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Boosts in brain signal variability track liberal shifts in decision bias

  1. Niels A Kloosterman  Is a corresponding author
  2. Julian Q Kosciessa
  3. Ulman Lindenberger
  4. Johannes Jacobus Fahrenfort
  5. Douglas D Garrett  Is a corresponding author
  1. Max Planck UCL Centre for Computational Psychiatry and Ageing Research, Germany
  2. Center for Lifespan Psychology, Max Planck Institute for Human Development, Germany
  3. Department of Experimental and Applied Psychology, Vrije Universiteit Amsterdam, Netherlands
  4. Department of Psychology, University of Amsterdam, Netherlands
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Cite this article as: eLife 2020;9:e54201 doi: 10.7554/eLife.54201

Abstract

Adopting particular decision biases allows organisms to tailor their choices to environmental demands. For example, a liberal response strategy pays off when target detection is crucial, whereas a conservative strategy is optimal for avoiding false alarms. Using conventional time-frequency analysis of human electroencephalographic (EEG) activity, we previously showed that bias setting entails adjustment of evidence accumulation in sensory regions (Kloosterman et al., 2019), but the presumed prefrontal signature of a conservative-to-liberal bias shift has remained elusive. Here, we show that a liberal bias shift is reflected in a more unconstrained neural regime (boosted entropy) in frontal regions that is suited to the detection of unpredictable events. Overall EEG variation, spectral power and event-related potentials could not explain this relationship, highlighting that moment-to-moment neural variability uniquely tracks bias shifts. Neural variability modulation through prefrontal cortex appears instrumental for permitting an organism to adapt its biases to environmental demands.

Introduction

We often reach decisions not only by objectively weighing different alternatives, but also by allowing subjective biases to influence our choices. Ideally, such biases should be under internal control, allowing us to flexibly adapt to changes in task context while performing a challenging task. Specifically, contexts which prioritize target detection benefit from a liberal response strategy, whereas a conservative strategy should be used at times when it is important to avoid errors of commission (e.g. false alarms). Adaptive shifts in decision bias are presumed to rely on prefrontal cortex (Rahnev et al., 2016), but despite growing interest (Chen et al., 2015; Reckless et al., 2014; Windmann et al., 2002), the spatio-temporal neural signature of such within-person bias shifts is currently unknown.

One candidate neural signature of decision bias shifts that has not been considered thus far is the variability of brain activity, as reflected in its moment-to-moment irregularity. Temporal neural variability is a prominent feature in all types of neural recordings (single-cell, local field potentials, EEG/MEG, fMRI) and has traditionally been considered noise that corrupts neural computation (Dinstein et al., 2015; Faisal et al., 2008). In contrast, heightened neural variability is increasingly proposed to support cognitive flexibility by allowing the brain to continuously explore its dynamical repertoire, helping it to quickly adapt to and process a novel stimulus (Ghosh et al., 2008; Misić et al., 2010). Indeed, a growing body of evidence suggests that neural variability can prove optimal for neural systems, allowing individuals to perform better, respond faster, and adapt quicker to their environment (Garrett et al., 2015, Garrett et al., 2013a, Garrett et al., 2011).

One tangible possibility is that cognitive flexibility emerges when a neural system avoids locking into a stereotypical, rhythmic pattern of activity, while instead continuously exploring its full dynamic range to better prepare for unpredictably occurring events. Consistent with this notion of exploration, influential attractor models of neural population activity (Chaudhuri et al., 2019; Inagaki et al., 2019; Wimmer et al., 2014) typically contain a ‘noise’ component that drives a dynamical system from attractor state to attractor state within a high-dimensional state space (Deco et al., 2009; Deco and Romo, 2008). This element of noise might indeed correspond to modulations of moment-to-moment neural variability during cognitive operations that can be empirically observed. Here, we perform a crucial test of the utility of temporal neural variability in the context of adaptive human decision making. In line with recent ideas that a high-fidelity, more variable neural encoding regime may be particularly required in more complex, non-deterministic situations (Garrett et al., 2020; Marzen and DeDeo, 2017; Młynarski and Hermundstad, 2018), we hypothesized that increased neural variability might underlie a state of higher receptiveness to and preparedness for events of interest that are not predictable in time, permitting the adoption of a more liberal bias toward confirming that such an event has indeed occurred.

Interestingly, improved cognitive function has also recently been linked to reduced neural variability, in line with the presumed corruptive role of noise for cognitive operations (Faisal et al., 2008). In particular, transient variability decreases after stimulus onset – called ‘quenching’ (Churchland et al., 2010) – have been proposed to reflect the settlement of an attractor into a stable state (Churchland et al., 2010; Schurger et al., 2015; Wang, 2002), with quenching reportedly being stronger during conscious perception relative to when a stimulus passes unseen (Schurger et al., 2015). Stronger quenching has also been reported in observers with higher perceptual sensitivity (Arazi et al., 2017), in line with a central assumption of signal detection theory (SDT) that internal noise is detrimental for sensitivity and thus should be suppressed (Green and Swets, 1966). To attend to this conceptual discrepancy, we further asked whether a quenching effect can also be observed in moment-to-moment variability, and if so, whether it reflects adaptive decision bias shifts and perceptual sensitivity.

We investigated these issues using previously published data from humans performing a continuous target detection task under two different decision bias manipulations, while non-invasively recording their electroencephalogram (EEG) (Kloosterman et al., 2019). Sixteen participants (three experimental sessions each) were asked to detect orientation-defined squares within a continuous stream of line textures of various orientations and report targets via a button press (Figure 1A). In alternating 9-min blocks of trials, we actively biased participants’ perceptual decisions by instructing them either to report as many targets as possible (liberal condition), or to only report high-certainty targets (conservative condition). We played auditory feedback after errors and imposed monetary penalties to enforce instructions.

Figure 1 with 1 supplement see all
Experimental paradigm and behavioral results.

(A) Top, target and non-target stimuli. Subjects detected targets (left panel) within a continuous stream of diagonal and cardinal line stimuli (middle panel), and reported targets via a button press. In different blocks of trials, subjects were instructed to actively avoid either target misses (liberal condition) or false alarms (conservative condition). Auditory feedback was played directly after the respective error in both conditions (right panel). Bottom, time course of an experimental session. The two conditions were alternatingly administered in blocks of nine minutes. In between blocks participants were informed about current task performance and received instructions for the next block. Subsequent liberal and conservative blocks were paired for within-participant analyses (see panel D, and Figure 3C). (B) Distributions of participants’ criterion in both conditions. A positive criterion indicates a more conservative bias, whereas a negative criterion indicates a more liberal bias. (C) Lines indicating the criteria used by each participant in the two conditions, highlighting individual differences both in overall criterion (line intercepts), and in the size of the criterion shift between conditions (slopes). (D) Within-person bias shifts for liberal–conservative block pairs (see panel A, bottom). Participants were sorted based on average criterion shift before plotting.

In our previous paper on these data, we reported within-participant evidence that decision bias in each condition separately is implemented by modulating the accumulation of sensory evidence in posterior brain regions through oscillatory EEG activity in the 8–12 Hz (alpha) and gamma (60–100 Hz) frequency ranges (Kloosterman et al., 2019). In no brain region, however, did we find a change-change relationship between participants’ liberal–conservative shifts in decision bias and in spectral power, despite substantial available data per participant (on average 1733 trials) and considerable inter-individual differences in the bias shift. Reasoning that moment-to-moment variability of neural activity may instead better capture the adaptive bias shift from person to person, potentially revealing its hypothesized prefrontal signature, we here measured temporal variability in the EEG data using a novel extension of multi-scale entropy (MSE)(Costa et al., 2002). We then tested for a change-change relationship by correlating within-person liberal–conservative shifts in decision bias with those estimated via our modified MSE (mMSE) measure. We indeed found that those participants who shifted more toward a liberal bias (in line with task demands) also showed a stronger boost in mMSE. This relationship could not be explained by overall EEG signal variation, band-specific spectral power, and event-related potentials, highlighting the unique contribution of moment-to-moment neural variability to the bias shift. Finally, we show that interactions between spectral power and phase in low frequencies (1–3 Hz) may underlie the observed effects.

Results

Large individual differences in the extent of decision bias shift

Participants differentially adopted the intended decision biases in the respective conditions, as quantified by the criterion SDT measure of bias (Green and Swets, 1966). Subjects assumed a lower criterion (more liberal bias) when target detection was emphasized (c = –0.13, standard deviation (SD) 0.4) and adopted a higher criterion (more conservative bias) when instructed to avoid false alarms (c = 0.73, SD 0.36; liberal vs. conservative, p=0.001, two-sided permutation test, 1000 permutations) (Figure 1B). Participants varied substantially not only in the average criterion they used across the two conditions (range of c = –0.24 to 0.89), but also in the size of the criterion shift between conditions (range of ∆c = –1.54 to –0.23). Highlighting the extent of individual differences, participant’s biases in the two conditions were only weakly correlated (Spearman’s rho = 0.24, p=0.36), as can be seen from the subjects’ large variation in criterion intercept and slope between the two conditions (Figure 1C). Moreover, each participant’s bias shift also fluctuated spontaneously over the course of the experiment, as indicated by variation in criterion differences between successive, nine-minute liberal and conservative blocks (participant-average SD 0.37, Figure 1D). Participants also varied widely in their ability to detect targets (range in SDT d´ 0.26 to 3.97), but achieved similar d´ in both bias conditions (rho = 0.97, p<0.001, Figure 1—figure supplement 1). Moreover, the liberal–conservative bias shift was only weakly correlated with a shift in sensitivity across participants (rho = 0.44, p=0.09), indicating that the bias manipulation largely left perceptual sensitivity unaffected. In our previous paper on these data (Kloosterman et al., 2019), we also quantified decision bias in these data in terms of the ‘drift bias’ parameter of the drift diffusion model (Ratcliff and McKoon, 2008). We chose to focus on SDT criterion in the current paper due to its predominant use in the literature and its comparably simpler computation, while noting the substantial overlap between the two measures as indicated by their high correlation (rho = –0.89, as reported in Kloosterman et al., 2019). Taken together, we observed considerable variability in the magnitude of the decision bias shift as a result of our bias manipulation, both at the group level and within single individuals.

Measuring neural variability with modified multi-scale entropy

We exploited the between- and within-participant variations in liberal–conservative criterion differences to test our hypothesis that a larger boost in brain signal variability should reflect a more liberal bias shift. To this end, we developed a novel algorithm based on multi-scale entropy (MSE) that directly quantifies the temporal irregularity of the EEG signal at shorter and longer timescales by counting how often temporal patterns in the signal reoccur during the signal’s time course (Costa et al., 2002Figure 2A, bottom). In general, signals that tend to repeat over time, such as neural oscillations, are assigned lower entropy, whereas more irregular, non-repeating signals yield higher entropy. Please see the Materials and methods section for a step-by-step description of the MSE computation in our EEG data.

mMSE estimation procedure.

(A) Discontinuous entropy computation procedure. Data segments of 0.5 s duration centered on a specific time point from each trial’s onset (top row) are selected and concatenated (middle row). Entropy is then computed on this concatenated time series while excluding discontinuous segment borders by counting repeats of both m (here, m = 1 for illustration purposes) and m+1 (thus 2) sample patterns and taking the log ratio of the two pattern counts (bottom row). We used m = 2 in our actual analyses. The pattern similarity parameter r determines how lenient the algorithm is toward counting a pattern as a repeat by taking a proportion of the signal’s standard deviation (SD), indicated by the width of the horizontal gray bars. The pattern counting procedure is repeated at each step of the sliding window, resulting in a time course of entropy estimates computed across trials. (B) ‘Filt-skip’ coarsegraining procedure used to estimate entropy on longer timescales, consisting of low-pass filtering followed by point-skipping. Filter cutoff frequency is determined by dividing the data sampling rate (here, 256 Hz i.e. 1 sample per 3.9 ms) by the index of the timescale of interest (top row). The signal is then coarsened by intermittently skipping samples (bottom row). In this example, every second sample is skipped at timescale 2, resulting in two different time courses depending on the starting point. Patterns are counted independently for both starting points and summed before computing entropy.

We developed time-resolved, modified MSE (mMSE), that differs from traditional MSE in two ways. First, slower timescales are usually assessed in conventional entropy analysis by ‘coarsening’ the data through averaging of data samples close to each other in time, and repeating the pattern counting operation (see Figure 2A). Although this method can remove faster dynamics from the data in a straightforward way, it is prone to aliasing artifacts and thereby possibly obscures genuine entropy effects in the data. Therefore, we instead coarsened the data by applying a Butterworth low-pass filter followed by skipping of data points (Figure 2B), thereby retaining better control over the frequencies present in the coarsened signal (Semmlow, 2014; Valencia et al., 2009). Second, conventional entropy analysis requires substantial continuous data (in the order of minutes) for robust estimation, which makes the standard method unsuitable for studying brief, transient cognitive operations such as perceptual decision making. To investigate entropy dynamics over time, we calculated entropy across discontinuous data segments aggregated across trials via a sliding window approach (Grandy et al., 2016Figure 2A, top), allowing us to examine entropy fluctuations from moment to moment. Please see Materials and methods for details on the various analysis steps and our modifications of the MSE algorithm.

Larger boosts in frontal entropy track more liberal decision bias shifts

We tested for a relationship between shifts in decision bias and neural variability from the conservative to the liberal conditions by Spearman-correlating joint modulations of mMSE and criterion across participants (averaged over the three sessions), for all electrodes, time points, and timescales. Strikingly, we found a negative cluster of correlations in mid- and left-frontal electrodes (p=0.015, cluster-corrected for multiple comparisons [Maris and Oostenveld, 2007]) indicating that participants who showed a larger bias shift from the conservative to the liberal condition were those who also exhibited a larger boost in frontal entropy (Figure 3A). The cluster ranged across timescales from ~20 to 164 ms, with most of the cluster located after trial initialization (solid vertical line in Figure 3A). To illustrate this correlation, we obtained a point estimate of mMSE per participant by averaging liberal–conservative mMSE within the significant cluster, and plotted the across-participant change-change correlation (rho = –0.87) with criterion in a scatter plot (Figure 3B). Since this correlation is bound to be significant due to averaging across significantly correlating time-timescale bins from the principal analysis, we consider it a descriptive statistic and refrain from reporting its p-value. We employ the participant-wise mMSE point estimates to examine the relationship with other neural measures (see next sections). In contrast to these correlational results, we found no significant clusters (main effect) when contrasting the two conditions. To provide an intuition of the mMSE values that fed into the correlation analysis, we plotted the subject-averaged mMSE values within the cluster separately for the two conditions (Figure 3—figure supplement 1). This indeed shows highly similar subject-average mMSE for the two conditions, highlighting the lack of a main effect of condition in our data. Taken together, we observed a strong change-change correlational link in frontal brain regions between liberal–conservative shifts in mMSE and decision bias, suggesting that participants with a stronger increase in temporal neural variability from to conservative to the liberal condition achieved a greater liberal bias shift.

Figure 3 with 5 supplements see all
Change-change correlation between liberal–conservative shifts in mMSE and bias.

(A) Significant negative electrode-time-timescale cluster observed via Spearman correlation between liberal–conservative mMSE and liberal–conservative SDT criterion, identified using a cluster-based permutation test across participants to control for multiple comparisons. Correlations outside the significant cluster are masked out. Left panel, time-timescale representation showing the correlation cluster integrated over the electrodes included in the cluster, indicated by the black dots in the topographical scalp map in the right panel. Dot size indicates how many time-timescale bins contribute to the cluster at each electrode. Color borders are imprecise due to interpolation used while plotting. The solid vertical line indicates the time of trial onset. The dotted vertical line indicates time of (non)target onset. Right panel, scalp map of mMSE integrated across time-timescale bins belonging to the cluster. p-Value above scalp map indicates statistical significance of the cluster. The black triangle indicates participants’ median reaction time, averaged across participants and conditions. (B) Scatter plot of the correlation after averaging mMSE within time-timescale-electrode bins that are part of the three-dimensional cluster. Since the cluster was defined based on significant change-change correlations, averaging mMSE across the significant time-timescale-electrode bins before correlating represents no new information. Thus, the scatter plot serves only to illustrate the negative relationship identified in panel A. Both Pearson’s r and Spearman’s rho are indicated. We report no p-values since the bin selection procedure guarantees significance, and consider the correlation a descriptive statistic only. (C) Within-participant mMSE vs. criterion slopes across liberal–conservative block pairs completed across the experiment. rrm, repeated measures correlation across all block pairs performed after centering each participant’s shifts in mMSE and criterion around zero by removing the intercept. Gray lines, individual participant slopes fit across liberal–conservative mMSE vs criterion block pairs. Black line, slope averaged across participants.

Entropy-bias correlations are also present within participants and in split data

Correlating brain and behavior across a relatively modest number of participants can be unreliable (Yarkoni, 2009), depending on the amount of data underlying each observation. Therefore, we next employed two complementary approaches to strengthen evidence for the observed link between shifts in neural variability and decision bias. We first asked whether mMSE and bias were also linked within participants across the nine liberal–conservative block pairs that each participant performed throughout the three sessions (see Figure 1A, bottom for task structure and Figure 1D for criterion shifts in single block pairs). Critically, we observed a negative repeated measures correlation (Bakdash and Marusich, 2017) between within-participant shifts in criterion and mMSE (rrm = –0.19, p=0.046, Figure 3C), providing convergent within-person evidence for a link between shifts in decision bias and neural variability. Second, we tested whether the observed across-participant correlation was present within two separate halves of the data after an arbitrary split based on odd and even trials. We found significant change-change correlations in both data halves, indicating reliable between-subject associations (odd, rho = –0.77, p=0.001; even, rho = –0.75, p=0.001)(Figure 3—figure supplement 2A and 2B). In contrast to the significant change-change correlation, we found no significant single-condition correlations between mMSE and criterion (conservative: rho = –0.12, p=0.66, liberal: rho = –0.21, p=0.43) and no significant difference in correlation strength (∆rho = –0.09, p=0.7, non-parametric correlation difference test, 10.000 permutations). This indicates that the change-change correlation was not driven exclusively by one of the two conditions, but rather that their difference reveals the strong relationship observed in the present data.

The entropy-bias relationship is not explained by total signal variation or spectral power

Next, we investigated whether the entropy-behavior correlation could alternatively be explained by total signal variation (quantified via the signal SD), or spectral power. Specifically, the variance structure of a signal can influence entropy estimates through the pattern similarity (r) parameter (width of gray bars in Figure 2), even when this parameter is recomputed for each timescale after coarsening, as we did (Kosciessa et al., 2020). In addition, E/MEG data is often quantified in terms of oscillatory spectral power in canonical delta (1–2 Hz), theta (3–7 Hz), alpha (8–12 Hz), beta (13–30 Hz) and gamma (60–100 Hz) bands, which might be able to explain the entropy results through a similar dependency. (See Kloosterman et al., 2019 for detailed spectral analysis of the current dataset). Therefore, we tested whether the ∆bias-∆entropy correlation could be explained by broadband signal SD and band-specific spectral power. To make the computation of spectral power and entropy as similar as possible, we used the same 0.5 s sliding window and 50 ms step size for spectral analysis (1 s window to allow delta power estimation, see Materials and methods), and selected spectral power within the same electrodes and time points in which the mMSE effect was indicated.

Strikingly, we found that the ∆bias-∆entropy correlation remained strong and significant both when controlling for signal SD (partial rho = –0.82, p<0.0001), and even when controlling for all major power bands simultaneously (delta, theta, alpha, beta, gamma; partial rho = –0.75, p=0.005). See Figure 3—figure supplement 2 for correlations between mMSE and various potentially confounding factors. We also found similar results when separately controlling for signal SD within each time-timescale bin while correlating modulations of mMSE and criterion in all electrodes, time points, and timescales (Figure 3—figure supplement 3A). Importantly, the results did depend on our modified entropy estimation method, since the frontal correlation cluster was smaller and non-significant when performing the ∆bias-∆entropy correlation using conventional MSE combined with our novel sliding window approach (cluster p=0.37) (Costa et al., 2002Figure 3—figure supplement 3B). In contrast to mMSE, spectral power was not linked to the bias shift. We found no significant clusters when correlating the liberal–conservative shifts in bias versus raw spectral power and versus percent signal change power modulation using either the condition-specific pre-stimulus baseline, or a condition-average baseline subtraction (Figure 3—figure supplement 4). Finally, statistically controlling for the participants’ perceptual ability to detect targets, quantified as the liberal–conservative shift in SDT sensitivity measure d´ (Green and Swets, 1966) did not affect the relationship (partial rho = –0.88, p<0.0001), indicating that perceptual sensitivity could not explain our results. Taken together, neither overall signal variation, nor spectral power, nor perceptual sensitivity could account for the observed correlation between shifts in mMSE and decision bias, highlighting the unique ability of mMSE to capture these behavioral differences.

Entropy-bias relationship is not explained by event-related potentials

Next, we investigated whether event-related potentials (ERPs), as a relatively simple and widely used EEG metric, could explain the observed link between shifts in criterion and entropy (Luck et al., 2000). We computed ERPs for the liberal and conservative conditions by averaging trial time courses and tested them against each other for all electrodes and time points using the cluster-based permutation test. We observed one significant positive cluster (p=0.001, cluster-corrected, indicating a stronger ERP for the liberal condition) over central and parietal electrodes, and one negative cluster (p=0.001) in midfrontal, central and parietal electrodes (Figure 3—figure supplement 4). The timing and topography of the positive ERP cluster closely corresponded to the centroparietal positivity (CPP) signal thought to reflect sensory evidence accumulation (O'Connell et al., 2012). This is in line with our previous report of increased evidence accumulation in the liberal condition (Kloosterman et al., 2019). Importantly, when repeating the change-change correlation between liberal–conservative ERPs and criterion as performed for mMSE, we found no significant clusters (lowest p-value positive cluster, p=0.69; negative cluster, p=0.23). Furthermore, we repeated the mMSE analysis after removing the ERP from the overall EEG activity by subtracting the event-related potential (computed by averaging all trials within a condition, session, and participant) from each single trial. ERP subtraction from single trials is typically performed to remove stimulus-evoked activity and focus on ongoing or ‘induced’ neural activity (Klimesch et al., 1998). The bias-entropy correlation remained virtually unchanged after removing the ERP (rho = –0.90 with removal versus rho = –0.87 without removal). See Misić et al., 2010 for similar evidence of independence of MSE from ERPs. Taken together, these results suggest that liberal–conservative ERPs cannot account for the brain-behavior link observed between shifts in bias and entropy.

Entropy-bias relationship possibly mediated by power-phase interactions in the delta range

Given that overall signal variation, spectral power, and ERPs were not able to explain our entropy findings, it remains an open question as to which aspect of the EEG signal underlies the observed link between entropy and decision bias shifts. Since we previously found stronger midfrontal oscillatory activity in these data in the delta/theta (2–6 Hz) frequency range (Kloosterman et al., 2019), we next examined the impact of systematically removing the lowest frequencies in the data on the strength of the observed brain-behavior relationship. To this end, we performed entropy analysis after applying a high-pass filter with 1, 2, or 3 Hz cutoff frequencies to the time-domain data (filter order of 4, trials mirror-padded to 4 s to allow robust estimation [Cohen, 2014]). Note that we applied a 0.5 Hz high-pass filter during data preprocessing to remove slow drift in all cases. To quantify the strength of the brain-behavior correlation at each filtering step, we averaged mMSE within the time-space-timescale cluster that showed the strong negative correlation in our principal (non-filtered) analysis (see Figure 3B) and plotted scatterplots of the correlation.

Figure 4 shows the results of this analysis for non-filtered data (Figure 4A, copied from Figure 3B), as well as for 1, 2, and 3 Hz high-pass filters (Figure 4B-D). Interestingly, we found that the brain-behavior relationship progressively weakened with higher cutoff frequencies, such that the correlation was non-significant after applying a 3 Hz high-pass filter before entropy analysis. Whereas this finding suggests that these low frequencies contribute to our entropy effects, our control analysis in Figure 3—figure supplement 2I indicates that statistically controlling for 1–2 Hz (delta) power does not affect the brain-behavior relationship. One explanation for these seemingly incongruent results could be the different ways in which oscillatory phase is treated in these two analyses: whereas statistically controlling for delta power does not take delta phase into account, the high-pass filter removes both power and phase information from the signal before entropy is computed. Taken together, these analyses reveal that the lowest frequencies present in the data might play a role in the entropy-behavior relationship, possibly through non-linear interactions between spectral power and phase of these frequencies.

Liberal–conservative change-change correlation between mMSE and decision bias for non-filtered data (A) and after 1,2, and 3 Hz high-pass filtering (B C and D).

Entropy quenching is not related to behavior

Finally, we tested whether variability ‘quenching’ was related to behavior in our data. Specifically, improved perceptual sensitivity has been linked to transient, post-stimulus decreases in neural variability (Arazi et al., 2017; Churchland et al., 2010; Schurger et al., 2015). Quenching is directly predicted by attractor models of brain organization (Wang, 2002) and is consistent with the main principle of signal detection theory that suppression of neural noise enhances perception (Green and Swets, 1966). Quenching has also been reported in the human EEG over visual cortex in terms of a variance reduction across trials following stimulus onset (Arazi et al., 2017), although this type of quenching can be attributed to the well-known suppression of low-frequency (alpha and beta) spectral power following stimulus onset (Daniel et al., 2019). To our knowledge, only Arazi et al., 2017 report an across-participant correlational link between perceptual sensitivity and variance quenching; however, in that study, this correlation could be explained by elevated absolute variability in the pre-stimulus period and not by brain activity in the post-stimulus period, suggesting that higher pre-stimulus variability was the more relevant factor for behavior. Nonetheless, we tested the link between entropy quenching and behavior in our data without any strong prior hypothesis.

To investigate this issue, we computed mMSE quenching by converting the raw mMSE values into percentage modulation from the pre-stimulus baseline and testing this modulation against zero. Besides a lateral occipital enhancement of mMSE modulation (Figure 5A) that could not be explained by spectral power modulation (Figure 5B), we also found a suppression of mMSE with a focal, mid-occipital topography, in line with quenching (Figure 5C). This focal topography was highly similar to that of the SSVEP evoked by the strong, visual stimulation frequency at 25 Hz (see Figure 3A of Kloosterman et al., 2019. In addition, spectral analysis of the ERP-subtracted data also revealed involvement of the subharmonic of this stimulation frequency at 12.5 Hz (data not shown). The highly periodic nature of this boosted SSVEP is bound to decrease the temporal irregularity of the signal, which could explain the observed mMSE suppression. In addition, the effect is strongest in shorter time scales below 40 ms because of the progressive low-pass filter implemented for longer timescales in the coarse graining procedure, which removes these SSVEP-related frequencies from timescales slower than ca. 40 ms. mMSE quenching was indeed strongly positively correlated with low-frequency power encompassing 12.5 and 25 Hz (Figure 5D). Thus, the strongly periodic SSVEP boost after stimulus onset likely increased the temporal regularity of the EEG signal, which in turn suppressed post-stimulus entropy and manifested as quenching.

mMSE modulation with respect to pre-trial baseline.

(A) Significant positive cluster observed in longer timescales after normalizing mMSE values to percent signal change (psc) units with respect to the pre-trial baseline (–0.2 to 0 s) and averaging across conditions. (B) Correlation between mMSE modulation in the positive cluster depicted in A and spectral power modulation in midfrontal electrodes. Left panel, 3–7 Hz; right panel, 12–30 Hz. (C and D) As B but for the posterior negative cluster. (E) Significant positive cluster observed in mid-frontal electrodes in the liberal–conservative contrast of mMSE modulation. (F) Significant cluster resulting from the correlation between liberal–conservative mMSE modulation with liberal–conservative SDT criterion. Conventions as in Figure 3.

Contrasting transient mMSE percentage modulation between the two conditions, we found a significant positive cluster in midfrontal electrodes, indicating a stronger transient mMSE increase following trial onset in the liberal condition (Figure 5E). Furthermore, when change-change correlating liberal–conservative mMSE modulation and criterion, we observed a left-lateralized negative cluster in temporal electrodes, but no cluster in occipital electrodes (Figure 5F). Finally, we found no significant cluster when correlating liberal–conservative mMSE quenching with shifts in perceptual sensitivity (d´). Taken together, although we did find occipital, transient entropy quenching likely due to the strengthened SSVEP response, we found no convincing link between entropy quenching and behavior.

Discussion

The ability to engage decision biases allows organisms to adapt their decisions to the context in which choices are made. Frontal cortex has previously been shown to be involved in adaptive bias shifts in humans (Chen et al., 2015; Rahnev et al., 2016; Reckless et al., 2014; Windmann et al., 2002) and monkeys (Ferrera et al., 2009), but its spatiotemporal neural signature has to date remained elusive. Here, we provide first evidence that greater bias shifts are typified in those subjects who exhibit greater shifts in frontal mMSE after stimulus onset, suggesting that mMSE provides a core signature of such adaptive behavioral shifts. Importantly, the relationship occurred independent of total brain signal variation, oscillatory neural dynamics, and ERPs. Moreover, it was observed at longer time scales, for which estimation was biased in a large amount of previous work (Kosciessa et al., 2020). Since the results were exclusively observed with principled extensions of the mMSE algorithm, our finding provides initial evidence for the unique value of brain signal irregularity at longer time scales.

The observed relationship between shifts in bias and neural variability in anterior brain regions complements our previous findings in the frequency domain that humans can intentionally control prestimulus 8–12 Hz (alpha) oscillatory power in posterior regions to adaptively bias decision making (Kloosterman et al., 2019). Notably, we previously observed increased oscillatory 2—6 Hz (theta) power in the liberal condition in the same midfrontal electrodes implicated here in the ∆bias-∆entropy correlation, but this theta power difference was not significantly correlated with the bias shift (rho = 0.23, p=0.39). This suggests that the bias shift may be reflected both in low-frequency spectral power and entropy in midfrontal regions, but that only entropy is linked to bias shift magnitude. One possible explanation for such a dissociation is that spectral power exclusively reflects the amplitude of oscillatory signal contributions while discarding their phase information. In contrast, entropy is sensitive to both variations in the magnitude as well as the phase of signal fluctuations. This notion is also in line with our finding that low-frequency spectral power is insufficient to explain our observed brain-behavior relationship, while the presence of these frequencies (including narrowband non-linear phenomena such as phase resets or temporal dependencies in the amplitude of signals [Linkenkaer-Hansen et al., 2001]) during entropy estimation is sufficient and necessary for the relationship to emerge (Figure 4). Moreover, whereas spectral analysis strictly assumes a sinusoidal waveform of EEG signal fluctuations (Cole and Voytek, 2017; Jones, 2016), entropy analysis is agnostic to the shape of the waveforms present in the signal. Entropy thus provides a more unrestricted description of moment-to-moment fluctuations in neural activity that is highly predictive of decision bias shifts across participants in our data. Our results suggest that entropy taps into information in the EEG signal that is not available in ERPs and spectral power – the most popular analysis methods used in the field. Intriguingly, this suggests that many previous E/MEG studies analyzing ERPs and/or spectral power might have structurally overlooked a crucial property of the EEG signal that is in fact strongly linked to behavior. It could thus be that many interesting brain-behavior links are still hidden in existing EEG datasets, which can now be uncovered using mMSE.

Despite the consistent liberal decision bias shift that participants exhibited between the two conditions and the strong change-change correlation between entropy and behavior, mMSE was not significantly higher on average in the liberal condition. This is in contrast to the raw alpha and theta power differences that we reported previously, which did show significant condition differences (see Kloosterman et al., 2019). Strikingly, we show here that the shift in mMSE did correlate with the liberal–conservative bias shift, whereas the shifts in alpha and theta did not. This indicates that inter-individual differences in mMSE may be sensitive to behavioral adjustments even in the absence of a group-wise shift. A possible explanation for such a dissociation is that a main effect and a correlation address somewhat divergent research questions that may conflict with each other. On the one hand, a main effect tends to occur when subjects respond similarly to an experimental condition, which typically requires that individual differences be relatively small. On the other hand, chances of detecting a correlation with behavior typically increase when individual differences are larger, (e.g. Lindenberger et al., 2008). Thus, the common presumption that a main effect of condition is a prerequisite for detecting behavioral effects is unfounded in our view. Therefore, we did not a priori hypothesize a main effect of condition in the liberal–conservative contrast, but rather focused our hypotheses on inter-individual adjustments in mMSE that tracked the magnitude of the individual bias shift. We indeed observed a significantly stronger mMSE transient increase (main effect) after trial onset in the liberal condition once the data were baseline corrected (as is common in time-frequency EEG analysis), but the change-change correlation with behavior was weaker using baseline corrected mMSE (Figure 5F).

In apparent contrast to the view that neural variability facilitates cognition, previous work has suggested that a temporary stabilization of neural activity after stimulus onset (quenching, quantified as a transient suppression of time-domain variance) is beneficial for perception (Arazi et al., 2017; Schurger et al., 2015). We also observed a suppression in baseline-corrected mMSE, likely due to increased regularity of the time-domain signal due to the boosted power at the SSVEP frequency (Kloosterman et al., 2019). Previous work has linked variance quenching to post-stimulus suppression of rhythmic low-frequency (alpha and beta) power (Daniel et al., 2019). Future work could investigate whether entropy indeed increases after suppression of these temporally regular signals. Crucially, however – and divergent from our finding that boosting variability is coupled to an adaptive bias shift – we found no evidence for a change-change relationship between entropy quenching and decision bias or perceptual sensitivity. Since the relations between quenching observed in neural spiking (Churchland et al., 2010), trial-by-trial variance of E/MEG (Arazi et al., 2017), and mMSE are currently unclear, further investigation on this issue is needed (Garrett et al., 2013b). Future studies could also explore how neural variability quenching and boosting in different timescales are related to various aspects of decision making such as perceptual sensitivity and different kinds of biases (Fleming et al., 2010; Talluri et al., 2018; Urai et al., 2019), as well as to confidence and metacognitive processes (Fleming and Dolan, 2012; Yeung and Summerfield, 2012). Furthermore, individual decision bias has also been linked to the magnitude of transient dilations of the pupil (de Gee et al., 2017, de Gee et al., 2014) and to entropy of EEG (Waschke et al., 2019), suggesting that pupil-linked neuromodulation (Joshi and Gold, 2020) could be related to decision bias through adjustments to moment-to-moment neural variability. Further investigation of such relationships could yield fruitful insights about the neurochemical mechanisms underlying associations between neural variability and higher order cognitive function (Alavash et al., 2018; Garrett et al., 2015).

Our findings may have important implications for dynamical attractor models of neural population activity, which have become increasingly influential in recent years (Chaudhuri et al., 2019; Inagaki et al., 2019; Wimmer et al., 2014). Attractor models cast cognitive outcomes (e.g. decisions, perceptual experiences, or retention of an item in working memory) as low-dimensional, stable states (‘attractors’) within a high-dimensional energy landscape (Deco et al., 2009; Deco and Romo, 2008). These models typically contain a noise component that enables probabilistic exploration of the energy landscape, increasing chances of attraction to the most optimal state (e.g. the correct decision) and limiting the likelihood of settling too rigidly into any particular state. In multi-stable visual perception, for example, noise is thought to underlie the spontaneous, flexible switching between perceptual states reported by observers while viewing bi-stable visual illusions (Kloosterman et al., 2015; Moreno-Bote et al., 2007). Our results suggest that an element of noise facilitating cognitive flexibility might translate into modulations of moment-to-moment neural variability that can be measured in cortical population activity. Future dynamical attractor modeling work could investigate exactly which characteristics of this noise component underlie effective exploration of the state space within these models, for example by modulating noise amplitude as well as the relative contribution of different noise frequencies (noise color). Modeling insights could then guide the search for signatures of noise supporting cognitive operations in moment-to-moment neural variability.

Our results suggest that dynamic adjustment of neural variability in frontal regions is related to adaptive behavior. Based on our findings, we speculate that heightened frontal entropy results from a more dynamic, irregular neural regime that enables an individual to be more prepared to process and act upon uncertain, yet task-relevant information. We believe that quantifying shifts in neural entropy could help elucidate the mechanisms allowing organisms to adapt to their environment and ultimately increase their chances of survival.

Materials and methods

Key resources table
Reagent type
(species) or resource
DesignationSource or referenceIdentifiersAdditional information
Biological sample (Humans)ParticipantsKloosterman et al., 2019https://doi.org/10.7554/elife.37321See Subjects section in Materials and methods
Software, algorithmMATLABMathworksMATLAB_R2016b, RRID:SCR_001622
Software, algorithmPresentationNeuroBSPresentation_v9.9, RRID:SCR_002521
Software, algorithmStatistical AnalysisRR version 4.0.1, RRID:SCR_001905
Software, algorithmCustom analysis codeKloosterman et al., 2019https://github.com/kloosterman/critEEG
Software, algorithmCustom analysis codeKloosterman et al., 2019https://github.com/kloosterman/critEEGentropy
Software, algorithmCustom analysis codeKloosterman, 2020https://github.com/LNDG/mMSE/FieldTrip-compatible toolbox
OtherEEG data experimental taskKloosterman et al., 2019https://doi.org/10.6084/m9.figshare.6142940

We report a novel analysis of a previously published dataset involving a target detection task during two different decision bias manipulations (Kloosterman et al., 2019).

Subjects 

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Sixteen participants (eight females, mean age 24.1 years,±1.64) took part in the experiment, either for financial compensation (EUR 10,– per hour) or in partial fulfillment of first year psychology course requirements. Each participant completed three experimental sessions on different days, each session lasting ca. 2 hr, including preparation and breaks. One participant completed only two sessions, yielding a total number of sessions across subjects of 47. Due to technical issues, for one session only data for the liberal condition was available. One participant was an author. All participants had normal or corrected-to-normal vision and were right handed. Participants provided written informed consent before the start of the experiment. All procedures were approved by the ethics committee of the University of Amsterdam.

Stimuli

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Stimuli consisted of a continuous semi-random rapid serial visual presentation (rsvp) of full screen texture patterns. The texture patterns consisted of line elements approx. 0.07° thick and 0.4° long in visual angle. Each texture in the rsvp was presented for 40 ms (i.e. stimulation frequency 25 Hz) and was oriented in one of four possible directions: 0°, 45°, 90° or 135°. Participants were instructed to fixate a red dot in the center of the screen. At random inter trial intervals (ITI’s) sampled from a uniform distribution (ITI range 0.3–2.2 s), the rsvp contained a fixed sequence of 25 texture patterns, which in total lasted one second. This fixed sequence consisted of four stimuli preceding a (non-)target stimulus (orientations of 45°, 90°, 0°, 90°, respectively) and twenty stimuli following the (non)-target (orientations of 0°, 90°, 0°, 90°, 0°, 45°, 0°, 135°, 90°, 45°, 0°, 135°, 0°, 45°, 90°, 45°, 90°, 135°, 0°, 135°, respectively) (see Figure 1A). The fifth texture pattern within the sequence (occurring from 0.16 s after sequence onset) was either a target or a nontarget stimulus. Nontargets consisted of either a 45° or a 135° homogenous texture, whereas targets contained a central orientation-defined square of 2.42° visual angle, thereby consisting of both a 45° and a 135° texture. 50% of all targets consisted of a 45° square and 50% of a 135° square. Of all trials, 75% contained a target and 25% a nontarget. Target and nontarget trials were presented in random order. To avoid specific influences on target stimulus visibility due to presentation of similarly or orthogonally oriented texture patterns temporally close in the cascade, no 45° and 135° oriented stimuli were presented directly before or after presentation of the target stimulus. All stimuli had an isoluminance of 72.2 cd/m2. Stimuli were created using MATLAB (The Mathworks, Inc, Natick, MA) and presented using Presentation version 9.9 (Neurobehavioral systems, Inc, Albany, CA).

Experimental design

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The participants’ task was to detect and actively report targets by pressing a button using their right hand. Targets occasionally went unreported, presumably due to constant forward and backward masking by the continuous cascade of stimuli and unpredictability of target timing (Fahrenfort et al., 2007). The onset of the fixed order of texture patterns preceding and following (non-)target stimuli was neither signaled nor apparent. At the beginning of the experiment, participants were informed they could earn a total bonus of EUR 30, -, on top of their regular pay of EUR 10, - per hour or course credit. In two separate conditions within each session of testing, we encouraged participants to use either a conservative or a liberal bias for reporting targets using both aversive sounds as well as reducing their bonus after errors. In the conservative condition, participants were instructed to only press the button when they were relatively sure they had seen the target. The instruction on screen before block onset read as follows: ‘Try to detect as many targets as possible. Only press when you are relatively sure you just saw a target.’ To maximize effectiveness of this instruction, participants were told the bonus would be diminished by 10 cents after a false alarm. During the experiment, a loud aversive sound was played after a false alarm to inform the participant about an error. During the liberal condition, participants were instructed to miss as few targets as possible. The instruction on screen before block onset read as follows: ‘Try to detect as many targets as possible. If you sometimes press when there was nothing this is not so bad.’ In this condition, the loud aversive sound was played twice in close succession whenever they failed to report a target, and three cents were subsequently deducted from their bonus. The difference in auditory feedback between both conditions was included to inform the participant about the type of error (miss or false alarm), to facilitate the desired bias in both conditions. After every block, the participant’s score (number of missed targets in the liberal condition and number of false alarms in the conservative condition) was displayed on the screen, as well as the remainder of the bonus. After completing the last session of the experiment, every participant was paid the full bonus as required by the ethical committee.

Participants performed six blocks per session lasting ca. 9 min each. During a block, participants continuously monitored the screen and were free to respond by button press whenever they thought they saw a target. Each block contained 240 trials, of which 180 target and 60 nontarget trials. The task instruction was presented on the screen before the block started. The condition of the first block of a session was counterbalanced across participants. Prior to EEG recording in the first session, participants performed a 10 min practice run of both conditions, in which visual feedback directly after a miss (liberal condition) or false alarm (conservative) informed participants about their mistake, allowing them to adjust their decision bias accordingly. There were short breaks between blocks, in which participants indicated when they were ready to begin the next block.

Behavioral analysis 

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We defined decision bias as the criterion measure from SDT (Green and Swets, 1966). We calculated the criterion c across the trials in each condition as follows:

c =-12 [Z(Hitrate) + Z(FArate)]

where hit-rate is the proportion target-present responses of all target-present trials, false alarm (FA)-rate is the proportion target-present responses of all target-absent trials, and Z(...) is the inverse standard normal distribution. Furthermore, we calculated perceptual sensitivity using the SDT measure d´:

d' =ZHitrate- Z(FArate)

EEG recording

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Continuous EEG data were recorded at 256 Hz using a 48-channel BioSemi Active-Two system (BioSemi, Amsterdam, the Netherlands), connected to a standard EEG cap according to the international 10–20 system. Electrooculography (EOG) was recorded using two electrodes at the outer canthi of the left and right eyes and two electrodes placed above and below the right eye. Horizontal and vertical EOG electrodes were referenced against each other, two for horizontal and two for vertical eye movements (blinks). We used the FieldTrip toolbox (Oostenveld et al., 2011) and custom software in MATLAB R2016b (The Mathworks Inc, Natick, MA; RRID:SCR_001622) to process the data. Data were re-referenced to the average voltage of two electrodes attached to the earlobes. We applied a Butterworth high-pass filter (fourth order, cutoff 0.5 Hz) to remove slow drifts from the data.

Trial extraction

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We extracted trials of variable duration from 1 s before target sequence onset until 1.25 after button press for trials that included a button press (hits and false alarms), and until 1.25 s after stimulus onset for trials without a button press (misses and correct rejects). The following constraints were used to classify (non-)targets as detected (hits and false alarms), while avoiding the occurrence of button presses in close succession to target reports and button presses occurring outside of trials: 1) A trial was marked as detected if a response occurred within 0.84 s after target onset; 2) when the onset of the next target stimulus sequence started before trial end, the trial was terminated at the next trial’s onset; 3) when a button press occurred in the 1.5 s before trial onset, the trial was extracted from 1.5 s after this button press; 4) when a button press occurred between 0.5 s before until 0.2 s after sequence onset, the trial was discarded. After trial extraction, the mean of every channel was removed per trial.

Artifact rejection

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Trials containing muscle artifacts were rejected from further analysis using a standard semi-automatic preprocessing method in Fieldtrip. This procedure consists of bandpass-filtering the trials of a condition block in the 110–125 Hz frequency range, which typically contains most of the muscle artifact activity, followed by a Z-transformation. Trials exceeding a threshold Z-score were removed completely from analysis. We used as the threshold the absolute value of the minimum Z-score within the block, + 1. To remove eye blink artifacts from the time courses, the EEG data from a complete session were transformed using independent component analysis (ICA), and components due to blinks (typically one or two) were removed from the data. In addition, to remove microsaccade-related artifacts we included two virtual channels in the ICA based on channels Fp1 and Fp2, which included transient spike potentials as identified using the saccadic artefact detection algorithm from Hassler et al., 2011. This yielded a total number of channels submitted to ICA of 48 + 2 = 50. The two components loading high on these virtual electrodes (typically with a frontal topography) were also removed. Blinks and eye movements were then semi-automatically detected from the horizontal and vertical EOG (frequency range 1–15 Hz; z-value cut-off four for vertical; six for horizontal) and trials containing eye artefacts within 0.1 s around target onset were discarded. This step was done to remove trials in which the target was not seen because the eyes were closed. Finally, trials exceeding a threshold voltage range of 200 mV were discarded. To attenuate volume conduction effects and suppress any remaining microsaccade-related activity, the scalp current density (SCD) was computed using the second-order derivative (the surface Laplacian) of the EEG potential distribution (Perrin et al., 1989).

ERP removal

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In a control analysis, we removed stimulus-evoked EEG activity related to external events by computing the event-related potential (ERP) and subtracting the ERP from each single trial prior to entropy or spectral analysis. This was done to focus on ongoing (termed ‘induced’, [Klimesch et al., 1998]) activity. To eliminate differences in evoked responses between sessions and conditions, we performed this procedure separately for ERPs computed in each condition, session, and participant.

Entropy computation

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We measured temporal neural variability in the EEG using a form of multiscale entropy (MSE)(Costa et al., 2002), which we modified in several ways. MSE characterizes signal irregularity at multiple time scales by estimating sample entropy (SampEn) of a signal’s time series at various sampling rates. The estimation of SampEn involves counting how often specific temporal patterns reoccur over time, and effectively measures how unpredictably the signal develops from moment to moment. At a given time scale, the estimation of SampEn consists of the following steps:

  1. A to-be-counted temporal ‘template’ pattern consisting of m samples is selected, starting at the beginning of the time series.

  2. The data is discretized to allow comparing patterns of samples rather than exact sample values (which are rarely exactly equal in physiological timeseries). A boundary parameter r is used to determine whether other patterns in the time series match the template. r denotes the proportion of the time series standard deviation (SD, see also Figure 2A), within which a pattern is a match, as follows:

    • Boundaryparameter=r×SD(1)
  3. Template pattern repeats throughout the time series are counted, yielding pattern count N(m).

  4. Steps 1 to 3 are repeated for patterns consisting of m+1 samples, yielding pattern count N(m+1).

  5. Steps 1 to 4 are iterated to assess each temporal pattern as a template once. Counts for each template pattern are then summed, yielding total counts across templates for N(m) and N(m+1).

  6. Finally, SampEn is computed as the logarithm of the ratio of the counts for m and m+1:

    • SampEn= lnN(m)N(m+1)(2)

Thus, SampEn estimates the proportion of similar sequences of m samples that are still similar when the next sample, that is m+1, is added to the sequence. Here, we use m=2 and r=0.5, as typically done in neurophysiological settings (Courtiol et al., 2016; Grandy et al., 2016; Richman and Moorman, 2000).

We have implemented three modifications of regular MSE that we outline in the next sections. We refer to our own measure as modified MSE (mMSE) throughout the manuscript.

MSE modification #1: multi-scale implementation through filtering and point skipping

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In multiscale entropy, the computation of SampEn is repeated for multiple time scales after progressively lowering the time series sampling rate by a process called 'coarsening' (Costa et al., 2002). By default, SampEn quantifies entropy at the time scale that corresponds to the sampling rate of the time series, which is typically in the order of milliseconds or lower in (non-downsampled) neurophysiological data. To enable estimation of entropy at longer time scales, the time series is typically coarsening by averaging groups of adjacent samples ('point averaging') and repeating the entropy computation (Costa et al., 2002). However, despite being straightforward, this method is suboptimal for eliminating short temporal scales from the time series. Point averaging is equivalent to low-pass filtering using a finite-impulse response filter, which does not effectively eliminate high frequencies (Semmlow, 2014; Valencia et al., 2009). For this reason, we used an improved coarsening procedure involving replacement of the multi-point average by a low-pass Butterworth filter, which has a well-defined frequency cutoff and precludes aliasing (Valencia et al., 2009Figure 2B, top). The filter cutoff frequency CutoffFreq is determined as:

(3) CutoffFreq= NyquistFreq×1scale number

where NyquistFreq is the highest estimable frequency given the signal’s sampling rate. This filtering ensures that an increasingly larger portion of the higher frequencies is removed for slower time scales. Note that low-pass filtering affects the temporal structure of the time-domain signal, which could hamper the interpretation of the EEG dynamics due to smearing of responses (Vanrullen, 2011). This issue is largely mitigated, however, due to the liberal–conservative subtraction that we perform before correlating with behavior, since this issue presumably affects both conditions similarly. Low-pass filtering is followed by a point-skipping procedure to reduce the sampling rate of the time series (Figure 2B, bottom). Since point-skipping omits increasingly large portions of the filtered time series depending on the starting point of the point-skipping procedure, we counted patterns separately for each starting point within a scale (see section Entropy computation above), summed their counts for N(m) and N(m+1) and computed entropy as described above.

MSE modification #2: Pattern similarity recomputed at each time scale 

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By increasingly smoothing the time series, coarse-graining affects not only the signal’s entropy, but also its overall variation, as reflected in the decreasing standard deviation as a function of time scale (Nikulin and Brismar, 2004). In the original implementation of the MSE calculation, the similarity parameter r was set as a proportion of the original (scale 1) time series’ standard deviation and applied to all the scales (Costa et al., 2002). Because of the decreasing variation in the time series due to coarse graining, the similarity parameter therefore becomes increasingly tolerant at slower time scales, resulting in more similar patterns and decreased entropy. This decreasing entropy can be attributed both to changes in signal complexity, but also in overall variation (Kosciessa et al., 2020; Nikulin and Brismar, 2004). To overcome this limitation, we recomputed the similarity parameter for each scale, thereby normalizing mMSE with respect to changes in overall time series variation at each scale.

MSE modification #3: Time-resolved computation 

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An important limitation of MSE is the need for substantial continuous data for robust estimation. Heuristically, the recommended number of successive data points for estimation at each scale is 100 (minimum) to 900 (preferred) points using typical MSE parameter settings (Grandy et al., 2016). This limitation precludes the application of MSE to neuroimaging data recorded during cognitive processes that unfold over brief periods of time, such as perceptual decisions. Grandy et al., 2016 has shown that the pattern counting process can be extended to discontinuous data segments that are concatenated across time, as long as the counting of artificial patterns across segment borders is avoided (as these patterns are a product of the concatenation and do not occur in the data itself). We applied the mMSE computation across discontinuous segments of 0.5 s duration (window size). To track the evolution of mMSE over the trial, we slid this window across the trials in steps of 50 ms from −0.2 s until 0.6 s, each time recomputing mMSE across segments taken from the time window in each trial.

Given our segments of 0.5 s window length sampled at 256 Hz, we computed mMSE for scales 1 (129 samples within the window) until 42 (three or four samples within the window, depending on the starting point). Note that using a pattern parameter m=2, a minimum of three samples within a segment is required to estimate entropy across the segments of continuous data, yielding a maximum possible scale of 42. In line with the MSE literature (Courtiol et al., 2016), we converted the time scale units to milliseconds by taking the duration between adjacent data points after each coarsegraining step. For example, time scale 1 corresponds to 1000 ms / 256 Hz = 3.9 ms, and time scale 42 to 1000 / (256/42) = 164 ms.

Spectral analysis

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We used a sliding window Fourier transform; step size, 50 ms; window size, 500 ms; frequency resolution, 2 Hz) to calculate time-frequency representations (spectrograms) of the EEG power for each electrode and each trial. We used a single Hann taper for the frequency range of 3–35 Hz (spectral smoothing, 4.5 Hz, bin size, 1 Hz) and the multitaper technique for the 36–100 Hz frequency range (spectral smoothing, 8 Hz; bin size, 2 Hz; five tapers)(Mitra and Bokil, 2007). See Kloosterman et al., 2019 for similar settings. Finally, to investigate spectral power between 1 and 3 Hz (delta band), we performed an additional time-frequency analysis with a window size of 1 s (i.e. frequency resolution 1 Hz) without spectral smoothing (bin size 0.5 Hz). Spectrograms were aligned to the onset of the stimulus sequence containing the (non)target. Power modulations during the trials were quantified as the percentage of power change at a given time point and frequency bin, relative to a baseline power value for each frequency bin. We used as a baseline the mean EEG power in the interval 0.4 to 0 s before trial onset, computed separately for each condition. If this interval was not completely present in the trial due to preceding events (see Trial extraction), this period was shortened accordingly. We normalized the data by subtracting the baseline from each time-frequency bin and dividing this difference by the baseline (x 100%). In an additional analysis, we performed a baseline correction by subtracting the condition-averaged pre-stimulus power, without converting into percent signal change.

Statistical significance testing of mMSE and spectral power and correlations across space, time, and timescales/frequencies

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To determine clusters of significant modulation with respect to the pre-stimulus baseline without any a priori selection, we ran statistics across space-time-frequency bins using paired t-tests across subjects performed at each bin. Single bins were subsequently thresholded at p<0.05 and clusters of contiguous time-space-frequency bins were determined. For the correlation versions of this analysis, we correlated the brain measure at each bin with the criterion and converted the r-values to a t-statistic using the Fisher-transformation (Fisher, 1915). We used a cluster-based procedure (Maris and Oostenveld, 2007) to correct for multiple comparisons using a cluster-formation alpha of p<0.05 and a cluster-corrected alpha of p=0.05, two-tailed (10.000 permutations). For visualization purposes, we integrated (using MATLAB’s trapz function) power or entropy values in the time-frequency/entropy representations (TFR/TTR) across the highlighted electrodes in the topographies. For the topographical scalp maps, modulation was integrated across the saturated time-frequency bins in the TFRs/TTRs. See Kloosterman et al., 2019 for a similar procedure in the time-frequency domain.

High-pass filtering analysis

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To examine the effect of systematically removing lower frequencies from the data before computing mMSE, we high-pass filtered the data using 1, 2 and 3 Hz high-pass filters (filter order of 4). We mirror-padded trials to 4 s to allow robust estimation (Cohen, 2014). After high-pass filtering, we performed mMSE analysis as reported above.

Correlation analysis

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We used both Pearson correlation and robust Spearman correlation across participants to test the relationships between the behavioral variables as well as with the EEG entropy and power (modulation). To test whether behavior and EEG activity were linked within participants, we used repeated measures correlation using the rmcorr package in R (R Development Core Team, 2020). Repeated measures correlation determines the common within-individual association for paired measures assessed on two or more occasions for multiple individuals by controlling for the specific range in which individuals’ measurements operate, and correcting the correlation degrees of freedom for non-independence of repeated measurements obtained from each individual (Bakdash and Marusich, 2017; Bland and Altman, 1995). To test whether spectral power could account for the observed correlation between criterion and mMSE, we used partial Spearman and Pearson correlation controlling for other variables. To test whether the mMSE-bias correlation was stronger in any of the two conditions, we used a non-parametric correlation difference test. Specifically, data was shuffled 10,000 times within each correlation data pair, each time taking the difference between correlations to generate a distribution of correlations differences under the null hypothesis. Finally, the r difference of the actual correlations was compared to this distribution to obtain a p-value.

Data and code sharing 

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The data analyzed in this study are publicly available on Figshare (Kloosterman et al., 2019). We programmed mMSE analysis in a MATLAB function within the format of the FieldTrip toolbox (Oostenveld et al., 2011). Our ft_entropyanalysis.m function takes as input data produced by Fieldtrip’s ft_preprocessing.m function. In our function, we employed matrix computation of mMSE for increased speed, which is desirable due to the increased computational demand with multi-channel data analyzed with a sliding window. The function supports GPU functionality to further speed up computations. The software can be found on https://github.com/LNDG/mMSE. A tutorial for computing mMSE within the FieldTrip toolbox can be found on the FieldTrip website (http://www.fieldtriptoolbox.org/example/entropy_analysis/). Analysis scripts for the current paper can be found on https://github.com/kloosterman/critEEGentropy (Kloosterman, 2020; copy archived at https://github.com/elifesciences-publications/critEEGentropy/).

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    Metacognition in human decision-making: confidence and error monitoring
    1. N Yeung
    2. C Summerfield
    (2012)
    Philosophical Transactions of the Royal Society B: Biological Sciences 367:1310–1321.
    https://doi.org/10.1098/rstb.2011.0416

Decision letter

  1. Michael J Frank
    Senior and Reviewing Editor; Brown University, United States
  2. Eelke Spaak
    Reviewer; Radboud University, Netherlands

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Thank you for submitting your article "Boosting Brain Signal Variability Underlies Liberal Shifts in Decision Bias" for consideration by eLife. Your article has been reviewed by Michael Frank as the Senior Editor and Reviewing Editor, and three reviewers. The following individual involved in review of your submission has agreed to reveal their identity: Eelke Spaak (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:

Kloosterman et al. conducted follow-up analyses of the data reported in their 2019 eLife paper. The experiment reported in both manuscripts required subjects to detect a relatively difficult perceptual target under instructions that either emphasized a liberal or a conservative decision bias, while recording EEG. In the previous paper the authors had reported that differences in oscillatory EEG activity in the alpha and the gamma range were associated with the different decision criteria. However, that study had not found any condition differences in the EEG signals that directly scaled with the individual differences in the liberal-conservative bias. The premise of the current study is that higher entropy in the brain response may underlie a regime that is more easily swayed in a particular direction and therefore can strategically implement a more liberal decision bias. Indeed, the authors report that within-subject, condition-specific differences in moment-to-moment EEG variability, as indexed by multi-scale entropy (mMSE), are strongly correlated with individual differences the decision-bias effect. These effects seemed located at frontal electrode sites and were observed across a relatively large span of time scales, and mainly after stimulus onset. The possibility that a liberal decision bias is implemented by upregulating neural noise is theoretically very interesting.

Essential revisions:

1) One of the conceptual issues with this paper is that no persuasive/convincing a priori theory given to relate these to concepts. More effort should be given to articulate the biological motivation to help readers appreciate the potential significance of the results. The authors interpret their results showing that "flexible adjustments of moment-to-moment variability in frontal regions may underlie strategic shifts in decision bias". However, the hallmark of a strategic effect is that the critical variable (i.e., entropy) actually differs on average between conditions that induce different strategies. However, inspection of figures suggests that liberal/conservative entropy condition differences were distributed rather evenly around zero (e.g., Figure 3B) – which is in contrast to the oscillatory effects in the previous paper that did show reliable condition differences. Thus, the results appear to suggest that while variability actually does affect the decision bias, it varies unsystematically across conditions within individuals. In other words, unless I am missing something it seems that the changes in entropy are not under top-down, strategic control. This aspect requires further discussion/analyses.

2) Power / sample size. In principle, the experimental design is adequate as it implements a robust within-subject bias manipulation (including substantial individual differences in this effect). The authors also develop a newly adapted, scale-free entropy measure that works within relatively short, concatenated time windows. The results seem surprisingly robust (a brain/behavior correlation of >.8) and are confirmed through within-subject block-by-block correlations (that were however considerably smaller). However, while the reported effects are highly significant, they also stem from analyses that seem relatively exploratory in nature (across all electrodes and time scales and time points), with a small sample of only 16 subjects. An independent replication would significantly strengthen the conclusions. Assuming my concern is valid and the main result is different than a-priori predicted (because it is not consistent with a strategic effect), the explanation comes across as more post-hoc, and as a consequence, the threshold for accepting a low-powered result would increase. The authors should therefore either replicate the experiment or provide strong arguments for why the concerns regarding robustness are unwarranted and/or why their results are consistent with a strategic effect after all.

To further unpack this statistical issue, with a relatively large search space (electrodes x time x timescale) plus multiple-testing correction only very high correlations can meet threshold. I find it difficult to determine whether or not this concern is real because I have a hard time fully understanding the cluster-correction procedure – in particular over which electrodes data were averaged for the scatterplot. In the topographic images there are some electrodes sites that seem to show significant correlations based on the coloring scheme, but there are also varying numbers of black circles (sometimes of varying size). Are results averaged cross colored electrodes, or "circled" electrodes? What is the significance of the circle size? The broader the base of averaging, the less I would be the concerned. I find the split-half robustness check with such a high correlation to begin with not extremely re-assuring. However, the fact that the relationship is also found within subjects (though much smaller) does clearly help.

3) All reviewers felt that the methods by which the mMSRE is computed should be better articulated, particularly given that the manuscript uses a modified version of a published technique. All details should be made explicit. To name just one example, in subsection “Entropy computation”: "estimation of SampEn involves counting… (p^m)…" Many of these statements are ambiguous – instead a step-by-step description of the algorithm should be given. Equations would also help to make the Materials and methods section more readable.

One reviewer also felt that it might help to restructure the Results section such that quantities closer to the measured data are presented first, before building on those to get to the change-change correlation. For example, the section should start with line graphs of mMSE over trial time per condition, etc. That way, readers can appreciate much better what is going on.

4) Reviewers also all agreed that the analyses should be repeated without first removing the ERPs. The authors subtract the condition-, session-, and participant-wise ERP from the raw trials before all analyses. While this is sometimes warranted, if the individual trial responses are not stereotypical, the subtraction procedure can actually add the (inverted) ERP back into the data. More specifically, ERP subtraction to obtain induced-only data is only justified if one can assume that the (single-trial) evoked response is independent from (i.e., adds linearly to) the "ongoing" activity. In the present study, the authors are specifically concerned with how ongoing activity influences the processing of new stimuli, thus by definition violating this assumption. Therefore, in this case, the subtraction of the ERP is problematic and should be avoided. Relatedly, another reviewer noted that one potential contributing factor to the results is that trials where a stronger (e.g. temporal) deviation of the EEG signal from the average ERP leads to lower entropy, since there the 'evoked' response is less efficiently removed, whereas in trials where the EEG resembles the ERP more closely, entropy will be higher since the stereotypical response has been removed. Thus, please repeat the analysis without removing the ERP and also show the ERPs to the different conditions.

5) The text in Results section suggests that the spectral analysis has been conducted on both baseline-corrected spectral values as well as raw power (but this is not stated in the methods section where it only mentions baseline corrected power values). Since the experimental design is blocked, looking at non-baseline corrected values is essential. I would like the authors to provide an analysis of spectral power (across frequency ranges) which is not baseline corrected, but where possibly the average power of each participant and electrode across conditions have been subtracted – to account for inter-individual differences in EEG signal power that may be unrelated to decision processes (conductivity, skull thickness, dipolar orientation etc).

6) The authors highlight that it might not be the theta-amplitude but other characteristics of the theta band oscillation that contribute to the findings. This would probably be best investigated by providing an analysis on bandpass-filtered data (ideally approximately within a broader range that encompasses the band where amplitude differences have been found within conditions – and compare these to other bands or the non-bandpass filtered signal.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your article "Boosting Brain Signal Variability Underlies Liberal Shifts in Decision Bias" for consideration by eLife. Your revised article has been reviewed by Michael Frank as the Senior Editor and Reviewing Editor, and two reviewers. The following individual involved in review of your submission has agreed to reveal their identity: Eelke Spaak (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.

We would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). Specifically, we are asking editors to accept without delay manuscripts, like yours, that they judge can stand as eLife papers without additional data, even if they feel that they would make the manuscript stronger. Thus the revisions requested below only address clarity and presentation.

Both reviewers found this version to be an improvement over the first iteration. The theoretical embedding in Introduction and Discussion is more convincing, and the clarity of the Methods is much improved. They were also happy to see that the results remain unaltered when ERPs are vs. are not subtracted, and the new addition of the high-pass filtering analysis gives a welcome piece of extra insight into what the mMSE metric is picking up on. The inclusion of ERP-based analyses is useful, as is the demonstration that filtering of lower frequencies modulates the observed relationships.

However, the following issues remained and should be addressed.

1) The reviewers were more or less convinced by the authors' narrative that across-participant correlations pick up on something different than condition-wise main effects. However, they both felt that it may be overreaching to interpret this effect as

"strategic" – which would really have required a main effect of the conservative vs. liberal condition. Both reviewers noted that the main points of the paper do not hinge on this being a true strategic, top-down controlled, effect, though, and hence we would like you to tone down these claims.

In more detail, points from each of the reviewers:

"The authors' argument: "certain participants may have used the correct and others the incorrect strategy" (Discussion section) is unsatisfactory. If that were the case, then the subgroup of participants with high behavioural conservative vs liberal criterion difference should show a stronger brain/behaviour change/change correlation than the subgroup of participants with a low behavioural con vs lib difference. That is a different prediction (i.e. an interaction between behavioural difference (group) and change/change correlation) than the existence of a significant change/change correlation per se. Based on Figure 3B, it's clear that such an interaction is not present in the data. Note that I do not suggest the authors actually test for this interaction! It's extremely derivative and would require far more participants than present here. I'm mentioning it to show that the authors' argument why the correlation can be a consequence of a strategic effect is invalid. Instead, the authors should probably concede that the effects reported here are likely non-strategic."

and

"I appreciate the full discussion of the mean vs. variability situation. I fully agree that correlations and mean effects provide orthogonal information and that it is logically possible that one half of the participants do strategically the right thing and the other to strategically the wrong thing, resulting in robust change-change effects in the absence of mean differences. My point is simply that it strikes me as rather implausible that our brain provides a strategic mechanism for such a fundamental problem as criterion setting that only half of the people are able to utilize in an adaptive manner. I wonder whether an alternative interpretation is that the variability waxes and wanes endogenously and/or differs across people in an uncontrollable manner, and that it is only through an additional, strategic process (e.g., indexed through the theta activity) that this variability is gated towards affecting the threshold setting. In other words, everybody knows when to reach for the hammer when needing to hit a nail, but the quality of the hammer varies between (and within) people. (Maybe this is even something that could be tested in the within subject analyses, by looking at the interaction between theta boosts and entropy in affecting behavior.)"

2) One of the reviewers noted that they still want to see "raw" mMSE values. The authors' reply ("plotting mMSE is tricky because it has time/space/timescale dimensions") is very unconvincing, since in Figure 3A they are showing change/change correlation values exactly for those three dimensions as well. So: the authors should simply please show two plots, exactly as in Figure 3A, one for Liberal, one for Conservative, while showing raw mMSE (condition- and subject-wise averaged) values, rather than change/change correlations. The channels picked for the time/timescale colour plot should be identical to those channels that come out of the change/change correlation cluster test, and the time/timescale voxels for the topoplot should be identical to those picked for that test as well (so basically use the same data selection as in Figure 3A; no need to separately test mMSE against zero or anything). Adding these plots (if the authors prefer: as a supplement) is critical for readers to appreciate what aspects of the signal mMSE (and the derived metrics of mMSE-change and its correlation with behaviour) is picking up on, and thus to allow them to evaluate the importance of the conclusions here.

3) It was suggested to show correlations in some condensed manner separately for liberal and conservative conditions (aside form mean values). The difference score sort of assumes that both conditions contribute, but that need not be the case. For example, it is at least possible that the relationship is produced through the liberal condition only, whereas the effect of variability might be squelched in the conservative condition (which actually would strengthen the strategy argument). Not likely, but worth exploring.

https://doi.org/10.7554/eLife.54201.sa1

Author response

Essential revisions:

1) One of the conceptual issues with this paper is that no persuasive/convincing a priori theory given to relate these to concepts. More effort should be given to articulate the biological motivation to help readers appreciate the potential significance of the results. The authors interpret their results showing that "flexible adjustments of moment-to-moment variability in frontal regions may underlie strategic shifts in decision bias". However, the hallmark of a strategic effect is that the critical variable (i.e., entropy) actually differs on average between conditions that induce different strategies. However, inspection of figures suggests that liberal/conservative entropy condition differences were distributed rather evenly around zero (e.g., Figure 3B) – which is in contrast to the oscillatory effects in the previous paper that did show reliable condition differences. Thus, the results appear to suggest that while variability actually does affect the decision bias, it varies unsystematically across conditions within individuals. In other words, unless I am missing something it seems that the changes in entropy are NOT under top-down, strategic control. This aspect requires further discussion/analyses.

We thank the reviewers for these points. We agree that our central hypothesis that increased moment-to-moment neural variability underlies a liberal decision bias should be articulated further and better embedded in a theoretical framework. Our fundamental hypothesis is that a neural system that is more dynamic and less predictable allows cognitive functioning to be more flexible and adaptive. We have now specified the theoretical underpinnings of our hypothesis better in the Introduction, based on three independent lines of research. First, we draw on evidence from studies showing that increased neural variability allows the brain to continuously explore possible internal states, which may help to respond flexibly whenever a task-relevant event occurs. Evidence for this idea comes both from resting-state connectivity work showing that neural noise is essential for the emergence of the coherent fluctuations of the default network (Ghosh et al., 2008), as well as from task data showing that more meaningful stimuli elicit higher levels of neural variability, suggesting more elaborate processing (Mišić et al., 2010). This notion is further reinforced by several papers from our lab showing that higher neural variability is associated with better cognitive performance (Garrett et al., 2015, 2013, 2011). Second, we draw from theoretical work suggesting that organisms can employ a high-fidelity neural regime that is able to mirror the complexity of the environment and thus increases chances of detecting relevant stimuli, but at the cost of higher energy demand than in a low-fidelity regime (Marzen and DeDeo, 2017). High-fidelity encoding has been proposed to be reflected in increased neural variability (Młynarski and Hermundstad, 2018), and we have recently provided initial empirical evidence for this idea (Garrett et al., 2020). Finally, we draw from influential dynamical attractor models of neural population activity, in which temporal neural variability (operationalized as “noise” in these models) enables probabilistic jumping across barriers within a high-dimensional energy landscape to allow settling into a low-dimensional attractor state that corresponds to a particular cognitive outcome (Deco et al., 2009; Moreno-Bote et al., 2007; Wimmer et al., 2014). Together, these lines of work suggest that neural variability supports cognitive function and flexibility, which we seek to reinforce and extend with the current study in the domain of decision biases.

The reviewers correctly state that on average (across participants), raw mMSE in frontal electrodes is not significantly higher in the liberal compared to the conservative condition (indicating no main effect of condition). This is in contrast to raw alpha and theta power differences, which significantly differed between conditions (see our previous paper). Paradoxically, however, we found that whereas the shift in mMSE did correlate with the liberal-conservative bias shift, the shifts in alpha and theta did not; this is indeed the “research advance” we provide with the current paper. We argue that an empirical dissociation of main effects and behavioral prediction is not unexpected. Although a main effect of experimental condition and a change-change correlation can in principle occur in parallel, inter-individual differences may be sensitive to behavioral adjustments even in the absence of a group-wise shift. The reason for this is that a main effect and a correlation address somewhat opposite research questions that can be in conflict with each other. On the one hand, a main effect tends to occur when subjects respond similarly to an experimental condition, which typically necessitates that individual differences are relatively small. On the other hand, chances of detecting a correlation with e.g., behavior typically increase when individual differences are larger (e.g., Lindenberger et al., 2008). In short, the presumption that a main effect of condition is a prerequisite for detecting behavioral effects is unfounded in our view. Further, the idea that evidence for top-down “strategies” requires a main effect of condition is also not warranted; certain subjects may use the correct and others the incorrect strategy, potentially leading to a lack of average across-subject condition effect, yet revealing why their behaviors differed on task. Therefore, we were not seeking to a priori hypothesize a main effect of condition in the liberal-conservative contrast, but rather focused our hypotheses on inter-individual adjustments in neural entropy that tracked the magnitude of the individual bias shift. The observed lack of a main effect combined with a strong correlation with the bias shift indicates that some participants indeed showed slightly higher mMSE in the conservative condition, but that these participants also showed the smallest bias shift between conditions. This suggests that these participants responded only weakly both on the neural and behavioral levels. Therefore, we argue that the changes in mMSE still reflect a strategic bias shift, even in the absence of a main effect. Finally, we note that we do indeed observe a significantly stronger transient mMSE increase after trial onset in the liberal condition (after baseline-correcting the data, as is common in time-frequency EEG analysis). Perhaps mediated by the logic outlined above, the change-change correlation with behavior is weaker in this version. We now discuss this issue regarding the link between main effect of condition and change-change correlation in the Discussion section of the manuscript.

2) Power / sample size. In principle, the experimental design is adequate as it implements a robust within-subject bias manipulation (including substantial individual differences in this effect). The authors also develop a newly adapted, scale-free entropy measure that works within relatively short, concatinated time windows. The results seem surprisingly robust (a brain/behavior correlation of >.8) and are confirmed through within-subject block-by-block correlations (that were however considerably smaller). However, while the reported effects are highly significant, they also stem from analyses that seem relatively exploratory in nature (across all electrodes and time scales and time points), with a small sample of only 16 subjects. An independent replication would significantly strengthen the conclusions. Assuming my concern is valid and the main result is different than a priori predicted (because it is not consistent with a strategic effect), the explanation comes across as more post-hoc, and as a consequence, the threshold for accepting a low-powered result would increase. The authors should therefore either replicate the experiment or provide strong arguments for why the concerns regarding robustness are unwarranted and/or why their results are consistent with a strategic effect after all.

Thank you for these valid points. In response to point 1 above, we have already argued that the lack of a main effect does not preclude the interpretation that interindividual differences in the magnitude of entropy shifts reflect strategic bias adjustments. For example, some participants have slightly higher entropy in the conservative condition, but their strategic bias shift was also small, hence eliminating a main entropy effect while retaining strong coupling in their changes. As noted in response to point 1, we have now motivated our hypothesis better and argue why we did not hypothesize a main effect of condition per se. Moreover, when baseline-correcting mMSE values, as routinely done in time-frequency analysis, we indeed observe a significant main effect of the bias manipulation with higher entropy in the liberal condition (Figure 6E), but a weaker change-change correlation with behavior. We chose to test the change-change relationship without first applying a pre-stimulus baseline correction of the mMSE values, because our block-wise design with continuous stimulation presumes the strategic bias also to be present before stimulus onset, and the mMSE computation already involves two within-subject normalizations, in contrast to raw spectral power, which is not grounded in a subject’s own brain activity in any way. Specifically, such grounding is ensured for mMSE by (1) the pattern similarity parameter controlling for the subject’s overall signal variation (SD), while (2) the division of m and m+1 pattern counts in the entropy computation normalizes the absolute counts of m and m+1 pattern matches. However, we also included the baseline-corrected results in our manuscript to investigate possible mMSE quenching effects and allow the comparison with the spectral power modulation results.

We were initially also surprised by the strong brain-behavior correlation, especially because none of the spectral or ERP measures shows any convincing, significant correlation. As noted in the manuscript, some correlation would be expected if these measures reflect a neural process central to the bias shift, given the large amounts of data per participant and the large inter-individual behavioral differences. Additionally, we found that the correlation was also significant for more spontaneous bias fluctuations within participants, suggesting that the observed link between mMSE and decision bias not only occurs under strategic control, but might also be subject to moment-to-moment fluctuations in attention or vigilance. In the end, the many controls (including ERPs and the new high-pass filtering analysis included in this revision) convinced us that entropy uniquely captures some part of the neural dynamics that more conventional measures do not.

We argue that a number of specifics of our cluster-based correlation analysis speak against the idea of overfitting a higher-dimensional spatiotemporal space. First, the spatial topography of our mMSE effect is highly similar to midfrontal theta, and even correlates with theta, suggesting overlapping neural sources. Second, the analysis shows that many time scales contribute to the correlation, suggesting that low frequencies such as delta/theta contribute to the correlation, given the progressive low-pass filtering with longer time scales (see also our new analysis reported under reviewer point 6). Previous work indeed has implicated delta/theta at frontal channels in strategic and cognitive control of decision making (Helfrich et al., 2017). Third, the correlation extends widely in the time dimension, suggesting a stable strategic bias shift over time, as was required of the participants in our block-wise design. Finally, the correlation analysis remains virtually unchanged independent of whether the event-related potential is removed before entropy analysis (see our response to reviewer point 4 for details), suggesting robustness (Mišić et al., (2010) found a similar result). Taken together, we feel that despite the unexpectedly strong brain-behavior link for mMSE, the results are robust and consistent with the literature in several dimensions. We have highlighted these various aspects better in the manuscript to communicate this more clearly. On a final note, we agree that our sample size, in terms of number of participants, is relatively small and that a replication of our findings in an independent sample of participants is highly desirable. Nevertheless, we think that the present results sufficiently strong and conceptually motivated to warrant publication on their own, given the massive amount of data within subjects and robustness against the many controls.

To further unpack this statistical issue, with a relatively large search space (electrodes x time x timescale) plus multiple-testing correction only very high correlations can meet threshold. I find it difficult to determine whether or not this concern is real because I have a hard time fully understanding the cluster-correction procedure-in particular over which electrodes data were averaged for the scatterplot. In the topographic images there are some electrodes sites that seem to show significant correlations based on the coloring scheme, but there are also varying numbers of black circles (sometimes of varying size). Are results averaged cross colored electrodes, or "circled" electrodes? What is the significance of the circle size? The broader the base of averaging, the less I would be the concerned. I find the split-half robustness check with such a high correlation to begin with not extremely re-assuring. However, the fact that the relationship is also found within subjects (though much smaller) does clearly help.

This comment made us aware that the way in which we plot the results was not entirely clear, so we have tried to improve this. For the correlation analysis, we used a cluster-based permutation test across the time, electrode and timescale dimensions. This analysis is highly similar to the commonly applied statistical testing of E/MEG spectral power (modulation) across the time, electrodes and frequency dimensions. To this end, we used the cluster-based statistics functionality in the ft_freqstatistics.m function (Maris and Oostenveld, 2007) as implemented in the FieldTrip toolbox (Oostenveld et al., 2011). As the reviewer points out, this method is most sensitive to strong correlations that extend widely across the three dimensions. However, we chose not to select an a priori region or time/timescale range of interest for investigating the correlation because we were interested whether there would be any region that would show an effect. Indeed, we found a strong, significant correlation for mMSE, but not spectral power, and now also not for ERPs (see reviewer point 4). Thus, despite being sensitive mostly to strong, extended clusters of correlations, the method allows us to reveal an effect for mMSE over and above other, conventional measures of neural activity without having to preselect timescales, timepoints and electrodes of interest.

Importantly, the scatter plot depicted in Figure 3B serves only to illustrate the cluster-based correlation test reported in Figure 3A, and bears no additional information over the statistical test reported in Figure 3A. We obtained this scatter plot by first averaging the liberal-conservative mMSE values across all the time-timescale-electrode bins that were within the significant three-dimensional cluster depicted in Figure 3A, and correlating with the liberal-conservative SDT criterion across participants. Given that the bins were preselected based on their correlation in the first place and then averaged, the reported correlation of rho = 0.87 represents an upper bound of the actual correlation. Electrodes included in the cluster are shown via black dots, and values were extracted exclusively within these significant channels. Since the coloring of the electrode locations is done through interpolation, it can occur that the indicated electrode locations do not exactly match the colors in the topoplots. Also, it can occur that no color is present at an electrode location – this indicates that although the electrode was represented in the cluster, its contribution was so small that it did not go outside the gray range of the color bar. We have now clarified these illustration principles in the legend of Figure 3A.

3) All reviewers felt that the methods by which the mMSRE is computed should be better articulated, particularly given that the manuscript uses a modified version of a published technique. All details should be made explicit. To name just one example, in subsection “Entropy computation”: "estimation of SampEn involves counting… (p^m)…" Many of these statements are ambiguous – instead a step-by-step description of the algorithm should be given. Equations would also help to make the Materials and methods section more readable.

We agree that our explanation of our modified MSE measure could be improved, so we have thoroughly revised the Materials and methods section with this point in mind. We now describe step by step how MSE is computed, and also provide equations that convey the logic of the computation. We hope that the reviewers find the entropy computation and our modifications now easier to understand. We now write the following in subsection “Entropy computation”:

We measured temporal neural variability in the EEG using multiscale entropy (MSE)(Costa et al., 2002). MSE characterizes signal irregularity at multiple time scales by estimating sample entropy (SampEn) of a signal’s time series at various sampling rates. The estimation of SampEn involves counting how often specific temporal patterns reoccur over time, and effectively measures how unpredictably the signal develops from moment to moment. At a given time scale, the estimation of SampEn consists of the following steps:[…]

Thus, SampEn estimates the proportion of similar sequences of m samples that are still similar when the next sample, i.e., m+1, is added to the sequence. Here, we use m=2 and r=0.5, as typically done in neurophysiological settings (Courtiol et al., 2016; Grandy et al., 2016; Richman and Moorman, 2000).”

We now also separately highlight our adaptations to this formula for clarity and comparability with previous implementations, please see Materials and methods section.

One reviewer also felt that it might help to restructure the Results section such that quantities closer to the measured data are presented first, before building on those to get to the change-change correlation. For example, the section should start with line graphs of mMSE over trial time per condition, etc. That way, readers can appreciate much better what is going on.

This is an interesting suggestion that we have given much thought while writing the manuscript. Since the mMSE output has three dimensions (time, space, and timescales), one issue with plotting one-dimensional time courses of mMSE as line graphs is that this requires an arbitrary choice of electrodes and timescales to average over before plotting. (A similar problem arises for the presentation of three-dimensional values of spectral power in time, space and frequency.) In addition, we do not first convert the mMSE into a percentage modulation from the pre-stimulus baseline, as is routinely done for spectral estimates, which prohibits a statistical test against zero that could help to select relevant electrodes and timescales. Please see our response to reviewer point 2 for why we chose to primarily work with raw, non-baseline-corrected mMSE values. Therefore, we reasoned that it might be misleading to show line graphs of mMSE and decided to go straight to the change-change correlation with behavior across all dimensions.

4) Reviewers also all agreed that the analyses should be repeated without first removing the ERPs. The authors subtract the condition-, session-, and participant-wise ERP from the raw trials before all analyses. While this is sometimes warranted, if the individual trial responses are not stereotypical, the subtraction procedure can actually add the (inverted) ERP back into the data. More specifically, ERP subtraction to obtain induced-only data is only justified if one can assume that the (single-trial) evoked response is independent from (i.e., adds linearly to) the "ongoing" activity. In the present study, the authors are specifically concerned with how ongoing activity influences the processing of new stimuli, thus by definition violating this assumption. Therefore, in this case, the subtraction of the ERP is problematic and should be avoided. Relatedly, another reviewer noted that one potential contributing factor to the results is that trials where a stronger (e.g. temporal) deviation of the EEG signal from the average ERP leads to lower entropy, since there the 'evoked' response is less efficiently removed, whereas in trials where the EEG resembles the ERP more closely, entropy will be higher since the stereotypical response has been removed. Thus, please repeat the analysis without removing the ERP and also show the ERPs to the different conditions.

We have given the relationship between the ERP and entropy much thought during this project, and decided to remove the event-related potentials (ERPs) in our initial submission for two reasons. First, we aimed to focus our analyses on neural activity that originates intrinsically in the brain, rather than being directly evoked by sensory stimulation. This was also motivated by our block-wise design which required our participants to keep a strategic bias online continuously. In addition, ERP removal also removed the strong steady-state visual evoked potential at 25 Hz in occipital electrodes that we reported in our previous paper (Kloosterman et al., 2019), which could affect the entropy estimates at faster scales. Second, when presenting the results to different audiences and during internal rounds of manuscript review we were often asked whether the entropy results could be explained by ERP differences between conditions, since computing ERPs is a well-known and comparably simpler analysis than entropy analysis. To address these issues, we decided to subtract the ERP before computing entropy in our initial submission. However, we agree with the reviewers that besides removing evoked responses, subtracting the ERP can have unwanted consequences such as introducing a sign-flipped ERP back into the data. We therefore repeated the analysis without removing the ERP and found very similar results, with a virtually unchanged negative change-change correlation between bias and entropy. This is in line with a previous paper that also showed similar MSE results with and without ERF removal in MEG data (Mišić et al., 2010). We now report the ERPs for the two conditions in Figure 3—figure supplement 4, and report their correlation with behavior. In the liberal-conservative contrast, we observed one positive cluster (i.e. stronger ERP for liberal) over central and parietal electrodes between 0.37 s and 0.8 s after trial onset, and one negative cluster in midfrontal, central and parietal electrodes slightly earlier in time. The timing and topography of the former, positive cluster closely corresponds to an ERP known as the centroparietal positivity (CPP), which reflects sensory evidence accumulation during perceptual decision making (O’Connell et al., 2012). This is consistent with our previous finding of increased evidence accumulation in the liberal condition (Kloosterman et al., 2019). Importantly for the current paper, we also performed the change-change correlation between ERPs and criterion across electrodes and time bins, and found no significant clusters (lowest cluster p-value p = 0.69 for positive cluster, and p = 0.23 for negative cluster). Taken together, these results suggest that ERPs time-locked to stimulus onset cannot account for the observed entropy results.

On a final note, we would like to point out that this result intriguingly suggests that the large field of ERP research (as perhaps the most widely used EEG analysis method) might have structurally overlooked a crucial property of the EEG signal that is in fact strongly linked to behavior, and that this link has remained hidden in many existing ERP-analyzed EEG datasets. We discuss these results and their significance in the manuscript in a new subsection “Entropy-bias relationship is not explained by event-related potentials and in the Discussion section.

5) The text in Results section suggests that the spectral analysis has been conducted on both baseline-corrected spectral values as well as raw power (but this is not stated in the methods section where it only mentions baseline corrected power values). Since the experimental design is blocked, looking at non-baseline corrected values is essential. I would like the authors to provide an analysis of spectral power (across frequency ranges) which is not baseline corrected, but where possibly the average power of each participant and electrode across conditions have been subtracted – to account for inter-individual differences in EEG signal power that may be unrelated to decision processes (conductivity, skull thickness, dipolar orientation etc)

Following the reviewers’ recommendations, we performed a baseline correction on the raw spectral power estimates by subtracting within each subject the across-condition average power in the pre-stimulus period (–0.4 to 0 s) from each time-frequency bin in each electrode. Please see the new Figure 3—figure supplement 3 for the results. Overall, the modulations using this baseline closely resemble the power modulations using a condition-specific baseline as reported in our previous paper (Kloosterman et al., 2019), including the SSVEP responses over posterior regions, gamma enhancement in occipital electrodes, and low-frequency suppression in central and occipital electrodes (Figure 3—figure supplement 3A and B). Contrasting the two conditions revealed stronger overall high frequency power as well as suppressed alpha-band activity for the liberal condition (panel C). Importantly, however, when change-change correlating liberal-conservative power modulation with the decision bias shift, we found no significant clusters (lowest cluster p = 0.26, Figure 3—figure supplement 3D). Thus, this specific baseline correction also did not reveal any across-participant link between spectral power modulation and decision bias, in line with a unique contribution of entropy shifts to the bias shift. Please note that since we now report non-ERP-removed results, we removed the prior analysis (i.e., spectral analysis on data with ERP-removed and per-condition baseline-corrected) from the current revised manuscript, but still report the lack of across-participant correlation between per-condition baseline corrected modulation and the bias shift in the manuscript. We refer to our previous paper for detailed spectral analysis with this per-condition baseline without ERP removal (Kloosterman et al., 2019).

6) The authors highlight that it might not be the theta-amplitude but other characteristics of the theta band oscillation that contribute to the findings. This would probably be best investigated by providing an analysis on bandpass-filtered data (ideally approximately within a broader range that encompasses the band where amplitude differences have been found within conditions – and compare these to other bands or the non-bandpass filtered signal.

An intriguing question indeed remains exactly which characteristic of the time-domain EEG signal underlies the link between mMSE and decision bias. Since we previously found stronger oscillatory activity in the delta/theta frequency ranges (2-6 Hz) in frontal electrodes (Kloosterman et al., 2019), we examined the impact of systematically removing the lowest frequencies from the data on the strength of the observed brain-behavior relationship. This reflects a stringent test for the necessity of narrowband frequency ranges for the brain-behavior relationship. To this end, we applied a Butterworth high-pass filter with different cutoff frequencies to the time-domain data (filter order of 4, trials mirror-padded to 4 s to allow robust estimation (Cohen, 2014), and subsequently applied mMSE analysis. To quantify the strength of the brain-behavior correlation at each filtering step and allow unbiased comparisons across cutoff frequencies, we finally averaged mMSE within the time-space-timescale cluster that showed the strong negative correlation in our principal (non-filtered) analysis (see Figure 3B), and plotted scatterplots of the correlation. Figure 4 shows the results of this analysis for non-filtered (original result, panel A), 1, 2, and 3 Hz high-pass filters (panels B-D). (Please note that we applied a 0.5 Hz high-pass filter on continuous data during preprocessing to remove drifts in all variants.) Interestingly, we observe that the brain-behavior relationship progressively weakens as the cutoff frequency increases, such that the correlation is non-significant (but still negative) after applying a 3 Hz high-pass filter prior to entropy estimation.

Whereas this finding suggests that these low frequencies are necessary for the mMSE-bias relationship, our previous control analyses reported in the initial submission indicate that statistically controlling for 1-2 Hz (delta) power does not affect the brain-behavior relationship (Figure 3—figure supplement 3G). One explanation for these seemingly incongruent results could be the different ways in which oscillatory phase is treated in these two analyses: whereas statistically controlling for delta power fully ignores phase, the high-pass filtering analysis removes both power and phase from the signal before entropy is computed. Moreover, the power control disregards potential interactions between 1-2 Hz and higher frequencies (e.g. theta) that could contribute to the relationship. Taken together, these analyses reveal that the lowest frequencies present in the data might play a role in the entropy-behavior relationship, possibly through non-linear interactions between spectral power and spectral phase of these frequencies. We have added this analysis to the manuscript and propose to address the exact non-linear relationships between entropy, spectral power and phase in future work.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

However, the following issues remained and should be addressed:

1) The reviewers were more or less convinced by the authors' narrative that across-participant correlations pick up on something different than condition-wise main effects. However, they both felt that it may be overreaching to interpret this effect as

"strategic" – which would really have required a main effect of the conservative vs liberal condition. Both reviewers noted that the main points of the paper do not hinge on this being a true strategic, top-down controlled, effect, though, and hence we would like you to tone down these claims.

In more detail, points from each of the reviewers:

"The authors' argument: "certain participants may have used the correct and others the incorrect strategy" (Discussion section) is unsatisfactory. If that were the case, then the subgroup of participants with high behavioural conservative vs liberal criterion difference should show a stronger brain/behaviour change/change correlation than the subgroup of participants with a low behavioural con vs lib difference. That is a different prediction (i.e. an interaction between behavioural difference (group) and change/change correlation) than the existence of a significant change/change correlation per se. Based on Figure 3B, it's clear that such an interaction is not present in the data. Note that I do *not* suggest the authors actually test for this interaction! It's extremely derivative and would require far more participants than present here. I'm mentioning it to show that the authors' argument why the correlation can be a consequence of a strategic effect is invalid. Instead, the authors should probably concede that the effects reported here are likely non-strategic."

and

"I appreciate the full discussion of the mean vs. variability situation. I fully agree that correlations and mean effects provide orthogonal information and that it is logically possible that one half of the participants do strategically the right thing and the other to strategically the wrong thing, resulting in robust change-change effects in the absence of mean differences. My point is simply that it strikes me as rather implausible that our brain provides a strategic mechanism for such a fundamental problem as criterion setting that only half of the people are able to utilize in an adaptive manner. I wonder whether an alternative interpretation is that the variability waxes and wanes endogenously and/or differs across people in an uncontrollable manner, and that it is only through an additional, strategic process (e.g., indexed through the theta activity) that this variability is gated towards affecting the threshold setting. In other words, everybody knows when to reach for the hammer when needing to hit a nail, but the quality of the hammer varies between (and within) people. (Maybe this is even something that could be tested in the within subject analyses, by looking at the interaction between theta boosts and entropy in affecting behavior.)"

We appreciate the reviewers’ arguments questioning our previous conclusion that a strategic modulation of neural variability underlies a strategic decision bias shift. Although we maintain that a main effect of neural variability does not speak to whether an individual may have been more or less strategic than another (which are individual differences dependent), we agree that both our general conclusion of a strategic origin of neural variability shifts, as well as of their causal role in the behavioral bias adjustment may have been unwarranted given the present data. For this reason, we have chosen to stay closer to the data and now interpret the results in light of the adaptive cognitive process that the experimental bias manipulations required of the subjects in order to avoid penalties. This relaxes the assumption that these neural shifts arose from a strategic process and allows for non-deliberative factors, while retaining the central notion supported by the experimental design that these shifts are behaviorally adaptive. Although we feel it is indeed highly plausible that subjects may have deliberately and strategically implemented a particular mindset while doing the task (as also suggested by the frontal topography of the correlation), estimating this in detail would require additional experiments to verify, involving e.g. verbal reports of the strategy subjects used to solve the task. To reflect this amended stance, our interpretation in the Discussion section now reads as follows:

“Here, we provide first evidence that greater bias shifts are typified in those subjects who exhibit greater shifts in frontal mMSE after stimulus onset, suggesting that mMSE provides a core signature of such adaptive behavioral shifts.”

Finally, we now refrain from drawing direct links between mMSE and strategy throughout the manuscript, and have changed the manuscript title to better reflect the correlational nature of our results (mMSE “tracks” bias shift instead of “underlies”). We hope this appropriately addresses the reviewers’ concerns that the neural variability shifts might not have been strategic.

2) One of the reviewers noted that they still want to see "raw" mMSE values. The authors' reply ("plotting mMSE is tricky because it has time/space/timescale dimensions") is very unconvincing, since in Figure 3A they are showing change/change correlation values exactly for those three dimensions as well. So: the authors should simply please show two plots, exactly as in Figure 3A, one for Liberal, one for Conservative, while showing raw mMSE (condition- and subject-wise averaged) values, rather than change/change correlations. The channels picked for the time/timescale colour plot should be identical to those channels that come out of the change/change correlation cluster test, and the time/timescale voxels for the topoplot should be identical to those picked for that test as well (so basically use the same data selection as in Figure 3A; no need to separately test mMSE against zero or anything). Adding these plots (if the authors prefer: as a supplement) is critical for readers to appreciate what aspects of the signal mMSE (and the derived metrics of mMSE-change and its correlation with behaviour) is picking up on, and thus to allow them to evaluate the importance of the conclusions here.

We agree with the reviewer that it is helpful to have some intuition of the actual mMSE values in the two conditions to appreciate the change-change behavioral correlation. Therefore, we have followed the reviewers request and now report subject-averaged topoplots and time-timescale colour plots of mMSE within the significant correlation cluster identified in Figure 3A, separately for the two conditions (see Figure 3—figure supplement 1). Indeed, we see that on the subject-averaged level, mMSE for the two conditions is highly similar, in line with our previously reported lack of a main effect of condition. Subtracting the two conditions indeed shows only small, non-significant differences between the conditions, (see Figure 3—figure supplement 1, bottom panels). This figure again highlights the dissociation between main effects and correlation in our data: while we see no main effect of condition, we do observe a strong across-participant correlation between liberal-conservative shifts in mMSE and criterion (Figure 3).

3) It was suggested to show correlations in some condensed manner separately for liberal and conservative conditions (aside form mean values). The difference score sort of assumes that both conditions contribute, but that need not be the case. For example, it is at least possible that the relationship is produced through the liberal condition only, whereas the effect of variability might be squelched in the conservative condition (which actually would strengthen the strategy argument). Not likely, but worth exploring.

To explore this possibility, we repeated the correlation separately for the conservative and liberal conditions and found weak, non-significant, negative correlations in both (conservative: rho = –0.12, p = 0.66, liberal: rho = –0.21, p = 0.43). Moreover, we found no significant difference in correlation strength between the conditions (liberal-conservative ∆rho = –0.09, p = 0.7, non-parametric correlation difference test, 10.000 permutations), suggesting that the correlation is not driven by only one of the two conditions. Rather, this finding suggests that focusing on the bias shift by taking the within-subject subtraction is indeed necessary to bring out the link with behavior, and that both conditions contribute. We now report these results in subsection “The entropy-bias relationship is not explained by total signal variation or spectral power”.

https://doi.org/10.7554/eLife.54201.sa2

Article and author information

Author details

  1. Niels A Kloosterman

    1. Max Planck UCL Centre for Computational Psychiatry and Ageing Research, Berlin, Germany
    2. Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Investigation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    kloosterman@mpib-berlin.mpg.de
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-1134-7996
  2. Julian Q Kosciessa

    1. Max Planck UCL Centre for Computational Psychiatry and Ageing Research, Berlin, Germany
    2. Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany
    Contribution
    Formal analysis, Methodology, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-4553-2794
  3. Ulman Lindenberger

    1. Max Planck UCL Centre for Computational Psychiatry and Ageing Research, Berlin, Germany
    2. Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany
    Contribution
    Supervision, Funding acquisition, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-8428-6453
  4. Johannes Jacobus Fahrenfort

    1. Department of Experimental and Applied Psychology, Vrije Universiteit Amsterdam, Amsterdam, Netherlands
    2. Department of Psychology, University of Amsterdam, Amsterdam, Netherlands
    Contribution
    Conceptualization, Resources, Data curation, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-9025-3436
  5. Douglas D Garrett

    1. Max Planck UCL Centre for Computational Psychiatry and Ageing Research, Berlin, Germany
    2. Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany
    Contribution
    Conceptualization, Software, Supervision, Funding acquisition, Investigation, Project administration, Writing - review and editing
    For correspondence
    Garrett@mpib-berlin.mpg.de
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-0629-7672

Funding

Max-Planck-Gesellschaft (Open-access funding)

  • Niels A Kloosterman
  • Julian Q. Kosciessa
  • Ulman Lindenberger
  • Douglas D Garrett

Deutsche Forschungsgemeinschaft (Emmy Noether Programme grant)

  • Niels A Kloosterman
  • Douglas D Garrett

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Ethics

Human subjects: Human subjects: Participants provided written informed consent before the start of the experiment. All procedures were approved by the ethics committee of the Psychology Department of the University of Amsterdam (approval identifier: 2007-PN-69).

Senior and Reviewing Editor

  1. Michael J Frank, Brown University, United States

Reviewer

  1. Eelke Spaak, Radboud University, Netherlands

Publication history

  1. Received: December 16, 2019
  2. Accepted: July 16, 2020
  3. Version of Record published: August 3, 2020 (version 1)

Copyright

© 2020, Kloosterman et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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