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Humans quickly learn to blink strategically in responseto environmental task demandsDavid Hoppea,b, Stefan Helfmannb, and Constantin A. Rothkopfa,b,c,1

aCentre for Cognitive Science, Technical University Darmstadt, 64283 Darmstadt, Germany; bInstitute of Psychology, Technical University Darmstadt, 64283Darmstadt, Germany; and cFrankfurt Institute for Advanced Studies, Goethe University, 60438 Frankfurt, Germany

Edited by Robert H. Wurtz, National Institutes of Health, Bethesda, MD, and approved January 17, 2018 (received for review August 11, 2017)

Eye blinking is one of the most frequent human actions. The con-trol of blinking is thought to reflect complex interactions betweenmaintaining clear and healthy vision and influences tied to centraldopaminergic functions including cognitive states, psychologicalfactors, and medical conditions. The most imminent consequenceof blinking is a temporary loss of vision. Minimizing this loss ofinformation is a prominent explanation for changes in blink ratesand temporarily suppressed blinks, but quantifying this loss isdifficult, as environmental regularities are usually complex andunknown. Here we used a controlled detection experiment withparametrically generated event statistics to investigate humanblinking control. Subjects were able to learn environmental regu-larities and adapted their blinking behavior strategically to betterdetect future events. Crucially, our design enabled us to developa computational model that allows quantifying the consequenceof blinking in terms of task performance. The model formalizesideas from active perception by describing blinking in terms ofoptimal control in trading off intrinsic costs for blink suppres-sion with task-related costs for missing an event under perceptualuncertainty. Remarkably, this model not only is sufficient to repro-duce key characteristics of the observed blinking behavior such asblink suppression and blink compensation but also predicts with-out further assumptions the well-known and diverse distributionsof time intervals between blinks, for which an explanation haslong been elusive.

eye blinks | interblink intervals | computational modeling | internal costs |individual differences

B linking is an omnipresent involuntary process, which humanscarry out 15–17 times per minute (1), on average. It primar-

ily serves the physiological purpose of cleaning the surface of theeye and providing a stable tear film (2), of preventing opticalaberrations (3–6), and thus maintaining good quality of vision(7). Besides these positive consequences, blinking has an imme-diate negative consequence on perception as during blinking thestream of visual information is interrupted (Fig. 1A). Moreover,in addition to the break of optic signals due to the occlusionof the pupil by the upper lid, neural processing is inhibited (8,9). This leads to perceptual gaps every 2–3 s. If not timed cor-rectly, these gaps can lead to negative outcomes in numeroussituations. In social interaction, for example, microexpressionshave a duration between 160 ms and 500 ms and can thereforeeasily be missed due to a blink (10). Indeed, humans have beenshown to reduce these gaps by combining blinks with saccades(11, 12), during which neuronal processing is also inhibited. Thesame has been shown for animals (13, 14). Overall, the positiveeffects of blinking on the maintenance of proper vision and thenegative effects of the interruption of vision constitute a funda-mental trade-off. Hence, controlling actively when to blink pro-vides a behavioral advantage compared with blinking at randompoints in time.

Investigations of the control of blinking have revealed anintriguing multitude of additional factors influencing humanblink rates so that blinking is often used as a behavioral markerfor a variety of internal processes. Blinking is closely intertwinedwith cognitive functions connected to dopamine (see ref. 15 fora recent review). In particular, blink rates reflect the progressof learning (16) and the perception of time (17). Blinking is also

affected by our current goals and actions. It depends on what taskwe are solving (see refs. 18–20 for reviews), how long we are onthe task (21), and how difficult the task is (22), and it is an indi-cator of what we remember afterward (23). Even the coordina-tion of blinks and saccades is influenced by cognitive factors (24).Finally, blinks have been shown to be synchronized across peo-ple during conversation and thus might play a role during humansocial communication (25). While blinking is clearly related tothese cognitive processes, it is still debated whether the appro-priate measure is the blinking rate during a task, the sponta-neous blinking rate, or possibly the distribution of times betweentwo consecutive blinks, the so-called interblink interval (IBI) dis-tribution, or whether these quantities are potentially inherentlyrelated (see ref. 26 for a recent discussion). Thus, a better under-standing of the process underlying blinking behavior is benefi-cial to understanding a wide range of perceptual and cognitiveprocesses.

Although numerous empirical studies have established theimportance of blinking, quantitative explanations have beenscarce. Current models assume a linear increase in urge whenblinking is suppressed (27) or an oscillating blink generator(28), but both models considered voluntary blink suppressionand do not incorporate any task-related influences. One rea-son might be that environmental regularities and task-relatedcosts are usually complex and unknown. The lack of quantita-tive models is surprising, considering the strong contingenciesbetween environmental statistics and gaze behavior, which havebeen explained successfully through modeling (29–32). As withblink rates, few computational approaches exist that describe thetemporal course of blinking. In particular, the IBI distribution is

Significance

Eye blinks serve the purpose of maintaining healthy vision butduring a blink visual information processing is interrupted.While a multitude of medical, cognitive, and psychological fac-tors have been shown to influence blinking, the present studyestablishes quantitatively how human blinking behavior isdynamically adapted to environmental task demands. In ourexperiment participants quickly learned to blink strategically.A minimal computational model captures the observed behav-ior as a trade-off between internal, physiological benefitsand external, task-related costs given perceptual uncertain-ties. Crucially, the model allows predicting an individual sub-ject’s temporal dynamics of blinking and provides an expla-nation of the long-known distribution of interblink intervals.Taken together, this provides a basis for future research usingblinking as a behavioral marker.

Author contributions: D.H. and C.A.R. designed research; S.H. performed research; D.H.and C.A.R. analyzed data; and D.H. and C.A.R. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.1 To whom correspondence should be addressed. Email: rothkopf@psychologie.tu-darmstadt.de.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1714220115/-/DCSupplemental.

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Fig. 1. Experimental design and stimulus genera-tion. (A) Schematic time course for a single blink(from ref. 9; reprinted with permission from AAAS).(B) Four different IBI distributions found by ref. 33(reprinted from ref. 33). The shapes are not equallyfrequent. Most subjects showed J-shaped (62%), sym-metric was the least often (4%), and bimodal andirregular comprised 12% and 22% of the cases,respectively. (C) Task design. In each block a gray dot(0.3�) moved on a circular trajectory for 100 consecu-tive laps. The trajectory was not visible to the subject.In each lap three to five events occurred. An eventcomprised the circle being replaced with a comic facefor 50 ms. Subjects attempted to detect as many ofthe events as possible by pressing a button. (D) Eventgeneration for a single block. Three to five eventsper lap were drawn from a mixture of a uniform anda Gaussian distribution. (D, Lower) Sample laps andevents are shown. Overall, four different conditionswere presented to the participants. The conditionsdiffered with respect to the mean of the Gaussiandistribution.

an active research area. In their seminal paper, Ponder andKennedy (33) found four different types of IBI distributions(Fig. 1B). Since then, many studies have presented similar resultsshowing that subjects’ IBI distributions show great variability(e.g., ref. 34). However, the origin of these different IBI distri-butions and their variability is unclear.

Here we address the question of how blinking behavior isrelated and adapted to the current task. We conducted a con-trolled blinking experiment with parametrically generated envi-ronmental statistics. Using an event detection paradigm, wecreated a direct connection between temporary loss of visualinformation due to blinking and task performance. Crucially,knowing the probabilistic structure of the task, we are able toinvestigate how blinks are linked to internal beliefs about taskparameters and how participants adapted their blinking to thetask. The computational model treats blinking dynamics as theresult of a trade-off between the physiological need to blinkand the task-related cost of blinking given subjects’ beliefs. Themodel captures our subjects’ strategic blinking behavior in theexperiment and provides a quantitative explanation for changesin blinking behavior. Importantly, based on the computationalmodel we derive the temporal structure of blinking behaviorincluding the IBI distribution on the basis of an individual sub-ject. This provides an explanation of the classic IBI distributionsobserved in numerous experiments and lays the groundwork forquantitative studies investigating blinking behavior, task struc-ture, and subjects’ perceptual uncertainties.

ResultsSubjects directed their gaze to a gray dot moving on a circulartrajectory (counterclockwise) displayed on a computer monitorto detect events (Fig. 1C). A circular trajectory was chosen toavoid blinks being triggered by saccades (11, 12). Velocity of thedot was chosen to lead to smooth pursuit without catch-up sac-cades. Events were defined by replacing the dot with a stylizedface for 50 ms. Hence, a normal blink (9, 35, 36) could lead tomissing an event. Events were generated probabilistically andwere drawn from a mixture of a Gaussian distribution (Fig. 1D)using a mixing weight of P =0.8 and a uniform distribution withmixing weight of 0.2. On each lap the number of events was ran-domly chosen between three and five. Over the course of 100consecutive laps subjects could learn the relationship betweenthe angle at which the dot was on its circular trajectory andthe probability of an event occurring. Overall, subjects com-pleted four blocks differing with respect to the location of theGaussian. Blocks were presented in a random order. After each

block subjects were given the percentage of detected events asfeedback.

Overall, 25 subjects (8 male) participated in the experiment inexchange for course credit. Their age ranged from 19 y to 56 y(M = 26.52, SD = 10.97). Seven subjects wore glasses; however,sufficient accuracy of the eye tracker and the detection of blinkswas ensured for all participants (see Materials and Methods fordetails on the detection of blinks).

Behavioral Results. Data from nine consecutive laps are shownfor a single participant in Fig. 2A. Visual inspection yields thefirst indications for a connection between event probability andblinking behavior. Overall, the distribution of blink locations forall participants showed a similar time course across all condi-tions (Fig. 2B, Top). As conditions differed only with respectto the mean of the Gaussian while sharing the same variance,data were aggregated by normalizing the event distribution topeak at 180� (Fig. 2B, Bottom). The data show that blinkingbehavior was clearly affected by the distribution of event prob-abilities. Instead of being distributed uniformly over the circle,two characteristics of the distribution of blinks can be observed:First, blinking is suppressed in the area of high event probabil-ity (HEP) (±2 SDs from the center of the mixture distribution).Fewer blinks occurred in the HEP area (blink rate rHEP = 11.28)compared with the remaining part (rnot HEP = 20.46; Fig. 2C).The 95% credibility interval for the difference in blinking rateswas [8.67, 9.67]. This indicates that blinking behavior is adaptedto the event distribution to avoid missing events. Second, visualinspection indicates an asymmetry of blinking counts before andafter the HEP region. Indeed, we found a higher number ofblinks after (blink rate rafter HEP = 25.16; Fig. 2D) than beforethe HEP region (blink rate rbefore HEP = 15.76; 95% credibilityinterval for the difference was [8.71, 10.01]).

To investigate how learning of the event distribution affectedblinking, we computed the proportion of blinks in the HEP areaover the course of the 100 laps (Fig. 2E). The proportion of blinksoccurring in the HEP region declined over the course of the firstlaps and was constant afterward. This indicates that in the begin-ning subjects learned the hidden event distribution by observingthe event locations. Bayesian change-point analysis (37) revealedthat the steady state was reached on average after about 13laps (95% credibility interval of the change point was [9.15,17.47]).

A Computational Model for Blinks. The design of our experimentgives access to the statistical structure of the task in terms of a

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Fig. 2. Behavioral results. (A) Raw data (blinks and events) for a single participant in nine consecutive laps. Top row depicts the temporal dynamics ofblinks and events. Bottom rows show histograms for the blinks and events aggregated over the angular locations of the laps. (B) Blinking frequencies overlocations within the circular trajectory. (Top) Histograms are shown for all four conditions. Center of the event-generating mixture distribution is indicatedby a green bar for each condition. (Bottom) Data from all conditions were normalized by rotation. The normalized event-generating distribution wascentered to 180�. (C) Comparison of the mean number of blinks aggregated for all conditions between the area ±2 SDs (HEP) from the center and theremaining part of the circle. Error bars correspond to the SEM. (D) Differences in number of blinks between the 60� area before and after the HEP area.Again, error bars correspond to the SEM. (E) Percentage of blinks occurring in the HEP area over the course of 100 laps. Chance level assumes that blinks areuniformly distributed over the circle (red dashed line). For the percentage of blinks occurring in the areas before and after the HEP area see Fig. S1C. Forthe course of absolute blink rates see Fig. S1 A and B.

probabilistic generative model. Crucially, we are able to deter-mine the loss of information due to a blink by quantifying theinfluence on task performance at each point in time during theexperiment. This is a distinct advantage compared with investi-gations studying human blinking behavior during reading or freeviewing, where it is difficult to capture the consequences of blink-ing quantitatively.

The computational model is motivated by capturing the fun-damental trade-off between costs and benefits of blinking andcomprises two distinct components that control blinking behav-ior: (i) internal costs for blink suppression and (ii) external task-related costs for blink execution. Internal costs for blink suppres-sion arise due to the subjects’ physiological need to blink fromtime to time to maintain healthy vision. Formally, we denote thecosts for blink suppression as cs . It is important to note that csdoes not depend on the current location within the lap, since itis independent of the task. Further, our data suggest that cs doesnot depend on the time since the last blink (Supporting Informa-

tion and Fig. S5). The second factor is the cost associated withblink execution ce(✓). It points in the direction opposite to cs ,as more blinks lead to higher costs. This component denotes theamount of task performance that is lost in the case of a blink. Inour experimental procedure this is the probability of detectingevents. In contrast to the costs for blink suppression cs , the task-related costs ce(✓) depend on the current angle and thereforeare not constant over the course of a lap (higher blink-relatedcosts in the HEP region). Whether to blink or not to blink at anypoint in time therefore can be described as a trade-off between csand ce(✓).

Here we assume that the probability of a blink occurring at anangle ✓ can be modeled as being inversely proportional to thesum of the costs of blink suppression cs and blink execution ce ,

P(blink at ✓ |↵, )_ 1(1�↵)cs +↵ce(✓, )

, [1]

where cs is the cost for blink suppression, ce(✓, ) is the costfor blink execution in terms of reduced task performance, ↵is between 0 and 1 and regulates how much weight is put onthe task, and = [mixing proportion, perceptual uncertainty]areparameters describing the subject’s belief about the experimentgiven previous observations. Intuitively, a weight of ↵=1 corre-sponds to blinking only because of the external task and there-fore suppressing blinks for maintaining vision while a weight of↵=0 corresponds to putting complete priority on maintaininghealthy vision and thereby blinking only to lubricate the cornea(Fig. 3A).

The cost for blinking ce(✓) is derived as the probability of miss-ing an event and therefore depends on the current angle ✓,

P(miss|✓,µ,�2, p)=n(✓)P(event at ✓ |µ,�2, p), [2]

where µ,�2 and p are the parameters of the mixture distributiongenerating the events, ✓ is a location during the lap, and n(✓)is the average number of events left at each location during aparticular lap (see Supporting Information for details).

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Fig. 3. Computational model results. (A) Schematic overview of the generative model. Our model forms a belief about the probabilistic nature of the taskenvironment. This belief structure is used for action selection while balancing multiple costs. For a more detailed visualization of the computational stepsinvolved in building our subjects’ belief see Fig. S2. (B) Model results for blinking behavior. Shown are number of blinks per degree (black line; also Fig. 2B)and the fitted model (orange line). (C) Model prediction of the temporal statistics of the blinking behavior. (Left) The distribution of the IBIs. The histogramdepicts all our subjects’ data. (Right) The distribution of number of blinks per lap. Data are shown in black, and model predictions are shown in orange.(D) Probability of blinking depending on the location on the circle (x axis, from 0� to 360�) and the time since the last blink (y axis, from 0 s to 5 s). (Right)Model predictions. (Left) Subject data. We weighted very short IBIs using a cumulative Gaussian (32). This accounts for motor delays, making two blinksoccurring with close to zero IBI very unlikely. (E) Single-participant results. From Top to Bottom: Blinking proportion over the circle, IBI distributions, blinksper lap, and blinking probability in the angle and time domain are shown for three participants. The fitted model is depicted in orange, and data are shownin black. Bottom row contains the theoretical distribution (Left), samples from the theoretical distribution matched to the number of blinks of the individualsubject (Center), and our subjects’ data (Right). Results for all participants can be found in Figs. S3 and S4 and Table S1.

The subjects’ belief about the costs for blinking is furthermoreinfluenced by their uncertainty about the true underlying eventdistribution during the experiment. We accounted for the imper-fect knowledge by assuming that subjects do not have access tothe exact parameters of the mixture distribution. In particular,we allowed the mixing proportion to be different from the truevalue that was used for event generation. In addition, we hypoth-esized that subjects have perceptual uncertainty given previousobservations about the exact parameters describing the Gaussiandistribution from which the events are drawn. Overall, fourparameters (mixing proportion p, cost trade-off ↵, average blink-ing rate r , and the spread of the temporal uncertainty) wereestimated from data across subjects. For parameter estimationonly data from the subjects’ steady-state behavior were used, asthe changes in blinking behavior at the beginning of a block arerelated to learning the new event distributions. Thus, changes inthe subjects’ belief, which occur during learning the experimentalstatistics at the beginning of a new block, would affect these esti-mates. Change-point analysis revealed that steady-state behaviorwas reached after 20 laps.

Model Results. We fitted our model to the aggregated blinkingdata. The result is shown in Fig. 3B. Our model is capable ofreflecting the characteristic course of blinking behavior. More-over, we are now able to link both main effects, blink suppressionas well as blink compensation, to computational quantities in ourmodel: (i) Blink suppression follows from putting a higher valueon the ongoing task. This leads to a higher proportion of blinksrelated to the ongoing external task. In the current experiment,this means that few blinks are carried out in those regions aroundthe circular trajectory of the target where the probability of anevent is high and thus the loss of task-related information is high.(ii) The asymmetric shape of the curve is due to uncertainties inthe subjects’ belief where exactly the probability of an event ishighest and the dynamic changes in this belief structure due toobserving events over the course of a lap. Specifically, similar toa survival process, the fewer events have been observed during alap, the higher the probability that an event is imminent. Finally,closer inspection of the probability of blinking in Fig. 3B revealsa less steep decrease in blinking probability at around 90�. Inthis region the belief that all events from the previous lap have

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already occurred is small given the perceptual uncertainty andpast event observations.

The results further suggest that the mixing rate of the mixturedistribution is underestimated by our subjects (p=0.58 com-pared with p=0.8). This is not surprising since learning a com-plex mixture distribution from noisy observations is a hard task(e.g., ref. 38). Hence, our subjects know less about the task statis-tics compared with an ideal observer. Perceptual uncertainty dueto observations of events as well as uncertainty from storingevents in memory was estimated to be �perc =29.6�.

A crucial property of the proposed model of the probabilityof blinking is that it allows deriving the temporal statistics ofsubjects’ blinking data. The probability of a specific IBI d (timebetween two consecutive blinks) can be computed as follows:Assume a blink occurring at a random location ✓ with probabil-ity P(blink at ✓). Since the next blink is executed at ✓+ d for thenext d time steps, no blink occurs. Finally, d time steps after thefirst blink the next blink occurs. This yields

P(blink at ✓ | d)=P(blink at ✓� d)

·"

✓�1Y

k=✓�d+1

(1�P(blink at ✓� k))

#·P(blink at ✓). [3]

IBI distributions can be obtained by repeating this process for allvalues of ✓ and d and averaging over ✓. Thus, our approach yieldsan analytic description of the distribution of IBIs as a productof geometric distributions, which has an intuitive link to blink-ing as sequential Bernoulli trials with varying probabilities. Notethat previous empirical studies have proposed a power-law dis-tribution to describe the IBI distributions (39). However, ourapproach explicitly incorporates the nonstationary nature of theblinking rate in our task. By using this procedure we are able torecover main characteristics of the temporal dynamics (Fig. 3 C

and D) of subjects’ blinks. Crucially, no further parameters needto be estimated.

As prior research on blinking has shown large individual dif-ferences, we fitted our model to each subject independently. Weestimated the parameters for the cost trade-off as well as for themean blinking rate on a subject-by-subject basis. The uncertain-ties about the temporal structure and the event-generating dis-tribution were assumed to be the same across participants. Wetherefore used the respective values estimated from the aggre-gated data. Results for three subjects are shown in Fig. 3E. Indi-vidual blinking strategies were highly variable and IBIs werequalitatively different across subjects. Remarkably, our modelcaptures and explains this variability. As a consequence, we areable to link qualitative differences in behavior between individu-als to quantitative differences in model components. The modelsuggests that the variability in blinking behavior can be ascribedto differences among subjects in motivational as well as physio-logical parameters. Specifically, three of the four IBI histogramshapes (J-shaped, bimodal, irregular) consistently found by pre-vious studies can be explained through motivational differencesacross subjects combined with the temporal structure of the task.The analysis further reveals that the least frequently found shape(symmetric) does not result from differences in the trade-offbetween task demands and physiological needs or from differ-ences in the general blinking rate.

Overall, participants detected 87% of all events. Two partic-ipants showed very low performance scores (smaller than 70%,>2�) and were excluded from the analysis. We tested whethersubjects who put greater weight on the external task, i.e., ahigher estimated ↵ parameter, showed better performance (Fig.S6). Linear regression revealed a significant relationship betweenthe individually estimated values for ↵ and the percentage ofdetected events, r(23)= 0.51, p=0.01. Importantly, this meansthat subjects blinked more strategically instead of less often,as we found no significant connection between smaller blinkingrates and higher performance, r(23)= 0.38, p=0.07.

DiscussionIn our study, we investigated how blinking behavior is relatedto internal costs and environmental visual demands. In partic-ular, while prior research has provided various accounts of thelink between blinks and task demands, there exists little workquantifying this connection. We created an event detection tasktailored to studying blinking behavior quantitatively. Subjectsdetected events while fixating on a moving dot. The event prob-ability was linked to the spatial location of the dot, a regular-ity subjects could learn over the course of the experiment. Ourdesign provides full control and knowledge regarding the tempo-ral statistics of the visual input as well as the reward structure ofthe task. In particular, the consequences of blinking on the lossof information can be quantified.

The probabilistic design of the experiment allowed developinga computational model of blinking behavior. The basic assump-tion is that blinking is the consequence of a trade-off between aninternal urge to blink to maintain healthy vision and external taskrequirements of not blinking when crucial information needs tobe acquired from the environment. Given subjects’ perceptualand memory uncertainties about the event-generating processin the experiment, it is possible to quantify the cost of blinkingin terms of task performance, i.e., the probability of detectingan event.

The behavioral data show two main effects: First, blinkingwas significantly suppressed in the HEP region, i.e., where mostevents occurred. Our computational model results suggest thatthis effect can be explained in terms of minimal loss of task-relevant information. This result is in accordance with priorresearch that reported a connection between blink suppressionand task performance (40). Also, in classical psychophysicalexperiments blinks have been shown to occur around the time ofresponse (41) and toddlers watching movies showed suppressedblinking at scenes containing affective and physical events (42).Thus, subjects who weighted costs associated with the exter-nal task more tended to blink more strategically and thereforeavoided blinking in the HEP region.

Second, more blinks occurred after the HEP region comparedwith before. Although the probability of missing an event is sym-metrical around the peak of the event-generating distribution,the observed blinking pattern is not. This asymmetry is pre-dicted by our model if we account for observations made over thecourse of a lap. The event probability and therefore the proba-bility of missing an event during a blink are proportional to thenumber of events left. Hence, blinking earlier in a lap leads togreater loss of detection performance. With every observed eventthe number of events left in a lap decreases. Finding this asym-metry of blinking strategies in our data reveals two properties ofour subjects’ information processing: Subjects learned the num-ber of events per lap and they were able to dynamically incor-porate recent information about observed events for decidingwhen to blink. Compensation between episodes of suppressionhas been reported in the past (40). While other studies arguethat blinks take on a role of breakpoints to facilitate mental pro-cessing (43), in our study, blinking was well described in terms ofcollecting maximal task-relevant information.

The distribution of IBIs is highly variable across humans (33).Four different shapes have been identified repeatedly: J-shaped,irregular plateau, bimodal, and symmetric (33, 44, 45). Here, weshowed that three of these shapes arise as an immediate conse-quence of the trade-off between internal and external task costs.Our model is capable of capturing the characteristics of the firstthree types (see also individual model fits for all data in Figs. S3and S4). One participant (subject 19 in Fig. S4), however, showeda symmetric distribution which was not well fitted by our model.One explanation could be that the symmetric shape (the leastoften according to ref. 33) does not arise from interacting withthe task but from physiological properties that were not capturedby our model.

Few models have been developed to describe blinking behav-ior. In their urge model, the authors of ref. 27 assumed a linear

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increase in urge when blinking is suppressed. However, themodel does not account for any external task-related influences.In another study (28) it was proposed that blinks are generatedby an oscillating blink generator. However, both studies used vol-untary blink suppression. Here we presented a computationalmodel that explicitly included task-related goals as well as intrin-sic costs, thereby building a natural connection to the reward-related learning literature involving dopamine. Hence, the modelcan be applied to a broader area of investigations as long assome properties about the environmental statistics are known.While we presented results for a psychophysical detection task,our approach is not limited to simple stimuli. Recent develop-ments in machine learning and deep neural networks (e.g., ref.46) have paved the way for retrieving statistical regularities evenin complex and dynamic visual scenarios. In combination withthese methods, our blinking model can readily be applied tomany real-world problems. Better understanding of and, in par-ticular, quantitative insights into human blinking behavior arealso relevant for building technical aid systems (ref. 47, for exam-ple) and detecting mental states during critical tasks to preventaccidents (48).

Materials and MethodsBlink Detection. Blinks were detected using an infrared eye-tracking device(Tobii EyeX eye tracker; 60 Hz). This technique has been used in past research(e.g., refs. 17 and 39). During blinking and thus closed eyes, the eye-trackingdevice loses track of the pupils and cannot determine the gaze location.These artifacts were identified and used to detect blinks by analyzing theirtemporal structure. We tested different thresholds on three subjects whilemanually recording blinks and chose the threshold with the best agreement.For the analysis, blinks were treated as point processes. Using this proce-dure we found similar statistics regarding blink rates and IBIs compared withstudies using magnetic search coils (e.g., ref. 18), manual video analysis (45),and EEGs (23).

Experiment Setup. The test subjects were seated in front of a computerscreen (Flatron W2242TE monitor; 1,680 ⇥ 1,050-pixel resolution, 60-Hzrefresh rate) at a distance of about 55 cm. All experimental proce-dures were carried out in accordance with the guidelines of the GermanPsychological Society and approved by the ethics committee of theDarmstadt University of Technology. Subjects gave informed consent andwere aware that their eye movements were recorded; however, they weretold about the purpose of the task after the experiment to prevent con-scious control of the blinking behavior.

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Supporting Information

Hoppe et al. 10.1073/pnas.1714220115SI Materials and Methods

Belief About Number of Events Left. The belief about the prob-ability of missing an event depends on how many events havealready been seen over the course of the current lap. To describeour subjects’ belief, we computed the average number of eventsobserved up to a certain point within the lap. This was done forall locations in the lap, parameterized by the angle ✓,

n(✓) = n � n

✓Z

0

P(event at ⌧ | µ,�2, p)d⌧, [S1]

where P(event at ⌧) is the probability of an event at an angle ⌧[this corresponds to our mixture of U(0, 360) and N (180, 30) at alocation ⌧ ], (µ,�2, p) are the parameters of the event-generatingdistribution, and n is the mean number of events per lap.

Procedure and Feedback. The experiment was conducted in singlesessions. Subjects confirmed the detection of an event by press-ing a button on a keyboard. If the button press occurred withina 1-s time range subsequent to the event, the event was regardedas detected. If no button was pressed, the event was marked asmissed. Missing an event produced a sound to signal the missto the subject. A different sound was played in the case of aresponse without prior event. The sounds served as feedback tohelp the subject learn the event distribution. Additional feedbackwas given to the subject after each block in the form of a score(one point per detected event, minus one point for button presseswithout events, zero points for missed events).

Constant Costs for Blink Suppression. Our computational blinkingmodel assumes that the costs for blink suppression cs are con-stant and therefore neither depend on the current location ✓ inthe lap nor depend on the time since the last blink d (IBI). Thefirst independence follows from the definition of the cost as taskindependent, but the second one is not apparent. While we donot claim that costs do not increase at all with time, we provideevidence that for the durations between two blinks observed inthe current experiments, costs indeed did not increase signif-icantly. To this end, we tested whether the costs for blinkingdepend on how much time has passed since the last blink. Thestatistical independence assumption in our model can be formal-ized as

P(blink |✓, d) ?= P(blink |✓). [S2]

This formalization provides a way to test whether costs for blinksuppression depend on the IBI. If the assumption holds, weexpect P(blink |✓) not to be affected by the value of d ; i.e., themarginal distribution of blinks over a lap should not be differentif the time since the last blink is 4 s instead of 2 s, for example.On the other hand, if costs for blink suppression increase withthe time passed since the last blink, we expect a more even blinkdistribution for longer IBIs, as with greater costs for blink sup-pression less value is given to the task. We tested this empiricallyusing our data by comparing the conditional probability of blinksat a location ✓ for the following ranges for d :

P(blink |✓, 0s < d < 2s)?= P(blink |✓, 2s < d < 4s)

?= · · · ?

= P(blink |✓, 8s < d < 10s). [S3]

To test our hypothesis by applying Eqs. S2 and S3, we need tocompute the conditional probability P(blink |✓, d). Using basicprobability theory we obtain

P(blink |✓, d) = P(blink , ✓, d)/P(✓, d), [S4]

where P(blink , ✓, d) is the joint probability of our blinking data(Fig. S5A, Left, the same as in Fig. 3D in the main text) andP(✓, d) is the probability of being at a location ✓ after d shave passed since the last blink. Hence, we must normalize theblinking probability at a location ✓ and IBI d by the probabil-ity of reaching location ✓ d s after the last blink. To computethe conditional probability P(blink |✓, d) we first need to obtainP(✓, d). We can compute this quantity from our blinking dataas follows (Fig. S5A, Center): For each blink (tuple of location✓ and IBI d) we can reconstruct all of the points (✓, d) thathave been visited since the last blink. In our experiment, the tar-get stimulus moves with constant angular velocity on a circulartrajectory. The velocity was 60�/s. Hence, we move through theparameter space along a line with slope 60�/s (gray and blacklines in Fig. S5A, Center). The probability P(✓, d) is the normal-ized number of times each point Q (✓q , dq) is visited. P(✓, d)clearly is not uniform; instead it is strongly influenced by whereblinks occurred in the lap. For example, fewer blinks occurredin the HEP region (120�–240�). Hence, the location (✓ = 60,d = 4) is not visited often (Fig. S5A, Center, dark blue value),as the point is reached only if the last blink occurred in theHEP region (shown by the gray line). We now can computeP(blink |✓, d) according to Eq. S4. The results are shown inFig. S5A, Right.

Our initial question, whether costs for blink suppression canbe assumed to be independent of the time since the last blink,can be tested using P(blink |✓, d). We computed P(blink |✓) forfive different ranges of d (Fig. S5B). Our results indicate thatblinking behavior does not change dependent on the time sincethe last blink. This suggests that for IBIs between 0 s and 10 s,which comprise 93% of all blinks in our experiment, costs can beassumed to be constant.

We additionally used our behavioral results in Fig. S5B tocheck whether longer times since the last blink lead to dif-ferences in the trade-off between costs for blink suppressionand costs for blink execution. Therefore, we divided the lapinto three equally sized areas: before HEP (0�–120�), HEP(120�–240�), and after HEP (240�–360�). If the cost for blink-ing increased with time, then blinks with greater IBIs shouldless reflect the task-related costs for greater IBIs (Fig. S5C,Top Left), leading to smaller differences in the proportionof blinks across the areas. If, on the other hand, costs areconstant, we would not expect a change in the relative dis-tribution of blinks across the three areas (Fig. S5C, Top

Right). Our results (Fig. S5C, Bottom) clearly favor constantcost. Blinking was not suppressed less in the HEP region forgreater IBIs.

Hoppe et al. www.pnas.org/cgi/content/short/1714220115 1 of 7

Fig. S1. (A) Blink rate over the course of each block. Blink rates increase over the course of the first 20 laps. Note that these initial data were not used inthe blinking model, but that instead only steady-state behavior data were used. (B) Blink rates over the course of the 100 laps aggregated over all blocks.Different lines correspond to blink rates in the different areas. The black line corresponds to the blink rate in the area before the HEP region, the dark grayline corresponds to the blinks occurring after the HEP region, and the light gray line corresponds to the blink rate within the HEP region. (C) Proportionof blinks occurring in the different regions over the course of the 100 laps (Fig. 2E in the main text). Colors refer to the same regions as in B. The relativedecrease in blinks occurring in the HEP region (light gray) is accompanied by a relative increase of blinks after the HEP region (dark gray) while the proportionof blinks in the region before HEP is roughly constant (black).

Hoppe et al. www.pnas.org/cgi/content/short/1714220115 2 of 7

Fig. S2. Steps of the computational model describing subjects’ belief about the event probabilities. (A) Starting point for modeling our subjects’ belief is theprobability distribution of the events. Subjects do not have access to the true distribution, and therefore we allowed for uncertainty about the mixing weightof the mixture distribution. Next, we incorporated recent observations by computing the average number of events seen during a lap. We used this to weightthe probability of an event by the number of events left in a lap, n(✓). Finally, we accounted for uncertainty regarding the current location. Computationally,this was done by convolving the belief using a Gaussian distribution accounting for this position uncertainty. (B) Belief about the event probability andtherefore the probability of missing an event due to blinking. The belief is shown using the parameters estimated from the aggregated data. At the end ofa lap (I) the event probability increases as it becomes more likely that the new lap has started. The probability of being in the next round saturates but theHEP region is not reached yet (II). Finally, there is a steep increase of event probability at the HEP region (III), which is followed by a decrease caused by boththe decreasing probability of a single event and the decreasing number of events left in the lap.

Hoppe et al. www.pnas.org/cgi/content/short/1714220115 3 of 7

1 2 3 4

5 6 7 8

9 10 11 12

Fig. S3. Individual data and model fits for all participants (1–12). For each subject the blinking rate over the circle (First row), the distribution of IBIs (Second

row), and the distribution of blinks per lap (Third row) are shown. Fourth row depicts the density of blinks in the location on the circle (x axis) versus timesince last blink (y axis) plane (Fig. 3 D and E in the main text).

Hoppe et al. www.pnas.org/cgi/content/short/1714220115 4 of 7

13 14 15 16

17 18 19 20

21 22 23 24

Fig. S4. Individual data and model fits for all participants (13–24). Details are the same as in Fig. S3.

Hoppe et al. www.pnas.org/cgi/content/short/1714220115 5 of 7

0

Fig. S5. Evidence for constant costs of blink suppression for the observed IBI. (A) Derivation of the blink probability p(blink|✓, d). (A, Left) The blinkingdensity P(blink, ✓, d) is shown dependent on the location within a lap (x axis, from 0� to 360�) and the time since the last blink (y axis, from 0 s to 10 s)(Fig. 3D in the main text). For example, the value at the white cross depicts the proportion of blinks occurring at location 180� in the lap and simultaneouslyoccurring 2 s after the last blink. Importantly, this implies that the last blink occurred at location 60� (180� �2s·60�/s), since the angular velocity of the visualtarget in the experiment was 60�/s. (A, Center) Probability distribution of how often each combination of a position in the lap and a time since the last blinkis reached in our experiment. Not all combinations of (✓, d) are equally likely as they are heavily affected by the uneven distribution of blinks over the courseof a lap (Fig. 3B in the main text). For illustration purposes, three blinks (depicted by white crosses) are shown together with the corresponding two IBIs (gray,interval between blink I and blink II; black, interval between blink II and blink III). Blink I occurs at location 180�. As can be seen by following the gray line,the same location (180�) is reached again exactly after 6 s. After 8 s blink II is executed and following the black line leads to blink III. (A, Right) The blinkprobability for each combination of location in the lap and time since the last blink is shown. This can be computed as P(blink, ✓, d)/P(✓, d). (B) Proportion ofblinks over the course of the laps computed separately for different IBIs. The colors correspond to the areas in A, Right. For example, the blue line depicts themean blinking proportion given that the time since the last blink is between 0 s and 2 s. We used a bin size of 1/3 s for the time since the last blink (0–0.33 s, ... ,1.66–2 s) and computed the mean for the six resulting values at each location. Error bars correspond to the SD. (C) Schematic course of blinking proportionsfor the three areas (before HEP, HEP, after HEP). If costs increased with IBI (Top Left), blinking would become less affected by task-related costs. For constantcosts (Top Right) this should not be the case. C, Bottom shows the proportion of blinks dependent on the time since the last blink. Overall, this provides clearevidence that costs for blink suppression were constant over the IBI durations in our experiments.

Hoppe et al. www.pnas.org/cgi/content/short/1714220115 6 of 7

0.75 0.80 0.85 0.90 0.95 1.00

Performance (% detected events)

0.0

0.2

0.4

0.6

0.8

1.0

Fitte

d co

st p

aram

eter

-�

Fig. S6. Relationship of the ↵ parameter fitted to individual subjects and task performance. Solid line depicts the regression curve.

Table S1. Individual parameter estimates for all subjects

Subject Performance Blink rate Blink rate estimate Cost trade-off

1 0.879 6.37 6.54 0.684102 0.905 6.95 7.30 0.650633 0.942 4.42 4.50 0.657054 0.933 24.42 24.86 0.591445 0.847 38.95 39.03 0.210026 0.946 7.67 7.98 0.769297 0.948 5.50 5.56 0.852488 0.936 7.75 7.77 0.243989 0.919 4.20 4.36 0.5762010 0.818 22.70 22.70 0.2050911 0.640 18.30 18.21 0.4443212 0.888 14.50 14.46 0.1887113 0.894 27.35 27.27 0.4701214 0.876 12.92 12.92 0.3673115 0.939 26.95 26.84 0.3545416 0.912 10.77 11.07 0.6268717 0.938 7.25 7.29 0.7723618 0.928 6.07 6.07 0.7249519 0.933 16.65 16.78 0.4493320 0.587 11.68 12.00 0.8267021 0.769 6.90 6.90 0.5282622 0.900 29.30 30.05 0.6839123 0.764 30.22 30.21 0.2962224 0.952 6.50 6.79 0.8955925 0.913 2.92 2.93 0.72884

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