December 2024
Volume 65, Issue 14
Open Access
Visual Psychophysics and Physiological Optics  |   December 2024
Serial Dependence in Smooth Pursuit Eye Movements of Preadolescent Children and Adults
Author Affiliations & Notes
  • Bao Hong
    School of Psychology and Cognitive Science, East China Normal University, Shanghai, China
    NYU-ECNU Institute of Brain and Cognitive Science at New York University Shanghai, Shanghai, China
  • Jing Chen
    NYU-ECNU Institute of Brain and Cognitive Science at New York University Shanghai, Shanghai, China
    Faculty of Arts and Science, New York University Shanghai, Shanghai, China
    Institute of Brain and Education Innovation, East China Normal University, Shanghai, China
    Shanghai Center for Brain Science and Brain-Inspired Technology, Shanghai, China
  • Wenjun Huang
    School of Psychology and Cognitive Science, East China Normal University, Shanghai, China
    NYU-ECNU Institute of Brain and Cognitive Science at New York University Shanghai, Shanghai, China
  • Li Li
    School of Psychology and Cognitive Science, East China Normal University, Shanghai, China
    NYU-ECNU Institute of Brain and Cognitive Science at New York University Shanghai, Shanghai, China
    Faculty of Arts and Science, New York University Shanghai, Shanghai, China
    Institute of Brain and Education Innovation, East China Normal University, Shanghai, China
    Shanghai Center for Brain Science and Brain-Inspired Technology, Shanghai, China
  • Correspondence: Li Li, Faculty of Arts and Science, New York University Shanghai, Rm S706, 567 West Yangsi Road, Pudong New District, Shanghai 200126, China; [email protected]
  • Footnotes
     BH and JC contributed equally to this work.
Investigative Ophthalmology & Visual Science December 2024, Vol.65, 37. doi:https://doi.org/10.1167/iovs.65.14.37
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      Bao Hong, Jing Chen, Wenjun Huang, Li Li; Serial Dependence in Smooth Pursuit Eye Movements of Preadolescent Children and Adults. Invest. Ophthalmol. Vis. Sci. 2024;65(14):37. https://doi.org/10.1167/iovs.65.14.37.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose: Serial dependence refers to the attraction of current perceptual responses toward previously seen stimuli. Despite extensive research on serial dependence, fundamental questions, such as how serial dependence changes with development, whether it affects the perception of sensory input, and what qualifies as serial dependence, remain unresolved. The current study aims to address these questions.

Methods: We tested 81 children (8–9 years) and 77 adults (18–30 years) with an ocular tracking task in which participants used their eyes to track a target moving in a specific direction on each trial. This task examined both the open-loop (pursuit initiation) and closed-loop (steady-state tracking) smooth pursuit eye movements.

Results: We found an attractive bias in pursuit direction toward previously seen target motion direction during pursuit initiation but not sustained pursuit in both children and adults. Such a bias displayed both feature- and temporal-tuning characteristics of serial dependence, showed oblique–cardinal directional anisotropy, and was more pronounced in children than adults. The greater effect of serial dependence around oblique than cardinal directions and its increased magnitude in children compared to adults can be explained by the larger variability in pursuit direction around oblique directions and in children, as predicted by the Bayesian framework.

Conclusions: Serial dependence in smooth pursuit occurs early during pursuit initiation when the response is driven by the perception of sensory input. Age-related changes in serial dependence reflect the fine-tuning of general brain functions, enhancing precision in tracking a moving target and thus reducing serial dependence effects.

Approximately a decade ago, two independent research groups discovered a novel history effect in visual perception, distinct from other history effects induced by priming, hysteresis, explicit memory, or expectation, known as the serial dependence.1,2 The studies conducted by these two groups have shown that when observers assess the orientation1 or the numerosity2 of a sequence of stimuli, their judgments on the current trial exhibit a significant bias toward the orientation or numerosity seen on the previous trial, even when the orientation or numerosity changes randomly throughout the sequence. This discovery reveals a distinctive temporal characteristic of visual perception: although visual input changes randomly over time, current visual perception is still systematically attracted to the previously seen inputs. 
These two initial studies on visual perception of orientation and numerosity1,2 catalyzed extensive research on serial dependence, revealing its presence in a wide variety of tasks, including color and face perception,3,4 decision-making,57 and memory.811 Moreover, serial dependence extends beyond vision to other sensory modalities, such as audition6,1214 and olfaction.15 The observation of serial dependence in such a broad spectrum of tasks and senses suggests that it is a general brain function that could change with development. However, despite the extensive research on serial dependence, there is a lack of studies examining it from a developmental perspective (see Hallez et al.,16 however, for a study in time perception), which can shed light on how general brain functions change with brain maturity. Therefore, the first aim of the current study is to address this issue with a large sample of preadolescent children and adults. 
With the rapid growth of research on serial dependence over the past decade, debates and questions regarding the impact and the nature of this phenomenon have emerged.1719 One contentious issue revolves around the level at which serial dependence operates—whether it affects perception of sensory input (perceptual stage)1,2024 or occurs at later stages such as memory and decision-making (postperceptual stage).511 The initial study on perception of orientation1 proposed that serial dependence occurs at the perceptual stage. The authors used the method of adjustment in their experiments where participants were asked to reproduce the observed stimulus feature by adjusting a response probe. This method, however, involved both perceptual and postperceptual processes.5 For instance, stimuli had to be held in short-term memory before the adjustment response was made, and subsequent decisions about how to adjust the response probe based on the remembered stimulus features were required. Therefore, the possibility that the serial dependence observed in their study occurred at the postperceptual rather than the perceptual stage is not excluded.5 
Several later studies tried to rule out the involvement of postperceptual processes, either by minimizing memory effects in the method of adjustment11,22 or by using different experimental paradigms that reduced postperceptual involvement, such as the two-alternative forced-choice task1,5 and the detection task.20 However, the results of these studies are inconsistent. A recent proposal is that serial dependence may not be confined to a single stage but can occur at any stage from perception to memory and decision-making.25 
To address this controversy, in the current study, we used an ocular tracking task to examine whether there is serial dependence in smooth pursuit eye movement responses and, if so, at what stage it operates. Specifically, this task, designed to examine smooth pursuit and dynamic motion-processing abilities,2628 asked participants to use their eyes to follow an unpredictable moving target, mimicking smooth pursuit eye movements that commonly happen in daily life. The smooth pursuit in this task naturally consists of two distinct stages: an early stage known as pursuit initiation and a subsequent stage referred to as steady-state tracking (i.e., sustained pursuit). Pursuit initiation signifies the initial open-loop ocular tracking response where smooth pursuit eye movements are driven by visual perception of target motion signals,29 and steady-state tracking refers to the subsequent closed-loop response where smooth pursuit is primarily driven by extra-retinal signals (such as efference copy) to correct tracking errors.30,31 
Although several studies have reported that serial dependence exists in smooth pursuit eye movements, these studies exclusively examined pursuit initiation.21,32,33 It remains in question whether serial dependence also happens in sustained pursuit. The second aim of the current study is thus to address this question by testing serial dependence in both the initiation and sustained pursuit responses. We will compare the patterns of results between children and adults to determine how developmental changes affect the manifestation of serial dependence in these two stages of smooth pursuit eye movements. 
In a recent meta-analysis and review paper, Manassi et al.19 proposed that, despite extensive research on serial dependence, the field still lacks a clear operational definition of serial dependence. This lack of clarity blurs the distinctions between serial dependence and other history effects caused by priming, hysteresis, explicit memory, or expectation. In an effort to differentiate serial dependence from other history effects, Manassi et al.19 proposed several characteristics for serial dependence. The two most commonly seen characteristics are feature tuning and temporal tuning. Specifically, feature turning refers to that serial dependence occurs only between similar features (e.g., if the direction of target motion in the current trial is 0°, the pursuit direction would be biased toward a previously seen target motion direction of 45° rather than 90°), and temporal tuning refers to that serial dependence decays with time (e.g., the pursuit response is influenced by the direction of target motion seen in the previous trial more than in earlier trials). Although several studies have reported that pursuit speed or direction can be biased toward previously seen target motion signals,21,3234 none of these studies has tested a sufficiently large range of speed or direction of target motion to examine whether this attractive bias manifests the feature- and temporal-tuning characteristics of serial dependence. The third aim of the current study is thus to address this issue. We sampled target motion directions from the entire circular angle space (0°–360°) to investigate whether pursuit direction exhibits any attractive bias toward previously seen target motion direction that can be qualified as feature- and temporal-tuning characteristics of serial dependence and, if so, how such characteristics change with development. 
Sampling target motion directions from the entire circular angle space also allows us to investigate whether serial dependence is uniform across different pursuit directions. Previous studies have found a directional anisotropy in the precision of pursuit direction35,36—that is, pursuit direction in response to target motion direction is more precise around cardinal (e.g., up–down, left–right) than oblique directions. According to the Bayesian ideal observer model,17,37 larger noise or variations (i.e., lower precision) in performance would increase the reliance on previously seen stimuli for performance optimization, leading to a larger serial dependence effect. Based on this logic, the directional anisotropy in the precision of pursuit direction should lead to a similar directional anisotropy in serial dependence in the pursuit response. However, no studies to date have examined this effect. The fourth aim of the current study is thus to address this issue. Given that previous research on directional anisotropy in the precision of pursuit direction is limited to adult participants,35,36 we will also compare the performance of children and adults to reveal any effect of developmental changes on the directional anisotropy in serial dependence in the pursuit response. 
Methods
Participants
In total, 108 children aged 8 to 9 years (second and third graders) participated in this study. They were recruited from six primary schools in the Putuo District in Shanghai. Eighty-eight adults aged 18 to 30 years (undergraduate and graduate students) participated in this study as the control group. (This age range of adult participants is common in studies comparing eye movements in children and adults. Further data analysis confirmed that this age range of adults did not affect our findings; see Supplementary Material.) They were recruited from East China Normal University in Shanghai. All had normal or corrected-to-normal vision. None of them, by self-report or by parents’ report, had any neurologic or oculomotor anomalies or were on any medication known to affect the oculomotor system. None had prior knowledge of the purpose of the study. Twenty-one children and eight adults were excluded from the data analysis due to not passing the calibration procedure for eye movement recording or not being able to follow the instructions or complete the experiment. In addition, four children and two adults were excluded from the data analysis due to technical issues with the equipment or experimenter errors, and two children and one adult were excluded because their eye -movement data were too noisy (e.g., disturbed by blinks or other artifacts) to produce enough valid trials (at least 1/3 of the total 90 trials) for data analysis. This yielded a final sample of 81 children (female/male: 47/34; mean age ± SD: 8.6 ± 0.4 years) and 77 adults (female/male: 43/34; mean age ± SD: 22.7 ± 2.6 years; see the flowchart in Supplementary Fig. S1 for the inclusion and exclusion of participants). 
Ethical approval for this project was obtained from the ethics committee of East China Normal University and the Institutional Review Board of New York University Shanghai. Oral informed assent and written informed consent were obtained from all children and their legal guardians, respectively. Written informed consent was obtained from all adult participants. 
Ocular Tracking Task
We used an ocular tracking task based on a modified version of the classic step-ramp paradigm26 to measure participants’ smooth pursuit eye movements along a specific direction in the fully sampled circular angle space.38,39 To make the duration of this task more child-friendly, we used a shortened 90-trial version of the original task. The shortened ocular tracking task took approximately 8 minutes to finish and has been shown to be effective in detecting impaired ocular tracking performance in people after acute low-dose alcohol administration.40 
It has been reported that specific features of the target have different effects on the ocular tracking performance of children and adults.41 Specifically, children performed better when tracking colored, cartoon animal characters compared to inanimate objects such as white spots, whereas adults did not show any statistically significant difference in performance. To avoid any underestimation of children's ocular tracking performance (and thus leading to an overestimation of the difference in ocular tracking abilities between children and adults), we used a cartoon duck face instead of the traditional light spot as a moving target in the current study. 
Each trial started with the cartoon duck face (0.64°H × 0.64°V; see Fig. 1) appearing in the center of a black background on a computer screen. Participants were instructed to fixate on the target and click the mouse button to start a trial when they were ready. After a randomized delay drawn from a truncated exponential distribution (mean: 700 ms; minimum: 200 ms; maximum: 5000 ms), the target made an initial step off the center of the screen. It then moved back at a constant speed, passing its original screen location, and continued to move toward the screen edge until it disappeared from the screen (see Fig. 1). To minimize the likelihood of an initial catch-up saccade, the step amplitude was set such that the target always crossed its original location at 200 ms after the motion onset.26 To maintain a high degree of spatiotemporal uncertainty of the target motion, on each trial, we randomly varied the target motion speed between 16° and 24°/s, the target motion direction between 2° and 358° in 4° increments without replacement (thus 90 angles in total corresponding to 90 trials), and the target motion duration between 700 and 1000 ms. Participants were instructed to keep their head still and track the target with their eyes as long as it was visible. Because participants performed this task without knowing the time, the speed, the direction, or the duration of the target motion, this task minimized expectation or prediction effects and maximized the use of target motion signals on the ocular tracking performance. 
Figure 1.
 
An illustration of the display for the ocular tracking task with the target being the cartoon duck face (image source: https://clipart.info/tsumtsumclipart; licensed under CC BY 4.0; no modifications). Each trial was initiated by participants clicking a mouse button after fixating on the target in the center of the screen. The target then made an initial step off the center of the screen (i.e., target step). Immediately after the step, the target moved back at a constant velocity and across its original location (i.e., the initial fixation location denoted by the red dashed outline) at 200 ms after the motion onset and then onward until it disappeared from the screen (i.e., target ramp motion). The size of the target is scaled up for illustration purposes.
Figure 1.
 
An illustration of the display for the ocular tracking task with the target being the cartoon duck face (image source: https://clipart.info/tsumtsumclipart; licensed under CC BY 4.0; no modifications). Each trial was initiated by participants clicking a mouse button after fixating on the target in the center of the screen. The target then made an initial step off the center of the screen (i.e., target step). Immediately after the step, the target moved back at a constant velocity and across its original location (i.e., the initial fixation location denoted by the red dashed outline) at 200 ms after the motion onset and then onward until it disappeared from the screen (i.e., target ramp motion). The size of the target is scaled up for illustration purposes.
The visual stimuli were programmed in MATLAB (MathWorks, Natick, MA, USA) using Psychophysics Toolbox 342,43 and were presented on a 27-in. LCD monitor (ASUS VG278 Series; ASUS, Taipei, Taiwan, China) for all participants except for two children, who viewed the visual stimuli on a 23.8-in. LCD monitor (DELL S2417DG; DELL, Round Rock, TX, USA). (Because we ensured consistency in setting up visual stimuli across monitors (e.g., the resolution and refresh rate of the display, the size, contrast, color, and movement range of the visual stimuli), and statistical analysis did not show any significant difference including or excluding the data from these two children [see Supplementary Material], we decided to keep the data from these two children in the current study.) All display monitors had a resolution of 1024 × 768 pixels and a refresh rate of 120 Hz. The movement range of the visual stimuli was within 24°H × 24°V. Participants were seated in a dark room with their head stabilized by a chin and forehead rest at a viewing distance of 56.5 cm. Their eye movements were recorded monocularly by an infrared camera-based eye tracker (Eyelink 1000; SR Research, Ottawa, Canada) in a desktop mount configuration at a 1000-Hz sampling rate. 
To ensure the accuracy of eye movement recording, the experiment started with a standard 9-point calibration–validation routine. The ocular tracking task only proceeded after a successful calibration, as defined by the Eyelink software. To maintain the recording accuracy throughout the experiment, we conducted a fixation check every 30 trials in which participants were asked to fixate a red dot in the center of the screen. We compared the values of the recorded position of the central fixation point to those in the initial calibration routine. A difference of ≥2° would trigger a new 9-point calibration–validation routine. Eye movement data were collected monocularly from the dominant eye, except for 9 of 81 children and 2 of 77 adults whose nondominant eye was used due to the failure of the calibration procedure with their dominant eye. (We used the pointing test to identify the dominant eye, which required participants to keep both eyes open and point their finger at a distant object. Participants then closed their left or right eye in turn, and the eye with which the finger remained aligned with the object during monocular sighting was defined as the dominant eye. This test belongs to the category of sighting dominance tests44 that are commonly used and highly reliable.45,46) The total duration of the experiment was less than 20 minutes. 
To avoid fatigue, all participants were encouraged to take a break before each fixation check while keeping their head still on the chin and forehead rest. They could also request and then take breaks at any time during the experiment. To maintain attention on the task, verbal praise (e.g., “good job”) was given via a computer synthesized voice at the end of each trial, and a random high score of 90 to 100 was displayed on the screen at the end of the task, regardless of their actual ocular tracking performance. This was particularly important for maintaining children's engagement in the task. 
Data Analysis
We recorded the time series of the eye and the target positions. Before performing any analysis, we detected and removed saccades using the standard method.44 Specifically, we processed the eye velocity traces using a median filter with a 100-ms window to estimate the smooth pursuit component of the oculomotor response. After estimating this component, we subtracted it from the original velocity trace to obtain a “saccadic velocity trace.” Subsequently, we computed the cross-correlation between this “saccadic velocity trace” and a saccadic velocity template to obtain a likelihood metric for saccade occurrence at each time point. We then identified potential saccades using a likelihood threshold of 0.125°. To refine the detection, we defined that a saccade should have a minimum duration of 24 ms and a minimum refractory period of 16 ms between consecutive saccades. 
We followed the established procedures as described in previous studies38,39 to analyze the de-saccade data to examine both the open-loop (pursuit initiation) and the closed-loop (steady-state tracking) ocular tracking responses. We used the data within the 160-ms interval immediately following smooth pursuit onset as the open-loop response driven by visual perception of target motion signals.29,35 We used data in the interval from 400 to 700 ms after target motion onset as the closed-loop response driven primarily by efference copy signals to correct tracking errors.31,38 
To ensure the quality of the data, we excluded trials where blinks or other artifacts obscured the data in part of the trial, but this occurred relatively rarely. On average, 82 ± 1 (mean ± SE) and 87 ± 0.4 out of 90 trials were used in the data analysis for children and adults, respectively. 
Serial Dependence Effect
To examine the degree to which pursuit direction was affected by target motion direction in the previous trials, we first calculated the target-relative moving direction (DRn), which is the difference between the target motion direction in the current and the nth previous trial (n = 1, 2, 3, etc.). A positive value indicates the target motion direction in the previous trial is more clockwise than in the current trial, and a negative value indicates the opposite. The range of DRn is between –180° and 180° (a complete circle) in 4° increments. The first trial of this experiment was not considered to have a previous trial. 
For each participant, on each trial, we then calculated the pursuit direction error (DE), which is the difference between participants’ smooth pursuit direction and the target motion direction. A positive value indicates the pursuit direction is more clockwise than the target motion direction, and a negative value indicates the opposite. We calculated DE for the 160-ms interval of the open-loop response and the 300-ms interval of the closed-loop response, respectively. Following previous practice,45,46 for each participant group, we excluded the outlier trials with DE exceeding three standard deviations from the data analysis, which resulted in 1.44% (children) and 1.26% (adults) of trials removed from the open-loop response analysis and 3.45% (children) and 1.47% (adult) of trials removed from the closed-loop response analysis, respectively. The data exclusion was not biased toward any specific participant. The maximum number of trials removed was six trials for a child and four trials for an adult participant in the open-loop response analysis, and eight trials for a child and five trials for an adult participant in the closed-loop response analysis. 
To measure the degree to which pursuit direction was affected by previously seen target motion direction, we pooled DE and the corresponding DRn across all participants in each group and fitted the first derivative of Gaussian (DoG) function to the data using constrained nonlinear minimization of the residual sum of squares. The function is given by  
\begin{eqnarray} {D_E} = awc{e^{ - {{\left( {w{D_{Rn}}} \right)}^2}}}{D_{Rn}},\quad \end{eqnarray}
(1)
where a is the amplitude of the effect of the previous target motion direction on the current pursuit direction (i.e., the amplitude of serial dependence). A positive value of a indicates the current pursuit direction is biased toward the previously seen target motion direction (an attractive bias), and a negative value indicates the opposite (a repulsive bias). A value of zero indicates no bias. w is the inverse of the width of the fitted curve, indicating the value of DRn corresponding to the peak of the curve, and c is a constant \(\sqrt 2 /{e^{ - 0.5}}\)
Direction Noise
To measure the variations in pursuit direction, we first calculated the standard deviation of the pursuit direction at each target motion direction and its two closest neighboring directions (adjusted for the expected 4° differences, given that the target motion direction is evenly distributed from 2° to 358° with a 4° spacing). For example, if the pursuit directions at three consecutive target motion directions of 26°, 30°, and 34° are 25°, 31°, and 36°, respectively, then the standard deviation of the pursuit direction at the target motion direction of 30° is the standard deviation of (25° + 4°), 31°, and (36° – 4°). We then averaged the standard deviations of the pursuit directions across the 90 target motion directions to obtain overall pursuit direction noise. 
Directional Anisotropy
The direction noise and the size of serial dependence described above were calculated across the entire 360° circular angle space, assessing the overall precision and bias in pursuit direction. To examine whether there is any directional anisotropy in the precision of pursuit direction, we first divided the 360° circular angle space into eight segments based on the four cardinal directions (0° right, 90° up, 180° left, and 270° down) and the four oblique directions (45°, 135°, 225°, and 315°). Each segment was centered on one of these eight canonical directions, with angles varying by ±22.5°. The 90 trials of the ocular tracking task containing 90 target motion directions (2°–358° in 4° increments) were thus divided into eight data sets. To illustrate, trials with target directions of 2°, 6°, 10°, 14°, 18°, 22°, 338°, 342°, 346°, 350°, 354°, and 358° fell into the 0° canonical segment (i.e., 0° ± 22.5°). We pooled the data across participants, resulting in four cardinal (0°, 90°, 180°, and 270°) and four oblique (45°, 135°, 225°, and 315°) direction data sets for each participant group. 
We measured the precision of pursuit direction around the four cardinal and the four oblique directions using the established method in previous studies.35,36,47 Specifically, in each data set, we compared the pursuit direction in a given trial to the data set’s canonical direction and then converted it into a binary response (i.e., clockwise or counterclockwise relative to the canonical direction). We also computed the deviation of the target motion direction from the data set’s canonical direction in this trial, with positive values indicating counterclockwise deviations and negative values indicating clockwise deviations. For each data set, we plotted the percentage of counterclockwise binary pursuit responses across participants against the deviation of the target motion direction from the data set’s canonical direction. We then fitted the percentage data with a cumulative Gaussian function using the maximum likelihood method of the Palamedes Toolbox in MATLAB48 to obtain an oculometric curve. The standard deviation (SD) of the best-fitting Gaussian, inversely related to the slope of the oculometric curve, served as an indicator of the precision of the pursuit direction. A smaller SD corresponds to a steeper oculometric curve, indicating a more precise pursuit direction response to the target motion direction. 
We measured the directional anisotropy in serial dependence in pursuit direction by calculating the effect of previously seen target motion direction on current pursuit direction using the data from the four cardinal and the four oblique direction data sets. We calculated the size of serial dependence in each data set using the same method as described earlier in the “Serial Dependence Effect” section. 
Statistical Analysis
To determine whether there is serial dependence in smooth pursuit, we conducted permutation tests, as is commonly used in serial dependence studies,1,3 to examine whether the amplitude of serial dependence (a) was significantly larger than zero. Specifically, we shuffled the values of the target-relative moving direction (DRn) while leaving the corresponding pursuit direction error (DE) in place (see Equation 1). We then fit the DoG function to the shuffled data set and repeated this process 10,000 times to generate a null distribution of a. The observed a was compared against this null distribution to obtain a P value that indicates the proportion of a in the null distribution that was equal to or larger (in absolute value) than the observed a
To assess whether serial dependence in smooth pursuit changes with development, we conducted permutation tests to compare a values between children and adults. Specifically, we randomly selected a value from the null distribution of a for children and adults, respectively, and calculated their difference. This process was repeated 10,000 times (without replacement) to generate the null distribution of a differences. The observed a difference was compared against this null distribution of a differences to obtain a P value that indicates the proportion of a differences in the null distribution that was equal to or larger (in absolute value) than the observed a difference. 
To examine whether the overall precision in pursuit direction changes with development, we performed an independent samples t-test to compare the overall pursuit direction noise between children and adults. To investigate the extent of directional anisotropy in the precision of pursuit direction and serial dependence and how this anisotropy changes with development, we conducted two separate 2 (participant group: children versus adults) × 2 (target motion direction: cardinal versus oblique) mixed-design aligned rank transform (ART) ANOVAs (nonparametric equivalent of parametric ANOVAs)49—one on the SDs of the best-fitting Gaussian functions for the pursuit direction data and one on the a values. 
All statistical analyses described above were performed with R,50 except for the permutation tests, which were conducted with MATLAB (MathWorks, R2020b). A P value of less than 0.05 was considered statistically significant. When reporting P values of a series of comparisons below 0.05, we reported Ps < the largest P value (always round up) in that series. Conversely, when reporting P values in a series of comparisons above 0.05, we reported Ps > the smallest P value (always round down) in that series. 
Results
Overall Performance
Figure 2A plots the group mean of open-loop (left panel) and closed-loop (right panel) pursuit direction error (DE) against target-relative moving direction of the first previous (i.e., 1-back) trial (DR1). As shown in the figure, for both children and adults, during pursuit initiation, when the target motion direction in the previous trial was clockwise to that in the current trial, the pursuit direction error in the current trial was also clockwise for both children and adults. The same trend was also observed for the counterclockwise direction, displaying an attractive serial dependence effect. This effect was tuned to target-relative moving direction as captured by the DoG curve with a statistically significant larger-than-zero amplitude of 4.31° at the target-relative moving direction of 55.41° for children (P = 0.0018, permutation test) and an amplitude of 2.64° at the target-relative moving direction of 52.76° for adults (P = 0.0025). The permutation test for group comparison revealed that the serial dependence effect was significantly stronger in children than in adults (P = 0.041). However, during steady-state tracking, no such effect was observed in either children or adults (amplitude: –0.77°, P = 0.095 for children and amplitude: 0.29°, P = 0.26 for adults). 
Figure 2.
 
Experiment data. (A) Group mean (thin dotted lines) of open-loop (left) and closed-loop (right) pursuit direction error (DE) and ±1 SE (shaded areas) as a function of the target-relative moving direction of the first previous (i.e., 1-back) trial (DR1). “CCW” and “CW” on the x-axis indicate that the target motion direction in the previous trial was counterclockwise (CCW) or clockwise (CW) to that in the current trial. “CCW” and “CW” on the y-axis indicate that pursuit direction was CCW or CW to the target motion direction in the current trial. Thick solid lines indicate the fitted DoG curves. The amplitude of the DoG curve (a) indicates the size of serial dependence. (B) The size of serial dependence (a) in the open-loop response for the previous one to five trials (i.e., 1-back to 5-back). Error bars represent bootstrapped 95% confidence intervals. (C) Histograms and Gaussian fits of the overall pursuit direction noise in the open-loop response for children (green bars and lines) and adults (gray bars and lines). *P < 0.05. **P < 0.01.
Figure 2.
 
Experiment data. (A) Group mean (thin dotted lines) of open-loop (left) and closed-loop (right) pursuit direction error (DE) and ±1 SE (shaded areas) as a function of the target-relative moving direction of the first previous (i.e., 1-back) trial (DR1). “CCW” and “CW” on the x-axis indicate that the target motion direction in the previous trial was counterclockwise (CCW) or clockwise (CW) to that in the current trial. “CCW” and “CW” on the y-axis indicate that pursuit direction was CCW or CW to the target motion direction in the current trial. Thick solid lines indicate the fitted DoG curves. The amplitude of the DoG curve (a) indicates the size of serial dependence. (B) The size of serial dependence (a) in the open-loop response for the previous one to five trials (i.e., 1-back to 5-back). Error bars represent bootstrapped 95% confidence intervals. (C) Histograms and Gaussian fits of the overall pursuit direction noise in the open-loop response for children (green bars and lines) and adults (gray bars and lines). *P < 0.05. **P < 0.01.
To evaluate how the serial dependence effect in the open-loop response attenuated with the number of intervening trials, we separately fitted the DoG function to the pursuit direction error (DE) as a function of the target-relative moving direction of the nth previous (i.e., n-back, n > 1) trial (DRn) in sequence. The permutation tests showed a statistically significant larger-than-zero amplitude (a) for up to three previous trials for children (Ps < 0.022) and four previous trials for adults (Ps < 0.035) (see Fig. 2B). The stronger serial dependence effect, as indicated by a larger a for children than adults observed in the 1-back trial, was not observed in the 2-back or 3-back trials (Ps > 0.73). The comparison permutation tests showed that for children, a decreased quickly with intervening trials, and the drop became significant from the 1-back (4.31°) to the 2-back trial (1.93°, P = 0.017). For adults, the decrease in a with intervening trials was more gradual and became significant from the 1-back (2.61°) to the 5-back trial (0.49°, P = 0.014). 
To examine the relationship between the serial dependence effect and the precision of smooth pursuit, we compared the overall pursuit direction noise between children and adults. Figure 2C plots the histograms of the overall pursuit direction noise in the open-loop response for 81 children and 77 adults. An independent samples t-test revealed that children had larger pursuit direction noise than adults (mean ± SE: 11.72 ± 0.34 vs. 9.50 ± 0.43, t(156) = 4.11, P < 0.001, Cohen's d = 0.65), indicating their lower precision in smooth pursuit direction than adults. 
In the current study, the target motion speed was randomly picked from a small range (16°–24°/s) on each trial. This randomization aimed to minimize the expectation effect on smooth pursuit. A study with nonhuman primates has found that pursuit direction on the current trial can be affected by both target motion direction and speed in the previous trial.32 To evaluate whether the serial dependence effect observed in the current study may also be affected by previously seen target motion speed, we calculated the difference between the target motion speed on the current trial and the previous trial (DSP). We then grouped the trials with speed difference <1°/s (children: 1582 trials; adults: 1711 trials) and the trials with speed difference >4°/s (children: 1481 trials; adults: 1510 trials). This was to maximize the speed difference in these two groups of trials to examine whether the size of serial dependence in these two groups differed from each other. Figure 3 plots the group mean of open-loop pursuit direction error (DE) as a function of the target-relative moving direction of the first previous trial (DR1) for the two groups of trials along with the data from all trials (as plotted in the left panel of Fig. 2A) for adults (left panel) and children (right panel). The permutation tests did not reveal any significant difference in the size of serial dependence (a) for any pairwise comparison for both adults (Ps > 0.82) and children (Ps > 0.51). This confirmed that it was the target motion direction but not speed in the previous trial that affected pursuit direction in the current trial. 
Figure 3.
 
Effect of previous target speed on serial dependence. Group mean (thin dotted lines) of open-loop pursuit direction error (DE) and ±1 SE (shaded areas) as a function of the target-relative moving direction of the first previous trial (DR1)for the two groups of trials with small (DSP <1°, red) and large (DSP >4°, blue) target speed differences along with the data from all trials (black) for adults (left) and children (right). “CCW” and “CW” on the x-axis indicate that the target motion direction in the previous trial was counterclockwise (CCW) or clockwise (CW) to that in the current trial. “CCW” and “CW” on the y-axis indicate that pursuit direction was CCW or CW to the target motion direction in the current trial. Thick solid lines indicate the fitted DoG curves. The amplitude of the DoG curve (a) indicates the size of serial dependence.
Figure 3.
 
Effect of previous target speed on serial dependence. Group mean (thin dotted lines) of open-loop pursuit direction error (DE) and ±1 SE (shaded areas) as a function of the target-relative moving direction of the first previous trial (DR1)for the two groups of trials with small (DSP <1°, red) and large (DSP >4°, blue) target speed differences along with the data from all trials (black) for adults (left) and children (right). “CCW” and “CW” on the x-axis indicate that the target motion direction in the previous trial was counterclockwise (CCW) or clockwise (CW) to that in the current trial. “CCW” and “CW” on the y-axis indicate that pursuit direction was CCW or CW to the target motion direction in the current trial. Thick solid lines indicate the fitted DoG curves. The amplitude of the DoG curve (a) indicates the size of serial dependence.
Directional Anisotropy
Due to the fact that we only observed serial dependence in the open- but not closed-loop pursuit response in both children and adults, we specifically examined directional anisotropy in the open-loop pursuit response. 
Directional Anisotropy in the Precision of Pursuit Direction
 Figure 4 plots the percentage of counterclockwise binary pursuit responses in each participant group against the deviation of the target motion direction from the data set’s canonical direction for the four cardinal (0°, 90°, 180°, and 270°) and the four oblique (45°, 135°, 225°, and 315°) direction data sets along with the fitted oculometric curves. For both children and adults, the oculometric curves are steeper for target motion direction around the cardinal than the oblique directions, indicating a more precise pursuit direction response to target motion direction around the cardinal than the oblique directions. For ease of comparison, Figure 5A plots the SD of the best-fitting Gaussian function (i.e., the inverse of the slope of the oculometric curve) for each participant group for the four cardinal and the four oblique direction data sets in polar coordinates. 
Figure 4.
 
The percentage of counterclockwise binary pursuit responses in each participant group as a function of the deviation of target motion direction from each data set’s canonical direction for the four cardinal (0°, 90°, 180°, and 270°; upper) and the four oblique direction data sets (45°, 135°, 225°, and 315°; lower). Data are fitted with cumulative Gaussian functions (solid and dashed lines).
Figure 4.
 
The percentage of counterclockwise binary pursuit responses in each participant group as a function of the deviation of target motion direction from each data set’s canonical direction for the four cardinal (0°, 90°, 180°, and 270°; upper) and the four oblique direction data sets (45°, 135°, 225°, and 315°; lower). Data are fitted with cumulative Gaussian functions (solid and dashed lines).
Figure 5.
 
Polar plots of (A) the precision (standard deviation of the best-fitting Gaussian function) and (B) the size of serial dependence (a) in pursuit direction for the four cardinal (0°, 90°, 180°, and 270°) and the four oblique (45°, 135°, 225°, and 315°) direction data sets. The dashed lines in (B) represent a values across the 360° circular angle space, as plotted in Figure 2A.
Figure 5.
 
Polar plots of (A) the precision (standard deviation of the best-fitting Gaussian function) and (B) the size of serial dependence (a) in pursuit direction for the four cardinal (0°, 90°, 180°, and 270°) and the four oblique (45°, 135°, 225°, and 315°) direction data sets. The dashed lines in (B) represent a values across the 360° circular angle space, as plotted in Figure 2A.
We then conducted a 2 (participant group: children versus adults) × 2 (target motion direction: cardinal versus oblique) mixed-design ART ANOVA on the SDs in Figure 5A. Both the main effects of participant group and target motion direction were significant (F(1, 6) = 17.45, P = 0.0058, and F(1, 6) = 27.93, P = 0.0019, respectively), and their interaction effect was not significant (F(1, 6) = 0.046, P = 0.84). While both groups exhibited higher precision of pursuit direction around cardinal than oblique axes, the overall precision of pursuit direction was significantly lower in children than in adults, consistent with the overall pursuit direction noise data (see Fig. 2C). 
Directional Anisotropy in Serial Dependence in Pursuit Direction
 Figure 5B plots the size of serial dependence (a) for each participant group in polar coordinates. We also conducted a 2 (participant group: children versus adults) × 2 (target motion direction: cardinal versus oblique) mixed-design ART ANOVA on a values in Figure 5B. Both the main effects of participant group and target motion direction were significant (F(1, 6) = 37.69, P < 0.001, and F(1, 6) = 38.89, P < 0.001, respectively), and their interaction effect was not significant (F(1, 6) = 1.83, P = 0.22). While both groups exhibited a larger size of serial dependence for target motion direction around cardinal than oblique axes, the overall size of serial dependence was significantly larger in children than adults. 
In summary, the directional anisotropy in serial dependence in pursuit direction corresponds with the directional anisotropy in the precision of pursuit direction. That is, for both children and adults, the larger variances in pursuit direction around oblique than cardinal directions coincide with the larger reliance on previously seen target motion direction for the current pursuit direction around oblique than cardinal directions. 
Discussion
In the current study, we examined serial dependence in smooth pursuit eye movements by testing a large sample of preadolescent children (aged 8–9 years) and young adults (aged 18–30 years). We found that for both children and adults, pursuit direction during pursuit initiation, but not sustained pursuit, was pulled toward previously seen target motion direction. Such an attractive bias displayed both feature- and temporal-tuning characteristics of serial dependence, exhibited oblique–cardinal directional anisotropy, and was larger in children than adults. We draw several conclusions from these findings given as follows. 
First, the serial dependence effect on pursuit direction was observed during pursuit initiation in the open-loop response, where smooth pursuit eye movements were driven by visual perception of target motion signals. In contrast, no such an effect was observed during sustained pursuit in the closed-loop response, where smooth pursuit eye movements were primarily driven by extra-retinal signals (such as efference copy) to correct any tracking errors. This supports the claim that serial dependence affects the perception of sensory input instead of occurring at later stages such as memory and decision-making.5,7,11 
Although it is possible that the serial dependence effect observed in our study occurred in the motor response of eyes rather than was truly of perceptual nature, we found it unlikely because much evidence supports a shared sensory source between pursuit initiation and perception,35,5153 with about 95% of pursuit variations accounting for sensory estimation errors.54,55 This indicates that noise from the motor response of eyes contributes minimally to pursuit variations. Using tasks other than ocular tracking, many studies have found that the attractive bias in serial dependence does not depend on motor response.1,22,56,57 Accordingly, the serial dependence effect on pursuit direction during pursuit initiation observed in the current study is unlikely due to a bias in motor response. 
Second, the attractive bias in the current pursuit direction toward previously seen target motion direction during pursuit initiation has both the feature- and temporal-tuning characteristics of serial dependence as proposed by Manassi et al.19 As shown in Figure 2A, the pursuit direction error on the current trial displays an S-shape relationship with the target-relative moving direction of the previous trial. This S-shape relationship, indicating the feature-tuning characteristic of serial dependence,1,12,31 was not observed in the previous study that also found an attractive bias in pursuit direction toward previously seen target motion direction in macaque monkeys.32 This could be due to their limited sampling of target motion directions that did not cover the entire 360° circular angle space as in our current study. In addition, as shown in Figure 2B, the size of the attractive bias decreased with the number of intervening trials and was significantly larger than zero for up to three previous trials in children and four previous trials in adults. This temporal-tuning characteristic of serial dependence has been reported by previous studies using a variety of perceptual judgment tasks (such as orientation,1 spatial location,22 and face58) but not by studies using ocular tracking tasks.21,3234 Accordingly, our study is the first to reveal an attractive bias in smooth pursuit direction toward previously seen target motion direction that can be truly qualified as the serial dependence effect. 
Notably, children display a different temporal-tuning characteristic compared with adults. Specifically, as the number of intervening trials increases, the size of serial dependence decreases more rapidly in children than in adults. Previous research that asked participants to compare the current stimulus with the stimulus from the nth previous trial found that the ability of children to maintain past information declined faster than that of adults.59,60 The faster decline in maintaining past information in children likely contributes to the quicker convergence to a null serial dependence effect with intervening trials in children than adults, as observed in the current study. 
Third, the larger size of serial dependence in pursuit direction in children than in adults can be explained by the Bayesian ideal observer model proposed by Cicchini et al.17,37 The model predicts that larger noise or variations in pursuit direction would increase the reliance on the previously seen target motion for the optimization of smooth pursuit tracking performance (i.e., maximize error reduction). In the current study, variations in pursuit direction during pursuit initiation (measured by the pursuit direction noise) are larger in children than adults. This is consistent with previous findings showing that children aged 8 to 9 years have not yet reached the level of precision in judging motion direction as seen in adults.6264 Accordingly, children relied more on the previously seen target motion that led to the larger serial dependence effect on the current pursuit direction. Variations in pursuit direction during pursuit initiation have been reported to arise mainly from the noise in the neural response to target motion signals in the middle temporal area (MT) of the macaque brain.54,55,61 Indeed, a neuroimaging study has indicated that the gray matter volume of area MT has not fully matured in children at this age compared to adults.65 The larger variations in pursuit direction observed in children than in adults might thus be related to the immaturity of brain regions in charge of perceptual processing of visual motion information. 
To the best of our knowledge, the study by Hallez et al.16 on time perception is the only other study that has contrasted serial dependence in normally developing children and adults. They found that, in comparison to adults, time reproductions in younger children (5 years old) were biased more toward the duration presented in the most recent trials. We propose that our explanation also applies to their finding. That is, the change of serial dependence effect with age reflects the fine-tuning of general brain functions, which leads to improved precision in perceptual processing and thus decreased serial dependence effect. 
In the primate visual system, the proportion of neurons selective for visual stimuli along the cardinal axis is larger than that for the oblique axis,6669 and such a directional anisotropy has been linked to behavioral performance on a variety of tasks such as orientation discrimination7072 and motion discrimination.73,74 In the current study, we observed an oblique–cardinal directional anisotropy in the precision of pursuit direction in response to target motion direction in a 360° circular angle space in both children and adults. More importantly, such a directional anisotropy covaries with the directional anisotropy of the serial dependence effect in smooth pursuit. This covariance can also be explained under the framework of the Bayesian ideal observer model (i.e., the larger variations in pursuit direction around oblique than cardinal directions lead to more reliance on previously seen target motion direction for pursuit response and thus the larger serial dependence effect around oblique than cardinal directions). 
While our study successfully recruited a relatively large sample size, comprising 81 children and 77 adults, limitations should be noted. One of the primary limitations is the narrow age range of the child participants (8–9 years). This limited age range constrains our ability to fully capture the broader developmental trajectory of serial dependence in smooth pursuit. Consequently, our findings provide only a partial view of the developmental trajectory, potentially missing key insights into how these processes evolve over time. To address this limitation, future studies should aim to include a broader age range of children. By doing so, future research can build upon our findings and offer new perspectives on the developmental processes in question. Such an approach would contribute to a deeper and more thorough understanding of developmental trajectories, ultimately leading to more informed theories and interventions. 
Acknowledgments
The authors thank Yi Jie (E'Jane) Li for her assistance with data collection and her helpful comments on a previous draft of the paper and two anonymous reviewers for their helpful comments, which have significantly improved the quality and clarity of our manuscript. 
Supported by research grants from the National Natural Science Foundation of China (32071041, 32161133009, 31800904), Shanghai Science and Technology Committee (20ZR1439500, 19JC1410101), China Ministry of Education (ECNU 111 Project, Base B1601), NYU Shanghai (the major grant seed fund and the boost fund), and East China Normal University (the “Flower of Happiness” Fund Pilot Project, 2019JK2203). 
Disclosure: B. Hong, None; J. Chen, None; W. Huang, None; L. Li, None 
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Figure 1.
 
An illustration of the display for the ocular tracking task with the target being the cartoon duck face (image source: https://clipart.info/tsumtsumclipart; licensed under CC BY 4.0; no modifications). Each trial was initiated by participants clicking a mouse button after fixating on the target in the center of the screen. The target then made an initial step off the center of the screen (i.e., target step). Immediately after the step, the target moved back at a constant velocity and across its original location (i.e., the initial fixation location denoted by the red dashed outline) at 200 ms after the motion onset and then onward until it disappeared from the screen (i.e., target ramp motion). The size of the target is scaled up for illustration purposes.
Figure 1.
 
An illustration of the display for the ocular tracking task with the target being the cartoon duck face (image source: https://clipart.info/tsumtsumclipart; licensed under CC BY 4.0; no modifications). Each trial was initiated by participants clicking a mouse button after fixating on the target in the center of the screen. The target then made an initial step off the center of the screen (i.e., target step). Immediately after the step, the target moved back at a constant velocity and across its original location (i.e., the initial fixation location denoted by the red dashed outline) at 200 ms after the motion onset and then onward until it disappeared from the screen (i.e., target ramp motion). The size of the target is scaled up for illustration purposes.
Figure 2.
 
Experiment data. (A) Group mean (thin dotted lines) of open-loop (left) and closed-loop (right) pursuit direction error (DE) and ±1 SE (shaded areas) as a function of the target-relative moving direction of the first previous (i.e., 1-back) trial (DR1). “CCW” and “CW” on the x-axis indicate that the target motion direction in the previous trial was counterclockwise (CCW) or clockwise (CW) to that in the current trial. “CCW” and “CW” on the y-axis indicate that pursuit direction was CCW or CW to the target motion direction in the current trial. Thick solid lines indicate the fitted DoG curves. The amplitude of the DoG curve (a) indicates the size of serial dependence. (B) The size of serial dependence (a) in the open-loop response for the previous one to five trials (i.e., 1-back to 5-back). Error bars represent bootstrapped 95% confidence intervals. (C) Histograms and Gaussian fits of the overall pursuit direction noise in the open-loop response for children (green bars and lines) and adults (gray bars and lines). *P < 0.05. **P < 0.01.
Figure 2.
 
Experiment data. (A) Group mean (thin dotted lines) of open-loop (left) and closed-loop (right) pursuit direction error (DE) and ±1 SE (shaded areas) as a function of the target-relative moving direction of the first previous (i.e., 1-back) trial (DR1). “CCW” and “CW” on the x-axis indicate that the target motion direction in the previous trial was counterclockwise (CCW) or clockwise (CW) to that in the current trial. “CCW” and “CW” on the y-axis indicate that pursuit direction was CCW or CW to the target motion direction in the current trial. Thick solid lines indicate the fitted DoG curves. The amplitude of the DoG curve (a) indicates the size of serial dependence. (B) The size of serial dependence (a) in the open-loop response for the previous one to five trials (i.e., 1-back to 5-back). Error bars represent bootstrapped 95% confidence intervals. (C) Histograms and Gaussian fits of the overall pursuit direction noise in the open-loop response for children (green bars and lines) and adults (gray bars and lines). *P < 0.05. **P < 0.01.
Figure 3.
 
Effect of previous target speed on serial dependence. Group mean (thin dotted lines) of open-loop pursuit direction error (DE) and ±1 SE (shaded areas) as a function of the target-relative moving direction of the first previous trial (DR1)for the two groups of trials with small (DSP <1°, red) and large (DSP >4°, blue) target speed differences along with the data from all trials (black) for adults (left) and children (right). “CCW” and “CW” on the x-axis indicate that the target motion direction in the previous trial was counterclockwise (CCW) or clockwise (CW) to that in the current trial. “CCW” and “CW” on the y-axis indicate that pursuit direction was CCW or CW to the target motion direction in the current trial. Thick solid lines indicate the fitted DoG curves. The amplitude of the DoG curve (a) indicates the size of serial dependence.
Figure 3.
 
Effect of previous target speed on serial dependence. Group mean (thin dotted lines) of open-loop pursuit direction error (DE) and ±1 SE (shaded areas) as a function of the target-relative moving direction of the first previous trial (DR1)for the two groups of trials with small (DSP <1°, red) and large (DSP >4°, blue) target speed differences along with the data from all trials (black) for adults (left) and children (right). “CCW” and “CW” on the x-axis indicate that the target motion direction in the previous trial was counterclockwise (CCW) or clockwise (CW) to that in the current trial. “CCW” and “CW” on the y-axis indicate that pursuit direction was CCW or CW to the target motion direction in the current trial. Thick solid lines indicate the fitted DoG curves. The amplitude of the DoG curve (a) indicates the size of serial dependence.
Figure 4.
 
The percentage of counterclockwise binary pursuit responses in each participant group as a function of the deviation of target motion direction from each data set’s canonical direction for the four cardinal (0°, 90°, 180°, and 270°; upper) and the four oblique direction data sets (45°, 135°, 225°, and 315°; lower). Data are fitted with cumulative Gaussian functions (solid and dashed lines).
Figure 4.
 
The percentage of counterclockwise binary pursuit responses in each participant group as a function of the deviation of target motion direction from each data set’s canonical direction for the four cardinal (0°, 90°, 180°, and 270°; upper) and the four oblique direction data sets (45°, 135°, 225°, and 315°; lower). Data are fitted with cumulative Gaussian functions (solid and dashed lines).
Figure 5.
 
Polar plots of (A) the precision (standard deviation of the best-fitting Gaussian function) and (B) the size of serial dependence (a) in pursuit direction for the four cardinal (0°, 90°, 180°, and 270°) and the four oblique (45°, 135°, 225°, and 315°) direction data sets. The dashed lines in (B) represent a values across the 360° circular angle space, as plotted in Figure 2A.
Figure 5.
 
Polar plots of (A) the precision (standard deviation of the best-fitting Gaussian function) and (B) the size of serial dependence (a) in pursuit direction for the four cardinal (0°, 90°, 180°, and 270°) and the four oblique (45°, 135°, 225°, and 315°) direction data sets. The dashed lines in (B) represent a values across the 360° circular angle space, as plotted in Figure 2A.
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