application of polynomial detrend to baseline adjustment, the transformed signal displayed oscillations around zero, similar to the raw EEG. Subsequently, we calculated event-related averages and grand averages of log-transformed low beta-band amplitudes, employing a methodology akin to standard ERP data analysis. Additionally, scalp activity topographic maps were produced using the group mean voltage at each electrode, averaged over a significantly different section time window (see below).

We compared the SST and PST using a paired t-test for the four calculated parameters of (1) PE at response, (2) response error, (3) PE at point (0.02–4.60 s), and (4) eye position of the XY coordinate at point (0.02–4.60 s).

The participants were then divided into two groups of eight each: those with a small PE and those with a large PE at response. Next, the four parameters of the Small PE Group and the Large PE Group at response were compared using an unpaired t-test.

Statistical analyses were performed with SPSS (version 26, IBM Corp., Armonk, NY, USA). The significance level was set at p 0.05. Regarding the parameters of (3) PE at point (0.02–4.60 s), and (4) eye position of the XY coordinate at point (0.02–4.60 s), we used the Benjamini/Hochberg false discovery rate correction method. All significant values remained significant with the correction, however as recommended the unadjusted p-values are reported.

Non-parametric paired permutation tests [31, 32] were used to examine group differences in (1) PST vs. SST, (2) Small PE Group at response vs. Large PE Group at response, and each parameter for time (in 1 ms intervals throughout the recording epoch) and space (25 EEG channels) using EMSE Suite v5.6 (Cortech Solutions, Inc.). To address multiple comparisons across the visible section (ranging from 0 s to 2.300 s after target onset), the permutation test was utilized to compute p-values that were corrected for spatial effects. Based on the methodology described by Koshizawa et al. [14] and Naccache et al. [33], an effect was considered statistically significant if the corresponding p-value was less than 0.05 and maintained for a minimum duration of 10 ms. In addition, the topographic maps of scalp activity were produced only for the significantly different sections.

There was no significant difference with PE in response to the target arrival point between the PST and SST (4.04 $\pm$ 1.36° PST vs. 3.60 $\pm$ 1.33° SST; t(15) = 1.43, p = 0.17) (Fig. 2a).

Using response error as a parameter, participants showed a delayed reaction time in the PST compared with the SST (0.54 $\pm$ 0.75 s PST vs. 0.32 $\pm$ 0.85 s SST; t(15) = 2.46, p = 0.02) (Fig. 2b).

The time series data of the PE to the target arrival point during each task are presented in Fig. 2c. Compared with the PST, the PE to target arrival point during the SST was significantly decreased at 0.40–4.60 s (0.40–0.56 s; p 0.05, 0.58–1.34, 4.46–4.60 s; p 0.01, 1.36–4.44 s; p 0.001) after target onset.

The time series data of the eye position of the X coordinate during each task are presented in Fig. 2d. Compared with the PST, the X coordinate eye position during the SST was significantly increased at 0.48–4.52 s (0.48–0.66, 4.46–4.52 s; p 0.05, 0.68–1.44, 4.24–4.44 s; p 0.01, 1.46–4.22 s; p 0.001) after target onset.

Time series data of the Y-coordinate eye position during each task are presented in Fig. 2e. Compared with the PST, the eye position of the Y coordinate during the SST was significantly increased at 0.02–4.60 s (0.02–0.36, 0.46–1.44, 4.46–4.60 s; p 0.01, 0.38–0.44, 1.46–4.44 s; p 0.001) after target onset.

Compared with the Large PE Group at response, the PE at response to target arrival point in the Small PE Group at response was significantly decreased (2.43 $\pm$ 0.69° Small PE Group at response vs. 4.77 $\pm$ 1.35° Large PE Group at response; t(14) = –3.52, p = 0.003) (Fig. 3a).

There was no significant difference in response error to target arrival point between the Small PE Group at response and the Large PE Group at response (0.20 $\pm$ 0.82 s Small PE Group at response vs. 0.44 $\pm$ 0.89 s Large PE Group at response; t(14) = –0.66, p = 0.52) (Fig. 3b).

The PE time series data to the target arrival point during each condition are presented in Fig. 3c. Compared with the Large PE Group at response, the PE to the target arrival point in the Small PE Group at response was significantly decreased at 0.50–0.68 s (p 0.05), 3.00–4.60 s (3.00–3.50 s, 3.74–4.60 s; p 0.05, 3.52–3.72 s; p 0.01) after target onset.

The time series data of the eye position at the X coordinate during each task are presented in Fig. 3d. Compared with the Large PE Group at response, the eye position of the X coordinate of the Small PE Group at response was significantly increased at 0.50–0.88 s (p 0.05), 2.68–4.60 s (2.68–2.96 s, 4.38 s, 4.46 s, 4.50–4.54 s; p 0.05, 2.98–4.36 s, 4.40–4.44 s, 4.48 s, 4.56–4.60 s; p 0.01) after target onset.

There was no significant difference in the eye position of the Y coordinate between the Small PE Group at response and the Large PE Group at response (Fig. 3e).

We performed non-parametric paired permutation tests to examine the differences between activity during the PST and SST at each electrode position during the 2.300 s visible section of the trajectory. EEG spectra of low beta frequency (13–15 Hz) were analyzed using the Hilbert transform. Fig. 4 shows the average time series EEG data for each task (PST and SST) only for electrodes for which significant differences were noted. A non-parametric paired permutation test revealed that low beta frequency activity was higher during the SST than during the PST at Oz from 0 to 0.010 s (p 0.05), at Cz from 0.156 to 0.245 s (p 0.05), at CP2 from 1.761 to 1.774 s (p 0.05) and 1.794 to 1.819 s (p 0.05), and from 1.824 to 1.850 s (p 0.05) after the onset of the moving target (Fig. 4 left side). The topography of the significantly different sections of these electrodes is also shown in Fig. 4 (right side).

Additionally, we performed a non-parametric unpaired permutation test to examine differences between the Small PE Group at response and Large PE Group at response at each electrode position during the 2.300 s visible section of the trajectory. EEG spectra of low beta frequency (13–15 Hz) were analyzed using the Hilbert transform. Fig. 5 shows the average time series EEG data for each task (Small PE Group at response and Large PE Group at response) only for electrodes for which significant differences were noted. A non-parametric paired permutation test revealed that low beta frequency activity was higher in the Small PE Group at response than in the Large PE Group at P7, from 0.105 to 0.185 s (0.105–0.166 s, 0.168–0.170 s, 0.175–0.185 s; p 0.05, 0.167 s, 0.171–0.174 s; p 0.01) after the moving target onset (Fig. 5 left side). The topography of the significantly different sections of these electrodes is also shown in Fig. 5 (right side).

There was no significant difference in PE in response to the target arrival point between the PST and the SST. Because the accuracy of gaze tracking performance was not important for the interception accuracy in previous studies, in which the best interception players showed an accuracy of ball tracking similar to that of the worst players [34], it was assumed that it is possible to predict the position and time of arrival of a moving target without tracking it. Therefore, it was clarified that the arrival position can be predicted successfully even if the participant does not “strategically” follow the target with eyes.

The target arrival point during the SST, compared with the PST, was significantly decreased from the PE at point (0.02–4.60 s) to at 0.40–4.60 s point after target onset. Time series data of the eye position of the X- and Y-coordinates were also significantly different between the PST and SST at approximately similar sections. In the PST, the participant was instructed to pursue the target. Therefore, when the pursuit strategy is used, a large PE in time series data to the target arrival point inevitably occurs because the target is followed in this case. A response delay occurs when tracking a target that moves parabolically with pursuit eye movements [15]. Using response error as a parameter, the PST showed a delayed reaction compared with the SST, which can be mentioned as one of the results showing that the PST follows the target. On the other hand, in the SST, the user was instructed to quickly move the eye to the target arrival point as soon as the target arrival point is predicted. Therefore, the SST had a lower PE to the target arrival point at an early stage compared with the PST (Fig. 3c). Especially around 2.70 s, the PE and the Y-coordinate eye position to the target arrival point suddenly dropped. As a result, since the visual information of moving targets cannot be obtained at least in the section where the target is occluded, in the SST, all experimental participants are considered to have moved their eyes to the target arrival point.

Compared with the Large PE Group at response, the PE in response to the target arrival point in the Small PE Group was significantly decreased by approximately 2°. There was no significant difference in response error to the target arrival point between the Small PE Group at response and the Large PE Group at response. This result is natural because the participants were grouped based on PE at response rather than on the response error in comparison.

Then, with the time series results, compared with the Large PE Group at response, the PE to the target arrival point in the Small PE Group at response was significantly decreased at 0.50–0.68 s after target onset. Time series data of the eye position of the X-coordinate were also significantly different between the Small PE Group and Large PE Group in response to approximately similar sections. On the other hand, there was no significant difference in time series data of the eye position of the Y-coordinate between the Small PE Group and the Large PE Group at response. Since the lack of a direct relationship between the ocular pursuit performance and the participant’s catching ability has been clarified in previous studies, it might be not necessary to continue the pursuit eye movement to accurately predict the target position [34]. Therefore, for the Small PE Group at response, these results suggest that immediately after the target starts moving, the participant detects the speed and direction of the target, knows the target arrival point at this early stage (0.50–0.68 s), does not follow the target, and directs the eyes to the vicinity of the target arrival point. Additionally, compared with the Large PE Group at response, the PE to the target arrival point in the Small PE Group at response was significantly decreased at 3.00–4.60 s after target onset. The significant difference in this period is considered to be the result reflecting the PE at response.

First, as for both topography in Fig. 4, the potential in the frontal region is high in both PST and SST. The frontal regions become functional by 3 to 4 months of age, forming part of the cerebellar network that predicts eye movements [35]. By 4 months of age, the prefrontal cortex is functional, as evidenced by ERPs, particularly for anticipatory or reactive saccades [36]. Canfield and Kirkham [37] suggest that frontal eye field may be operative even earlier, by 3 months of age. In other words, frontal regions play a very important role as a basic level of executive function (early cortical network) when performing tasks that require anticipatory or reactive saccades, such as the tasks in this study. Therefore, the topography results with high potentials in the frontal region in both PST and SST might reflect the “predictive control of eye movements” associated with “maturation of the visual motor system and its relationship with large-scale brain networks”.

In the following EEG discussion section, with reference to Koessler et al. [38], we will identify the region located at the electrode where a significant difference has occurred, and proceed with the discussion based on the localization of that region. Koessler et al. [38] clarified the cranio-cerebral correlation in the 10-10 system, facilitating improved accuracy of brain surface imaging and aiding electrophysiological analyzes such as the localization of cortical generators in superficial focal areas [38]. Conversely, Lantz et al. [39] state that a setup of at least 63 electrodes is essential for optimal source localization of the underlying EEG source. The number of electrodes recorded in this study is smaller than that. Therefore, multiple neural generators may contribute to the evoked activity recorded at a particular electrode. This compromises the precise correspondence between a single electrode and its responsible neural source. As we proceed with the ensuing discussion, we will take the above points into consideration.

Oz corresponds to brodmann area (BA) 18 (0.3 $\pm$ 5.9 mm in x, –97.1 $\pm$ 5.2 mm in y, and 8.7 $\pm$ 11.62 mm in z with Talairach stereotactic coordinates) [38], which is located in the secondary visual cortex, where low beta activity was significantly higher during the SST than during the PST at 0–0.010 s after target onset. Topography showed an increase in positive potentials around the secondary visual cortex during the SST than during the PST at 0–0.010 s after target onset. Thut et al. [40] reported that changes in 14 Hz EEG activity in the secondary visual cortex reflect preparation for visual events occurring at a predictable position. Additionally, Thut et al. [40] reported that the changes in 14 Hz EEG activity in the secondary visual cortex can be used to calculate an index for the momentary bias of visuospatial attention that predicts the processing speed of forthcoming, lateralized visual targets, and, to some extent, the detection rate. When the target starts moving, a saccade strategy for visuospatial attention is required by quickly moving the eyes to the arrival position as soon as it can be predicted. Therefore, the higher low beta activity (14 Hz EEG) in the secondary visual cortex at 0–0.010 s after target onset during the SST may reflect visuospatial attention to the moving target.

Cz corresponds to BA4 (0.8 $\pm$ 4.9 mm in x, –21.9 $\pm$ 9.4 mm in y, and 77.4 $\pm$ 6.7 mm in z with Talairach stereotactic coordinates) [38] and is located in the primary motor cortex, where low beta activity during the SST was significantly higher than that during the PST at 0.156–0.245 s after the onset of target movement. In addition, topography showed an increase in positive potentials around the primary motor cortex during the SST than during the PST at 0.156–0.245 s after target onset. The modulation of sensorimotor areas occurs through a combination of bottom-up processing, dependent on the sensory input modality, and top-down mechanisms driven by the properties of the attended stimulus [41]. A saccade strategy is required to quickly move the gaze to the arrival position as soon as it can be predicted. Hence, the increased low beta activity observed in the primary motor cortex at 0.156–0.245 s after target onset during the SST might indicate the involvement of tracking moving targets. This phenomenon likely occurs due to the combined operation of bottom-up processes, such as processing target velocity and direction, and top-down processes related to attention to moving target.

CP2 corresponds to BA7 (25.8 $\pm$ 6.2 mm in x, –47.1 $\pm$ 9.2 mm in y, and 66.0 $\pm$ 7.5 mm in z with Talairach stereotactic coordinates) [38] and is located in the posterior parietal lobe. In this area, low beta activity was significantly higher during the SST than during the PST at 1.761–1.774 s, 1.794–1.819 s, and 1.824–1.850 s after target onset. Topography showed an increase in positive potentials around the posterior parietal lobe during the SST than during the PST at 1.761–1.850 s after target onset. According to the findings of Morris et al. [42], the posterior parietal lobe assumes a critical role in the conversion of visual signals from the retina into spatial or craniotopic coordinates. This process is instrumental in performing spatial computations essential for perception and motor planning. According to the proposal by Leigh and Zee [12], the posterior parietal cortex exhibits a greater degree of involvement in directing attention compared to its role in generating eye movements. A saccade strategy is required to quickly move the gaze to the arrival position as soon as it can be predicted. During the SST after 1.761–1.774 s, 1.794–1.819 s, and 1.824–1.850 s, the eye position at the X coordinate was positioned around 800 pixel, near where the target reached (approximately 1000 pixels). Hence, the observed low beta activity in the posterior parietal lobes during the SST might be associated with attentional focus on the position near where the target will reach compared to that in the PST.

P7 corresponds to BA19 (–55.9 $\pm$ 4.5 mm in x, –64.8 $\pm$ 5.3 mm in y, and 0.0 $\pm$ 9.3 mm in z with Talairach stereotactic coordinates) [38] in the left hemisphere and is located in the MT visual area, where low beta activity was significantly higher in the Small PE Group than the Large PE Group at response time 0.105–0.185 s after target onset. In addition, topography showed an increase in positive potentials around the MT in the Small PE Group than in the Large PE Group at response at 0.105–0.185 s after target onset. The MT area plays a critical role in detecting the speed and direction of moving targets as well as generating eye-tracking responses, as observed by Leigh and Zee [12]. Numerous studies have provided compelling evidence supporting the involvement of MT neurons in detecting target speed, as demonstrated by the findings of Liu and Newsome [13]. Compared with the Large PE Group at response, the PE to the target arrival point in the Small PE Group at response was significantly decreased at 0.50–0.68 s after target onset. These results suggest that immediately after the target starts moving, the participant detects the speed and direction of the target, knows the target arrival point at this early stage (0.50–0.68 s), does not follow the target, and directs their eyes near the arrival point of the target. In order to reduce PE to the point where the target will reach, low beta activity in the MT of the Small PE Group at 0.105–0.185 s after target onset may more accurately allow detection of the speed and direction of the moving target compared to that in the Large PE Group at response.