To make sense of the world around us, we must combine information from multiple sources while taking into account how reliable they are. When crossing the street, for example, we usually rely more on input from our eyes than our ears. However, we can reassess the reliability of the information: on a foggy day with poor visibility, we might prioritize listening for traffic instead.

But how do we assess the reliability of information generated within the brain itself? We are able to see because the brain constructs an image based on the patterns of activity of light-sensitive proteins in a part of the eye called the retina. However, there is a point on the retina where the presence of the optic nerve leaves no space for light-sensitive receptors. This means there is a corresponding point in our visual field where the brain receives no visual input from the outside world. To prevent us from perceiving this gap, known as the visual blind spot, the brain fills in the blank space based on the contents of the surrounding areas. While this is usually accurate enough, it means that our perception in the blind spot is objectively unreliable.

To find out whether we are aware of the unreliable nature of stimuli in the blind spot, Ehinger et al. presented volunteers with two striped stimuli, one on each side of the screen. The center of some of the stimuli were covered by a patch that broke up the stripes. The volunteers’ task was to select the stimulus with uninterrupted stripes. The key to the experiment is that if the central patch appears in the blind spot, the brain will fill in the stripes so that they appear to be continuous. This means that the volunteers will have to choose between two stimuli that both appear to have continuous stripes. If they have no awareness of their blind spot, we might expect them to simply guess. Alternatively, if they are subconsciously aware that the stimulus in the blind spot is unreliable, they should choose the other one.

In reality, exactly the opposite happened: the volunteers chose the blind spot stimulus more often than not. This suggests that information generated by the brain itself is sometimes treated as more reliable than sensory information from the outside world. Future experiments should examine whether the tendency to favor information generated within the brain over external sensory inputs is unique to the visual blind spot, or whether it also occurs elsewhere.

In order to make optimal and adaptive decisions, animals integrate multiple sources of sensory information across time and space. One of the prime examples of this is observed when animals are confronted with coherently-moving stimuli during random-dot motion experiments. In such experiments, performance and the corresponding neural activity vary proportionally to signal strength in a way that is consistent with the progressive integration of evidence over time (Shadlen et al., 1996; Shadlen and Newsome, 2001). Besides temporal accumulation, sensory integration is also possible by combining the information from multiple sensory sources (Quigley et al., 2008; Schall et al., 2009; Hollensteiner et al., 2015; Wahn and König, 2015a, 2015b, 2016).

In the case of multisensory perception, several experiments have shown that integration often occurs in a statistically optimal way. This has been best demonstrated in cue-integration tasks in which humans perform as if they were weighting the different sources of information according to their respective reliabilities (Ernst and Banks, 2002; Alais and Burr, 2004; Körding and Wolpert, 2004; Tickle et al., 2016). This form of statistical inference has also been demonstrated for cortical neurons of the monkey brain, with patterns of activity at the population level that are consistent with the implementation of a probabilistic population code (Gu et al., 2008; Fetsch et al., 2011).

In most of these sensory integration experiments, the perceptual reliability of different inputs is probed through quantitative manipulations of the inputs’ signal-to-noise ratios (Heekeren et al., 2004; Tassinari et al., 2006; Bankó et al., 2011). However, some percepts are unreliable not because they are corrupted by noise but because they are inferred only from the context and thus intrinsically uncertain. This occurs naturally in monocular vision at the physiological blind spot, where content is ‘filled-in’ based on information from the surroundings. In this case, no veridical percept is possible at the blind spot location. Even though changes in reliability due to noise directly result in behavioral consequences, the effects of the qualitative difference between veridical and inferred percepts, that are otherwise apparently identical, are unknown.

We recently reported differences in the processing of veridical and inferred information at the level of EEG responses (Ehinger et al., 2015). We demonstrated that a qualitative assessment of differences in reliability exists at the neural level in the form of low- and high-level trans-saccadic predictions of visual content. Notably, active predictions of visual content differed between inferred and veridical visual information presented inside or outside the blind spot. Although no difference was found between low-level error signals, high-level error signals differed markedly between predictions based on inferred or veridical information. We concluded that the inferred content is processed as if it were veridical for the visual system, but knowledge of its reduced precision is nevertheless preserved for later processing stages.

In the present experiment, we address whether such an assessment of a dichotomous, qualitative difference in reliability is available for perceptual decision-making. Using 3D shutter glasses, we presented one stimulus partially in the participant’s blind spot to elicit filling-in and a second stimulus at the same eccentricity in the nasal field of view outside of the blind spot. The subject’s task was to indicate which of the two stimuli was continuously striped and did not present a small orthogonal inset (see Figure 1a). Crucially, stimuli within the blind spot are filled-in and thus perceived as continuous, even when they present an inset. In the diagnostic trials, both stimuli were physically identical and continuous, and subjects were confronted with an ambiguous decision between veridical and partially inferred stimuli.

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We evaluated two mutually exclusive hypotheses on how perceptual decision-making could proceed when confronted with an ambiguous decision between veridical and inferred percepts. In the first case, we hypothesized that subjects are unable to make perceptual decisions based on an assessment of differences in reliability between veridical and inferred stimuli. Therefore, subjects would have an equal chance of selecting stimuli presented inside or outside the blind spot. Alternatively, it might be possible to use the information about the reduced reliability of filled-in information. In this case, we expect subjects to follow an optimal strategy and trust a stimulus presented outside the blind spot, where the complete stimulus is seen, more often than when the stimulus is presented inside the blind spot, where it is impossible to know the actual content within the filled-in part.

We conducted five experiments (see Figure 1 and the methods for a detailed description of the tasks). The first one tested the presence of a bias against the blind spot location; the other four experiments were replications of the first experiment with additional control conditions. In the first two controls, we tested the existence of biases between the nasal and temporal visual fields at locations other than the blind spot. In the third control, we tested whether an opposite bias existed when the task was reversed. The last experiment controls whether the observed bias could be explained by probability matching.

Experiment 1

In the first experiment, 24 subjects performed a 2-AFC task in which they had to indicate which of two stimuli was continuously striped instead of presenting a small orthogonal central inset (Figure 1a,b). The stimuli were presented simultaneously in the periphery at the locations of the blind spots or at equivalent eccentricity on the opposite side (Figure 1c,d). We used a 3D monitor and shutter glasses that allowed for the controlled monocular display of the stimuli. That means each stimulus was visible to a single eye only. There were always two stimuli, therefore, in a given trial either one or both eyes were stimulated (Figure 1b). Importantly, subjects always perceived the two stimuli at the same locations, to the left and the right of the fixation cross. In this experiment there were perceptually ambiguous trials, where two continuous stimuli were perceived, and unambiguous trials where one stimulus contained a visible inset.

In the unambiguous trials, an orthogonal inset was present in one of the stimuli. Importantly, in these trials, the stimulus with the inset was outside the blind spot and therefore clearly visible. As expected, subjects performed with near-perfect accuracy (Figure 2, unambiguous trials, blue data), choosing the continuous stimulus in an average of 98.8% of trials (95%-quantile over subjects [96.4–100%]).

Figure 2

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There were two types of ambiguous trials. In the first type (Figure 2, ambiguous control, red data), one of the following applied: both stimuli were continuous and appeared outside the blind spots in the nasal visual fields (Figure 2, row 3); both were continuous and appeared inside the blind spots (Figure 2, row 4); or one was continuous, the other had an inset, and both appeared inside the blind spots with the inset either in the left or the right blind spot (Figure 2, rows 5 and 6). In the case when a stimulus with an inset was present, this central part was perfectly centered inside the blind spot (Figure 1a), and in consequence was perceived as continuous due to filling-in. Thus, in all four versions, subjects perceived two identical stimuli, and there was no single correct answer. In this type of ambiguous trial, subjects showed a small global leftward bias and chose the left stimulus in 53.6% of trials (Figure 2, continuous vertical line). In addition, no difference can be seen between the perception of pairs of filled-in stimuli and pairs of veridical continuous stimuli (Figure 2, rows 3 vs. 4–6). This type of ambiguous control trial confirms that filling-in was accurately controlled in our experiment.

In the second type of ambiguous trials one stimulus was presented inside and the other outside the blind spot (Figure 2, ambiguous diagnostic, data in green). This allowed us to test directly between two rival predictions: whether subjects will show a bias against the stimulus that is partially inferred (inset area inside the blind spot) and in favor of the veridical stimulus (in the opposite visual field), or no bias. Selecting the filled-in stimulus is a suboptimal decision because the stimulus presented partially in the blind spot is the only one which could possibly contain the inset. This is explicit in the cases where an inset is shown in the blind spot but rendered invisible by filling-in (Figure 2a, ambiguous trials with an inset stimulus). To analyse the data, we modeled the probability increase of choosing the right stimulus if the right stimulus was presented in either the temporal visual field of the right eye (blind spot) or the nasal visual field of the left eye (non-blind spot). A similar factor was used for the left stimulus. Subsequently, the two one-sided model estimates were collapsed to a single measure of preference for stimulus presented at the nasal or temporal visual field (outside or inside the blind spot respectively). As a model for inference, we used a Bayesian generalized mixed linear model. There were three additional factors in the model (handedness, dominant eye, and precedent answer) that are not the focus of the experiment and are thus reported in the methods section (see ‘Effects not reported in the Results section’).

Figure 2a (ambiguous diagnostic, data in green) and 2b show that subjects indeed presented a bias. However, in contrast to our expectations, subjects were more likely to choose the filled-in percept with a 15.01% preference for stimuli presented in the temporal visual field ($CD{I}_{95}$8.49–21.08%). In other words, when subjects had to decide which of the two stimuli (both perceived as being continuous, and in most cases actually physically identical) was less likely to contain an inset, they showed a bias for the one in which the critical information was not sensed directly but inferred from the surrounding spatial context. Remarkably, this result is at odds with both of our experimental predictions that postulated either no bias or a bias in favor of the veridical stimulus.

Experiment 2

The second experiment was designed to replicate the unexpected result of the first experiment and evaluate whether the blind spot bias observed was due to systematic differences between nasal and temporal retinae. In experiment 1, we presented stimuli at mirror eccentricities inside and outside the blind spot, that is, temporal and nasal respectively (see Figure 1c). In experiment 2, we tested whether the bias in experiment 1 was specific to the blind spot location or related to known differences between the temporal and nasal retina (Fahle and Schmid, 1988). There is higher photoreceptor density (Curcio et al., 1990), spatial resolution (Rovamo et al., 1982), luminance discrimination (Pöppel et al., 1973) and orientation discrimination (Paradiso and Carney, 1988) at locations that project to the nasal retina (the temporal visual field where the blind spots are located). Thus, we repeated our experiment with a new group of subjects (n = 27) and an additional experimental condition. In this new condition, the two stimuli were displayed at symmetrical locations above the blind spot (25° above the horizontal meridian; see Figure 1d, purple location). The results of this second experiment replicate the observations of experiment 1 (Figure 3a): subjects showed a bias for selecting the stimulus presented inside the blind spot (12.5%, ${\text{CDI}}_{95}$7.35–17.49%). However, subjects also presented a bias in the control condition, toward the stimuli presented in the temporal visual field above the blind spot (6.63%, ${\text{CDI}}_{95}$0.77–12.3%). The bias was nevertheless stronger inside the blind spot (paired difference: 6.11%, ${\text{CDI}}_{95}$1.16–10.78%). In summary, additionally to the bias inside of the blind spot area, we observed that subjects also showed a smaller bias for stimuli presented to the nasal retina (temporal visual field).

Figure 3

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Experiment 4

The results of the three previous experiments suggest that subjects considered the filled-in percept a better exemplar of a continuous non-inset stimulus, in disregard of the physical possibility of the presence on an inset inside the blind spot. To confirm this, we performed a fourth experiment with a new group of subjects (n = 25). This experiment was identical to the first experiment, except that in this case, the subjects’ task was to choose the stimulus with an inset, instead of the continuous one. In this case, if a filled-in stimulus is indeed considered a more reliable exemplar of a continuous stimulus, the non blind spot stimulus should be preferred in the diagnostic trials. This was the case; subjects showed a bias for selecting the stimulus presented outside the blind spot (7.74%, $CD{I}_{95}$1.56–13.68%, Figure 4a), thus resulting in the expected reversal of the bias pattern observed in the first three experiments. This pattern is again suboptimal, since this time the filled-in stimulus is the one that could conceal the target. The result of this experiment indicates that the observed biases do not correspond to an unspecific response bias for the blind spot, and instead are a consequence of considering the inferred percepts as more reliable exemplars of a continuous stimulus.

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Reaction time analysis

A bias for the temporal visual field, especially the blind spot, could also be reflected in the distribution of reaction times. We compared the reaction times of trials where subjects selected a stimulus in the temporal visual field against trials where the stimulus in the nasal visual field was selected. The reaction time analysis was not a planned comparisons, thus, in contrast to the other analyses presented here, it is explorative. In the first experiment, we observed an average reaction time of 637 ms (minimum subject average: 394 ms, maximum 964 ms; Figure 5). We used a linear mixed model to estimate the reaction time difference for selecting a stimulus presented inside the blind spot (temporally) against one outside the blind spot (nasally). In the first experiment, after excluding three outliers, we observed this effect with a median posterior effect size of 13 ms faster reaction times when selecting the blind spot region ($CD{I}_{95\%}$ 2–42 ms). The three outliers (on the right of the vertical dashed line in Figure 5) were identified visually and removed because they were distinctively different from the rest of the population. The mean of the outliers was 5.2 SD away from the remaining subjects. The outliers were nevertheless in the same direction of the reaction time effect and did not change its significance (with outliers, 63 ms, $CD{I}_{95}$7–124 ms). However, faster reaction times while selecting the blind spot stimulus were not present individually in the other four experiments. The nominal differences were in the same direction as experiment 1 but not significant (Exp.2: 4 ms, $CD{I}_{95}$−14–23 ms; Exp.3: 22 ms. $CD{I}_{95}$−3–39 ms; Exp.4: −1 ms $CD{I}_{95}$−20–21 ms; Exp.5: 4 ms $CD{I}_{95}$−15–23 ms). Non-significant results were obtained for the other locations tested (above Exp.2: 8 ms, $CD{I}_{95}$−38–53 ms; above Exp.4: 8 ms $CD{I}_{95}$−17–32 ms; outward: 2 ms $CD{I}_{95}$−13–16 ms; inward: 4 ms, $CD{I}_{95}$−29–37 ms). After combining all data (without experiment 4 as the task was reversed), we observed a reduced reaction time for decisions for the blind spot stimulus with 10 ms ($CD{I}_{95}$2–17 ms) but not in any other location. We do not find this small bias in any experiment individually (except Exp. 1) but only after pooling over experiments and therefore, we should interpret it cautiously. In conclusion, subjects selected stimuli in the blind spot slightly faster than stimuli outside the blind spot. The same effect does not appear for the other temporal control locations.

Figure 5

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Combined effect estimates over all experiments

For an overview of all experiments and the results of a Bayesian logistic mixed effects model that combines all experiments, see Figure 6, Figure 6—figure supplement 1 and Supplementary file 1. In the combined model, we did not find any differences between the temporal field effects at locations other than the blind spots (Figure 6, fourth last to second last row). That is, the temporal field effects of the locations inward, outward and above were not different from each other. For the sake of clarity, we combined these location levels. Keeping everything else constant, we observed that if we present one stimulus in the blind spot against the equidistant nasal location, subjects are 13.82% ($CD{I}_{95}$10.84–16.78%, t-test, t = 8.7, df = 98, p<0.001) more likely to choose the stimulus in the blind spot. This bias is stronger than the effect observed elsewhere in the temporal field by 9.35% ($CD{I}_{95}$ 6.25%–12.47%; paired t-test, t = 4.8, df = 74, p<0.001). In summary, subjects showed a robust bias for the blind spot locations that could not be explained by a non-specific bias for the temporal visual field. In conclusion, when confronted with an ambiguous choice between veridical and inferred sensory information, human subjects showed a suboptimal bias for inferred information.

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When confronted with identical physical stimulation, subjects showed a consistent bias for blind spot inferred percepts which was stronger than the bias at any other location in the temporal visual field.

Why do subjects choose the blind spot location when it is objectively the least reliable? Our interpretation takes the results at face value: subjects must possess at least implicit information about whether a percept originates from the blind spot in order to show a bias for or against it. At the same time, the veridical information from the other stimulus is also available. This indicates that perceptual decision-making can rely more on inferred than veridical information, even when there is some knowledge about the reduced reliability of the inferred input available in the brain (Ehinger et al., 2015). This is also supported by the results of the reaction time analyses that indicated a faster evidence accumulation for the inferred percepts. In other words, the implicit knowledge that a filled-in stimulus is objectively less reliable does not seem to be used for perceptual decision-making. This suboptimal decision between qualitatively different veridical and inferred inputs is in contrast to properties of standard sensory integration. There, reduced reliability derived from noisy but veridical signals results in a corresponding weighting of inputs and consequently in optimal decisions (Körding et al., 2007). In the following, we discuss two potential explanations of this discrepancy of processing filled-in information and standard sensory integration. The first explanation focuses on physiological properties of neuronal and small circuits’ response properties at and around the blind spot region. The second explanation addresses the conceptual level and uses the general notion of predictive coding.

First, although the filled-in percept is by definition independent of the stimulus within the blind spot, it is nevertheless based on the information sensed by the region around the blind spot in the nasal retina. We might assume that an area, e.g. in the nasal retina around the blind spot region, that has a lower contrast threshold also shows stronger neuronal signals for super-threshold stimuli. This could in principle lead to a filled-in stimulus with increased salience as compared to the veridical stimulus. Effectively, this explanation proposes that differences in physiological properties of nasal and temporal retinae are transferred to the filling-in process making it the ‘better’ candidate stimulus in an ambiguous condition. Above we already introduced some evidence for psychophysical differences between the nasal and temporal visual field (Fahle and Schmid, 1988). There is also some evidence for the superiority of the blind spot in a Vernier task (Crossland and Bex, 2009). The areas around the blind spot showed greater performance compared to areas at similar eccentric locations in the nasal visual field. It is still unclear whether this goes over and beyond the aforementioned temporal/nasal bias. Unfortunately, this explanation runs into the problem that the sensitivity in the region corresponding to the blind spot in the other eye is also enhanced compared to regions at similar eccentricities (Wolf and Morandi, 1962; Midgley, 1998). This suggests that differences between the eyes in the area around the blind spot should be the smallest within the contrast between temporal and nasal retina. Moreover, we explicitly controlled for temporal-nasal differences in experiments 2 and 3, and found that it is not enough to explain the effect specific to the blind spot. Thus, an explanation of the observed effects based on known differences in retinal properties is currently tentative at best.

An alternative explanation is based on the framework of predictive coding (Friston et al., 2006, 2012; Summerfield and de Lange, 2014). Specifically, context information of static stimuli would be used to predict local stimulus properties leading to the phenomenon of filling-in. The predicted sensory input would then be compared to the incoming sensory input, and an error signal representing the mismatch would be returned. In the absence of veridical information, no deviation and thus no error signal would occur. Effectively, the filled-in signal might have less noise. Reduced noise, in turn, results in a smaller prediction error and higher credibility at later stages. A faster reaction time to the filled-in stimulus compared to the veridical stimulus could suggest that the integration process is indeed biased with less noise. In summary, although the results reported here seem compatible with the predictive coding framework, this explanation presently remains vague and speculative.

In conclusion, we find a new behavioral effect where subjects prefer a partially inferred stimulus to a veridical one. Though both appear to be continuous, the filled-in one could hide an inset and is, therefore, less reliable. In this perceptual decision-making task, subjects do not make use of high-level assessments about the reliability of the filled-in stimulus. Even more so, they prefer the unreliable percept.

Many of the methods are taken from Ehinger et al., 2015. All data and analyses are available at https://osf.io/wphbd.

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Thank you for submitting your article "Mind over matter: A perceptual decision bias toward filled-in stimuli in the blind spot" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and David Van Essen as the Senior Editor. The following individual involved in review of your submission has agreed to reveal his identity: Jeff Beck (Reviewer #1).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Summary:

This manuscript investigates whether there is bias towards a target with more complete sensory input compared to a less informative stimulus that is "filled-in". The major finding is that the blindspot-covering stimulus (regardless of whether it included an orthogonal inset) was selected in favor of the completely viewed stimulus. This is an unexpected and intriguing finding, and seems like eLife material. However, the reviewers had a number of comments, many related to clarity. In addition, it seems that one more control experiment is needed to really nail this result.

Essential revisions:

1) In the first experiment, ten trial types were used (shown in Figure 2). What varied was whether either of the stimuli included an inset, and whether they were presented in the blindspot. It is not clear, however, how many times each of these trial types were used. This may be relevant because if pooling across trials reveals a bias such that presentation of a stimulus inside the blindspot is actually predictive of it being the correct choice, then of course it is not suboptimal for subjects to be biased towards the blindspot stimulus.

2) During screening, when subjects were shown "a single stimulus in the periphery either inside or outside the blindspot in the left or right visual field", the first block of trials was used as training. The description of this procedure ("an inset stimulus inside the blind spot should have been reported as no inset") suggests that subjects received corrective feedback, such that every time a blindspot stimulus was shown the correct response was "no inset" – regardless of whether there was or wasn't an inset in the actual stimulus shown. If this was the case, then this training could explain the bias of subjects preferring the blindspot stimulus in later phases of the experiment(s). Please explain and discuss how this potential confound can be excluded based on your current results, or run a new experiment in which this is controlled for.

3) Finally, one control was notably missing from the experiments: a variant in which subjects have to choose the stimulus with (rather than without) the inset. If the authors' conclusions are correct, the observed biases should be reversed: the blindspot stimulus should be chosen less than the non-blindspot stimulus in ambiguous trials. Experiments should be performed to confirm this. We do not take lightly the requirement of additional experiments, but in this case the result is so unexpected (a good thing) that it's necessary to rule out all reasonably likely explanations.

4) It seems like the main analysis for the accuracy results was a linear mixed model fit. However, the only time this is mentioned in the main text is the caption of Figure 3b. Mentioning it so briefly is misleading, since that makes it seem like the linear model was used only for this later analysis (and another for the reaction time analyses). In addition, earlier captions refer to a bootstrap method suggesting that method was the main analysis. Secondarily, the bootstrap method is not clearly distinguished in the Methods. It is possibly buried in the section about blindspot calibration.

We'll leave it up the authors how to clarify this. One possibility is to introduce the linear model early in the Results, since this seems essential to interpreting the Results. The other is to put a clear explanation in Methods, and refer to it in results where appropriate. In any case, the bootstrap method should be clearly distinguished and explained (avoiding jargon) in the Methods.

5) There are a number of covariates that the authors seem to include in the linear model. These are buried in the other findings in the Methods (subsection “Effects not reported in the result section”). For example, there are eye dominance, perseverative (more likely to repeat an answer), or stereotypical (alternate answers, stick to the same answer) effects. These should be clearly explained, all in one place, either in the Results or Methods (if it's the latter, with appropriate pointers in the main text). The authors should also think about presenting the screening test results in the main text, including evidence (as alluded to in the subsection “Screening”) that failed screening was not related to the blindspot calibration.

6) Some goodness of fit measure should be given for the model fits.

7) The authors should provide some significance testing, including details on how these are calculated.

8) It seems that during a single test that only one eye is receiving input, while the other is completely blinded (not receiving visual input). Please make this more explicit in the text. Instead of using jargon like monocular display in the second paragraph of the Results. Explicitly state that for each test one eye sees both targets while the other is completely blinded and then point to Figure 1b. If both eyes are receiving input, as possibly suggested in the seventh paragraph of the Results (mention of binocular rivalry) then this is completely unclear and needs to be clarified earlier in the text and Figure 1.

9) There is an alternative explanation of these results that is somewhat orthogonal to the predictive coding explanation. Throughout experiment 1 subjects are shown patches at two different locations and those patches occur with equal frequency, but are never perceived to occur in the blindspot. Nonetheless, subjects maintain a strong prior belief that the target should occur with equal frequency at each location and so in the presence of enough ambiguity they may be inclined to 'guess' in the place where they have never seen the target, either because of the gambler's fallacy, or because of probability matching. I think the math actually checks out. There are 10 experimental conditions 2 of which are unambiguous providing 1 confirmed vote that the target has occurred outside left and one for outside right. If you want to end up guessing that the target as occurred at each location inside/outside/left/right you need a spurious guess at the blindspot location when the alternative was a non-blindspot location which would predict a behavioral bias of 100% toward the blindspot in that condition. Therefore, any inclination toward probability matching or a gamblers fallacy would have predicted this result.

We admit that this is a bit speculative, but it's something the authors might want to think about. To look for probability matching and gamblers fallacy, one need only to look at the effects of the previous trials on the current one. If a subject has chosen A a few more times than average this should create a bias toward B. If that's not the case, then this explanation can be ruled out.

10) The Discussion (and the corresponding part of the Abstract) linking these results to predictive coding was confusing – even in the best case, pretty substantial additional assumptions are needed to accommodate these results within the framework of predictive coding. It might be better to publish these results on face value, as they are, rather than trying to squeeze them into the procrustean framework of an inappropriate theory. The contrast between predictive coding and theories positing "a hierarchy of increasingly refined representations", which is only referred to in the Abstract as if this study was specifically testing it – which is obviously not the case – is particularly unclear.

Essential revisions:

1) In the first experiment, ten trial types were used (shown in Figure 2). What varied was whether either of the stimuli included an inset, and whether they were presented in the blindspot. It is not clear, however, how many times each of these trial types were used. This may be relevant because if pooling across trials reveals a bias such that presentation of a stimulus inside the blindspot is actually predictive of it being the correct choice, then of course it is not suboptimal for subjects to be biased towards the blindspot stimulus.

Done. We provide a new supplementary figure that details the randomization of all experiments. This includes the three experiments presented in the initial manuscript plus two new controls. Now it is possible to evaluate in detail that the described effects are not produced by a bias in the trial pooling (see the answer to comment 9 for further explanations). We clarified the manuscript and added the corresponding links to the randomization figure where appropriate. The complexity of the trial pooling is now better communicated (see subsections “Experiment 5”, “Task” and the new Figure 1—figure supplement 1).

2) During screening, when subjects were shown "a single stimulus in the periphery either inside or outside the blindspot in the left or right visual field", the first block of trials was used as training. The description of this procedure ("an inset stimulus inside the blind spot should have been reported as no inset") suggests that subjects received corrective feedback, such that every time a blindspot stimulus was shown the correct response was "no inset" – regardless of whether there was or wasn't an inset in the actual stimulus shown. If this was the case, then this training could explain the bias of subjects preferring the blindspot stimulus in later phases of the experiment(s). Please explain and discuss how this potential confound can be excluded based on your current results, or run a new experiment in which this is controlled for.

Done. We apologize for this misunderstanding. Subjects did not receive any feedback. This is now explicit in the manuscript. We also report more detailed on the reasons why subjects failed our screen experiment. See subsection “Screening” and the answer to 5.

3) Finally, one control was notably missing from the experiments: a variant in which subjects have to choose the stimulus with (rather than without) the inset. If the authors' conclusions are correct, the observed biases should be reversed: the blindspot stimulus should be chosen less than the non-blindspot stimulus in ambiguous trials. Experiments should be performed to confirm this. We do not take lightly the requirement of additional experiments, but in this case the result is so unexpected (a good thing) that it's necessary to rule out all reasonably likely explanations.

Done. We agree that this additional control is useful and performed as requested. The control experiment confirms our prediction. This new control (Experiment 4) is an exact repetition of experiment 1, except that subjects were requested to select the stimulus with the inset instead of the continuous one. As predicted, the bias was reversed; in ambiguous diagnostic trials, subjects showed a bias for the non-blind spot stimulus. This result indicates that subjects were indeed trying to follow the instructions during ambiguous trials, and strengthen our conclusion that, in the original experiments, they chose the blind spot stimulus because it is considered a better exemplar of a continuous stimulus. This result also excludes explanations based on non-specific biases for the blind spot stimulus. This is now described in the Results subsection (“Experiment 4”) in Figure 4 and in the Discussion (third paragraph). Additionally, subjects performing experiment 4 were identical to the subjects performing experiment 5 (Experiment 5 was always performed after experiment 4). In the later experiment, they performed the original task, choose the stimulus without inset. Thus, we have data for both tasks within the same subjects. We observe a strong negative correlation. Thus, indication that subjects who biased their choices towards the stimulus outside of the blind spot in experiment 4, biased their choices towards the stimulus inside the blind spot in experiment 5 (as found before in Experiment 1-3).

4) It seems like the main analysis for the accuracy results was a linear mixed model fit. However, the only time this is mentioned in the main text is the caption of Figure 3b. Mentioning it so briefly is misleading, since that makes it seem like the linear model was used only for this later analysis (and another for the reaction time analyses). In addition, earlier captions refer to a bootstrap method suggesting that method was the main analysis. Secondarily, the bootstrap method is not clearly distinguished in the Methods. It is possibly buried in the section about blindspot calibration.

We'll leave it up the authors how to clarify this. One possibility is to introduce the linear model early in the Results, since this seems essential to interpreting the Results. The other is to put a clear explanation in Methods, and refer to it in results where appropriate. In any case, the bootstrap method should be clearly distinguished and explained (avoiding jargon) in the Methods.

Done. There was a confusion when we used the linear mixed model and when we used a bootstrapping procedure. We clarified in the manuscript that all our conclusions are only based on the Generalized Linear Mixed Model Line (subsection “Experiment 1”, fourth paragraph). We used the bootstrapping procedure only to visualize summary statistics in the figures and to summarize the location and sizes of the blind spots as described in the respective Methods section. We improved the manuscript and made it clear in the captions, which values are bootstrapped marginal summaries and what values represent posterior model estimates. The bootstrap used for visual display is now described more prominently in the Methods section (subsection “Bootstrap in figures”). In addition, we introduce the linear model early in the Results part (subsection “Experiment 1”, fourth paragraph).

5) There are a number of covariates that the authors seem to include in the linear model. These are buried in the other findings in the Methods (subsection “Effects not reported in the result section”). For example, there are eye dominance, perseverative (more likely to repeat an answer), or stereotypical (alternate answers, stick to the same answer) effects. These should be clearly explained, all in one place, either in the Results or Methods (if it's the latter, with appropriate pointers in the main text).

Done. Thank you for this excellent suggestion. We added clear pointers in the manuscript (subsection “Experiment 1”, fourth paragraph). We also improved upon the description part in the Methods (subsection “Effects not reported in the result section”).

The authors should also think about presenting the screening test results in the main text, including evidence (as alluded to in the subsection “Screening”) that failed screening was not related to the blindspot calibration.

Done. We classified the failed screening subjects in multiple categories. See subsection “Screening”.

6) Some goodness of fit measure should be given for the model fits.

Done. We added a new supplementary figure illustrating the multiple different posterior predictive checks we performed. Our model captures the main portions of the data well both at the subject and group levels. We also added a paragraph the text that clearly describes our procedure and rationale for the posterior predictive checks (subsection “Posterior predictive model checking” and Figure 6—figure supplement 2).

7) The authors should provide some significance testing, including details on how these are calculated.

Done. While a Bayesian quantification of the posterior can be used for inference on the data, we additionally performed t-tests on the main two questions: Is there a bias for the blind spot (p<0.001) and is it greater than in the other tested locations (p<0.001). These tests can be found in subsection “Combined effect estimates over all experiments”.

8) It seems that during a single test that only one eye is receiving input, while the other is completely blinded (not receiving visual input). Please make this more explicit in the text. Instead of using jargon like monocular display in the second paragraph of the Results. Explicitly state that for each test one eye sees both targets while the other is completely blinded and then point to Figure 1b. If both eyes are receiving input, as possibly suggested in the seventh paragraph of the Results (mention of binocular rivalry) then this is completely unclear and needs to be clarified earlier in the text and Figure 1.

Done. This was indeed worded a bit confusing. We improved on the passages mentioned: If one stimulus is partially inside the blind spot and the other outside, they are always shown in one eye. In other conditions (e.g. both stimuli outside the blind spot) stimuli could have been presented been presented to both eyes (but in this case, each stimulus to only one eye). We improved the text (subsection “Experiment 1”, first paragraph) and included a new Panel in Figure 1.

9) There is an alternative explanation of these results that is somewhat orthogonal to the predictive coding explanation. Throughout experiment 1 subjects are shown patches at two different locations and those patches occur with equal frequency, but are never perceived to occur in the blindspot. Nonetheless, subjects maintain a strong prior belief that the target should occur with equal frequency at each location and so in the presence of enough ambiguity they may be inclined to 'guess' in the place where they have never seen the target, either because of the gambler's fallacy, or because of probability matching. I think the math actually checks out. There are 10 experimental conditions 2 of which are unambiguous providing 1 confirmed vote that the target has occurred outside left and one for outside right. If you want to end up guessing that the target as occurred at each location inside/outside/left/right you need a spurious guess at the blindspot location when the alternative was a non-blindspot location which would predict a behavioral bias of 100% toward the blindspot in that condition. Therefore, any inclination toward probability matching or a gamblers fallacy would have predicted this result.

We admit that this is a bit speculative, but it's something the authors might want to think about. To look for probability matching and gamblers fallacy, one need only to look at the effects of the previous trials on the current one. If a subject has chosen A a few more times than average this should create a bias toward B. If that's not the case, then this explanation can be ruled out.

Done. This comment raised a possible confound that we did not consider before and that potentially could invalidate the purpose and interpretation of the experiment (i.e., that the effects are not related to the blind spot and filling-in phenomena but only to the probability structure of the task). Thus, we are thankful for the given opportunity to evaluate, and finally rule-out, these alternative explanations. We do this by an analysis of data presented before as well as a new experiment. As the gambler fallacy and probability matching explanation predict different behaviors we addressed them separately.

The results cannot be explained by the gambler fallacy. This type of bias is for the non-experienced alternative, so, as during unambiguous trials subjects never experienced an inset in the blind spot location, their ‘gamble’ in ambiguous diagnostic trials (one stimulus inside the blind spot and one outside) would have to be to choose the stimulus outside the blind spot. As the result shows the opposite bias, we can safely disregard this option.

A probability matching explanation had a much stronger case as an alternative explanation for the results presented here. As correctly noted by the reviewers, subjects never experience an inset in the blind spot during unambiguous trials, thus representing a base rate of 100% non-inset stimulus in the blind spot. Then, in ambiguous trials subjects might respond based on this base rate resulting in a bias in the same direction as observed. However, we can exclude this explanation based on a detailed analysis of the trial pooling of the control experiment 2 and on the results of a new control (experiment 5).

The trial pooling of the control positions in experiment 2 holds some evidence against a probability matching explanation. If the subjects were biased according to the base rate of continuous stimulus during the unambiguous trials, this should also be evident in the control position (‘above’). There are two different ways a base rate can be constructed that would nevertheless result in similar behaviors. In the first case, the base rate is calculated individually for each position in term of the probability of displaying a continuous stimulus during unambiguous trials. In experiment 2, the base rate for continuous stimulus in the above position, is 0.41 (84/120, Figure 1—figure supplement 1, 2^nd row, columns 6-8 and 10-12) for temporal stimuli and.6 (108/180, Figure 1—figure supplement 1, 2^nd row, columns 5-7 and 9-11) for nasal stimulus (these are the probabilities of a stimulus in a given position being continuous and do not need to add up, since there are trials in which both stimuli are in the temporal or nasal fields). Accordingly, during ambiguous trials, this will predict a slight bias for the nasal position in the control above position, which is opposite to what was observed. In the second case, the base rate is calculated for the relevant position contrasts (the diagnostic trials in which stimuli are presented to the temporal and nasal field of the same eye). In this case, the base rate during unambiguous trial is.33 (36/108, Figure 1—figure supplement 1, 2^nd row, columns 6-7 and 10-11) for a continuous stimulus being presented on the temporal location and the complement.77 (72/108, same) for the nasal position, thus again predicting a bias for the nasal location in opposition to what we observed. In summary, the behavior observed for the control locations indicated that subjects were not using a probability matching strategy during ambiguous trials.

Although the above analysis already indicates that a probability matching explanation is unlikely, it would require considerable effort by the readers to evaluate it, and we did not feel completely satisfied by it. Therefore, to ensure that probability matching was not driving the observed bias we performed a new control experiment. This was a repetition of experiment 2 but with a different pooling structure. The crucial difference was that in the new control, subjects never experience an inset in the temporal field control positions ‘above’ (red frame columns 6,8,11, and 12 in Figure 1—figure supplement 1). This makes the probability structure of the control position trials equivalent to one of the blind spot trials. Therefore, if the bias observed was due to probability matching, this should now be equal in the control position. The result of this control experiment shows that (1) we replicate for the fourth time the bias to the blind spot (with a new group of subjects), (2) the control position show a reduced bias compared to the blind spot (same result as in experiment 2), thus discarding that the effect in the blind spot is due to a probability matching bias.

The rationale to exclude a probability matching explanation and the new control is now described in the Results subsection (“Experiment 5”), in Figure 4, and Figure 4—figure supplement 1.

10) The Discussion (and the corresponding part of the Abstract) linking these results to predictive coding was confusing – even in the best case, pretty substantial additional assumptions are needed to accommodate these results within the framework of predictive coding. It might be better to publish these results on face value, as they are, rather than trying to squeeze them into the procrustean framework of an inappropriate theory. The contrast between predictive coding and theories positing "a hierarchy of increasingly refined representations", which is only referred to in the Abstract as if this study was specifically testing it – which is obviously not the case – is particularly unclear.

Done. We agree that the previous presentation was too strong in terms of testing the predictive coding framework (although we view it slightly more benevolent) and we revised them accordingly. Specifically, we simplified the Discussion and focused it on why the results are unexpected. It provides an explicitly speculative explanation on why subjects choose suboptimally but we removed all theoretical links that were before not well substantiated. We still think that predictive coding offers a very useful way to think about this problem and discuss it appropriately (Discussion, fourth paragraph). The Abstract and Introduction were changed correspondingly.

Author details

1. Benedikt V Ehinger

   Neurobiopsychology, Institute of Cognitive Science, University of Osnabrück, Osnabrück, Germany

   Contribution

   BVE, Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   behinger@uos.de

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0002-6276-3332

2. Katja Häusser

   Neurobiopsychology, Institute of Cognitive Science, University of Osnabrück, Osnabrück, Germany

   Contribution

   KH, Data curation, Software, Formal analysis, Investigation, Visualization, Methodology

   Competing interests

   The authors declare that no competing interests exist.

3. José P Ossandón

   1. Neurobiopsychology, Institute of Cognitive Science, University of Osnabrück, Osnabrück, Germany
   2. Biological Psychology and Neuropsychology, University of Hamburg, Hamburg, Germany

   Contribution

   JPO, Conceptualization, Supervision, Validation, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing

   Contributed equally with

   Peter König

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0002-2539-390X

4. Peter König

   1. Neurobiopsychology, Institute of Cognitive Science, University of Osnabrück, Osnabrück, Germany
   2. Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany

   Contribution

   PK, Conceptualization, Supervision, Funding acquisition, Validation, Writing—original draft, Project administration, Writing—review and editing

   Contributed equally with

   José P Ossandón

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0003-3654-5267

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