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Article  |   February 2025
Metrics of two-dimensional smooth pursuit are diverse across participants and stable across days
Author Affiliations & Notes
  • Yao Yan
    Department of Physiology and Biomedical Discovery Institute–Neuroscience Program, Monash University, Clayton, Victoria, Australia
    [email protected]
  • Yilin Wu
    Department of Physiology and Biomedical Discovery Institute–Neuroscience Program, Monash University, Clayton, Victoria, Australia
    [email protected]
  • Hoi Ming Ken Yip
    Department of Physiology and Biomedical Discovery Institute–Neuroscience Program, Monash University, Clayton, Victoria, Australia
    [email protected]
  • Nicholas Seow Chiang Price
    Department of Physiology and Biomedical Discovery Institute–Neuroscience Program, Monash University, Clayton, Victoria, Australia
    [email protected]
  • Footnotes
     YY and YW contributed equally to this article.
Journal of Vision February 2025, Vol.25, 5. doi:https://doi.org/10.1167/jov.25.2.5
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      Yao Yan, Yilin Wu, Hoi Ming Ken Yip, Nicholas Seow Chiang Price; Metrics of two-dimensional smooth pursuit are diverse across participants and stable across days. Journal of Vision 2025;25(2):5. https://doi.org/10.1167/jov.25.2.5.

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Abstract

Smooth pursuit eye movements are used to volitionally track moving objects, keeping their image near the fovea. Pursuit gain, the ratio of eye to stimulus speed, is used to quantify tracking accuracy and is usually close to 1 for healthy observers. Although previous studies have shown directional asymmetries such as horizontal gain exceeding vertical gain, the temporal stability of these biases and the correlation between oculomotor metrics for tracking in different directions and speeds have not been investigated. Here, in testing sessions 4 to 10 days apart, 45 human observers tracked targets moving along two-dimensional trajectories. Horizontal, vertical, and radial pursuit gain had high test–retest reliability (mean intraclass correlation 0.84). The frequency of all saccades and anticipatory saccades during pursuit also had high test–retest reliability (intraclass correlation coefficients = 0.66 and 0.73, respectively). In addition, gain metrics showed strong intermetric correlation, and saccade metrics separately showed strong intercorrelation; however, gain and saccade metrics showed only weak intercorrelation. These correlations are likely to originate from a mixture of sensory, motor, and integrative mechanisms. The test–retest reliability of multiple distinct pursuit metrics represents a “pursuit identity” for individuals, but we argue against this ultimately contributing to an oculomotor biomarker.

Introduction
Moving objects in the environment can be deliberately and accurately tracked using smooth-pursuit eye movements, which minimize the retinal motion smear arising from a mismatch between the speed of the tracked object and eye speed (Lisberger, 2015). Reduced motion smear can improve motion prediction and assessment of properties such as the spin of the object (Bahill, Baldwin, & Venkateswaran, 2005; Spering, Schütz, Braun, & Gegenfurtner, 2011) but may more generally impair motion perception throughout the visual field (Vater, Klostermann, Kredel, & Hossner, 2020). Rapid saccades compensate for the position error that steadily accumulates during tracking, because in most cases pursuit gain (the ratio of eye to stimulus speed) is less than unity. Suppression of motion processing associated with these saccades is another challenge for visual perception (Ibbotson, Price, Crowder, Ono, & Mustari, 2007; Krekelberg, 2010). Despite the fundamental nature of eye movements and the thousands of instances of smooth tracking and tens of thousands of saccades humans make every day, there are substantial interindividual differences in tracking performance and large direction-dependent biases within individuals (Bargary et al., 2017; Goettker & Gegenfurtner, 2024; Liston & Stone, 2014). Here, we explore the common origins of these variations and their stability over time. 
Good tracking performance is predominantly associated with a pursuit gain close to 1, accompanied by early onset of tracking with high initial acceleration, maintained low position error, and a low rate of saccades. Even though the same constraints and motor adaptation should equally calibrate pursuit in any direction, horizontal smooth pursuit performance is commonly reported to be smoother and more accurate than vertical smooth pursuit. Although most studies report horizontal versus vertical tracking differences at the population level (Baloh, Yee, Honrubia, & Jacobson, 1988; Collewijn & Tamminga, 1984; Grant, Leigh, Seidman, Riley, & Hanna, 1992; Grönqvist, Gredebäck, & von Hofsten, 2006), it is less common to examine individual-level data. Two notable studies showed consistently higher horizontal than vertical gain in five out of five participants (Rottach et al., 1996) and 18 out of 20 participants (Ke, Lam, Pai, & Spering, 2013). This bias was preserved during straight-line tracking of diagonal motion, which includes horizontal and vertical components. Interestingly, in both studies, participants with relatively high gain for horizontal tracking tended to have higher gain for vertical tracking, and those with higher gain for one type of trajectory (e.g., a triangular wave) had higher gain for other speeds or trajectories (e.g., a sinusoid). This correlation in gain across directions and trajectories suggests there is a common velocity-independent factor underlying an individual's pursuit performance, but this has not been systematically studied. 
A second type of direction-dependent bias emerges when comparing upward and downward tracking. Although many studies have low sample sizes and have reported mixed results or no significant differences between up and downward tracking (Marti, Bockisch, & Straumann, 2005; Rottach et al., 1996), an important study with 40 participants and multiple experiments showed that most subjects had higher downward than upward gain (Ke et al., 2013). This finding was consistent across speed and was observed for tracking of targets shown on the upper and lower halves of the monitor. The correlation between an individual's performance on multiple tracking tasks suggests an underlying common neural control mechanism for pursuit; however, the directional asymmetries suggest that the reliability of sensory processing may also depend on tracking direction. Collectively, it is not known how direction asymmetries arise, how consistent they are over time, and whether they reflect sufficient independence to have potential utility in biomarkers or biometrics. 
Impaired smooth pursuit has long been considered an endophenotype of schizophrenia; however, pursuit metrics do not currently offer diagnostic utility or the ability to predict treatment efficacy (Lieberman, Small, & Girgis, 2019). Further, smooth pursuit gain is reduced in a range of conditions including autism, attention-deficit/hyperactivity disorder, and Parkinson's disease, suggesting that oculomotor impairments may simply reflect generalized neurological impairments, challenging their use as a biomarker (Bansal, Ford, & Spering, 2018; Fletcher & Sharpe, 1988; Hong et al., 2008; Levy, Sereno, Gooding, & O'Driscoll, 2010; Mani, Asper, & Khuu, 2018; Takarae, Minshew, Luna, Krisky, & Sweeney, 2004). Many previous studies of smooth pursuit have relied on a small number of stimulus trajectories and a limited number of performance metrics, so a simple way to expand the potential utility of oculomotor testing is to use more tests and calculate more metrics. In a 15-minute test session involving pursuit of constant-velocity targets, the distributions of 10 metrics were characterized in a population of 41 participants, and test–retest reliability was demonstrated in six participants (Liston & Stone, 2014). Whereas Liston and Stone (2014) tested multiple speeds and directions, they did not examine the reliability of these measures in a large cohort. The idea of an “oculomotor signature” was more thoroughly developed in a study involving 1058 individuals and assessment of test–retest reliability in 105 individuals (Bargary et al., 2017). This study extracted 21 metrics from a 25-minute testing session involving saccades, anti-saccades, and smooth pursuit. Promisingly for biomarker development, both studies demonstrated that, even with healthy populations, there are large interindividual variations in metrics of timing, accuracy, precision, and smoothness of tracking eye movements, with most metrics showing twofold or greater differences across participants. Although most metrics were strongly correlated within individuals, both studies (Bargary et al., 2017; Liston & Stone, 2014) examined correlations between data measured in the same session and sometimes the same trials, making the correlations susceptible to artificial inflation due to session-level factors such as vigilance or motivation. A more recent study with 50 participants used eight distinct tasks requiring saccades, pursuit, or perceptual reports of stationary and moving targets (Goettker & Gegenfurtner, 2024). The authors reported correlations between saccadic and pursuit performance, but only if the relevant sensory information was matched. In this case, sensory information refers to whether behavior is guided by information about stimulus position or velocity. Although Bargary et al. (2017) and Goettker and Gegenfurtner (2024) demonstrated test–retest reliability in a large cohort, they only used horizontal pursuit, and the reliability of directional biases remains unclear. 
Here, we quantified intercorrelations between families of metrics of smooth pursuit, allowing us to explore if an oculomotor identity or biomarker could be improved by incorporating metrics of tracking in two dimensions. In two sessions, 45 participants tracked 11 different trajectories that included a range of speeds with triangular waveforms, horizontal and vertical sinusoids, and circles. We demonstrated (1) excellent test–retest reliability of pursuit gain, position error and saccade rates for pursuit in all directions, including circles; (2) strong intercorrelations among different metrics recorded in different test sessions; and (3) the ability to reliably decode participant identity, based only on pursuit metrics. Mechanistically, this is consistent with arguments that a common mechanism underlies pursuit gain regardless of direction, as well as the coordination of smooth tracking and saccades (Goettker & Gegenfurtner, 2021; Krauzlis, 2004; Orban de Xivry & Lefèvre, 2007). Further, as individual biases appear stable across test sessions, interindividual differences in this coordination may arise due to variations in sensory processing of motion velocity, motor control, or sensorimotor integration. 
Methods
Participants
All procedures were approved by the Monash Human Research Ethics Committee, and volunteers gave informed written consent. Each participant attended two 30- to 60-minute testing sessions 4 to 10 days apart. Cohort 1, tested in 2022, involved 12 adult participants (eight females, four males), who included one of the authors and 11 volunteers recruited from an undergraduate neuroscience unit. Cohort 2, tested in 2023, involved 33 adult participants (25 females, eight males), including three of the authors and 30 volunteers who were compensated for their time. All participants had normal or corrected-to-normal vision and no known neurological or oculomotor conditions. The non-author volunteers had no, or very limited prior psychophysical testing experience and were naïve with respect to the aims of the study. 
We initially aimed to recruit 28 participants, as this would allow us to detect an intraclass correlation coefficient (ICC) of 0.8 as significantly different (p < 0.05) from a minimum acceptable reliability of 0.5 with 80% power. We tested all participants who initially responded to the second round of recruitment. This study was not pre-registered and complies with transparency and openness guidelines. 
Visual stimuli and behavioral task
Participants were comfortably seated facing a Display++ LCD monitor (120-Hz refresh rate, 1920 × 1080 pixels, 705 × 395 mm; Cambridge Research Systems, Rochester, UK). Chin and forehead rests were used to stabilize the head and maintain a viewing distance of 57 cm. Stimuli were generated using MATLAB (MathWorks, Natick, MA) and the Psychophysics Toolbox extensions (Kleiner et al., 2007) under the control of custom code in Neurostim (Github, 2022). 
Eye movements were recorded using a non-invasive, video-based eye tracker with a sampling frequency of 1000 Hz (EyeLink 1000; SR Research, Ottawa, Canada). Before each block of trials, participants completed a calibration procedure requiring them to fixate targets in a nine-point grid. Trials were presented in blocks of 18 to 54 trials, with extended breaks between blocks. 
On each trial, a stationary white target (234 cd/m2) appeared against a neutral gray background (117 cd/m2). Participants were required to fixate the target for 600 ms, after which it would move for 6000 ms (Cohort 1) or 4500 ms (Cohort 2) along a predefined trajectory. Trials with eye position errors exceeding 6° or interrupted by blinks were stopped and randomly shuffled into the remaining set of trials; therefore, participants were encouraged to blink between rather than during trials. Although the threshold for tracking errors was quite generous, we had no evidence from our analysis that any participants were not actively engaging with the task. However, due to the difficulty that many participants had with completing trials in Cohort 1 (totaling 6600 ms without blinking), we shortened the trial duration for Cohort 2. To combine data for both cohorts, we analyzed only the first 4500 ms of tracking from the trials seen by Cohort 1. 
For Cohort 1, we used nine trajectories of motion (sinX, sinY, and circ in Figure 1). For Cohort 2, we added two new triangular ramp trajectories (triX). The triangular ramps were repeated 20 times within a session; the sinusoidal and circular trajectories were repeated eight times. Trajectories were interleaved. As the ramp trajectories were only seen by Cohort 2, our sample sizes were 33 participants for those trajectories and 45 participants for all other trajectories. 
Figure 1.
 
Horizontal and vertical stimulus positions associated with the 11 trajectories.
Figure 1.
 
Horizontal and vertical stimulus positions associated with the 11 trajectories.
The triangular ramps had constant speed of 10°/s or 20°/s. On each trial, the spot started 10° to the left of the middle of the screen and moved 20° to the right, then reversed direction and moved 20° to the left. It then continued following the triangle waveform for 4500 ms. The sinusoidal trajectories were all one-dimensional sinusoids starting in the middle of the screen and commencing with motion either to the right or upward. The circular trajectories started at their rightmost point and commenced moving upward. For the sinusoidal and circular stimuli, we used three amplitude–frequency combinations (amplitudes of 6°, 3°, and 2°; frequencies of 0.25, 0.5, and 0.75 Hz). These were chosen to match the peak speed across the trajectories. 
Data preprocessing
Eye position data sampled at 1000 Hz from all participants were recalibrated, smoothed, differentiated, desaccaded, and downsampled before extracting metrics to summarize pursuit performance. First, eye positions on each trial were recalibrated to compensate for slight head movements between trials that artificially inflate errors in eye position. We found separate horizontal and vertical offsets and scaling factors that minimized the sum of the squared error between the stimulus and eye position, from 300 ms after the target began moving until the end of the trajectory. The recalibrated eye position data were smoothed and differentiated using a Savitzky–Golay filter with order 3 and frame length of 51 samples. Saccades were initially detected based on periods when horizontal or vertical eye speed exceeded 16°/s (or 25°/s for trajectory triX2, which had a constant speed of 20°/s). For analyses of gain and position error, we ignored a time window extending from 33 ms before the eye speed first crossed the threshold until 33 ms after the eye speed dropped below the threshold. To match the oculomotor data to the stimulus presentation rate, we downsampled the eye position and speed traces from 1000 to 120 Hz using the finite impulse response anti-aliasing lowpass filter implemented by the resample function in MATLAB. 
Oculomotor metrics
We calculated metrics of pursuit that focused on: (1) the gain of eye speed; (2) positional errors; and (3) saccade frequency (Table 1). Metrics of smooth pursuit were derived from the downsampled (120 Hz), desaccaded position and speed data. Metrics of saccades were derived from the 1000-Hz data. For all trials, we analyzed only the period from 300 to 4500 ms after motion onset. 
Table 1.
 
Description of oculomotor metrics calculated for each trial. The abbreviated names are used in subsequent figures.
Table 1.
 
Description of oculomotor metrics calculated for each trial. The abbreviated names are used in subsequent figures.
For each trial, gain was calculated as the temporal mean of the ratio of eye speed to stimulus speed throughout the trial. For the one-dimensional eye movements, when calculating gain, we additionally excluded periods when the stimulus speed was below 2°/s and periods when the eye and stimulus moved in opposite directions. For the horizontal triangular waves, to avoid including periods of trajectory prediction around the time that the stimulus abruptly changed direction, we excluded periods within 300 ms of a direction change. Gain was calculated separately for horizontal and vertical eye movements (gainX, gainY) and for the component of radial eye velocity aligned with the instantaneous stimulus direction (gainR). Positional errors were quantified using the root mean square error (RMSE) between the stimulus position and the smoothed eye position trace with saccades intact. 
Saccade metrics included the frequency of all saccades (saccAll), catch-up saccades (saccCatch), and anticipatory saccades (saccAntic). Catch-up and anticipatory saccades do not have standard definitions (Smyrnis, 2008), but here are defined as saccades that were aligned within ±45° of the target direction and having an amplitude of at least 1.5°. The endpoints of catch-up saccades fell short of the target, but endpoints of anticipatory saccades fell beyond the target. Across participants, mean ± SD rates of all saccades, catch-up saccades, and anticipatory saccades were 3.03 ± 0.99, 1.14 ± 0.26, and 0.66 ± 0.27 saccades per second. These high rates reflect the long trial durations and continuously changing target velocities. To represent the signals used to plan saccades, we also characterized the position error (saccPos) and retinal slip speed (saccSlip) 150 ms before the peak eye speed observed during each saccade (de Brouwer, Yuksel, Blohm, Missal, & Lefèvre, 2002). 
Measures of correlation
To quantify test–retest reliability for each metric, we used the form of ICC that measures absolute agreement among measurements, also known as criterion-referenced reliability. This is sensitive to (i.e., reduced by) any group-level shifts in performance between test sessions. ICCs were measured between groups of trials in Session 1 and Session 2 (between-session reliability) and between odd and even trials in each session (within-session reliability). Within-session reliability was calculated for each session, and we report the average value for the two sessions. 
To quantify consistency between different metrics, we used Pearson correlation. In this case, ICC would not be appropriate because there is no reason to anticipate identical values for metrics associated with, for example, tracking gain and saccade frequency. To improve the robustness of our intermetric correlations, we report only correlations between metrics computed in different sessions (e.g., metric X in Session 1 was correlated with metric Y in Session 2, not with metric Y in Session 1). 
Although there are no standardized qualitative labels for ICCs of different magnitudes, ICC < 0.5 is considered relatively poor, and ICC > 0.8 is potentially clinically significant and likely to be necessary for use as a biomarker (Cicchetti, 1994). Note that the sample sizes required to detect ICCs of 0.5 and 0.8 with 80% power are just eight and 28 participants, respectively; with our actual sample size of 45, most of our observed correlations would have been significant. Therefore, we performed null hypothesis significance testing of ICC values relative to a minimum acceptable reliability of 0.5. As we calculated ICCs for multiple metrics, we set an acceptable false discovery rate of p < 0.05 and controlled for multiple comparisons using the Benjamini–Hochberg method. 
Individual identification
We attempted to match individual participants between testing sessions using the metrics of their smooth pursuit. We used a 1-nearest neighbor (1-NN) classification strategy; each participant was correctly identified if their collective metrics recorded in Session 2 were closer to their own Session 1 metrics than all other participants’ metrics. Separation of datapoints was determined using Euclidean distance in an N-dimensional space, where N was the number of metrics used by the classifier. Data for each metric were z-scored before inclusion in the classifier. A benefit of 1-NN classification is that it does not require cross-validation and does not suffer from overfitting, but it does require access to a complete training set, as all metrics had to be calculated for all participants in Session 1. Each participant was tested independently; therefore, the chance rate of correctly matching an individual participant was 1/n, where n = 45, the number of participants. The chance rate of overall decoding performance was the proportion of all participants that were correctly identified and was also 1/n
Results
We examined the test–retest reliability of nine oculomotor metrics applied to smooth pursuit tracking of 11 distinct motion trajectories, which included horizontal triangles and sinusoids, vertical sinusoids, and circles. Figure 2 shows one participant's horizontal and vertical eye position, speed, and gain for single trials of a horizontal triangle wave, sinusoidal wave, and circular motion. Tracking was generally smooth and closely followed the target position apart from occasional saccades, which were particularly common at the onset of tracking (Figures 2A to 2C). Saccades were removed in the display of eye speed (Figures 2D to 2F). Instantaneous gain was calculated as the ratio of eye speed to stimulus speed, determined separately for horizontal and vertical components of motion. To focus on closed-loop smooth pursuit and exclude periods contaminated by saccades or strong elements of trajectory prediction, our calculation of gain for each trial excluded periods within 300 ms of a step change in motion velocity, when stimulus speed was below 2°/s, and when the eye and stimulus were moving in opposite directions (Figures 2G to 2I). Gain for each trial was calculated by averaging across the remaining time points and was subsequently averaged across all eight trials (sinusoidal and circular waveforms) or 20 trials (triangular waveforms). 
Figure 2.
 
Smooth pursuit tracking of moving targets. (AC) Horizontal and vertical eye position for a single trial of horizontal triangle (A), horizontal sinusoid (B), and circular (C) stimulus motion (trajectories triX1, sinX1, and circ1, respectively). (DI) Corresponding eye speeds (DF) and horizontal gain (GI) after desaccading and removing periods of rapid stimulus acceleration. Crosses on the right of panels G to I indicate mean gain across time for the trial.
Figure 2.
 
Smooth pursuit tracking of moving targets. (AC) Horizontal and vertical eye position for a single trial of horizontal triangle (A), horizontal sinusoid (B), and circular (C) stimulus motion (trajectories triX1, sinX1, and circ1, respectively). (DI) Corresponding eye speeds (DF) and horizontal gain (GI) after desaccading and removing periods of rapid stimulus acceleration. Crosses on the right of panels G to I indicate mean gain across time for the trial.
Pursuit metrics show strong test–retest reliability
To illustrate the test–retest reliability of pursuit, Figure 3A shows each observer's horizontal gain for the two test sessions, measured during the fastest sinusoidal trajectory (sinX3: amplitude 2°, frequency 0.75 Hz). Both the ICC and Pearson correlation were significantly greater than 0.5 (ICC = 0.82, p < 0.001; r = 0.84, p < 0.001; see Methods for our approach to assessing the significance of correlations). Although the average gain across participants was significantly higher in Session 2 (t-test, t(44) = –3.05, p = 0.0038), this represents only a 3.3% change between sessions, and similar changes were not consistently observed for other trajectories. We used the form of ICC that quantifies absolute agreement among measurements; it is sensitive to, and reduced by, any systematic shifts in value between test sessions. Therefore, the strong ICC persisted despite the small increase in gain. To determine the expected ceiling on correlation values between sessions, we examined the within-session, or split-half, reliability based on odd and even trials. ICC and Pearson correlation had similar, significant values for this grouping (Figure 3B) (ICC = 0.81, p < 0.001; r = 0.81, p < 0.001), suggesting excellent test–retest reliability both within and between the sessions. 
Figure 3.
 
Pursuit metrics were stable within and between sessions. (A) Horizontal gain (gainX) for a sinusoidal stimulus trajectory (sinX3) in two testing sessions had high ICC and Pearson correlation. Each marker shows data from an individual participant (n = 45). (B) Horizontal gain from the same data in panel A, shown for odd and even trials. (CF) ICCs (C, D) and Pearson correlations (E, F) for combinations of 11 motion trajectories and nine metrics. Red outlined pixels in panels C to F correspond to the metric–trajectory combinations shown in panels A and B. Correlations are based on 45 participants, except for trajectories tri1 and tri2, which had 33 participants. Horizontal gains were not calculated for vertical trajectories and vice versa. Black regions in insets below panels C and D indicate regions for which ICCs were significantly greater than 0.5 (F-test, p < 0.05; Benjamini–Hochberg control for false discovery rate).
Figure 3.
 
Pursuit metrics were stable within and between sessions. (A) Horizontal gain (gainX) for a sinusoidal stimulus trajectory (sinX3) in two testing sessions had high ICC and Pearson correlation. Each marker shows data from an individual participant (n = 45). (B) Horizontal gain from the same data in panel A, shown for odd and even trials. (CF) ICCs (C, D) and Pearson correlations (E, F) for combinations of 11 motion trajectories and nine metrics. Red outlined pixels in panels C to F correspond to the metric–trajectory combinations shown in panels A and B. Correlations are based on 45 participants, except for trajectories tri1 and tri2, which had 33 participants. Horizontal gains were not calculated for vertical trajectories and vice versa. Black regions in insets below panels C and D indicate regions for which ICCs were significantly greater than 0.5 (F-test, p < 0.05; Benjamini–Hochberg control for false discovery rate).
Figures 3C and 3D show the intersession reliability and split-half reliability for all metrics and trajectories, based on the ICC. Vertical gains were not calculated for horizontal trajectories and horizontal gains were not calculated for vertical trajectories; these pixels are left empty. In general, gain metrics showed high ICC between sessions: for all gain metrics and across all trajectories the minimum ICC was 0.76 and the mean was 0.84. Further, ICCs for all gain metrics were significantly greater than 0.5; insets show in black the metric–trajectory combinations with ICC significantly greater than 0.5 (F-test, p < 0.05, Benjamini–Hochberg control for false discovery rate). Metrics based on saccades were also strongly correlated but had lower test–retest reliability than gain metrics. For example, the mean ICC across trajectories for the frequency of all saccades (saccAll) was 0.66, and for the frequency of anticipatory saccades (saccAntic) it was 0.73. Pearson correlations showed similar trends (Figures 3E and 3F), but, because they do not incorporate the possibility of systematic changes in mean between sessions, they are shown here only for comparison with later analyses correlating different metrics, which do not allow application of ICCs. 
Directional biases are stable across time
Systematic directional asymmetries in smooth pursuit are commonly reported, notably higher gain and lower saccade rates for horizontal versus vertical pursuit and downward versus upward pursuit (Ke et al., 2013; Rottach et al., 1996). We examined how robust these biases are across sessions and whether systematic biases are evident in individuals and at the population level. To quantify these asymmetries, we first focused on gain ratios calculated for high-speed sinusoidal trajectories, comparing leftward versus rightward motion, upward versus downward motion, and horizontal versus vertical motion (Figures 4A to 4C). The asymmetries are quantified as the log of the gain ratio, log2(gaindir1/gaindir2), such that positive values indicate higher gain for direction 1 and negative values indicate higher gain for direction 2. The use of the log transform ensures that 0 indicates no bias and allows the application of arithmetic means. 
Figure 4.
 
Individual direction asymmetries in gain but not saccades were stable over time. Pursuit gains and saccade rates were calculated separately for each motion direction. (A) Left/right gain asymmetry, shown as the ratio log2(gainleft/gainright), was correlated between sessions. (B, C) Up/down gain asymmetry (B) and horizontal/vertical gain asymmetry (C) were highly correlated between sessions. (D, E) ICCs for directional biases in gain (D) and saccade (E) rates. (F, G) Mean biases across participants for gain (F) and saccade (G) rates. Black regions in the insets show ICCs that were significantly greater than 0.5 or biases significantly different from 0 (Benjamini–Hochberg controlled for false discovery rate). Colored outlines for trajectory sin3 in panels D and F summarize data in panels A to C. Horizontal/vertical gain ratios for sinusoids were calculated from gains measured using different stimuli. All other gain ratios were calculated from gains measured during different time windows of the same trials (n = 45 participants for all data).
Figure 4.
 
Individual direction asymmetries in gain but not saccades were stable over time. Pursuit gains and saccade rates were calculated separately for each motion direction. (A) Left/right gain asymmetry, shown as the ratio log2(gainleft/gainright), was correlated between sessions. (B, C) Up/down gain asymmetry (B) and horizontal/vertical gain asymmetry (C) were highly correlated between sessions. (D, E) ICCs for directional biases in gain (D) and saccade (E) rates. (F, G) Mean biases across participants for gain (F) and saccade (G) rates. Black regions in the insets show ICCs that were significantly greater than 0.5 or biases significantly different from 0 (Benjamini–Hochberg controlled for false discovery rate). Colored outlines for trajectory sin3 in panels D and F summarize data in panels A to C. Horizontal/vertical gain ratios for sinusoids were calculated from gains measured using different stimuli. All other gain ratios were calculated from gains measured during different time windows of the same trials (n = 45 participants for all data).
Surprisingly, the ICC for the left/right gain ratio was significantly greater than 0.5 (ICC = 0.68, p = 0.0498) (Figure 4A), suggesting that individual observers’ directional biases are relatively stable across time. However, at the population level, there was no systematic preference for rightward or leftward motion, with the mean gain ratio of –0.02 not significantly different from 0 (t-test, t(44) = –0.80, p = 0.43), and this p value did not survive controlling for false discovery rate. Previous studies have reported higher gain for downward than upward tracking, predicting that we should predominantly observe negative values in the calculation of log2(gainup/gaindown). However, although there was excellent agreement between the gain ratios for the two sessions (ICC = 0.89), the mean bias of 0.06 indicated a slight advantage for tracking of upward motion and was not significantly different from zero (t-test, t(44) = 1.66, p = 0.10) (Figure 4B). Consistent with previous studies, we observed a strong positive bias in the calculation of log2(gainhorizontal/gainvertical), with a mean bias of 0.16 that was significantly greater than 0 (t-test, t(44) = 5.08, p < 0.01). Our data also demonstrate that this bias was robust at the level of individual observers across sessions (ICC = 0.84) (Figure 4C). 
We examined the ICC and mean biases for left/right, up/down, and horizontal/vertical gain ratios for all stimulus trajectories (Figures 4D and 4F). Although 15 of 18 ICCs were significantly greater than 0.5 after correcting for false discovery rate, only biases in the horizontal/vertical gain ratio were consistently significantly different from zero, and biases were largest for the sinusoidal trajectories. This analysis is problematic for the circular trajectories, because the instantaneous direction for these trajectories continually changes, and almost all time points have components of both horizontal and vertical motion. For the three sinusoidal speeds, the mean horizontal/vertical gain ratio was 0.14, indicating that, across observers, the horizontal gain was 10% higher than the vertical gain. 
Given the robust directional biases in pursuit gain, we also examined directional biases in saccade rates, focusing only on the sinusoidal trajectories because of the previously identified challenges with segregating directional components during the circular trajectories. We separately calculated ratios for the rate of all saccades, anticipatory saccades, and catch-up saccades for both up/down tracking and horizontal/vertical tracking. No conditions were associated with ICCs significantly greater than 0.5 (Figure 4E), but there were some consistent biases across observers in the saccade rate ratios (Figure 4G). Notably, averaged across the three sinusoidal speeds, the mean anticipatory saccade rate ratio for horizontal/vertical tracking was –0.95, indicating that anticipatory saccades were 1.93 times more likely for vertical than horizontal tracking. Both anticipatory and catch-up saccades were also more common for downward than upward tracking. These biases were somewhat expected, as trajectories associated with higher pursuit gain are also associated with a lower rate of saccades. In the next section, we explore correlations among the different metrics. 
Gain and saccade metrics are separately intercorrelated
Given the robust test–retest reliability of many metrics of smooth pursuit, we explored the correlations between metrics, ultimately allowing us to assess how many underlying factors account for the inter-individual variations in performance. We focus on the nine main metrics (Table 1), ignoring the separate directional metrics developed in Figure 4Figure 5 shows the 99 × 99 intersession correlation matrix for all metric–trajectory combinations. To give a visual indication of the robustness of the results, we did not collapse correlations across sessions by averaging across the antidiagonal; that is, the correlation of metric XSession1 with YSession2 is shown separately from the correlation of metric XSession2 with YSession1. Critically, we also avoided calculating correlations between two metrics calculated within a single session, preventing artificial inflation of correlations due to session-level effects such as differences in vigilance, motivation, or training. 
Figure 5.
 
Gain metrics were intercorrelated with other gain metrics but not with saccade metrics. Intersession Pearson correlations are shown for 99 metric–trajectory combinations, grouped by the nine metrics (black lines). Expanded text in the top right shows the sequence of trajectories within each group. Horizontal gains were not calculated for vertical trajectories and vice versa; these regions are left blank (correlation 0).
Figure 5.
 
Gain metrics were intercorrelated with other gain metrics but not with saccade metrics. Intersession Pearson correlations are shown for 99 metric–trajectory combinations, grouped by the nine metrics (black lines). Expanded text in the top right shows the sequence of trajectories within each group. Horizontal gains were not calculated for vertical trajectories and vice versa; these regions are left blank (correlation 0).
Pixels along the antidiagonal in Figure 5 correspond to intersession correlations of the same metric–trajectory combinations. These are the same correlations shown in Figure 3E, so it is expected that they would be exclusively positive and mostly strong (median = 0.76, minimum = 0.31). Pixels within the black-outlined squares centered on the antidiagonal correspond to application of the same metric to different trajectories; these also show generally strong correlations, indicating the consistency of each metric regardless of the choice of trajectory. For example, the median correlation is r = 0.70 for the 11 × 11 pixels within the outlined square corresponding to gainR from Session 1 and Session 2, and r = 0.72 for RMSE from Session 1 and Session 2. In contrast, the median correlation within the pixels corresponding to saccCatch in the two sessions is r = 0.45, and there is substantial heterogeneity among correlations found for the different trajectories. This may be because the catch-up saccade metric is unreliable but also may reflect the strong dependence of this metric on the speed, direction, and predictability of the trajectory. The lack of correlation between anticipatory and catch-up saccades likely reflects trade-offs in function: Any anticipatory saccade greatly reduces the need for a catchup saccade and vice versa. 
Notably, apart from some conditions associated with the triangular stimuli, there was strong intercorrelation among all gain measures (horizontal, vertical, and radial), and these were strongly negatively correlated with the RMSE for position. This reflects that some individuals had consistently high gain and low position error for pursuit tasks in any direction, whereas other individuals consistently had low gain and high position error. The block of gain measures also showed high correlation with metrics associated with the rate of anticipatory saccades and the position error at the time of saccade initiation, but was not correlated with the overall rate of saccades or the rate of catch-up saccades. This suggests that maintaining high gain and low RMSE is associated with making relatively few anticipatory saccades, which are usually of small amplitude. 
Whether positive or negative, the strong intercorrelations among most metric–trajectory combinations suggests that relatively few components can account for the overall variance in the correlation matrix. We performed principal component analysis (PCA) on the raw data (45 participants × 91 metric–trajectory combinations) and found that the first three PCs explained 44.3%, 22.0%, and 12.5% of the variance across participants; eight components were necessary to explain 95% of the variance across participant scores. This demonstrates that, although many metrics are highly correlated, there are subtle differences in what they capture at the individual participant level; knowledge of multiple metrics is required to distinguish between individuals. Separately, we performed a second PCA analysis on the metric–trajectory correlation matrix in Figure 5. Visualizing the PCA coefficients for each metric–trajectory combination grouped by metric highlights two features. First, there was an inverse relationship between gain and RMSE, and, second, gain and RMSE were orthogonal or distinct from the rate of saccades (Figure 6). Note that this second form of PCA only accounts for common variation in the correlation coefficients, not in the underlying metrics for each participant. 
Figure 6.
 
PCA coefficients for each metric–trajectory combination in Figure 5. Combinations are color coded by metric. These first two PCs account for 88.4% and 5.9% of overall variance in the correlation matrix shown in Figure 5. Note that the first two PCs of the raw data account for a smaller proportion of the variance: 44.3% and 22%.
Figure 6.
 
PCA coefficients for each metric–trajectory combination in Figure 5. Combinations are color coded by metric. These first two PCs account for 88.4% and 5.9% of overall variance in the correlation matrix shown in Figure 5. Note that the first two PCs of the raw data account for a smaller proportion of the variance: 44.3% and 22%.
Individuals can be identified based on pursuit metrics
A starting point for developing a biomarker or biometric is the ability to reliably distinguish individuals or assign them to groups. The high intraclass correlations we demonstrated in a healthy population suggest the suitability of pursuit metrics for use as a biometric because individual responses are reliable and responses are distributed, or variable, across the population. However, the structure of correlations (Figure 5) and the high proportion of variance in these correlations accounted for by a single component (Figure 6) are less promising, suggesting that many metrics must reflect common underlying mechanisms. Further, the large variance in each metric across our healthy population suggests that biomarker development will require large changes in pursuit performance (i.e., large effect size) to segregate disease populations. To explore the utility of pursuit metrics as a biomarker or biometric, we quantified our ability to individually identify participants using a 1-NN decoding strategy. In this scheme, we attempted to identify every participant from their data recorded in Session 2, based only on the proximity of their datasets between sessions. Only Cohort 2 viewed the triangular wave stimuli; therefore, we decoded metrics only from the nine sinusoidal and circular trajectories. We did not measure horizontal gain for vertical stimuli and vertical gain for horizontal stimuli, leaving the decoder with a total pool of 75 metric–trajectory combinations for our 45 participants. 
When the 1-NN decoder had access to only a single metric–trajectory combination, decoding performance quantified as correctly identified participants varied from zero to seven out of 45 (15.6%; median = 3 out of 45, or 6.7%) (Figure 7A). Chance performance for such a decoder was low (one out of 45, or 2.22%), and, based on the binomial distribution, false positive rates of 5%, 1%, and 0.1% led to the identification of just three, four, and five participants. Figure 7B illustrates the performance of a decoder with access to only two metrics from the circ2 trajectory: vertical gain and the rate of catch-up saccades. Connected markers show the data for a single participant in the two sessions; markers are filled if the participant was correctly matched between sessions using only these two metrics. Overall, the performance was 14 out of 45 participants (31.1%). 
Figure 7.
 
Subjects had a “pursuit identity.” (A) Decoding performance of a 1-NN decoder using individual metric–trajectory combinations. Combinations are in the same order as in Figure 5 and are color coded as in Figure 6. There were 45 participants; chance performance was 2.22%. (B) Visualization of nearest-neighbor decoding with two metrics (gainY and saccCatch) extracted from a single trajectory. Each data point shows performance of one participant in one session; data recorded in the two sessions for each participant are linked. Participants that were correctly matched between sessions are shown as filled markers. Overall performance of this decoder was five out of 45, or 11.1%. (C) Decoding performance of 1-NN decoders trained with the limited number of metrics indicated on the abscissa. Each dot shows the performance of a different decoder with access to randomly selected metrics. The solid red line shows the mean performance across 100 random decoders of each size. The magenta line shows mean performance across 100 5-NN decoders; that is, a test subject was considered correctly matched if they were within the five nearest neighbors in the training set. (D) Mean error distance of the decoders in panel C, quantified as the number of mismatched participants (gray markers in the inset) between the predicted and actual participant (black markers in the inset). The inset illustrates a decoder based on two metrics. Black filled markers represent data for Sessions 1 and 2 for a single participant. Gray-filled markers show participants that are closer to the Session 1 data than the correct match, giving an error distance of 3.
Figure 7.
 
Subjects had a “pursuit identity.” (A) Decoding performance of a 1-NN decoder using individual metric–trajectory combinations. Combinations are in the same order as in Figure 5 and are color coded as in Figure 6. There were 45 participants; chance performance was 2.22%. (B) Visualization of nearest-neighbor decoding with two metrics (gainY and saccCatch) extracted from a single trajectory. Each data point shows performance of one participant in one session; data recorded in the two sessions for each participant are linked. Participants that were correctly matched between sessions are shown as filled markers. Overall performance of this decoder was five out of 45, or 11.1%. (C) Decoding performance of 1-NN decoders trained with the limited number of metrics indicated on the abscissa. Each dot shows the performance of a different decoder with access to randomly selected metrics. The solid red line shows the mean performance across 100 random decoders of each size. The magenta line shows mean performance across 100 5-NN decoders; that is, a test subject was considered correctly matched if they were within the five nearest neighbors in the training set. (D) Mean error distance of the decoders in panel C, quantified as the number of mismatched participants (gray markers in the inset) between the predicted and actual participant (black markers in the inset). The inset illustrates a decoder based on two metrics. Black filled markers represent data for Sessions 1 and 2 for a single participant. Gray-filled markers show participants that are closer to the Session 1 data than the correct match, giving an error distance of 3.
Giving the decoder access to more metric–trajectory combinations should improve decoding performance only if they contain independent information; however, as shown in Figure 5, the fact that a single PC accounted for just under 50% of the overall variation in metric–trajectory combinations demonstrates that these combinations are not independent. We explored the impact of this finding on decoders that incorporate between one and 75 metrics. We generated 100 decoders of each size, randomly assigning metrics to each decoder. Decoding performance reached 28 out of 45 (62.2%) when all 75 metrics were included, but on average was 50% when 20 metrics were included (Figure 7C). We also explored a more lenient version of decoding, in which identification was considered successful if the participant's data in Session 1 were included within the five nearest participants to their Session 2 data. In this case, performance reached 80% with 75 metrics and 74% with 20 metrics. Finally, we summarized decoding performance using an error distance. For each resampled decoder, this was the mean number of participants whose Session 1 data were closer to the target participant's Session 2 data than the target's own Session 1 data. Error distance fell rapidly with increasing metrics, saturating at approximately four individuals by 20 metrics (Figure 7D). The high performance of the strict and lenient identification tasks and the corresponding small error distances illustrate that substantial independent information was contained across the range of pursuit metrics. Critically, a substantially larger sample size is required to better assess how well such an approach to identification could work in a larger population. 
Discussion
We demonstrated the high test–retest reliability of nine oculomotor metrics that quantify pursuit gain, position error, and saccade rates during tracking of 11 distinct motion trajectories. Directional biases in gain (left vs. right, up vs. down, and horizontal vs. vertical) were stable within individuals between sessions, and at the group level we observed a significant advantage for horizontal versus vertical tracking. We did not replicate an earlier reported advantage for downward versus upward tracking at the group level. Building on the test–retest reliability of individual metrics, we demonstrated significant intercorrelations among metrics recorded in different test sessions. These were the strongest between metrics of gain and RMS error, regardless of direction or trajectory. Saccade rates were less well correlated, potentially reflecting the quantized nature and stochastic timing of these events. Finally, we reliably decoded observer identity within a 45-participant group, based on metrics obtained within a testing session. Below, we discuss the sources of individual variations and how they might be isolated, followed by a consideration of what may limit the incorporation of pursuit metrics into biomarkers. 
Sources of individual variation
Interindividual variations in smooth pursuit metrics have many underlying causes. Our participants were ostensibly healthy, with no known oculomotor disorders; therefore, although the variations in our sample were substantial, they may be small relative to clinical populations. The diverse origins of impaired oculomotor control point to both the susceptibility of oculomotor circuitry to disease and the dependence of eye movements on distributed circuits and types of processing throughout the nervous system. Impaired oculomotor control can arise from localized damage to visual cortex, cerebellum, or brain stem along with generalized damage due to traumatic brain injury (Mani et al., 2018). Various drugs have neuro-ophthalmological side-effects, notably the antidepressant nefazodone, which leads to dyskinetopsia (Horton & Trobe, 1999). Numerous neurological and psychiatric conditions are also associated with impairments in motion perception and oculomotor control, including autism spectrum disorder, Alzheimer's disease, attention-deficit/hyperactivity, schizophrenia, and Parkinson's disease (Fletcher & Sharpe, 1988; Levy et al., 2010; Takarae et al., 2004). In healthy, neurotypical individuals, it is likely that oculomotor variations reflect interindividual variations in the same neural modules and circuitry that are more substantially impacted by brain damage, drugs, and disease. Some of these variations likely reflect experience and practice; for example, national-level baseball players have better tracking performance than age-matched non-players (Chen, Stone, & Li, 2021). Below, we discuss four main neural factors that may account for inter-individual variation in pursuit. 
First, the origin of some interindividual variation must be purely sensory, reflecting the sensitivity of each observer's visual motion processing and known contribution of sensory variations to motor variability (Egger & Lisberger, 2022; Osborne, Lisberger, & Bialek, 2005; Rasche & Gegenfurtner, 2009). In studies exploiting individual differences, we demonstrated that the precision of motion direction perception and smooth eye movements are correlated (Blum & Price, 2014; Price & Blum, 2014), and others have shown that distinct mechanisms associated with high- and low-level speed perception are correlated with pursuit initiation and maintenance (Wilmer & Nakayama, 2007). Impaired sensory motion processing is also commonly reported in people with schizophrenia (Chen, 2011) and in some studies of people with autism (Dakin & Frith, 2005), which may account for their impaired pursuit performance. Given the great diversity of factors that account for overall visual perception (Grzeczkowski, Clarke, Francis, Mast, & Herzog, 2017), it is plausible that much of the interindividual variation in pursuit originates in sensory processing. 
Second, at the far end of the visuomotor hierarchy, purely motor and anatomical factors vary between individuals, including differences in the reliability of oculomotor control signals and inferred anatomical differences in the oculomotor plant—the eye globe and surrounding tissue, including muscles (Komogortsev, Karpov, Price, & Aragon, 2012). Although horizontal and vertical pursuit primarily depend on activation of distinct muscle pairs and oculomotor nuclei, it is unclear if the directional asymmetries in pursuit have sensory or motor origins. Regardless, the existence of these asymmetries is surprising given that the oculomotor system continuously adapts its gain to compensate for systematic errors (Fukushima, Tanaka, Suzuki, Fukushima, & Yoshida, 1996). This suggests that there is insufficient sensitivity in the internal monitoring of eye speed errors during pursuit to allow further adaptation, that different errors can be tolerated for pursuit in different directions, or possibly that further training and testing would reduce these directional asymmetries. 
Third, as pursuit motor commands are refined through the integration of sensory information with an efferent copy or corollary discharge of the motor command, an individual's relative gain for sensory and efferent signals is critical. This integration dramatically affects trajectory prediction during tracking and is a key computation thought to be affected in schizophrenia (Bansal et al., 2018). The role of trajectory prediction has been studied using tasks that require predictive acceleration in response to changes in velocity (e.g., circular trajectories or step changes in direction or speed) or a requirement to maintain eye velocity when a target transiently disappears or is retinally stabilized (Hong, Avila, & Thaker, 2005; Hong et al., 2008; Thake et al., 2003). 
Fourth, although not assessed here, the speed of information processing differs among individuals, manifesting in pursuit as differences in onset latency and initial acceleration (Bargary et al., 2017; Goettker & Gegenfurtner, 2024). Electrophysiological studies have demonstrated that pursuit latency is weakly correlated with neural processing in the middle temporal (MT) sensory area and is more strongly correlated with motor neuron activity in the floccular complex and abducens nucleus (Lee, Joshua, Medina, & Lisberger, 2016). These cumulative effects suggest that interindividual differences may exist at every level of the sensorimotor processing hierarchy. One reason why this may lead to differences in the speed of information processing is that the interpretation of the neural activity in one brain area by a second neural population depends on accurate decoding and is likely limited by suboptimal inference (Beck, Ma, Pitkow, Latham, & Pouget, 2012). Interindividual differences in decoding thresholds will then affect information processing speed and accuracy. However, although the speed of information processing is relatively easily quantified, it is not clear how decoding mechanisms and thresholds are affected by disease. 
Two additional factors may also affect the quantification of interindividual differences and should be controlled in experimentation. A participant's level of motivation and engagement with the task may systematically affect their performance. For example, if a participant is bored or less motivated in the second testing session, then the associated performance reduction would also reduce observed intraclass correlations. Related to this, we observed that, for many participants, gain tended to decline between the start and end of each trial (data not shown), which could reflect fatigue or declining attention. Our relatively long trials (>5 seconds without a blink) therefore mix cognitive and sensorimotor factors, which could be exploited in the future as a way of capturing more dimensions of interindividual variance. 
Separately, the way in which the participant physically interfaces with the testing equipment may lead to directional biases that artificially inflate interindividual differences. Our monitor was at a fixed height, but participants could adjust the chair and chinrest to comfortable heights. Different sitting positions may lead to systematic differences in head pitch and neck angle between participants, creating a vertical offset between a participant's neutral or resting eye position and the center of the monitor. A large offset would mean that tracking in opposing vertical directions also involved tracking predominantly toward or away from the neutral position. This could account for some of the previous challenges in observing consistent up-versus-down gain asymmetries. Ke et al. (2013) attempted to address this by presenting targets moving in the upper and lower parts of their monitor; however, as these trials were blocked, it is possible that the participants changed head pitch between blocks. To address this, future experiments could compare tracking toward and away from the neutral eye position and monitor head stability. 
Are oculomotor biomarkers feasible?
We observed substantial heterogeneity in our metrics of pursuit performance in a healthy population. Despite the strong correlations among many metrics, we needed eight principal components to explain 95% of the variance in participant performance, accounting for our ability to reliably decode individual identity. In the context of a biomarker, test–retest reliabilities of ICC = 0.7 have been described as the “worst acceptable value,” ICC > 0.8 as “potentially clinically significant,” and ICC > 0.9 as “ideal” (Barch, Carter, & CNTRICS Executive Committee, 2008; Cicchetti, 1994). Most of our metrics had near-ideal ICCs, hinting at their possible contribution to a biomarker that incorporates diverse behavioral tasks, but we believe that solely pursuit-based biomarkers remain infeasible. 
Oculomotor impairments have been associated with neurological conditions for over a century (Diefendorf & Dodge, 1908) and are the basis of well-established qualitative assessments of neurodegenerative disorders (Anderson & MacAskill, 2013). Further, a standardized suite involving 180 step-ramp pursuit trials (∼15 minutes) in a range of directions and speeds (Liston & Stone, 2014) showed utility for detecting and characterizing sensorimotor deficits associated with traumatic brain injury (Liston, Wong, & Stone, 2017). Unfortunately, although numerous companies promise diagnostic power for a multitude of conditions based on eye movements observed during common tasks, such as pursuit, antisaccades, reading, and viewing of faces and scenes, commercial solutions for neurological diagnosis remain unavailable. 
A major limitation of most potential biomarker studies that assess test–retest reliability in oculomotor metrics is that they ignore heterogeneity in healthy populations, fatigue, aging, and learning. First, we note that observing a high ICC for a metric in a healthy control population could be indicative of difficulties in using that metric as a biomarker. High ICC implies relatively large variance across the healthy population, often necessitating an implausibly large effect size to reliably distinguish patient and control populations. Second, sleep loss and circadian misalignment produce reliable changes in pursuit metrics, but sleep level is challenging to control in a patient population (Stone, Tyson, Cravalho, Feick, & Flynn-Evans, 2019). Third, aging tends to impair the gain and acceleration of smooth pursuit and decrease the accuracy of saccades to moving targets (Kanayama et al., 1994; Morrow & Sharpe, 1993; Paige, 1994). Although we did not recruit participants with a diverse age range, this would potentially have increased ICC measures, given the short test–retest separation we used, but studies using long-term follow-ups of individuals would show reduced ICCs. Further, any biomarker incorporating these metrics would have to be normalized for age, increasing its complexity. 
Oculomotor learning takes many forms. Over weeks of testing, we have shown changes in the gain of reflexive ocular following in macaques (Hietanen, Price, Cloherty, Hadjidimitrakis, & Ibbotson, 2017), suggesting that smooth pursuit gain may also change on long time scales. We are not aware of specific studies of this in humans, but other changes are evident within days of specific training. In patients with ocular muscle weakness, restricting presentation monocularly to the weak eye improved pursuit gain over a few days (Optican, Zee, & Chu, 1985). In separate studies, if stimulus speed or direction is consistently manipulated shortly after pursuit onset, after daily training involving hundreds of trials the oculomotor system learns to change eye velocity to match the timing of the target velocity changes (Kahlon & Lisberger, 1996; Medina, Carey, & Lisberger, 2005). Finally, in healthy participants asked to maintain their eye speed during the transient disappearance of a tracked target, pursuit gain increases after 8 to 10 days of training, accompanied by a reduction in saccade frequency (Madelain & Krauzlis, 2003). Collectively, these experiments illustrate the plasticity in the oculomotor system, which may impact the reliability of any biomarker that involves repeated testing. 
Conclusions
Although the successful incorporation of smooth pursuit metrics into biomarkers for disease remains uncertain, our work demonstrates the benefit of using interindividual diversity to understand the mechanisms underlying oculomotor behavior. Future work should combine the individual differences approach with diverse tasks that isolate aspects of oculomotor control to characterize the different mechanisms involved in generating reliable tracking. This might include paradigms that allow characterization of open- and closed-loop pursuit (Wilmer & Nakayama, 2007), require integration of static cues and anticipation (Kowler, Rubinstein, Santos, & Wang, 2019), combine pursuit and perceptual reports (Spering & Gegenfurtner, 2007), or that determine pursuit maintenance in the absence of a visual target (Trillenberg et al., 2017). In addition, motor learning in the context of oculomotor behaviors is relatively unexplored. Finally, as natural tracking behavior involves targets that continually change speed and direction, we believe the use of two-dimensional trajectories that are more complex than the triangles, sinusoids, and circles used here will provide insights into short-term plasticity, longer term learning, and prediction in the oculomotor system. 
Acknowledgments
Supported by the ARC Discovery Project (DP210102107 awarded to NSCP). 
Commercial relationships: none. 
Corresponding author: Nicholas Seow Chiang Price. 
Address: Department of Physiology and Biomedical Discovery Institute–Neuroscience Program, Monash University, Clayton, Victoria, Australia 
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Figure 1.
 
Horizontal and vertical stimulus positions associated with the 11 trajectories.
Figure 1.
 
Horizontal and vertical stimulus positions associated with the 11 trajectories.
Figure 2.
 
Smooth pursuit tracking of moving targets. (AC) Horizontal and vertical eye position for a single trial of horizontal triangle (A), horizontal sinusoid (B), and circular (C) stimulus motion (trajectories triX1, sinX1, and circ1, respectively). (DI) Corresponding eye speeds (DF) and horizontal gain (GI) after desaccading and removing periods of rapid stimulus acceleration. Crosses on the right of panels G to I indicate mean gain across time for the trial.
Figure 2.
 
Smooth pursuit tracking of moving targets. (AC) Horizontal and vertical eye position for a single trial of horizontal triangle (A), horizontal sinusoid (B), and circular (C) stimulus motion (trajectories triX1, sinX1, and circ1, respectively). (DI) Corresponding eye speeds (DF) and horizontal gain (GI) after desaccading and removing periods of rapid stimulus acceleration. Crosses on the right of panels G to I indicate mean gain across time for the trial.
Figure 3.
 
Pursuit metrics were stable within and between sessions. (A) Horizontal gain (gainX) for a sinusoidal stimulus trajectory (sinX3) in two testing sessions had high ICC and Pearson correlation. Each marker shows data from an individual participant (n = 45). (B) Horizontal gain from the same data in panel A, shown for odd and even trials. (CF) ICCs (C, D) and Pearson correlations (E, F) for combinations of 11 motion trajectories and nine metrics. Red outlined pixels in panels C to F correspond to the metric–trajectory combinations shown in panels A and B. Correlations are based on 45 participants, except for trajectories tri1 and tri2, which had 33 participants. Horizontal gains were not calculated for vertical trajectories and vice versa. Black regions in insets below panels C and D indicate regions for which ICCs were significantly greater than 0.5 (F-test, p < 0.05; Benjamini–Hochberg control for false discovery rate).
Figure 3.
 
Pursuit metrics were stable within and between sessions. (A) Horizontal gain (gainX) for a sinusoidal stimulus trajectory (sinX3) in two testing sessions had high ICC and Pearson correlation. Each marker shows data from an individual participant (n = 45). (B) Horizontal gain from the same data in panel A, shown for odd and even trials. (CF) ICCs (C, D) and Pearson correlations (E, F) for combinations of 11 motion trajectories and nine metrics. Red outlined pixels in panels C to F correspond to the metric–trajectory combinations shown in panels A and B. Correlations are based on 45 participants, except for trajectories tri1 and tri2, which had 33 participants. Horizontal gains were not calculated for vertical trajectories and vice versa. Black regions in insets below panels C and D indicate regions for which ICCs were significantly greater than 0.5 (F-test, p < 0.05; Benjamini–Hochberg control for false discovery rate).
Figure 4.
 
Individual direction asymmetries in gain but not saccades were stable over time. Pursuit gains and saccade rates were calculated separately for each motion direction. (A) Left/right gain asymmetry, shown as the ratio log2(gainleft/gainright), was correlated between sessions. (B, C) Up/down gain asymmetry (B) and horizontal/vertical gain asymmetry (C) were highly correlated between sessions. (D, E) ICCs for directional biases in gain (D) and saccade (E) rates. (F, G) Mean biases across participants for gain (F) and saccade (G) rates. Black regions in the insets show ICCs that were significantly greater than 0.5 or biases significantly different from 0 (Benjamini–Hochberg controlled for false discovery rate). Colored outlines for trajectory sin3 in panels D and F summarize data in panels A to C. Horizontal/vertical gain ratios for sinusoids were calculated from gains measured using different stimuli. All other gain ratios were calculated from gains measured during different time windows of the same trials (n = 45 participants for all data).
Figure 4.
 
Individual direction asymmetries in gain but not saccades were stable over time. Pursuit gains and saccade rates were calculated separately for each motion direction. (A) Left/right gain asymmetry, shown as the ratio log2(gainleft/gainright), was correlated between sessions. (B, C) Up/down gain asymmetry (B) and horizontal/vertical gain asymmetry (C) were highly correlated between sessions. (D, E) ICCs for directional biases in gain (D) and saccade (E) rates. (F, G) Mean biases across participants for gain (F) and saccade (G) rates. Black regions in the insets show ICCs that were significantly greater than 0.5 or biases significantly different from 0 (Benjamini–Hochberg controlled for false discovery rate). Colored outlines for trajectory sin3 in panels D and F summarize data in panels A to C. Horizontal/vertical gain ratios for sinusoids were calculated from gains measured using different stimuli. All other gain ratios were calculated from gains measured during different time windows of the same trials (n = 45 participants for all data).
Figure 5.
 
Gain metrics were intercorrelated with other gain metrics but not with saccade metrics. Intersession Pearson correlations are shown for 99 metric–trajectory combinations, grouped by the nine metrics (black lines). Expanded text in the top right shows the sequence of trajectories within each group. Horizontal gains were not calculated for vertical trajectories and vice versa; these regions are left blank (correlation 0).
Figure 5.
 
Gain metrics were intercorrelated with other gain metrics but not with saccade metrics. Intersession Pearson correlations are shown for 99 metric–trajectory combinations, grouped by the nine metrics (black lines). Expanded text in the top right shows the sequence of trajectories within each group. Horizontal gains were not calculated for vertical trajectories and vice versa; these regions are left blank (correlation 0).
Figure 6.
 
PCA coefficients for each metric–trajectory combination in Figure 5. Combinations are color coded by metric. These first two PCs account for 88.4% and 5.9% of overall variance in the correlation matrix shown in Figure 5. Note that the first two PCs of the raw data account for a smaller proportion of the variance: 44.3% and 22%.
Figure 6.
 
PCA coefficients for each metric–trajectory combination in Figure 5. Combinations are color coded by metric. These first two PCs account for 88.4% and 5.9% of overall variance in the correlation matrix shown in Figure 5. Note that the first two PCs of the raw data account for a smaller proportion of the variance: 44.3% and 22%.
Figure 7.
 
Subjects had a “pursuit identity.” (A) Decoding performance of a 1-NN decoder using individual metric–trajectory combinations. Combinations are in the same order as in Figure 5 and are color coded as in Figure 6. There were 45 participants; chance performance was 2.22%. (B) Visualization of nearest-neighbor decoding with two metrics (gainY and saccCatch) extracted from a single trajectory. Each data point shows performance of one participant in one session; data recorded in the two sessions for each participant are linked. Participants that were correctly matched between sessions are shown as filled markers. Overall performance of this decoder was five out of 45, or 11.1%. (C) Decoding performance of 1-NN decoders trained with the limited number of metrics indicated on the abscissa. Each dot shows the performance of a different decoder with access to randomly selected metrics. The solid red line shows the mean performance across 100 random decoders of each size. The magenta line shows mean performance across 100 5-NN decoders; that is, a test subject was considered correctly matched if they were within the five nearest neighbors in the training set. (D) Mean error distance of the decoders in panel C, quantified as the number of mismatched participants (gray markers in the inset) between the predicted and actual participant (black markers in the inset). The inset illustrates a decoder based on two metrics. Black filled markers represent data for Sessions 1 and 2 for a single participant. Gray-filled markers show participants that are closer to the Session 1 data than the correct match, giving an error distance of 3.
Figure 7.
 
Subjects had a “pursuit identity.” (A) Decoding performance of a 1-NN decoder using individual metric–trajectory combinations. Combinations are in the same order as in Figure 5 and are color coded as in Figure 6. There were 45 participants; chance performance was 2.22%. (B) Visualization of nearest-neighbor decoding with two metrics (gainY and saccCatch) extracted from a single trajectory. Each data point shows performance of one participant in one session; data recorded in the two sessions for each participant are linked. Participants that were correctly matched between sessions are shown as filled markers. Overall performance of this decoder was five out of 45, or 11.1%. (C) Decoding performance of 1-NN decoders trained with the limited number of metrics indicated on the abscissa. Each dot shows the performance of a different decoder with access to randomly selected metrics. The solid red line shows the mean performance across 100 random decoders of each size. The magenta line shows mean performance across 100 5-NN decoders; that is, a test subject was considered correctly matched if they were within the five nearest neighbors in the training set. (D) Mean error distance of the decoders in panel C, quantified as the number of mismatched participants (gray markers in the inset) between the predicted and actual participant (black markers in the inset). The inset illustrates a decoder based on two metrics. Black filled markers represent data for Sessions 1 and 2 for a single participant. Gray-filled markers show participants that are closer to the Session 1 data than the correct match, giving an error distance of 3.
Table 1.
 
Description of oculomotor metrics calculated for each trial. The abbreviated names are used in subsequent figures.
Table 1.
 
Description of oculomotor metrics calculated for each trial. The abbreviated names are used in subsequent figures.
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