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Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook
Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.
We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.
In this paper we apply symbolic transformations as a visualisation technique for analysing rhythm production. It is shown that qualitative information can be extracted from the experimental data. This approach may provide new insights into the organisation of temporal order by the brain on different levels of description. A simple phenomenological model for the explanation of the observed phenomena is proposed.
We analyse time series from a study on bimanual rhythmic movements in which the speed of performance (the external control parameter) was experimentally manipulated. Using symbolic transformations as a visualization technique we observe qualitative changes in the dynamics of the timing patterns. Such phase transitions are quantitatively described by measures of complexity. Using these results we develop an advanced symbolic coding which enables us to detect important dynamical structures. Furthermore, our analysis raises new questions concerning the modelling of the underlying human cognitive-motor system.
The fast and the slow of skilled bimanual rhythm production : parallel versus integrated timing
(2000)
We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.
The launch-site effect, a systematic variation of within-word landing position as a function of launch-site distance, is among the most important oculomotor phenomena in reading. Here we show that the launch-site effect is strongly modulated in word skipping, a finding which is inconsistent with the view that the launch-site effect is caused by a saccadic-range error. We observe that distributions of landing positions in skipping saccades show an increased leftward shift compared to non-skipping saccades at equal launch-site distances. Using an improved algorithm for the estimation of mislocated fixations, we demonstrate the reliability of our results.
The aim of this work was to verify the processing of pronominal anaphora by children that have attention deficit hyperactivity disorder or dyslexia. The sample studied consisted of 75 children that speak German, which read two texts of 80 words containing pronominal anaphora. The eye movements of all participants were recorded and, to make sure they were reading with attention, two activities that tested reading comprehension were proposed. Through the analysis of eye movements, specifically the fixations, the data indicate that children with disorders have difficulty to process the pronominal anaphora, especially dyslexic children.
Background
Body image distortion is highly prevalent among overweight individuals. Whilst there is evidence that body-dissatisfied women and those suffering from disordered eating show a negative attentional bias towards their own unattractive body parts and others’ attractive body parts, little is known about visual attention patterns in the area of obesity and with respect to males. Since eating disorders and obesity share common features in terms of distorted body image and body dissatisfaction, the aim of this study was to examine whether overweight men and women show a similar attentional bias.
Methods/Design
We analyzed eye movements in 30 overweight individuals (18 females) and 28 normalweight individuals (16 females) with respect to the participants’ own pictures as well as gender-
and BMI-matched control pictures (front and back view). Additionally, we assessed body image and disordered eating using validated questionnaires.
Discussion
The overweight sample rated their own body as less attractive and showed a more disturbed body image. Contrary to our assumptions, they focused significantly longer on attractive
compared to unattractive regions of both their own and the control body. For one’s own body, this was more pronounced for women. A higher weight status and more frequent body checking predicted attentional bias towards attractive body parts. We found that overweight adults exhibit an unexpected and stable pattern of selective attention, with a distinctive focus on their own attractive body regions despite higher levels of body dissatisfaction. This positive attentional bias may either be an indicator of a more pronounced pattern of attentional avoidance or a self-enhancing strategy. Further research is warranted to clarify these results.
Background
Body image distortion is highly prevalent among overweight individuals. Whilst there is evidence that body-dissatisfied women and those suffering from disordered eating show a negative attentional bias towards their own unattractive body parts and others’ attractive body parts, little is known about visual attention patterns in the area of obesity and with respect to males. Since eating disorders and obesity share common features in terms of distorted body image and body dissatisfaction, the aim of this study was to examine whether overweight men and women show a similar attentional bias.
Methods/Design
We analyzed eye movements in 30 overweight individuals (18 females) and 28 normalweight individuals (16 females) with respect to the participants’ own pictures as well as gender-
and BMI-matched control pictures (front and back view). Additionally, we assessed body image and disordered eating using validated questionnaires.
Discussion
The overweight sample rated their own body as less attractive and showed a more disturbed body image. Contrary to our assumptions, they focused significantly longer on attractive
compared to unattractive regions of both their own and the control body. For one’s own body, this was more pronounced for women. A higher weight status and more frequent body checking predicted attentional bias towards attractive body parts. We found that overweight adults exhibit an unexpected and stable pattern of selective attention, with a distinctive focus on their own attractive body regions despite higher levels of body dissatisfaction. This positive attentional bias may either be an indicator of a more pronounced pattern of attentional avoidance or a self-enhancing strategy. Further research is warranted to clarify these results.
Even during visual fixation of a stationary target, our eyes perform rather erratic miniature movements, which represent a random walk. These "fixational" eye movements counteract perceptual fading, a consequence of fast adaptation of the retinal receptor systems to constant input. The most important contribution to fixational eye movements is produced by microsaccades; however, a specific function of microsaccades only recently has been found. Here we show that the occurrence of microsaccades is correlated with low retinal image slip approximate to 200 ms before microsaccade onset. This result suggests that microsaccades are triggered dynamically, in contrast to the current view that microsaccades are randomly distributed in time characterized by their rate-of-occurrence of 1 to 2 per second. As a result of the dynamic triggering mechanism, individual microsaccade rate can be predicted by the fractal dimension of trajectories. Finally, we propose a minimal computational model for the dynamic triggering of microsaccades
Microsaccades are miniature eye movements produced involuntarily during visual fixation of stationary objects. Since their first description more than 40 years ago, the role of microsaccades in vision has been controversial. In this issue, Martinez-Conde and colleagues present a solution to the long-standing research problem connecting this basic oculomotor function to visual perception, by showing that microsaccades may control peripheral vision during visual fixation by inducing flips in bistable peripheral percepts in head-unrestrained viewing. Their study provides new insight into the functional connectivity between oculomotor function and visual perception
Using a serial search paradigm, we observed several effects of within-object fixation position on spatial and temporal control of eye movements: the preferred viewing location, launch site effect, the optimal viewing position, and the inverted optimal viewing position of fixation duration. While these effects were first identified by eye-movement studies in reading, our approach permits an analysis of the functional relationships between the effects in a different paradigm. Our results demonstrate that the fixation position is an important predictor of the subsequent saccade by influencing both fixation duration and the selection of the next saccade target.
Lisa Schwetlick et al. present a computational model linking visual scan path generation in scene viewing to physiological and experimental work on perisaccadic covert attention, the act of attending to an object visually without obviously moving the eyes toward it. They find that integrating covert attention into predictive models of visual scan paths greatly improves the model's agreement with experimental data. <br /> How we perceive a visual scene depends critically on the selection of gaze positions. For this selection process, visual attention is known to play a key role in two ways. First, image-features attract visual attention, a fact that is captured well by time-independent fixation models. Second, millisecond-level attentional dynamics around the time of saccade drives our gaze from one position to the next. These two related research areas on attention are typically perceived as separate, both theoretically and experimentally. Here we link the two research areas by demonstrating that perisaccadic attentional dynamics improve predictions on scan path statistics. In a mathematical model, we integrated perisaccadic covert attention with dynamic scan path generation. Our model reproduces saccade amplitude distributions, angular statistics, intersaccadic turning angles, and their impact on fixation durations as well as inter-individual differences using Bayesian inference. Therefore, our result lend support to the relevance of perisaccadic attention to gaze statistics.
Saccades move objects of interest into the center of the visual field for high-acuity visual analysis. White, Stritzke, and Gegenfurtner (Current Biology, 18, 124–128, 2008) have shown that saccadic latencies in the context of a structured background are much shorter than those with an unstructured background at equal levels of visibility. This effect has been explained by possible preactivation of the saccadic circuitry whenever a structured background acts as a mask for potential saccade targets. Here, we show that background textures modulate rates of microsaccades during visual fixation. First, after a display change, structured backgrounds induce a stronger decrease of microsaccade rates than do uniform backgrounds. Second, we demonstrate that the occurrence of a microsaccade in a critical time window can delay a subsequent saccadic response. Taken together, our findings suggest that microsaccades contribute to the saccadic facilitation effect, due to a modulation of microsaccade rates by properties of the background.
Hulleman & Olivers' (H&O's) model introduces variation of the functional visual field (FVF) for explaining visual search behavior. Our research shows how the FVF can be studied using gaze-contingent displays and how FVF variation can be implemented in models of gaze control. Contrary to H&O, we believe that fixation duration is an important factor when modeling visual search behavior.
Eye-movement control during scene viewing can be represented as a series of individual decisions about where and when to move the eyes. While substantial behavioral and computational research has been devoted to investigating the placement of fixations in scenes, relatively little is known about the mechanisms that control fixation durations. Here, we propose a computational model (CRISP) that accounts for saccade timing and programming and thus for variations in fixation durations in scene viewing. First, timing signals are modeled as continuous-time random walks. Second, difficulties at the level of visual and cognitive processing can inhibit and thus modulate saccade timing. Inhibition generates moment-by-moment changes in the random walk's transition rate and processing-related saccade cancellation. Third, saccade programming is completed in 2 stages: an initial, labile stage that is subject to cancellation and a subsequent, nonlabile stage. Several simulation studies tested the model's adequacy and generality. An initial simulation study explored the role of cognitive factors in scene viewing by examining how fixation durations differed under different viewing task instructions. Additional simulations investigated the degree to which fixation durations were under direct moment-to-moment control of the current visual scene. The present work further supports the conclusion that fixation durations, to a certain degree, reflect perceptual and cognitive activity in scene viewing. Computational model simulations contribute to an understanding of the underlying processes of gaze control.
In this article, we revisit the mindless reading paradigm from the perspective of computational modeling. In the standard version of the paradigm, participants read sentences in both their normal version as well as the transformed (or mindless) version where each letter is replaced with a z. z-String scanning shares the oculomotor requirements with reading but none of the higher-level lexical and semantic processes. Here we use the z-string scanning task to validate the SWIFT model of saccade generation [Engbert, R., Nuthmann, A., Richter, E., & Kliegl, R. (2005). SWIFT: A dynamical model of saccade generation during reading. Psychological Review, 112(4), 777-813] as an example for an advanced theory of eye-movement control in reading. We test the central assumption of spatially distributed processing across an attentional gradient proposed by the SWIFT model. Key experimental results like prolonged average fixation durations in z-string scanning compared to normal reading and the existence of a string-length effect on fixation durations and probabilities were reproduced by the model, which lends support to the model's assumptions on visual processing. Moreover, simulation results for patterns of regressive saccades in z-string scanning confirm SWIFT's concept of activation field dynamics for the selection of saccade targets.
When watching the image of a natural scene on a computer screen, observers initially move their eyes toward the center of the image—a reliable experimental finding termed central fixation bias. This systematic tendency in eye guidance likely masks attentional selection driven by image properties and top-down cognitive processes. Here, we show that the central fixation bias can be reduced by delaying the initial saccade relative to image onset. In four scene-viewing experiments we manipulated observers' initial gaze position and delayed their first saccade by a specific time interval relative to the onset of an image. We analyzed the distance to image center over time and show that the central fixation bias of initial fixations was significantly reduced after delayed saccade onsets. We additionally show that selection of the initial saccade target strongly depended on the first saccade latency. A previously published model of saccade generation was extended with a central activation map on the initial fixation whose influence declined with increasing saccade latency. This extension was sufficient to replicate the central fixation bias from our experiments. Our results suggest that the central fixation bias is generated by default activation as a response to the sudden image onset and that this default activation pattern decreases over time. Thus, it may often be preferable to use a modified version of the scene viewing paradigm that decouples image onset from the start signal for scene exploration to explicitly reduce the central fixation bias.
Eye movements depend on cognitive processes related to visual information processing. Much has been learned about the spatial selection of fixation locations, while the principles governing the temporal control (fixation durations) are less clear. Here, we review current theories for the control of fixation durations in tasks like visual search, scanning, scene perception, and reading and propose a new model for the control of fixation durations. We distinguish two local principles from one global principle of control. First, an autonomous saccade timer initiates saccades after random time intervals (local-I). Second, foveal inhibition permits immediate prolongation of fixation durations by ongoing processing (local-II). Third, saccade timing is adaptive, so that the mean timer value depends on task requirements and fixation history (Global). We demonstrate by numerical simulations that our model qualitatively reproduces patterns of mean fixation durations and fixation duration distributions observed in typical experiments. When combined with assumptions of saccade target selection and oculomotor control, the model accounts for both temporal and spatial aspects of eye movement control in two versions of a visual search task. We conclude that the model provides a promising framework for the control of fixation durations in saccadic tasks.
Visual information processing is guided by an active mechanism generating saccadic eye movements to salient stimuli. Here we investigate the specific contribution of saccades to memory encoding of verbal and spatial properties in a serial recall task. In the first experiment, participants moved their eyes freely without specific instruction. We demonstrate the existence of qualitative differences in eye-movement strategies during verbal and spatial memory encoding. While verbal memory encoding was characterized by shifting the gaze to the to-be-encoded stimuli, saccadic activity was suppressed during spatial encoding. In the second experiment, participants were required to suppress saccades by fixating centrally during encoding or to make precise saccades onto the memory items. Active suppression of saccades had no effect on memory performance, but tracking the upcoming stimuli decreased memory performance dramatically in both tasks, indicating a resource bottleneck between display-controlled saccadic control and memory encoding. We conclude that optimized encoding strategies for verbal and spatial features are underlying memory performance in serial recall, but such strategies work on an involuntary level only and do not support memory encoding when they are explicitly required by the task.
Bayesian selection of Markov Models for symbol sequences application to microsaccadic eye movements
(2012)
Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.
In this study we re-evaluate the estimation of the self-similarity exponent of fixational eye movements using Bayesian theory. Our analysis is based on a subsampling decomposition, which permits an analysis of the signal up to some scale factor. We demonstrate that our approach can be applied to simulated data from mathematical models of fixational eye movements to distinguish the models' properties reliably.
Background
Body image distortion is highly prevalent among overweight individuals. Whilst there is evidence that body-dissatisfied women and those suffering from disordered eating show a negative attentional bias towards their own unattractive body parts and others' attractive body parts, little is known about visual attention patterns in the area of obesity and with respect to males. Since eating disorders and obesity share common features in terms of distorted body image and body dissatisfaction, the aim of this study was to examine whether overweight men and women show a similar attentional bias.
Methods/Design
We analyzed eye movements in 30 overweight individuals (18 females) and 28 normal-weight individuals (16 females) with respect to the participants' own pictures as well as gender- and BMI-matched control pictures (front and back view). Additionally, we assessed body image and disordered eating using validated questionnaires.
Discussion
The overweight sample rated their own body as less attractive and showed a more disturbed body image. Contrary to our assumptions, they focused significantly longer on attractive compared to unattractive regions of both their own and the control body. For one's own body, this was more pronounced for women. A higher weight status and more frequent body checking predicted attentional bias towards attractive body parts. We found that overweight adults exhibit an unexpected and stable pattern of selective attention, with a distinctive focus on their own attractive body regions despite higher levels of body dissatisfaction. This positive attentional bias may either be an indicator of a more pronounced pattern of attentional avoidance or a self-enhancing strategy. Further research is warranted to clarify these results.
During reading, saccadic eye movements are generated to shift words into the center of the visual field for lexical processing. Recently, Krugel and Engbert (Vision Research 50:1532-1539, 2010) demonstrated that within-word fixation positions are largely shifted to the left after skipped words. However, explanations of the origin of this effect cannot be drawn from normal reading data alone. Here we show that the large effect of skipped words on the distribution of within-word fixation positions is primarily based on rather subtle differences in the low-level visual information acquired before saccades. Using arrangements of "x" letter strings, we reproduced the effect of skipped character strings in a highly controlled single-saccade task. Our results demonstrate that the effect of skipped words in reading is the signature of a general visuomotor phenomenon. Moreover, our findings extend beyond the scope of the widely accepted range-error model, which posits that within-word fixation positions in reading depend solely on the distances of target words. We expect that our results will provide critical boundary conditions for the development of visuomotor models of saccade planning during reading.
Control of fixation duration during scene viewing by interaction of foveal and peripheral processing
(2013)
Processing in our visual system is functionally segregated, with the fovea specialized in processing fine detail (high spatial frequencies) for object identification, and the periphery in processing coarse information (low frequencies) for spatial orienting and saccade target selection. Here we investigate the consequences of this functional segregation for the control of fixation durations during scene viewing. Using gaze-contingent displays, we applied high-pass or low-pass filters to either the central or the peripheral visual field and compared eye-movement patterns with an unfiltered control condition. In contrast with predictions from functional segregation, fixation durations were unaffected when the critical information for vision was strongly attenuated (foveal low-pass and peripheral high-pass filtering); fixation durations increased, however, when useful information was left mostly intact by the filter (foveal high-pass and peripheral low-pass filtering). These patterns of results are difficult to explain under the assumption that fixation durations are controlled by foveal processing difficulty. As an alternative explanation, we developed the hypothesis that the interaction of foveal and peripheral processing controls fixation duration. To investigate the viability of this explanation, we implemented a computational model with two compartments, approximating spatial aspects of processing by foveal and peripheral activations that change according to a small set of dynamical rules. The model reproduced distributions of fixation durations from all experimental conditions by variation of few parameters that were affected by specific filtering conditions.
In humans and in foveated animals visual acuity is highly concentrated at the center of gaze, so that choosing where to look next is an important example of online, rapid decision-making. Computational neuroscientists have developed biologically-inspired models of visual attention, termed saliency maps, which successfully predict where people fixate on average. Using point process theory for spatial statistics, we show that scanpaths contain, however, important statistical structure, such as spatial clustering on top of distributions of gaze positions. Here, we develop a dynamical model of saccadic selection that accurately predicts the distribution of gaze positions as well as spatial clustering along individual scanpaths. Our model relies on activation dynamics via spatially-limited (foveated) access to saliency information, and, second, a leaky memory process controlling the re-inspection of target regions. This theoretical framework models a form of context-dependent decision-making, linking neural dynamics of attention to behavioral gaze data.
The interplay between cognitive and oculomotor processes during reading can be explored when the spatial layout of text deviates from the typical display. In this study, we investigate various eye-movement measures during reading of text with experimentally manipulated layout (word-wise and letter-wise mirrored-reversed text as well as inverted and scrambled text). While typical findings (e.g., longer mean fixation times, shorter mean saccades lengths) in reading manipulated texts compared to normal texts were reported in earlier work, little is known about changes of oculomotor targeting observed in within-word landing positions under the above text layouts. Here we carry out precise analyses of landing positions and find substantial changes in the so-called launch-site effect in addition to the expected overall slow-down of reading performance. Specifically, during reading of our manipulated text conditions with reversed letter order (against overall reading direction), we find a reduced launch-site effect, while in all other manipulated text conditions, we observe an increased launch-site effect. Our results clearly indicate that the oculomotor system is highly adaptive when confronted with unusual reading conditions.
Microsaccades - i.e., small fixational saccades generated in the superior colliculus (SC) - have been linked to spatial attention. While maintaining fixation, voluntary shifts of covert attention toward peripheral targets result in a sequence of attention-aligned and attention-opposing microsaccades. In most previous studies the direction of the voluntary shift is signaled by a spatial cue (e.g., a leftwards pointing arrow) that presents the most informative part of the cue (e.g., the arrowhead) in the to-be attended visual field. Here we directly investigated the influence of cue position and tested the hypothesis that microsaccades align with cue position rather than with the attention shift. In a spatial cueing task, we presented the task-relevant part of a symmetric cue either in the to-be attended visual field or in the opposite field. As a result, microsaccades were still weakly related to the covert attention shift; however, they were strongly related to the position of the cue even if that required a movement opposite to the cued attention shift. Moreover, if microsaccades aligned with cue position, we observed stronger cueing effects on manual response times. Our interpretation of the data is supported by numerical simulations of a computational model of microsaccade generation that is based on SC properties, where we explain our findings by separate attentional mechanisms for cue localization and the cued attention shift. We conclude that during cueing of voluntary attention, microsaccades are related to both - the overt attentional selection of the task-relevant part of the cue stimulus and the subsequent covert attention shift.(C) 2017 Elsevier Ltd. All rights reserved.
Skilled reading requires information processing of the fixated and the not-yet-fixated words to generate precise control of gaze. Over the last 30 years, experimental research provided evidence that word processing is distributed across the perceptual span, which permits recognition of the fixated (foveal) word as well as preview of parafoveal words to the right of fixation. However, theoretical models have been unable to differentiate the specific influences of foveal and parafoveal information on saccade control. Here we show how parafoveal word difficulty modulates spatial and temporal control of gaze in a computational model to reproduce experimental results. In a fully Bayesian framework, we estimated model parameters for different models of parafoveal processing and carried out large-scale predictive simulations and model comparisons for a gaze-contingent reading experiment. We conclude that mathematical modeling of data from gaze-contingent experiments permits the precise identification of pathways from parafoveal information processing to gaze control, uncovering potential mechanisms underlying the parafoveal contribution to eye-movement control.
Skilled reading requires information processing of the fixated and the not-yet-fixated words to generate precise control of gaze. Over the last 30 years, experimental research provided evidence that word processing is distributed across the perceptual span, which permits recognition of the fixated (foveal) word as well as preview of parafoveal words to the right of fixation. However, theoretical models have been unable to differentiate the specific influences of foveal and parafoveal information on saccade control. Here we show how parafoveal word difficulty modulates spatial and temporal control of gaze in a computational model to reproduce experimental results. In a fully Bayesian framework, we estimated model parameters for different models of parafoveal processing and carried out large-scale predictive simulations and model comparisons for a gaze-contingent reading experiment. We conclude that mathematical modeling of data from gaze-contingent experiments permits the precise identification of pathways from parafoveal information processing to gaze control, uncovering potential mechanisms underlying the parafoveal contribution to eye-movement control.
In an influential theoretical model, human sensorimotor control is achieved by a Bayesian decision process, which combines noisy sensory information and learned prior knowledge. A ubiquitous signature of prior knowledge and Bayesian integration in human perception and motor behavior is the frequently observed bias toward an average stimulus magnitude (i.e., a central-tendency bias, range effect, regression-to-the-mean effect). However, in the domain of eye movements, there is a recent controversy about the fundamental existence of a range effect in the saccadic system. Here we argue that the problem of the existence of a range effect is linked to the availability of prior knowledge for saccade control. We present results from two prosaccade experiments that both employ an informative prior structure (i.e., a nonuniform Gaussian distribution of saccade target distances). Our results demonstrate the validity of Bayesian integration in saccade control, which generates a range effect in saccades. According to Bayesian integration principles, the saccadic range effect depends on the availability of prior knowledge and varies in size as a function of the reliability of the prior and the sensory likelihood.