Neurobehavioural characterisation and stratification of reinforcement-related behaviour

Reinforcement-related cognitive processes, such as reward processing, inhibitory control and social–emotional regulation are critical components of externalising and internalising behaviours. It is unclear to what extent the deficit in each of these processes contributes to individual behavioural symptoms, how their neural substrates give rise to distinct behavioural outcomes and whether neural activation profiles across different reinforcement-related processes might differentiate individual behaviours. We created a statistical framework that enabled us to directly compare functional brain activation during reward anticipation, motor inhibition and viewing emotional faces in the European IMAGEN cohort of 2,000 14-year-old adolescents. We observe significant correlations and modulation of reward anticipation and motor inhibition networks in hyperactivity, impulsivity, inattentive behaviour and conduct symptoms, and we describe neural signatures across cognitive tasks that differentiate these behaviours. We thus characterise shared and distinct functional brain activation patterns underling different externalising symptoms and identify neural stratification markers, while accounting for clinically observed comorbidity. On the basis of the IMAGEN database of 2,000 Caucasian adolescents, Jia et al identify neural patterns of activity during reward anticipation and motor inhibition associated with different externalising symptoms for ADHD and conduct problems.


NATuRE HuMAN BEHAvIouR
It is unclear whether and how the reinforcement-related cognitive processes are modulated to achieve the observed behavioural differences among these disorders. Identifying the brain activity patterns related to various manifestations of dysfunctional reinforcement-related behaviour might aid in the characterization of underlying biological mechanisms, and in the identification of targets for therapeutic intervention 5 . Furthermore, clinically relevant psychiatric symptoms are typically characterized by dysfunctions not only in one but often in several reinforcement-related cognitive processes. For example, ADHD symptoms are known to involve dysfunctional inhibitory control 1 , as well as dysfunctional reward processing 6 . We were interested in dissecting the contribution of different domains of reinforcement-related cognitive processes to distinct disorder symptoms, and thus characterizing a profile of brain activation specific for each disorder.
Whereas animal models have identified networks of multiple cortical and subcortical brain regions involved in reinforcementrelated cognitive processes 7 , analyses in humans are often based on a few predefined regions of interest (ROIs). These include the ventral striatum and orbitofrontal cortex (OFC) for reward processing 8 , the right inferior frontal cortex (rIFC) for inhibitory control 9 and the amygdala and superior temporal sulcus (STS) for social-emotional regulation 10,11 . Often, the underlying assumption is that a cognitive process can be represented by a few key brain regions. However, we 12 and others [13][14][15][16] have shown that task-induced brain activity may involve a complex network of cortical and subcortical brain regions. What we do not know is how activity in these networks relates to observable behaviour.
In this paper, we provide a systematic characterization of brain activity in reinforcement-related behaviour, measuring blood oxygen level-dependent (BOLD) response during tasks targeting reward anticipation, motor inhibition and social-emotional processing. We compare their common and distinct brain activity patterns and assess the modulation of task-specific networks in externalizing (for example, hyperactivity, inattention, impulsivity and conduct symptoms) and internalizing behavioural symptoms (for example, emotional and anxiety symptoms) 17 . We also identify signatures of brain activity across tasks that best characterize symptoms of externalizing disorders, as well as helping to distinguish one symptom domain from the other.

Results
Summary of the analysis strategy. We aimed to compare brain activity during functional neuroimaging tasks measuring reward anticipation, motor inhibition and social-emotional processing of 1,506 14-year-old adolescents from the IMAGEN (reinforcementrelated behaviour in normal brain function and psychopathology) project 4 . Of the 1,506 participants investigated in this study, clinical development and well-being assessment (DAWBA) ratings were available from 1,190 individuals. Of these individuals, 131 had one or more diagnoses; 33 individuals were diagnosed with ADHD, 59 with emotional problems, 12 with anxiety (general + other) and 33 with depression (major + other). We reduced the dimensionality of brain activation by applying a weighted voxel co-activation network analysis (WVCNA) 12,18 , followed by a hierarchical clustering analysis. The combination of both methods could efficiently reduce dimensionality while still preserving localized network features from WVCNA. We then calculated the overall correlation between functional MRI (fMRI) clusters and symptoms of externalizing or internalizing behaviours using ridge-regularized canonical correlation analysis (RCCA) 19 -a method to detect multivariate relationships between different data types.
First, we tested for an overall significant correlation of externalizing or internalizing symptoms with brain network activation across all fMRI tasks. In cases where we established an overall correlation, we looked for associations of each fMRI network with externalizing or internalizing behaviours. Finally, we investigated the sensitivity and specificity of fMRI clusters across different behaviour components. This workflow is shown in Fig. 1.
Identification of reinforcement-related brain fMRI networks. We defined brain networks underlying reinforcement-related behaviour by using the monetary incentive delay (MID) task to measure reward processing 20 , the stop signal task (SST) to assess motor inhibition 21 and the emotional faces task (EFT) to examine social-emotional processing 22 . In these tasks, we analysed contrasts that were most relevant to the reinforcement-related behaviour and eliciting the largest BOLD difference; namely, the large win versus no win contrast during the reward anticipation phase in the MID task, the successful stop versus successful go contrast in the SST, and the angry face versus control contrast in the EFT. Symptoms of -ADHD -ODD/CD -Anxiety -Depression MID Fig. 1 | Workflow of the analyses. We included the MID task 6 as a measure of reward processing, the SST 52 as a measure of impulsivity (motor inhibition) and the EFT 22 as a measure of social-emotional processing, for which the figures of experimental models were adapted from previous publications 6,22,52 . Only strong brain activation (effect size: Cohen's D > 0. 30) was included in the analyses. The WVCNA, in combination with a further hierarchical clustering, was implemented to establish the brain fMRI networks. The RCCA was adopted to evaluate the overall correlation between the brain networks and reinforcement-related behaviours. Based on the RCCA results, we identified the neural signatures across three brain fMRI networks for each reinforcementrelated behaviour. ITI, intertrial interval.

NATuRE HuMAN BEHAvIouR
We applied WVCNA 12,18 , which was established by combining the scale-free network assumption with a dynamic cut of the dendrogram 23 , to maximize the resolution of localized brain network features (see Methods for details). Using this approach, we identified in the MID a brain network consisting of 500 nodes (25,130 voxels; Fig. 2a), 487 nodes (24,571 voxels) in the SST (Fig. 2b) and 79 nodes (3,923 voxels) in the EFT (Fig. 2c). We further removed redundant information by applying an additional hierarchical clustering on these nodes with a static cut at the 90th percentile, keeping the 10% most distinctive branches (representing clusters) in each dendrogram. This two-step procedure enabled us to efficiently reduce dimensionality while still preserving localized network features from WVCNA (Supplementary Table 1a-c). Using this approach, we identified 46 clusters in MID, 41 clusters in SST and nine clusters in EFT (Supplementary Table 1a-c and Extended Data Fig. 1).
In all three networks, activated clusters were widely spread across cortical and subcortical regions, as well as in the cerebellum ( Fig. 2 and Extended Data Fig. 2). Brain regions activated in the three networks were often overlapping (Fig. 2d). It is notable that none of the ROIs typically associated with reward processing, impulsiveness or social-emotional processing was specific to their corresponding networks. For example, the ventral striatum and OFC (which are typically linked to reward processing 8 ) were activated in both the MID task and the SST, whereas the rIFC (which is often associated with inhibitory control 9 ) was activated in both the SST and EFT. The STS, which is regarded as an essential component of the social brain 11 , was also activated in both the SST and EFT. The dorsal amygdala (a central node of emotional processing 10 ) was activated not only in the EFT but also in the MID task. However, some activations were network specific. For example, distinct activations were seen in the superior post-central gyrus (that is, the superior primary somatosensory cortex), primary auditory cortex (PAC), dorsal striatum and most of the cerebellar vermis during the MID task, in the frontal operculum, the orbital part of the rIFC, the inferior primary somatosensory cortex and the lingual part of the cerebellar vermis during the SST, and in the medial OFC, dorsal posterior cingulate cortex, temporal pole and ventral amygdala during the EFT (Fig. 2d and Extended Data Fig. 2).
Modulation of reinforcement-related brain fMRI networks in different behaviours. Clinical psychopathology in adolescents is grouped into externalizing and internalizing disorders 24 . We were interested in examining whether externalizing and internalizing  , the angry face versus the control face in the EFT (c) and overlay of the results for all three tasks (d). MID, SST and EFT are represented by red, blue and green, respectively. Activation levels were measured as the −log 10 (transformed P value) and only voxels with P < 1.0 × 10 −34 (that is, Cohen's D > 0.3) are shown. L, left; R, right.

NATuRE HuMAN BEHAvIouR
behavioural symptoms correlate with distinct configurations of reinforcement-related networks. From the strength and difficulties questionnaire (SDQ) and DAWBA, we selected the entry-level questions, including 44 externalizing items covering symptoms of ADHD (23 items), oppositional defiant disorder (ODD; 11 items) and conduct disorder (CD; ten items), and 21 internalizing items covering symptoms of depression (12 items) and anxiety (8 items) ( Table 1; see Methods for more details). To evaluate the overall relationship between behavioural symptoms and patterns of brain activation, we carried out RCCA 19 . This method seeks to find subsets of variables in two datasets that best correlate with each other while stabilizing the result through penalization of correlations within each dataset. We first investigated the overall correlation between externalizing behaviours and 96 clusters from the three fMRI networks and found a significant canonical correlation (η 2 = 0.854 denotes the proportion of behaviour variance explained by the fMRI and is analogue to R 2 in the multiple linear regression model; 90% confidence interval (CI) = 0.839 to 0.869; adjusted η 2 = 0.160; d.f. fMRI = (1,506, 96); d.f. behaviour = (1,506, 44); permutation test P value (P perm ) < 0.001; see Methods (for details), Table 2 and Supplementary Table 2). Please note that a predefined scheme of regulation parameters was evaluated throughout for all RCCAs and highly stable results were obtained (as shown in Extended Data Fig. 3). For simplicity, we only show the results with a regulation parameter of 0.1 in the main text. The number of permutations to calculate P values in this

NATuRE HuMAN BEHAvIouR
and all subsequent analyses was 10,000 unless otherwise specified. Also, presented P values were always corrected for experimentwise multiple comparisons wherever applicable. We then investigated the RCCA between internalizing behaviours and the same 96 fMRI clusters, but found no overall significance (η 2 = 0.574; 90% CI = 0.547 to 0.602); adjusted η 2 = −0.024; d.f. fMRI = (1,506, 96); d.f. behaviour = (1506,20); P perm = 0.786; see Extended Data Fig. 4 for more results with alternative parameters). We also did not find significant overall correlations with internalizing behaviours when analysing each fMRI network separately (Extended Data Fig. 4). We therefore constrained our subsequent analyses to externalizing behaviours only.

Functional brain characterization of behaviours across different tasks.
While both reward anticipation and motor inhibition networks showed significant canonical correlations with ADHD behaviours, neither correlation between the first components of the RCCA (its square is known as Roy's largest root (R Roy ) 25 ) was significant on its own (reward anticipation: R Roy = 0.234; Fisher R-to-Z transformed correlation (Z Fisher ) = 0.237; 90% CI for Z Fisher = 0.202 to 0.274; P perm = 0.087; motor inhibition: R Roy = 0.225; Z Fisher = 0.229; 90% CI for Z Fisher = 0.193 to 0.266; P perm = 0.151), and these correlations were additionally shown to be significantly smaller than a meaningful effect through an equivalence test for inferiority 26 (reward anticipation: t = −3.98 and P < 0.001 for an upper equivalence bound (Z U ) of 0.324; motor inhibition: t = −4.06 and P < 0.001 for Z U = 0.319; lower equivalence bound (Z L ) = −∞; Z U was calculated as the estimated inflation of Z Fisher plus a small effect size ΔZ = 0.1 (ref. 27 ); see Methods for details). These results therefore showed that the overall significant correlation was unlikely to be represented by an individual RCCA component. Therefore, we hypothesized that distinctive neural bases may underlie different ADHD behaviours and investigated profiles across brain networks that may characterize the ADHD components hyperactivity, inattention or impulsivity (see Methods). As the factors generated by RCCA are not optimized to detect differences in the brain function underlying these behaviours, we applied a more sensitive multiple linear regression model. Together, reward anticipation and motor inhibition networks were found in significant association with the summed score (that is, the total score) of ADHD behaviours (R 2 = 0.085; 90% CI = 0.063 to 0.106; adjusted R 2 = 0.029; F (87, 1,418) = 1.51; P = 0.002; where R 2 is the coefficient of determinant that represents the proportion of behavioural variance explained by the fMRI networks in the multiple linear model), as well as the total scores of the ADHD components hyperactivity (R 2 = 0.089; 90% CI = 0.067 to 0.110; adjusted R 2 = 0.033; F (87, 1,418) = 1.58; P < 0.001), impulsivity (R 2 = 0.077; 90% CI = 0.057 to 0.098; adjusted R 2 = 0.021; F (87, 1,418) = 1.37; P = 0.017) and inattention (R 2 = 0.079; 90% CI = 0.058 to 0.100; adjusted R 2 = 0.022; F (87, 1,418) = 1.40; P = 0.011). However, we did not find evidence for identical associations of these ADHD behaviours with reward anticipation and motor inhibition networks: while the motor inhibition network was found in significant association with the total scores of all three ADHD components (hyperactivity: R 2 = 0.045; 90% CI = 0.028 to 0.061; adjusted R 2 = 0.018; F (41, 1,464) = 1.67;   For each behaviour component, the prominent clusters in each brain network were identified if their univariate correlations with the sum of the corresponding behaviour items (that is, those in the column 'Primary behaviour') were significant after correction for multiple comparisons through 10,000 permutations (column 'P corrected '). For all prominent clusters identified in the first step, we further explored their univariate correlations with the remaining behaviour components (that is, those in the column 'Exploratory analyses). See Supplementary Tables 2-4 for the complete results. a These P values were evaluated based on 10,000 permutations to correct for multiple comparisons in the corresponding exploratory tests.
fMRI signature for hyperactivity. The hyperactivity total score was significantly associated with reduced activation in six out of 46 brain regions in the reward anticipation network. These were the superior parietal lobule (SPL), middle central sulcus (mid-CS), thalamus, PAC, middle cingulate cortex (MCC) and superior frontal junction (SFJ) (Fig. 3a, Table 3 and Supplementary Table 2). We investigated the specificity of the observed associations and found that the SPL, mid-CS and thalamus were also associated with inattention. The mid-CS and MCC were associated with ODD/CD behaviours, whereas no significant association was found with impulsivity (Table 3 and Supplementary Table 2). The brain regions showed no significant difference in association strength with hyperactivity and with inattention (ΔZ sum = −0.142; 95% CI = −0.384 to 0.100; P perm = 0.834) or with ODD/CD behaviours (ΔZ sum = −0.128; 95% CI = −0.377 to 0.121; P perm = 1) (Table 4), and these associations were further found to be significantly smaller than a meaningful effect size with equivalence tests (inattention: t = 3.71 and P one tailed < 0.001 for ΔZ L = −0.10; t = 6.02; P one tailed < 0.001 for ΔZ U = 0.10; ODD/CD behaviours: t = 3.71 and P one tailed < 0.001 for ΔZ L = −0.10; t = 5.72; P one tailed < 0.001 for ΔZ U = 0.10). In contrast, the brain regions showed a significantly weaker association in the case of impulsivity (ΔZ sum = −0.308; 95% CI = −0.522 to −0.094; P perm = 0.017) ( Table 4).
Thus, our findings suggest a shared specificity of brain activation during reward anticipation in hyperactivity, inattention and ODD/ CD behaviours, but not in impulsivity (Fig. 3e). However, in the motor inhibition network, despite the overall significant association, none of the six brain regions was significantly associated with hyperactivity (Supplementary Table 3a), suggesting that the observed overall association was based on multiple fMRI regions of the motor inhibition network, each with a minor contribution.
fMRI signature for impulsivity. The left temporoparietal junction (TPJ) of the motor inhibition network was associated with impulsivity (R = −0.092; 95% CI = −0.142 to −0.041; t = −3.563; P perm = 0.010) (Fig. 3b, Table 3 and Supplementary Table 3b), and additionally (in exploratory analyses) with hyperactivity (R = −0.067; 95% CI = −0.117 to −0.016; t = −2.59; P perm = 0.025) and ODD/CD behaviours (R = −0.071; 95% CI = −0.118 to −0.017; t = −2.64; P perm = 0.016), but not with inattention (R = −0.058; 95% CI = −0.109 to −0.008; t = −2.270; P = 0.062) ( Table 3 and Supplementary  Table 3b), where no significant difference in the strength of association was observed (ΔZ hyperactivity = −0.025; 95% CI = −0.073 to 0.022; P perm = 0.823; ΔZ inattention = −0.033; 95% CI = −0.079 to 0.012; P perm = 0.456; ΔZ ODD/CD = −0.021; 95% CI = −0.069 to 0.027; P perm = 1) ( Table 5). These associations were found to be significantly smaller than a meaningful effect size with equivalence tests (hyperactivity: t = 3.10 and P one tailed < 0.001 for L ΔZ = −0.10; t = 5.17 and P one tailed < 0.001 for ΔZ U = 0.10; inattention: t = 2.86 and P one tailed = 0.002 . c, Motor inhibition network underlying inattention (green; right aIFS). d, Motor inhibition network underlying ODD/CD behaviours (orange; right inferior frontal gyrus + anterior insula and right aIFS). e, Neural signatures of ADHD and ODD/CD behaviours. For each neural network identified in a-d, its correlations with the corresponding primary behaviour and the rest of the ADHD or ODD/CD behaviours were compared and the corresponding relative strengths of the correlations are plotted (red: hyperactivity; blue: impulsivity; green: inattention; orange: ODD/CD behaviours). P values for pairwise significant differences after correction for multiple testing are provided. Table 4 | Evaluating the specificity of prominent brain regions for hyperactivity during reward anticipation The specificity of prominent brain regions for hyperactivity was evaluated by comparing their correlations and associations with those for the rest of the behaviours (that is, the ADHD constructs impulsivity and inattention, as well as ODD/CD behaviours). For each brain region, its correlations with all behaviours were first transformed into normally distributed Z scores (columns labelled 'Z hyperactivity ', 'Z impulsivity ', 'Z inattention ' and 'Z ODD/CD ') through the Fisher transformation, and the pairwise differences (columns labelled 'ΔZ') were then tested against the null using both Steiger's test (columns labelled 'Steiger's Z statistic' and 'P Steiger ') and permutation test (column labelled 'P perm '), both of which provided very similar results. The overall significance throughout all brain regions was then evaluated based on the summed ΔZ value across all brain regions using a permutation test. The number of permutations was set to 10,000. All P values presented in the table were based on two-tailed tests without correction for multiple testing.  The specificity of prominent brain regions for the corresponding behaviours was evaluated by comparing their correlations/associations with those with the rest behaviours from ADHD constructs and ODD/CD behaviours. For each brain region, its correlations with all behaviours were first transformed into normally distributed Z scores (columns labelled 'Z hyperactivity ', 'Z impulsivity ', 'Z inattention ' and 'Z ODD/CD ', respectively) through the Fisher transformation, and the pairwise differences (column labelled 'ΔZ') were then tested using both Steiger's test (columns labelled 'Steiger's Z statistic' and 'P Steiger ') and the permutation test (column labelled 'P perm '), both of which provided very similar results. When there were multiple prominent regions, their overall significance was then evaluated based on the summed absolute ΔZ across all brain regions using a permutation test. The number of permutations was set to 10,000. All P values were based on two-tailed tests without correction for multiple testing.
In conclusion, ADHD and ODD/CD may share several distinctive neural bases during reward anticipation and motor inhibition.

Discussion
Here, we characterize clinically relevant behaviours in adolescents by describing brain activation during reinforcement-related cognitive processes. These behaviours include externalizing symptoms of hyperactivity, impulsiveness, inattention, oppositional defiance and conduct, and internalizing symptoms of anxiety and depression. We have used quantitative measures to assess these behaviours, as empirical evidence shows that psychopathology is generally more dimensional than categorical 28 -one of the basic premises of the research domain criteria 29 . We interrogated the neural basis of each of these behaviours by measuring brain activity during reinforcement-related cognitive tasks of reward processing, motor inhibition and social-emotional processing.
We found that activation of similar brain regions is often associated with different tasks (and behaviours). While well-known representative brain areas (for example, the ventral striatum and OFC for reward anticipation 8 , the rIFC for inhibitory control 9 , and the amygdala and STS for social-emotional processing 10,11 ) were activated as expected, these activations were not restricted to one task alone (Fig. 2d). This might represent the involvement of shared cognitive components in different behaviours that might be less specific to individual tasks. For example, the ventral striatum activation during motor inhibition was due to the anticipation of a random event 30 , thus the anticipatory component was shared with the reward anticipation network, which activates the same region. In some instances, it may also be caused by brain activation that reflects task presentation (for example, motor cortex activation in the active MID task and SST, but not during passive viewing in the EFT). Our observation is consistent with the notion of a basic neural function that underlies a complex profile of different behaviours 31 .
However, the overlap of brain activation across cognitive tasks might also indicate the presence of different functional or structural domains within a given brain region that relate differentially to each task 32 . This latter hypothesis is supported by the observation of low correlations of the same brain regions across tasks. In contrast, we found high correlations between different brain regions within each task, suggesting network constellations that are specific to each individual cognitive task. This specificity was further suggested by the observation that the variances of hyperactivity explained by reward anticipation and motor inhibition networks are additive (that is, the adjusted R 2 values were 0.033, 0.013 and 0.018 for both networks, reward anticipation and motor inhibition, respectively), and thus not overlapping. The specificity of cognitive neural networks might thus be defined as much by their internal collaborative structure as by the individual brain regions involved 33 .
We also found highly activated regions (Cohen's D > 0.30) in the MID task that were not expected to be activated in the anticipation of a visually presented reward. These included the PAC, which we observed to be activated in the absence of any auditory stimulus. As the PAC has been found to predict reward value 16 and is associated with anticipatory motor response 34 upon auditory stimulation, our findings point towards the possibility of the PAC underlying these cognitive processes in a way that is not dependent on the quality of the sensory stimulus. In addition, wide areas within the somatosensory cortex were also activated in the MID task, further suggesting the recruitment of sensory cortices (including the visual cortices) during reward anticipation irrespective of the quality of the signal input 35 .
We found a strong overall correlation (adjusted η 2 = 0.160; that, is 16% of variance was explained after adjusting for inflation due to the involvement of multiple variables) of neural networks with externalizing behaviours (ADHD and ODD/CD), particularly in reward anticipation and motor inhibition, but did not observe a significant correlation with internalizing behaviours (adjusted η 2 = −0.024). While ADHD behaviours were related to both reward anticipation and motor inhibition networks, we found specific neural signatures that distinguished each of the individual behaviours. While brain activity in the reward anticipation network was correlated with both hyperactivity and inattention (Table 3), their activation patterns were not significantly different ( Fig. 3e and Table 4), and were in fact equivalent. However, in the motor inhibition network, the correlation with inattention was significantly stronger than that with hyperactivity ( Fig. 3e and Tables 3 and 5), consistent ResouRce NATuRE HuMAN BEHAvIouR with a greater effort to maintain sustained attention during the task. This interpretation is supported by the strong correlation during successful motor inhibition of inattention with rIFC activity (Fig. 3c and Table 3)-a brain region previously implicated in attentional detection, monitoring and motor inhibition 9 .
In contrast, for impulsivity, we found no significant correlation with the reward anticipation network. In the motor inhibition network, its strongest correlation was with activation of the left TPJ ( Fig. 3b and Table 3), which, however, shows no significant differences from (and in practice, appears equivalent to) the correlations between left TPJ activation and both hyperactivity and inattention ( Fig. 3e and Table 5). This observation is in line with the previous finding of reduced bilateral TPJ activity in patients with ADHD 36 .
We thus identified neural signatures that distinguish hyperactivity, inattention and impulsivity on the basis of brain activation patterns during reward anticipation and motor inhibition. These signatures enable a more refined characterization of ADHD behaviour than the currently used distinction between motivational and motor inhibitory processes 37 .
ODD/CD behaviours were related to the motor inhibition network, but not reward anticipation, which is in line with previous findings 38,39 . Activation patterns for ODD and CD behaviours in the motor inhibition network were similar, although dominated by ODD behaviours, suggesting a shared neural basis (Supplementary Table 4) 40 . Surprisingly, we were not able to distinguish between activation patterns in the motor inhibition network in conduct and inattention symptoms (Fig. 3c-e and Tables 3 and 5), which were also found to be practically equivalent. While this may indicate in part a shared neural basis, the phenotypic differences between these behaviours also suggest the presence of a distinguishing cognitive domain, which we did not capture in our tasks. Nevertheless, the shared neural signatures between ODD/CD and ADHD symptoms indicate a shared neural basis underlying the high comorbidity between ODD/CD and ADHD 41,42 , supporting the idea of unifying ADHD and ODD/CD into a single spectrum disorder 43 .
It is a limitation of this work (and indeed of all task-based fMRI studies) that none of the tasks selected represents all aspects of the behavioural domain interrogated. For example, the research domain criteria divide reward processing into three different constructs and nine sub-constructs. The MID task interrogates only two sub-constructs: reward anticipation and early response to reward. Nonetheless, it is well established that the MID task, SST and EFT capture important and clinically relevant aspects of reward processing 12 , impulsiveness (in particular, response inhibition) 44 and social-emotional processing 10 , respectively. While we showed distinctive patterns in neural networks that stratify ADHD subtypes/components during reward anticipation (that is, the motivational pathway) and motor inhibition, the explained variance from individual regions of these neural networks is low (R 2 < 1%), which might be partly due to a task-dependent, incomplete representation of neural pathways underlying ADHD. However, given that together the neural networks could explain up to 16% of the variance of externalizing behaviours (that is, adjusted η 2 = 0.160 for RCCA after adjusting for the number of variables; also note that this effect could be even larger should the ridge regularization not be applied), the observed small effect size in the univariate analyses might be due to two additional factors. First, the current behavioural constructs (for example, hyperactivity, impulsivity and inattention of ADHD) might themselves hide heterogeneity, leading to reduced explanation of variance. Second, neural networks might not be homogenous (for example, despite a significant overall association of the motor inhibition network with hyperactivity across all 40 brain clusters (adjusted R 2 = 0.018), no cluster survived correction for multiple comparisons; Supplementary Table 3a). This is in striking contrast with the greater homogeneity of the reward anticipation network, for which six out of 46 brain clusters were in significant association with hyperactivity (Table 3 and Supplementary Table 2), despite smaller overall explained variance (adjusted R 2 = 0.013). Thus, the reduced effect size may highlight the heterogeneity of behavioural components as well as neural networks.
Our approach provides a unified framework with which to investigate brain activity in reinforcement-related behaviour, enabling the characterization of shared and distinct functional brain activation patterns that underlie different externalizing symptoms. It also resulted in the identification of neural signatures that may help to stratify these symptoms, while accounting for clinically observed comorbidity. female-to-male ratio = 783/723) from the baseline assessment of the IMAGEN sample were included in the analyses. Of the 1,506 participants investigated in this study, clinical DAWBA ratings were available from 1,190 individuals. Of these individuals, 131 had one or more diagnoses: 33 individuals were diagnosed with ADHD, 59 had emotional problems, 12 had anxiety (general + other) and 33 had depression (major + other). Detailed descriptions of this study have previously been published 4 . Gender, handedness and imaging sites were regressed out before the canonical correlation analyses were conducted, and for the rest of the analyses.

SDQ and DAWBA.
The SDQ 45 is a brief 25-item behavioural screening tool probing hyperactivity, emotional symptoms, conduct problems, peer problems and prosocial behaviour in 3-to 16-year-old children. In the current study, we chose parent-rated hyperactivity (five items) and conduct problems (five items) to represent externalizing problems, and child-rated emotional problems (five items) to represent internalizing problems (Table 1). This choice was based on findings that externalizing problems scores from parents are more reliable than those from children themselves, and vice versa 46 .
In DAWBA 47 , similar to SDQ, parent-rated ADHD and ODD/CD items, as well as child-rated specific phobia, social phobia, general anxiety, fear and depression items (Table 1), were included in the analyses. fMRI data acquisition and analysis. Structural and functional MRI data were acquired at eight IMAGEN assessment sites with 3T MRI scanners from different manufacturers (Siemens, Philips, General Electric and Bruker). The scanning variables were specifically chosen to be compatible with all scanners. The same scanning protocol was used at all sites. In brief, high-resolution T1-weighted three-dimensional structural images were acquired for anatomical localization and co-registration with the functional time series. BOLD functional images were acquired with a gradient-echo, echo-planar imaging sequence. For all tasks, 300 volumes were acquired for each participant, and each volume consisted of 40 slices aligned to the anterior commission/posterior commission line (2.4-mm slice thickness; 1 mm gap). The echo time was optimized (echo time = 30 ms; repetition time = 2,200 ms) to provide reliable imaging of subcortical areas.
Functional MRI data were analysed with SPM8 (http://www.fil.ion.ucl.ac. uk/spm). Spatial pre-processing included: slice time correction to adjust for time differences due to multi-slice imaging acquisition; realignment to the first volume in line; nonlinear warping to the MNI (Montreal Neurological Institute) space (based on a custom echo-planar imaging template (53 × 63 × 46 voxels) created out of an average of the mean images of 400 adolescents); resampling at a resolution of 3 × 3 × 3 mm 3 ; and smoothing with an isotropic Gaussian kernel a full width at halfmaximum value of 5 mm.
At the first level of analysis, changes in the BOLD response for each subject were assessed by linear combinations of experimental conditions at the individual subject level. For each experimental condition (for example, the large win condition during the anticipation phase of the MID task), each trial was convolved with the haemodynamic response function to form regressors that accounted for potential noise variance (for example, head movement) associated with the processing of reward anticipation. Estimated movement parameters were added to the design matrix in the form of 18 additional columns (three translations, three rotations, three quadratic translations and three cubic translations, plus a shift of ±1 TR (repetition time) for each translation).
For the MID task anticipation phase, we contrasted brain activation during anticipation of a large win (represented by a circle with three horizontal lines in Fig. 1 and Extended Data Fig. 5) versus anticipation of no win (represented by ResouRce NATuRE HuMAN BEHAvIouR a triangle in Fig. 1 and Extended Data Fig. 5). For the EFT, we contrasted brain activation during viewing of an angry face versus a viewing control (circles). For the SST, we contrasted brain activation during successful stop versus successful go. The single-subject contrast images were then used in the population-based weighted voxel co-activation network analysis.
MID task for fMRI. Participants performed a modified version of the MID task to examine neural responses to reward anticipation and reward outcome 20 . The task consisted of 66 10-s trials. In each trial, participants were presented with one of three cue shapes (250 ms) denoting whether a target (white square) would subsequently appear on the left or right side of the screen and whether zero, two or ten points could be won in that trial. After a variable delay (4,000-4,500 ms) of fixation on a white crosshair, participants were instructed to respond with a left or right button press as soon as the target appeared. Feedback on whether and how many points were won during the trial was presented for 1,450 ms after the response (Extended Data Fig. 5) 6 . Using a tracking algorithm, task difficulty (that is, target duration, which varied between 100 and 300 ms) was individually adjusted such that each participant successfully responded on ~66% of trials. Participants had first completed a practice session outside the scanner (~5 min), during which they were instructed that for each five points won they would receive one food snack in the form of small chocolate candies.
Based on previous research suggesting reliable associations between ADHD symptoms and fMRI BOLD responses measured during reward anticipation, the current study used the contrast of anticipation of a high win versus anticipation of no win. Only successfully hit trials were included here.

Emotional reactivity fMRI model (EFT).
This task was adapted from ref. 22 . Participants watched 18-s blocks of either a face video (depicting anger or neutrality) or a control stimulus (Extended Data Fig. 6) 22 . Each face video comprised a black and white video clip (200-500 ms) of a male or female face. Five blocks each of angry and neutral expressions were interleaved with nine blocks of the control stimulus. Each block contained eight trials of six face identities (three female). The same identities were used for the angry and neutral blocks. The control stimuli were black and white concentric circles expanding and contracting at various speeds that roughly matched the contrast and motion characteristics of the face clips.
The neutral blocks contained emotional expressions that were not attributable to any particular emotion (for example, nose twitching); however previous research has suggested that neutral stimuli are not always interpreted as such. Functional imaging studies have found significant activation of the amygdala in response to the presentation of neutral faces in healthy adult males 48 , patients with social anxiety and matched control participants 49 , adolescents with conduct disorder problems 50 and young men with violent behaviour problems 51 . This suggests that neutral faces may be interpreted as emotionally ambiguous. This study focused specifically on the effects of viewing angry faces (versus control faces) to eliminate this ambiguity so that any significant relationships between behaviour and brain activity could be interpreted as the consequence of viewing negative social stimuli (anger).

SST for fMRI.
Participants performed an event-related SST designed to study neural responses to successful and unsuccessful inhibitory control 21 . The task was composed of go trials and stop trials. During go trials (83%; 480 trials), participants were presented with arrows pointing either to the left or to the right. During these trials, subjects were instructed to make a button response with their left or right index finger corresponding to the direction of the arrow. In the unpredictable stop trials (17%; 80 trials), the arrows pointing left or right were followed (on average, 300 ms later) by arrows pointing upwards; participants were instructed to inhibit their motor responses during these trials (Extended Data Fig. 7) 52 . A tracking algorithm changed the time interval between go signal and stop signal onsets according to each subject's performance on previous trials (average percentage of inhibition over previous stop trials, recalculated after each stop trial), resulting in 50% successful and 50% unsuccessful inhibition trials. The inter-trial interval was 1,800 ms. The tracking algorithm of the task ensured that subjects were successful on 50% of stop trials and worked at the edge of their own inhibitory capacity.
Population-based WVCNA. The WVCNA 12,18 was applied to parcellate those highly co-activated voxels in all three fMRI contrasts (for example, the large win versus no win contrast anticipation phase of the MID task, the angry face versus control contrast of the EFT, and the successful stop versus successful go contrast of the SST. Such a parcellation procedure could effectively reduce the dimensionality without losing too much information. The procedure is summarized below. Pre-processing. For all three tasks, the initial pre-processing steps involved removing null voxels (including out-brain voxels based on an automated anatomical labelling template) and potential participant outliers from the contrast data based on low inter-sample correlations. The activation maps of pre-processed data were then generated, and only those positive activations with at least a medium effect size (that is, Cohen's D > 0.3; see the following section for more details) were included in the following analyses.
Parameter selection. To minimize the arbitrary choice of parameters, we took the default and suggested settings of the R package WGCNA 53 , except for the soft thresholds of adjacency matrices, which were determined as seven for the MID task, eight for the EFT and seven for the SST, based on the fitness of scale-free topology criteria (Extended Data Fig. 8). The above adjacency matrices were then used to generate the topology overlapping matrices, which captured both the direct and indirect connections among voxels. The hierarchical clustering was then applied on the distance matrices as 1 minus the topology overlapping matrices and, together with the dynamic cut-tree function, the fMRI modules were generated as functional ROIs. The first principle component of each module was included in the following analysis to represent brain activation (or BOLD response). No merge of modules was conducted after the hierarchical clustering to avoid using an arbitrary threshold.
Effect size threshold for brain activation. Cohen's D was defined as β 1 Àβ 2 σpooled I . Cohen proposed (reluctantly) to use Cohen's D = 0.5 for a two-sample t-test, as well as an alternative option of using the correlation coefficient r = 0.3 as the threshold for a median effect size 27 . As pointed out by Cohen, these two effect sizes (that is, D and r) could be mutually transformed (that is, a two-sample t-test could alternatively be understood as testing for a correlation between the group label and the pooled sample) so that (in case the variances are equal in both groups and the total sample is N): where t is the t statistic and k is determined by the percentage of each group in the full sample (that is, p and q, respectively) as ffiffiffiffiffiffiffiffiffi ffi 1=pq p I , for which the minimum value 2 is acquired when the sample sizes are equal in both groups (that is, p = q). A clear difference between D and r in a two-sample t-test could therefore be readily understood as while the achieved statistical power depends on the exact sample size in each group for Cohen's D, the achieved statistical power of r (that is, the correlation coefficient) only depends on the full sample size. Therefore, the proposed thresholds for median effect size (that is, D = 0.5 and r = 0.3) are not equivalent, and r = 0.3 is more stringent than D = 0.5 (r ≤ 0.243 depending on the exact sample size in each group). This highlights the fact that the choice of a threshold for effect size is flexible in certain ways, if not completely arbitrary.
However, in the case of a one-sample t-test with the same definition of D, the relationship between the t statistic and effect size D now changes to t ffiffiffi Therefore, Cohen's D in a one-sample t-test shares a similar relationship to the achieved statistical power with the correlation coefficient r in a two-sample t-test in that only the total sample size matters. Therefore, to achieve the same statistical power as for r = 0.30 (that is, the threshold of the median effect size) with the same sample size, the equivalent Cohen's D of a one-sample t-test could be calculated as 0.32. In addition, Cohen 27 also discussed the differences in Cohen's D between two-sample and one-sample t-tests (case 3 in chapter 2). He suggested using the transformation D 1�sample ¼ D 2�sample = ffiffi ffi 2 p I to re-calculate the critical values for the one-sample t-test, for which the corresponding threshold of the median effect size is therefore D = 0.35. However, this transformation aims to achieve equal statistical power between the one-sample and two-sample t-tests on the condition that the sample size in the one-sample t-test is half of that in the two-sample t-test, with balanced sample sizes in both groups.
Despite alternative strategies in calculation, both thresholds are indeed similar; therefore, we used Cohen's D = 0.30 as the threshold of the median effect size for a one-sample t-test, which is agreeable with both calculations when keeping one decimal. RCCA. Canonical correlation analyses (CCAs) have been widely used to investigate the overall correlation between two sets of variables 54 . However, in our case, due to high intra-correlations in both brain fMRI networks and behavioural items, multicollinearity was a potential risk factor that could jeopardize the validity of following statistical inference. Therefore, we adopted the RCCA proposed by ref. 19 , where two ridge-regularization parameters, λ x and λ y , are added to the diagonals of corresponding covariance matrices to avoid the singularity.
As our purposes were not to maximize the power of prediction, instead of estimating the optimal regulation parameters 55 , we fixed the regulation parameters across all analyses. Although multiple predefined regulation parameters were investigated (that is, 0.1, 0.2, 0.3, 0.4 and 0.5) for both λ values, the significance of major results was consistent throughout all settings (Extended Data Fig. 3); therefore, we simply report the P values and relevant statistics based on the regulation parameter 0.1. It is also noteworthy that optimization of the regulation parameter almost surely invalidates any attempt to calculate internalized P values through the permutation test, unless the optimization procedure is also permuted, which is very difficult (if not impossible) due to the extremely high computational demands of optimization at each iteration. It should also be noted that current optimization procedures of CCA-related approaches focus on maximizing the prediction power for the first component and are therefore not a real optimum for our purpose of evaluating the overall correlation described below.

NATuRE HuMAN BEHAvIouR
RCCA was then applied on two sets of standardized variables to investigate their overall correlation. For each correlation, the P value or significance level was determined using permutation tests, where the individual IDs of behaviour items were randomly shuffled at each iteration to generate the null distribution of statistics of interest. Particularly, we used the eta square (η 2 ) to represent the proportion of mutually explained variance between the two sets of variables. This is analogous to the R 2 value (that is, the coefficient of determination) in a multiple linear model. η 2 was defined as 1 − λ Wilks , where λ Wilks (Wilks's lambda) is a commonly used effect size in CCA 56 and could be calculated as the multiplication of unexplained variance for the correlation of each pair of components: denotes the squared correlation (that is, the mutually explained variance) between the ith pair of RCCA components, and k denotes the total number of CCA components for each set of variables. Note that η 2 , similar to R 2 , increased when more variables were included in the CCA, even if all of these variables were completely irrelevant. Therefore, we further included an adjusted η 2 (analogous to the adjusted R 2 ) to correct for the inflation in η 2 caused by the increased number of variables as: where η 2 0 I represents the expected η 2 under the null hypothesis that there is no relationship between the two sets of variables (that is, it acts as a measure of inflation in η 2 ), and can be directly estimated through the permutation test. Clearly, η 2 adj I is a monotonic increasing function of η 2 , where η 2 adj I tends to 0 when η 2 ! η 2 0 I , and to 1 when η 2 → 1.

Comparison of related associations/correlations through permutation.
To compare two correlations, a Fisher's transformation is normally applied to first normalize the distributions of correlations. The transformed correlations, now following the normal distribution, can then be compared directly, and the corresponding differences should also follow a normal distribution 59 . However, estimation of the variance of such a difference should properly consider the relationship of variables involved in calculating the correlations. For example, in the present paper, we are interested in the difference between two correlations that share one variable in common (that is, in the form of cor(A,B) versus cor(A,C). While the analytical solution of the variance estimation for the above case has been extensively investigated in the past 60-62 , we additionally implemented the permutation process to empirically investigate the variance, which is not only known to be robust even if the normality assumption has been violated, but also enables us to investigate multiple comparisons together, where the variance of summed absolute differences under the null hypothesis could be directly estimated through the permutation process.
In the present paper, we directly calculated the P value (which was determined by the underlying variance) of the observed summed absolute difference through a permutation process as the chance of randomly observing (that is, at each permutation iteration) a summed absolute difference larger than the original observation. For comparison purposes, we included the results from Steiger's test 61 in the relevant tables, which were highly similar to the results using the permutation test.
Equivalence test. Whenever a null result was observed from a statistical test, no meaningful statistical inference could be drawn unless a proper test was conducted to show that the observed non-significant effect size was indeed smaller than a meaningful threshold. In the present study, we adopted the equivalence test through a 'two one-sided test' procedure 26 in which the observed effect size was tested against a lower equivalence bound (with a null hypothesis that the observed effect size was lower than this lower bound) and an upper equivalence bound (with a null hypothesis that the observed effect size was larger than this upper bound). If both tests were significant, we could then conclude that the observed effect size was statistically smaller than a meaningful one; hence, in a sense, equivalent to zero. In cases in which we were only interested in a one-tailed test (for example, we were only interested in a positive correlation or R 2 ), it was "also possible to test for inferiority, or the hypothesis that the effect is smaller than an upper equivalence bound, by setting the lower equivalence bound to ∞" 26 . This strategy was generally applicable even without knowledge of the exact distribution of the observed effect size (such as in the RCCA), for which the confidence interval could be established based on variance estimated through methods such as bootstrap or jackknife.
Equivalence test for the first eigenvalue of RCCA. Due to the fact that correlations between RCCA components are forced non-negative, a test for the first eigenvalue is equivalent to that for the correlation (for which the square is also known as Roy's largest root) between the first pair of components in the RCCA. We therefore only tested for inferiority in the corresponding equivalence test (that is, where Z L was set as to −∞ and Z U (that is, Z Fisher , Fisher's r-to-z transformed correlation) was calculated as the inflated Z Fisher0 between the first components of the RCCA under the null hypothesis (estimated through permutation) plus a small effect size, q = 0.1, suggested by Cohen (that is, the difference between two Fisher-transformed correlations, known as Cohen's q 27 ). The standard deviation (σ z ) of the observed Z Fisher could be estimated through jackknife 57,58 , and the corresponding t statistic for the one-tailed test could be calculated as t = (Z Fisher Equivalence test for comparison of related correlations. Similar to above, the corresponding lower and upper equivalence bounds (ΔZ L and ΔZ U ) of Fisher's r-to-z transformed correlation Z Fisher were set as −0.1 and 0.1, to represent a tiny effect size (Cohen's D = 0.1). The variance σ 2 Z À Á I of the observed Z Fisher was estimated through jackknife, and the corresponding t statistics of one-tailed tests for the lower and upper bounds could be given as (0.1 + Z Fisher )/σ Z and (Z Fisher − 0.1)/σ Z , respectively.
Data distribution assumptions. Normality assumptions were made for all regression or correlation coefficients where either t statistic or F statistic test was applied. While the normality assumption was not formally tested, it has been guaranteed by the central limit theorem given the large sample in the present data 63 . For the RCCA-related analyses, no assumption for data distribution was made as the null distributions were estimated directly through permutation.
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October 2018
Corresponding author(s): Gunter Schumann Last updated by author(s): Jan 14, 2020 Reporting Summary Nature Research wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency in reporting. For further information on Nature Research policies, see Authors & Referees and the Editorial Policy Checklist.

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Describe the software used to collect and analyze the flow cytometry data. For custom code that has been deposited into a community repository, provide accession details. Design specifications MID: The task consisted of 66 10-second trials. In each trial, participants were presented with one of three cue shapes (cue, 250 ms) denoting whether a target (white square) would subsequently appear on the left or right side of the screen and whether 0, 2 or 10 points could be won in that trial. After a variable delay (4,000-4,500 ms) of fixation on a white crosshair, participants were instructed to respond with left/right button-press as soon as the target appeared. Feedback on whether and how many points were won during the trial was presented for 1,450 ms after the response. with arrows pointing either to the left or to the right. During these trials, subjects were instructed to make a button response with their left or right index finger corresponding to the direction of the arrow. In the unpredictable Stop trials (17%; 80 trials), the arrows pointing left or right were followed (on average 300 ms later) by arrows pointing upwards; participants were instructed to inhibit their motor responses during these trials.

Cell population abundance
EFT: Participants watched 18-second blocks of either a face movie (depicting anger or neutrality) or a control stimulus. Each face movie showed black and white video clips (200-500ms) of male or female faces. Five blocks each of angry and neutral expressions were interleaved with nine blocks of the control stimulus. Each block contained eight trials of 6 face identities (3 female). The same identities were used for the angry and neutral blocks. The control stimuli were black and white concentric circles expanding and contracting at various speeds that roughly matched the contrast and motion characteristics of the face clips.
Behavioral performance measures For both event related tasks MID and SST, performance tracking systems were implemented to adjust difficulty of the tasks to ensure the overall performance of each participant (i.e. successfully responded on ~66% of trials in the MID and 50% successful rate in inhibition trials in the SST). As a passive viewing task, there is no performance measure for the EFT.

Acquisition
Imaging type(s) BOLD  Functional MRI data were analysed with SPM8 (Statistical Parametric Mapping, http://www.fil.ion.ucl.ac.uk/spm). Spatial preprocessing included: slice time correction to adjust for time differences due to multi-slice imaging acquisition, realignment to the first volume in line, non-linearly warping to the MNI space (based on a custom EPI template (53x63x46 voxels) created out of an average of the mean images of 400 adolescents), resampling at a resolution of 3x3x3mm3 and smoothing with an isotropic Gaussian kernel of 5 mm full-width at half-maximum. Normalization see above Normalization template see above

Noise and artifact removal
At the first level of analysis, changes in the BOLD response for each subject were assessed by linear combinations at the individual subject level, for each experimental condition (e.g. reward anticipation high gain of Monetary Incentive Delay (MID) task), each trial was convolved with the hemodynamic response function to form regressors that account for potential noise variance, e.g. head movement, associated with the processing of reward anticipation. Estimated movement parameters were added to the design matrix in the form of 18 additional columns (three translations, three rotations, three quadratic and three cubic translations, and every three translations with a shift of ±1 TR).

Statistical modeling & inference
Model type and settings At the first level of analysis, changes in the BOLD response for each subject were assessed by linear combinations at the individual subject level. For the second level analysis, we establish the following contrasts: For the MID anticipation phase we contrasted brain activation during 'anticipation of high win [here signaled by a circle] vs anticipation of no-win [here signaled by a triangle]'; For the emotional faces task (EFT) we contrasted brain activation during 'viewing Angry Face vs viewing Control [circles]'; For the stop signal task (SST) we contrasted brain activation during 'successful stop vs successful go'. The single-subject contrast images were then taken to the population-based weighted co-activation network analysis.

Effect(s) tested
For the activations of each contrast, the one-sample t-test was applied for each voxel.
Specify type of analysis: Whole brain ROI-based Both Statistic type for inference (See Eklund et al. 2016) Ridge-restricted canonical correlation analysis (RCCA) was applied to detect the overall correlation between fMRI clusters generated from WVCNA and internalising/externalising behaviours.