Examining the neurostructural architecture of intelligence: The Lothian Birth Cohort 1936 study

Examining underlying neurostructural correlates of speciﬁc cognitive abilities is practically and theoretically complicated by the existence of the positive manifold (all cognitive tests positively correlate): if a brain structure is associated with a cognitive task, how much of this is uniquely related to the cognitive domain, and how much is due to covariance with all other tests across domains (captured by general cognitive functioning, also known as general intelligence, or ‘ g ’)? We quantitatively address this question by examining associations between brain structural and diffusion MRI measures (global tissue volumes, white matter hyperintensities, global white matter diffusion fractional anisotropy and mean diffusivity, and FreeSurfer processed vertex-wise cortical volumes, smoothed at 20mm fwhm) with g and cognitive domains (processing speed, crystallised ability


General intelligence
Brain MRI

Cortical volume
White matter a b s t r a c t Examining underlying neurostructural correlates of specific cognitive abilities is practically and theoretically complicated by the existence of the positive manifold (all cognitive tests positively correlate): if a brain structure is associated with a cognitive task, how much of this is uniquely related to the cognitive domain, and how much is due to covariance with all other tests across domains (captured by general cognitive functioning, also known as general intelligence, or 'g')?We quantitatively address this question by examining associations between brain structural and diffusion MRI measures (global tissue volumes, white matter hyperintensities, global white matter diffusion fractional anisotropy and mean diffusivity, and FreeSurfer processed vertex-wise cortical volumes, smoothed at 20mm fwhm) with g and cognitive domains (processing speed, crystallised ability, memory, visuospatial ability).The cognitive domains were modelled using confirmatory factor analysis to derive both hierarchical and bifactor solutions using 13 cognitive tests in 697 participants from the Lothian Birth Cohort 1936 study (mean age 72.5 years; SD ¼ .7).Associations between the extracted cognitive factor scores for each domain and g were computed for each brain measure covarying for age, sex and intracranial volume, and corrected for false discovery rate.
There were a range of significant associations between cognitive domains and global MRI brain structural measures (r range .008 to .269,p < .05).Regions implicated by vertexwise regional cortical volume included a widespread number of medial and lateral areas of the frontal, temporal and parietal lobes.However, at both global and regional level, much of the domain-MRI associations were shared (statistically accounted for by g).Removing g-Introduction Evidence for the neurobiological bases of complex behaviour supports an integrative network view, whereby higher cognitive functioning is underpinned by multiple partiallyoverlapping brain processes and connected regions (Bressler & Menon, 2010;Sporns, 2013).Explanatory frameworks include Executive Functioning (Miller, 2000), Multiple Demand Network (Duncan, 2010) and the Parieto-Frontal Integration Theory (Jung & Haier, 2007).Such concepts e which are not mutually exclusive (Camilleri et al., 2018;Deary et al., 2021) e are also compatible with statistical evidence that cognitive test scores tend to correlate positively, as first shown by Spearman (1904), and subsequently by countless other studies (Jensen, 1993(Jensen, , 2000;;Neisser et al., 1996), indicating that individual differences in cognitive abilities are not orthogonal.Put plainly, those who score higher on some cognitive tests tend also to do so on other types of cognitive tests across a variety of domains.A substantial proportion of between-person differences across diverse cognitive test scores can be represented by a single underlying factor of general cognitive ability (also known as general intelligence, or 'g').However, it remains unclear how far associations between brain measures and cognitive test scores are domain-specific, versus overlapping, or attributable to g.Given that individual differences in g are associated with many important life outcomes such as levels of education (Deary et al., 2007;Neisser et al., 1996), career success (Gottfredson, 1997;Strenze, 2007), lifelong health (Deary et al., 2004a;Wrulich et al., 2013) and longevity (Calvin et al., 2017;Whalley et al., 2001), establishing the unique and overlapping cerebral correlates of both g and specific cognitive domains is of interest to both cognitive neuroscientists and cognitive epidemiologists.
There is a modest but replicable positive correlation between total brain volume and g, with estimates of magnitude tending to fall around r ¼ ~.28 (Cox et al., 2019;Gignac & Bates, 2017;McDaniel, 2005;Pietschnig et al., 2015;Ritchie et al., 2018).However, knowing that brain size is modestly related to g is relatively uninformative of more specific neurobiological bases.Widespread reports of associations between g and global grey matter (GM) measures such as cortical thickness, surface area, volume (Camilleri et al., 2018;Deary et al., 2004aDeary et al., , 2007;;Gottfredson, 1997;Jensen, 1993Jensen, , 2000;;Neisser et al., 1996;Spearman, 1904;Strenze, 2007), and both ageing-related white matter damage (white matter hyperintensities; WMH) (Deary et al., 2006;Puzo et al., 2019;Ritchie et al., 2015a) and microstructural properties of white matter (WM) pathways (Charlton et al., 2007;Chiang et al., 2009;Deary et al., 2006;Penke et al., 2012;Puzo et al., 2019;Ritchie et al., 2015aRitchie et al., , 2015b;;Tamnes et al., 2010;Yu et al., 2008) support the idea that cognitive processes rely on both the efficient functioning of brain cells predominantly found in grey matter, and also by efficient transmission of action potentials to distal cortical regions, via, for example, adequate axonal myelination.However, not all regions of the brain are equally associated with general cognitive differences; there is evidence of differential regional associations with g across the cortex.Regional cortical correlates of g from structural and functional MRI studies among healthy adults and children typically identify associations in lateral prefrontal and occipital lobes, cingulate, insula, and lateral and medial temporal and parietal loci; such areas notably co-localise with regions implicated in the P-FIT (Jung & Haier, 2007), multiple demand network (Camilleri et al., 2018;Duncan, 2010), fronto-parietal control network (Marek et al., 2018), superordinate cognitive control network (Miller, 2000;Niendam et al., 2012), and extrinsic mode network (Hugdahl et al., 2019).
Given extensive g associations across the cortex, it is important, particularly given different ideas about the theoretical nature of g (Conway et al., 2021;Duncan, 2010;Jung & Haier, 2007;Kovacs et al., 2016), to know how the neuroanatomical correlates of specific cognitive domains relate to one another, and to those of g.Only a handful of studies to-date have examined whether, and where, g and more specific cognitive abilities share neuroanatomical substrates.Colom et al. (2009) used voxel-based morphometry in 100 healthy adults to explore associations between regional GM volume and orthogonal factors of fluid, crystallised, spatial intelligence, each measured using three tests, and higher order factor g derived from all tests.These factors were associated with both overlapping and unique regions, with overlapping regions found across lateral regions in the frontal, parietal, temporal and occipital cortex, reflecting the P-FIT (Jung & Haier, 2007), and additional unique regional associations with g in the dorsolateral prefrontal cortex, primary somatosensory cortex, fusiform gyrus and auditory cortex (Colom et al., 2009).In a study of 207 healthy children and adolescents, Karama et al. (2011) regressed scores of three cognitive domains, derived from seven tests, against extracted g scores, to calculate 'g-independent' domain scores.After adjusting for g, they found all previously significant associations between cognitive domains and cortical thickness were fully attenuated (Karama et al., 2011).These results were replicated in adolescents and young adults (Menary et al., 2013), but may not be generalisable to older populations due to changes which occur across the life-course.With a clinical sample of 241 patients with focal brain damage, Gl€ ascher et al. ( 2009) used voxel-based lesion symptom mapping to map four cognitive indices derived from 13 cognitive tests: verbal comprehension, perceptual organisation, processing speed and working memory.After removing all shared variance, thus accounting for g, cortical associations were considerably restricted, with no remaining loci for processing speed.Areas where lesions were associated with overlapping cognitive domains included the left inferior frontal cortex, insular cortex, frontopolar cortex, and parietal cortex.In a series of lesion-mapping studies, Barbey and colleagues also reported evidence that g shared substantial cortical loci with emotional intelligence (Barbey et al., 2014a) cognitive flexibility (Barbey et al., 2013), and working memory (Barbey et al., 2014b).
Thus, there exists convergent but limited evidence that gcortical associations at least partly overlap with those cortical loci associated with more specific cognitive abilities.Nevertheless, sample sizes have typically been modest (studies ranging from 100 to 241 participants) which reduces the statistical power with which one can reliably identify domainspecific (non-g) loci of small effects.Furthermore, no study has explored this in a large non-clinical sample, which is important so as to avoid limitations typically associated with clinical samples, such as confounding factors due to diverse lesion aetiology and tissue involvement, lack of control groups and low statistical power.It is also important to consider this question in older adults; results from younger samples may not be generalizable.This is particularly important in order to consider individual differences in cognitive ageing, given the distinction between ageing trajectories of crystallised (verbal) ability versus more fluid aspects of g (Deary et al., 2009) and how important this may be for understanding the brain structural basis of poorer cognitive ageing.Some studies in non-clinical samples have also not included extensive cognitive batteries; domains were derived from as few as two tests by Karama et al. (2011) and Colom et al. (2009), which may lead to the introduction of test-specific error in latent factor estimations.
To partly address limitations in the field to date, the present study investigates the global and regional brain correlates of four major cognitive domains (processing speed, crystallised ability, memory, and visuospatial ability) and how and where they overlap with g in 697 older adults, using 13 varied cognitive tests.Concomitant cognitive and brain imaging data are drawn from the Lothian Birth Cohort 1936 study (LBC1936; Taylor et al., 2018;Wardlaw et al., 2011) Wave 2 (the first wave at which brain MRIs were collected alongside cognitive testing) when participants were ~73 years old.We provide global brain, and then vertex-wise cortical volumetric, analyses of the degree to which there are shared and unique cerebral correlates of each cognitive domain beyond g.Importantly, we model the common and unique cognitive covariances in two ways: using a bifactor model of g and cognitive domains, and single-order models which independently indicate each domain and g.This approach, in line with previous research (Protzko & Colom, 2021), allows us address the possibility that when cognitive tests are modelled in a more traditional hierarchical structure (Fig. 1c) the latent measure of g is directly indicated by the cognitive domains (see Fig. 1c), and so might artificially inflate the degree of spatial overlap between the cognitive domains and with g itself when modelled upon the cortex.Thus, by implementing bifactor (Fig. 1a) and single-order models of g (Fig. 1b), we ensure a more stringent test of brain overlaps between g and cognitive domains (by increasing 'statistical distance' between domains and g in so far as it is possible).First, we will examine global structural associations between cognitive domains and g with volumes of total brain (TBV), grey matter (GM), normal-appearing white matter (NAWM) and white matter hyperintensities (WMH), and with general factors of white matter microstructure, fractional anisotropy (gFA) and mean diffusivity (gMD).In line with previous literature, we expect to find significant associations between g and cognitive domains with these global measures.However, we hypothesise that, after removing g-related covariance from cognitive domain scores, magnitudes of associations between cognitive domains and global measures will be substantially attenuated.Second, regional structural associations will be explored at the level of the individual vertex.We will spatially map individual associations between each cognitive domain and g with cortical volume.We will then map associations between g and non-g components of cognitive domains with cortical volume in order to examine the degree to which cognitive domains and g relate to common and unique aspects of regional cortical structure.In line with conceptualisations of g as deriving from overlapping activity of multiple cognitive operations across a distributed cortical network (Jung & Haier, 2007), we expect that the majority of these regional associations with cognitive domains will be accounted for by g.We therefore hypothesise that regional cortical associations with g and cognitive domains will show substantial overlap with one another in distributed regions, particularly in frontal and parietal regions, resembling the P-FIT regions as outlined above (Jung & Haier, 2007).In turn, we hypothesise that g will display very few, if any, unique associations with any cortical regions, in line with this conceptualisation of g.

Methods
We report how we determined our sample size, all data exclusions, all inclusion/exclusion criteria, whether inclusion/ exclusion criteria were established prior to data analysis, all manipulations, and all measures in the study.The baseline sample size (N ¼ 1,091) represents all those who were recruited at the initial wave after responding to invitations (based on NHS Community Health Index identification or media advertisements), being born in 1936 and not having received a diagnosis of dementia (Deary et al., 2012).

Study design
The current study focuses on Wave 2 data, when participants had their first MRI brain scan at mean age 73 (n ¼ 866).Information on recruitment and testing of LBC1936 participants has been well characterised elsewhere (Deary et al., 2012;Taylor et al., 2018).After exclusion of participants with missing cognitive or MRI data, the analytic sample included 697 participants.
Participants gave written consent before participating in each wave.Ethical approval was obtained from Multi-Centre Research Ethics Committee for Scotland (MREC/01/0/56; Wave 1), the Lothian Research Ethics Committee (LREC/2003/ 2/29; Wave 1), and the Scotland A Research Ethics Committee (07/MRE00/58; Wave 2).We provide scripts and all vertex-wise results (t-stats, p-values, and FDR-corrected q-values) in fsaverage space in the research team's github page: https:// github.com/LothianBirthCohorts/neurostructural_architecture_of_intelligence.Data access requests can be made to the Lothian Birth Cohorts at https://lothian-birthcohorts.ed.ac.uk/ and shared under a formal Data Transfer Agreement.The present research uses previously-collected and ederived cognitive and neuroimaging data according to published protocols.None of the present analyses were preregistered prior to the research being conducted.

Cognitive
Participants completed an extensive battery of cognitive tests, 13 of which were used to create scores for four distinct cognitive domains based on previous analysis (Ritchie et al., 2016): processing speed, crystallised ability, memory and visuospatial ability.Processing speed consisted of Wechsler Adult Intelligence Scale 3rd edition (WAIS-III UK ; Weschler, 1998) subtests Symbol Search and Digit-Symbol Substitution, and Four-Choice Reaction Time and Inspection Time scores.Four-Choice Reaction time measures time taken to correctly classify a number on a screen by pressing the corresponding numbered button (Deary et al., 2001).During Inspection Time, participants view a line shape that is immediately masked after durations of 6e200 msec, and indicate whether the left or right side of the shape was longest.Final score is total correct responses across all 150 trials (Deary et al., 2004b).Crystallised ability comprised a phonemic verbal fluency test (C, F, L; Lezak et al., 2004), the National Adult Reading Test (NART; Nelson & Willison, 1991), and the Wechsler Test of Adult Reading (Wechsler, 2001) Folstein et al., 1975).

MRI acquisition and analysis
LBC1936 MRI data acquisition protocol has been described previously (Wardlaw et al., 2011) and is described in further detail in Supplementary Methods.The MRI scan in a GE Signa Horizon HDx 1.5T clinical scanner (General Electric, Milwaukee, WI), equipped with a manufacturer supplied 8-channel phased-array head coil, included T1-and diffusion-weighted sequences.
Structural brain volume variables were segmented using a semi-automated multi-spectral technique (Hernandez et al., 2012).Global structural measures for analysis included TBV, GM, NAWM and WMH volumes.Local processing and quality control of cortical reconstruction and segmentation was conducted using Freesurfer v5.1 on T1-weighted volumes.Analyses were adjusted for intracranial volume (ICV) to consider brain atrophy due to age (Royle et al., 2013).Residuals from this correction therefore allow us to account for instances where, for example, two individuals with the same brain volume might have experienced more less atrophy from their maximal healthy size (as indicated by ICV).This correction e in older participants such as the present sample e theoretically amplifies associations between brain volumes and cognitive functioning, since in older age, cognitive measures are a conflation of i) initial brain volumes prior to agerelated declines, and ii) the extent of ageing-related change an individual has subsequently experienced (Clayden et al., 2011;Royle et al., 2013).
As previously reported (Ritchie et al., 2015b), general measures of white matter microstructure were used to indicate the shared variance among FA and MD measures of 12 major WM tracts (the genu and splenium of the corpus callosum, and bilateral anterior thalamic radiations, cingulum, arcuate fasciculus, uncinate fasciculus and inferior longitudinal fasciculus) obtained from diffusion MRI and probabilistic neighbourhood tractography (Clayden et al., 2011).Mean measures of FA and MD were calculated for each bilateral WM tract from the left and right aspect of the tracts, resulting in 7 measures of FA and 7 of MD.Using confirmatory factor analysis (CFA), these were used to derive general factors of FA (gFA) and MD (gMD), which accounted for 37.9% and 39.4% variance respectively, and which were extracted as vectors for subsequent analyses.The model fit indices were as follows: for gFA, CFI ¼ .974,TLI ¼ .961,RMSEA ¼ .054,and SRMR ¼ .030;and for gMD, CFI ¼ .977,TLI ¼ .966,RMSEA ¼ .054and SRMR ¼ .028.

Cognitive modelling
We used two approaches to model g and cognitive domains.First, using a bifactor CFA model to remove g-related variance from cognitive domain scores, we extracted latent factor scores for each cognitive domain (processing speed, crystallised ability, memory, visuospatial ability) and g.In this model, g is indicated by all 13 cognitive tests and the cognitive domains are the residual, non-g, covariances, modelled as cognitive domain factors orthogonal to g.Second, g was defined as a single-order factor indicated by all 13 cognitive test scores, similar to above.In separate models, each of the cognitive domains, as indicated by their relevant cognitive test scores, were modelled and extracted from single-order CFA models (see Fig. 1b).For each participant, we extracted two sets of scores for each cognitive domain and g, one set from the bifactor CFA model (in which g variance is removed from the cognitive domain scores) and one from the singleorder CFA model (in which g variance is not removed from the cognitive domain scores).

Global structural associations
Global brain structure (TBV, GM, NAWM, WMH) and WM microstructure (gFA, gMD) were included as predictors in regressions to examine their associations with cognitive domain and g scores.For each cognitive domain, we provided the estimates for both the single-order cognitive domains, and their corresponding bifactor scores (i.e. when g had been removed).All analyses were adjusted for age and sex, and regressions with global brain structure measures were adjusted for intracranial volume (ICV) to estimate and correct for brain atrophy due to age (Royle et al., 2013).To circumvent variance inflation due to multicollinearity between global brain structure measures and ICV (high model variance inflation factors), we created models of the residuals of these measures on all covariates, then correlated these with cognitive domain and g scores.We thus report correlation coefficients (Pearson's r) values, standard error (SE) and pvalues.

Regional analyses
Regional associations with vertex-wise cortical volume were examined using linear regression with the SurfStat toolbox (Worsley et al., 2008) in MATLAB (v2012a; The MathWorks Inc, 2012) in 622 participants who had extracted latent cognitive scores and complete MRI data.All regressions were adjusted for age, sex and ICV, and significance-values were corrected for multiple comparisons across all vertices using FDR correction (q-value of .05).Greater associations with cognitive domains and g were represented in t-maps by 'hotter' colours on the colour spectrum, and all images were scaled to the same limits to aid comparison of relative effect size across analyses.
First, we illustrate the similarity between the spatial regional correlates of cortical volume and cognitive domains, using the cognitive domains scores extracted from the singleorder CFAs (i.e.where domain factor scores retain g variance).
Next, we identified cortical associations with (single-order) g, and quantitatively compared the spatial patterning of cortical associations across g and cognitive domains.We reported i) the number of common and unique significant vertices, and ii) the spatial agreement as indicated by t-value correlations (we expected that vertices with higher t-values for g would also be vertices that had higher t-values for cognitive domains.For ii), we computed the spatial overlap (r) both as a function of all vertices across the cortex (k ¼ 308,802), and also restricted to only those vertices where q < .05.Overlapping and distinct patterns of regional association were also illustrated using conjunction plots, which visually display vertices (at q < .05)that have associations with multiple domains, and conditional analyses to show regions with significant (q < .05)associations unique to only one domain or g.

Descriptives
Analyses In the set of single-order models indicating g and cognitive domains, g explained 31.3% of variance in test scores, and domains of processing speed explained 48.3%, crystallised ability 67.0%, memory 41.5% and visuospatial ability 34.4%; we present loadings for single-order modelled scores in Supplementary Fig. 2. Indicators of model fit were deemed acceptable (CFI ¼ .966,TLI ¼ .957,RMSEA ¼ .060,SRMR ¼ .041).A correlation matrix showing correlation coefficients (Pearson's r) between derived domain and g scores from each of these sets of models is provided in Supplementary Table 3.

Global brain structure
A correlation matrix of brain variables is provided in Supplementary Table 4.In regressions using single-order derived scores of cognitive domains and g, greater TBV, GM, NAWM volumes, higher FA, and lower WMH and MD were associated with better cognitive scores (Fig. 2, Supplementary Table 5, standardised coefficient range .008 to .269,FDR corrected p values < .05),with the exception of crystallised ability which was associated with only TBV (r ¼ .160,p ¼ <.001), GM (r ¼ .142,p ¼ <.001) and NAWM (r ¼ .102,p ¼ .007).However, compared to these single-order models, there was a marked attenuation of significant association magnitudes in regressions using bi-factor derived scores ( A comparison of coefficients from single-order and bifactor derived scores are presented in Fig. 2 and Supplementary Table 5.In analyses of bifactor-derived scores, coefficients for associations across all global structural measures were attenuated for processing speed a mean of 27.9%, memory by 38.5%, crystallised ability by 58.7%, and visuospatial ability by 59.7%; associations with the latter three were mostly nonsignificant across global measures.Percentage attenuation for each global measure is presented in Supplementary Table 6.Associations with g were mostly unchanged, with average .8%attenuation.

Regional analyses
Regional domain associations with single-order derived domain scores are displayed in Fig. 3. Greater processing speed and visuospatial ability were associated with greater volume in distributed vertices bilaterally across the lateral and medial temporal, lateral parietal, lateral occipital and mainly left lateral and medial frontal lobes.The strongest magnitudes were in medial and anterior lateral temporal lobes, with noticeable involvement of motor and somatosensory cortices.Greater crystallised ability and memory displayed limited associations mainly in the lateral and medial temporal and lateral parietal lobes, with some prominent associations between memory and the posterior lateral and anterior medial temporal lobe.
We then used these scores to quantitatively assess the spatial cortical overlap between single-order modelled g and cognitive domains.This allowed the neuroanatomical patterns of association to reveal overlapping associations across the cortex, in contrast to partialling g out of the domains prior to regressing these on brain (as in the bifactor model).Greater cortical volume was associated with greater g in vertices distributed across the cortex, including a widespread number of medial and lateral areas of the frontal, temporal and parietal and occipital lobes (Fig. 5a and b).Notably, when considering the 177816 vertices which were significantly associated with g (FDR Q < .05),there was substantial overlap with cognitive domains; only 5565 (3.13%) vertices were unique to g alone.In total, g shared 138017 of these significant vertices with processing speed (77.6%), 41112 with crystallised ability (23.1%), 39295 with memory (22.1%) and 157220 with visuospatial ability (88.4%).The extent of overlap is presented visually in Fig. 5c, showing cortical loci that display   5. c o r t e x 1 7 8 ( 2 0 2 4 ) 2 6 9 e2 8 6 Fig. 3 e Vertex-wise associations between cortical volume and single-order derived cognitive domains.Left column provides the magnitude of associations (t-maps) whereby hotter colours denote larger positive associations between cortical volume and cognitive scores.Right column shows the corresponding FDR-corrected q-values.Models corrected for age, sex and ICV.All t-value maps were scaled to the same limits to aid visual comparison of relative effect size.Equivalent maps for bifactor models are presented in Fig. 4.
Fig. 4 e Vertex-wise associations between cortical volume and bifactor derived cognitive domains.Left column provides the magnitude of associations (t-maps) whereby hotter colours denote larger positive associations between cortical volume and cognitive scores.Right column shows the corresponding FDR-corrected q-values.Models corrected for age, sex and ICV.All t-value maps were scaled to the same limits to aid visual comparison of relative effect size.
c o r t e x 1 7 8 ( 2 0 2 4 ) 2 6 9 e2 8 6 Fig. 5 e Significant associations (FDR Q < .05) of cortical volume with g and cognitive domains from single-order (top half; ad) and bifactor models (bottom half; e-h), showing regions associated with g, areas of overlap between g and cognitive overlapping associations with g and cognitive domains, and Fig. 5d, showing areas with unique associations with g or a domain across the cortex.Supplementary Figs. 3 and 4, and Supplementary Table 7 indicate that visuospatial and processing speed (5104 vertices) and visuospatial and memory (57 vertices) shared only very limited cortical loci that were independent of g.Moreover, as displayed in Table 2, those vertices most strongly correlated with g were also those more strongly correlated with overlapping cognitive domains (r range: .809 to .909,p values < .001).Pearson's correlations were also calculated including only vertices which had significant associations with scores in FDR corrected q-maps; these values, presented on the lower diagonal of Table 2, were more conservative due to considering range-restricted values across the cortex, but were still significant (r range .301 to .820,p < .001).Finally, we performed the same analyses as above but using bifactor-derived scores, having 'partialled out' g statistically from domain scores.Cognitive domains now showed more limited associations with cortical volume (Fig. 4), with crystallised ability and memory showing no significant regional associations with volume at q < .05.However, in spite of having putatively removed g related variance from the cognitive domains, faster processing speed was associated in limited regions in medial temporal and occipital regions, and anterior regions of the left lateral temporal lobe, and greater visuospatial ability was associated with greater volume in limited clusters bilaterally in lateral temporal and posterior lateral parietal regions (Fig. 4).Vertices associated with g were almost identical in bifactor and single-order models (see Fig. 5e and f).Overlapping and unique vertices across domains and g are shown in Fig. 5g and h.The majority of those loci which retained significant associations with cognitive domains mostly overlapped with g (Fig. 6, left) with only limited unique non-g associations for processing speed (medial occipital, lateral temporal and right lateral frontal lobes; unique vertices: 16907, overlapping: 3175) and visuospatial ability (medial parietal lobes; unique: 3190, overlapping: 469; Fig. 6, right).

Discussion
In a large sample of older adults from the LBC1936 study, we assessed the extent to which neurostructural correlates of different cognitive domains are shared or unique.This is the first study to assess this research question in a large nonclinical sample of older adults, with a comprehensive battery of cognitive tests (at least 3 indicators per factor), and careful statistical treatment so as to provide a stringent test of the potential separability of unique aspects of cognitive domains from the shared covariances across cognitive tests, as measured by g.We found domain-specific associations at the level of global brain structure and regional cortical associations, but the majority were shared (statistically accounted for by g).In regional cortical analyses, there were substantial domains, and regions unique to each domain.a & e) t-values; b & f) FDR corrected q values; c & g) conjunction plot showing cortical loci that display overlapping associations with g and cognitive domains; d & h) conditional analyses breaking down non-overlapping areas, showing each locus associated uniquely with g or a cognitive domain.Models corrected for age, sex and ICV.All t-value maps were scaled to the same limits to aid comparison of relative effect size.
Fig. 6 e Total number of overlapping vertices which showed significant associations (FDR Q < .05) in regional analyses of single-order and bifactor-derived scores of g and cognitive domains, illustrating proportion of FDR significant vertices which are shared across domains (blue) or unique to the domain (red).Numerical labels show total number of FDR significant vertices for each cognitive domain.
overlapping associations between vertex-wise volume with cognitive domains and g, and limited unique associations with g, processing speed, visuospatial ability, and memory.
There was an overlap in magnitude of regional associations, such that the relative strength of regional associations at each vertex was correlated across domains and g.Results were replicated using both bifactor and single-order derived cognitive scores: brain structural correlates of cognitive domains in this sample are almost entirely shared with other domains, with the possible exception of processing speed.

Global brain structure
In line with previous research, most measures indicating better brain health with age, including greater TBV, GM, NAWM volumes, and gFA, and lower WMH volumes and gMD, were significantly associated with greater g using single-order modelled scores.Scores of cognitive domains broadly mirrored these associations, with significant associations with most global measures.As predicted, we observed a greatly attenuated pattern of associations after removing grelated covariance from domain scores by conducting these same regressions with bi-factor derived domain scores, suggesting g accounted for many of these associations.Processing speed was a notable outlier, retaining attenuated but significant associations with all global measures, indicating an association independent of g, contradictory to previous studies (Tamnes et al., 2010).This is interesting when one considers that g tends to be highly correlated with tests which load highly on processing speed latent factors, such as reaction time (Jensen, 1993), and that correlation magnitude tends to increase with age (Der et al., 2017).This has practical implications: studies examining structural correlates of g with few indicators, particularly including tests of processing speed, may uncover associations with the domain of processing speed rather than g.Overall, it would appear that g accounts for the majority of global structural associations with domains, with the exception of processing speed which retained all significant associations after the removal of grelated covariance.
Overall, the majority of regional domain-specific associations were also associated with g, and thus, g appeared to account for the majority of associations.This is particularly notable for crystallised ability and memory, which had extremely limited unique associations.
It is noteworthy, however, that there were still overlapping associations in these analyses, mainly driven by overlap between g and with processing speed, despite having removed grelated covariance.That is, even when using a measure of processing speed that is statistically orthogonal to g, it's cortical correlates show large but not perfect spatial overlap with areas implicated in all other cognitive domains (as operationalised with g), alongside smaller loci in occipital, temporal and frontal lobes.This potentially special status for processing speed is further corroborated when considering the global structural analyses, where its associations were far less subject to attenuation that were other domains.This may suggest that g and processing speed, although closely related and engaging almost exactly the same neurostructural system, are at least partly dissociable with only partly overlapping cerebral correlates.This idea is particularly interesting in light of existing work suggesting processing speed should be considered to have a special place within cognitive ability (Spearman, 1904), for example, models proposing hierarchical relationships between cognitive ability, processing speed and white matter (Kievit et al., 2018).
Though comparatively weak and less widespread, both global and regional brain associations also remained for visuospatial ability, after having accounted for g, and this was true even for the more stringent bifactor models when considering total brain volume and grey matter.It is interesting to note that these regions overlap with those implicated in g.As such, our results might indicate that having larger volumes in those areas is related to individuals who have both higher general ability (across domains) but also additionally have higher visuospatial ability, above and beyond that.Whereas these findings motivate further examination of the interplay between processing speed and g, we urge caution in reading too far into these results as implicating specific processes being underpinned by specific brain facets or regions.Observing associations between measures such as total brain and regional volume may be useful, particularly if triangulated with other methods, but these data (using fairly macroscale brain readouts) are not sufficiently explanatory in isolation.Our methods are correlational in nature, and as previously discussed, the associations found here show structures which are associated with cognitive performance, rather than those which are necessary to support those processes (Price et al., 1999).Consider, for example, the unexpected but often-found associations between cognitive factors such as g and motor and somatosensory regions (also found here for processing speed and visuospatial ability).These regions and their functions are well-studied, so it is unclear whether these regions support higher cognitive functions, or whether they are an artefact (Deary et al., 2021), for which lesion studies are informative.One recent lesion mapping study (Ciplotti et al., 2022) indicated that the frontal lobes (and right more strongly than left) are predominantly important for a progressive matrix task (often considered a good indicator of fluid intelligence; our matrix reasoning task loaded on g at about .6 in the present manuscript).Further, though the extent of overlap highlights the problem of g in neuropsychological research, it is important to note that this does not render any associations in overlapping regions unimportant; it simply means that these associations are not necessarily domain-specific, and thus associations should be interpreted with care.
We should note here that our statements about the cognitive domain-level correlations with brain being 'accounted for' by g is an arithmetical rather than an ontological statement.That is, we treat the variable 'g' as an index of the shared variance among cognitive tests, and employ that to understand how far the MRI correlates of nominallyseparate cognitive domains are, in fact, distinct versus shared.As stated at the outset of the manuscript, we consider this to be of considerable practical use, though we are also keen to point out here that when we use terminology such as 'g accounting for' domain-MRI associations, we restrict ourselves to a statistical commentary rather than wishing to draw ontological conclusions about the nature of g and its mechanistic relationship with cognitive domains from these correlational data.For example, we note that whereas much of the vertex-wise patterning of domain associations is (statistically) accounted when including g as a covariate, one might equally point to the fact that there are virtually no g-specific vertices either, which might militate against the notion of g as a cognitive function in its own right, or that specific abilities which are perfectly co-localised in the brain are key mechanisms for general cognitive differences, and accords with lesion-symptom mapping studies which find little-to-no g-specific lesion loci, especially for memory and verbal domains (Barbey et al., 2012;Bowren et al., 2020).Nevertheless, we show that the nominally distinct cognitive domains measured here have predominantly shared associations with brain structural and diffusion measures.

Strengths and limitations
We explored this research question in a large, non-clinical sample of older adults, thus avoiding issues inherent in clinical samples, such as confounding factors due to diverse lesion aetiology, as well as allowing sufficient statistical power to reliably detect smaller effect sizes than had previously been possible (e.g. a more stringent test of whether there might be subtle domain-specific unique brain associations).In addition, we used a large and well-validated cognitive test battery to indicate latent g and cognitive domain scores (Deary et al., 2010).LBC1936 participants are restricted in age range and have similar cultural backgrounds, therefore limiting some potential sources of confounding (Hofer et al., 2001), though also limiting the extent of our findings' generalisability.Moreover, we corrected brain volumetric data for ICV in our analyses since it is important to consider differences in atrophy (brain volumes in the context of maximal healthy size) in this uniformly older sample (Clayden et al., 2011;Royle et al., 2013).However, these results may therefore be less directly relevant to the uncorrected volumetric correlations among cognitive domains in younger samples.We also applied careful advanced statistical analyses to model the cognitive scores, and to assess the extent of spatial overlap among domains in multiple ways.Finally, our method of vertex-wise analyses were agnostic to any particularly limiting imposition of cortical boundaries.This study also has limitations.This sample is restricted and self-selecting, and it has previously been noted that LBC1936 participants tend to have greater cognitive ability, physical fitness, and be of a higher social class than the average population (Deary et al., 2012;Taylor et al., 2018), limiting generalisability.In addition, braineintelligence relationships in older age may differ to relationships at other ages, meaning our results may not reflect relationships across the lifespan, though our recent meta-analysis did not suggest that this was a concern in a large meta-analysis of ~40,000 adults (Moodie et al., 2023).Moreover, whereas our study was comparatively well-powered, we do not rule out the possibility that there are more extensive domainspecific cortical correlates (independent of g) that we did not have sufficient power to detect.Similarly, it is feasible that cognitive test-specific cortical correlates are more spatially diverse than those of the cognitive domains (which index only the common variance across that subgroup of tests) and are more likely to show spatially distinct signals independent of g.Finally, whereas we chose to fit a bifactor model to the cognitive data specifically to test the extent to which there remained neurostructural correlates that were not related to g, we are aware of the controversy surrounding bifactor models in terms of their interpretability and apparent model fit (Bonifay et al., 2016;Murray and Johnson, 2013;Reise et al., 2016).That is, we do not pass direct judgement on the interpretability of the non-g residual domains (which we agree are difficult to conceptualise), and acknowledge that it may have good fit in part because bifactor models tend to overfit by modelling noise that is otherwise partialled out in hierarchical modelling, rather than because it has superior/valid ontological traction.

Conclusion
Using extensive cognitive and neuroimaging data, we show that the neurostructural correlates of latent cognitive domains (speed, crystallised, visuospatial and memory) are largely common when considering both global and regional measures, with the possible exception of the domain of processing speed.Associations between cognitive domains and global brain measures were attenuated between 25.6 and 57.9% on average after accounting for g, and regional analyses revealed significant spatial overlaps in regions which were correlated with cognitive domains and g.Importantly, this appears to be the case regardless of the method used to model the overlap of non-orthogonal cognitive data; these patterns replicated using both bifactor and single order modelled factors of domains and g.Thus, it appears latent cognitive domains have limited unique cerebral correlates among a large sample of community-dwelling older adults.

Fig. 1 e
Fig. 1 e Diagram of global brain-cognitive analyses.Diagrams illustrating: (a) a bifactor model of cognitive ability including cognitive domains and g, latent cognitive domains (representing only non-g variance in the domains) derived from observed cognitive test scores; (b) latent individual cognitive domains and g, derived from single-order CFA models of observed cognitive test scores; (c) solely for comparison, a traditional hierarchical model, with latent g as indicated by latent cognitive domains, indicated by individual cognitive tests.

Fig. 2 e
Fig. 2 e Comparison of effect size (Pearson's r) and standard error bars for regression outcomes from single-order and bifactor-derived scores; dark bars represent single-order derived score associations, and light bars represent bifactorderived score associations.p values: ***<.001,**<.01, *<.05.TBV: total brain volume, GM: grey matter volume, NAWM: normal appearing white matter volume, WMH: white matter hyperintensity volume; gFA: general factor of fractional anisotropy, gMD: general factor of mean diffusivity.Coefficients and p-values are reported in Supplementary Table5.
were conducted on a sample of 697 LBC1936 participants (333 male), with mean age 72.5 years (SD ¼ .707),who reported a mean 10.8 years (SD ¼ 1.141) of formal education.Further sample characteristics are summarised (mean, SD, N) in Table 1.Cognitive and MRI information on distributions and outliers is presented in Supplementary Table 1, and correlations between cognitive tests can be found in Supplementary Table 2.
Model fit statistics for the bifactor CFA model indicated a good fit following non-significant negative variance in the 'verbal paired associates' variable being set to 0 to allow the model to converge on in-bound estimates.In this model, g explained 31.1% of variance in cognitive test scores.Of the residual test score variance after partialling out g, processing speed explained 21.0%, crystallised ability 31.2%,memory27.6%,and visuospatial ability 17.3%.Indicators of model fit were deemed acceptable (CFI ¼ .965,TLI¼.958,RMSEA¼.060,SRMR¼.042).Bifactor model loadings are presented in Supplementary Fig.1.

Table 1 e
Participant characteristics.

Table 1 e
(continued ) Note. gFA: general factor of white matter fractional anisotropy; gMD: general factor of white matter mean diffusivity.

Table 2 e
Spatial agreement of cortical vertex-wise patterning of associations across cognitive factors.
Figures reported: Correlations (Pearson's r) between vertex-wise t-values of associations between cognitive factors and cortical volume.Top diagonal: correlations across entire cortex (N ¼ 308,802).Bottom diagonal: correlations calculated on a factor by factor basis, including only vertices which had significant associations with cognitive domain scores in FDR corrected q-maps; number of vertices included in each analysis as follows: processing speed N ¼ 152085; crystallised ability N ¼ 41274; memory N ¼ 39937; visuospatial ability N ¼ 183014; g N ¼ 177816.p values: ***<.001,**<.01, *<.05 after adjustment for multiple comparisons.