Eye movements and visual attention are intimately
related. The major function of saccadic eye movements
is to move objects of interest into the fovea, the retinal
region of highest acuity, for close inspection during the
following fixation (Findlay & Gilchrist, 2003). Fixating
an object means overtly attending to it. However, attention
can also be covert—that is, dissociated from fixation po-
sition. When covert shifts of attention are induced with a
centrally presented cue, responses to targets subsequently
appearing at the cued peripheral location (valid-cue tri-
als) are faster than responses to targets at the opposite
location (invalid-cue trials; Posner, 1980; Posner, Sny-
der, & Davidson, 1980). With the phrase “covert shifts
of attention,” reference is made to the absence of large
saccadic eye movements during the cue–target interval
(CTI). Whereas covert attention shifts are by definition
not accompanied by overt saccades, there is evidence that
sac cades are obligatorily preceded by covert shifts of at-
tention (i.e., processing at the saccade target is enhanced
before saccade execution; Deubel & Schneider, 1996;
Hoffman & Subramaniam, 1995; Kowler, Anderson,
Dosher, & Blaser, 1995).
A measure that can be used to track the deployment of
covert attention may be useful in a number of contexts.
Given the close relationship between saccades and visual
attention, one might wonder whether traces of covert at-
tention shifts can be detected in oculomotor activity during
fixations. Since the absence of saccades during covert at-
tention shifts does not imply the absence of fixational eye
movements, microsaccades—small saccade-like move-
ments with amplitudes ,1º that occur during attempted
ocular fixation (see Engbert, 2006, for a review)—have
been proposed as a measure of covert attention. Given the
result that microsaccades and saccades are probably regu-
lated by the same physiological structures at the level of
the superior colliculus (SC; Hafed, Goffart, & Krauzlis,
2009; Rolfs, Kliegl, & Engbert, 2008) and downstream
(van Gisbergen, Robinson, & Gielen, 1981), a relation-
ship between covert attention and microsaccades may not
be particularly surprising. In fact, evidence in favor of
such a relationship has been presented: A considerable
amount of research has demonstrated effects of attentional
cue presentation on rate and direction of microsaccades
(Corneil, Munoz, Chapman, Admans, & Cushing, 2008;
Engbert & Kliegl, 2003; Galfano, Betta, & Turatto, 2004;
Gowen, Abadi, Poliakoff, Hansen, & Miall, 2007; Hafed
& Clark, 2002; Kohama & Usui, 2002; Laubrock, Eng-
bert, & Kliegl, 2008; Turatto, Valsecchi, Tamè, & Betta,
2007).
A number of physiological control loops at several lev-
els converge on the SC. For example, there is the low-level,
reflexive, retino-tectal loop bypassing even the lateral
geniculate nucleus. At higher levels, the SC receives cor-
tical input from perceptual areas, from parietal cortex, and
683 © 2010 The Psychonomic Society, Inc.
When do microsaccades follow spatial attention?
Jochen Laubrock and reinhoLd kLiegL
University of Potsdam, Potsdam, Germany
Martin roLfs
University of Potsdam, Potsdam, Germany
and CNRS and Université Paris Descartes, Paris, France
and
raLf engbert
University of Potsdam, Potsdam, Germany
Following up on an exchange about the relation between microsaccades and spatial attention (Horowitz, Fenc-
sik, Fine, Yurgenson, & Wolfe, 2007; Horowitz, Fine, Fencsik, Yurgenson, & Wolfe, 2007; Laubrock, Engbert,
Rolfs, & Kliegl, 2007), we examine the effects of selection criteria and response modality. We show that for
Posner cuing with saccadic responses, microsaccades go with attention in at least 75% of cases (almost 90% if
probability matching is assumed) when they are first (or only) microsaccades in the cue–target interval and when
they occur between 200 and 400 msec after the cue. The relation between spatial attention and the direction of
microsaccades drops to chance level for unselected microsaccades collected during manual-response conditions.
Analyses of data from four cross-modal cuing experiments demonstrate an above-chance, intermediate link for
visual cues, but no systematic relation for auditory cues. Thus, the link between spatial attention and direction
of microsaccades depends on the experimental condition and time of occurrence, but it can be very strong.
Attention, Perception, & Psychophysics
2010, 72 (3), 683-694
doi:10.3758/APP.72.3.683
J. Laubrock, laubrock@uni-potsdam.de

684 Laubrock, kLiegL, roLfs, and engbert
Fencsik, Fine, Yurgenson, & Wolfe, 2007; Horowitz, Fine,
et al., 2007; Laubrock et al., 2007). Horowitz, Fencsik,
et al. based their conclusion that “the predictive power
of microsaccades is, for practical purposes, negligible”
(2007, p. 367) on two findings. First, they did not observe
a large microsaccade–target congruency (MTC) effect on
reaction times (RTs) in addition to the cue validity effect.
In the present article, we argue that an index of attention
must be related to attention, but need not produce effects
in addition to the effects of attention. Imagine that we had
lost part of the protocol of the experimental design and
wanted to guess whether the cue on a given trial was valid
or not. If this judgment is aided by knowledge of MTC,
then microsaccades can be taken as indicators of attention.
Thus, we predict faster RTs on trials with target- congruent
microsaccades than on trials with target-incongruent
microsaccades.
The strength of the relation between microsaccade pa-
rameters and RT varies strongly with experimental ma-
nipulations and microsaccade time of occurrence (Kliegl,
Rolfs, Laubrock, & Engbert, 2009). For example, micro-
saccades occurring shortly before the response drastically
increase RT. Horowitz, Fine, et al. (2007) used a fairly
wide time window (400 msec), thereby potentially includ-
ing late microsaccades, and also averaging over the effects
of sequences of microsaccades with opposite directions.
The robust microsaccadic rate modulations suggest that
effects of attention will strongly depend on time relative to
cue presentation. We here suggest that mainly microsac-
cades occurring in a relatively circumscribed interval
about 200–400 msec after cue presentation are modu-
lated by attention shifts in Posner-type cuing tasks (see
also Engbert, 2006). We predict that if microsaccades in
the CTI are taken from that interval, they will be related to
RT. If, on the other hand, microsaccades are selected from
a period later in the trial, then they may not be related to
performance at all, or may even adversely affect it.
Second, Horowitz, Fine, et al. (2007) argued that some-
times attention might go the wrong way. They predicted
that on these “attentional mistake” trials, if microsaccades
indicated the direction of attention, performance should
be better when microsaccades point toward the target than
when they point away from the target. Empirically, how-
ever, they observed slower RTs in this case. In a response
(Laubrock et al., 2007), we showed this result to be an
artifact of trial selection. Figure 1 illustrates why. The root
(left part) of the probability tree reflects the experimental
design (neutral cues are left out for simplicity): The va-
lidity of arrow cues was v 5 .80, and .20 of trials were
invalid. Moving to the right, we assume that attention fol-
lows these cues with probability w. Thus “attentional mis-
takes” occur with probability 12w. The products of the
respective path probabilities yield estimates that attention
is located either at the upcoming target (green ovals) or
opposite to it (red ovals), given valid and invalid cues.1
Our main theoretical interest concerns the unknown
probability x with which microsaccades follow spatial
attention. As we have argued above, it is likely that the
relationship between microsaccade and attention is not
perfect—that is, x , 1.00—and thus, with probability
from the frontal eye fields. Given this variety of inputs,
it can be expected that the relationship (if any) between
microsaccades and covert attention is not determined by
a single process. Indeed, microsaccades may also result
from other, not primarily attention-related processes (see
Rolfs, 2009, for a comprehensive review), such as fixa-
tion control (e.g., Engbert & Kliegl, 2004; Mergenthaler
& Engbert, 2007), perceptual disambiguation (e.g., Cui,
Wilke, Logothetis, Leopold, & Liang, 2009; Laubrock,
Engbert, & Kliegl, 2008; Starzynski & Engbert, 2009;
Troncoso, Macknik, Otero-Millan, & Martinez-Conde,
2008; van Dam & van Ee, 2006), and perceptual fading
(e.g., Engbert & Mergenthaler, 2006; Hsieh & Tse, 2009;
Martinez-Conde, Macknik, Troncoso, & Dyar, 2006;
Troncoso, Macknik, & Martinez-Conde, 2008), suggest-
ing a less than perfect agreement between the direction of
attention and the direction of microsaccades.
Thus, we need to know more precisely about the input–
output relations of the attention–microsaccade system in
order to make microsaccades a useful measure of covert
attention. To achieve this, it is necessary to collect data on
the microsaccadic response in tasks known to affect covert
attention. Empirically, whereas strong microsaccade rate
modulations are observed even for irrelevant visual and
auditory stimuli (Rolfs et al., 2008), effects on microsac-
cade direction depend on when in the CTI the microsac-
cade occurs, and are sensitive to a variety of experimental
manipulations (overview in Rolfs, 2009), relating, for
example, to the type of cue (arrow or color, Engbert &
Kliegl, 2003; central or peripheral, Gowen et al., 2007;
Laubrock, Engbert, & Kliegl, 2005), to the modality of
the cue or the target (visual or auditory; Rolfs, Engbert, &
Kliegl, 2005), or to the type of response required (manual
or saccadic; Laubrock, Engbert, Rolfs, & Kliegl, 2007).
There appears to be a strong link between the orienting
system and microsaccade rate, and a weaker link between
higher level attentional systems and microsaccade direc-
tion. Importantly, these effects are not purely cue driven.
For example, an arrow cue biases microsaccade direction
only under attention-shift instructions (to detect change
in the periphery), but not under instructions to detect a
central change (Engbert & Kliegl, 2003).
Given these results, Horowitz, Fine, Fencsik, Yurgen-
son, and Wolfe’s claim (2007, p. 356) that “fixational eye
movements are not an index of covert attention” was a bit
of a surprise to us. Whereas we think that this conclusion
may be premature, clearly, the relationship between atten-
tion and microsaccades needs to be more fully specified.
The present article aims at contributing to a closer speci-
fication of when and how microsaccades are affected by
attention. Here we investigate the effect of response mo-
dality and of different selection criteria on the relationship
between microsaccades and attention in the Posner cuing
task. We also present a reanalysis of the effects of visual
and auditory cues on attention shifts toward visual or audi-
tory targets (Rolfs et al., 2005).
The background of the present research is a stimulat-
ing exchange about the question of whether fixational eye
movements—in particular, microsaccades—can serve as
an indicator of spatial attention shifts at all (Horowitz,

spatiaL cues and Microsaccade direction 685
metry, if w . x (a mild boundary condition by no means
implying that x 5 .5), then the selection on valid-cue tri-
als will be dominated by cases in which attention is at the
cued target, but microsaccades do not follow attention.
Importantly, “attentional mistake” cases as defined by
Horowitz, Fine, et al. (2007)—that is, with microsaccades
toward the target (MTC1), but away from the cue—come
exclusively from invalid-cue trials, whereas “attentional
mistake” cases with microsaccades away from both the
target (MTC2) and the cue come exclusively from valid-
cue trials. Because the observable outcomes are deter-
mined by attention rather than by “attentional mistakes”
in the paths vw(12x) and (12v)w(12x), the contrast of
RTs from these outcomes will also reflect this difference;
hence, it is not particularly surprising that RT is faster for
valid-cue, MTC2, than for invalid-cue, MTC1, cases.
12x there are also cases in which microsaccades are not
an indicator of attention. Adding these branches to the
tree, we arrive at the set of possible terminal outcomes.
However, these outcomes are still not directly observable.
Instead, what is observable are microsaccades directed
toward (MTC1, green boxes) or away from (MTC2, light
red boxes) the target.
The selection of trials employed by Horowitz, Fine, et al.
(2007) ignores the fact that for x , 1.00, two paths lead to
the empirically observable outcome “microsaccades not
at target” (MTC2) in the upper branch of Figure 1. The
associated probabilities are obtained by multiplication:
p1 5 vw(12x) and p2 5 v(12w)x. Note that only p2 con-
tains the “attentional mistake” cases Horowitz, Fine, et al.
intended to analyze, whereas in p1, attention is actually at
the target, only the microsaccade is not. Indeed, by sym-
Valid cue
w
1–w
Invalid cue
w
1–w
Microsaccade with attention
x
Microsaccade not with attention
1–x
Microsaccade with attention
x
Microsaccade not with attention
1–x
Microsaccade with attentionx
Microsaccade not with attention
1–x
Microsaccade with attention
x
Microsaccade not with attention
1–x
v = 0.8
1–v
Microsaccade not
at target, MTC–
Attention
at target
Attention
not at target
Microsaccade
at target, MTC+
Attention
at cue
Attention
not at cue
Attention
at cue
Attention
not at cue
Figure 1. Multinomial tree model about the relation between the direction of spatially cued attention, cue validity, and
direction of microsaccades. Neutral cues are omitted to avoid clutter. Validity for direction cues was fixed at v 5 .80. The
parameter w captures assumptions about attentional strategies—that is, about the probability that attention is indeed
shifted in accordance with the cue; the range of reasonable values is between w 5 v (probability matching) and w 5 1.00
(optimal attention shifts). The legend in the lower left corner explains the shape and color codes: Colors classify atten-
tion (ovals) or microsaccades (rectangles) with respect to the target; the dark gray and light gray colors indicate shifts
toward and away from the target, respectively. At the behavioral level, we can only observe whether microsaccades are
target congruent (dark gray rectangles) or target incongruent (light gray rectangles), because we cannot directly observe
where attention is shifted. For example, on valid-cue trials (upper branch), we can only observe whether a microsaccade
is directed at the target (dark gray rectangles) or not (light gray rectangles), but not whether attention is directed at the
target (dark gray oval) or not (light gray oval). Hence, observed microsaccade–target congruency contains a mixture of
instances involving attention at the target and away from the target. However, the observed probabilities constrain the
possible values of the latent probabilities x and w, because they are the sum of the products of the path probabilities lead-
ing to the rectangles of the given color. We are primarily interested in determining boundaries for x, the probability that
the direction of attention determines the direction of microsaccades. These could indicate, for example, no relation (x 5
.50), an intermediate relation (x 5 .75), or a deterministic link (x 5 1.00). MTC, microsaccade–target congruency.

spatiaL cues and Microsaccade direction 687
ning 61.5º around the target was defined as the response saccade.
Saccade latency was defined as the latency between target presen-
tation and response saccade onset. Manual responses were scored
as incorrect if the wrong target location was reported; saccadic
responses were scored as incorrect if they landed in the wrong
target region.
Microsaccade detection. We used the same algorithm to detect
microsaccades with amplitudes ,1º in the interval from 50 msec be-
fore cue onset to the (manual or saccadic) response. We considered
only binocular microsaccades—that is, microsaccades detected in
both eyes with temporal overlap of at least one data sample. Trials in-
cluding saccades larger than 1º prior to the response were discarded,
as were trials with no responses and saccade latencies shorter than
70 msec. The 18 participants contributed a total of 34,082 trials, in
which 37,181 microsaccades were detected.
Classification of type of microsaccade. For analyses of the
relation between microsaccade occurrence and response times,
microsaccades during the CTI were classified into three groups:
(1) single microsaccades (N 5 10,518) from trials in which only
one microsaccade occurred during the CTI, (2) the first of several
microsaccades (N 5 8,220), and (3) the last of several microsac-
cades (N 5 8,220) from trials in which more than one microsaccade
occurred during the CTI. Note that groups 2 and 3 are based on the
same trials. Therefore, differential effects of the direction of first
and last microsaccades on RT cannot be due to differences in trial
selection. On average, the horizontal directions of first and last mi-
crosaccades were negatively correlated (r 5 2.389) (range between
subjects: 2.16 to 2.67), and the average N of trials per subject with
more than one microsaccade was 443. The mean times of occur-
rence were 363 msec (SE 5 13 msec), 273 msec (SE 5 12 msec),
and 561 msec (SE 5 21 msec) after the cue for single, first, and last
microsaccades, respectively.
RESuLTS
Reaction Times and Errors
For the analysis of cue validity effects, mean RTs from
correct trials were submitted to an ANOVA with cue
validity (valid, neutral, invalid) and response modality
(manual, saccadic) as within-subjects factors. Saccadic
RTs were faster than manual RTs [M 5 181 vs. 335 msec;
F(1,17) 5 227, MSe 5 2,823, p , .001]. Cue validity had
the expected effect, with valid cues leading to faster RTs
(236 msec) than neutral cues (263 msec) or invalid cues
(279 msec) [F(2,34) 5 65, MSe 5 267, p , .001]. Cue
validity and response modality interacted, with manual
RTs showing a greater cue validity effect (see Table 1 for
means). Separate analyses for each response modality
showed that cue validity had a significant effect within
each response modality [manual, F(2,34) 5 852, MSe 5
254, p , .001; saccadic, F(2,34) 5 16, MSe 5 106, p ,
the analyses, 1 because of equipment failure, and the other because
of a very high number of errors.
Apparatus
Each subject was seated in a silent and darkened room with his
or her head positioned on a chinrest, 50 cm in front of a computer
screen. Stimuli were presented on a 19-in. EYE-Q 650 CRT (reso-
lution of 1,024 3 768 pixels or 36º 3 27º of visual angle; refresh
rate 100 Hz). Eye-position data were recorded and available online
using a head-mounted EyeLink II system (SR Research, Osgoode,
ON, Canada) with a sampling rate of 500 Hz and a noise-limited
spatial resolution better than 0.01º. An Apple Power Macintosh G4
computer controlled stimulus display and response collection, using
MATLAB (MathWorks, Natick, MA, USA) with the Psychophysics
(Brainard, 1997; Pelli, 1997) and Eyelink (Cornelissen, Peters, &
Palmer, 2002) toolboxes. Manual responses were mapped to the left
control key (left) or the right arrow key (right) on a standard Apple
USB keyboard.
Design
In a factorial design, the experimental factors of response mo-
dality (manual, saccadic) and cue validity (valid, invalid, neutral
with a proportion of 4:1:1, respectively) and the control variable of
target location (left, right) were varied within subjects. The experi-
ment lasted for six sessions of 312 trials each (plus repeated trials;
see below). Within each session, response modality was blocked,
leading to 156 trials each with manual and saccadic responding.
The order of blocks was switched between sessions and balanced
across subjects. Cue validity and target location were randomized
within blocks.
Procedure
A trial started with presentation of a central fixation cross (.73º
side length) and a fixation check, which required gaze to be within
a square of 2º side length at the screen center. Following successful
fixation, the fixation cross remained on screen during a fixation
period (1.5–2 sec; all randomized timings here were drawn from
a uniform distribution). Next, the fixation cross turned into a cue
(two lines were added to the cross, connecting its vertical wings to
one of the horizontal wings, thereby creating an arrow to the left
or to the right), which remained on screen for the duration of the
CTI (0.5–1.5 sec). The target was a disk of 0.73º diameter with its
center presented at 12.4º horizontal eccentricity, whose appearance
on one of the sides of the screen served as a go signal. Fixation
was continuously checked before target onset, requiring gaze to
stay within a central 3º square. The target remained on screen for
1 sec or until response, whichever came earlier. Whereas subjects
were informed that they had to fixate the central cross before tar-
get onset, instruction stressed that the primary task was to report
target location. For saccadic responding, gaze was required to be
detected for at least 200 msec in a 3º square centered on either of
the possible target locations. The next trial started after an intertrial
interval of 0.5 sec.
Invalid trials due to failed fixation at the beginning of the trial or
during the trial before the time of the go signal were canceled, as
were trials in which no response was detected. Canceled trials were
repeated at the end of a block in a random order. Drift correction was
performed every 12 trials, and the eyetracker was recalibrated after
every 24 trials or whenever the fixation check failed repeatedly.
Data Analysis
Saccade detection. In saccade blocks, response saccades were
detected offline using a new version (Engbert & Mergenthaler,
2006) of the algorithm by Engbert and Kliegl (2003). Velocities
were computed from subsequent samples in the series of eye posi-
tions recorded after target presentation. Saccades were detected
in 2-D velocity space using thresholds for peak velocity (6 SD)
and minimum duration (6 msec, or three data samples). The first
saccade that landed at one of the two potential target regions span-
Table 1
Means and Standard Errors (Between Subjects) for Reaction
Times (RTs; Keypresses or Saccade Onset Latencies) and
Errors, Broken Down by Response Modality and Cue Validity
Response Cue RT (msec) % Error
Modality Validity M SE M SE
Manual Invalid 369 12.8 4.94 1.43
Neutral 339 15.1 2.30 1.24
Valid 300 11.5 1.45 1.18
Saccadic Invalid 188 5.5 0 –
Neutral 185 5.2 0 –
Valid 170 3.4 0 –

spatiaL cues and Microsaccade direction 689
Table 2
Predicted (Bold Font) and Observed (Regular Font) Probabilities of Target-
Congruent (MTC: 1) and Target-Incongruent (MTC: 2) Microsaccades Following
Valid, Invalid, and Neutral Cues for Multinomial Tree Model (See Figure 1)
Valid Invalid Neutral
Cues Cues Cues N
MTC 1 2 1 2 1 2
Model: x 5 1.0, w 5 1.0 .67 .00 .00 .17 .08 .08
Model: x 5 1.0, w 5 .8 .53 .13 .03 .13 .08 .08
Saccadic (200–400; single & first MS) .52 .17 .04 .12 .07 .07 5,784
Model: x 5 .75, w 5 1.0 .50 .17 .04 .13 .08 .08
Saccadic (CTI; single & first MS) .46 .22 .06 .10 .08 .08 10,504
Model: x 5 .75, w 5 .8 .43 .23 .06 .11 .08 .08
Saccadic (CTI; single, first, last MS) .40 .27 .07 .09 .08 .08 15,293
Manual (200–400; single & first MS) .40 .27 .07 .10 .08 .08 5,042
Manual (CTI; single & first MS) .36 .32 .07 .09 .08 .09 9,972
Manual (CTI; single, first, last MS) .34 .34 .08 .08 .08 .08 14,556
Model: x 5 .5 .33 .33 .08 .08 .08 .08
Note—Predicted probabilities for models are printed in bold, assuming the optimal observer
model (w 5 1.00) and the probability matching model (w 5 .80), and three different values
for the probability that microsaccades follow attention (no relation, x 5 .50; intermediate
link, x 5 .75; deterministic link, x 5 1.00). Observed probabilities for saccadic and manual
responses are listed in proximity to model predictions of best correspondence. Rows are sorted
by the probability of observing target-congruent microsaccades on valid-cue trials. MTC,
microsaccade– target congruency; CTI, cue–target interval; MS, microsaccade.
Time From Cue (msec)
M
ic
ro
sa
cc
ad
e
Ra
te
0.000
0.001
0.002
0.003
0.004
0.005
0.000
0.001
0.002
0.003
0.004
0.005
0.000
0.001
0.002
0.003
0.004
0.005
Single MS
0 200 400 600 800 1,000
First MS
0 200 400 600 800 1,000
Last MS
0 200 400 600 800 1,000
Valid
N
eutral
Invalid
Response
Manual RT
Saccadic RT
MS−Target
Congruency
Incongruent
Congruent
Figure 4. Microsaccade rates across the cue–target interval for target-congruent (gray lines) and target-incongruent (black lines)
microsaccades broken down by type of microsaccades (panel columns: single, first of several, last of several), cue validity (panel rows:
invalid, neutral, valid), and response modality (manual: thin lines; saccadic: thick lines). Note that target-incongruent rates for invalid
cues (bottom row of panels) reflect cue-congruent rates. Thus, cues induce a pronounced peak in microsaccade rate at around 200 msec
in the cue–target interval. Graph produced with ggplot (R Development Core Team, 2009; Wickham, 2009). MS, microsaccade.

690 Laubrock, kLiegL, roLfs, and engbert
the probabilities would be even higher (x 5 .88, saccadic;
x 5 .66, manual).
If, on the other hand, all microsaccades within the
CTI are included, then the link between microsaccades
and attention appears to be rather weak (optimal: x 5
.62 sac cadic; x 5 .53 manual; probability matching: x 5
.70 saccadic; x 5 .54 manual). This is at least partly due to
inclusion of the last of several microsaccades, the direction
of which is negatively correlated with the direction of the
first of several microsaccades (see above), and therefore
often directed away from the cue. Indeed, if only the last of
several microsaccades or a single microsaccade late in the
trial were inspected, then the conclusion would be that mi-
crosaccades are negatively correlated with attention (x 5
.43, for shift and saccadic or manual responses; x 5 .38, for
probability matching and saccadic or manual responses).
Microsaccade–Target Congruency
As a Predictor of Reaction Times
Can MTC recover some of the RT benefits introduced
by the cues? If microsaccades are related to attention, then
RTs on trials with target-congruent microsaccades should
be shorter than on trials with target-incongruent microsac-
cades. We specified a linear mixed model (LMM) using
restricted marginal likelihood estimates (R package lme4;
Bates & Maechler, 2009) to predict RT as a function of
the following predictors (including interactions): MTC
(w 5 .8, w 5 1.0) and microsaccade validity (x 5 .5,
x 5 .75, x 5 1.0). The empirical probabilities are listed
for different selection criteria. Rows are sorted by the
probability of observing target-congruent microsaccades
on valid-cue trials.
Manual-response blocks. Starting at the bottom of
Table 2, we note a very close correspondence between the
independence model (x 5 .5) and all (unselected) micro-
saccades from manual-response blocks. This result rep-
licates Horowitz, Fine, et al. (2007). The next two lines
(1) leave out last microsaccades and, in addition, (2) se-
lect microsaccades only from a CTI time window of 200–
400 msec, placed around the peak rate visible in Figure 3.
Clearly, for these selections the empirical probabilities are
increasingly similar to the multinomial model assuming
probability matching and an intermediate link between
spatial attention and subsequent direction of microsac-
cade (x 5 .75).
Saccadic-response block. The unselected sample
of microsaccades from saccadic-response trials is quite
similar to this intermediate-link model. If we include only
single and first microsaccades from the 200- to 400-msec
time window and again assume probability matching, then
the empirical probabilities agree almost perfectly with the
theoretical probabilities computed on the assumptions of a
deterministic link between spatial attention and microsac-
cade direction.
Probability estimates that microsaccades go with
attention. For a quantitative estimate of the probability
that microsaccades indicate attention, we fit the multino-
mial model to each subject’s data, simultaneously fitting
the observed probabilities of MTC for all levels of cue
validity. Technically, this was achieved by minimizing a
cost function defined by the sum of the squared devia-
tions of the empirically observed probabilities from the
theoretically predicted probabilities of microsaccades di-
rected at or away from the target (i.e., the terminal nodes
in the model in Figure 1), assuming (1) Bayesian optimal-
ity; that is, observers always shift their attention with the
cue, or (2) probability matching; that is, observers shift
their attention with the cue proportional to cue validity.
The parameter to be minimized was x, the probability that
microsaccades follow attention. The model was fit to in-
dividual observers’ data, and mean results are reported
in Table 3.
We used this analysis to test the influences of response
modality and of the selection criteria employed (i.e.,
which microsaccades to include in the analysis). Results
indicate that both factors have an influence. First, micro-
saccades are more indicative of attention shifts for sac-
cadic than for manual responses. Thus, the responsiveness
of the oculomotor system to attentional cues is modified
by response demands. Second, if the analysis is restricted
to first or single microsaccades occurring 200–400 msec
after the cue, then even under the conservative assump-
tion that subjects always shift their attention with the cue
according to Bayesian optimality, the probability that mi-
crosaccades follow attention is relatively high (x 5 .77 for
saccadic responding, x 5 .61 for manual responding). If
subjects were choosing a probability-matching strategy,
Table 3
Probability That Microsaccades Went With Attention
Optimal
Probability Attention
Matching, Shifting,
Response Condition and w 5 .80 w 5 1.00
Microsaccade Selection Criterion M SE M SE
Saccadic (200–400; single or first MS) .88 .08 .77 .10
Saccadic (200–400; first MS) .86 .08 .77 .10
Saccadic (0–500, single MS) .86 .08 .74 .10
Saccadic (CTI; single MS) .82 .09 .71 .11
Saccadic (CTI; single or first MS) .81 .09 .70 .11
Saccadic (CTI; first MS) .78 .10 .68 .11
Saccadic (CTI; any MS) .70 .11 .62 .11
Saccadic (500–1,000; single MS) .57 .12 .54 .12
Saccadic RT (CTI; last MS) .38 .11 .43 .12
Manual (200–400; first MS) .72 .11 .65 .11
Manual (200–400; single or first MS) .66 .11 .61 .12
Manual (0–500; single MS) .61 .11 .57 .12
Manual (CTI; first MS) .59 .12 .55 .12
Manual (CTI; single or first MS) .58 .12 .55 .12
Manual RT & single MS .58 .12 .55 .12
Manual (CTI; any MS) .54 .12 .53 .12
Manual (CTI; last MS) .46 .12 .47 .12
Manual (500–1,000; single MS) .38 .11 .43 .12
Note—Predicted probabilities x that microsaccades went with attention,
given the empirically observed microsaccade– target congruencies
(MTCs), and assumptions about the probability w that attention is
directed by the cue (probability matching, w 5 .80; optimal atten-
tion shifts, w 5 1.00), for various microsaccade selection criteria.
Predictions were derived per subject by minimizing the sum of squared
deviations of observed MTC probabilities from predictions generated by
the model (see Figure 1). Table cells contain the mean predicted prob-
ability across subjects and the associated standard error of proportions
(SE). Table rows are sorted by x in decreasing order within each response
modality. MS, microsaccade; CTI, cue–target interval.

spatiaL cues and Microsaccade direction 691
sumption that subjects shift spatial attention with a prob-
ability matching cue validity, the strength of the SA–MD
link increases to almost 90%.
Thus, counter to Horowitz, Fine, et al.’s (2007) claim,
microsaccades can be quite reliable indicators of spatial
attention. Note, however, that when we analyze the data in
more aggregated form—using a wider time window, simi-
lar to the way Horowitz, Fine, et al. did—we replicate their
result of a near absence of the SA–MD link. Obviously,
we are only at the beginning of detailing the conditions
under which the link is reliable, but our analyses do give
information about some of the major constraints. We will
discuss five of them.
First (single) microsaccade. The SA–MD link is prob-
ably strongest for the first (or only) microsaccade after the
cue. This result was foreshadowed by a striking difference
for the rate–direction signature of last microsaccades: They
lack the suppression and rebound effect (see Figure 4). In
contrast, there are microsaccade-related modulations of
RTs that appear to be strongest for the last microsaccade
in the CTI (Kliegl et al., 2009). Thus, temporal proximity is
critical. Quite possibly, effects related to first and last mi-
crosaccades reflect different underlying mechanisms.
Last microsaccade. Although the effects are not very
strong, effects observed in last microsaccades suggest
that oculomotor activity later in the trial fluctuates back
(congruent, incongruent), response modality (manual,
saccadic), and session (linear and quadratic trends). Sub-
jects were specified as a random factor. We included
only first microsaccades occurring 200–400 msec after
cue presentation. In addition to response modality (M 5
2140, SE 5 3, t 5 246) and the linear contrast of ses-
sion (M 5 22,619, SE 5 372, t 5 27), MTC (M 5 220,
SE 5 3, t 5 27) had a strong effect, indicating 20 msec
shorter RTs with target-congruent microsaccades. This
was modulated by an interaction of MTC and response
modality (M 5 9, SE 5 3.9, t 5 2.3), meaning that the
RT benefit of target-congruent saccades (11 msec) was
smaller for saccadic than for manual responding—which
is likely due to a scaling of RT benefits with absolute RT.
In summary, target congruency of first postcue microsac-
cades went along with an RT benefit.
Visual–Auditory Cross-Modal Validation
of Spatial Attention Effect
As an additional check on the conditions under which
the various predictions of the multinomial tree models
hold, we reanalyzed data from four experiments reported
by Rolfs et al. (2005; also Kliegl et al., 2009). In this study,
visual or auditory peripheral cues preceded visual or audi-
tory targets with a CTI of 1 sec. The task was a very diffi-
cult discrimination task using manual responses to red and
green visual targets and to low- and high-pitched tones,
respectively. Microsaccades were classified by whether
their direction was congruent with the target location or
not (using polar quadrants). Table 4 lists estimated prob-
abilities that microsaccades went with attention, assuming
either probability matching or optimal attention shifting,
and for microsaccades selected according to different
criteria. The first postcue microsaccades indicated atten-
tion shifts only if the cue was visual, but not if auditory
cues were used (for which, if anything, there seems to be
a negative correlation between the directions of early mi-
crosaccades and attention).
Figure 5 displays the x values computed from the MTC
probabilities of valid cues, separately for 200-msec bins of
the CTI for each of the four experiments. For the visual-
cue conditions (panels VV and VA) there are distinct
peaks for the MTC probability for the interval from 200
to 400 msec with an x value of about .75, and also effects
in the subsequent interval indicating that the attention ef-
fect in this difficult task is more sustained than in the easy
Posner-type cuing tasks reported above. In contrast, for
auditory-cue conditions, the x values hover around the
chance level of .50 across the entire CTI.
DISCuSSION
The results establish a relatively tight relationship of
early, cue-related microsaccades with the direction of
spatial attention. There are experimental conditions and
time windows during which microsaccades go in the di-
rection of spatial attention more than 77% of the time (in
the following, we will call this the “SA–MD link”), even
under the conservative assumption that subjects always
shift their attention with the cue. With the more liberal as-
Table 4
Predicted Probabilities x That
Microsaccades Went With Attention for
the Cross-Modal Cuing Experiment (Rolfs et al., 2005)
Optimal
Probability Attention
Matching, Shifting,
Cue Type and Microsaccade w 5 .80 w 5 1.00
Selection Criterion M SE M SE
Visual (200–400; single or first MS) .74 .10 .65 .11
Visual (200–400; first MS) .69 .11 .65 .11
Visual (CTI; first MS) .62 .11 .57 .12
Visual (CTI; single or first MS) .61 .11 .57 .12
Visual (0–500; single MS) .57 .12 .54 .12
Visual (CTI; single MS) .57 .12 .54 .12
Visual (CTI; any MS) .56 .12 .53 .12
Visual (500–1,000; single MS) .47 .12 .48 .12
Visual (CTI; last MS) .44 .12 .46 .12
Auditory (CTI; last MS) .51 .12 .51 .12
Auditory (CTI; single MS) .51 .12 .50 .12
Auditory (CTI; any MS) .50 .12 .50 .12
Auditory (CTI; first MS) .49 .12 .49 .12
Auditory (CTI; single or first MS) .48 .12 .49 .12
Auditory (200–400; single or first MS) .47 .12 .48 .12
Auditory (200–400; first MS) .47 .12 .48 .12
Auditory (500–1,000; single MS) .46 .12 .48 .12
Auditory (0–500; single MS) .46 .12 .48 .12
Note—The presentation format is like in Table 3. Assumptions about
the probability w that attention is directed by the cue (probability match-
ing, w 5 .80; optimal attention shifts, w 5 1.00) were varied. Predic-
tions were derived per subject by minimizing the sum of squared devia-
tions of observed MTC probabilities from predictions generated by the
model (see Figure 1). Table cells contain the mean predicted probability
across subjects and the associated standard error of proportions (SE).
Table rows are sorted by x in decreasing order within each cue type.
MS, microsaccade; CTI, cue–target interval; MTC, microsaccade–
target congruency.

692 Laubrock, kLiegL, roLfs, and engbert
that other auditory cues may trigger visual spatial atten-
tion, we consider the clear pattern of results reported here
as a validation of the assumption that we are primarily
looking at visual spatial attention.
We demonstrated that under specific experimental con-
ditions and using specific selection criteria, microsac cades
follow spatial attention in the CTI to a remarkably high de-
gree. Why are some microsaccades affected by attention,
whereas others are not? Although Bridgeman and Palca
(1980) assumed in their pioneering work that “the func-
tion of microsaccades is unknown” (p. 817), later results
indicate that microsaccades are the expression of ongo-
ing physiological processes whose main functions might
be maintenance of fixation (Engbert & Kliegl, 2004) and
prevention of perceptual fading (Engbert & Mergenthaler,
2006; Martinez-Conde et al., 2006). We think that atten-
tion and other higher level cognitive processes (maybe
due to their influence on collicular activity) are modulated
upon the physiological signal expressed by these ongo-
ing processes. Our results indicate that initial, cue-driven
shifts of visual attention are likely to be expressed in mi-
crosaccade direction, whereas later processes of maintain-
ing attention at the target are not expressed, at least not in
the present task.
We need to qualify our results with respect to the hori-
zontal cue–target arrangement. Given that microsaccades
detected with our equipment and algorithm are predomi-
nantly horizontally oriented (Engbert, 2006, Figure 5), we
think that potential biases of microsaccade orientation by
vertical attention shifts will be much harder to detect.
Finally, a correlation of microsaccades with visuospa-
tial attention within cuing paradigms does not necessarily
mean that cues cause attention shifts, which in turn cause
microsaccades. Alternatively, cues could independently
cause attention shifts and microsaccades. Thus, it remains
to fixation or even in the opposite direction. This possi-
bly reflects that attention goes back to fixation (Laubrock
et al., 2005) or in the opposite direction (Rolfs, Engbert,
& Kliegl, 2004; see also Galfano et al., 2004, for uninfor-
mative cues). Alternatively, it could be indicative of an
attempt to prevent premature responding.
Time window. The SA–MD link is strongest for micro-
saccades in the time window of highest cue-directed rates.
The suppression- overshoot pattern has been found in vir-
tually all studies of microsaccades in attentional cuing
with human subjects (but not with monkeys, where the
overshoot is missing; see, e.g., Cui et al., 2009). The peak
itself appears to be sensitive to task demands: It shifts to-
ward longer times when the task demands increase. Here
we reported analyses from a very easy task with an early
peak around 300 msec and from a fairly difficult task with
a late peak around 400 msec. The SA–MD link went with
the peak.
Saccadic response stronger than manual response. We
found the strongest SA–MD link for a saccadic response in
an easy task with central informative cues. This link was
stronger than for a manual response with the same experi-
mental demand. We speculate that preparing for a saccadic
response globally enhances the visual responsiveness in the
superior colliculus, effectively driving the response system
closer to threshold. Within the appropriate time window,
the SA–MD link was of intermediate strength for manual
responses; it was far from eliminated. Interestingly, for the
visual-cue conditions of the cross-modal study, the link was
of about the same magnitude despite the large differences
in task difficulty.
Visual cues. The SA–MD link was found for visual cues
but not for auditory cues. Interestingly, the modality of
the target did not matter in the crossmodal study (see Fig-
ure 5). Although we would certainly not want to rule out
Microsaccade (MS) Time of Occurrence (msec)
Pr
ob
ab
ili
ty
(M
S
W
ith
A
tt
en
tio
n)
.2
.3
.4
.5
.6
.7
.8
.9
VV
100 300 500 700 900
VA
100 300 500 700 900
AV
100 300 500 700 900
AA
100 300 500 700 900
Figure 5. Probability that microsaccade follows attention [i.e., x 5 p(MTC & valid cues) 2 0.16)/.48] at centers of six 200-msec bins
of microsaccade onset times in cue–target interval (0–200, 201–400, etc.). VV 5 visual cue, visual target; VA 5 visual cue, auditory
target; AV 5 auditory cue, visual target; AA 5 auditory cue, auditory target. Data are from four experiments reported in Rolfs et al.
(2005). Graph produced with ggplot (R Development Core Team, 2009; Wickham, 2009).

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to be seen whether the attention–microsaccade relation-
ship also holds for other forms of attention—for example,
endogenous, top-down attention shifts in the absence of
cues. These are inherently more variable, both temporally
and interindividually; thus, their correlates will be harder
to observe. Further research is needed to establish such
effects. Some hints in the literature, such as results from
ambiguous apparent motion perception, where reports
of changes in the perceptual interpretation of ambigu-
ous stimuli temporally follow microsaccades (Laubrock
et al., 2008), or results from a visual oddball task, where
microsaccade rate is modulated by task relevance and the
proportion of targets (Valsecchi, Dimigen, Kliegl, Som-
mer, & Turatto, 2009), suggest that such a relationship can
in principle be expected.
One novel aspect of our data is that microsaccade ampli-
tudes are modulated by whether or not they are related to
visual attention. One might speculate that some microsac-
cades result from the inhibition of saccades. In summary,
our results indicate that if the attentional signal is strong
enough and not smeared out over time, then chances are
that it will be expressed in microsaccade direction. Some,
but not all microsaccades provide a window on visuospa-
tial attention.
AuTHOR NOTE
We thank Todd Horowitz, Jeremy Wolfe, Bruce Bridgeman, and an
anonymous reviewer for helpful comments on an earlier version of this
article. This research was supported by Deutsche Forschungsgemein-
schaft (Grants KL-955/3 and KL/955-6). Data and R scripts are avail-
able upon request. Correspondence related to this article may be sent to
J. Laubrock or R. Kliegl, Department of Psychology, University of Pots-
dam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany (e-mail:
laubrock@uni-potsdam.de or kliegl@uni-potsdam.de).
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NOTE
1. Why should attention not always follow the cue—that is, w , 1.00?
The case of w 5 1.00 indicates subjects who perform according to Bayes-
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both empirical (Jonides, 1980) and theoretical (Gallistel, 1990) reasons
for why subjects in a potentially unstable environment are often likely to
allocate their attention somewhat more in accordance with probability
matching. Furthermore, due to fluctuations of vigilance, it is likely that
the limiting case of w 5 1 is hardly ever reached in reality. Although we
cannot directly observe w, the usually robust cue validity effects in RT
assure us that we can probably safely assume that .80 , w , 1.00; that is,
the true probability that subjects shift their attention with the cue lies be-
tween probability matching (w 5 .80) and Bayesian optimality (w 5 1).
(Manuscript received August 14, 2008;
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