Terminology and definitions

For the rest of this study, we define strictly the following networks: frontoparietal networks/FPNs (dorsolateral prefrontal, orbital and polar frontal cortex, sensorimotor paralobular and mid cingulate, insular and frontal opercular, superior parietal and IPS, inferior parietal, anterior cingulate), frontotemporal networks/FTNs (inferior frontal, posterior opercular, early auditory, auditory association), sensorimotor networks/SMNs (premotor, somatosensory and motor, sensorimotor paralobular and mid cingulate, early auditory, early visual, insular and frontal opercular), visual networks/VNs (primary visual, early visual, dorsal stream, ventral stream, MT+ complex), eDMN (posterior cingulate, inferior parietal, medial temporal, lateral temporal, anterior cingulate and medial prefrontal, temporal–parietal–occipital junction [TPOJ], hippocampus), fronto-occipital networks/FONs (involving VNs and frontal areas), and task positive networks/TPNs (primarily: insular and frontal opercular, premotor, superior parietal and IPS, inferior parietal, auditory association, early auditory, and generally throughout all lobes of the brain).

Similarly, we define strictly the anatomical grouping: occipital lobe (equivalent to visual networks), temporal (lateral, medial, TPOJ, early auditory, auditory association), parietal (superior parietal and IPS, inferior parietal), cingulate (anterior/posterior/midline), frontal (dorsolateral prefrontal, inferior frontal, orbital and polar frontal, medial prefrontal and anterior cingulate, premotor, insular and frontal opercular), operculum (posterior/insular and frontal opercular) and the subcortex (FreeSurfer regions; basal ganglia [caudate, putamen, globus pallidus]).

Any discussion denoting genetically influenced (or genetic effects) or environmentally influenced (or environmental effects) especially in the context of sex-specific comparisons, refer to comparisons of sex-specific individual differences in resting state functional connectivity influenced by genetics (or environment, if that is being discussed). For example, the statement “group A was more influenced by genetics than group B” would be strictly in terms of individual differences (and contingent on and with respect to the specific samples). Likewise, at the group level it would be population-level individual differences. And, for the trait(s) in question, influence is taken to mean that the trait is associated with that respective concept (e.g., for genetically or environmentally influenced, genetic factors are associated or environmental factors are associated, respectively). Dominance/Nonadditive Genetics, D, in the context of the ACE/ADE model findings is representing nonadditive genetics in total (inclusive of dominance and epistasis), and is therefore referred to as nonadditive genetics beyond this point. It should also be kept in mind that the findings are specific to the cohort investigated. Finally, any reference of the F-test beyond this point is in relation to that pertaining to variances and of the proposed approach.

Population results

Between MZ and DZ twin groups, 61,805 subtracted connection distributions were normal. Of those, 2580 out of 71,631 connections showed significant difference in variance (corrected p < .05), and all connections had greater variances in the DZ group. Out of 2580, 1321 were intrahemispheric (704 connections were left-hemispheric, 617 right-hemispheric), 1257 interhemispheric, and 2 bilateral brainstem (Figure 1).

At the population level, there appeared to be a posterior to anterior gradient of more to less genetic influence, both at the parcel- and at the network-level, with visual, temporal, parietal > frontal (Figures 1 and 3, left panel).

There was a high number of genetically-influenced functional (GIF) connections involving posterior to posterior regions of the brain: occipital or VNs, temporal cortices, as well as midline brain cortices (Figures 1 and 3, left panel; Table 2 and Figure S5, left panel).

There was a low number or paucity of GIF connections involving anterior to anterior/posterior regions of the brain: Frontofrontal, FPNs, FTNs, FONs involving dorsolateral prefrontal, orbital and polar frontal, inferior frontal, insular and frontal opercular, posterior opercular, premotor cortices as well as very low number of GIF connections involving subcortical/noncortical regions—hippocampus (also relative density) > basal ganglia, thalamus, nucleus accumbens, amygdala, ventral diencephalon, brainstem, and cerebellum. These findings were seen both at the parcel level as well as at the overall network level (Figures 1 and 3, left panel; Table 2 and Figure S5, left panel).

Assumption testing (population)

Between MZ and DZ twin groups (inclusive of males and females), 65,371 connections satisfied the classical twin design assumptions, and 43,476 connections satisfied the normality constraint. Jointly, 39,735 connections remained after exclusion by normality and classical twin design assumptions to investigate the influence from genetics and the environment. The following significant connections based on the four variance components using the ACE/ADE model approach were found of the aforementioned subset.

Additive genetics

Nine hundred eighty-eight out of 71,631 connections showed significant influence by additive genetics. Out of 988, 489 were intrahemispheric (217 connections were left-hemispheric, 272 right-hemispheric) and 499 interhemispheric (Figure 4, top left panel). Relative contribution of narrow-sense heritability (additive genetics, h²) demonstrated highest additive-GIF connection number across posterior–posterior regions of the brain: temporal cortices, parietal cortices, cingulate, and sensory areas, with a general preference for posterior (parietal/temporal/occipital) > frontal (excluding anterior cingulate and insular and frontal opercular cortex). There was a paucity of frontofrontal, and frontoposterior (frontal to FPN, FTN, FON) (outside of anterior cingulate and insular and frontal opercular cortex) additive-GIF connections in general. The hippocampus, considering its relative capacity for connections, was highly influenced as well. Notably, insular and frontal cortex, an FPN, had high additive genetic number with a variety of sensory and eDMN regions (Figures 4, top left panel and S6, h²).

There was a very low to absent additive genetic count across the rest of the subcortical/noncortical regions (Figures 4, top left panel and S6, h²).

Nonadditive genetics

One thousand five hundred fifty-nine out of 71,631 connections showed significant influence by nonadditive genetic effects. Out of 1559, 810 were intrahemispheric (359 connections were left-hemispheric, 451 right-hemispheric), 747 interhemispheric, and 2 bilateral brainstem (Figure 4, top right panel).

There was highest nonadditive-GIF connection number across posterior–posterior brain regions (visual/parietal/temporal cortices), cingulate, and frontal cortices (insular and frontal opercular cortex).

There was moderate nonadditive-GIF count across the dorsolateral prefrontal cortex. Overall, there was medium count across frontofrontal and a low-medium count across frontal-posterior (frontal with FPNs > frontal with FTNs, FONs). The hippocampus was moderately influenced considering its relative size.

There was a very low nonadditive-GIF connection number across the rest of the subcortical/noncortical regions in general (less so than additive genetic influence, however: see caudate, thalamus, brainstem, ventral diencephalon, amygdala, cerebellum) (Figures 4, top right panel and S6, d²).

Shared environment

Two out of 71,631 connections showed significant influence by shared environmental effects. Out of 2, 1 was intrahemispheric (0 connections were left-hemispheric, 1 right-hemispheric) and 1 interhemispheric (Figure 4, bottom left panel). The relative contribution of shared environmental effects appeared marginal in quantity and had no appreciable pattern (Figure 4, bottom left panel).

Unshared environment

A total of 24,612 out of 71,631 connections showed significant influence by unshared environmental effects. Out of 24,612, 12,145 were intrahemispheric (5707 connections were left-hemispheric, 6438 right-hemispheric), 12,295 interhemispheric, and 172 bilateral brainstem connections (Figure 4, bottom right panel).

There was a general gradient of very high to low number of unshared environmental influence with high to low counts being: frontofrontal, FPNs, FONs, FTNs, and midline eDMN/cingulate > parietal/temporal > visual regions, albeit connections were influenced throughout. There was a substantially high density (normalized) of unshared environmentally influenced noncortical/subcortical regions in the brain with cerebellum, nucleus accumbens, thalamus, putamen and amygdala being most environmentally influenced (Figures 4, bottom right panel, S6, e² and S9 G).

Overall findings

Overall there were notable additive-GIF connections (988), which were a fraction of that of nonadditive-GIF connections (1599), although overlap is possible. There were nearly negligible effects (2 counts) of the shared environment on connections, and there were substantial connections (24,612) (>9.5× relative to nonadditive or additive genetics together assuming no overlap) influenced by the unshared environment or measurement error. Compared with unshared environmental effects, genetic effects generally highly influenced in number posterior–posterior (parietal/temporal/occipital) regions more than anterior, with the exception of the cingulate regions and insular and frontal opercular cortex; conversely environmental effects generally had the opposite pattern (of frontal > posterior) with substantially greater number of connections throughout the brain. Generally, nonadditive > additive genetic effects, but had relatively similar overall count patterns with deviation (Figure S6, h², d²; Figure 4, top left and top right panels; and Figure SA, row G). Specific sensory regions and processing were notable for both influences: audition, insular and frontal cortex, and vision. There was moderate genetic influence of the hippocampus compared with the rest of the subcortical structures, whereas the environment influenced the cerebellum, nucleus accumbens, thalamus, putamen and amygdala the most across the subcortex (Figure S9 G).

Comparison with proposed approach

Similar to the approach proposed, at the population level, the ACE/ADE model results corroborated the pattern of findings of a genetic influence gradient present primarily across a temporal/parietal/visual (posterior) > frontal fashion (Figure SA, row G).

Considering both additive and nonadditive genetics, there was in agreement with the method proposed, a high number of GIF connections involving primarily posterior cortices: occipital (dorsal/ventral stream, MT+ complex), parietal, temporal (excluding early auditory) as well as midline brain regions. Medial temporal cortex was more relatively influenced in the proposed approach, however. Additionally, the less influenced regions were similar in that respect as well, with an overall lower number of GIF connections involving frontofrontal, FPNs > FTNs, and FONs (with the exception of the insular and frontal cortex for the ACE/ADE model). Finally, the lowest in count connections were generally found to be subcortical/noncortical, in agreement with the proposed approach findings (however, there were seemingly no nucleus accumbens parcels influenced by genetics in the ACE/ADE approach, which may be due to the types of hypothesis testing chosen). The hippocampus, notably, was more influenced in the ACE/ADE model in general (both additively and nonadditively). [Correction added on 10 May 2023, after first online publication: complex.]

In terms of similarity in influence accounting for the amount of findings (e.g., 2580 in F-test), the proposed approach was most similar to the nonadditive genetic findings (and if not then additionally additive effects) as shown in Figure SA and Table S1 (using 100,000 permutations in the permutation test) across many regions of the brain for those most highly or lowly influenced, albeit with deviation as listed in the table (not highlighted blue—indicates either h²/d² deviated from F-test in terms of p-values <.025 (significantly high relative density results) or p-values >.975 (visually [nonsignificant] low relative density results) or the F-test was outside these p-value ranges; Table S1). The p-values in general were in a close range (between ACE/ADE estimates and the F-test) for those that did not show significance, with the primary exception of medial temporal cortex and early visual cortex, in which the F-test demonstrated significant influence relative to the ACE/ADE model. The general concentrations across posterior (parietal/temporal (lateral)/visual) were comparable across the approaches (more so for nonadditive genetics than additive genetics, in ACE/ADE, however) (Figure SA, row G).

In comparison to the delineated results determined by separating additive and nonadditive genetics, visual network genetic effects were much more prevalent in general with respect to nonadditive genetic influence. In general, the proposed analysis results as a whole closely corroborated with strictly the nonadditive genetic influence components of the ACE/ADE model, albeit, both ACE/ADE model findings had patterns which overlapped with the distribution of the proposed findings, even if not identically (Figures 3, left panel and 4, top left and top right panels). [Correction added on 05 September 2023, after first online publication: added: panel.]

Any deviations from the two approaches may be due to proportionately more connections possible, the framework itself, or its assumptions. Although in proportion these results may vary across the different approaches, and the ACE/ADE model delineates more specifically, under certain assumptions and methodology that the genetic influence is teased apart as additive or nonadditive genetics, the general finding appears consistent with some deviation. One key point to note is that the comparison with the ACE/ADE model is essentially viewing its results as a binary “cartographer's map,” which is useful in practice and for visually understanding the general distribution of influenced traits in the brain; however, there was a difference in hypothesis testing compared with the approach proposed, and so the connections that are notable may necessarily be different ultimately.

Males

Comparing only male twins (F-test for MMZ versus MDZ), 64,373 subtracted connection distributions were normal. Of those, 1524 connections (794 intrahemispheric [519 left, 275 right], 730 interhemispheric) showed significant differences in variance (corrected p < .05) and all connections had greater variances in the MDZ group (Figure 3, middle panel, Table 2; Figure 2a,c). Two hundred seventy-seven of these 1524 connections were exclusive to the male group (these connections showed the opposite effect in females, i.e., larger variances in the FMZ twin group compared with FDZ). There were extensive number of GIF connections in males involving VNs (dorsal stream), eDMN with other TPNs (occipital, parietal, temporal, cingulate, frontal cortices) which were seen in the network–network and parcel–parcel interactions (Table 2, Figures 2, left panel and 3, middle panel). [Correction added on 05 September 2023, after first online publication: added: panel.]

Females

Comparing only female twins, 62,720 subtracted connection distributions were normal. Of those, 178 connections (102 intrahemispheric [46 left, 56 right], 75 interhemispheric, one from left hemisphere to brainstem [Bilateral BrainStem—Left Nucleus Accumbens]) showed significantly greater variance (corrected p < .05) in the DZ group, and three connections (Right Area V3B-Right Area 9-46d, Right Area V3B-Left Area 9-46d, Right Frontal Opercular Area 4-Right VentroMedial Visual Area 2) showed the opposite effect (Table 2, Figure 2b,d). Ten of these 178 connections were exclusive to the female group (these connections showed the opposite effect in males, i.e., larger variances in MMZ compared with MDZ). The most significant GIF connections and network interactions in females involved VNs (dorsal and ventral stream, MT+ complex), medial temporal (trending toward significance; Table 2), lateral temporal, superior parietal, anterior cingulate, posterior cingulate (high number of connections, although not significant in terms of relative density in Table 2) (Figures 2 and 3, right panel; Table 2).

Males versus females

Specific networks with high GIF connection number in males and low genetic influence in females include sensorimotor systems (somatosensory and motor cortex, paracentral lobule, early auditory cortex, early visual cortex), caudate, and thalamus. Specific networks with high relative density of genetic influence in females and low genetic influence in males include MT+ complex, neighboring visual areas and ventral stream visual cortex (Table 2, Figure 2).

Other cortical regions

Although at the network level (Table 2), frontal regions (excluding anterior cingulate) were not significant for males or females, specific parcels of these networks were significantly involved in males more so than females (Figure 2).

Subcortical/noncortical

Genetics appeared to influence a moderate amount of connections involving cortico-basal-ganglia-thalamic-cortical > ventral diencephalon, cerebellar, amygdala, globus pallidus, and putamen regions predominantly in males (with brainstem and accumbens marginally present for females and not males).

Overall patterns

There were over eight (>8.5) times as many significant connections in males (1524) compared with females (178) (Figures 2 and 3, middle and right panels). There was also a greater genetic influence in terms of intra and internetwork interactions of eDMN and TPNs in males than in females (Figures 2 and 3, middle, right panels). In terms of low-level or primary systems, there was greater genetic influence of involvement of primary sensorimotor networks (visual, auditory, paracentral lobular, somatosensory, and motor networks) in males than females (Figure 3, middle, right panels). Overall, therefore, the TPNs, eDMN, sensorimotor, subcortical/noncortical systems were significantly genetically influenced much more in males than females. See Appendix S1 for the full list of connections that were significant (Bonferroni: resultant p-values multiplied by number of tests) at the parcel level (Table S3a–c).

Assumption testing (male)

Between Male MZ and DZ twin groups, 64,890 connections satisfied the classical twin design assumptions, and 61,059 connections satisfied the normality constraint. Jointly, 55,382 connections remained after exclusion by normality and classical twin design assumptions to investigate the influence from genetics and the environment. The following significant connections based on the four variance components using the ACE/ADE model approach were found of the aforementioned subset.

Additive genetics (male)

Three hundred thirty four out of 71,631 connections showed significant influence by additive genetics. Out of 334, 167 were intrahemispheric (78 connections were left-hemispheric, 89 right-hemispheric) and 167 interhemispheric (Figure 5, top left panel). Additive-GIF connections had highest number across cingulate (anterior, posterior, mid [borderline]), sensorimotor cortex (somatosensory and motor cortex), visual networks (MT+ complex and neighbors, ventral stream > dorsal stream), temporal cortices (lateral temporal, temporal–parietal-occipital junction, auditory association cortex), and frontal cortices (insular and frontal opercular, orbital and polar frontal cortices) (Figures 5, top left panel and S7, h²). There was modest/well-tempered interplay of eDMN and TPNs. [Correction added on 13 March 2023, after first online publication: added text: (anterior, posterior, mid [borderline]). Replaced dorsal stream, ventral stream with: ventral stream > dorsal stream.]

There was a very low number of additive-GIF connections across the subcortex: hippocampus, caudate, ventral diencephalon, amygdala, and cerebellum joint with lateral temporal cortex (Figures 5, top left panel and S7, h²). [Correction added on 13 March 2023, after first online publication: thalamus was replaced by ventral diencephalon.]

Nonadditive genetics (male)

A total of 3435 out of 71,631 connections showed significant influence by nonadditive genetic effects. Out of 3435, 1708 were intrahemispheric (975 connections were left-hemispheric, 733 right-hemispheric), 1724 interhemispheric, and 3 bilateral involving the brainstem (Figure 5, top right panel). Nonadditive-GIF connections were highest in number across eDMN with other TPNs (with superior/inferior parietal, dorsolateral prefrontal and insular and frontal opercular cortex as the main networks). Separately and overlapping, basic primary sensorimotor systems were involved (auditory, vision, somatosensory, and motor complex cortices) (Figure 5, top right panel).

There was a low-very low count (and in consideration of their relative connection capacity) of subcortical/noncortical region with the exception of: hippocampus, basal ganglia (caudate, putamen), ventral diencephalon, thalamus, and cerebellum (Figures 5, top right panel and S7, d²).

Shared environment (male)

Six out of 71,631 connections showed significant influence by shared environmental effects. Out of six, two were intrahemispheric (2 connections were left-hemispheric, 0 right-hemispheric) and four interhemispheric (Figure 5, bottom left panel). The relative contribution of shared environmental effects appeared marginal in quantity for males, with no appreciable pattern (Figure 5, bottom left panel).

Unshared environment (male)

A total of 18,105 out of 71,631 connections showed significant influence by unshared environmental effects. Out of 18,105, 8920 were intrahemispheric (4105 connections were left-hemispheric, 4815 right-hemispheric), 9024 interhemispheric, and 161 bilateral brainstem connections (Figure 5, bottom right panel). Environmentally-influenced connections were prominent throughout the brain. In general, there was a gradient of very high to low number of unshared environmental connections of frontofrontal, unrestricted FPNs, FONs, FTNs, and midline eDMN/cingulate > parietal/temporal > posterior/visual regions. Additionally, there was a substantially high density (normalized) of unshared environmentally influenced noncortical/subcortical regions in the brain (Figures 5, bottom right panel and S7, e²). The most prominent environmentally influenced regions were the nucleus accumbens, amygdala, cerebellum, and ventral diencephalon (Figure S9 M).

Overall findings (male)

Overall there were notable additive-GIF connections (334), but demonstrably more (10×) nonadditive-GIF connections (3435), although overlap is possible. There were nearly negligible effects (6 counts) of the shared environment on connections, and there were predominant connections (18,105) (>4.8× relative to nonadditive or additive genetics together assuming no overlap) influenced by the unshared environment or measurement error. Similar to the group (population) level, compared with unshared environmental effects, genetic effects generally influenced posterior regions (parietal/temporal > visual) more than anterior (frontal) (with the exception of midline brain regions, e.g., anterior cingulate and insular and frontal opercular cortex), whereas environmental effects generally had the opposite pattern (of frontal > posterior) when considering amount of connections influenced (but overall still influenced throughout the brain, and especially subcortical regions when considering normalization). Interactions of sensorimotor areas (SMNs/TPNs) were evident for both additive and nonadditive genetics as well (Figures 5, top left and top right panels and SA, row M; Table S1). While the hippocampus, basal ganglia (caudate, putamen), ventral diencephalon, thalamus, and cerebellum were the most genetically influenced of the subcortex, there was overlap in that the nucleus accumbens, amygdala, cerebellum, and ventral diencephalon were the most influenced by the environment (or measurement error). Notably, the delineation between how additive genetics and nonadditive genetics influence the brain did not necessarily show the same overall brain-wide trend (gradient) (Figures 5, top left and top right panels and SA, row M). [Correction added on 05 September 2023, after first online publication: added: panels.]

Comparison with proposed approach (male)

Similar to the method proposed, for males, the ACE/ADE model results in general corroborated the pattern of findings of a genetic influence gradient across parietal/temporal > frontal regions. Specifically, in agreement was high number of GIF connections across midline brain regions (cingulate), parietal, temporal cortices (lateral temporal, medial temporal, auditory association cortex; Figures 5, top left and top right panels, S7, VG, h², d², and SA, row M). Broadly this result agrees with the overall influence across eDMN with TPNs in males as in the proposed approach, albeit this finding was far more substantial in nonadditive genetics as opposed to additive genetics (10× connections). [Correction added on 13 March 2023, after first online publication: added: finding.]

The proposed approach had agreement (relative to the maximum of the results found in either approach) with nonadditive genetics, and in this circumstance, nonadditive genetics overshadows additive genetics in amount, perhaps denoting an overall direction of genetic influence (albeit both should be considered, and additive genetics had moderate deviation with the proposed approach across several regions; Figure SA, row M). Sensorimotor areas also had a high number of connections across both approaches (regardless of additive or nonadditive genetics; Figure SA, row M and Table S1). Insular and frontal opercular cortex and dorsolateral prefrontal cortex findings had agreement (more so for nonadditive genetics, particularly again as nonadditive genetics overshadows additive genetics). There was high interactivity of the eDMN with TPNs in general agreeing with the proposed approach (pattern of nonadditive > additive effects).

Hippocampus, caudate, thalamus, ventral diencephalon, and cerebellum (as well as marginally putamen, amygdala, and globus pallidus) were influenced in both approaches (with more substantial influence in nonadditive as opposed to additive genetics). Higher proportionate findings were in the ACE/ADE model framework, in general.

There were substantially more notable connections (again attributing to the cartographer's map concept) in the case of the ACE/ADE model (3435 + 334: ACE/ADE > 1524: proposed). Considering both additive and nonadditive genetics, there was general agreement with the method proposed, although in proportion and in specifics the results may vary.

Assumption testing (female)

Between female MZ and DZ twin groups, 67,186 connections satisfied the classical twin design assumptions, and 48,334 connections satisfied the normality constraint. Jointly, 45,341 connections remained after exclusion by normality and classical twin design assumptions to investigate the influence from genetics and the environment. The following significant connections based on the four variance components using the ACE/ADE model approach were found of the aforementioned subset.

Additive genetics (female)

Six hundred ninety-nine out of 71,631 connections showed significant influence by additive genetics. Out of 699, 379 were intrahemispheric (165 connections were left-hemispheric, 214 right-hemispheric), 317 interhemispheric, and 3 bilateral from the brainstem (Figure 6, top left panel).

The highest additive-GIF connection counts were parietal, temporal cortex (lateral, TPOJ, auditory association cortex), midline eDMN/cingulate (posterior cingulate cortex), VNs (MT+ complex, ventral stream, dorsal stream), and frontal (insular and frontal opercular cortex).

There was a low-moderate number of additive genetic influence across FPNs. There was a very low number across the rest of the subcortical/noncortical regions in general, with the exception of the hippocampus considering its relative connection capacity, and marginally the brainstem and cerebellum (Figures 6, top left panel and S8, h²).

Nonadditive genetics (female)

Six hundred eighty four out of 71,631 connections showed significant influence by nonadditive genetic effects. Out of 684, 376 were intrahemispheric (161 connections were left-hemispheric, 215 right-hemispheric) and 308 interhemispheric (Figure 6, top right panel).

The highest number of nonadditive-GIF connections was across parietal cortex (superior parietal and IPS cortex), midline eDMN/cingulate (posterior/anterior cingulate), visual networks (MT+ complex, ventral stream > dorsal stream), temporal cortex (lateral), and other frontal regions/FPNs (insular and frontal opercular cortex, dorsolateral prefrontal cortex, orbital and polar frontal cortex). There was a moderate number across the nucleus accumbens and hippocampus, considering their connection capacity (Figure 6, top right panel).

There was a low-very low count across subcortical/noncortical regions, however, certain regions did have minimal frequency in the subcortex (e.g., marginally: cerebellum, thalamus, basal ganglia [putamen, globus pallidus, caudate]) (Figures 6, top right panel and S8, d²).

Shared environment (female)

Sixty-six out of 71,631 connections showed significant influence by shared environmental effects. Out of 66, 38 were intrahemispheric (15 connections were left-hemispheric, 23 right-hemispheric) and 28 interhemispheric (Figure 6, bottom left panel). The relative contribution of shared environmental effects was predominantly involving the dorsolateral prefrontal cortex, and with its most notable effects with primarily visual areas (FONs; dorsolateral prefrontal with: early visual cortex, dorsal stream, ventral stream, MT+ Complex) and somatosensory/motor cortex (Figure 6, bottom left panel).

Unshared environment (female)

A total of 26,554 out of 71,631 connections showed significant influence by unshared environmental effects. Out of 26,554, 13,001 were intrahemispheric (6332 connections were left-hemispheric, 6669 right-hemispheric), 13,413 interhemispheric, and 140 bilateral brainstem connections (Figure 6, bottom right panel). Environmentally-influenced connections were prominent throughout the brain. In general, there was a gradient of very high to low number of unshared environmental connections of frontofrontal, unrestricted FPNs, FONs, FTNs, and midline eDMN/cingulate > parietal/temporal > posterior/visual regions. Additionally, there was a substantially high density (normalized) of unshared environmentally influenced noncortical/subcortical regions in the brain (Figures 6, bottom right panel and S8, e²). The most prominent environmentally influenced regions were the nucleus accumbens, amygdala, thalamus, cerebellum, and globus pallidus (Figure S9 F).

Overall findings (female)

Overall, there was comparable additive-GIF connections (699) to that of nonadditive-GIF connections (684), although overlap is possible. There was a moderate (albeit magnitude 10× lesser than either set of genetically-influenced connections) amount of shared environment influenced connections (66), and there were substantial connections (26,554) (>19× relative to nonadditive genetics or additive genetics together assuming no overlap) influenced by the unshared environment or measurement error. There was a genetic influence gradient across parietal, temporal, and visual (posterior) > anterior regions of the brain, with moderately similar but slightly different distributed patterns when it came to delineating between the two genetic effects (Figure SA, row F—relative number, gradient; Table S1—accounting for total connections found, permutation test). Additionally, genetics broadly influenced the eDMN and visual networks in females with certain frontal involvement (dorsolateral prefrontal, orbital/polar, insular/frontal). Relative to genetic influence, shared environmental effects appeared to influence dorsolateral prefrontal cortex (with visual cortices) (FON) and somatosensory/motor cortex, and unshared environment effects (as well as environmental influence in the widest sense) had an influence with the opposite directionality (frontal to posterior) to that of genetics when considering amount of connections influenced. There was substantial presence of environmental influence across the brain, and the subcortical regions after considering the capacity for connections were notably affected: nucleus accumbens, amygdala, thalamus, cerebellum, and globus pallidus.

Comparison with proposed approach (female)

Relative to the method proposed, for females, the ACE/ADE model results corroborated the pattern of findings in that genetics (additive and nonadditive) influenced primarily visual networks (MT+ complex, dorsal/ventral stream), superior parietal and IPS cortex, cingulate (anterior/posterior), and lateral temporal cortex, with additive and nonadditive effects displaying different GIF connection number magnitude depending on the region (Figure S8, VG, h², d²). Visually, nonadditive genetics as compared with the proposed approach results (Figure 6, top right panel vs. Figure 3, right panel) appeared to potentially have the same highly influenced locations of connections, ignoring the greater eDMN and TPN involvement in females for the ACE/ADE model (at least partially due to higher proportionate findings). [Correction added on 05 September 2023, after first online publication: changed “last” to “right” panel.]

There were substantially more genetically-influenced connections in general (699 + 684: ACE/ADE > 178: proposed), as well as those involved in temporal, frontal, and midline brain regions in the ACE/ADE model compared with the approach proposed (Figure SA, row F).

Lateral temporal cortex also remained in high counts (relatively) regardless of approach and influence, but medial temporal cortex was relatively moderately less influenced in the ACE/ADE model than the proposed approach. Parietal lobe findings across either approach were closely matched (albeit with slight differences based on additive vs. nonadditive genetics). Less influenced primary sensory areas (somatosensory and motor cortex, mid cingulate cortex, premotor cortex, early auditory cortex, auditory association cortex) matched in relative magnitude as well across approaches (Figure S8, h², d²). However, again, dorsolateral prefrontal cortex was more pronounced in its influence by nonadditive genetics (Figure S8, h², d²). Taken altogether, any conflicting findings may be due to a difference in hypothesis testing, estimation, or the assumptions of the respective methods. Relative to the proposed approach, there was much greater eDMN with TPN involvement in females in the ACE/ADE approach, especially given the substantial difference in amount of genetically-influenced connections.

Again, divergently, there being many more connections present in the ACE/ADE model could potentially be due to the aforementioned limitations, as well as intrinsic model assumptions.

Qualitative sex-level individual differences, overall findings

Qualitative sex-level individual differences, comparison with proposed approach

In comparison to the proposed approach, although there were many more genetically-influenced connections in the ACE/ADE model approach, notably in terms of nonadditive genetics (additive genetics is comparable across males/females and may overlap with nonadditive genetics as well), males had roughly 5× more connections (3435) than females (699), in the same direction but disparate and not proportionate to the >8.5 times in the proposed approach (1524 genetic connections for males, 178 genetic connections for females). In contrast with the proposed approach, auditory systems were relatively equally distributed in genetically-influenced count in females compared with males in the ACE/ADE model approach, but that is not considering the substantial amount of total connections males had with respect to females (for which male nonadditive genetic influence is overall higher in these systems), and visual networks were comparably genetically influenced in males and females (although proportionately different). In agreement with the proposed approach although not to the same scale, there was greater genetic influence in terms of intra and internetwork interactions of eDMN and TPNs for individual differences in males compared with individual differences in females. [Correction added on 05 September 2023, after first online publication: added: individual differences in, twice.]

There was high genetic influence across individual differences in males and low genetic influence across individual differences in females in terms of sensory areas (somatosensory and motor cortex, paracentral lobule, early auditory cortex), caudate (nonadditive genetic influence primarily), and thalamus (nonadditive genetic influence primarily) as in the proposed approach. The same pattern was found in the ACE/ADE approach in that females had high relative density for MT+ complex and ventral stream whereas males did not, at least in terms of nonadditive genetics (which is 10× more than additive genetics for males). For additive genetics, males had partially (visually high [significant, p < .025] or low [nonsignificant, p > .975]) comparable relative density in these regions to that found in the proposed approach (Figures S7 and S8; Table S1). [Correction added on 05 September 2023, after first online publication: added: across individual differences, twice.]

The cortical regions found in the proposed approach for both males and females (dorsolateral prefrontal, inferior frontal, insular/frontal opercular, orbital and polar frontal premotor) were all found to be highly influenced by genetics (additive and nonadditive) as in the ACE/ADE model approach as well, with nonadditive genetics influence highly present on all, but most strongly on dorsolateral prefrontal and insular/frontal opercular. Comparatively, males had a much greater count than females, albeit females had a higher relative count for orbital/polar frontal (Figures S7 and S8).

In agreement with the subcortical findings of the proposed approach, individual differences in males had greater genetic influence across cortico-basal-ganglia-thalamic-cortical regions, ventral diencephalon, cerebellum, amygdala, globus pallidus, and putamen as relative to individual differences in females (typically with respect to nonadditive genetics). Additionally, females appeared to have more nucleus accumbens nonadditive-GIF connections as relative to males, similar to the proposed approach (Figures S7 and S8). [Correction added on 05 September 2023, after first online publication: added: individual differences in, twice.]

Overall, as in the proposed approach, although the proportion and specifics may differ, in terms of rsFC individual differences, individual differences in males were in general more notably genetically influenced in terms of TPNs, eDMN, sensorimotor, and subcortical systems compared with individual differences in females, generally in the context of nonadditive genetics. [Correction added on 05 September 2023, after first online publication: added: individual differences in, twice.]

Additive genetics

Out of the 334 connections that were highly influenced for males, and the 699 that were highly influenced across females, after requiring joint normality and valid classical twin design assumptions (from the individual male and female analyses) across both of these sets of connections, there were a total of 807 connections that could be compared between MZ and DZ (and which also overlapped to a degree between males and females in terms of significance). That is, of this initial set, 230 connections were highly influenced for males, 9 for males and females, and 568 for females.

The result of the FDR (Bonferroni) correction demonstrated that of the highly influenced additive genetic effects across males and females, there were 648 (582) that were rejected. 171 (156) connections were males > females, and 477 (426) were females > males.

Overall, this corroborated the trend that females had more additive-genetically-influenced connections than that of males.

Nonadditive genetics

Out of the 3435 connections that were highly influenced for males, and the 684 that were highly influenced across females, after requiring joint normality and valid classical twin design assumptions (from the individual male and female analyses) across both of these sets of connections, there were a total of 2625 connections that could be compared between MZ and DZ (and which also overlapped to a degree between males and females in terms of significance). That is, of this initial set, 2083 connections were highly influenced for males, 44 for males and females, and 498 for females.

The result of the FDR (Bonferroni) correction demonstrated that of the highly influenced nonadditive genetic effects across males and females, there were 2056 (909) that were rejected. 1796 (776) connections were males > females, and 260 (133) were females > males.

Overall, this corroborated the trend that males had substantially more nonadditive genetically-influenced connections than that of females.

Detailed view

Comparing total trending patterns across Figure S6 (VG—F-test) vs. SV2 (VG—Levene's test without normality), of the more prevalent counts, there were more notable relative concentrations of dorsal stream, MT+ complex, auditory association cortex, and inferior parietal cortex using the F-test than Levene's test (with the full set of connections). Otherwise, the trends were similar (other than magnitude of count which the F-test had considerably more connections).

The absence of findings (e.g., in the subcortex, and other more nuanced differences) in Levene's test may be due to the F-test false positive rate, Levene's test false negative rate (reduction of true positives), absence of constraints of normality for Levene's test, or the error rates in general of the study, all also contingent on the data distributions themselves. [Correction added on 13 March 2023, after first online publication: replaced paragraph with: Detailed view sub-section.]

Males

For results that were not constrained by normality, between male MZ and male DZ groups, 1760 connections were significant in total out of 71,631 connections. Out of 1760, 868 connections were intrahemispheric (563 left-hemispheric, 305 right-hemispheric), 888 were interhemispheric, and 4 were bilateral brainstem. There were 291 connections exclusive to males (as opposed to females) unconstrained by normality. [Correction added on 13 March 2023, after first online publication: added: There were 291 connections exclusive to males (as opposed to females) unconstrained by normality.]

For the results constrained by normality, there was a total of 1228 connections significant out of 71,631 connections after normality reduction. Out of 1228 connections, 626 were intrahemispheric (410 left-hemispheric, 216 right-hemispheric), 599 interhemispheric, and 3 were bilateral brainstem. There were 196 connections exclusive to males (as opposed to females) under constraints of normality. [Correction added on 13 March 2023, after first online publication: added: There were 196 connections exclusive to males (as opposed to females) under constraints of normality.]

In terms of the number of connections found in the F-test, there was a moderate drop (1524 to 1288 considering same normality constraints). This finding may be attributed to the more anticonservative versus more conservative nature of the F-test and Levene's test, respectively.

In terms of the pattern of findings of Levene's test in either case relative to that mentioned with the F-test in Section 3.2.1, in the previously described network count trends (ignoring relative density), the main difference was an alteration in the notability of the dorsal versus ventral stream (though not remarkably), and more pronounced dorsolateral prefrontal cortex involvement (Figures 3, after 3 middle panel, S7 VG, 8a,c, 9, after 9 middle panel, SV1 middle panel). The areas with notable count were lateral temporal, superior parietal and IPS, cingulate, dorsolateral prefrontal (being a high-counted region for clarity exception relative to the F-test findings), somatosensory and motor cortex, and visual networks (dorsal and ventral stream). Otherwise, for the normality constrained Levene's test, and similarly for the full-set of connections using Levene's test, the trends were present as previously with additional deviation (Figure SV1).

Detailed view

Comparing total trending patterns across Figure S7 (VG—F-test) vs. SV3 (VG—Levene's test without normality, i.e., not constrained to a subset of connections as with the F-test), of the more prevalent counts, there were more notable relative concentrations of dorsal stream, superior parietal and IPS cortex, inferior parietal cortex, and moderately higher concentration (again relative to other counts) for mid cingulate cortex, anterior cingulate cortex, orbital and polar frontal cortex, caudate, thalamus and dorsolateral prefrontal cortex for the F-test than Levene's test; there were more notable instances of early auditory cortex and ventral stream for Levene's test as opposed to the F-test. Otherwise, there were general similarities for the remaining regions. [Correction added on 05 September 2023, after first online publication: deleted: male exclusivity and. Added: 8a,c. Added: The areas with notable … visual networks (dorsal and ventral stream). Replaced last sentence with: Detailed view sub-section.]

Females

For results that were not constrained by normality, between female MZ and DZ groups, 92 connections were significant in total out of 71,631 connections. Out of 92, 58 were intrahemispheric (27 left-hemispheric, 31 right-hemispheric), 34 interhemispheric, and there were no bilateral brainstem connections. [Correction added on 13 March 2023, after first online publication: replaced: male with female.]

For the results constrained by normality, there was a total of 79 connections out of 71,631 after normality reduction. Out of 79 connections, 52 connections were intrahemispheric (24 left-hemispheric, 28 right-hemispheric), 27 interhemispheric, and there were no bilateral brainstem connections. There were 7 connections exclusive to females regardless of normality constraints. [Correction added on 13 March 2023, after first online publication: added: There were 7 connections exclusive to females regardless of normality constraints.]

Given the small amount of connections in general for females, there were marked differences in that shown in Levene's test due to a less discernible pattern in general from females, much of which may be due to the dropping of significant results by about half (Figures 3, before right panel, S8 VG, 8b,d, 9, after 9 right panel, after SV1 right panel). In general, however, the top most notable network counts belonged to: ventral stream, temporal cortices (medial, lateral, both on lower end), superior parietal and IPS cortex, inferior parietal cortex, posterior cingulate cortex, anterior cingulate cortex, MT+ complex, and orbital and polar frontal cortex (Figures SV4 VG, SV6 F), which agreed with the findings for females from the F-test (ignoring relative density).

Detailed view

Comparing total trending patterns across Figure S8 (VG—F-test) vs. SV4 (VG—Levene's test without normality), perhaps the most notable deviations from the F-test result were that of the dorsal stream (more prominent using the F-test), ventral stream, inferior parietal, MT+ complex, and orbital polar frontal cortex (less pronounced using the F-test); additionally Levene's test had a loss of one brainstem connection (Figures SV4 VG, SV6 F, 9 right panel). [Correction added on 05 September 2023, after first online publication: added: panel. Added: b, d. Added: panel. Added: panel. Added: MT+ complex. Deleted: female exclusivity and. Replaced last sentence with: Detailed view sub-section.]

Males versus females

Using the more stringent constrained and unconstrained by normality Levene's test, the difference in male and female significantly influenced connections notably increased in amplitude from the F-test result (range: >15.5 [different subsets of possible connections for males vs. females] to >19.1 [no normality, all connections considered]), where the least biased proportion of male to female genetic influence connection count is arguably >19.1×.

The same overall pattern of eDMN and TPN interactions for males being greater (in count) than that for females, along with (albeit with proportionate differences) sensorimotor systems, basal ganglia (excluding globus pallidus), ventral diencephalon, cerebellum, amygdala, thalamus, putamen, and frontal regions being more notable in males as opposed to females is comparable between the F-test and Levene's test. These findings support the validity of the F-test result, with the main exceptions of globus pallidus being absent and a reduction in the presence of connections across the cortico-basal-ganglia-thalamic-cortical loop in Levene's test for males, and brainstem being absent in Levene's test for females (Figures 9 middle, right panels, SV1 middle, right panels).

For normalization (similar to relative density) type results, the normalization figures shown in the appendix of Levene's test and F-test differ in respects (Figures S5, SV7, SV12), however.

Again, for any differences, any difference in findings in the results may be due to the F-test false positive rate, Levene's test false negative rate (reduction of true positives), absence of constraints of normality for Levene's test, or the error rates in general of the study, all also contingent on the data distributions themselves. [Correction added on 05 September 2023, after first online publication: added: (in count). Replaced scaling with proportionate. Added: and a reduction in the presence of connections across the cortico-basal-ganglia-thalamic-cortical loop. Added: For normalization (similar to relative density) type results … contingent on the data distributions themselves.]

Additive genetics

A total of 1405 out of 71,631 connections showed significant influence by additive genetics. Out of 1405, 708 were intrahemispheric (319 connections were left-hemispheric, 389 right-hemispheric) and 697 interhemispheric (Figure 10, top left panel).

There was a high relative level (count) of influence across visual networks (dorsal stream, ventral stream, MT+ complex), insular and frontal opercular cortex, parietal cortices, cingulate (posterior, anterior), and temporal cortices (lateral temporal, TPOJ, auditory association cortex). In general, in agreement with that with the DE model, there was a pattern of posterior (visual/temporal/occipital) > frontal (excluding anterior cingulate, insular and frontal opercular cortex), with there being a paucity of frontofrontal, frontoposterior connections, in general. [Correction added on 13 March 2023, after first online publication: replaced paragraph with: There was a high relative level … frontoposterior connections in general.]

The hippocampus was highly influenced as well considering its connection capacity. There was a very low to absent presence of influence across subcortical/noncortical regions (highest: hippocampus, very low: putamen, otherwise absent) (Figure 10, SV2 h²), results which in pattern generally agreed with that of the original ACE/ADE model (without DE). [Correction added on 13 March 2023, after first online publication: added: (highest: hippocampus, very low: putamen, otherwise absent).]

Nonadditive genetics

A total of 195 out of 71,631 connections showed significant influence by nonadditive genetics. Out of 195, 95 were intrahemispheric (30 connections were left-hemispheric, 65 right-hemispheric), 99 interhemispheric and 1 bilateral brainstem (Figure 10, top right panel).

Influence count was high across frontal cortices (dorsolateral prefrontal cortex, orbital and polar frontal cortex), cingulate (posterior, anterior), inferior parietal cortex, and lateral temporal cortex. There was medium to high influence count of insular and frontal opercular cortex, and medium influence across visual networks as well as TPOJ. There was low to very low influence count of caudate, thalamus, hippocampus, brainstem, and cerebellum, and absent presence across the rest of the subcortex. There was a considerable drop in number of nonadditive-GIF connections when excluding DE, and there were demonstrable differences (e.g., less noteworthy visual networks) in this circumstance, possibly instead migrating across other influences when DE is excluded (Figures SV2 d², 10, top right panel).

Shared environment

A total of 2 out of 71,631 connections showed significant influence by shared environmental effects. Out of 2, 1 was intrahemispheric (0 connections were left-hemispheric, 1 right-hemispheric) and 1 was interhemispheric (Figure 10, bottom left panel). The pattern remains similar as that with the DE model (Figure 4, bottom left panel).

Unshared environment

A total of 25,983 out of 71,631 connections showed significant influence by unshared environmental effects. Out of 25,983, 12,841 were intrahemispheric (6059 connections were left-hemispheric, 6782 right-hemispheric), 12,964 interhemispheric and 178 bilateral brainstem (Figure 10, bottom right panel). The pattern remains similar as that with the DE model (Figure 4, bottom right panel).

Detailed view

Comparing total trending patterns across Figure S8 (with DE) vs. SV4 (without DE), in terms of the total effect of h², there was a general similar trend across either model selection inclusion/exclusion. In terms of the total effect of d², there were notable differences in the distribution of parcel concentrations; namely, inferior parietal, superior parietal and IPS, insular and frontal opercular, visual networks (ventral/dorsal stream), TPOJ, and subcortical regions were reduced when the DE model was excluded. Nucleus accumbens and inferior frontal cortex were more notable when DE was excluded, albeit with respect to the smaller total max count (and similarly for other frontal regions). In terms of c² there appeared to be no notable difference (possibly identical), and in terms of e², there was no considerable difference.

Comparison to proposed approach

The proposed approach findings in terms of visual networks, and in terms of the general pattern (e.g., visual/temporal/parietal > frontal) are in general agreement with the additive genetic influence findings. Nonadditive genetics had a notably different pattern in this circumstance, and most of the effect was found to be in additive genetics. For subcortical findings, additive genetics influenced hippocampus and putamen, while nonadditive genetics influenced cerebellum, brainstem, ventral diencephalon, thalamus, hippocampus, and caudate (again for both no influence across nucleus accumbens was present). [Correction added on 13 March 2023, after first online publication: replaced paragraph with: Influence count was high across frontal cortices … 10, top right panel). And the following sub-sections were included: Shared environment, Unshared environment, Detailed view and Comparison to proposed approach.]

Male rsFC phenotype model of ACE/ADE (without DE) distribution

After excluding connections which violated the classical twin design and normality assumptions (total remaining: 55,382), based on the model offering the smallest AIC at the group level, per connection the best model fit was ACE (79 counts), AE (26,403), CE (3245 counts), ADE (13,905 counts), and E (11,750 counts) out of 71,631. [Correction added on 13 March 2023, after first online publication: deleted: and can be seen in Appendix Section S12. Deleted last sentence. Added: (c² not altered in general, e² higher in count, but overall pattern the same). Also, the following sub-section was included: Male rsFC phenotype model of ACE/ADE (without DE) distribution.]

Additive genetics (male)

A total of 763 out of 71,631 connections showed significant influence by additive genetics. Out of 763, 374 were intrahemispheric (202 connections were left-hemispheric, 172 right-hemispheric) and 389 interhemispheric (Figure 11, top left panel).

There was high influence count across cingulate (anterior, posterior, mid [borderline]), temporal cortices (lateral temporal, auditory association), superior parietal and IPS cortex, sensorimotor cortex (somatosensory and motor cortex), frontal cortex (insular and frontal opercular cortex), and visual networks (ventral stream > dorsal stream, MT+ complex). There was a medium influence across frontal cortices (excluding anterior cingulate, insular and frontal opercular), TPOJ, inferior parietal cortex, and medial temporal cortex. There was a low presence of connections for hippocampus, amygdala, caudate, ventral diencephalon, and cerebellum joint with lateral temporal cortex; and there was absent influence presence across the rest of the subcortex (Figures SV3 h², 11, top left panel). [Correction added on 05 September 2023, after first online publication: replaced paragraph with: There was high influence count across cingulate … (Figure SV3 h², Figure 11, top left panel).]

In comparing Figure 11 top left panel with that of Figure 5 top left panel, there was an enhancing effect (due to additional additive-GIF connections), but a general subset of connections remained the same. The most notable differences were in orbital/polar frontal cortex and TPOJ; otherwise, the pattern, along with well-tempered interplay of eDMN and TPNs, generally agreed with the result of including DE. [Correction added on 13 March 2023, after first online publication: added: top left panel. Added: top left panel. Added: The most notable differences were … result of including DE.]

Nonadditive genetics (male)

A total of 1708 out of 71,631 connections showed significant influence by nonadditive genetics. Out of 1708, 864 were intrahemispheric (469 connections were left-hemispheric, 395 right-hemispheric), 841 interhemispheric and 3 bilateral brainstem (Figure 11, top right panel).

There was a high influence presence across parietal cortex, cingulate (posterior, anterior > mid [borderline]), and frontal (dorsolateral prefrontal cortex, insular, and frontal opercular cortex). Visual networks (dorsal stream, ventral stream, MT+ complex, early visual cortex), sensory areas (premotor, somatosensory and motor, mid cingulate), temporal (medial, lateral), and frontal (orbital and polar frontal, inferior frontal) had a medium connection count. There was a low to very low count across the subcortex, with pallidum, brainstem, nucleus accumbens (absent), and amygdala being the lowest of the counts in agreement with the result with the DE model (Figure SV3 d², Figure 11, top right panel). In agreement with the result with DE, nonadditive-GIF connections were highest across eDMN with other TPNs as listed (superior/inferior parietal, dorsolateral prefrontal, and insular and opercular cortex as the most notable networks). Also in agreement are the primary sensorimotor systems involved (albeit, there is a reduction in influence count, most notably in terms of vision). [Correction added on 13 March 2023, after first online publication: replaced paragraph with: There was a high influence presence across parietal cortex … most notably in terms of vision).]

In comparing Figure 11 top right panel with that of Figure 5 top right panel, there was an alteration effect (due to removal of substantial nonadditive-GIF connections), but much of the general pattern remained in-tact (with deviation, also as discussed above).

Shared environment (male)

A total of 6 out of 71,631 connections showed significant influence by shared environmental effects. Out of 6, 2 were intrahemispheric (2 connections were left-hemispheric, 0 right-hemispheric) and 4 were interhemispheric (Figure 11, bottom left panel). The pattern remains similar to that with the DE model (Figure 5, bottom left panel).

Unshared environment (male)

A total of 20,853 out of 71,631 connections showed significant influence by unshared environmental effects. Out of 20,853, 10,303, were intrahemispheric (4769 connections were left-hemispheric, 5534 right-hemispheric), 10,365 interhemispheric and 185 bilateral brainstem (Figure 11, bottom right panel). The pattern remains similar to that with the DE model (Figure 5, bottom right panel).

Detailed view (male)

Comparing total trending patterns across Figure S7 (with DE) vs. SV3 (without DE), in terms of the total effect of h², there was a general similar trend outside of specifically for the more notable concentrations of counts, TPOJ and orbital and polar frontal cortex being higher with DE than without, and insular and frontal opercular cortex, hippocampus, and superior and IPS cortex being higher without DE than with DE; otherwise, in general the patterns were similar for the more pronounced effects. In terms of the total effect of d², there were notable differences in the distribution of parcel concentrations; namely in SV3 (without DE), dorsolateral prefrontal, orbital and polar frontal, and inferior frontal were notable, and there was a lack of marked concentration of visual networks (dorsal/ventral stream, MT+ complex), somatosensory and motor cortex, mid cingulate, lateral temporal cortex, and TPOJ. There was also a lessening of influence for hippocampus (DE > no DE) and greater effect (relative to count) for caudate (no DE > DE), among other subtle but generally reductive effects (across no DE) in the subcortex. The most notable regions generally remained similar in ranking, regardless of model exclusion, other than TPOJ. In terms of c² there was identical distribution, and in terms of e², there was no considerable difference.

Female rsFC phenotype model of ACE/ADE (without DE) distribution

After excluding connections which violated the classical twin design and normality assumptions (total remaining: 45,341), based on the model offering the smallest AIC at the group level, per connection the best model fit was ACE (492 counts), AE (23,020), CE (11,537 counts), ADE (2594 counts), and E (7698 counts) out of 71,631. [Correction added on 05 September 2023, after first online publication: added: top right panel. Added: top right panel. Added at last sentence: “also as discussed above.” Also, the following sub-sections were included: Shared environment (male), Unshared environment (male), Detailed view (male) and Female rsFC phenotype model of ACE/ADE (without DE) distribution.]

Additive genetics (female)

A total of 898 out of 71,631 connections showed significant influence by additive genetics. Out of 898, 488 were intrahemispheric (208 connections were left-hemispheric, 280 right-hemispheric), 407 were interhemispheric and 3 were bilateral brainstem connections (Figure 12, top left panel).

Visual networks (dorsal stream, ventral stream, MT+ complex), temporal (auditory association cortex, lateral temporal, TPOJ), parietal, cingulate (posterior cingulate cortex), and frontal (insular and frontal opercular cortex) had high influence count. There was medium-low count across FPNs (e.g., anterior cingulate, frontal regions), hippocampus, medial temporal, early visual, and somatosensory and motor cortex. There was very low to negligible counts (marginal: brainstem and cerebellum) across the rest of the subcortex (Figures SV4 h², 12, top left panel). [Correction added on 13 March 2023, after first online publication: replaced paragraph with: Visual networks (dorsal stream, ventral stream, MT+ complex) … (Figures SV4 h², 12, top left panel).]

In comparing Figure 12 top left panel with that of Figure 6 top left panel, there was general agreement in the pattern displayed (given the same subset of connections retained), and the general pattern listed remained the same. [Correction added on 13 March 2023, after first online publication: added: top left panel. Added: top left panel. Added: and the general pattern listed remained the same.]

Nonadditive genetics (female)

A total of 191 out of 71,631 connections showed significant influence by nonadditive genetics. Out of 191, 104 were intrahemispheric (40 connections were left-hemispheric, 64 right-hemispheric), and 87 were interhemispheric (Figure 12, top right panel).

There was a high influence count across the cingulate (posterior, anterior), frontal (dorsolateral prefrontal and orbital and polar frontal), lateral temporal cortex, and MT+ complex. There was a high-medium influence count across inferior frontal cortex, insular and frontal opercular cortex, and inferior parietal cortex.

There was a medium-very low count across visual networks (excluding MT+ complex), temporal cortices (medial temporal, auditory association > TPOJ), superior parietal and IPS cortex, posterior opercular cortex, early auditory cortex, somatosensory and motor cortex, and the subcortex (nucleus accumbens > hippocampus, basal ganglia [caudate, globus pallidus], and thalamus, the rest absent) (Figures SV4 d², 12, top right panel).

These findings are in partial agreement (ignoring count, given the substantial decrease between that with DE and without DE) but in general have a large degree of variation from the model with DE incorporated.

Shared environment (female)

A total of 66 out of 71,631 connections showed significant influence by shared environmental effects. Out of 66, 38 were intrahemispheric (15 connections were left-hemispheric, 23 right-hemispheric), and 28 were interhemispheric (Figure 12, bottom left panel). The pattern remains similar to that with the DE model (Figure 6, bottom left panel).

Unshared environment (female)

A total of 27,803 out of 71,631 connections showed significant influence by unshared environmental effects. Out of 27,803, 13,661 were intrahemispheric (6646 connections were left-hemispheric, 7015 right-hemispheric), 13,997 interhemispheric and 145 bilateral brainstem (Figure 12, bottom right panel). The pattern remains similar to that with the DE model (Figure 6, bottom right panel).

Detailed view

Comparing total trending patterns across Figure S8 (with DE) vs. SV4 (without DE), in terms of the total effect of h², there was a general similar trend across either model selection inclusion/exclusion. In terms of the total effect of d², there were notable differences in the distribution of parcel concentrations; namely, inferior parietal, superior parietal and IPS, insular and frontal opercular, visual networks (ventral/dorsal stream), TPOJ, and subcortical regions were reduced when the DE model was excluded. Nucleus accumbens and inferior frontal cortex were more notable when DE was excluded, albeit with respect to the smaller total max count (and similarly for other frontal regions). In terms of c² there appeared to be no notable difference (possibly identical), and in terms of e², there was no considerable difference. [Correction added on 04 September 2023, after first online publication: replaced last clause with: “(nucleus accumbens > hippocampus, basal ganglia [caudate, globus pallidus], and thalamus, the rest absent) (Figures SV4 d², 12, top right panel)”. And included: “These findings are in partial agreement … DE incorporated”. Also, the below mentioned sub-sections are included: Shared environment (female), Unshared environment (female), and Detailed view.]

Additive genetics (male vs. female)

Females had more, although not substantially more, connections across additive genetics (female: 898, male: 763). Females had more notable eDMN and visual network involvement across additive genetics relative to males (albeit males had involvement as well), and males had greater additive-GIF connections present across sensorimotor and certain frontal areas than that of females. These trends (including higher superior parietal and IPS cortex involvement and hippocampal involvement for females) are in agreement with the findings with the DE model. Both males and females also had comparable auditory association cortex involvement (Figure SV3 h² and Figure SV4 h²). In terms of the subcortex, females had hippocampus, brainstem, and cerebellum connections, and males had hippocampus (mainly) and putamen (marginally) connections, which differ from that found while including DE. For further specifics on the differences (relative to max count), see Figures 11 top left panel, SV3 h², 12 top left panel, and SV4 h². [Correction added on 13 March 2023, after first online publication: replaced paragraph with: Females had more … top left panel, and SV4 h².]

Nonadditive genetics (male vs. female)

There were demonstrably more nonadditive-GIF connections across males (1708) as compared with females (191) (>8.9×), and subsequently, greater eDMN, TPN and visual network interactions in males as opposed to females (in partial agreement with the model including DE) (Figure SV3 d² and Figure SV4 d²), and in general agreement with the proposed approach findings (in terms of count and general comparative pattern). Males had notable influence across the majority of the subcortex and in count (outside of nucleus accumbens) relative to females. Females had influence primarily across nucleus accumbens, hippocampus > thalamus, basal ganglia (globus pallidus, caudate). These subcortical findings are in general agreement (with some exceptions—no putamen for females) with the results with DE. However, unlike that with DE, influence across females generally was less concentrated visually. There was also higher influence (in count) across temporal and parietal cortices in general for males than females, with the main exception (in terms of relative to proportion) of females having greater influence across lateral temporal cortex than males. For further specifics on the differences (relative to max count), see Figures 11 top right panel, SV3 d², 12 top right panel, and SV4 d². [Correction added on 13 March 2023, after first online publication: replaced paragraph with: There were demonstrably … top right panel, and SV4 d².]

Takeaways of ACE/ADE model with and without DE

In comparison to the models with DE, there are a few takeaways. First, one potential speculative argument against the idea that the DE model should not be selected due to the principle of marginality is that, while it is true the D term represents interaction effects in theory, in the means it is actually being calculated, the model itself is possibly agnostic to that information (that domain knowledge), and the principle of marginality may not apply. Additionally, the D term is often underestimated and A overestimated when parameters are dropped from the model (Ozaki et al., 2011). And, the case with the DE model will result in a more unlikely outcome, but which may be more all-encompassing and agnostic (less presumptive) of possibilities, as opposed to this corresponding result without the DE model, which is conservative in general (but present with less potential statistical limitations). In either case, what remains true for both circumstances (with and without DE) is that there is a substantial difference between males and females in terms of d² influence (>8.9× in this instance, >5× otherwise, albeit limited by normality constraints and different subsets of connections between males and females). What differs between ACE/ADE without DE versus with DE is an increase in overall attribution to h² and e² for all groups moderately to substantially, and an overall decrease substantially of d², but still highly notable across males. The results for h² are generally comparable regardless of group with that without the DE model (with some deviation); however, for d², the pattern that remains most intact and in proportion is that for males, and not the other groups. Additionally, considering the alteration of nonadditive genetics and additive genetics, instead of a 10× difference for males (nonadditive: additive), the proportion drops to 2.2×. Similarly, for females, the proportion of additive:nonadditive genetics increases to 4.8× from approximately an even distribution (1:1). For normalization (similar to relative density) type results, the normalization figures shown in the appendix of DE versus no DE show differences in that respect (Figures S13-15, SV13-15), which was not a primary focus of this study, however. [Correction added on 05 September 2023, after first online publication: replaced paragraph with: In comparison to the models … was not a primary focus of this study, however.]

Overall patterns

There were over 8.5-19.1 (validated with Levene's test to be in the range of >15-19) times more significant functional connections that were genetically influenced in males (1528) than females (178). There were also greater genetically-influenced network–network interactions noted in males than females. These patterns suggest males may be more functionally influenced by genetics than females in terms of sex-specific individual differences (of the resting state brain). With respect to the ACE/ADE model findings, although proportionately the connections differed, as was noted in terms of nonadditive genetics (as additive genetics was compared to nonadditive genetics, relatively smaller in difference across males and females), males had greater than five times more highly influenced connections (3435 with DE, 1708 without) than females (684 with DE, 191 without) (relative to 2× more females than males for additive genetics specifically). This proportionate finding (>5-8.9×) was comparable to the approach proposed (>8.5-19.1×), and also may suggest greater influence of genetics in males as opposed to females in terms of sex-specific individual differences. [Correction added on 10 May 2023, after first online publication: influence.]

Cortical regions

As noted at the population level, individual differences in primarily males were under extensive genetic influence in terms of network interactions involving visual, parietal, temporal cortices, as evidenced by the findings of either approach, as both the ACE/ADE model and the proposed approach agreed, with the delineation that both males and females had additive genetic influence in these visual, parietal, temporal network interactions; but males had even greater nonadditive genetic influence (in count) and in proportion relative to that of females in these networks. In addition, individual differences in males were more genetically-influenced in terms of network interactions involving auditory-language related cortices compared with individual differences in females, as evidenced by both the proposed approach findings, and the ACE/ADE model findings across nonadditive genetics but not additive genetics in these areas (in terms of count, females had more additive genetic influence in auditory areas, and relative density significance (limited to the F-test) but nonadditive genetic effects were much higher (in count) than additive genetic effects in males, and higher overall (in count) than additive and nonadditive genetic effects in females). This ACE/ADE finding remained true when excluding the DE model for females (in terms of count), but had comparable nonadditive and additive effects in males. This finding suggests that in terms of individual differences in resting state functional connectivity, males may be more influenced by genetics and that females may be more environmentally influenced in terms of auditory–language systems than males. This outcome may explain some of the differences in auditory–language system functions reported between males and females (Clements et al., 2006). [Correction added on 05 September 2023, after first online publication: added: individual differences in, three times. Added: in count, twice. Added: in terms of count. Added: (limited to the F-test).]

As noted at the population level, individual differences in primarily males (and relatively marginally females) were under extensive genetic influence in terms of interactions involving the eDMN which is considered a central hub of the brain for various low-level cognitive and affective processes such as internal monitoring, rumination, and evaluation of self and others, as noted previously (Ames et al., 2008; Buckner et al., 2008; De Brigard et al., 2015; Denny et al., 2012; Hagmann et al., 2008; Jenkins et al., 2008; Leech & Sharp, 2014; Lois & Wessa, 2016; Mitchell et al., 2005; Nejad et al., 2013; Posner et al., 2013; Raposo et al., 2011). In addition, individual differences in males also were more genetically influenced (and teased apart by the ACE/ADE model as primarily nonadditive genetic influence, albeit additive genetics was present) compared with individual differences in females in terms of intranetwork and internetwork interactions between eDMN and other brain regions (occipital, temporal, parietal, and frontal regions) involved in various task-oriented processes and attending to and interacting with the environment which comprise part of the Task Positive Networks (TPNs) (Adolphs, 2006; De Brigard et al., 2015; Denny et al., 2012; Jenkins et al., 2008; Mahy et al., 2014; Raposo et al., 2011; Saxe, 2006; Schurz & Perner, 2015). [Correction added on 05 September 2023, after first online publication: removed: in terms of individual differences. Added: individual differences in, three times.]

Sensorimotor regions

In addition, individual differences in males were more genetically-influenced in terms of network interactions involving primary sensorimotor cortices (audition, vision, somatosensory and motor cortices) compared with individual differences in females, as evidenced by both the proposed approach findings, and the ACE/ADE with DE model findings across both additive but more substantially nonadditive genetics for males; for females, nonadditive and additive contributions were generally similar outside of audition in these areas. If the DE model is not considered, then there is a similar pattern for males, but for females, additive effects are more explanatory than nonadditive effects, in general. [Correction added on 10 May 2023, after first online publication: individual differences in, twice.]

Subcortical/noncortical regions

Thalamus and basal ganglia (caudate) regions demonstrated a significant number of connections (and notable influence of primarily nonadditive genetic connections in the ACE/ADE approach) with each other as well as cortical regions in males which may be due to the cortico-basal-ganglia-thalamic-cortical feedback loops needed to maintain or sustain activity in these lateral cortical regions involved in various high-level and low-level cognitive processes (Alexander, 1986). Ventral diencephalon showed significant connections (and which were influenced by nonadditive genetics in ACE/ADE) in males which control autonomic functions. Cortico-cerebellar involvement was noted more in males (and which was influenced by nonadditive genetics in ACE/ADE) than females which are involved in processes such as providing error correction and feedback to cortical processes (Habas et al., 2009).

There were also over 8.5-19.1 times more genetically influenced functional connections for males (1524 proposed method, 3435 nonadditive genetic connections if including DE, 1708 if excluding, in ACE/ADE) than for females (178 proposed method, 684 nonadditive genetic connections if including DE, 191 if excluding, in ACE/ADE, a 5-8.9× difference in ACE/ADE) suggesting that individual differences in male resting state brains may be more genetically influenced than that of females replace with. This result may suggest individual differences due to genetics in males (more) versus females (less) in terms of interplay of attending to task-oriented interactions with the environment (TPNs) versus internal and external interactions with self and others (eDMN), SMN, and subcortical/noncortical regions. Overall, these findings suggest that for the young adult cohort investigated, individual differences in males may be more functionally influenced by genetics and that individual differences in females may be more environmentally-influenced in terms of TPN, eDMN, sensorimotor, subcortical networks, and cerebellum. This outcome may explain some of the differences in functions reported between males and females (Andreano et al., 2013; Clements et al., 2006; Jäncke, 2018). [Correction added on 05 May 2023, after first online publication: Added: individual differences in, three times.]

Levene's test vs. F-test

There are strong proponents for the exclusion of usage of the F-test, especially when normality is in doubt, given the false positive rate and false negative rate issue when it comes to very high or low kurtic data which cannot always be assessed (Hosken et al., 2018). As these limitations of the F-test are established, with the caveat that in general when sample sizes are large, or when normality is not in doubt, the F-test can be a more effective test in general than other variance equality tests (Nordstokke & Zumbo, 2007), further studies should be cautious in their immediate usage of the F-test, especially if not considering any normality tests in conjunction. At the same time, it could be argued that (without reference to the ground truth), that by pairing the F-test with a strong normality test such as Shapiro-Wilk (it too being dependent on the sample size, and data distribution), the anticonservative nature of the F-test in conjunction with the normality tests to restrict the issue could lead to the balance between anticonservative and conservative effects. However, that is at the additional cost of 1) pre-testing effects on the error rate, and 2) the exclusion in the case of the application at hand, of certain connections. One view in this study is that normality testing can be viewed as a kind of filter for the cartographer's map concept (although this view has limitations statistically).

Regardless, this study validated and corroborated the general trend count of the F-test findings of the proposed approach with Levene's test (although in terms of raw count of connections there was moderate to substantial difference, e.g., at the group level >1000 connections, and the differences between males and females became more pronounced in proportion, upon using Levene's test). The deviation of findings may possibly be due to any of the trade-offs above mentioned, and what also may be due to the conservative nature of Levene's test (potential high reduction of true positives). Therefore, keeping all of these factors in mind for future studies, it is recommended that, when it comes to application of the proposed method, the pairing between the F-test and stringent normality testing be further investigated to ensure appropriateness, and when in doubt about normality, avoid using the F-test by itself and instead compare with Levene's test (or use Levene's test solely). Additionally, as per (Nordstokke & Zumbo, 2007), the median-based Levene's test may be preferable (as in this study) in general (although specifics will vary), and other versions may give coverage that is poor and has similar performance to when the F-test is not accounted for in terms of its sensitivity to normality or sample size. [Correction added on 13 March 2023, after first online publication: replaced and relates with: and has similar performance.]

DE vs. no DE (and parameter indeterminacy)

There is contention in the field regarding whether the DE model should be used. The DE model was incorporated in an agnostic fashion prior to validation of the ACE/ADE model results without the DE model. However, upon validating the results with model selection which excludes the DE model, there are considerable changes to the cartographer maps that are generated (in principle it is explainable because by excluding DE as a possibility, that biases the model preference to A, C or E, and vice versa). The discrepancy highlights, outside of the limitations of the DE model itself, the confounding of variables in the ACE model framework (e.g., A and D), and given lack of ground truth, especially in the context of generating cartographer maps, more emphasis should be directed perhaps away from using strictly AIC (and the limitations of unsubstantial model fit differences between models). Upon viewing the results provided (with and without DE), inclusion of DE could be considered more conservative in terms of assumptions, whereas exclusion of DE could be more conservative in terms of likelihood and potential arguable avoidance of certain statistical limitations that inclusion of DE may be susceptible to. In either case, it is recommended that, even though there is the benefit of being agnostic to the outcome for the DE model, given its consequential potential power and statistical issues, as well as theoretical low-likelhood, if it is used, relevant estimates from ADE (with those respective tradeoffs and benefits) should also be included (if using traditional AIC). That is to say, evaluate both (and consider avoiding using DE if in doubt, or when not considering it in a probabilistic sense as discussed next). [Correction added on 13 March 2023, after first online publication: replaced statistical limitations with: avoidance of certain statistical limitations that inclusion of DE may be susceptible to.]

Relatedly, parameter indeterminacy is a concept that (Keller, 2005) discusses at length, and proposes an interesting solution, which may be logical in the future application of the ACE/ADE model portion of cartographer mapping. Specifically, the idea of generating a space of possible outcomes, and generating maps based on multiple possible models may be of interest in the future, especially given the importance of the estimated maps in how they may guide future researchers, and given the lack of the ground truth being present. Specifically, (Keller, 2005) stresses that the value of r (which has a relationship of rV_NA = 1/4V_D + V_I,S,DZ and of (1-r)V_NA = 3/4V_D+ΔV_I as formulated in this study), used for V_NA which encompasses V_D and higher order epistatic effects (V_I) and which can range from 0 – 0.25 for DZ twins, along with the various models (ACE, ADE, AE, DE, CE), are assumptions that are inherent in generating estimates. Given this fact, it was suggested that the models and r could be used altogether to create a joint space of what is unlikely (albeit possible) to likely, and that these assumptions should be made explicit and kept in mind since they affect the result ultimately. [Correction added on 10 May 2023, after first online publication: replaced an indirect relationship of Δ in ΔV_I with: a relationship of rV_NA = 1/4V_D + V_I,S,DZ and of (1-r)V_NA = 3/4V_D+ΔV_I.]

Additional future directions

When considering the results represented as part of a cartographer's map of influence in terms of individual differences, a few factors should be noted. 1) The cartographer's map, as indicated by AdminNeale, should be considered a rough map which is useful for future exploration, but may have errors in specifics (as with age-old cartographer maps), and which would be most appropriate for those applications which are low-risk, (e.g., not clinical trials). 2) The cartographer map is dependent on a few factors: A) the data (and its distribution), how it is acquired, sampled and processed (e.g., even the data may generate spurious connections in terms of rsFC and has its own true positive and false positive rate, ignoring statistical tests), B) the technique, or instruments to analyze the map (in this case, the statistical tests used, their limitations and cut-offs, or the software such as OpenMx), and C) how the model or problem itself is formulated and inherent assumptions (the proper or guided question and problem formulation that are being considered, for example, when considering model types—e.g., including or excluding DE—may change the outcome). It might be argued that each statistical test, with their own limitations, may allow the user to glean different information from the cartographer's map created, as each test has distinct properties contingent on the data—that is, each will have a different set of true positive, false positive, true negative and false negative rates, which can be beneficial dependent on the application and purpose. [Correction added on 13 March 2023, after first online publication: replaced old-age with: age-old. Replaced “the data and how it is acquired and sampled” with: “the data (and its distribution), how it is acquired, sampled and processed (e.g., even the data may generate spurious connections in terms of rsFC and has its own true positive and false positive rate, ignoring statistical tests)”. Added: and inherent assumptions. Replaced “true positives, false positives, true negatives and false negatives” with: “true positive, false positive, true negative and false negative rates”.]

Although for the sake of comparison this study did not incorporate any correction scheme to the ACE/ADE model results (e.g., the cartographer maps relevant), in future studies, it may be of value to do so. Based on the cartographer map concept, it may be beneficial to apply additional correction to obtain a different set of properties which would elucidate different information (e.g., the level of correction itself can result in a different signal-to-noise-ratio, or SNR of the map, which may highlight different features). And, similar to other cases, it is also possible that each rendition of a cartographer map may encode intrinsically different covariate information if not previously addressed. It may be of value in the future to provide maps with different covariates accounted for distinctly, and to see whether that accounts for changes in certain regions of the map (e.g., visually), as that may provide unique sets of information based on the application. Another element which could be focused on as well, and which ultimately will result in different maps of use for validation and alternative information, would be the parcellation scheme (and relatedly, resolution, definition, and parcels) used (e.g., the parcellation choice affects the amount of connections possible when comparing across groups). [Correction added on 05 September 2023, after first online publication: added paragraph.]

Specific to the ACE/ADE model, the maps reported in this study were restricted by normality and classical twin design assumption constraints and hence are incomplete—given the amount of connections possible, future studies should focus on amending this restriction issue, while still maintaining quality of the result. Modeling the problem (without DE, for example) dynamically changes the best fit model possibilities, which may be more insightful with regard to certain information as opposed to others, when the ground-truth expected model is unknown, and with trade-offs in statistical and theoretical ramifications. However, as mentioned previously, a manner of designing a joint space of all model possibilities and assumptions may be of future interest which is informative and agnostic. Finally, more objective means to quantify and validate the maps (e.g., the counts that are represented in this study, from high to low, or relative density and density in general, which was not as emphasized as counts and relative counts), may be of interest in the future. In any case, for whatever set of choices are determined, it is recommended it be stated explicitly, justified, and the corresponding limitations and implications stated.