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Global saccadic adaptation
Martin Rolfs a,b,*, Tomas Knapen b,c, Patrick Cavanagh b
aNew York University, Department of Psychology, 6 Washington Place, 10003 New York, NY, USA
bUniversité Paris Descartes, Laboratoire Psychologie de la Perception, 45 rue des Saints-Pères, 75006 Paris, France
cUniversity of Amsterdam, Department of Psychology, Roeterstraat 15, 1018 WB Amsterdam, The Netherlands
a r t i c l e i n f o
Article history:
Received 20 December 2009
Received in revised form 10 June 2010
Keywords:
Motor plasticity
Motor learning
Adaptation
Eye movements
Saccade
Oculomotor control
a b s t r a c t
Our actions need constant calibration to arrive accurately at locations of their intended goals; errors in
execution must drive rapid adjustments. As an example, saccadic eye movements are vital for bringing
objects of interest into the high-acuity center of vision and they must be continually tuned to compensate
for ongoing changes in body, muscle strength and neural variability. This adaptation of eye movement
responses can be induced artificially by systematically displacing the saccade targets by a constant pro-
portion during each saccade. Observers do not notice these shifts and yet the oculomotor system does,
rapidly compensating for the landing error until the saccades finally land close to the artificially displaced
target. This recalibration has been described as spatially selective, dropping off with distance in direction
and amplitude from the adapted saccade vector. However, we now report that this local adaptation prop-
erty is a consequence of adapting to only one direction at a time, the method generally used in previous
studies. When we induced adaptation in all directions, using a quasi-random walk where each target was
displaced 25% back toward to the previous fixation, we found strong, spatially generalized adaptation
that could not be accounted for by an accumulation of many vector-specific adaptations. This global
adaptation is a plausible strategy for calibration given the absence of any obvious growth changes or
muscle deficits that would lead to vector specific losses and it provides a robust model for testing motor
calibration.
 2010 Elsevier Ltd. All rights reserved.
1. Introduction
Plasticity is a fundamental prerequisite of goal-directed behav-
ior as it maintains an accurate calibration of motor acts to percep-
tual input. The necessity of this calibration process is particularly
evident for saccades, the rapid eye movements that we generate
several times per second to bring objects of interest onto the fovea,
the site of high visual acuity. It has been shown that if the position
of a saccade target is systematically shifted during several succes-
sive saccades, its amplitude adapts to compensate for the shift
(McLaughlin, 1967). This recalibration process is known as saccadic
adaptation (Hopp & Fuchs, 2004) and takes place while the obser-
ver is often oblivious to the intra-saccadic displacements (Bridg-
eman, Hendry, & Stark, 1975). Saccadic adaptation is considered
to be quite local—specific to the adapted vector and dropping off
quickly with distance in polar coordinates. This vector-specificity
is a robust finding, shown consistently in monkeys (Deubel,
1987; Noto, Watanabe, & Fuchs, 1999; Straube, Fuchs, Usher, &
Robinson, 1997; Watanabe, Noto, & Fuchs, 2000) and humans (Al-
bano, 1996; Alahyane, Devauchelle, Salemme, & Pélisson, 2008;
Collins, Doré-Mazars, & Lappe, 2007; Deubel, 1987; Frens & van
Opstal, 1994; Miller, Anstis, & Templeton, 1981). In fact, opposite
gain changes can be obtained for saccades in the same direction
if their amplitudes differ sufficiently (Watanabe et al., 2000). Based
on these results it has been claimed that a critical neural substrate
determining saccadic adaptation lies in those oculomotor struc-
tures where saccades are still represented as vectors, e.g., the supe-
rior colliculus (SC) or the frontal eye fields (Hopp & Fuchs, 2004,
2006), rather than in more peripheral structures that implement
their global horizontal and vertical component signals sent to the
extraocular muscles (Sparks, 2002). Indeed, recent evidence sug-
gests a causal role of the SC in sending instructive signals for sacc-
adic adaptation (Kaku, Yoshida, & Iwamoto, 2009).
While the specificity of these processes is impressive, the func-
tion of vector-specific saccadic adaptability has been puzzling. Sac-
cade performance is affected by many factors such as fluctuations
in alertness due to fatigue (Barton, Jama, & Sharpe, 1995), rest, the
consumption of stimulating substances, as well as long-term fac-
tors like growth, aging (Warabi, Kase, & Kato, 1984), strengthening,
weakening or even palsy of (Abel, Schmidt, Dell’osso, & Daroff,
1978; Kommerell, Oliver, & Theopold, 1976) or lesions to the extra-
0042-6989/$ - see front matter  2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.visres.2010.06.010
* Corresponding author at: Université Paris Descartes, Laboratoire Psychologie de
la Perception, 45 rue des Saints-Pères, 75006 Paris, France. Fax: +33 1 42863322.
E-mail address: martin.rolfs@gmail.com (M. Rolfs).
URL: http://www.martinrolfs.de (M. Rolfs).
Vision Research 50 (2010) 1882–1890
Contents lists available at ScienceDirect
Vision Research
journal homepage: www.elsevier .com/locate /v isres

Author's personal copy
ocular muscles (Optican & Robinson, 1980; Snow, Hore, & Vilis,
1985). All of these factors have global effects on saccades, but
the accumulation of adaptation of saccades in all different direc-
tions independently would be slow and inefficient (Scudder, Bato-
urina, & Tunder, 1998). Moreover, due to the statistical nature of
the external and internal environments, the errors that saccadic
adaptation corrects occur at many different scales in both time
and space. Because of this generality, it is not surprising that motor
adaptation occurs at many different timescales (Körding, Tenen-
baum, & Shadmehr, 2007; Srimal, Diedrichsen, Ryklin, & Curtis,
2008), and spatially general adaptation, the opposite of direction-
ally specific adaptation, may also be expected. In fact, a recent
study by Garaas, Nieuwenhuis, and Pomplun (2008) reported rapid
changes in saccade gain when a visual search display was gaze-
contingently shifted in the direction opposite each eye movement.
Pursuing other goals, this study did not investigate whether gener-
alized recalibration relies on mechanisms of plasticity that are dif-
ferent from those studied in the saccadic adaptation literature.
Introducing a new, generalized version of the classical adapta-
tion paradigm (McLaughlin, 1967), we now provide detailed evi-
dence for a separate, global recalibration process of saccade gains
that accumulates more strongly than vector-specific adaptation.
Twelve human observers continuously re-fixated a visual target
stepping in a quasi-random walk across the display (Fig. 1A, top
row), allowing us to measure the baseline gain of saccades for dif-
ferent directions and amplitudes before adaptation (distribution of
possible target steps shown in Fig. 1B). One hundred of these test
trials were followed by a block of 200 adaptation trials (Fig. 1A,
middle row), which differed across the three different conditions.
The distribution of possible target steps in adaptation trials are
shown in Fig. 1C. During Global adaptation (Fig. 1A and C, left col-
umns), the saccade target continued stepping along a quasi-ran-
dom path. However, the presaccadic target was displaced during
each saccade to end up 25% closer to the initial fixation position
(back-step), where it was seen by the observer after the saccade.
During One-way adaptation (Fig. 1A and C, middle columns), only
8 saccades in one direction were adapted, while return saccades
in the opposite direction did not trigger a trans-saccadic back-step
of the target. In this condition we replicated the classical finding
that adaptation drops off as a function of saccade direction. Finally,
during Two-way adaptation (Fig. 1A and C, right columns), a condi-
tion designed to control if consistent visual feedback across all tar-
get steps explains the data obtained in the Global adaptation
paradigm, we adapted 8 saccades in two opposite directions at
the same time. Following the adaptation block, we tested for
changes in saccade amplitudes by running another block of 100
test trials, which where randomly interleaved with another 200
adaptation trials to keep up adaptation (Fig. 1A, bottom row). Com-
paring the time course and spatial transfer of adaptation across
these conditions, we reveal a general recalibration of saccade gains,
pointing to basic saccadic adaptation mechanisms at the final
stages of oculomotor processing whose neurophysiological corre-
lates have yet to be explored.
2. Methods
2.1. Observers
We tested 12 observers (6 female, age 19–32, 8 right-eye dom-
inant, 10 right-handed); all but author TK and colleague RA were
naïve to the goals of the study. They had normal or corrected-to-
normal vision and gave their informed consent before study partic-
ipation. The experiments were conducted in accordance with the
Declaration of Helsinki.
2.2. Experimental setup and stimuli
Observers sat in a silent and dimly lit room with the head posi-
tioned on a chin rest, 63 cm in front of a computer screen. Stimuli
were red (3.5 cd/m2) and black (0.15 cd/m2) 0.2-diameter dots on
a gray background (16.5 cd/m2), presented on a 22” Formac ProN-
B
Test trials
4º
12º
Fixation
Global / One-way /
Two-way
Sa
m
pl
ed
d
is
tri
bu
tio
n
of
ta
rg
et
lo
ca
tio
ns
reference frame: retina
Two-wayGlobal
4º
12º
One-way
8º
Non-adapting target
(return saccades)
Adapting
target
C Adaptation trials
Sa
m
pl
ed
d
is
tri
bu
tio
n
of

ta
rg
et
lo
ca
tio
ns
reference frame: retina
Ad
ap
ta
tio
n
(2
00
tr
ia
ls
)
Po
st
-a
da
pt
at
io
n
(1
00
+
2
00
tr
ia
ls
)
Pr
e-
ad
ap
ta
tio
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(1
00
tr
ia
ls
)
A Global
1
2
34
5
1
2
3
4
5
1
2
3
45
One-way
1 2
3
4
5
1 2 3 45
12
3
4 5
Two-way
1
2
3
4 5
123
4 5
1
2
3
4 5
reference frame: screen
Adapting target
steps back 25%
during the saccade
Non-adapting target
does not move
during the saccade
Pre-saccadic
target
Post-saccadic
target
Fixation
Pre-saccadic
target
Post-saccadic
displaced target
Fixation
Legend
Fig. 1. Experimental procedure in the three adaptation conditions. A For each of the three blocks of trials in an experiment, five subsequent example target steps (see Legend)
are shown as they occurred on the screen. Numbers are placed next to the pre-saccadic target. In the One-way and Two-way adaptation blocks, target vectors fall on the same
path, because only horizontal saccades were used. B and C Illustration of the pool of target steps sampled in test and adaptation trials, respectively, for each of the three
adaptation conditions. Filled green and blue regions indicate that target steps distributed across the depicted annulus, including any direction between 0 and 359 and any
amplitude between 4 and 12. For comparison, filled gray regions highlight these annuli in the depiction of One-way and Two-way adaptation trials. Legend Two types of
target steps used; Non-adapting (green): single saccade-triggering target step; Adapting (blue): saccade-triggering target step, stepped back 25% intra-saccadically. (For
interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
M. Rolfs et al. / Vision Research 50 (2010) 1882–1890 1883

Author's personal copy
itron 22800 screen with a spatial resolution of 768  1024 pixels
run at a vertical refresh rate of 145 Hz. Gaze position of the dom-
inant eye was recorded and available online using an EyeLink
1000 Desktop Mount (SR Research, Osgoode, Ontario, Canada) with
an average spatial resolution of 15 to 30 min-arc, sampling at
1000 Hz. The experiment was controlled by an Apple MacPro com-
puter; manual responses were recorded through a standard key-
board. The software controlling stimulus presentation and
response collection was implemented in MATLAB (MathWorks, Na-
tick, Massachusetts, USA), using the Psychophysics (Brainard,
1997; Pelli, 1997) and EyeLink toolboxes (Cornelissen, Peters, &
Palmer, 2002).
2.3. Procedure
Observers performed three conditions, each separated by at
least a week, their order counterbalanced across observers. An
experiment consisted of three blocks of trials, a pre-adaptation
block (100 test trials), an adaptation block (200 adaptation trials),
and a post-adaptation block (100 test trials and 200 adaptation tri-
als randomly interleaved, to maintain adaptation at a constant le-
vel). Fig. 1A shows examples of the paths these target steps
created. On every trial, the direction of the saccade to be made
was drawn randomly from the pool of possible target steps, illus-
trated in Fig. 1B and C, with the constraint that the fixation target
was displaced within the invisible borders of a circular field (diam-
eter of 24 centered on the screen; dashed line in Fig. 1A). The first
trial started from the screen center and subsequent trials contin-
ued from the latest target position. In test trials, target steps could
be in any direction (0–359, in steps of 1), with an amplitude
range of 4–12 (in steps of 0.04, the size of a pixel on the screen).
In adaptation trials, possible target steps differed between experi-
ments. In the Global adaptation experiment, we sampled from the
same range of target steps in adaptation trials as in test trials, thus
all adaptation trials included an intra-saccadic back-step. In the
One-way adaptation experiment, the 200 adaptation trials con-
sisted of 8 target steps, either to the left (six observers) or to the
right (remaining six observers), that were followed by an intra-
saccadic back-step and an equivalent amount of return target-
steps in the opposite direction. These non-adapting trials were
interspersed for two reasons: to remain within the circular area
and to replicate traditional studies on saccadic adaptation, in
which adapting target steps are usually followed by a (non-
adapted) return saccade to a fixation location. Finally, the Two-
way adaptation experiment was identical to the One-way, except
that we adapted 8 saccades to the left and to the right at the same
time. Hence, all saccade-triggering target-steps were followed by a
back-step of the target during the saccade.
Each trial started with a small red fixation target. When fixation
had been detected continuously for 200 ms in a circular fixation
area (diameter of 3 centered on the target), the target turned black
and, after a fixation period of 500–1000 ms, jumped to a new posi-
tion. Observers were instructed to follow the target with the eyes.
In test trials, target position was not changed during the saccade.
Eye position was monitored throughout the trial. In adaptation tri-
als sampling an adapting saccade target vector, saccades triggered
an immediate back-step of the target stimulus, placing it 25% clo-
ser to its previous location. Saccades were detected online as soon
after target presentation as the eyes left the boundary of the fixa-
tion area. The next trial started 750 ms later. When fixation broke
due to blinks or large eye movements during the fixation period, a
warning appeared on the screen asking observers to maintain fix-
ation and the trial was rerun immediately.
In every back-step trial the target was displaced before the eye
landed, during saccadic suppression of displacement (Bridgeman
et al., 1975). Observers were instructed to press a key immediately
whenever they saw a displacement of the target during the eye
movement. This occurred in 1.8%, 1.6%, and 0.9% of all back-step
trials (hits), primarily during the first trials in the adaptation block,
and in 0.5%, 0.7%, and 1.0% of the non-adapting trials (false alarms)
in One-way, Two-way, and Global adaptation conditions, respec-
tively. Fig. 2 shows the frequency of perceptual reports across
the entire experiments.
The first two blocks were preceded by a standard nine-point
grid calibration–validation procedure of the eye tracker. During
the second and third block, i.e., after adaptation had started, cali-
bration was repeated whenever fixation could no longer be de-
tected in the fixation area (due to blinks or anticipatory eye
movements). To prevent the incorporation of saccadic adaptation
in the calibration, eye positions on calibration targets were ac-
cepted manually and only after several seconds.
2.4. Data analysis
All data of observers where One-way adaptation was applied to
leftward saccades was mirrored along the vertical axis and then
underwent a common analyses scheme with the data of observers
where the adaptation was applied to rightward saccades. Offline
saccade detection was based on an algorithm described by Engbert
and Mergenthaler (2006). Smoothed velocities were computed
using a moving average over five subsequent eye position samples
in a trial. Saccades were detected as outliers in 2D-velocity space,
exceeding the median velocity by 5 SD for at least 8 ms (eight sub-
sequent samples). Overshoots in saccades often result in the detec-
tion of two saccades, thus events separated by 20 ms or less were
merged into a single saccade. Response saccades were defined as
the first saccade that brought the eye to a circular region around
the presaccadic target with a radius of half its eccentricity. We ex-
cluded 4.6% of all trials from further analyses because blinks, no re-
sponse saccade, or saccades larger than 1 before the response
saccade were detected.
All confidence intervals were computed using standard boot-
strapping techniques. For a given dependent variable, we gener-
ated 1000 bootstrap samples (sampling with replacement) from
our original sample of 12 data sets. The variable’s standard devia-
tion across these 1000 bootstrap samples is a reliable estimator of
the standard error of the population (Efron & Tibshirani, 1993); by
multiplying it by 1.96, we obtained a 95% confidence interval.
Hence, we can be 95% certain that it contains the true mean of
the population. Where confidence intervals are reported for data
curves (e.g., in Fig. 4), we first computed curves for each individual
and then submitted these to the bootstrapping procedure.
The computation of baseline saccade gains (see Appendix A) as
well as all smoothing was done using the nonparametric LOWESS
procedure (Cleveland, 1979), a robust locally weighted regression
One−way
Two−way
Global
Trial number
R
ep
or
t [
%
]
100 200 300 400 500 600
0
0.01
0.02
0.03
Pr
e-
ad
ap
ta
tio
n
Ad
ap
ta
tio
n
Po
st
-a
da
pt
at
io
n
Fig. 2. The percentage of trials on which observers reported perceiving displace-
ments of the target across the saccade is plotted as a function of trial number in the
three subsequent blocks. Note that the area under each curve corresponds to the
total percentage of trials with reports (temporal resolution is 1 trial), resulting in
very low values at the y-axis. Shaded regions show 95% confidence intervals.
1884 M. Rolfs et al. / Vision Research 50 (2010) 1882–1890

Author's personal copy
with a bisquare weight function. The smoothness factor f was gen-
erally set to 0.3 (proportion of data used in fitting each value), ex-
cept in the time course analyses where data were smoothed to a
lesser extent to not average out fast changes in the proportion of
adaptation. Here f was adjusted for each condition separately such
that only the eight nearest data points contributed to each com-
puted value.
3. Results
3.1. Baseline data
In the pre-adaptation test trials, our observers exhibited clear
individual baseline patterns of saccadic under- or overshoots as a
function of target direction. These patterns did not show system-
atic differences across conditions. However, because they varied
considerably across observers and sessions, the proportion of adap-
tation was expressed relative to these baseline values. To this end,
all saccade amplitudes were transformed to saccade gains (saccade
amplitude divided by the target step amplitude), expressed as a
proportion of potential adaptation (henceforth, proportion of adap-
tation), and baseline-corrected using the data collected in the pre-
adaptation block (see Appendix A for a detailed description of this
procedure). Full or 100% adaptation would bring the adapted sac-
cades 75% of the distance to the target as the target was always
stepped back by 25% before the saccade landed. Thus, proportions
of 0 signify that saccades land close to the presaccadic target
(where they would land before adaptation); proportions of 1 sig-
nify that saccades move the eyes only 75% of that amplitude, so
that they land close to where the post-saccadic, displaced target
is presented in adapting trials.
3.2. Time course of adaptation
First, we analyzed the evolution of adaptation across adaptation
trials in the adaptation blocks of our experiments. Individual evo-
lutions of the proportion of adaptation were smoothed and subse-
quently averaged across observers. Fig. 3A shows the resulting
curves for each of the three conditions tested; individual data are
plotted as thin gray lines in the background. For all three condi-
tions, the proportion of adaptation changed rapidly over the first
trials and decelerated continuously before reaching an asymptotic
level of about 0.5–0.7 (corresponding to a 12.5–17.5% change in
saccade gain). For comparison, we superimposed these curves in
Fig. 3B. Evidently, the average change in adaptation in the Global
condition was at least as fast as adaptation in the One-way condi-
tion even though many different directions were recalibrated
rather than one principal direction.1
To compare the speed of adaptation across conditions in a quan-
titative manner, we drew 1000 bootstrap samples from the data
pool, computed their averages, and for each of them fitted an expo-
nential function of the form
c^ðtÞ ¼ c cets; ð1Þ
where c is the asymptotic proportion, s is the rate constant of the
adaptation process, and t denotes the trial. This function assumes
that the average proportion of adaptation is zero in the first trial,
which was set to be the case for each sample. The fits of this func-
tion to the original sample averages are shown as dashed lines in
Fig. 3B; the average parameters (±95% confidence intervals) ob-
tained are shown in Fig. 3C. While Global adaptation reached the
highest asymptote, it also had the shortest rate constant, that is, it
evolved at the highest speed. The asymptotic proportion of adapta-
tion was slightly lower for One-way adaptation and again slightly
lower for Two-way adaptation. Conversely, the rate constants ob-
tained in these conditions were slightly longer than in the Global
adaptation condition. These results suggest that despite the fact
that only one or two saccade vectors were adapted at the same
time, adaptation in these conditions was not faster than in the Glo-
bal adaptation condition. It is also noteworthy that while the expo-
nential fits describe well the evolution of adaptation in the One-way
and Two-way conditions, they tend to underestimate both the ini-
tial speed and the asymptote of adaptation in the Global condition.
The time course of Global adaptation was better fit by a power law
function. Conducting similar analyses as the ones reported here
using power law fits yielded the same pattern of results.
Adaptation trial number
Pr
op
or
tio
n
of
a
da
pt
at
io
n
Post−adaptationAdaptation
20 40 60 80 100 120 140 160 180
0
0.2
0.4
0.6
0.8
Adaptation trial number
Two−way adaptation
20 40 60 80 100
0
0.5
1
0
0.2
0.4
0.6
G
lo
ba
l
O
ne
−w
ay
Tw
o−
w
ay
As
ym
pt
ot
e
Parameter
estimates
0
10
20
30
R
at
e
co
ns
ta
nt

Global adaptation
0
0.5
1
Pr
op
or
tio
n
of
a
da
pt
at
io
n
One−way adaptation
0
0.5
1
BA C
Global
One−way
Two−way
Fit Data
Fig. 3. Time course of adaptation. (A) The evolution of adaptation across adaptation trials in the adaptation block is plotted for each of the three conditions tested. Bold lines
show the average across individual data (thin gray lines). (B) Superimposed average time courses of adaptation in the three conditions (solid lines) and exponential fits of
these average curves (dashed lines). Note that although the Global condition includes saccades in all directions, the rate of adaptation was similar to that in the other
conditions. The error bars to the right show the average proportion of adaptation in adaptation trials of the post-adaptation block with 95% confidence intervals. (C) Estimates
of the rate constants and asymptotic proportions of adaptation for the three conditions tested. Error bars are standard errors of the mean.
1 We ensured the validity of this comparison by juxtaposing the time course of
Global adaptation trials with target steps in the amplitude range of One-way
adaptation (6.5–9.5) to that of other amplitudes. Speed and magnitude of adaptation
were virtually identical between these two subsets of trials, reassuring us that there
was no systematic disadvantage for saccades in the medium amplitude range, hence,
for the One-way condition.
M. Rolfs et al. / Vision Research 50 (2010) 1882–1890 1885

Author's personal copy
3.3. Spatial extent of adaptation
The polar plots in Fig. 4A show the proportion of adaptation ob-
served in the post-adaptation test trials as a function of target direc-
tion and averaged across 12 observers (means are shown with 95%
confidence bands). In the Global adaptation condition (panel one in
Fig. 4A) saccades of all directions were strongly adapted. The aver-
age proportion of adaptation obtained in this condition was about
0.5 (corresponding to a 12.5% change in saccade gain). In contrast,
One-way adaptation resulted in a vector-specific, though broadly
tuned recalibration of saccade gains (panel two in Fig. 4A) having
a maximum average proportion of adaptation of about 0.44 (corre-
sponding to a 11% change in saccade gain) in the direction of
adaptation, dropping to 0 for saccades in the opposite direction,
replicating the well-established direction-specific adaptation con-
sistently found in this paradigm (e.g., Deubel, 1987; Frens & van Op-
stal, 1994). Two-way adaptation yielded a similar pattern of
adaptation transfer, but affecting both leftward- and rightward sac-
cades (panel three in Fig. 4A). Thus, adaptation was strongest near
the adapted, horizontal saccade directions and somewhat weaker
for vertical saccades. In all conditions, the directional extent of
the adaptation is broader in the downward direction. The individual
data contributing to these averages (shown in Fig. 4B) and similar
individual data in other studies (Deubel, 1987; Frens & van Opstal,
1994) suggest that this biased pattern is not an exception.
The top row of panels in Fig. 4C shows the mean differences in
the proportion of adaptation as a function of target direction and
for all combinations of conditions: Global vs. One-way, Two-way
vs. One-way, and Global vs. Two-way adaptation. The scale ranges
between 0.5 and 0.5 (corresponding to ±12.5% change in saccade
gain), with positive values depicting greater adaptation in the first
than in the second condition. Departures of the shaded 95% confi-
dence band from zero (the center ring highlighted in dark gray in
each polar plot) reveal significant differences between conditions.
As shown in the first polar plot of Fig. 4C, Global adaptation af-
fected saccade gains much stronger than One-way adaptation for
all saccade directions except a wedge of about 60 sourrounding
the saccade direction adapted in One-way adaptation. Also, adap-
tation is greater in the Two-way than in the One-way condition
(second polar plot in Fig. 4C), but only for saccades opposite the
direction of the adapted saccade vector in the One-way condition.
Finally, Global adaptation achieves significantly greater adaptation
in the vertical directions as compared to Two-way adaptation
(third polar plot in Fig. 4C). Global adaptation was not inferior to
Two-way adaptation in any direction.
We conducted equivalent analyses on the transfer of adaptation
across different saccade amplitudes. The results are shown in the
bottom panels of Fig. 4A. Across saccade amplitudes, as across sac-
cade directions Global adaptation resulted in stronger adaptation
than the two other conditions (bottom panels in Fig. 4C). The level
of adaptation was largely independent of the amplitude of the sac-
cade target step. This could be expected for the Global adaptation
condition, but we found the same amplitude-independence for the
One-way and Two-way conditions and even for test saccadeswithin
±30 of the direction that was adapted in the One-way condition
(dashed lines), in line with a general gain control mechanism affect-
ing saccades of all amplitudes (Deubel, Wolf, & Hauske, 1986; Deu-
bel, 1987).2
B
1
0
1
0
1
0
1
0 0
1 1
0
1
0
1
0
1
0
1
0
1
0
1
0
Observer 01 Observer 02 Observer 03
Observer 06Observer 05Observer 04
Observer 09Observer 08Observer 07
Observer 12Observer 11Observer 10
1
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0
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Amplitude [deg]
1
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0
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Amplitude [deg]
1
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0
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Amplitude [deg]
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op
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n
of
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One-wayA Two-wayGlobal
4 8
Amplitude [deg]
4 8 12
Amplitude [deg]
0
0.5
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Amplitude [deg]
0.5
0
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0
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0
Global – Two-wayGlobal – One-way
D
iff
er
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ce
in
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C Two-way – One-way
Pr
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of
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Fig. 4. Spatial extent of adaptation. A The proportion of adaptation after Global, One-way-, and Two-way adaptation is plotted as a function of target direction (upper panels)
and amplitude (lower panels). Thick, colored lines represent the average across observers; shaded areas provide 95% confidence intervals. For comparison, dashed lines in the
lower panels show the results for target directions within ±30 of the direction that was adapted in the One-way condition. Error bars are 95% confidence intervals. B
Individual data as a function of target direction for the 12 observers contributing to the averages in A. C Differences in the proportion of adaptation between Global – One-way
adaptation, Two-way – One-way adaptation, and Global – Two-way adaptation are shown as a function of target step direction (upper panels) and amplitude (lower panels).
For each comparison, positive values signify stronger adaptation in the first compared to the latter condition. Shaded 95% confidence bands reveal significant inter-condition
differences when they do not overlap with zero. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2 An analysis of all subjects’ data combined suggested that adaptation showed
some selectivity as a function of saccade amplitude in the adapted directions but the
test of these 2D-landscapes versus the equivalent landscape with gain equalized
along each direction (set to the mean at that direction so having no amplitude-
specific pattern) showed no significant difference. So we conclude that the amplitude
specific pattern did not reach significance.
1886 M. Rolfs et al. / Vision Research 50 (2010) 1882–1890

Author's personal copy
3.4. Global adaptation is not accumulated vector-based adaptation
We observed a global change in saccade gains in the Global
adaptation condition, which may be the result of either (1) a recal-
ibration of saccade gains accumulating across many individually
adapted vectors or (2) a fast and global recalibration mechanism.
The fact that the direction-independent recalibration of saccade
gains in the Global adaptation condition was of a similar magni-
tude and developed at a comparable speed as the direction-specific
adaptation in the One-way condition render the first hypothesis
unlikely; further analyses let us reject it. First, we show that the
amount of adaptation accumulated in the Global condition is sig-
nificantly higher than that in the other conditions. Second, based
on our results in the One-way condition, we simulate an accumu-
lation of adaptation across many directions and show that this
simulation falls short of predicting the results of our Global adap-
tation condition.
3.4.1. Amount of accumulated adaptation
One direct test of the accumulation hypothesis is to compute
and compare the area under the curve for all three conditions. In-
deed, the far greater adaptation resulting from global adaptation is
evidenced by the fact that when taking the area under the curve as
a proxy, Global condition accumulated 2.44 ± 0.91 (mean and 95%
confidence intervals) times as much adaptation as the One-way
condition, and even 1.35 ± 0.18 times that in the Two-way condi-
tion. Since confidence intervals of these ratios do not overlap with
1, these differences are significant. Two-way adaptation was
1.81 ± 0.66 times as strong as One-way adaptation, again different
from 1. The expected sum of two individual One-way adaptation
processes is 2, well within the confidence limits of this ratio.
In the analysis of adaptation as a function of saccade amplitude,
the Global condition accumulated 2.39 ± 0.89 times as much adap-
tation as the One-way condition, and 1.32 ± 0.16 times that in the
Two-way condition. Again, since confidence intervals of these ra-
tios do not overlap with 1, these differences are significant. Two-
way adaptation was 1.93 ± 0.63 times as strong as One-way adap-
tation. This ratio is significantly different from 1. It is, however,
very close to 2, the expected sum of two individual One-way adap-
tation processes, showing that unlike the Global adaptation condi-
tion, the Two-way adaptation, can be explained as an accumulation
of direction-selective adaptation that is estimated from the One-
way data.
3.4.2. Simulation of global adaptation as accumulation of vector-
specific adaptation
The result that Global adaptation accumulated more than two
times the adaptation achieved in the One-way condition while
evolving at a similar (or faster) speed suggests that one can not ex-
plain the adaptation in the Global condition from the characteris-
tics of One-way adaptation. To test this idea directly, we ran
simulations of a simple, data-driven dynamic model generating
predictions for the speed and magnitude of Global adaptation if
it had been a result of accumulated direction-specific adaptation.
First, we quantified the spatial properties of adaptation in the
One-way condition. To do this, we took all subjects’ data and fit a
von Mises shaped function to the strength of the adaptation as a
function of target direction. The von Mises distribution is the circu-
lar version of a normal distribution and is given by
Mð/jl;jÞ ¼ e
jcosð/lÞ
2pI0ðjÞ
; ð2Þ
where j defines the width of the circular distribution (for j = 0 val-
ues are uniformly distributed across angles /), l is the direction of
the maximum of the distribution, and I0 is a modified Bessel func-
tion of order 0. While l and j define the shape of the data, we intro-
duce two additional parameters, cM and b, which allow to scale and
offset the obtained von Mises distribution, respectively.
The resulting function, fitted to the One-way data, can be writ-
ten as follows:
MOneð/jl;j; b; cMÞ ¼ bþ cMejcosð/lÞ; ð3Þ
which we will henceforth refer to as MOne(/). We can incorporate
the spatial and temporal characteristics of One-way adaptation into
a model in order to simulate the system’s behavior when given the
global saccadic adaptation paradigm as input. Because saccadic
adaptation is driven by post-saccadic visual error (Noto & Robinson,
2001; Wallman & Fuchs, 1998) on a trial-by-trial basis (Srimal et al.,
2008), any model of saccadic adaptation should incorporate this vi-
sual error signal and the current state of adaptation. For One-way
adaptation, we know both the time course of adaptation and its
resultant directional profile and these are used as the parameters
of a simple leaky-integrator model,
Að/; t þ 1Þ ¼ 1 1sOne
 
Að/; tÞ þ 1sOne
MOneð/ /tÞ; ð4Þ
where the adaptation for any direction / at trial t + 1, A(/, t + 1), is
computed as the weighted average of the current state of adapta-
tion for that direction, A(/, t), and the incurred input signal (visual
error) impinging on that direction, MOne(/  /t), i.e., MOne(/) shifted
by the current target direction /t. In this model, the input signal has
a strong impact at early trials, driving adaptation at a high speed,
but as adaptation accumulates the input’s influence diminishes,
leading to a saturation of the adaptation process. Both MOne(/)
and sOne were derived from the results of the One-way condition
and so this model, when run with an input sequence corresponding
to a One-way condition experiment, reproduces the time-course
and directional extent of One-way adaptation (see Fig. 5A and C;
note that in this illustration, for the sake of comparability, we ex-
press the proportion of adaptation relative to the asymptotic adap-
tation obtained for rightward saccades in the One-way condition).
If the results of our Global condition are explicable from the re-
sults of the One-way condition, using a sequence of adapting sac-
cades from a Global condition experiment this model should
produce the results from our Global condition. However, if Global
saccadic adaptation engages additional adaptive processes, One-
way adaptation cannot explain the full extent of the results of
our Global condition. In this case, this simulation should result in
less adaptation than is the case in the One-way condition. Note
that here we have assumed that adaptation is not amplitude-spe-
cific, an assumption that is known to be incorrect (Watanabe
et al., 2000). However, we find no evidence of this amplitude spec-
ificity in our data, so for reasons of simplicity we chose to omit this
factor.
Fig. 5B and C show that running the simulation described above,
using an input pattern taken from an actual Global adaptation
experiment, i.e., a random sequence of target directions (see lower
panel in Fig. 5C), results in far lower levels of adaptation (solid red
lines) than is actually the case in the Global condition (dashed red
lines). Clearly, Global adaptation when built up out of accumulated
vector-specific adaptation as found in the One-way condition does
not explain the amount of adaptation we found in our Global con-
dition experiments. This result indicates that Global saccadic adap-
tation involves additional adaptive processes.
4. Discussion
We introduced a generalized version of the classical saccadic
adaptation paradigm, providing a consistent postsaccadic cue to
miscalibration of saccade gain in all directions. In response to this
M. Rolfs et al. / Vision Research 50 (2010) 1882–1890 1887

Author's personal copy
cue, we observe a fast and powerful recalibration process for sacc-
adic eye movements, globally reducing the gain for all saccade vec-
tors tested. We also replicated the well-documented finding of
direction-specific adaptation in our One-way condition (Albano,
1996; Alahyane et al., 2008; Collins et al., 2007; Deubel, 1987;
Frens & van Opstal, 1994; Noto et al., 1999; Miller et al., 1981; Stra-
ube et al., 1997). Clearly, this vector-based adaptation can not ac-
count for our results, because adaptation in the One-way
condition would have had to be significantly stronger than adapta-
tion in the Global condition. That was not the case. Despite the fact
that a broad range of saccade vectors was adapted in the Global
adaptation condition, adaptation proportion developed at a similar
speed as in the One-way adaptation condition, and similar asymp-
totes for the adapted saccades were achieved in both conditions. If
anything, our time course analyses indicate a slightly faster recal-
ibration of saccade gains in the Global adaptation condition, sug-
gesting that the underlying processes, even though affecting all
vectors in general and accumulating almost 2.5 times as much
adaptation, are not slower than those implementing vector-spe-
cific adaptation. This conclusion is corroborated by the fact that
the attempt to model Global adaptation as accumulating vector-
based adaptation resulted in less than half the adaptation observed
in that condition. So, without specifically adapting saccades of a
certain direction and amplitude (but adapting many others), these
saccades are adapted equally strongly using Global adaptation as
when they were explicitly adapted using the traditional paradigm.
Two potential mechanisms for global adaptation are possible
(1) the presence of consistent error signals rather than the incon-
sistent error signals in the traditional one-way adaptation where
one direction is adapted but the return is not; and (2) the existence
of a general gain control for all saccades. The results of the Two-
way adaptation condition studied here enable us to evaluate the
relative contributions of these two factors. In this condition, con-
sistent feedback was provided for all saccades triggered during
adaptation, yet these saccades were always in two opposite direc-
tions. The first of the above hypotheses would predict a similar
transfer of adaptation as in the Global adaptation condition. How-
ever, transfer in the Two-way adaptation condition closely mim-
icked the combination of two One-way adaptation processes,
replicating earlier findings (Deubel, 1987). Moreover, large differ-
ences in adaptation were obtained between Global and Two-way
adaptation for saccade directions furthest from those adapted in
Two-way adaptation. We conclude, therefore, that vector-specific-
ity is or has evolved to be (by accumulation of evidence across tri-
als that specific saccade directions need a gain change) the
dominant factor in Two-way adaptation. Alternatively, vector-
specificity in the Two-way condition may be the result of inconsis-
tent error feedback for non-adapted directions, which are only trig-
gered in non-adapting test trials. Thus, adaptation in these
directions may have quickly recovered during the first test trials.
A re-analysis of our data rendered this possibility unlikely: Even
if only the first few post-adaptation test trials were analyzed, we
obtained similar directional transfer (see Fig. 6).
A fast global recalibration mechanism of saccade gains seems at
odds with results from a study by Scudder et al. (1998). These
authors compared saccadic adaptation when monkeys made sac-
cades to random locations in either a 1 by 2 or a 5 by 3 position grid
of possible target locations. In that study, adaptation was found to
evolve slower if more target locations were possible, as predicted
by an accumulation of multiple vector-based adaptation pro-
cesses. Unfortunately, the authors collapsed hundreds of adapta-
tion trials into a single data point, veiling any potential fast
adaptation mechanisms if they were present. Moreover, the
differences between their study and ours are numerous, including
A B C
Fig. 5. Results obtained from a simulation of the leaky-integrator model. A and B Final spatial extent (thick lines) of One-way (A) and Global (B) adaptation for the simulation
run shown in panel C. Thin solid lines depict the gradual change in adaptation as across trials; brighter colors depict earlier trials. Dashed lines provide the actual average data
for reference (as reported in Fig. 4A). C Time course of adaptation for rightward saccades (the results for Global adaptation hold for all saccade directions). During adaptation,
One-way and Global condition sequences of input (middle panel) differ. The stimulation protocol in the One-way condition provides constant high input for the adaptation of
rightward saccades (black), whereas the global condition’s stimulation protocol provides weaker and highly variable input (red), due to varying target angles, /(t), in the
Global condition (lower panel). The simulated time-course of adaptation (upper panel) in the Global condition (red solid line; shaded area provides 95% confidence interval
across 1000 simulation runs), compared to the adaptation in this direction in the One-way condition (black solid lines) mirrors the difference between the input patterns.
Again, dashed lines provide the actual average data for reference (as reported in Fig. 3B). Clearly, accumulated vector-based adaptation does not account for the high levels of
adaptation found in the Global condition (dashed red line). Note that for the sake of comparability, the proportion of adaptation was normalized, i.e., expressed relative to the
asymptotic adaptation obtained for rightward saccades in the One-way condition. (For interpretation of the references to color in this figure legend, the reader is referred to
the web version of this article.)
0.5
0
0.5
0
0.5
0
Global Two-wayGlobal One-way
G
ai
n
di
ffe
re
nc
e
Two-way One-way
Fig. 6. Differences in the proportion of adaptation between Global – One-way
adaptation, Two-way – One-way adaptation, and Global – Two-way adaptation are
shown as a function of target step direction when analyzing only the first 20 test
trials of the post-adaptation block. Conventions as in Fig. 4C. Despite a higher level
of noise resulting from the reduced amount of data, the differences between
conditions closely mimic those obtained using the entire set of test trials.
1888 M. Rolfs et al. / Vision Research 50 (2010) 1882–1890

Author's personal copy
species and procedure. One difference that we feel could be critical
is that we found the global adaptation when the direction and
amplitude of target steps were unpredictable whereas the target
steps in Scudder et al’s procedure were highly predictable (there
were strong biases in amplitude and direction). This predictability
may have favored the contribution of the direction-specific saccade
adaptation mechanisms over any global mechanism.
What is a likely neural locus of global saccadic gain adaptation?
Many previous studies of saccadic adaptation have focused on ocu-
lomotor areas that encode saccades as a vector rather than their
components (review in Hopp & Fuchs, 2004), pre-eminently the
SC, the most peripheral of these structures. Recent evidence sug-
gests that amplitude changes in saccade adaptation are accompa-
nied by changes in firing rates and/or movement fields of
corresponding SC neurons (Takeichi, Kaneko, & Fuchs, 2007). These
changes may either be a manifestation of amplitude recalibration,
or themselves trigger oculomotor learning further downstream
(Kaku et al., 2009). Due to its vector specificity, the SC is no likely
candidate for a general recalibration mechanism, unless consistent
visual cues to miscalibration for all saccades result in a super-addi-
tive lateral potentiation of learning, affecting many (or all) SC neu-
rons concurrently. More likely, Global adaptation triggered learning
in more peripheral sites, including the cerebellar fastigial oculomo-
tor region, which strongly projects to saccadic burst neurons in the
brainstem (Scudder, McGee, & Balaban, 2000). At this final stage of
oculomotor processing, the duration of bursts projected to motor-
neurons controlling the extraocular muscles linearly relates to sac-
cade amplitude. Hence, only one parameter needs adjustment to
similarly affect saccadic gain of many saccades at the same time.
The properties demonstrated here for a general recalibration mech-
anism for saccades pinpoints these potential neurophysiological
correlates and may help explain the conflicting results in many of
the studies using variants of the traditional paradigm.
While it had been shown previously that motor adaptation
develops simultaneously at many different temporal scales (Kör-
ding et al., 2007), our data provide evidence for the idea that
goal-directed behavior unfolds and develops on many different
spatial scales as well. These processes are the basis of our success-
ful interaction with the environment, and generalization across
many different motor acts, shown here for saccades in all direc-
tions, is an integral part of this plasticity.
Acknowledgments
We thank Claudia Buß for help with data acquisition. This work
was supported by the 7th Framework Program of the European
Commission (Marie Curie International Outgoing Fellowship
235625 awarded to M.R.) and by a Chaire d’Excellence grant to P.C.
Appendix A
A.1. Baseline correction of saccade gains
Individuals may differ in the amount of undershoot or over-
shoot they produce when making saccades to visual targets, and
these biases in saccade gain may differ as a function of saccade
direction. To determine baseline biases in saccade gain as a func-
tion of target direction we applied LOWESS regressions to the
pre-adaptation test data. The proportion of adaptation of any sac-
cade in a given target direction was then expressed relative to this
baseline. Fig. 7A helps illustrating this procedure. To facilitate com-
parison to post-adaptation data, we will plot all data as a propor-
tion of adaptation, that is, we will express the difference of
saccade gain from 1 relative to the gain change to be induced by
the intra-saccadic back-step (0.25). The gray dots in the polar plot
in Fig. 7A show one observer’s data from the pre-adaptation test
2
0
−2
2
0
−2
2
0
−2
2
0
−2
LOWESS regression for
pre-adaptation data
Residuals of
that regression
2
0
−2
2
0
−2
Two-way
Global
One-way
A
C
B2
0
−2
Observer 05
2
0
−2
Observer 05
Ba
se
lin
e
pr
op
or
tio
n
o
f a
da
pt
at
io
n
Ba
se
lin
e
pr
op
or
tio
n
of
a
da
pt
at
io
n
Pr
op
or
tio
n
of
a
da
pt
at
io
n
Fig. 7. Pre-adaptation data and baseline-correction. A Polar plot showing the baseline proportion of adaptation as a function of target direction in the pre-adaptation test
block of the Global adaptation condition for one observer. Gray dots show single saccade data, the thick gray line shows the LOWESS regression. Positive values reveal that on
average the observer undershot and fell slightly short of the targets. B Smoothed pre-adaptation baseline data from 12 observers in three conditions (left panel) and the
residuals of these regressions on the data (right column) for the three conditions tested. Residuals do not reveal any systematic biases in the regression procedure. C Data
from test trials in the post-adaptation block were expressed relative to the regression of the pre-adaptation test data (thick gray line shown with residuals; see text for
details). Pink dots are single saccades; the thick red line shows the smoothed average. As highlighted by the gray shaded area, saccades in all directions had were affected by
Global adaptation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
M. Rolfs et al. / Vision Research 50 (2010) 1882–1890 1889

Author's personal copy
trials in the Global adaptation condition; the thick line shows the
result of the LOWESS regression. The deviation of this regression
line from zero towards positive values indicates that this observer
had substantial undershoot even before adaptation took place. In
addition, this undershoot differs slightly as a function of saccade
direction. This pattern of baseline data is a well known character-
istic of rapid eye movements and was observed for many of our
observers. Fig. 7B shows LOWESS regressions of the pre-adaptation
test data for all observers (left column) along with the residuals
(right column) for each condition separately. Plotting the baseline
data as a proportion of adaptation highlights that without correct-
ing for these individual and direction-specific biases, we might
have overestimated the effects of adaptation.
Saccade amplitudes of test trials in the pre-adaptation block
represent a baseline for the effects of adaptation in the adaptation
and post-adaptation blocks. However, contrary to previous work
on saccadic adaptation using only a limited number of target direc-
tions, we triggered saccades with random directions. Saccade gains
and, thus, the proportion of adaptation differ greatly as a function
of saccade direction and these dependencies vary considerably
across observers and sessions (see Fig. 7B). Therefore, our measure
of adaptation had to be expressed relative to the directionally spe-
cific baseline under- or overshoot obtained in the LOWESS regres-
sion of the baseline pre-adaptation data. Thus, for each observer,
we computed the proportion of adaptation of each saccade relative
to those in pre-adaptation test trials. The pink dots in the polar plot
in Fig. 7C show the result for the same observer as in Fig. 7A, for the
post-adaptation test trials following Global adaptation. The thick
red line is the LOWESS regression on this data. The pre-adaptation
regression is again represented by a thick gray line (now a circle,
due to the baseline-correction procedure), its residuals are shown
as thin gray lines protruding from it. The change in the proportion
of adaptation due to Global adaptation is highlighted by the shaded
area.
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