No need to choose: independent regulation of cognitive stability and flexibility challenges the stability-flexibility tradeoff

Raphael Geddert; Tobias Egner

doi:10.1037/xge0001241

. Author manuscript; available in PMC: 2023 Dec 1.

Published in final edited form as: J Exp Psychol Gen. 2022 May 26;151(12):3009–3027. doi: 10.1037/xge0001241

No need to choose: independent regulation of cognitive stability and flexibility challenges the stability-flexibility tradeoff

Raphael Geddert ^1,^2,^*, Tobias Egner ^1,²

PMCID: PMC9670017 NIHMSID: NIHMS1792154 PMID: 35617233

Abstract

Adaptive behavior requires the ability to focus on a current task and protect it from distraction (cognitive stability) as well as the ability to rapidly switch to another task in light of changing circumstances (cognitive flexibility). Cognitive stability and flexibility have been conceptualized as opposite endpoints on a stability-flexibility tradeoff continuum, implying an obligatory reciprocity between the two: greater flexibility necessitates less stability, and vice versa. Surprisingly, rigorous empirical tests of this critical assumption are lacking. Here, we acquired simultaneous measurements of cognitive stability (congruency effects) and flexibility (switch costs) on the same stimuli within the same task, while independently varying contextual demands on these functions with block-wise manipulations of the proportion of incongruent trials and task switches, respectively. If cognitive stability and flexibility are reciprocal, increases in flexibility in response to higher switch rates should lead to commensurate decreases in stability, and increases in stability in response to more frequent incongruent trials should result in decreased flexibility. Across three experiments, using classic cued task switching (Experiments 1 and 3) and attentional set shifting (Experiment 2) protocols, we found robust evidence against an obligatory stability-flexibility tradeoff. Although we observed the expected contextual adaptation of stability and flexibility to changing demands, strategic adjustments in stability had little influence on flexibility, and vice versa. These results refute the long-held assumption of a stability-flexibility tradeoff, documenting instead that the cognitive processes mediating these functions can be regulated independently – it is possible to be both stable and flexible at the same time.

Introduction

Adaptive behavior requires the ability to focus on a single task and protect it from distraction (cognitive stability), as well as the ability to rapidly switch tasks in light of changing circumstances (cognitive flexibility). For example, while reading a book in a busy coffeeshop, one must ignore the sounds of nearby conversations and other distractions. Conversely, reading the same book during one’s subway commute to work requires switching between focusing on the book and monitoring the stops to ensure one exits at the correct destination. As these examples illustrate, neither high stability nor flexibility is inherently preferable; rather, it is the capacity to dynamically match one’s level of stability or flexibility to optimally suit one’s current context – a marker of strategic cognitive control – that is crucial for successfully navigating different environments. Accordingly, impaired regulation of stability and flexibility has been implicated in numerous psychiatric disorders, including autism spectrum disorder (D’Cruz et al., 2013; Kenworthy et al., 2008; Poljac & Bekkering, 2012) and attention deficit hyperactive disorder (Cepeda et al., 2000; Corbett et al., 2009; Craig et al., 2016). Therefore, understanding the mechanisms mediating cognitive stability and flexibility is of vital importance to both basic and translational research.

Due to their seemingly contradictory nature, cognitive stability and flexibility have commonly been conceptualized as antagonists in an optimization problem, the so-called stability-flexibility tradeoff (Braem & Egner, 2018; Dreisbach & Fröber, 2019; Goschke, 2013). Inherent in this conceptualization is the assumption that stability and flexibility are opposing endpoints on a stability-flexibility continuum, and are thus reciprocal – more stability necessarily comes at the cost of less flexibility, and vice versa. For example, (Goschke, 2003, 2013) proposed a single meta-control parameter (the “updating threshold”) that determines the ease with which one can switch tasks and protect a task set from distraction. When this threshold is low, task-set updating (i.e., task switching) is easy but task-set shielding is commensurately impaired. When the threshold is high, task switching is more difficult but in turn the current task set is well protected from interference. This reciprocity perspective has been a central tenet of the vast majority of literature on cognitive flexibility (Dreisbach & Fröber, 2019; Schlüter et al., 2019; Serrien & O’Regan, 2019; Siqi-Liu & Egner, 2020). However, despite its parsimony, the critical assumption of reciprocity and antagonism between stability and flexibility arguably remains unproven. The goal of the current study was to provide a stringent empirical test of the validity of this fundamental assumption.

Evidence from Task Switching Studies

Support for the reciprocity view of cognitive stability and flexibility comes primarily from cued task switching (TS) experiments. Here, participants are usually required to switch between two or more tasks based on trial-by-trial cues (Kiesel et al., 2010; Koch et al., 2018; Vandierendonck et al., 2010). For instance, they may be cued to either classify a number as odd or even, or as greater or less than some reference value. The ubiquitous finding of a switch cost (slower and more error-prone task performance on task switches versus task repetitions) is commonly used as an indicator of one’s level of cognitive flexibility (Braem & Egner, 2018; Dreisbach & Fröber, 2019), with smaller switch costs indicating a more flexible task focus. Of particular importance to the present discussion is that switch costs often interact with a concurrent measure of cognitive stability in these experiments, namely the cross-task response congruency effect (Meiran & Kessler, 2008; Muhmenthaler & Meier, 2021). This congruency effect refers to the finding that when two tasks have to be performed with overlapping response sets, performance is slower and more error-prone for stimuli that are associated with different responses under the two task rules (incongruent stimuli) than stimuli that require the same response under both rules (congruent stimuli). Similar to switch costs, cross-task congruency effects are often interpreted to reflect a set point on the stability-flexibility continuum (Dreisbach & Fröber, 2019), with smaller congruency effects reflecting less cross-task interference, and thus a more stable task focus. Crucially, under this type of task design, the cross-task congruency effect is often found to be higher on task switch trials compared to repetition trials (Kiesel et al., 2010; Wendt & Kiesel, 2008). This interaction between task switching and cross-task congruency effects has been interpreted as supporting the reciprocity assumption of stability and flexibility, as it implies that task set shielding (cognitive stability) is weakened when people are required to switch tasks (i.e., be cognitively flexible), and vice versa.

Assessing the relationship between switch costs and cross-task congruency effects to gauge the relationship between task-set updating and shielding is an important advance on having only a single metric (e.g., switch cost) that is simply assumed to reflect both flexibility and stability levels, because independent metrics are required for a proper empirical test of the assumption that stability and flexibility are inversely yoked. However, a critical analysis of the switch cost – congruency interaction effect throws its support for the reciprocity view of cognitive stability-flexibility into question. First, this interaction is not ubiquitous, with some studies failing to find this effect (Li et al., 2019). Additionally, this interaction effect can be driven by floor/ceiling effects in the congruent trial task repetition condition (Gustavson et al., 2017; Marian et al., 2014; Steyvers et al., 2019) – if performance cannot get faster or more accurate in this condition, the difference between congruent task repetition and switch trials will necessarily be compressed compared to the difference between task repetition and switch trials in the incongruent conditions. Finally, and perhaps most importantly, this metric does not actually assess the reciprocity between dynamic contextual adjustments of cognitive stability and flexibility. In particular, the task switch-congruency interaction effect reflects the extent to which, given a particular level of flexibility, switch costs and congruency effects are related to one another, but it does not tap into whether strategic adjustments in cognitive stability or flexibility – the hallmark of cognitive control – are reciprocal (and thus, inter-dependent) or can occur independently.

Evidence from Reward Studies

Other evidence for the reciprocity assumption of stability and flexibility comes from work investigating the influence of affective states and reward on cognition. Positive affect has been shown to enhance cognitive flexibility but at the cost of increased distractibility (for reviews see Goschke & Bolte, 2014 and Dreisbach & Fröber, 2019). Additionally, different types of reward appear to have dissociable influences on stability and flexibility, and cognitive control more generally. Whereas performance non-contingent rewards reduce proactive control, performance-contingent rewards have the opposite effect (Chiew & Braver, 2014; Fröber & Dreisbach, 2014, 2016b). More specifically, high performance-contingent rewards tend to promote stability in terms of proactive control (Chiew & Braver, 2014; Locke & Braver, 2008) or cue maintenance at the cost of reduced flexibility (Hefer & Dreisbach, 2017), although it has been demonstrated that changing reward prospects from one trial to the next promotes flexibility instead (Fröber & Dreisbach, 2016a; Shen & Chun, 2011), particularly when reward prospects increase. Performance-contingent rewards have also been shown to reduce switch costs (Kleinsorge & Rinkenauer, 2012). Finally, some evidence also suggests that the effect of reward on stability and flexibility is determined by the perceived effort needed to receive task rewards (Müller et al., 2007). Together, these studies are consistent with the idea of reciprocity between cognitive stability and flexibility, although they did not explicitly test for it, since they invariably examined either stability or flexibility, but not both. More stringent tests for reciprocity must necessarily involve simultaneous and independent measurements of stability and flexibility in order to ascertain whether strategic adjustments in one domain affect the other.

Such simultaneous stability and flexibility measurements have to date been only minimally employed. In one such study, (Braem, 2017) found that selectively rewarding task switches during cued task switching not only increased subsequent voluntary task switching but also increased congruency effects. This result is consistent with another cued-task switching study (Dreisbach & Wenke, 2011) demonstrating that irrelevant stimulus feature changes interacted with response repetition effects only in the case of task switches, suggesting that task shielding was reduced during switching. Similar to the switch cost – congruency interaction, however, the latter finding does not address whether strategic adjustments in cognitive stability and flexibility are reciprocal (i.e., there were no manipulations of switch rates or rewards). The former finding then is arguably the most compelling evidence in favor of reciprocity, since it demonstrates the simultaneous influence of rewarded task switching on both voluntary task switching and congruency effects. Then again, this study employed a between-subjects design and only investigated the effect of rewarding flexibility, not the effect of rewarding stability, and thus could not probe the reciprocity of stability and flexibility in both directions (Braem, 2017). A different study independently manipulated flexibility-related task parameters at a more sustained, global, versus a more transient, local level (Fröber et al., 2018). This work examined the interaction between context effects and reward prospects on stability and flexibility, and found that increasing reward prospects transiently increase flexibility even in the case of global contexts that promote sustained stability (Fröber et al., 2018). This finding has been interpreted to suggest that local and global regulation of stability and flexibility may be independent of each other, although each of these hypothesized mechanisms is nevertheless envisaged as performing a balancing act between stability and flexibility demands (Dreisbach & Fröber, 2019). In sum, work in reward and affect has in general been consistent with the reciprocity assumption of stability and flexibility, but never conclusively verified its existence, nor demonstrated a clear untethering of the two.

Evidence from Modeling and Neuroscience

Finally, some evidence for the stability - flexibility tradeoff comes from modeling. In particular, (Musslick et al., 2018) used a recurrent neural network model to simulate the influence of a meta-control parameter (the gain of the network’s activation function) and demonstrated that various constraints on control could promote cognitive stability (i.e., decreased congruency effects) at the expense of decreased cognitive flexibility (i.e., higher switch costs), and vice versa. (Musslick et al., 2019) then analyzed this model from a dynamical system perspective, and found that by formally defining cognitive stability and flexibility in terms of attractors one could demonstrate a tradeoff between stability and flexibility. Crucially, this study also ran a behavioral experiment in human participants to examine the influence of low versus high proportion of cued task switches between groups, and found that although the switch proportion manipulation resulted in reduced switch costs in the high switch proportion group, there was no significant difference between groups in terms of congruency costs. Although there was a significant difference between groups in the gain parameter as predicted by the model, participants’ gains were significantly lower than optimal, and the manipulation of flexibility (i.e., switch proportion) did not have the expected impact on congruency effects. It thus remains relatively ambiguous whether strategic adjustments of stability and flexibility are in fact reciprocal in human behavior.

Alternatively, cognitive flexibility and stability could rely on processes that are in principle independent of each other. While independent mechanisms for shielding and updating task sets could still be functionally reciprocal, independence would in principle also allow for a non-reciprocal relationship. This premise implies that, in certain circumstances, one could simultaneously engage in both flexible and stable behavior. Although counterintuitive, such a situation may not be that uncommon. For example, we may need to flexibly switch between various relevant tasks (e.g., between reading a book and listening for one’s stop during a commute) while simultaneously ignoring other, unimportant distractors (e.g., nearby strangers’ conversations). In line with the idea of separable mechanisms of stability and flexibility, the neuroscience literature has pinpointed distinct loci of Dopaminergic (DA) action in mediating the protection versus updating of task sets (reviewed in Cools & D’Esposito, 2011), with DA levels in prefrontal cortex underpinning cognitive stability (Crofts et al., 2001; Durstewitz et al., 2000; Roberts et al., 1994) and DA levels in the striatum underpinning cognitive flexibility (Collins et al., 2000; Crofts et al., 2001). While DA-mediated functions in the prefrontal cortex and striatum often display an inverse pattern, a truly reciprocal relationship between the two has been considered unlikely in this literature (Cools & D’Esposito, 2011). Similarly, many clinical disorders, such as ADHD, are characterized by a combination of both inflexibility and distractibility (Barkley, 1997), suggesting that stability and flexibility rely on fundamentally distinct processes, even though they may often display an inverse relationship. Nevertheless, the above studies also fail to address directly the question of whether contextual adjustment of cognitive stability and flexibility are independent, as they typically examined these processes in isolation, considering cognitive flexibility in situations (or time points) where only shifting is required or incentivized, and stability in situations (or time points) where only shielding is necessary or incentivized (Cools et al., 2007). Moreover, this literature has also not examined the critical case of the interplay of dynamic contextual adjustments of stability and flexibility.

The Current Study

Ultimately then, we conclude that the assumption of reciprocity, or conversely independence, between contextually appropriate levels of cognitive stability and flexibility (i.e., the stability-flexibility tradeoff) remains insufficiently tested. In the present study, we therefore sought to empirically evaluate this assumption by gauging whether contextual adaptation of cognitive flexibility reciprocally influences stability, one the one hand, and whether contextual adaptation of cognitive stability reciprocally influences flexibility, on the other hand.

To this end, we here combined classic cued task switching (Experiments 1 and 3) and attentional set shifting (Experiment 2) protocols - allowing us to simultaneously measure switch costs and congruency effects - with a well-established approach for inducing strategic adaptation of on-task stability and between-task flexibility. In particular, we independently manipulated the block-wise proportion of congruent (vs. incongruent) trials and the proportion of task switch (vs. repeat) trials. The former block-wise manipulation of congruency is known to produce the “list-wide proportion congruent” (LWPC) effect, whereby the mean congruency effect is substantially smaller when incongruent trials are frequent than when they are rare (Bugg & Chanani, 2011; Gratton et al., 1992; Logan & Zbrodoff, 1979, for reviews, see Bugg, 2017; Bugg & Crump, 2012). This observation has been interpreted as, and modeled by, a strategic up-regulation in on-task focus (i.e., cognitive stability) in response to frequent conflict from incongruent distractors (Botvinick et al., 2001; Jiang et al., 2014). Similarly, the latter, block-wise manipulation of switching is known to produce the “list-wide proportion switch” (LWPS) effect, whereby the mean switch cost is substantially reduced when switching is required more frequently (Dreisbach & Haider, 2006; Monsell & Mizon, 2006; Schneider & Logan, 2006; Siqi-Liu & Egner, 2020). Accordingly, the LWPS effect has been interpreted as reflecting strategic adjustments in switch-readiness (i.e., cognitive flexibility) to suit the changing contextual needs for more or less switching (Braem & Egner, 2018; Dreisbach & Fröber, 2019)¹.

By independently varying the block-wise incidence of congruent versus incongruent, and task repeat versus switch trials, we could thus assess how these changing contextual demands, supposed to promote either stability or flexibility, affect mean switch cost and congruency effects. In line with large literatures on the LWPC and LWPS effects, we expected to observe smaller congruency effects (more stability) in blocks where incongruent trials are frequent than when they are rare, and smaller switch costs (more flexibility) in blocks where switch trials are frequent than when they are rare. Crucially, this novel design allowed us to additionally examine whether the anticipated contextual adaptation in stability (the LWPC effect) would impact switch costs (flexibility), and conversely, whether the anticipated contextual adaptation in flexibility (the LWPS effect) would impact the congruency effect (stability). If cognitive stability and flexibility were truly reciprocal, then a greater proportion of switch trials should not only decrease switch costs, due to a greater readiness to switch to the alternative task (flexibility), but should also increase cross-task congruency effects, as enhanced flexibility would be accompanied by reduced shielding of the relevant task set, and thus a greater susceptibility to interference from the stimulus features that are relevant to the alternative set. By the same token, a greater proportion of incongruent trials should not only result in smaller congruency effects, due to increased focus on the currently task-relevant stimulus features (stability), but should also increase switch costs, as enhanced focus on the relevant stimulus features would make it more difficult to release and shift that focus to the currently irrelevant stimulus features when the alternative task set is cued. By contrast, if it were possible to regulate cognitive stability and flexibility levels independently of each other, we would not expect the LWPC effect to modulate switch costs or the LWPS effect to modulate congruency effects. To preview our findings, over three experiments we observed consistent evidence against the notion of stability and flexibility being reciprocal.

Experiment 1

As an initial test of the assumed inter-dependence between the regulation of cognitive flexibility and stability, we leveraged a classic task-switching paradigm. Here, participants are cued on each trial to apply one of two possible categorization rules to a stimulus that could be classified by either rule (i.e., a bivalent stimulus). We employed bivalent task stimuli and overlapping responses across the two task sets, such that alongside these task-switching requirements, some stimuli required the same motor response across sets (congruent stimuli) and others required the alternate response (incongruent stimuli). As in the prior literature, we treated congruency effects (incongruent minus congruent trial performance) as a measure of cognitive stability, and task switching costs (task switch minus task repeat trial performance) as a measure of cognitive flexibility. Finally, we manipulated the frequency of congruent/incongruent and repeat/switch trials over blocks of trials, allowing us to answer the critical question of whether strategically adapting stability also affects flexibility, and whether strategically adapting flexibility also affects stability.

Methods

Participants:

We based our target sample size on two recent task switching studies documenting robust adjustments in flexibility based on switch proportion or reward manipulations (Braem, 2017; Siqi-Liu & Egner, 2020). Sample sizes in the relevant experiments ranged from 40 to 56. We therefore targeted a sample size of 60. 65 participants completed the experiment on Amazon Mechanical Turk for financial compensation. 5 participants (7.7%) were excluded for failing to meet the accuracy criterion (>75% correct), leaving a final sample of 60 participants (43 male, 17 female; age range: 25 – 67, mean: 38.85, SD: 10.48). The study was approved by the Duke University Campus Institutional Review Board.

Stimuli and Procedure:

Task stimuli consisted of single digits (1 – 9 excluding 5) presented centrally, surrounded by a colored rectangular frame (blue or red; Figure 1). Participants were required to indicate either the digit’s parity (i.e., is the digit odd or even?) or its magnitude (i.e., is the digit less or greater than 5?) based on the color of the frame that surrounded the number. Color-to-task mapping was randomized across participants. Participants used their left and right index fingers placed on the ‘Z’ and ‘M’ keys, respectively, to respond to both tasks. Category-response mapping (i.e., ‘Z’ = odd, ‘M’ = even and vice versa; ‘Z’ = less than 5, ‘M’ = greater than 5 and vice versa) was randomized across participants. Each trial began with a fixation cross (500 ms), followed by stimulus presentation. Stimulus presentation lasted for 1500 ms or until a response was recorded. Each trial was followed by an intertrial screen for 1200 – 1400 ms (jittered in 50 ms increments) that provided participants with feedback on their response (“Correct”, “Incorrect” or “Too Slow” if they failed to respond within 1500 ms).

Because the response keys for the magnitude and parity tasks overlapped, each trial could be classified as either congruent or incongruent, based on whether the keys for both tasks for a given stimulus matched or not. For example, if the parity task mapped even digits to the ‘Z’ key and odd digits to the ‘M’ key, and if the magnitude task mapped low digits to the ‘Z’ key and high digits to the ‘M’ key, then low even digits (i.e., 2 or 4) would be congruent whereas high even digits (i.e., 6 or 8) would be incongruent. The cross-task congruency effect (slower and more error-prone performance on incongruent than congruent trials) served as a measure of cognitive stability, with smaller congruency effects indicating a more stable, better shielded, task focus. Trials were also classified as repeat or switch trials based on whether or not the task cue changed between trials (i.e., a parity trial following a magnitude trial would be a switch trial). The switch cost (slower and more error-prone performance on switch than repeat trials) served as a measure of cognitive flexibility, with smaller switch costs indicating a greater readiness to switch, or a more flexible state.

The experiment began with a practice phase consisting of 3 blocks of 16 trials each. The first practice block consisted entirely of parity trials and the second of magnitude trials, with the order of those two practice blocks being randomized over participants. The third practice block consisted of a mix of parity and magnitude task trials, as in the main task. Participants were required to repeat each practice block until they achieved at least 75% accuracy. The main experiment consisted of 4 blocks of 128 trials each. Importantly, we varied the relative frequency of incongruent (vs. congruent) stimuli and the frequency of switch (vs. repeat) trials across blocks. Specifically, blocks could consist of either 25% or 75% incongruent stimuli combined with either 25% or 75% switch trials, resulting in 4 possible switch/congruency proportion combinations. The block order was counterbalanced across participants using a Latin square design. These frequency manipulations allowed us to examine strategic adaptation in performance to independently changing stability and flexibility demands via the LWPC and LWPS effects.

Design and Analysis:

The experiment corresponded to a 2 (task sequence: switch vs. repeat) x 2 (stimulus congruency: congruent vs. incongruent) x 2 (switch proportion: 25% vs. 75%) x 2 (incongruency proportion: 25% vs. 75%) factorial design. With 128 trials per block, this meant that there were 8 trials in the rarest condition (e.g., congruent, repeat trials in the 75% incongruent, 75% switch condition) and 72 in the most common condition (e.g., incongruent, switch trials in the 75% incongruent, 75% switch condition). Importantly, the analyses that evaluated the effects of interest to our hypotheses – the two-way interactions between the list-wide proportion congruency/switch factors and trial types – involved cell sizes of 192, 192, 64, and 64 trials. The main dependent variable of interest was response time (RT) as an index of cognitive processing efficiency. We therefore ran an omnibus repeated measures analysis of variance (rmANOVA) of subjects’ mean RT with the independent variables of task sequence (switch vs. repeat), stimulus congruency (congruent vs. incongruent), block-wise switch proportion (25% vs. 75%), and block-wise incongruency proportion (25% vs. 75%). We expected to observe standard congruency effects (a main effect of stimulus congruency) and switch costs (a main effect of task sequence), as well as a LWPC effect (an interaction between stimulus congruency and congruency proportion) and a LWPS effect (an interaction between task sequence and switch proportion). In order to test our primary question regarding the interdependency of stability and flexibility, we tested whether the effect of stimulus congruency was modulated by switch proportion and whether the effect of task sequence was modulated by congruency proportion. Although only of secondary interest, we also examined higher order three-way interactions that might reveal additional nuances in the relationship between stability and flexibility.

Additionally, in order to test the strength of theoretically meaningful null effects (notably, the possible absence of the interactions predicted by a stability-flexibility tradeoff), we also ran an identical Bayesian repeated measures ANOVA in JASP (Version 0.15, JASP Team, 2021). Bayesian techniques offer numerous advantages over frequentist approaches, including the ability to interpret evidence in favor of null hypotheses (Dienes, 2014) and are now commonly considered superior to traditional frequentist approaches (Rouder et al., 2009, 2012; Wagenmakers, 2007). We used the default JASP prior for fixed effects, which is a weakly-informative prior described by a Cauchy distribution centered around zero and with a width parameter of 0.5 (Rouder et al., 2012). This corresponds to a probability of 70% that the effect size lies between −1 and 1, which is considerably more conservative than the implicit uniform prior used in conventional frequentist analyses, as the latter places equal weight on both small and extremely large effect sizes. Inverse bayes factors (BF₀₁) were computed for each candidate model relative to the best-fitting model and indicate the likelihood ratio of marginal likelihoods (Kass & Raftery, 1995). Performance accuracy was only of secondary interest but was also fully analyzed, identically to RT.

Transparency and Openness:

We report how we determined our sample size, all data exclusions, all manipulations and experimental measures, and follow JARS (Kazak, 2018). All data and task/analysis code are available at https://github.com/rmgeddert/stability-flexibility-tradeoff. Data were analyzed using R, version 4.0.2 (R Core Team, 2020) and JASP (JASP Team, 2021). The study’s design and analysis were not preregistered.

Results

Trial exclusions:

For the accuracy analysis, we analyzed all trials excluding practice trials and the first trial of each block (since these can be neither switch nor repeat trials). For the reaction time (RT) analysis, we further excluded all incorrect trials (7.9% of trials) and any trials where participants responded greater than 3 times the standard deviation from the mean of their response RTs (0.6% of remaining trials). We also excluded all trials where participants responded faster than 300 ms and slower than 1500 ms (<0.1% of remaining trials).

RT Analysis:

The mean RT for each cell of the experimental design is displayed in Figure 2a, and descriptive statistics can be found in Table S1. We observed a significant main effect of task sequence (i.e., switch cost), as reflected in slower RTs for switch trials (M_switch = 879 ms, 95% CI [850, 908]) compared to repeat trials (M_repeat = 797 ms, 95% CI [768, 826]; F(1, 59) = 149.72, p < .001, η_p² = .717), and a significant main effect of stimulus congruency, due to slower RTs for incongruent (M_incongruent = 872 ms, 95% CI [843, 901]) compared to congruent stimuli (M_congruent = 804 ms, 95% CI [775, 833]; F(1, 59) = 98.91, p < .001, η_p² = .626). There was also a significant interaction between task sequence and stimulus congruency (F(1,59) = 7.82, p = .007, η_p² = .117), as congruency effects were larger on switch (M_{congruencyeffect} = 77 ms, 95% CI [62, 92]) compared to repeat trials (M_{congruencyeffect} = 60 ms, 95% CI [45, 74]), as occasionally reported in the literature (e.g., Kiesel et al., 2010; Wendt & Kiesel, 2008). Finally, we also observed main effects of both LWPS (F(1,59) = 22.07, p = .001, η_p² = .272) and LWPC (F(1,59) = 5.39, p = .024, η_p² = .084), due to slower RTs in the 75% switch condition (M₇₅ = 851, 95% CI [822, 880]) than the 25% switch condition (M₂₅ = 825, 95% CI [797, 854]) and in the 75% incongruency condition (M₇₅ = 848, 95% CI [818, 877]) than the 25% incongruency condition (M₂₅ = 828, 95% CI [799, 858]), respectively.

Importantly, we also observed evidence for strategic adaptation in switch-readiness and task-focus. First, we found a significant interaction between task sequence and the block-wise switch proportion (i.e., 25% vs. 75% switch trials; F(1,59) = 116.09, p < .001, η_p² = .663), i.e., the LWPS effect, as switch costs were smaller in the 75% switch proportion condition (M_switchcost= 41 ms, 95% CI [26, 56]) than in the 25% switch proportion condition (M_switchcost = 122 ms, 95% CI [107, 138]; Figure 2b). Second, we also observed a significant interaction between congruency and the block-wise congruency proportion (F(1,59) = 27.38, p < .001, η_p² = .317), i.e., the LWPC effect, as congruency effects were smaller in the 75% incongruency proportion condition (M_{congruencyeffect} = 44 ms, 95% CI [28, 60]) than in the 25% incongruency proportion condition (M_{congruencyeffect} = 92 ms, 95% CI [76, 109]; Figure 2e). These results replicate a large body of prior findings in the literature, suggesting that adaptive cognitive control processes enable increased cognitive flexibility (i.e., decreased switch costs) in contexts of frequent switching and increased cognitive stability (i.e., decreased distractibility) in contexts case of frequent incongruent trials.

Our primary effect of interest was the interaction between block-wise switch proportion and congruency effects, and conversely, between block-wise congruency proportion and switch costs. We found neither of these interactions to be significant. There was no interaction between the switch proportion and congruency (F(1,59) = 2.02, p = .161, η_p² = .033; Figure 2d). A Bayesian repeated measures ANOVA found the best-fitting model to be task_sequence + congruency + LWPS + LWPC + task_sequence * LWPS + congruency * LWPC. Bayesian model comparison of the congruency * LWPS interaction found a BF₀₁ value of 7.1, indicating that there was more than 7 times more evidence for the model without this interaction effect, indicating medium to strong evidence in support of the null hypothesis. Likewise, there was also no significant interaction between congruency proportion and task sequence (F(1,59) = 1.74, p = .192, η_p² = .029), with a BF₀₁ = 6.7 relative to the best-fitting model (above) without this interaction term (Figure 2c). Together, these analyses show robust evidence in support of the null hypothesis of no interaction between the LWPC factor and switch costs nor between the LWPS factor and the congruency effect. Finally, none of the other interactions in the 4-way rmANOVA were significant either (all p ≥ .146).

Accuracy Analysis:

Mean accuracy for each condition is displayed in Figure S1 and listed in Figure S2. Accuracy was subject to ceiling effects, such that the distribution of participants’ scores violated assumptions of normality (Shapiro-Wilk W = 0.81, p < .001) and homogeneity (Levene’s Test F = 18.8, p < .001) of variance. Results should therefore be interpreted with caution. There was a significant main effect of task sequence, with participants responding more accurately on repeat (M_repeat = 92.5%, 95% CI [91.2, 93.7]) compared to switch trials (M_switch = 88.9%, 95% CI [87.3, 90.6]; F(1, 59) = 30.35, p < .001, η_p² = .340), as well as a significant main effect of stimulus congruency, with participants responding more accurately on congruent (M_congruent = 94.8%, 95% CI [93.8, 95.8]) compared to incongruent trials (M_incongruent = 86.7%, 95% CI [84.7, 88.6]; F(1,59) = 81.15, p < .001, η_p² = .579). The interaction between task sequence and congruency was significant as well (F(1,59) = 5.48, p = .023, η_p² = .085), as congruency effects were larger on switch (M_{congruencyeffect} = 9.3%, 95% CI [7.2, 11.3]) compared to repeat trials (M_{congruencyeffect} = 7.0%, 95% CI [4.9, 9.0]). There was also a main effect of switch proportion (F(1,59) = 4.87, p = .031, η_p² = .076) due to higher accuracy in the 25% switch condition (M₂₅ = 91.3%, 95% CI [89.9, 92.8]) than the 75% switch condition (M₇₅ = 90.1%, 95% CI [88.7, 91.5]), but the main effect of congruency effect was not significant (F(1,59) = 3.17, p = .080, η_p² = .051).

As in the RT analysis, there were significant interactions between block-wise switch proportion and task sequence (F(1,59) = 19.25, p < .001, η_p² = .246) and between block-wise congruency proportion and stimulus congruency (F(1,59) = 38.86, p < .001, η_p² = .397). Specifically, accuracy switch costs were smaller for the 75% switch condition (M_switchcost = 1.6%, 95% CI [0.02, 3.1]) compared to the 25% switch condition (M_switchcost = 5.4%, 95% CI [3.9, 6.9]), and the congruency effect was smaller for the 75% incongruent condition (M_{congruencyeffect} = 4.3%, 95% CI [2.2, 6.5]) compared to the 25% incongruency condition (M_{congruencyeffect} = 11.9%, 95% CI [9.8, 14.1]). Unlike the RT analysis, there was a significant interaction between the block-wise switch proportion and stimulus congruency, with the congruency effect being larger for the 75% switch proportion (M_{congruencyeffect} = 9.5%, 95% CI [7.5, 11.5]) compared to the 25% switch proportion condition (M_{congruencyeffect} = 6.8%, 95% CI [4.7, 8.8]; F(1,59) = 8.39, p = .005, η_p² = .125). A Bayesian rmANOVA found a best-fitting model of task_sequence + congruency + LWPC + LWPS + task_sequence * LWPS + congruency * LWPC + congruency * LWPS, also containing this significant interaction. Compared to this best-fitting model, the model without this term (as in the RT analysis) had a BF₀₁ = 1.5, suggesting only anecdotal evidence in favor of the model with this interaction term. The interaction between task sequence and congruency proportion was not significant (F(1,59) = 0.14, p = .709, η_p² = .002), with the best model with this term having a BF₀₁ = 8.2, suggesting strong evidence against this interaction. None of the other interactions were significant (all p ≥ .166).

Discussion

Our primary effects of interest for Experiment 1 were the interaction between block-wise switch proportion and congruency effects, and conversely, between block-wise congruency proportion and switch costs in response time data. If the classically held assumption of a cognitive stability-flexibility tradeoff were true, increased cognitive flexibility induced by frequent switching should also increase the distracting impact of incongruent stimuli, and likewise, increased cognitive stability induced by frequent incongruent stimuli should increase switch costs. Critically, we found little evidence for inter-dependence between adaptations in stability and flexibility. Although there were numerical differences in switch costs between congruency proportions and in congruency effects between switch proportions in the direction predicted by a stability-flexibility tradeoff, these differences were not reliable as indicated by the conventional ANOVA, and the corresponding interaction terms were refuted by Bayesian analyses. Note that this was not due to a lack of power for detecting two-way interaction effects, as we found substantial evidence for interactions between congruency proportions and congruency effects (the LWPC effect) and task sequence proportions and switch costs (the LWPS effect). These results indicate that increases in task focus towards a particular task set (protecting it from cross-task interference) has no effect on one’s ability to nevertheless switch tasks, and likewise, that being more ready to switch tasks has no effect on how much other tasks interfere with the currently active task set. The accuracy analysis recapitulated the above effects but also included an interaction between task sequence and congruency proportion; however, the Bayesian rmANOVA was unable to differentiate between models with this term and without. Thus, this interaction should be interpreted cautiously, especially given that accuracy data also violated key distributional assumptions of the ANOVA. Overall, the results of Experiment 1 thus suggest that the regulation of cognitive stability and flexibility do not seem to be inversely yoked to each other.

Experiment 2

Experiment 1 assessed the inter-dependence of regulating stability and flexibility in a classic task switching protocol, where cognitive flexibility is operationalized as switching between different task rules. In Experiment 2, we sought to investigate whether the independence between control over stability and flexibility that we observed in the context of task switching would replicate in (and thus, generalize to) another common probe of cognitive flexibility, namely, attentional set shifting (Dias et al., 1996; Robbins, 2007). In set shifting experiments, participants are cued to shift attention between different features of a compound stimulus to guide their response, but unlike in task switching, the basic task rule remains the same. One example is the classic Navon (or global-local) task (Navon, 1977, 2003), where participants are presented with large (“global”) letter shapes made up of small (“local”) letters, which can be either congruent or incongruent with the global shape (Figure 3). On each trial, participants are cued to classify the stimulus based on either the global or local feature. Thus, trials where the relevant feature differs from the previous trial require a shift in attentional set, either from focusing on global to focusing on local information, or vice versa, and this shift cost represents an index of cognitive flexibility. Moreover, given the bivalent nature of the stimuli, combined with overlapping response sets, the irrelevant stimulus feature in this task can produce strong interference (congruency) effects, which can in turn be used as an index of cognitive stability. In Experiment 2, we therefore adopted the Navon task as a means to manipulate demands on, and measure effects of, cognitive stability and flexibility in the domain of attentional set shifting.

Figure 3: — The trial structure for Experiment 2 consisted of an intertrial fixation cross preceding stimulus presentation (a large ‘S’ or ‘H’, made of smaller ‘S’s or ‘H’s), with a colored rectangle (blue or red) cueing participants to identify the global or local letter, followed by accuracy feedback.