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\begin{document}

\title{Cognitive-perceptual traits influence use of physics laws to enhance
visual motion tracking}



\author[1]{Chloe Cooper}%
\author[2]{Andrew Meso}%
\affil[1]{Bournemouth University}%
\affil[2]{King's College London Institute of Psychiatry Psychology and Neuroscience}%


\vspace{-1em}



  
  \date{June 05, 2024}


\begingroup
\let\center\flushleft
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\selectlanguage{english}
\begin{abstract}
Schizophrenia and Autism Spectrum Disorder (ASD) can disrupt cognition
and consequently behaviour. Traits of ASD and the subclinical
manifestation of schizophrenia, schizotypy, have been studied in healthy
populations with overlap found in trait profiles linking ASD social
deficits to negative schizotypy, and ASD attention to detail to positive
schizotypy. Here, we probed the relationship between sub-trait profiles,
cognition and behaviour, using a predictive tracking task to measure
individual eye movements under three gravity conditions. 48 healthy
participants tracked an on-screen bouncing ball under familiar gravity,
inverted antigravity and horizontal gravity control conditions while eye
movements were recorded and dynamic performance quantified. Participants
completed ASD and Schizotypy inventories generating highly correlated
scores, r = 0.73. All tracked best under the gravity condition,
producing anticipatory downward responses from stimulus onset under
gravity which were delayed upwards under antigravity. Tracking
performance was not associated with overall ASD or schizotypy trait
levels. Combining measures using Principal Components Analysis (PCA), we
decomposed the inventories into sub-traits unveiling interesting
patterns. Positive Schizotypy was associated with ASD dimensions of
rigidity, odd behaviour and face processing, and which all linked to
anticipatory tracking responses under atypical antigravity. In contrast,
negative schizotypy was associated with ASD dimensions of social
interactions and rigidity, and to early stimulus-driven tracking under
gravity. There was also substantial nonspecific overlap between ASD and
Schizotypy dissociated from tracking. Our work links positive-odd traits
with anticipatory tracking when physics rules are violated, and
negative-social traits with the application of expected physics.%
\end{abstract}%



\sloppy


\textbf{Cognitive-perceptual traits influence use of physics laws to
enhance visual motion tracking}

Chloe Cooper\textsuperscript{1,3} and Andrew Isaac
Meso\textsuperscript{2,3}

\textsuperscript{1}Acute Inpatient Psychology, Dorset Healthcare
University NHS Foundation Trust, Poole, UK

\textsuperscript{2}Neuroimaging Department, Institute of Psychiatry,
Psychology and Neuroscience, King's College London, UK

\textsuperscript{3}Psychology \& Interdisciplinary Neuroscience Group,
Bournemouth University, Poole, UK

Keywords:

Eye movements, Schizotypy, ASD, Anticipatory tracking, Gravity

Journal

European Journal of Neuroscience, Research Report

Number of Figures: 3

Number of Tables: 1

Word count (7681)

Abstract(245), Introduction (979), Methods (1029), Results(1605) and
Discussion (2179)

Abbreviations

SATQ -- Subthreshold Autism Trait Questionnaire, SPQ -- Schizotypal
Personality Questionnaire, RMSE -- Root Mean Square (position tracking)
Error, PCA -- Principal Component Analysis, FEF -- Frontal Eye Fields

\textbf{Abstract}

Schizophrenia and Autism Spectrum Disorder (ASD) can disrupt cognition
and consequently behaviour. Traits of ASD and the subclinical
manifestation of schizophrenia, schizotypy, have been studied in healthy
populations with overlap found in trait profiles linking ASD social
deficits to negative schizotypy, and ASD attention to detail to positive
schizotypy. Here, we probed the relationship between sub-trait profiles,
cognition and behaviour, using a predictive tracking task to measure
individual eye movements under three gravity conditions. 48 healthy
participants tracked an on-screen bouncing ball under familiar gravity,
inverted antigravity and horizontal gravity control conditions while eye
movements were recorded and dynamic performance quantified. Participants
completed ASD and Schizotypy inventories generating highly correlated
scores, r = 0.73. All tracked best under the gravity condition,
producing anticipatory downward responses from stimulus onset under
gravity which were delayed upwards under antigravity. Tracking
performance was not associated with overall ASD or schizotypy trait
levels. Combining measures using Principal Components Analysis (PCA), we
decomposed the inventories into sub-traits unveiling interesting
patterns. Positive Schizotypy was associated with ASD dimensions of
rigidity, odd behaviour and face processing, and which all linked to
anticipatory tracking responses under atypical antigravity. In contrast,
negative schizotypy was associated with ASD dimensions of social
interactions and rigidity, and to early stimulus-driven tracking under
gravity. There was also substantial nonspecific overlap between ASD and
Schizotypy dissociated from tracking. Our work links positive-odd traits
with anticipatory tracking when physics rules are violated, and
negative-social traits with the application of expected physics.

\textbf{Keywords} : Eye movements, Schizotypy, ASD, Anticipatory
tracking, Gravity



\textbf{Introduction}

Schizophrenia and Autism Spectrum Disorders (ASD) are common
heterogenous conditions that have historically been considered distinct.
Recently, cognitive and behavioural overlap between them has been
suggested, following observations that they share similarities in
psychosocial and pathophysiological features and phenotypes that may be
signatures of underlying comorbidity (Chisholm, Lin, Abu-Akel \& Wood,
2015). Clinically-motivated research has focused on practical rigid
diagnostic clarification with limited consideration of variation within
specific symptoms (Ford, Apputhurai, Meyer, \& Crewther, 2018).
Improving the mechanistic understanding of variable cognition and
behaviour, and the underlying genetic and neural correlates is a crucial
step towards better characterisation, which could ultimately enhance
diagnostic and treatment practices (De Giorgi et al., 2019; Klopper et
al., 2017). We pursue a mechanistic approach here by probing phenotype
variability within a healthy population.

Schizotypy refers to a set of personality traits mirroring symptoms of
schizophrenia at a subclinical level, characterised by dimensions
(positive, negative and disorganised) that run on a continuum from
healthy to psychosis (Nelson, Seal, Pantelis, \& Phillips, 2013; Raine,
1991). In a large healthy sample (N=1678), Ford et al. (2018) used
latent profile analysis to identify eight clusters encompassing
dimensions of schizotypy and ASD. Subgroups involving psychosocial
difficulties represented a shared social autism-negative schizotypy
domain (Abu-Akel et al., 2017), an autism-schizotypy subgroup reflected
a non-specific overlap of ASD and schizotypal traits, while psychosis
and a moderate aspect of schizotypy appeared to be independent. Further
research identified consistent overlapping and diametrically opposed
facets of phenotypes. With a sample of N=640, Nenadi\selectlanguage{polish}ć \selectlanguage{english}et al. (2021) used
Principal Components Analysis (PCA) to study multiple psychometric
measures of schizotypy and ASD in a German and separate Swiss/French
population. They identified loss of function and communication deficits
as phenotypes of ASD traits showing convergence with negative and
disorganized features of schizotypy. However, attention to detail in ASD
was diametrically opposed to positive schizotypal trait dimensions.

Poor Smooth Pursuit Eye Movements (SPEM) are an established
endophenotype of schizophrenia and schizotypy. Deficits in motion
processing and target prediction in schizophrenia contribute to SPEM
abnormalities (Barnes, 2008) with findings replicated in schizotypy
(Koychev et al., 2016). Often thought of as two separate systems, SPEM
and saccadic movements form part of a single sensorimotor repertoire,
served by continuous estimates of future eye positions and
velocity-related error signals (Goettker \& Gegenfurtner, 2021). Along
the pathway driving the oculomotor response, there are dynamic
interactions between input, predictions and errors enabling tracking
whilst maintaining perceptual stability (Goettker, Braun, \&
Gegenfurtner, 2019). We previously showed that motion tracking under
gravity may present a means of studying individual differences in
incorporating predicted gravity into cognitive processing (Meso, De Vai,
Mahabeer \& Hills, 2020). Predictions of future positions of moving
objects exploit gravity and participants' eye movements are guided by
prediction to different extents (J\selectlanguage{ngerman}örges \& López-Moliner, 2019).
Observers are generally capable of distinguishing different settings of
gravitational acceleration of parabolic trajectories with poor precision
(Jörges, Hagenfeld, \& López-Moliner, 2018). ASD has also been shown to
drive deficits in ocular motor function with a recent review identifying
saccade accuracy, inhibitory control and impaired tracking as common
issues (Johnson, Lum, Rinehard \& Fielding, 2016). However, the
initiation of eye movements and disengaging from targets did not seem
impaired in ASD groups.

The functioning of the ocular motor system is underpinned by a network
of brain areas within cortex and beyond (Masson and Perrinet, 2012). The
cerebellum is integral to problem-solving in spatial orientation due to
its role in vestibular processing and representations of gravity needed
for behaviour rely on it (MacNeilage \& Glasauer, 2018). Cerebellar
lesion patients exhibited deficits in perception of gravitational
direction in a perceived tilt task (Dakin, Peters, Giunti \& Day, 2018).
Activity in the Frontal Eye Fields (FEF), an area that serves target
prediction with an internal representation, has been found to be reduced
during SPEM in schizophrenic patients (Faiola et al., 2020).
Corresponding reductions have not been observed in schizotypy (Meyhöfer
et al., 2015). Furthermore, using functional Magnetic Resonance Imaging
and connectivity analyses, patients with recent-onset psychosis and
low-schizotypy controls were indistinguishable based on brain activity
during SPEM performance. However, using machine-learning, participant
group classifications were made using a right FEF seed region, based on
its connectivity within subcortical and cortical structures, frontal
cortex, cerebellum and hypothalamus (Schröder et al., 2022). As
interconnected cortical areas MT (Middle Temporal) and MST (Medial
Superior Temporal) process visual motion signals producing commands for
smooth pursuit, FEF may regulate this output with real-time gain control
(Ono \& Mustari, 2012; Ono, 2015). These findings, which highlight a
potential predictive role for FEF within a wider network, suggest that
individual variation in SPEM ability is subtler than previously thought
and demands a fine-grained exploration of prediction, representation and
information integration mechanisms.

In a recent study, high schizotypy participants had worse performance
during predictive pursuit than a control low schizotypy group, but SPEM
in a sinusoidal tracking task showed no differences (Faiola, Meyhöfer \&
Ettinger, 2020). In the prediction task, participants tracked a stimulus
that moved at a constant velocity and was pseudorandomly blanked in half
the trials, with instructions given to continue eye movements during the
blank. These findings imply the prediction deficit is separate from
general SPEM performance even along a sinusoidal path, consistent with
findings of Meso et al., (2020), who manipulated prediction using two
gravity conditions. The current work will address three questions.
First, can we conceptually replicate the previous work on tracking under
gravity (Meso et al., 2020) with additional controls and the inclusion
of an ASD inventory? Second, can we unveil differences in tracking
performance dynamics and organise them in terms of anticipation
(pre-sensory response), early open-loop and later closed-loop responses?
Finally, can we characterise the multidimensional relationship between
schizotypy and ASD subtraits, and link these to eye-tracking measures
for a meaningful interpretation of clusters? We take a combined
experimental and theoretical approach and answer each one of these
questions in turn.

\textbf{Materials and Methods}

Participants We tested 48 participants (29 Female, 19 Male, Age M=22.1,
SD= 3.9, IQR = \{19,23\}) recruited by opportunity sampling at
Bournemouth University. Participants received £5 for their time. The
study was approved by the Research Ethics Committee of Bournemouth
University and was carried out in accordance with the principles of the
Declaration of Helsinki. Participant numbers could not be determined by
standard power calculation. Similar eye-tracking tasks require 6 to 10
participants (e.g. Meso, Montagnini, Bell, \& Masson, 2016; Meso, Gekas,
Mamassian, \& Masson, 2022), so trait inventory requirements determined
numbers. Previous power estimates suggested 45 participants (Meso, De
Vai, Mahabeer, \& Hills, 2020), as did a recent reliability and
replicability study on SPEM and traits (Schröder, Baumert, \& Ettinger,
2021).

Stimulus and Materials

Stimuli were generated on a Windows 7 PC running bespoke Matlab
(Mathworks) routines in Psychtoolbox (Brainard, 1997; Pelli, 1997).
Presentation was on a Cambridge Research Systems 32' Display++ Monitor
with 1920 x 1080-pixel resolution and 100Hz refresh rate. The monitor
was placed 80cm from participants. Eye movements were recorded from the
right eye using an SR Eyelink Video eye tracker operating at 1000Hz with
movement restricted by a head/chinrest. The stimulus was based on Meso
et al., (2020), with sizes scaled to an on-screen virtual square with
sides of 900pix containing the stimulus presentation area of 23.4
degrees of visual angle (°). The black ball had 0.21° diameter with
motion characterised by Equations (1) to (4).

V\textsubscript{x}(\emph{t} ) = \emph{d} \selectlanguage{english}[?]S\textsubscript{x} (1)

P\textsubscript{x}(\emph{t} ) = X\textsubscript{0} +\emph{d}
\selectlanguage{english}[?]S\textsubscript{x}\emph{t} (2)

V\textsubscript{x} in Equation (1) is the constant horizontal component
of the speed with S\textsubscript{x} set from \{4, 16\} deg/s for
fast/slow and direction \emph{d} set from \{-1,1\} for left/right. The
time-varying horizontal position P\textsubscript{x} in Equation (2)
depended on S\textsubscript{x} starting at the centre of the screen,
X\textsubscript{0}.

V\textsubscript{y}(\emph{t} ) = S\textsubscript{y} + \selectlanguage{greek}ε \selectlanguage{english}+\emph{g}
[?]\emph{t} (3)

P\textsubscript{y} (t) = Y\textsubscript{0} + (S\textsubscript{y} +
\selectlanguage{greek}ε\selectlanguage{english})\emph{t} + (\emph{g} [?]\emph{t} \textsuperscript{2})/2 (4)

V\textsubscript{y} in Equation (3) is the vertical speed component
initiated as S\textsubscript{y} = 2\selectlanguage{ngerman}°/s and \selectlanguage{greek}ε \selectlanguage{english}is a number from a flat
continuous distribution of \selectlanguage{ngerman}± \{0 to 0.5\}°/s away from the direction of
acceleration \emph{g} , which is ±9.81°/s\textsuperscript{2} for the
gravity (+) and antigravity (-) conditions. The position
P\textsubscript{y} in Equation (4) incorporates the initial position at
the centre of the screen Y\textsubscript{0} and the integration of
Equation (3) for position. The resulting motion is that expected for a
ball just smaller than a professional soccer ball.

Procedure Participants were screened for normal or corrected-to-normal
vision with a visual acuity letter chart. Bespoke Matlab programs were
used for trait inventories with mouse clicks to record responses. The
74-item Schizotypal Personality Questionnaire -- SPQ (Raine, 1991) and
24-item, 5-point Subthreshold Autism Trait Questionnaire -- SATQ (Kanne,
Wang, \& Christ, 2012) were used. The tracking task was separated into
three blocks of Gravity, Antigravity and Control. In the control
condition, stimulus orientation was rotated by 90 degrees from the
gravity condition so that vertical motion was defined by Equations (1)
and (2) and horizontal by (3) and (4) and gravity acted rightwards. Each
block had 160 trials of 1.25s duration with participant-initiated button
presses to proceed. Trials started with a 500ms central dark grey
fixation circle which disappeared at trial onset and the stimulus was
followed by a grey screen. Participants were instructed to fixate on the
central spot and track the ball as well as they could. Blocks contained
80 fast and 80 slow trials and lasted approximately 10 minutes. The task
interleaved the inventories with the conditions fixed in the same order
i.e. SPQ, gravity, SATQ, antigravity and control, with breaks in between
so that it lasted about 40 minutes. Changes from the procedure of Meso
et al., (2020), were that participants always started on the gravity
condition, trials were shorter (1.25s not 2s), tasks included the
control condition and we used a higher precision psychophysics screen,
the CRS Display++.

Design and data analysis

We used a multivariate within-participants design. The Independent
Variables were Gravity direction with three levels: Gravity (G) --
downwards acceleration, Antigravity (AG) -- upwards and Control (C) -
rightwards; ball Speed with two levels: Slow (4°/s) and Fast (16°/s).
The key measures were the two inventories: the SPQ and SATQ, RMSE (Root
Mean Square Error between dynamic eye position and ball position), and
Saccades (rates and sizes). We also recorded participant age and sex.
Data pre-processing to extract the RMSE and Saccades is detailed in Meso
et al., (2020). We reduced the RMSE responses to 25 samples, each
covering a 20ms window from onset at 0ms to 500ms. RMSE was measured for
the x-direction capturing responses to the motion component at
a\emph{constant speed} for conditions G and AG, and for the y-direction
capturing responses subject to \emph{acceleration due to simulated
rightward gravity} . We quantified learning as performance improvement
during a block of 80 trials, by subtracting averaged RMSE value for the
last 20 trials from that of the first 20 trials under the same speed
condition. Learning was positive if there was improvement. We analysed
the trait responses and a restricted subset of eye movement measures
focusing on (i) the relationship between SPQ and SATQ, (ii) the
relationship between the inventories and RMSE measures, (iii) the
relationship between the inventories and the saccades, and (iv) dynamic
changes in the relationships between both RMSE and saccades under the G
and AG conditions. For each of the four, we ran correlations with alpha
adjusted for the number of comparisons undertaken. (v) We also ran mean
comparisons between gravity conditions for RMSE, Saccades and
RMSE-learning. These were done using a Wilcoxon signed rank test because
of the deviations from normality. Finally, we ran a correlation type
Principal Components Analysis (Joliffe, 2002) to unpack the relationship
between a restricted set of 21 measures. These variables were selected
to cover sub-traits of the SPQ and SATQ, Saccade rates and amplitudes
and RMSE measures, both at stimulus onset (0ms) and during the open loop
of response (\textasciitilde{}160ms). Meaningful components were
identified using parallels analysis of the variance (Joliffe and Cadima,
2016). For simplicity, we focused analysis on the slow speed condition
which showed similar patterns to the faster condition but was an easier
tracking task.

\textbf{Results}

Tracking performance across gravity conditions

We measured the dynamic RMSE value (difference between onscreen ball and
eye position) every 20ms over the first 500ms, separately for horizontal
and vertical components. In the horizontal direction, with ball motion
at a constant speed (4 or 16°/s), average performance, RMSE-x gradually
worsened between 0 and 200ms. This was because horizontal direction was
unpredictable in each trial and the stimulus response, which started
around 85-95ms, required a catch-up saccade and so only improved after
200ms (Figure 1A and C, darker grey traces). For RMSE-y in the vertical
direction where acceleration acted, the gravity condition was the same
within each block of trials so motion could be predicted and anticipated
by the participant after some trials. The average response was therefore
about 0.5° from onset for the full 500ms (Figure 1B and D darkest grey
trace). In contrast, for the antigravity condition, average tracking was
worse at \textasciitilde{}0.8° from onset gradually improving until
300ms, implying there was an anticipatory antigravity response that was
less effective than under gravity (Figure 1B, D mid grey trace). This
result is consistent with the previous study (Meso et al., 2020), with
worse performance and slower dynamics under AG. The differences are
statistically evaluated in the next section. Importantly, the control
condition with horizontal gravity was similar to the gravity condition,
but with a baseline averaged initial performance of 0.6°, 0.1° worse
than the gravity condition (Figure 1A and C lightest grey trace). This
suggests there is a performance advantage for the downwards gravity
condition that is reduced by 0.1° in the horizontal rightward gravity
control condition.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1:} Dynamic RMSE performance measure in degrees plotted
on the ordinate axis, Mean and Standard Error for 48 participants,
against time in ms from stimulus onset on the abscissa for gravity
(black, G), anti-gravity (dark grey, AG) and control with horizontally
accelerating gravity (light grey and dash/dot lines, CO) conditions. (a)
For the horizontal direction in the slow condition. (b) Vertical
direction, slow condition showing worse performance for AG from onset to
200ms. (c) Horizontal fast condition with catch up saccades around
100-300ms. (d) Vertical fast condition similar to (b) with better
performance for G than AG.

ASD and SPQ traits and links to eye tracking

The Schizotypy Personality Questionnaire (SPQ) produced scores
comparable to previous work with Median = 16 and IQR = 18.5. Participant
scores were almost evenly distributed below 30 (See Figure 2A). The SATQ
produced scores comparable to previous work with Median = 17.5 and IQR =
11.5 and scores were approximately normally distributed (Figure 2B). We
ran a Pearson's correlation between the SPQ and SATQ and found a strong
relationship with \emph{r} = 0.735, p = 2.73 x
10\textsuperscript{-9}(Figure 2C). We did not decompose the SPQ and SATQ
sub-clusters, to avoid expansion to the 15 permutations (3 SPQ clusters
x 5 SATQ) and therefore used PCA. Instead, we first looked at the
relationship between the inventories and the vertical RMSE-y at stimulus
onset (0ms), which reflects anticipatory responses. For the four
comparisons using a Pearson correlation, we adjusted alpha for
significance to 0.0125. Under the gravity condition, there was a
near-zero correlation between the SPQ and RMSE-y with \emph{r} = -0.026,
p = 0.86, and similarly a low correlation between SATQ and RMSE-y at
with \emph{r} = -0.074, p = 0.62. Under the antigravity condition, there
was a low correlation between the SPQ and the RMSE-y with \emph{r} =
0.065, p = 0.66, and similarly between SATQ and RMSE-y with \emph{r} =
0.025, p = 0.86. There was therefore no significant relationship between
the trait measures and the tracking performance in the gravity direction
at onset (Figure 2D, E, G and H). We then analysed the relationship
between the traits and the eight saccade measures, adjusting the alpha
value for the Pearson correlations to 0.00625. Under the gravity
condition, there was a non-significant negative correlation between the
SPQ and the Saccade rate, \emph{r} = -0.169, p = 0.25, and similarly for
the SATQ and saccade rate, \emph{r} = -0.153, p = 0.30. Under the
antigravity condition, the correlation was near zero for the SPQ and the
saccade rates, \emph{r} = -0.047, p = 0.75, and the SATQ and the saccade
rate, \emph{r} = -0.039, p = 0.79. The traits showed little relation to
the rates (Figure 3A-D). For the saccade amplitudes, under the gravity
condition, there was a non-significant negative correlation between the
SPQ and the amplitudes, \emph{r} = -0.12, p = 0.40, and the SATQ and
amplitudes, \emph{r} = -0.12, p = 0.41. For the antigravity condition,
these were again near zero for SPQ and amplitude, \emph{r} = 0.041, p =
0.78, and SATQ and amplitude, \emph{r} = -0.017, p = 0.91. Traits showed
little relationship with the amplitudes (Figure 3E-H).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2:} Summary of 48 participants' data showing SPQ and SATQ
trait measures and vertical RMSE for the slow tracking condition. (a)
and (b) show the frequency distributions of SPQ and SATQ scores with
descriptive statistics. (c) Strong correlation between SPQ and SATQ
scores. (d) to (e) Weak correlation between SPQ and onset, 0ms, RMSE for
both gravity and antigravity conditions, and (f) moderate correlation
between gravity and antigravity RMSE. (g) to (i) weak correlation
between SATQ and onset, 0ms, RMSE for both conditions, G and AG, and
then the distributions of the onset y-RMSE values for gravity (darker)
and antigravity (lighter) showing separation between condition
performance. (j) to (l) show moderate correlation between gravity and
antigravity RMSE, increasing strength through 80ms, 160ms and 240ms. (m)
to (o) show distributions of y-RMSE distributions for gravity (darker)
and antigravity (lighter) which become less distinct over time from 80ms
to 240ms.

Eye tracking differences across gravity conditions

Tracking was measured separately across G and AG conditions both for the
constant speed component -- x and the accelerating component -- y. We
first considered the relationship between the tracking measures for the
accelerating direction RMSE -- y and for the G and AG conditions. We
carried out four Pearson's correlations to track this relationship
dynamically from onset (0ms) through to the closed-loop response at
240ms in four windows. Alpha was adjusted to 0.0125 for four
comparisons. There was a significant correlation between individual RMSE
-- y values across all the time windows: at 0ms, \emph{r} = 0.422, p =
0.00282; near response onset at 80ms \emph{r} = 0.472, p = 7 x
10\textsuperscript{-4}; during the open loop at 160ms \emph{r} = 0.481,
p = 5.47 x 10\textsuperscript{-4}; and during the closed loop \emph{r} =
0.532, p = 9.8 x 10\textsuperscript{-5}. Interestingly, the correlations
increase in strength over time from onset, suggesting that the earliest
anticipatory responses have less shared processing between the G and AG
stimulus cases than the later closed-loop response (Figure 2F, J-L). We
then tested for a difference in the RMSE -- y responses between the G
and AG conditions for the same sequential time windows. We used a
Wilcoxon signed rank test because of the non-parametric distributions
(see Figure 2I, M-O). There was a significant difference between the G
and AG responses for the earliest two windows, with the values at 0ms
for G: Median = 0.41\selectlanguage{ngerman}° and for AG: Median = 0.73°, with W = 167, p =
0.0000157, and at 80ms for G: Median = 0.37° and for AG: Median = 0.56°,
with W = 265, p = 0.000923. At 160ms and 240ms, there was no significant
difference between G and AG responses, with W = 513, p = 0.44, and W =
550, p = 0.70 respectively. Early responses in the gravity direction are
consistently best for the G condition and initially poorer for the AG
condition (Figure 2I, M-O). Similar differences are found between the G
and Control conditions. The pattern of results showing better
performance under G and delays under AG replicates previous findings
(Meso et al., 2020). We then compared the values of both saccade
measures under the two gravity conditions, adjusting alpha for the two
tests. For the rates, significantly fewer saccades are produced per
second under G: Median = 1.36 than under AG: Median = 1.58, W = 245, p =
0.000735. For the amplitudes, there is no significant difference in the
size of saccades produced under the G and AG conditions, W = 448, p =
0.15 (Figure 3I and J). Finally, we looked at the effect of learning
across trials for both the constant speed motion with RMSE -- x and the
motion subject to acceleration RMSE -- y and adjusted alpha for two
comparisons to 0.025. For the first (x), there is a difference between
the conditions with less learning under G: Median = -0.06° than AG:
Median = 0.03°, W = 319, p = 0.0058. For the accelerating condition (y),
learning is again lower for G: Median = -0.02° than AG: Median = 0.19°,
W = 248, p = 0.000488. This result suggests that performance in the
gravity condition did not generally improve over the course of trials
while that under the antigravity condition generally did, especially
under acceleration (Figure 3K-L).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3:} Relationship between trait measures and saccade
metrics and visualisations of estimates of learning through performance
improvements over conditions (see text for details). Eye movements here
are for the slow condition only. (a) to (d) Show weak negative
correlation between SPQ/SATQ and saccade rates under both gravity (G)
and antigravity (AG) conditions; those for gravity have higher values.
(e) to (h) Show weak correlations between SPQ/SATQ and saccade
sizes/amplitudes. (i) and (j) saccade rates and sizes show little
difference between gravity conditions. (k) and (l) RMSE learning i.e.
performance improvement during task shows no difference between gravity
and antigravity for the horizontal (x-direction), but more improvement
during the task for the vertical direction (y-direction) under the
antigravity condition with a median of 0.19\selectlanguage{ngerman}° compared with -0.02°.

Principal component analysis

Given the number of variables measured, we could not answer all
questions of interest using standard correlations and hypothesis-based
statistical tests without an explosion of familywise error. Like others
(Nenadi\selectlanguage{polish}ć \selectlanguage{english}et al., 2021, Meso et al., 2020) we took a data-driven approach
and identified variables of interest for a correlation-based PCA. We
selected a set of 21 measures from over 200 possible measures in the
multivariate experiment including the AGE, the three main clusters of
the SPQ, the five sub-traits of the SATQ, and eye tracking with both
saccade and RMSE measures for the G and AG condition. Table 1 contains
the PCA results with the 21 variables listed and their loadings for the
first seven components. These seven components in the table (in
descending order of their strength) are selected based on parallels
analysis restricting explained data variance to 75\%. We use the data
loadings to guide our qualitative description of each of the orthogonal
components. The first component is dominated by \emph{eye movement
measures} with little contribution from AGE and the inventories. It
likely captures individual differences in eye movements which make some
participants better at eye-tracking tasks than others. The second
component captures \emph{general overlap} between the SPQ and the SATQ,
unrelated to eye movements. The third component is dominated by
the\emph{positive cluster of the SPQ} and the \emph{odd, face and
rigidity}traits of the SATQ. In addition, eye movement for \emph{open
loop constant speed tracking (160ms)} and \emph{anticipatory antigravity
tracking} responses and learning. The fourth captured \emph{negative
SPQ} and \emph{social interaction} and \emph{rigidity of the SATQ} . For
eye movements, \emph{saccade rates/amplitudes} and \emph{open loop and
anticipatory tracking under the gravity} condition. The fifth
captured\emph{social interactions} and \emph{odd clusters of the SATQ}
and for eye movements, \emph{saccade rates} and \emph{learning under the
gravity} condition. Both the fourth and fifth components had a
contribution from AGE, but this was not considered reliable because of
our narrow spread of participant ages. The sixth and seventh components
were difficult to characterise, with the former being predominantly
driven by eye movements and the latter by traits.

\textbf{Table 1} : Principal component Analysis results looking at the
relationship between variables covering the inventories, saccade metrics
and tracking performance in the form of RMSE. The first seven components
explaining 75\% of the variance are included. Selected variable labels
are given in the first column. Numbers represent variable loadings with
higher loadings above \textbar{}0.20\textbar{} highlighted.\selectlanguage{english}
\begin{longtable}[]{@{}llllllllll@{}}
\toprule
& & & \textbf{COMPONENT \#} & \textbf{COMPONENT \#} & \textbf{COMPONENT
\#} & \textbf{COMPONENT \#} & \textbf{COMPONENT \#} & \textbf{COMPONENT
\#} & \textbf{COMPONENT \#}\tabularnewline
\midrule
\endhead
& & & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} &
\textbf{6} & \textbf{7}\tabularnewline
& & \textbf{Variance (\%)} & 20.0 & 17.9 & 10.2 & 8.3 & 7.3 & 5.6 &
4.8\tabularnewline
& \textbf{Variable Name} & & & & & & & &\tabularnewline
& AGE & & -0.02 & -0.16 & 0.03 & \textbf{-0.28} & \textbf{-0.39} & 0.10
& -0.17\tabularnewline
\textbf{(Qs)} & SPQ -- positive & & -0.02 & \textbf{0.38} &
\textbf{-0.23} & -0.02 & 0.03 & 0.19 & \textbf{-0.22}\tabularnewline
& SPQ - negative & & -0.11 & \textbf{0.35} & 0.11 & \textbf{-0.20} &
0.19 & 0.00 & -0.07\tabularnewline
& SPQ - disorganised & & -0.10 & \textbf{0.39} & -0.16 & 0.04 & -0.14 &
0.17 & -0.03\tabularnewline
& SATQ - Social Int. & & -0.08 & \textbf{0.31} & 0.06 & \textbf{-0.30} &
\textbf{0.28} & -0.13 & \textbf{0.38}\tabularnewline
& SATQ -- Odd & & -0.05 & \textbf{0.23} & \textbf{-0.31} & 0.11 &
\textbf{-0.34} & 0.19 & \textbf{0.24}\tabularnewline
& SATQ - Read Faces & & -0.04 & \textbf{0.35} & \textbf{0.24} & 0.00 &
-0.08 & -0.01 & \textbf{0.44}\tabularnewline
& SATQ - Language & & -0.16 & \textbf{0.30} & 0.02 & 0.11 & 0.01 & -0.13
& \textbf{-0.37}\tabularnewline
& SATQ - Rigidity & & -0.07 & \textbf{0.24} & \textbf{-0.23} &
\textbf{-0.29} & -0.04 & -0.03 & \textbf{-0.43}\tabularnewline
\textbf{(G)} & Saccades - Amplitude & & \textbf{0.33} & -0.02 & 0.00 &
-0.19 & \textbf{0.29} & -0.06 & 0.00\tabularnewline
& RMSE - y (0ms) & & \textbf{0.32} & 0.07 & -0.10 & \textbf{0.21} &
-0.08 & \textbf{-0.37} & -0.17\tabularnewline
& Saccades - rate (200ms) & & \textbf{-0.30} & -0.06 & -0.14 &
\textbf{0.35} & \textbf{0.31} & -0.07 & 0.03\tabularnewline
& RMSE - x (160ms) & & 0.14 & 0.17 & \textbf{0.52} & 0.18 & 0.05 & 0.18
& \textbf{-0.20}\tabularnewline
& RMSE - y (160ms) & & \textbf{0.23} & 0.17 & -0.07 & \textbf{0.43} &
-0.04 & \textbf{-0.36} & -0.09\tabularnewline
& RMSE - y, learn (0ms) & & -0.09 & -0.15 & -0.15 & 0.01 & \textbf{0.51}
& \textbf{0.24} & \textbf{-0.21}\tabularnewline
\textbf{(AG)} & Saccades - Amplitude & & \textbf{0.37} & 0.05 & -0.13 &
\textbf{-0.22} & \textbf{0.27} & 0.14 & 0.00\tabularnewline
& RMSE - y (0ms) & & \textbf{0.37} & 0.11 & \textbf{-0.20} & 0.04 & 0.06
& 0.10 & 0.19\tabularnewline
& Saccades - rate (200ms) & & \textbf{-0.34} & 0.02 & -0.17 &
\textbf{0.32} & \textbf{0.20} & 0.09 & 0.14\tabularnewline
& RMSE - x (160ms) & & 0.15 & 0.12 & \textbf{0.45} & \textbf{0.26} &
0.03 & \textbf{0.41} & -0.10\tabularnewline
& RMSE - y (160ms) & & \textbf{0.34} & 0.11 & -0.17 & 0.12 & 0.09 &
-0.03 & 0.10\tabularnewline
& RMSE - y, learn (0ms) & & 0.18 & -0.10 & \textbf{-0.25} & 0.14 & -0.10
& \textbf{0.53} & 0.04\tabularnewline
\bottomrule
\end{longtable}

\textbf{Discussion}

In this work, we studied the relationship between both ASD and
schizotypy traits, recently demonstrated to have overlapping
characteristics (Ford et al., 2018; Abu-Akel et al., 2017; Nenadi\selectlanguage{polish}ć \selectlanguage{english}et
al., 2021), and their association with cognition and behaviour probed
through a gravity tracking task (Meso et al., 2020). Both ASD and
Schizophrenia have been found to disrupt ocular motor function (Barnes,
2008; Johnson, Lum, Rinehard \& Fielding, 2016) and questions remain
about the commonality of the specific disruption. In this context, the
work involved a conceptual replication and extension of research which
introduced the gravity ball tracking task. We found that participants
were much better at tracking under the familiar gravity condition than
when the direction was inverted in the antigravity condition (Meso et
al., 2020). This tracking task was different from more widely used
predictive sinusoidal tracking with blanking along the trajectory
(Faiola, Meyh\selectlanguage{ngerman}öfer \& Ettinger, 2020), as participant performance could
be improved by the use of knowledge about gravity (Jörges \&
López-Moliner, 2017). In the current work, we similarly demonstrated an
advantage for the downward gravity condition over others and unpack the
multitude of results from the multivariate eye movement and inventory
measures by answering three broad questions. We first interpret the
findings in the context of replicating and extending Meso et al.,
(2020), with the inclusion of the ASD inventory and controls. Second, we
unveil differences in tracking dynamics and discuss their implications.
Finally, we characterise the multidimensional relationship between eye
movements, ASD traits and Schizotypy.

Replication of the gravity advantage in tracking

Participants were asked to track a moving ball in repeated trials within
blocks of separate gravity conditions. As such, within two or three
trials from the start of the block, participants could implicitly or
explicitly expect that the vertical component in the gravity and
antigravity conditions would have the same acceleration over trials
within the block. Under the gravity condition, all participants were
good at tracking throughout the half-second duration from motion onset
we analysed. Tracking was about 20\% better than under the control
condition, in which gravity acted in the rightward direction, suggesting
that implicit knowledge of the physics-based expectations of gravity
enhanced visual tracking (similarly suggested by Jörges \&
López-Moliner, 2019). The antigravity condition engendered much larger
individual differences in responses and poorer tracking. Some
participants were able to anticipate the accelerating response in the
upward direction before the visual system could produce a
stimulus-driven response, and most were able to improve to a point at
which tracking performance was best and at a plateau matched across all
conditions by about 300ms from onset. In the current work, we sought to
better understand these dynamic differences across conditions. Meso et
al., (2020) used linear mixed models to control for random effects and
identify a relationship between Schizotypy trait levels and both RMSE
and saccades which involved an interaction with gravity direction
condition. Here, we have extended this previous work, aiming to better
understand how the dynamic eye response depended on violations of the
physics of gravity and trait characteristics.

Schizotypy and ASD trait relationships

We used two established and quick-to-answer inventories: one for ASD --
the SATQ (Kane et al., 2012) and the other for schizotypy - the SPQ
(Raine, 1991). Individual scores for the two inventories were found to
be highly correlated. Large recent studies have shown that the two
conditions are related and suggested that individuals with a clinical
ASD diagnosis were about 3.5 times more likely to receive a concurrent
diagnosis of schizophrenia (Zheng, Zheng \& Zou, 2018). Similarly,
overlaps have been identified in traits of both ASD and Schizotypy in
healthy undiagnosed participants across multiple cultures (Abu-Akel et
al., 2017; Nenadi\selectlanguage{polish}ć \selectlanguage{english}et al., 2021). The heterogeneity of ASD and
Schizotypy traits means that the overlap can also be separated into
quite distinct clusters; for example, a first encompassing negative
schizotypy and poor social communication (ASD), a second encompassing
positive schizotypy and attention to detail (ASD) and a third with less
specific overlap (Abu-Akel et al., 2017; Nenadi\selectlanguage{polish}ć \selectlanguage{english}et al., 2021). Indeed,
our two inventories decomposed the trait measures into three broad
dimensions (from nine smaller ones) for Schizotypy and five dimensions
for ASD (Raine, 1991; Kane et al., 2012). We expected some of these
subtrait dimensions to be associated with the specific eye movement
metrics. When we measured the correlation between both overall single
trait levels and various eye movement measures, there were
unsurprisingly no significant relationships. Instead, this motivated the
use of a data-driven approach to parcel out the variance into the
various contributions in a similar way to what was achieved by the
linear mixed models in Meso et al., (2020), to observe more subtle
relationships.

Gravity direction performance and dynamics

The gravity condition was generally found to be better performed than
the antigravity condition. When the saccades were compared between these
conditions, there was a significant difference between rate of saccades
produced, with fewer saccades under the gravity conditions when compared
to the antigravity conditions. However, the sizes of these saccades were
not different. This may have been driven by more catch-up saccades in
the antigravity condition. We separated the tracking measure of RMSE
into four response epochs from anticipatory at onset, sensory response
threshold, open-loop response and finally a closed-loop response. This
was done to reduce the complexity of the continuous tracking responses
and capture key ocular motor signatures that isolate anticipatory
responses, in the absence of the stimulus from the earliest unelaborated
sensory responses and later responses which incorporate sensorimotor
feedback loops (Masson \& Perrinet, 2012; Meso et al., 2022). We first
looked at the correlation between the RMSE in the vertical response for
both the gravity and antigravity conditions across the four time
windows. All four windows showed a significant relationship between
performance in both gravity conditions, with the relationship weakest in
the anticipatory responses occurring before the sensory response was
visible and getting progressively stronger, with a peak in the last
closed loop epoch. This finding suggests that the anticipatory response
is at least partially driven by separate mechanisms in the gravity and
antigravity condition, with downward gravity able to draw on prior
knowledge about the physics rules in a fast, pre-attentive way (J\selectlanguage{ngerman}örges
\& López-Moliner, 2017). Further, in the antigravity condition, the RMSE
responses themselves were also poorest for the anticipatory condition
and subsequently less poor at the threshold of stimulus response in the
second epoch considered. Although, in both these earlier windows, RMSE
was significantly different from the gravity response. In the latter two
windows, responses were not different across the gravity and antigravity
conditions. Late in the ocular motor response, integrative processes
serving motion estimation incorporate visual feedback and therefore
error signals (Goettker, Braun, \& Gegenfurtner, 2019; Meso et al.,
2022). By contrasting these later open-loop and closed-loop responses to
the earlier epochs, we therefore expected to be able to separate motion
perception deficits previously characterised (Barnes, 2008) from
specifically prediction deficits (Koychev et al., 2016). On top of that,
in contrasting the gravity and antigravity conditions in the
multivariate analysis that followed, we have prediction scenarios
involving the overfamiliar case of downward gravity and the
rule-contravening case of antigravity, which unpacked some seeming
contradicting results on tracking deficits in schizotypy (Koychev et
al., 2016; Meyhöfer et al., 2015). We also calculated a measure of
learning to quantify improvement of performance over the course of a
block and found that learning improved more in the antigravity than
gravity condition, with a larger improvement of almost two and a half
times in the accelerating vertical direction when compared with the
constant speed horizontal direction. Participants were therefore able to
get slightly better over the course of the trials, particularly for the
antigravity condition in anticipating the upwards direction. This
learning could not however extend to a level to match the established
prior knowledge about the physics of gravity. The dynamic performance
measures, saccade metrics and learning measures were therefore all of
interest in the multivariate analysis involving trait measures.

Multidimensional patterns identified

We used PCA to unpack the relationships between the different variables
in this experiment and link the trait measures to the eye movements. PCA
has previously been used to study trait measures from healthy
populations (Nenadi\selectlanguage{polish}ć \selectlanguage{english}et al., 2021) and with eye-tracking metrics (Meso
et al., 2020). They were ideal in this scenario given the multiple
dimensions of the inventories (Raine, 1991; Kane et al., 2012)
reflecting the heterogeneity of the constructs of interest -- ASD trait
and schizotypy. We used a simple correlation form of PCA and parallels
analysis to restrict our components of interest to seven (Joliffe and
Cadima, 2016). The ordered components become progressively less strong
and therefore less dominant in the explanation of the trends in the
results. The first two of these components explaining 38\% of the
variance separately captured all-round eye movement performance at 20\%
and non-specific overlap between all dimensions of both inventories at
about 18\%. Interestingly, these dominant components may explain why
direct correlations between individual eye movement measures and the
inventories might not be expected to identify strong links. Instead,
these substantial separated parts of the variance may account for the
strong correlation between inventories, which has a non-specific profile
overlap previously proposed (Abu-Akel et al., 2017; Zheng, Zheng \& Zou,
2018).

The next two components together accounting for just under 20\% of the
variance were the most interesting in the current work. These separated
the negative schizotypy dimension from the positive dimension. In the
first of these, the Positive schizotypy was associated with the ASD
trait dimensions of oddness and rigidity and related with opposite sign
to the ability to read faces. This relationship is consistent with that
identified by Nenadi\selectlanguage{polish}ć \selectlanguage{english}et al. (2021). This component was also linked to
tracking performance in the constant speed horizontal direction during
the stimulus response, i.e. a tracking eye movement that is more general
and not dependent on prediction. In the vertical direction, however, the
association was with the antigravity condition in the anticipatory
response and antigravity learning metrics. Therefore, these eye
movements suggest for the first time that this
\emph{positive-odd}cluster of traits may relate to general motion
tracking, while also associated with an ability to adapt to motion that
contravenes expectations of the physics of gravity. This finding extends
that of Meso et al., (2020), as well as previous work using blanking
paradigms (Koychev et al., 2016).

The second of these components links the negative dimension of
schizotypy with the ASD trait dimensions of social interaction and
rigidity, consistent with previous work (Nenadi\selectlanguage{polish}ć \selectlanguage{english}et al., 2021; Ford et
al., 2018). This \emph{negative-social} component is also strongly
associated with tracking in the gravity direction, specifically under
the gravity condition, both in the anticipatory and the later open loop
response. This result is therefore consistent with the possibility that
participants' use of long term learned prior information about gravity
could be associated specifically with this negative-social dimension.
Indeed, it has been hypothesised that Schizophrenia is driven by poor
predictive mechanisms that should be based on learned rules (Millard,
Bearden, Karlsgodt, \& Sharpe, 2022) and gravity could represent such a
prior (J\selectlanguage{ngerman}örges \& López-Moliner, 2017; Meso et al., 2020).

Each of the three remaining components contributing just under 18\% of
the total variance were less reliably interpretable, either because of a
potentially spurious high age-related correlation, non-specific
associations with either eye movements or equally non-specific
relationships between inventory responses. The key finding in the
current work is therefore in the characteristic eye movements associated
with the \emph{positive-odd} and \emph{negative-social} trait
dimensions. Interestingly, in both cases, there is an association with
predictive tracking. In the case of \emph{negative-social} , this is the
application of physics rules associated with gravity. Following on from
the work of Faiola et al., (2020) and MacNeilage \& Glasauer, (2018), we
can make a testable prediction that downward gravity stimuli will
specifically drive predictive responses in both the FEF and the
cerebellum. On the other hand, the \emph{positive-odd} case is
associated with the learning of physics rules that enable prediction but
contravene expectations of natural physics. In such a context, we expect
that there will still be contributions from the FEF to support the
anticipatory aspects of the task, but less of a contribution from the
cerebellum in terms of physics rules of gravity (MacNeilage \& Glasauer,
2018; Dakin, Peters, Giunti \& Day, 2018).

Conclusion

In this work, we showed that the participant tracking of the motion of a
ball subjected to downward gravity was faster and better than tracking
under the contravention of physics rules introduced by our antigravity
condition. Performance, however, revealed large individual differences
which we analysed along with inventories of ASD traits and schizotypy,
to unveil two key findings which come with testable predictions. The
first is that the positive-odd cluster of characteristics is expected to
be specifically associated with the use of learnt rules that contravene
physics, while the second is that the \emph{negative-social} cluster is
expected to be associated with the use of an established potentially
pre-attentive prior. We therefore encourage colleagues to consider
testing these arising predictions in imaging, behavioural and clinical
studies.

\textbf{Acknowledgements}

We thank Bournemouth University for financial support during the
experiments and King's College London for subsequent financial support.
We also thank colleagues at the Institute de Neuroscience de la Timone
in Marseille for useful discussions during the preparation of the
manuscripts.

\textbf{Data Accessibility}

We will make data available following any requests. Following
publication, we will make anonymised data available online.

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