Experimental design

To compare their attentional fluctuations, we engaged 3 mice, 2 monkeys, and 11 humans in a simple two-alternative non-forced choice task, where they had to discriminate two leaf-shaped objects (Fig 1B). To elicit naturalistic fluctuations in attention, we employed an intuitive task structure (navigating towards food sources) based on naturalistic visual stimuli: leaves placed in a virtual reality (VR) environment consisting of a realistic grassy field and mountainous background, projected into a highly immersive dome surrounding the subjects (Fig 1A; see also [18]). The mice traversed this VR environment towards either object by running on a styrofoam ball; the monkeys and humans used a large trackball for this that they could operate with either one or both hands (monkeys), or the right hand only (humans). Subjects were freely viewing the stimuli and the environment.

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Fig 1. Experimental setup and path parameters.

A) Mice, monkeys, and humans were placed inside a large dome, on which the VR task was projected via a curved mirror. Mice traversed the VR by running on a trackball, while monkeys and humans did so by moving a trackball with their hands. B) The perceptual decision task involved moving towards either of two stimuli, a rewarded target (check mark) or an unrewarded distractor (x). Targets and distractors were selected from a range of morphed shapes between a pointy leaf and an hourglass (see Methods). C) The paths of the humans (top), monkeys (middle), and mice (bottom) towards the stimulus on several trials. Open circles denote reaction times and path colour denotes the ‘precision’ metric (see Methods - Metrics for the definition).

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We used the subjects’ trajectories through the virtual environment to capture their task performance in five parameters, mapped onto the two seminal axes of attention: accuracy and speed. Capturing each axis by more than one behavioural parameter allowed us to make more nuanced estimates of speed and accuracy on a single-trial basis, beyond what can be achieved, e.g., by binary classifications of hit and miss trials.

Three parameters were used to gauge task accuracy: instantaneous hit rate (correct vs incorrect or miss trials; henceforth indicated as hit rate), precision (how accurately subjects hit either of the stimuli relative to average successful hit location; see Fig 1C), and bias (the tendency to repeatedly approach objects on the same side, regardless of their identity). Both changes in precision and bias have previously been associated with different attentional states in mice [4,19]. The remaining two parameters specified speed: reaction time (the point in time the subject makes a turn towards one of the objects; see Fig 1C), and speed (average speed of moving through the VR environment from trial start to end). (For exact parameter definitions, see Methods - Metrics; for the distributions of these parameters for the three species, see S1 Fig.)

Models

The choice to categorise parameters as contributing either to the speed or accuracy dimension of task performance was made for conceptual reasons: we wanted to know how subjects navigated the well-known trade-off between speed and accuracy given their available attentional resources. This trade-off has classically been considered a fundamental feature of attentional processing [20]. To verify to what extent this conceptually driven choice tallied with the actual structure of our behavioural data, we quantified the relations between the five behavioural parameters (Fig 2A, middle). Specifically, we correlated the parameters’ overall time series (i.e., one value per trial, with all sessions within one species concatenated). The resulting correlation matrix consistently showed two clusters of correlated parameters: ‘hit rate’ and ‘bias’ as metrics quantifying performance accuracy, and ‘reaction time’, and ‘running speed’ as metrics quantifying performance speed, with low correlations between the two clusters (Fig 2A, left). Hierarchical clustering with silhouette analysis confirmed this two-cluster structure across all three species (S2 Fig). This pattern is in line with the notion that behavioural parameters cluster onto the two axes of accuracy and speed, along which task performance can fluctuate independently.

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Fig 2. Attentional metrics and models.

A) Five variables (middle) were derived from the VR paths: three concerning task accuracy (hit rate, precision, and bias) and two concerning speed (running speed and reaction time, RT). The correlation matrix of these variables (left) confirmed that the variables concerning the classes accuracy and speed were highly correlated within each class, but largely independent between the two classes, though precision showed only a weak association with either. The variables were therefore entered into two separate HMMs, the conjunction of which partitioned the data into four categories (right). B) Plotting a representative variable from each of the two classes (hit rate and reaction time) against each other and colouring the data by the four states, confirmed a correct partitioning of the data by the HMM conjunction, for humans (left), monkeys (middle), and mice (right). Legend of state colours: see C. C) The contribution of the five variables towards the partitioning into four states by the conjuncted HMMs was very similar between humans (left) and monkeys (middle). In mice (right), the precision variable had slightly different contributions towards the four states, but the overall pattern was similar to that of humans and monkeys. For this analysis, reaction time, bias and precision were inverted (marked as inv. in the labels) so that higher values in all metrics represent higher performance. All metrics were normalised to each species’ average values.

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Note however that the ‘precision’ variable did not seem to correlate strongly with either cluster, as reflected by its consistently low silhouette scores (0.05 - 0.17 across species, S2 Fig). Based on our conceptual rationale for including parameters in the two HMMs, we chose to include ‘precision’ in the ‘accuracy’ cluster - both because conceptually it captures aspects of performance accuracy rather than speed, and because empirically, ‘precision’ generally showed somewhat closer clustering with ‘hit rate’ and ‘bias’ than with ‘reaction time’, and ‘running speed’.

Attention is not the only factor shaping performance speed and accuracy - external factors like stimulus difficulty and history on a particular trial also play a decisive role. We hypothesised that dynamic changes in the two parameter clusters should reflect fluctuations in sustained attention beyond the performance differences elicited by specific trial attributes. To better capture such spontaneous fluctuations and minimise the contribution of trial attributes, we first smoothed the time series with a window size of 5 trials to reduce the influence of individual trial factors like stimulus difficulty (see Methods, also S3 Fig). To parcellate the time series into distinct attentional states, we used two independent Hidden Markov Models (HMMs; for details on the models, see Methods - HMMs). The accuracy and speed parameters were used as inputs into the two separate HMMs, each outputting two states: one model differentiating between slow and fast states, and one model differentiating between accurate and inaccurate states. The two HMMs were fit separately for each species; so even though humans and monkeys have generally better task performance than mice in absolute terms, we defined high- and low-performance states based on relative task performance per species. However, fitting the two HMMs on data of all species combined resulted in very similar state profiles (S4 Fig). The conjunction of the two HMM outputs resulted in four distinct state classifications: distracted (low accuracy and low speed), deliberate (high accuracy and low speed), impulsive (low accuracy and high speed), and efficient (high accuracy and high speed) (Fig 2A, right). Each task trial was labelled with one of these four states. It should be noted that these labels are intended solely for readability and are not meant to carry the connotations typically associated with terms like impulsivity or deliberateness in the literature [21,22].

To verify that these four HMM-derived states did not represent random data partitions, but could be related to more classical behavioural metrics of speed and accuracy, we visualised trials in the space of hit rate versus reaction time, coloured by their assigned state (Fig 2B). We observed that our states generally fall within the expected quadrants of the space (e.g., ‘efficient’ trials showing both fast reactions and high accuracy). In contrast, fitting a single 4-state HMM to all five behavioural variables yielded state profiles that were difficult to interpret, with inconsistent contributions of the different parameters (S5 Fig). However, some trials fall in other quadrants than one might expect based on a simple cut-off criterion. This is the case because by design the HMMs did not simply classify states linearly, but also captured temporal dependencies between trials by formalising them as state-to-state transition probabilities learned from the data. The HMM-generated states also appeared to partition trials sensibly for other read-out parameters like bias and running speed. One clear exception was the ‘precision’ parameter in monkeys and humans, which was not well-partitioned by the HMM states. This is consistent with the fact that precision is only weakly correlated with our speed and accuracy metrics, which suggests that it may capture a partially distinct aspect of performance, potentially more related to motor execution than to the perceptual decision-making. Another exception can be seen for reaction times in mice. This might be due to the mice continuously moving on the treadmill, potentially making reaction times more dependent on movement context (e.g., running speed at trial start) and more difficult to determine precisely (S6 Fig). Taken together, these observations support the use of the two-HMM architecture as a simple, hypothesis-driven way to characterise attentional fluctuations along speed and accuracy dimensions across species.

To complement the partitioning analysis, we investigated the relative representations of all five parameters in the two HMMs. As expected, in the accurate states, the three accuracy parameters had higher average values (and vice versa for the inaccurate states), whereas in the fast states, the speed parameters had higher means (Fig 2C). Importantly, this pattern appeared similar across the three species, indicating that these input parameters, despite being recorded in different ways (actual running for the mice, moving a trackball with the hand for monkeys and humans), all contributed similarly to defining each attentional state. Statistical tests of cross-species pattern similarity (see Methods, Analysis of dwell times and transitions) confirmed this finding (human-monkey: r = 0.96; human-mouse: r = 0.88; monkey-mouse: r = 0.87), even though the Euclidean distance between the parameter distributions of the different species was larger than expected by chance (p ≤ 0.015). Thus, the overall pattern of metric combinations that define each state appears conserved across species, but with significant differences in the exact values.

State characterization

Visualising states in time showed participants dwelling in states for several trials before transitioning to the next state (see Fig 3A for an example session). Across species, participants spent relatively more time in the accurate states (deliberate and efficient) than in the inaccurate states (distracted and impulsive) (Fig 3B). Statistical tests (see Methods, State occupancy across species) showed that the proportion of the distracted state was indeed not significantly different between the species (p = 0.22), whereas the proportions of the remaining three states showed significant differences: mice spent comparatively less time in the deliberate (p = 0.0002) and more time in the impulsive (p = 0.003) state, and monkeys spent less time in the efficient state (p = 0.002) than the other two species. Note that in the ‘distracted’ state, not all trials necessarily had slow and incorrect outcomes; just comparatively more than during the efficient (fast and correct) state.

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Fig 3. Model comparisons across species.

A) Partitioning the trials of an example session of humans (top), monkeys (middle) and mice (bottom) into the four states showed both long (several tens of trials) and short (just a few trials) stretches of a particular state. B) Overall time spent in each state was very similar for humans and monkeys, whereas mice spent less time in the deliberate, and more time in the efficient state. C) Proportion of time spent in each attentional state during the first and second half of sessions, shown separately for humans, monkeys, and mice. The asterisk denotes significant differences for all states (p < 0.05, permutation test).

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One potential confound is that performance speed and accuracy may be strongly shaped by internal variables that are not directly related to fluctuations in sustained attention, for instance, slow changes in fatigue (or in the case of monkeys and mice, satiety) throughout a session. While the drift correction implemented on the behavioural variables used for our HMM analysis (see Methods, Preprocessing) should account for such slow changes to some extent, they may still bias our analysis throughout the time course of a session. To check whether slow drifts in internal variables were driving the occurrence of our four performance states, we computed the relative proportion of the four states over the course of each session by splitting sessions into an early and a late half. As shown in Fig 3C, the proportions of the four different states remained stable between the first and second half of the session for humans and monkeys (permutation tests yielded p-values > 0.05, see Methods). In contrast, mice became progressively less accurate over time (p < 0.05, see Methods), possibly reflecting increasing fatigue or satiation. This suggests that the state transitions inferred here were not mainly driven by slow internal drifts, and can thus be seen as a viable proxy for more dynamic (presumably attention-driven) fluctuations.

State dynamics

Beyond the overall proportions at which the four different states occurred across species (see Fig 3B), their distribution over time may also vary. Anecdotally, many neuroscientists are familiar with the hugely different attention spans of different species; mice can often only be trained for 20–30 minutes at a time, whereas a typical human experiment lasts about an hour, and for a well-trained monkey, training times of up to 2–3 hours are not unusual. This suggests that state durations in mice might be shorter, and state transitions might occur more often than in humans and monkeys. To test this hypothesis, we computed the dwell times for all states (Fig 4A). This showed that durations spent in each of the four states were short, with a median of 5 trials and an interquartile range of roughly 3–8 trials across all species. Overall, species differences in dwell time were statistically significant but numerically small (mean dwell times between 6.2 and 6.9 trials; Kruskal-Wallis test, H = 9.68, p = 0.008; see Methods, Analysis of dwell times and transitions). For example, humans and monkeys spent comparatively longer uninterrupted sequences of trials in accurate than in inaccurate states (Fig 4A, left and middle); this was not the case for mice (Fig 4A, right). Control analyses with smoothing over window sizes between 2 and 20 trials confirmed that dwell times scale linearly with window size, for all states and in all species; therefore, any differences, e.g., across species or across different attentional states, cannot have been artificially introduced by data smoothing, which was applied equally to all data (S3 Fig).

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Fig 4. State temporal dynamics.

A) Dwell times show a large spread, but are on average very similar between the species. Within each species, interesting differences emerged; for instance, humans, tended to stay longer within an accurate than within an inaccurate state. B) Frequency analysis on the speed states (top) of humans (left), monkeys (middle) and mice (right) revealed a similar frequency peak in humans and monkeys around 55 trials, and a peak around 75 trials in mice. The grey area denotes the 95 percent confidence interval of shuffled trials (see Methods, section N). A red mark indicates a peak exceeding the 95% shuffled confidence interval. Bottom: same, but then for accuracy states.

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Even though the dwell times show a large spread for each species and state (Fig 4A), it could be that there is a preferred dwell time, which would imply the existence of a certain rhythm in the state durations. To examine this, we determined the frequency spectrum of the time series of all trials in all sessions (Fig 4B). As the two state sequences were largely independent (S7 Fig), we computed separate frequency spectra for each binary axis. Frequency spectra were computed using superlet analysis ([23]; see also Methods - Frequency Analysis). To our surprise, the frequency spectra along the speed axis revealed a prominent peak for all three species (Fig 4B, top). This peak was at a period of about 55 trials in humans and monkeys; for mice, it was slower, at a duration of about 75 trials (frequency spectra in the unit of seconds for all three species are shown in S8 Fig). Using session-wise peak positions within this low-frequency range (40–80 trials), we found no significant species differences in peak period (all Bonferroni-corrected p > 0.12; see Methods, Frequency Analysis). This suggests that there is an intrinsic, and potentially evolutionarily preserved, rhythm by which fast performance can typically be maintained for a period of tens of trials. Since peak frequencies can jitter across sessions, our frequency-by-frequency comparison to the shuffled spectra provides a conservative estimate of rhythmic structure; it may underestimate effects that are consistent in a broad low-frequency band but not perfectly aligned in their exact peak period. The frequency spectra of the accuracy axis revealed peaks at similar frequencies, however, these were much smaller and did not exceed the shuffled control, suggesting that performance accuracy varied less dynamically and rhythmically than speed (Fig 4B, bottom). In both axes, several small peaks were present at a faster time scale of 20–40 trials.

To assess whether fluctuations in speed and accuracy reflect coordinated attentional dynamics or rather independent latent processes, we investigated the temporal coordination between the speed-HMM and accuracy-HMM state sequences. First, we computed transition matrices on the sequences of the four ‘composite’ states (S7 Fig). However, as the composite labels are defined as the conjunction of two separately inferred state sequences, the resulting transition matrix can be largely predicted from the transition structure of these two original sequences. This yields much higher probabilities for transitions that change only speed or only accuracy than for transitions that require both sequences to switch on the same trial (i.e., between efficient and distracted, impulsive and deliberate). We therefore compared the observed transition matrices to a null distribution generated by independently shuffling the speed and accuracy state sequences (preserving dwell-time structure) before recombining them into composite states. Indeed, compared to this null, most transition probabilities were not significantly different, with only a small number of significant deviations, mostly in monkeys (S7 Fig).

We therefore focused on whether switch events in the two sequences are temporally coupled. Using a circular-shift null that preserves each sequence’s long-term structure while disrupting its alignment to the other sequence, we found a significant dependence between speed and accuracy switching in monkeys, with a peak at a lag of one trial. In mice and humans, we did not observe any dependence. Overall, this suggests that the two sequences are switching mostly independently, with some coordination between them in monkeys (S7 Fig).

Effect of external task attributes

The presence of a rhythmic component in the speed state fluctuations (and the absence of such a rhythm in the task structure) suggests that these fluctuations are internally generated rather than task-induced. To verify this, we made use of a task attribute that strongly affects task performance, namely task difficulty [24,25]. For all three species, the task included trials of varying levels of difficulty (see Methods for details). We examined the effect of task difficulty on state transitions by computing the average difficulty of the trials around the time of each speed-state transition (slow to fast states and fast to slow states). Any effect of task difficulty would have resulted in an uneven distribution of easy and difficult trials around the time of state transition; however, this was generally not observed (Fig 5). The few significant peaks were brief and inconsistent between the species and directions; there was no sustained ramp of greater difficulty before or after transitions. In monkeys, there were brief single-trials increases of difficulty during the fast states, which is in contrast to the typical pattern, where more difficult trials lead to longer reaction times [26]. This may reflect a species-specific (or individual) strategy to quickly skip particularly difficult trials, but would only apply to a small subset of trials. This suggests that the speed state transitions are generally self-generated, even though other stimulus-related factors such as their appearance might have played a role. Repeating this analysis for the accuracy states showed a more pronounced effect of task difficulty for humans and monkeys (S6 Fig), but again restricted to a single-trial peak. This effect is expected because the model in both of those species is highly sensitive to errors. A single especially difficult trial will likely result in an error, which is more often captured by the HMM as a brief transition to the inaccurate state. A final indication that we are witnessing internally generated attentional states rather than externally induced, task-related changes in performance is given by concurrent pupil size measurements in mice and monkeys: the relationship between our five input HMM parameters and pupil size in those two species followed an inverted U-shape, such that best performance (highest hit rate, lowest reaction time, etc.) was associated with intermediate pupil size, as is commonly reported in the literature [6,27–29] (see S10 Fig).

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Fig 5. Effect of task difficulty on state transitions.

Around the time of a state transition (at trial 0) from slow to fast (top row) or fast to slow (bottom row), the difficulty level of trials (black line) was not significantly different (except in three places) from the average difficulty (dotted line). The grey band shows the range of 1000 shuffled controls (see Methods). This indicates that the transitions between speed states are likely internally generated, as opposed to externally triggered, in all three species.

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Ethics statement

All animal experimental procedures were approved by the local ethics committee, Regierungspraesidium Darmstadt, under number F149/2000. The human experiments were approved by the ethics committee of the medical department of the Goethe University in Frankfurt under number 2021–252. Written consent was obtained from all participants prior to their participation.

Subjects and training

3 mice (FVB/BL6, male, 10–25 weeks old), 2 monkeys (Macaca mulatta, both male, 15 years old), and 11 humans (3 male, 8 female, mean age 25 years old) were used in this study. Training sessions for mice were conducted between 10am and 1pm, and typically lasted 30–60 minutes. Note that animals were housed in a reversed day-night cycle, so that all experiments were conducted during their active phase. Mice were typically trained for 5–12 sessions until they reached a consistent performance of around 70–80% correct responses in multiple stretches throughout a session. Training sessions for monkeys were typically conducted in the morning, and lasted about 60–90 minutes. The monkeys needed about 30 training sessions before reaching near-perfect, stable performance on the perceptual decision-making task. Humans received verbal instructions and a short practice of a few minutes before conducting the experiment, typically done in the afternoon and lasting for about one hour.

Experimental setup

Details of our experimental setup have been published previously [18]. Briefly, participants were placed inside a spherical dome (diameter 120 cm, 250°) onto which a virtual reality environment was projected via a curved mirror. The virtual reality was created using the game engine Unreal 4 and consisted of a grassy landscape with mountains in the background and a blue sky overhead, in the middle of which the two stimuli were displayed. To navigate the environment, macaques and human participants used a GK75-1602B 75mm trackball from NSI (Bilzen-Hoeselt, Belgium). Mice were placed on top of a 20 cm diameter Styrofoam ball suspended in the air (modified method from [53]). The movements of either device were translated into movement in the virtual environment.

Experimental paradigm

All three species performed the same simple two-choice visual discrimination task. They were presented with an ambiguous blurred stimulus that immediately divided into two stimuli with naturalistic shape and texture (see Fig 1B), which then swiftly moved through the VR environment to their final position next to each other at a reasonable distance in front of the participant. One of the two stimuli, the target, resembled a pointed-lobed leaf; the other stimulus, the distractor, resembled an hourglass. The perceptual similarity between the target and distractor was varied systematically by morphing the shapes into each other. Both shapes were filled with a uniform foliage texture in a blue-green colour. The colour was selected to be easily visible both for rodents and primates. The participants were required to navigate towards and then (virtually) collide with the target while ignoring the distractor. A collision with the target resulted in a drop of soy milk for the mice, a drop of juice for the monkeys, while humans did not receive a reward. Approximately 550 ms following the collision, the next trial started. Mice and monkeys performed the task until satiated; humans performed the task until reaching a minimum of 500 trials.

The task had several difficulty levels; on easy trials, subjects had to distinguish between two shapes resembling a pointed leaf and an hourglass, whereas on difficult trials, they distinguished between two morphed stimuli only slightly resembling a pointed leaf and an hourglass. Monkeys and humans were shown shapes of comparably high difficulty. Mice were presented with more discriminable stimuli, as the goal was not to test the limits of their visual discrimination ability but to produce a reliable behavioural response.

In humans, 11 sessions were recorded, totalling 5,314 trials. Data from monkeys included 9 sessions, totalling 7,504 trials, and data from mice spanned 13 sessions, totalling 3,903 trials.

Behavioural metrics

Each trial could have one of three outcomes: correct response (collided with the target stimulus), incorrect response (collided with the distractor) and miss (no stimulus chosen). On each trial, the path of the participant through the virtual environment was recorded and used to extract five metrics. Instantaneous hit rate was classified as a binary metric (correct (1) vs incorrect or miss (0)), which is later smoothed using a 5-trial sliding window during the preprocessing stage (see Methods - Data Preprocessing). Bias represents perseverative errors by identifying trials where the subjects repeated their previous choice despite the target appearing on the opposite side. It is a binary measure (biased (1), unbiased (0)) that reflects the tendency to choose the stimulus on the side of the previous response, regardless of the current target location. Precision quantifies how close each response endpoint was to the mean location of correct responses for that side (left/right), regardless of whether the current response was correct. The measure is normalised by the distance from the outer stimulus corner to the midpoint between stimuli and inverted so that higher values (0–1) indicate better precision. By computing this relative to successful responses within each session, the measure accounts for individual response biases and preferences (e.g., hitting the inner stimulus corner vs. the middle or differences between left and right responses). Reaction Time (RT) was defined as the first significant change in direction in the path towards one of the stimuli (see S1 Text). Speed refers to the average movement speed (VR units/s) of the participant in each trial.

Data preprocessing

The data was preprocessed in several steps. First, trials with missing values were removed, as well as trials with durations over 10 seconds and extremely short travel distances (path length <250 unreal units).

In humans, there was a learning curve in motor performance that was most noticeable in the reaction time and average running speed. To remove the learning period, we calculated a combined learning cutoff based on reaction time and speed using rolling averages compared to the stable mean of the second half of each session. Trials up to the cutoff were excluded to ensure that only stabilised performance was analysed. Mice and monkeys were already proficient in the task by the time of the sessions analysed here, so all data could be used. Next, in all species we performed drift correction on the continuous metrics (reaction time, speed and precision) by fitting a second-degree polynomial and subtracting the predicted trend, to remove any extremely slow fluctuations. We subsequently smoothed the data in all species by applying a centred rolling average with a window of 5 trials to suppress noisy single trials while minimally blurring the temporal structure, and to reduce the effect of single-trial difficulty. Finally, we applied the standard scaler to normalise the data. Within one species, each session was preprocessed individually and concatenated for further analysis.

Metrics clustering

We examined the similarity structure between behavioural metrics by computing pairwise Pearson correlation matrices (Hit Rate, Bias, Precision, RT, Speed) separately for each species and on the combined dataset. To visualise metric groupings, we performed hierarchical clustering using 1 - r as a distance measure with Ward’s linkage and plotted the resulting dendrograms alongside the correlation heatmaps. To quantify the separation between speed and accuracy metrics, we cut the dendrogram at two clusters and computed silhouette scores on the correlation-based distance matrix. Across all species and the combined dataset, the five metrics consistently split into an accuracy cluster (Hit Rate, Bias, Precision) and a speed cluster (RT, Speed), with silhouette scores of 0.32 (human), 0.51 (monkey), 0.23 (mouse), and 0.40 (combined).

HMMs

First, the five metrics were correlated with each other. Based on the resulting correlation analysis, they were divided into two axes: accuracy (hit rate, precision and bias) and speed (reaction time and speed). These two axes provided the input to two hidden Markov models (HMMs). For this analysis, we used an HMM with a Gaussian observation class, implemented in an SSM package [54]. As this is a hypothesis-driven analysis, we chose to split the data into 2 states. The models were trained on all the sessions concatenated, separately for each species. In order to offset state probabilities around the end of one session and the beginning of the next, we added 50 trial padding with a single value across metrics. The padding was reliably classified as a third state and discarded afterwards. Each model classified the trials as belonging to either of two states (accurate/inaccurate for the accuracy model, and slow / fast for the speed model). The conjunction of these classifications resulted in four states, occupying the quadrants of the speed/accuracy space: distracted (slow and inaccurate), deliberate (slow and accurate), efficient (fast and accurate), and impulsive (fast and inaccurate). Thus, each trial was assigned to one of these four states.

Shuffling

We used shuffling to assess the significance of observed behavioural patterns. The first two preprocessing steps were implemented before the shuffling (see Methods - Data Preprocessing). To create a null distribution, we randomly shuffled the behavioural values of the trials a thousand times. The shuffled trials belonged to the same recording session. We then applied the same data transformations that we used on the original data set, including detrending, smoothing and scaling. Following that, we trained HMMs on each shuffled dataset to create a null distribution for statistical comparisons.

Cross-species similarity of state fingerprints

For each session, we computed a 20-dimensional “fingerprint” by averaging the five behavioural metrics (hit rate, bias, precision, reaction time, and speed) within each of the four HMM states and concatenating these means. Session fingerprints were then averaged per species. For each species pair we quantified similarity using the Pearson correlation and Euclidean distance between fingerprints, and assessed whether distances were larger than expected by chance using a permutation test that shuffled species labels across sessions (5000 permutations).

State occupancy across species

For each session and state, we computed state occupancy as the proportion of trials assigned to that state. To test for species differences in occupancy, we used permutation tests on session-level values: a global test per state using the maximum pairwise difference in species means as test statistic, and pairwise tests per state and species pair, obtained by shuffling species labels between the two groups (5000 permutations, two-sided p-values).

Analysis of dwell times and transitions

Blocks of consecutive trials assigned to the same state were identified, and the times that such blocks lasted were termed the dwell times. Dwell times were statistically compared between the species using a Kruskal-Wallis test, followed by post-hoc Dunn’s tests with Bonferroni correction for multiple comparisons when significant differences were detected. Subsequently, we examined the transitions between the four states. We computed the probabilities of transitioning from each state to any other state, summarised in a transition matrix for each species. As our model features frequent self-transitions (staying in the same state for several trials), we subtracted the diagonal elements from the transition matrices and re-normalised the remaining probabilities. This transformation allowed us to better visualise and analyse the patterns of transitions between different attentional states. To assess whether these transition patterns differed significantly from chance, we performed a permutation test by independently block-shuffling the two constituent state sequences (speed and accuracy) 2,000 times each, and then recombining them into composite states. Block-shuffling preserved the original same-state run durations by permuting only the order of blocks rather than individual trials. For each transition, we computed two-sided p-values by comparing the observed transition probabilities to the null distribution generated by the shuffled sequences, applying FDR (Benjamini-Hochberg) correction for multiple comparisons across off-diagonal cells. To compare transition probabilities across species, we used a per-session species-label permutation test. For a global difference, we computed the Frobenius distance between each pair of species’ transition matrices and compared it to a null distribution generated by permuting session-level species labels (2,000 permutations; all pairs differed globally, p ≤ 0.0015). Specific state-transition differences were assessed per cell by comparing the observed pairwise difference to the permuted null distribution (FDR corrected), with 95% confidence intervals obtained via bootstrap (2,000 resamples).

Frequency analysis

To identify regular fluctuation patterns in the sequence of behavioural states, we used the time-frequency “superlets” method [23]. Superlets are an extension of the continuous wavelet transform: instead of using a single wavelet at each frequency, they use a set of Morlet wavelets with the same centre frequency but different numbers of cycles. For each time-frequency point, the responses of these wavelets are combined using a geometric mean. This allows for preserving the temporal precision of the shorter wavelets while gaining the better frequency resolution of longer wavelets, achieving “super-resolution” in both time and frequency. This makes it easier to detect short bursts of oscillations compared to standard wavelet or Fourier analysis.

To identify prominent periodic patterns in behavioural data, we focused on states of speed and states of accuracy separately. This way, we could decompose the binary signal (states 1 and 0) into the constituent frequencies. The state labels of all the sessions from a single species were concatenated and then padded with a mirror-reflected signal. In the case of our data, the time unit is one trial. We set the sampling rate to 1000 for convenience. We analysed the frequencies in the range of 6.7 (cycles/1000 trials) to 66.7 (cycles/1000 trials). This is equal to a range of 150–15 trials per cycle. The outcome of this is the frequency power over time for each of the sessions. We then computed an average power value per frequency, averaged across sessions. This resulted in a power spectrum with several peaks.

To assess peak significance, we generated a null distribution from 1000 shuffled datasets (see Methods - Shuffling). We then applied ‘superlets’ to each of the shuffled datasets and computed their power spectra. Values in the real power spectrum falling outside the 2.5th and 97.5th percentiles of this null distribution were considered significant.

To assess differences in the peaks between species, we identified the most prominent peak in the data, which was in the period range of 40–80 trials, and extracted the dominant peak from each session within this range. We then shuffled the species labels 5000 times, subsampling session counts to match each species, and compared the means of real peak distributions to the shuffled means.