The LEGO theory of the developing functional connectome

Decades of human magnetic resonance imaging (MRI) research demonstrate that variance in neuroimaging phenotypes, including functional connectivity, relate to genetics 1–5 and predict cognitive traits 6–9 . The functional connectome affords information transmission through the brain at various spatial scales, from global oscillations between broad cortical regions to fine-scale connections that underlie specific information processing 10,11 . In adults, while both the coarse-and fine-scale functional connectomes predict cognition 6,12–14 , the fine-scale connectome predicts twice as much cognitive variance 15 . Yet, past brain-wide association studies, particularly using large developmental samples, have limited their focus to the coarse connectome to understand the neural underpinnings of individual differences in cognition 8,9,16–18 . We studied resting-state fMRI in 1,115 children (including 389 twin pairs) and used functional alignment to afford access to individual differences in the fine-scale connectome 10,19,20 . We found that even though individual differences in the fine-scale connectome are more reliable than those in the coarse-scale connectome, they are less heritable. This surprising result indicates that genetically-determined versus experience-dependent factors in brain development have dissociable effects on these two spatial scales of the connectome. We show further that both connectome scales equally predict a more heritable trait (general cognitive ability) in childhood, but only the fine scale effectively predicts a more experience-driven trait (learning/memory). As such, the developing functional connectome resembles a LEGO Ⓡ set: the specific pieces a child has parameterizes what they will eventually build, but even when given identical sets, two children with unique experiences will build different creations. Prior alignment for individual differences 10,15,20,47 , the developmental 8,17 Recent massive numbers of subjects to reliably associate brain phenotypes with behavior, in developmental cohorts 16 . We show that hyperalignment and connectome granularity analyses are powerful tools for understanding these individual differences, without the need for thousands of individuals and data points for model cross-validation – our hyperalignment model was learned on 200 subjects and tested entirely on resting-state data, with less than 20 minutes per subject. Further, it was trained and tested on independent subjects to assure that increased reliability was driven by generalizable, shared signals rather than overfitting to subject-specific signals. Though statistically significant, our predictions accounted for relatively low variance in behavioral measures relative to similar studies in adults 6,14,15 . Task-based functional connectivity is often more stable and predictive of behavior than RSFC among adults 13,15 , but this is only with a sufficient amount of high-quality task data, which is known to be difficult to collect in children 35,48 . Individual differences in RSFC appear to be reliable in the ABCD dataset 17 , whereas the task fMRI has known reliability limitations 13 . Previous studies have shown that both the ABCD task and resting whole-brain coarse FC can predict individual cognitive measures such as the toolbox tasks 9 , with lower accuracy for the tasks comprising the learning/memory component than the general cognitive ability. and MR incidental findings were excluded from the present analysis.


Introduction
connectivity weight between the average pattern of a given parcel and those of each other parcel in the brain.

Establishing reliable connectomes
Variability in RSFC can reflect idiosyncrasies driven by cortical communication patterns indicative of neurocognitive variability, but it can also reflect artifacts due to data acquisition noise, movement, and functional-anatomical mismatch. In adult populations, brain parcellations (e.g. Glasser parcellation 40 ) average adjacent areas of cortex to improve signal-to-noise and reduce the dimensionality of the data. This approach assumes functional-anatomical correspondence will improve at the group level and comes at the cost of lower granularity.
Here, we analyze RSFC between subjects (see Table S1 for subject breakdown) using two methods of group alignment. The first uses a standard approach to align data in a common space based on anatomical location (anatomical alignment [AA]), while the second approach uses connectivity hyperalignment (CHA) 19 to learn a representational space based on common patterns of functional connectivity via an adapted Generalized Procrustes Analysis (see Methods for details). CHA allows for local remixing of vertex-wise functional connectivity patterns within an anatomically-constrained region 20 , thereby aligning common patterns of fine-scale information within broader regions of interest by removing idiosyncrasies caused by noise or functional-anatomical correspondence 10 . In contrast with coarse alignment, which averages across the region and can diminish differences across subjects, CHA affords fine-scale functional alignment: projecting all of the region's information patterns into high-dimensional common space to align information across subjects based on functional instead of anatomical information . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. topographies ( Figure 1B). Within this common space, individual differences in functional connectivity become more pronounced and reliable 39 , particularly at the fine-scale representational level, and are better predictive of cognitive traits 15 in adults. In contrast, previous studies have applied a reduced-dimensional hyperalignment algorithm (shared response model) to align child brain responses to an adult-defined common model as the two groups performed the same task 41 . To address the question of individual differences in fine-scale functional connectivity among children, we present (to our knowledge) the first derivation of a child-defined and applied model of shared brain function, which negates concerns about differences in cortical development or anatomy conflating functional connectivity patterns. We then address the relative effects of functional alignment versus simply higher-dimensional measurements by averaging the functionally-aligned CHA data and by retaining the high-dimensional, anatomically aligned data, to have a full comparison of AA coarse, AA fine, CHA coarse, and CHA fine-scale connectomes.
Our first analysis looks at the reliability of idiosyncrasies in functional connectivity patterns across connectome alignment and granularity. Here, idiosyncrasies are defined as how similar a subject's connectome is to their own connectome across split-halves, relative to their similarity to all other subjects. CHA, particularly at the fine scale, improves the reliability of functional connectivity over anatomical alignment alone ( Figure 2). Across all parcels, reliability of coarse connectomes increased from an average of r=0.34 ± 0.1 for AA to r=0.58 ± 0.08 for CHA.
Reliability of fine connectomes increased from an average of r=0.43 ± 0.11 for AA to r=0.86 ± 0.07 for CHA. After CHA, 100% of parcels at both scales showed greater reliability, and 99% of parcels showed greater reliability at the fine scale than the coarse scale. Notably, all four types of . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022.

Figure 2. Reliability of individual differences in functional connectivity profiles
A. Procedure: The reliability of individual differences in functional connectivity profiles between regions (defined with the Glasser parcellation 40 ) was analyzed with data from 526 unrelated subjects. Subjects' timeseries data for each parcel were split into two halves, which were hyperaligned into the trained common space separately. For each region, split timeseries data pre-and post-hyperalignment were used to compute functional connectivity profiles at the fine and coarse scales. Then individual dissimilarity matrices (IDMs) were computed across all pairs . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ; https://doi.org/10.1101/2022.05.24.493295 doi: bioRxiv preprint of subjects. The IDMs for each split were then correlated (Pearson's r) to get a measure of the reliability of individual differences captured by the regional functional connectivity profiles, presented on the cortex for the coarse and fine scales before and after hyperalignment. This approach is a variation of the "fingerprinting" 14,42 approach, whereby measured individual differences are more reliable if a subject is more similar to themselves across split-halves than to any other subject. B. The reliability of individual differences increases after hyperalignment for all parcels. 99% of fine connectivity profiles (darker) are more reliable than coarse ones (lighter) regardless of alignment type. C. Bars presented as the average reliability (Pearson's r) across all parcels in the Glasser parcellation. Error bars represent ± standard deviation from the mean.

Genetic control over the coarse-scale connectome
Our reliability analysis revealed that the fine-scale connectome is more reliable within individuals than the coarse scale, and this is particularly salient after connectivity hyperalignment (HA). Given that the fine-scale CHA data reveal more reliable, idiosyncratic functional connectivity patterns than the coarse data, we hypothesized it would be less influenced by genetics. In other words, the broad anatomical alignment would reflect the heritability of cortical anatomy previously shown 1,36,37 , but the functional alignment would disentangle the fine-scale functional differences in connectivity information, reflecting more reliable, behaviorally-informative individual differences driven by unique life experiences.
The heritability analysis used RSFC data from 778 subjects comprising 219 dizygotic twin pairs and 170 monozygotic twin pairs (see breakdown in Table S1). Functional connectomes of vertex-granularity are an inherently high-dimensional phenotype. To explicitly model the heritability of this phenotype, we used a multidimensional estimate of heritability 32 to model both the phenotypic similarity matrix between participants as well as the genetic kinship matrix (see Multidimensional heritability estimate for more information). As predicted, we find differential heritability according to the alignment and granularity of functional connectomes, where 99.6% . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ; https://doi.org/10.1101/2022.05.24.493295 doi: bioRxiv preprint percent of parcels are more heritable at the coarse scale than the fine scale (p<0.01) (Figure 3).
At the coarse scale, anatomically-aligned functional connectomes are significantly more . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. Heritability of functional connectivity profiles between regions (defined with the Glasser parcellation 40 ) was estimated using a multidimensional heritability model 32 using resting-state fMRI data from 778 9-10 year-olds (170 MZ pairs and 219 DZ pairs). Functional connectivity between a given parcel and all other parcels in the brain was calculated at fine and coarse granularities, before and after functional alignment. The coarse-grained connectivity profiles aligned based on cortical anatomy are the most heritable. B. For both anatomically-aligned and . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ; hyperaligned data, connectivity profiles are more heritable when calculated at the coarse scale than the fine scale (99.6 percent of the time). C. At the coarse scale, the anatomically aligned connectivity profiles are more heritable than the hyperaligned ones; this distinction dissipates at the fine scale, which is under comparatively minuscule genetic control. Bars presented as the mean heritability across all parcels in the Glasser parcellation and error bars presented as standard deviation.

Prediction of neurocognitive abilities
Having established that the coarse, anatomically-aligned functional connectome is under strong genetic control and that all connectomes showed reliability, we sought to demonstrate their functional significance by teasing apart connectome granularity as it relates to heritability versus behaviorally-relevant idiosyncrasies. Compared with brain structure, complex psychological traits are less heritable, but cognitive abilities are among the most heritable dimensions of human behavior 43 . Heritability of these traits vary by cognitive domain with higher estimates reported for general cognitive ability (h 2 = .67-.80) than for learning/memory (h 2 = .36-.56) 44 , which may be more sensitive to experiential factors. We leveraged this variation in heritability of cognitive traits to examine the functional significance of our heritability and reliability findings. General cognitive ability and learning/memory scores were defined based on previously reported principal components analysis of the NIH Toolbox tasks used in the ABCD study 45 . Because learning/memory is less heritable than general cognitive ability, we can compare variation in connectome heritability on prediction of cognitive phenotypes 44 . Since CHA improves reliability of individual differences in the fine-scale connectome, we expected CHA fine connectomes generally to be more predictive of cognitive performance (i.e., both general cognitive ability and learning/memory) than either CHA coarse, AA coarse or fine connectomes. Moreover, we expected the most heritable connectivity information (i.e., AA coarse) to better predict a more heritable cognitive ability (general ability) relative to a less heritable trait (learning/memory).
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ; We used PCA ridge regression to predict scores on these two cognitive domains from connectivity profiles at each scale. Models were scored as R 2 between predicted scores and true scores using nested cross-validation (see Neurocognition PC prediction analysis for more details), and significance of R 2 values were assessed with permutation tests (10,000 iterations per model). Model scores were compared across connectome types using 10,000 bootstrap iterations with resampling.
Overall, hyperaligned fine-scale connectomes best predicted individual differences in cognitive performance (i.e., both general cognitive ability and learning and memory). As hypothesized, the degree to which the coarse connectome also contributed to prediction was associated with the heritability of the trait. General cognitive ability has high heritability for a psychological trait (h 2 = .67-.80) 44 and was similarly predicted by CHA fine, AA coarse, and AA fine connectomes (average parcel R 2 ± s.d. across parcels; CHA fine = 0.0133 ± 0.021; AA fine = 0.0134 ± 0.020; AA coarse = 0.0124 ± 0.018; CHA fine vs. AA fine p = 0.30; CHA fine vs. AA coarse p = 0.23; AA fine vs. AA coarse p = 0.08) ( Figure 4). General cognitive ability was predicted with significantly lower accuracy by CHA coarse, suggesting that functionally aligning fine-scale information then smoothing over the functional information space actually diminishes the specificity of the information. After performing permutation tests at each parcel and thresholding at p < 0.01, 42%, 42.5%, 30.5%, and 43% of parcels predicted general cognitive ability significantly greater than chance at the AA coarse, AA fine, CHA coarse, and CHA fine scales respectively ( Figure S2A).
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made Learning/memory is regarded as a less heritable psychological trait (h 2 = .36-.56) 44 , so we hypothesized the heritable scaffolding of the connectome (AA coarse) would contribute less information to this prediction than to prediction of cognitive ability, and the trait would be predicted more strongly from the CHA fine connectome. As expected, prediction of learning/memory scores were significantly higher for the CHA fine connectome than for CHA coarse (CHA fine R 2 = 0.018 ± 0.012; CHA coarse R 2 = 0.011 ± 0.014; p < 0.0001), AA fine (0.008 ± 0.014; p = 0.09), or AA coarse (0.007 ± 0.014; p < 0.0001) ( Figure 4). The gap in the percentage of parcels surviving our permutation test was also more pronounced for this trait; 30%, 33%, 39%, and 61% for AA coarse, AA fine, CHA coarse, and CHA fine.
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ;

Figure 4: Prediction of neurocognitive PC loadings.
Distribution of R 2 values across all parcels for prediction of general cognitive ability (left) and learning/memory (right). Histogram heights correspond to density of scores and lines represent the mean of the score distribution. For the purpose of distribution matching, R 2 values are not thresholded here; thresholded R 2 values mapped to the cortical surface are displayed in Figure  S2.

Discussion
In this study, we sought to understand how individual differences are realized at different spatial scales of the developing connectome, and how the variability captured by connectome granularity relates to genetic control and cognitive traits. Prior work indicates that both coarse . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made and fine-scale functional connectivity predicts idiosyncrasies in cognitive phenotypes in adults [12][13][14][15] , and functional alignment (connectivity hyperalignment; CHA 19 ) improves access to this variability in the fine-scale connectome 15,39 . Yet, to date, studies have related functional connectivity in youth to individual differences in cognition or behavior by looking only at coarse scale information. This spatial averaging reduces dimensionality and smooths idiosyncratic anatomy across subjects. Using CHA, we reveal reliably idiosyncratic patterns of fine-scale functional connectivity in the developing brain. The coarse-scale connectome (AA coarse) shows moderately reliable idiosyncrasies (mean Pearson's r=0.34), versus the CHA fine connectome's mean reliability of r=0.86 ( Figure 2). Across the entire brain, individual differences in fine-scale connectivity are more reliable than in coarse-scale, indicating that the traditional coarse alignment approach diminishes the detailed, spatially-resolved topographies of information transfer in the developing brain.
By estimating the heritability of functional connectivity at each scale and alignment, we showed that idiosyncrasies in the fine-scale connectomes are dissociable from idiosyncrasies in the coarse scale connectome. Multiscale heritability analysis of coarse-scale, anatomically aligned connectomes attribute about 20% of variance to genetic relatedness, which converges with our expectations based on adult coarse RSFC estimates 21,22,32 and how neuroimaging phenotypes increase in heritability with age 1,3 . At the fine scale, our estimates drop to around 10% regardless of alignment technique, suggesting that at the fine scale, idiosyncrasies in connectivity are more related to experience than genetics.
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ; https://doi.org/10.1101/2022.05.24.493295 doi: bioRxiv preprint Individual differences captured by variable connectome granularity revealed a dissociation between the spatial scales of heritable and reliable patterns of functional connectivity. Our final analysis showed that this dissociation is also relevant in prediction of cognitive traits. Whereas both the most reliably idiosyncratic (CHA fine) and most heritable (AA coarse) connectomes were comparably predictive of general cognitive ability, a canonically heritable cognitive trait, the most reliably idiosyncratic connectome (CHA fine) was best predictive of a less heritable cognitive trait (learning/memory). Past studies using RSFC at a coarse scale from the ABCD dataset were only able to predict general cognitive ability and not learning/memory scores 8 . By improving the reliability of our data and accessing finer-scale information with CHA, we uncovered patterns of functional connectivity predictive of a more nuanced, experience-related cognitive trait (learning/memory).
Taken together, the link demonstrated here between reliable, heritable, and predictive scales of functional connectivity reveals the importance of nuanced, multi-scale connectivity analyses for building a holistic theory of individual differences during development. Consistent with the interactive specialization framework of functional brain development, the development of the functional connectome is not solely determined by a blueprint, but the interaction of a heritable template and individualized experience 46 . We present a novel approach to prediction of developing cognitive abilities from functional connectivity measured in different topographical representation spaces, by aligning information across brains based on functional alignment at high spatial resolution versus the traditional approach of coarse alignment (an adult-defined cortical atlas with averaging). Our study presents the first example of defining and applying a functional common space to a developmental cohort, negating the very issues that arise with . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made  10,15,20,47 , but it has remained underutilized in the developmental literature 8,17 . Recent work has recognized the need for massive numbers of subjects to reliably associate brain phenotypes with behavior, specifically in developmental cohorts 16 . We show that hyperalignment and connectome granularity analyses are powerful tools for understanding these individual differences, without the need for thousands of individuals and data points for model cross-validation -our hyperalignment model was learned on 200 subjects and tested entirely on resting-state data, with less than 20 minutes per subject. Further, it was trained and tested on independent subjects to assure that increased reliability was driven by generalizable, shared signals rather than overfitting to subject-specific signals. Though statistically significant, our predictions accounted for relatively low variance in behavioral measures relative to similar studies in adults 6,14,15 . Task-based functional connectivity is often more stable and predictive of behavior than RSFC among adults 13,15 , but this is only with a sufficient amount of high-quality task data, which is known to be difficult to collect in children 35,48 . Individual differences in RSFC appear to be reliable in the ABCD dataset 17 , whereas the task fMRI has known reliability limitations 13 . Previous studies have shown that both the ABCD task and resting whole-brain coarse FC can predict individual cognitive measures such as the toolbox tasks 9 , with lower accuracy for the tasks comprising the learning/memory component than the general cognitive ability.
With the substantial twin cohort, behavioral testing, and longitudinal neuroimaging data included in ABCD, future work could investigate the connection between heritability and predictivity of functional connectivity over time, as the heritability of both neurocognitive measures and . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made neuroimaging-based phenotypes increase with age 1,5,49,50 By breaking apart the pieces of the functional connectome into their coarse and fine structures, we can show how these scales snap together like LEGO pieces to scaffold and instantiate reliable idiosyncrasies in brain and behavior during development.

Participants
We considered data from the 11,875 children included in the Adolescent Brain Cognitive  27 . Their inclusion in the ABCD study affords unique access to the causal interrelation between genetics, environment, brain function, and cognition during development 1,5 .
The present study uses imaging and behavioral data from a subset of n=1,115 subjects from the original 11,875 subjects. Included subjects were enrolled in the University of Minnesota, Washington University in St. Louis, and University of Colorado-Boulder sites, which all use 3T . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made Siemens MRI scanners. We excluded Virginia Commonwealth University, the fourth Twin Site, as it uses a GE scanner, a potential confound in the current study 26 . ABCD study-wide exclusion criteria include a diagnosis of schizophrenia, moderate to severe autism spectrum disorder, intellectual disabilities, major and persistent neurological disorders, multiple sclerosis, sickle cell disease, seizure disorders like Lennox-Gastaut Syndrome, Dravet Syndrome, and Landau Kleffner Syndrome, or substance abuse disorders at time of recruitment. Subjects with mild autism spectrum diagnosis, history of epilepsy, traumatic brain injury, and MR incidental findings were excluded from the present analysis.

Resting state fMRI data collection
Structural and functional data from the three included sites were acquired using Siemens Prisma 3T scanners with a 32-channel head coil. Detailed acquisition parameters are previously described in the literature 26,51 . Scan sessions consisted of a high-resolution (1 mm 3 ) T1-weighted image, diffusion weighted images, T2-weighted spin echo images (1 mm 3 ), resting-state fMRI (rs-fMRI), and task-based fMRI. We utilized rs-fMRI solely in this study. rs-fMRI data were collected with an echo-planar imaging sequence with 2.4 mm voxels, TR = 800 ms, TE = 30 ms, and multiband slice acceleration factor = 6. Participants completed up to four runs of 5-minute resting state scans. Framewise integrated real-time MRI monitoring (FIRMM 52 ) was used to monitor subject head motion during data collection, and scan operators may have stopped resting-state data collection after three runs if 12.5 min of low-motion resting-state data had been collected.
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made Additional exclusions were made based on poor structural scan quality (determined with curated data release 2.0.1 sheet freesqc01.txt) or low quality/high motion resting state fMRI (determined as a score of zero for fsqc_qc or greater than one for fsqc_qu_motion, fsqc_qu_pialover, fsqc_qu_wmunder, or fsqc_qu_inhomohgeneity), as reported in prior studies 18  twins, and 337 singletons. All twin pairs were same-sex, and all subjects were between 9 and 10 years old. Included singletons were also balanced for ancestry, ethnicity, sex, and pubertal development with twins (Table S1). was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made

2021), which is based on the Human Connectome Project (HCP) Minimal Preprocessing
Pipeline 56 with additional modifications specifically for the ABCD dataset and summarized below.
The first stage of the pipeline, PreFreeSurfer, performs brain extraction, alignment, and N4 bias field correction on the T1w and T2w images. The second stage, FreeSurfer 57,58 , segments the resulting T1w images and identifies tissue boundaries to register to a FreeSurfer template and produces brain masks. The third stage, PostFreeSurfer, uses the brain masks to register T1w images to MNI space using ANTs symmetric image normalization method 59 . Surfaces are then transformed to standard space using spherical registration and converted to CIFTI format along with the standardized brain volumes. The fMRIVolume stage performs functional image distortion correction using reverse phase-encoded spin echo images to correct for local field inhomogeneities. Eta squared values are computed for each image to a participant-level average of all field maps, and the pair with the highest value (i.e., most representative of the average) was selected to avoid potential motion confounds. Finally, the fMRISurface stage performs 2-mm full-width half-max spatial smoothing.
DCAN BOLD Processing 60 is used to perform standard data processing. First, fMRI data are demeaned and detrended with respect to time. Covariates of no interest were regressed from the data, including mean white matter, cerebrospinal fluid, overall global signal, mean grayordinate timeseries, and 6-movement variables (X,Y,Z translation and roll, pitch, yaw rotation).
Timeseries data are then band-pass filtered between 0.008 and 0.09 Hz using a 2nd order Butterworth filter. Data is then filtered for respiratory motion for the frequencies (18,582 to . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ; https://doi.org/10.1101/2022.05.24.493295 doi: bioRxiv preprint 25.726 breaths per minute) of the respiratory signal, which has been shown to improve the stability of framewise displacement (FD) estimates 61 . "Bad" frames, where motion exceeds FD of 0.3 mm, are removed when demeaning and detrending such that denoising betas are only calculated for "good" frames. For the band-pass filtering, interpolation is used to replace those frames, so that pre-processing of the timeseries only includes "good" data but avoids aliasing due to missing timepoints. Finally, the filtered timeseries are normalized and concatenated across runs. The derivatives used in this analysis are *ses-baselineYear1Arm1_task-rest_bold_desc-filtered_timeseries.dtseries.nii.

Connectivity hyperalignment
We used connectivity hyperalignment 19 to functionally-align fine-scale connectivity information across subjects. Given the small quantity (1480 ± 142 TRs; mean±std) of resting state fMRI data available per subject, we chose to train the hyperalignment model common space using a cohort of 200 subjects who were then excluded from further analysis. These 200 training subjects were singletons enrolled at one of the three included sites and were matched with twin subjects on gender, pubertal development, age, and race/ethnicity (Table S1). The remaining 915 subjects (including the 389 twin pairs and 137 singletons) were used for subsequent analyses. Crucially, the hyperalignment model space never saw data from any subjects included in analyses during training.
We followed the same connectivity hyperalignment procedure for whole-cortex parcellation data as in our previous study 62 . We used the average timeseries for each of the 360 regions in the Glasser cortical parcellation 40 as connectivity targets and the vertices in each parcel as . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. We derived invertible transformation matrices for the remaining subjects' connectomes into the model space to map vertex timeseries from the anatomically-defined dimensions into the functionally-defined dimensions.

Functional connectivity profiles
After aligning the test data into a common functional space, we used functional connectivity profiles to summarize a brain region's correlation with the rest of the cortex. We defined fine-scale functional connectivity profiles as above, as the correlation between the timeseries of all 59,412 vertices in the cortex with the average timeseries of each parcel, resulting in a matrix of 59,412 by 360 correlation coefficients per subject. We also defined coarse-scale functional connectivity profiles as the correlation between the average timeseries for all pairs of parcels, . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ; https://doi.org/10.1101/2022.05.24.493295 doi: bioRxiv preprint resulting in a matrix of 360 by 360 correlation coefficients per subject ( Figure 1B). The fine-scale and coarse-scale connectomes were computed on data pre-and post-hyperalignment for each subject to evaluate the effect of functional alignment and connectome granularity on heritability, reliability, and predictivity.

Reliability
Given the high levels of noise and low reliability associated with developmental neuroimaging data 35,48,[63][64][65] as well as smaller (vertex-resolution) connectivity seeds 11 , we used hyperalignment to improve the reliability of individual differences in our data. That is, by finding a space that aligns patterns of functional connectivity across subjects (within anatomically constrained parcels), we correct more thoroughly for anatomical variability and improve access to reliable individual differences 10,47 We calculated the reliability of functional connectomes before and after hyperalignment as follows. For 526 unrelated subjects, we computed fine-scale functional connectomes from split-half timeseries (742 ± 71 TRs). We derived transformation matrices to rotate these connectomes into the common space separately, then aligned the split timeseries data using those transformations. We then computed functional connectivity profiles, as explained above, for each half separately. For each parcel at the fine and coarse scale separately, we used the vectorized functional connectivity profiles before and after hyperalignment and computed individual differences matrices (IDM) for each data split. These are subject-by-subject pairwise dissimilarity matrices, where each value in the matrix is the correlation distance (1 -Pearson's r) between two subjects' regional connectivity profiles. After computing IDMs, we took the upper triangle of the IDM and correlated them (Pearson's r) to measure the reliability of the individual differences in the functional connectomes across the split halves 39 . This metric reflects the . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ; https://doi.org/10.1101/2022.05.24.493295 doi: bioRxiv preprint reliability of the idiosyncrasies in a subject's functional connectomes, where subjects are more similar to themselves across split halves than they are to any other subject. We used a Mantel test 66,67 to perform statistical tests on IDMs with 10,000 permutations.

Multidimensional heritability estimation
Functional connectomes at vertex-granularity are an inherently high-dimensional phenotype; when dimensionality of the phenotype is collapsed, the reliability of individual differences decreases 39 . To offer greater statistical power in analyzing the heritability of this high-dimensional phenotype, we used a multidimensional estimate of heritability 32,68 to summarize the degree to which functional connectivity profiles for each parcel are under genetic control. We also investigated whether the alignment and granularity of the connectomes impact their heritability, which would indicate that the information highlighted by that type of connectome calculation is differentially impacted by genetics. Genetic kinship was estimated with SOLAR Kinship2 69 .

Neurocognition PC prediction analysis
Neurocognition principal components (neurocog PCs) 45 were derived from the neurocognitive battery included in the ABCD study. The neurocognitive battery includes the NIH Toolbox cognition measures covering episodic memory, executive function, attention, working memory, processing speed, and language abilities. The neurocog PCs were derived with a Bayesian Probabilistic Principal Components Analysis, which revealed a three-component solution. The three components roughly corresponded to general cognitive ability, executive function, and learning/memory. Since the NIH Toolbox tasks that canonically measure executive function did . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made  Figure S1A), as well as with Falconer's Formula 70 ( Figure S1B).
We predicted loadings onto the neurocognition principal components based on functional connectivity from our cohort of 526 unrelated subjects using a principal component ridge regression adapted from our previous study 62 . First, we used principal components analysis (PCA) to train principal components (PCs) to capture the main orthogonal dimensions along which individuals' connectivity profiles differ from one another. We then trained a ridge regression model to predict learning and memory scores from these PC scores, and tested the PCA and ridge regression models by predicting the learning and memory score of the held-out subjects. Model parameters (number of PCs and regularization parameter ɑ) were chosen with nested cross-validation using three sub-folds. Candidate model parameters were distributed evenly on a logarithmic scale, from 10 to 320 PCs and no PCs (no dimensionality reduction), and ɑ chosen from 121 values between 10 -20 to 10 40 . Models were evaluated using the cross-validated coefficient of determination R 2 , which shows the percent of variance in learning and memory scores accounted for by the prediction models. To assess statistical significance of model . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ; performance against chance, we used permutation testing with 1000 iterations of shuffling the behavioral scores.

Data availability
The ABCD study is longitudinal, so the data repository changes over time and can be found here: https://nda.nih.gov/abcd. In the current study, we used the ABCD data release 2.0.1, downloaded via ABCD-BIDS Community Collection 71 NDA Collection 3165.

Code availability
ABCD data preprocessing code can be found here: https://github.com/DCAN-Labs/abcd-hcp-pipeline. ABCD data processing code can be found here: https://github.com/DCAN-Labs/dcan_bold_processing. Code for running the multiscale heritability analysis can be found here: https://github.com/kevmanderson/h2_multi. Code for running the nested PCA ridge regression was based off: https://github.com/feilong/IDM_pred. All analysis code specific to this study will be released upon publication. Health and additional federal partners under award numbers U01DA041048,   U01DA050989, U01DA051016, U01DA041022, U01DA051018, U01DA051037,   U01DA050987, U01DA041174, U01DA041106, U01DA041117, U01DA041028 . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made

Institutes of
The copyright holder for this preprint (which this version posted May 24, 2022. ; https://doi.org/10.1101/2022.05.24.493295 doi: bioRxiv preprint was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made

Supplemental tables and figures
The copyright holder for this preprint (which this version posted May 24, 2022. ; Figure S1: Heritability of general cognitive ability and learning/memory loadings. Left: Heritability estimated with SOLAR Polygenic (covariate tested: site, age, sex, and ethnicity), presented as H2r and error bars representing standard error. Right: Heritability estimated with Falconer's formula (2 times intraclass correlation coefficients for monozygotic twins -dizygotic twins).
. CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made  . CC-BY 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted May 24, 2022. ; https://doi.org/10.1101/2022.05.24.493295 doi: bioRxiv preprint