Camille Michèle

Marie-Angèle Williams

PhD Franck Ramus

MSc Hugo Peyre

Tinca Polderman

Lothian Birth Cohorts Simon Cox

Marion Noulhiane

Nicolas Hoertel

Aurélien Allard

Antoine Marie

Charlotte Barot

Benoit Courson

Fabien Dézèque

Joffrey Fuhrer

Léo Fitouchi

Loïa Lamarque

Edgar Dubourg

Mélusine Boon Falleur

Léonard Guillou

Rita Abdel Sater

Coralie Chevalier

Nicolas Baumard

Hugo Mercier

Jacqueline Chloë

Alessia Emilie Guillaume

Will, Armand Raph F Julian

Raph P Arnaud

Coralie Lucas

Alex Arthur

LSCP Camille Michèle Williams
email: williams.m.camille@gmail.com

PhD/MD Ghislaine Labouret

Tobias Wolfram

MSc Judicael Fassaya

MSc Adoración Guzmán García

MSc Nicolas Gauvrit

Neuroanatomical Mediators of Environmental and Genetic factors, Cognitive Function, and Mental Disorders

Keywords: Intelligence, factor analyses, GWAS, polygenic scores, UK Biobank

and to the new friends I've made in Paris (Claire, Darby, Oskar

"What if you find nothing?" the jury asked. "Well, that's great!" I replied frantically.

"That way we know not to further invest in brain volumes but to focus on other cerebral properties or develop better neuroimaging tools!". Turns out they were right: Brain volumes are not great biomarkers or mediators of cognition and psychopathology.

It took a lot of perseverance over the last three years to reach this conclusion. But I would do it all again and I have many people to thank for that.

First, I'd like to thank my supervisors Franck Ramus and Hugo Peyre. I learned so much from them during my second year of my master's and Ph.D. I had a great experience, even if I spent half of my time working remotely. Their complementary skills, attitudes, and interests make them great supervisors. They were encouraging and let me grow at my own (sometimes very quick) pace. I know all students say that they'll be back, but I really will. I'll see you at the next team lunch with Lebanese mezze and snazzy cowboy boots! I owe a lot to my parents and sisters, who supported me without really understanding what I was working on or where I was headed in life. It took a while, but by the Fall semester of my third doctoral year, my dad finally stopped reminding me that private companies pay better than the public sector. So, thank you for your trust and encouragement! And thank you to my extended family for their support often miles and miles away! Thank you, Sacha Altay, for being my pillar over the last 5 years, during the master's program and the Ph.D. You helped me in so many ways that go beyond this dissertation. I am so lucky to have you and know that even if the academic job market may not be on our side, we always will find each other.

A special thank you to Alice Latimier, Ava Guez, Camila Scaff, and Monica Hegde, my master's and Ph.D. big sisters and mentors who always had valuable advice, and to Lilas Gurgand for being here for me during the ups and downs of this hectic last year! Thank you to Marie-Christine Lackenbacher for your encouragements and lab meeting treats, to Roberto Toro for being a key collaborator in all of our neuroimaging papers, to Ghislaine Labouret for her valuable contributions to our papers on intelligence, and to my interns, who were a pleasure to mentor. I also have COVID to thank. Without the pandemic, I don't know if I would have reached out to amazing established and up-and-coming researchers, Kathryn Paige Harden, Tobias Wolfram, and Travis Mallard, who even countries or oceans apart helped me achieve my goals. Seriously, thank you for taking a chance with me; I hope I proved you right!

English Abstract

The goal of this dissertation was to examine the extent to which neuroanatomical markers mediate the effects of childhood adversity and genetic predispositions on either general intelligence (g-factor) or general psychopathology measures in the UK Biobank.

In the first two papers, we established how global measures (e.g., Total Brain Volume, TBV) should be adjusted for when investigating regional effects independently from brain size in the UK Biobank (N = 40,028). We also examined the effects of age and sex, which influence brain anatomy. These analyses were performed on volumes (mainly grey matter), cortical thicknesses, and cortical surface areas and their asymmetries.

In a third paper, we created phenotypic and genetic measures of general intelligence for the mediation models: Using-factor analysis, we extracted a general intelligence score for a majority of UK Biobank participants that is partially corrected for sampling bias and estimated its quality. We then conducted a g-factor Genome-Wide Association Study (GWAS) on individuals in the UK Biobank without neuroimaging data (N= 187,288) and created a g-factor polygenic score (PGS) for individuals with neuroimaging data that explained 7.6% of the variance in intelligence (N = 26,819).

In a fourth paper, we created binary mental health disorder (MHD) measures for a majority of UK Biobank participants by combining data from probable diagnoses, self-reported medical diagnoses, and hospital diagnoses, and examined how the prevalence of these MHDs differed between individuals with high versus average intelligence. By using a g-factor that is partially adjusted for sampling bias, we showed that, contrary to some claims, highly intelligent individuals do not have a higher prevalence of psychiatric disorders.

In a fifth paper in preparation, we created phenotypic and genetic measures of psychopathology for the mediation models. We conducted factor analyses on the 10 binary MHDs from the fourth paper. For the genetic analyses, we conducted a GWAS of each MHD excluding individuals with neuroimaging data and meta-analyzed these GWAS results with publicly available GWAS results for these MHDs that excluded UK Biobank participants.

Using Genomic SEM, we applied the model structure identified from the phenotypic factor analyses to the genetic data. We then calculated PGSs for individuals with neuroimaging data (N = 26,610).

Finally, we examined whether global cerebral measures mediate the effects of psychopathology PGSs and childhood adversity on phenotypic psychopathology factors. In a sixth paper in preparation, we used the phenotypic and genetic g-factor measures from the third paper to examine the extent to which global and regional cerebral measures mediate the effects of the g-factor PGS and childhood adversity on the g-factor. We identified the regions that contribute to more intelligence than what is expected given their size and found that global measures were the primary mediators of the g-factor PGS' and childhood adversity's effects on the g-factor. Specifically, TBV was the greatest predictor of the g-factor and the strongest cerebral mediator of the g-factor PGS and childhood adversity. However, given that TBV only mediated only 7% of the g-factor PGS's effect on the g-factor, future studies should explore alternative cerebral measures. This dissertation offers guidelines to adjust for brain size, provides phenotypic and genetic measures of general intelligence, MHDs, and general psychopathology for future UK Biobank studies, and contributes to the scarce literature on the cerebral mechanisms underlying the effects of genetic and environmental factors on general cognition and psychopathology.

French Abstract L'objectif de cette thèse était d'examiner dans quelle mesure des mesures neuroanatomiques médient les effets des facteurs génétiques et environnementaux sur l'intelligence et la psychopathologie dans la cohorte UK Biobank.

Dans les deux premiers articles, nous avons déterminer la meilleure manière d'ajuster les mesures globales (par exemple, le volume cérébral total, VCT) pour étudier l'effet des régions cérébrales indépendamment des mesures globales. Nous avons appliqué ces modèles en examinant les effets de l'âge et du sexe sur la neuroanatomie. Ces analyses ont été effectuées sur les volumes cérébraux (principalement de matière grise), les épaisseurs corticales, les surfaces corticales et leurs asymétries.

Dans un troisième article, nous avons créé des mesures phénotypiques et génétiques de l'intelligence générale (facteur-g). Nous avons créé un facteur-g pour les participants du UK Biobank en corrigeant le biais d'échantillonnage et nous avons évalué sa validité. Nous avons ensuite mené une étude d'association pangénomique (GWAS) du facteur-g sur les individus de la cohorte UK Biobank sans données cérébrales (N=187 288) pour ensuite calculer un score polygénique du facteur-g (PGS) pour les individus avec des données cérébrales qui explique 7,6% de la variance de l'intelligence (N=26 819).

Dans un quatrième article, nous avons créé des catégories de troubles psychiatriques en agrégeant les nombreuses mesures de santé mentale disponibles dans la cohorte UK Biobank.

Nous avons examiné si la prévalence de ces troubles psychiatriques différait entre les individus avec un Haut Potentiel Intellectuel (HPI) et ceux d'intelligence moyenne. A partir du facteur-g corrigé pour le biais d'échantillonnage, nous avons montré que, contrairement à certaines affirmations, les individus HPI n'ont pas une prévalence plus élevée de troubles psychiatriques.

Dans un cinquième article en préparation, nous avons créé des mesures phénotypiques et génétiques de psychopathologie. Nous avons effectué des analyses factorielles sur les 10 troubles psychiatriques pour extraire un facteur général de psychopathologie ainsi que des facteurs pour les troubles externalisés, internalisés, et les troubles de la pensée. Au niveau génétique, nous avons réalisé un GWAS de chaque trouble psychiatrique en excluant les individus avec des données cérébrales. Puis, nous avons méta-analysé nos résultats avec ceux des autres GWAS. À l'aide de modèles d'équations structurelles génomiques, nous avons appliqué la structure des modèles phénotypiques aux données génétiques pour identifier les influences génétiques sous-jacents à nos facteurs. Nous avons ensuite calculé les scores polygéniques (PGSs) des individus disposant de données cérébrales (N=26,610). Enfin, nous avons examiné si les mesures cérébrales globales médiaient les effets des facteurs génétiques (PGS) et environnementaux sur la psychopathologie.

Dans un sixième article en préparation, notre objectif était d'identifier les mesures cérébrales globales et régionales qui médient les effets des PGS du facteur-g (calculé dans le troisième article) et de l'adversité de l'enfant sur le facteur-g. Les mesures globales étaient les principaux médiateurs des effets du PGS du facteur-g et de l'adversité de l'enfant sur le facteurg. Bien que le VCT fût le médiateur cérébral le plus fort du PGS du facteur-g et de l'adversité de l'enfant, le VCT ne médiait que 7% de l'effet du PGS du facteur-g sur le facteur-g. Les études futures devraient donc explorer des mesures cérébrales alternatives.

Cette thèse propose des recommandations pour modéliser les données neuroanatomiques et fournit des mesures phénotypiques et génétiques de l'intelligence générale, des troubles psychiatriques et de la psychopathologie pour les futures études sur UK Biobank. Elle contribue à l'élucidation des mécanismes cérébraux qui sous-tendent les effets des facteurs génétiques et environnementaux sur la cognition et la psychopathologie.

Introduction

Cognitive ability and psychopathology predict a variety of important life outcomes, including income, physical health, and mortality, and are influenced by genetic and environmental factors that act on the brain. Understanding the complex effects and interactions of each factor on cognition and psychopathology is crucial for the development of public policies and interventions aimed at reducing social inequalities and improving later life outcomes and for the development of behavioral and drug therapies and preventive medicine.

However, we are limited in our understanding of how environmental, genetic, and cerebral factors act on cognition and psychopathology due to the complexity of these associations, the small proportion of variance explained by each genetic, environmental, or cerebral marker, and the fact that few studies have collected multimodal data (i.e., behavioral, genetic, environmental, or cerebral marker). One of the few biomedical databases that meets these criteria is the UK Biobank, with its somatic, mental health, cognitive, brain imaging, genetic, health, and environmental data on more than 500,000 British middle-aged and older adults.

Therefore, the goal of this thesis was to capitalize on the richness of the UK Biobank and simultaneously examine environmental, genetic, and cerebral effects on psychopathology and cognitive abilities. Specifically, our aim was to examine the extent to which neuroanatomical measures mediate the effects that genes and the environment have on general cognitive abilities and psychopathology dimensions. Before arriving at the mediation analyses, we first investigated how global brain size should be taken into account when investigating regional cerebral effects and then created phenotypic and genetic measures of cognitive ability and psychopathology.

In the introduction, I will first describe why we study cognition and psychopathology and how cognitive tests and mental health disorder diagnoses can be summarized into a general intelligence factor and general psychopathology factors, respectively. Second, I will go over how nature and nurture contribute to these factors, focusing on major turning points of the genomic and post-genomic eras and their implications for disentangling environmental from genetic effects. Third, I will summarize studies on the cerebral correlates of general cognition and psychopathology and discuss papers that combine brain data with either environmental and/or genetic data to better understand cognition and mental health. Finally, I will present the gap in the literature when it comes to understanding the role of the brain on the influence that genetic and environmental factors exert on cognition and psychopathology and how this dissertation attempts to address this gap.

Why study the general intelligence and psychopathology factors?

1.1.Intelligence

Intelligence -the ability to learn, reason, and solve problems (Arvey et al., 1994) -is typically measured by psychometric tests that cover a variety of cognitive domains such as reasoning, verbal ability, processing speed, memory, executive function, memory, and spatial ability. Although these domains can be thought of as distinct, people who perform well on one domain tend to perform well on the others. This positive correlation across cognitive tests was coined by Spearman as the "positive manifold" (Spearman, 1904).

Using-factor analyses, he showed that the positive manifold could be reduced to a single dimension known as the general intelligence factor (g-factor). The g-factor not only provided a measure of a person's intellectual capacity but, according to Spearman, was also responsible for an individual's overall performance across cognitive tests [START_REF] Spearman | The Abilities Of Man[END_REF]. Although the g-factor and Intelligence Quotient (IQ) can be measured from the same cognitive tests, they are calculated slightly differently. Whereas IQ reflects a person's average performance across cognitive tests relative to a representative sample of the same-age national population, the gfactor can be derived from the first principal component of a principal component analysis (PCA), which captures common (shared) and unique (unshared) variance across all cognitive tests, or from a single factor confirmatory factor analysis (CFA), where a single unobserved (latent) variable captures common variance across all cognitive tests [ Box 1]. The g-factor accounts for around 40% of the variance in cognitive tests when calculated from a broad range of cognitive tests [START_REF] Carroll | Human Cognitive Abilities: A Survey of Factor-Analytic Studies[END_REF] and as long as the tests are diverse enough, the g-factors extracted from different cognitive tests are almost perfectly correlated [START_REF] Johnson | Just one g: Consistent results from three test batteries[END_REF][START_REF] Johnson | Still just 1 g: Consistent results from five test batteries[END_REF].

The positive manifold has been explained using alternative models to Spearman's g-factor (for review by [START_REF] Savi | The Wiring of Intelligence[END_REF]. For instance, the Cattel-Horn-Carrol Theory supports a multifactor and hierarchical model of intelligence, wherethe g-factor is divided into several broad domains (e.g., fluid reasoning, reading, processing speed, etc.), which are further separated into general abilities (Figure 1 from Deary et al., 2021;[START_REF] Mcgrew | CHC theory and the human cognitive abilities project: Standing on the shoulders of the giants of psychometric intelligence research[END_REF]. In contrast, the sampling model proposed that the positive correlations between tests came from the lack of specificity of cognitive tests: the positive correlation could be explained by different tests requiring similar overlapping cognitive abilities [START_REF] Thomson | A hierarchy without a general factor[END_REF][START_REF] Thomson | The factorial analysis of human ability[END_REF][START_REF] Thorndike | The measurement of intelligence[END_REF].

Later models of intelligence integrated genetic and environmental effects: The geneenvironment interaction model considered the effect of genes and childhood environment on later intelligence scores [START_REF] Dickens | Heritability estimates versus large environmental effects: The IQ paradox resolved[END_REF], 2002), whereas the network mutualism model proposed a network of cognitive domains mainly connected by positive reciprocal interactions with external environmental and genetic factors acting on each domain [START_REF] Van Der Maas | A dynamical model of general intelligence: The positive manifold of intelligence by mutualism[END_REF].

Recent models of intelligence are growing in complexity. The unified model of intelligence for instance combines hierarchical factor structures, sampling effects, and network models with external genetic and environmental influences (Van Der Maas et al., 2017). The idiographic network theory of intelligence captures the positive manifold and hierarchical structure while considering the dynamic changes in intelligence at the individual level [START_REF] Savi | The Wiring of Intelligence[END_REF].

Although there is no consensus on whether intelligence is one thing or multiple things (Van der [START_REF] Maas | The Network Approach to General Intelligence[END_REF] and what model best captures the underlying organization and dynamic nature of intelligence, the general intelligence factor is highly correlated with educational [START_REF] Deary | Intelligence and educational achievement[END_REF][START_REF] Neisser | Intelligence: Knowns and unknowns[END_REF], occupational (Schmidt & Hunter, 2004;Strenze, 2007), and health outcomes [START_REF] Batty | Childhood Mental Ability in Relation to Food Intake and Physical Activity in Adulthood: The 1970 British Cohort Study[END_REF][START_REF] Bratsberg | Childhood socioeconomic status does not explain the IQ-mortality gradient[END_REF][START_REF] Calvin | Intelligence in youth and all-cause-mortality: Systematic review with metaanalysis[END_REF]Calvin et al., , 2017Calvin et al., , 2017;;[START_REF] Caspi | Childhood forecasting of a small segment of the population with large economic burden[END_REF]Wraw et al., 2018), suggesting that the g-factor is a valid predictor of later life outcomes, even if it does not reflect the complex organization of intelligence.

[ Box 1] In Principal Component Analysis (PCA), the common and unique variance across variables is captured by each reduced variable (or component). Each component is created using a weighted average of a set of variables (Figure B2). Each weight corresponds to the correlation between a variable (e.g., cognitive test) and the reduced variable (e.g., g-factor of general intelligence). Component scores are obtained for each individual by calculating a weighted sum of scores.

In Factor Analyses, only the common variance across variables is captured by each reduced variable (latent factor). There are several types of models in factor analyses. The Exploratory Factor Analysis (EFA) model explores the underlying theoretical structure of the association between variables. Researchers use theory and statistical techniques, such as eigenvalues, to determine the number of factors to extract from the correlation matrix of the observed variables (e.g., cognitive tests). Factor analysis is then performed on a correlation matrix with a set number of factors to extract. Unlike PCA where the observed variables predict the component score, the latent factor is predicting the responses in the observed variables.

However, similarly to PCA, the relationship between the observed and latent variables is weighted and optimal loadings (weights) are created based on the correlation matrix (Field 2021). Variables that are more correlated with each other will load more strongly on the same factor.

The measurement model, or Confirmatory Factor Analysis (CFA), is used to test whether the measures of a construct are consistent with the researchers' understanding of that construct. Researchers test a theory-driven or exploratory factor model by examining the fit of their model, which reflects how well the implied covariance matrix of the model matches the data-driven covariance matrix. Factor analysis provides the optimal loadings between the latent and the observed variables based on the covariance matrix. Just like EFA, the latent factor is predicting the responses in the observed variables. The CFA model parameters (e.g., loadings, intercepts…) can then be used to predict individual factors that reflect the extent to which a person is situated on that latent factor.

1.2.Why Study General Intelligence?

Individual differences in intelligence are relatively stable across the life span [START_REF] Gow | Stability and change in intelligence from age 11 to ages 70, 79, and 87: The Lothian Birth Cohorts of 1921 and 1936[END_REF][START_REF] Von Stumm | Socioeconomic status and the growth of intelligence from infancy through adolescence[END_REF], although there is a peak of intelligence in adulthood and a decline thereafter that varies across cognitive tests [START_REF] Hartshorne | When Does Cognitive Functioning Peak? The Asynchronous Rise and Fall of Different Cognitive Abilities Across the Life Span[END_REF]. There is a moderate to strong correlation between early intelligence scores and educational outcomes, such as later school performance, highest qualification obtained, or years of completed education [START_REF] Deary | Intelligence and educational achievement[END_REF][START_REF] Roth | Intelligence and school grades: A meta-analysis[END_REF]. For example, the g-factor from a cognitive battery test at the age of 11 was correlated at 0.8 with the g-factor from a UK national exam (the General Certificate of Secondary Education, GCSE) at 16 years old [START_REF] Deary | Intelligence and educational achievement[END_REF] and correlated 0.6 with a g-factor at 88 years old [START_REF] Deary | The Stability of Intelligence From Childhood to Old Age[END_REF]. While these longitudinal studies suggest that this association may stem from a selection process, whereby more intelligent individuals complete more years of education (Deary & Johnson, 2010), education may also influence intelligence scores. A recent meta-analysis of 42 datasets found that each year of education can increase IQ by up to 1-5 IQ points, even after correcting for Socioeconomic Status (SES) and publication bias amongst other things [START_REF] Ritchie | How Much Does Education Improve Intelligence? A Meta-Analysis[END_REF]. For now, it is unclear whether the beneficial effects of education are greater for individuals with initially higher or lower cognitive abilities, even if a study showed that education could have an equalizer effect, benefiting more individuals with initially lower cognitive abilities [START_REF] Hansen | The effect of schooling and ability on achievement test scores[END_REF].

Intelligence is also associated with occupational outcomes, such as occupation and performance, adult SES, and social mobility -the change of an individual from one social position to another [START_REF] Deary | Intergenerational social mobility and mid-life status attainment: Influences of childhood intelligence, childhood social factors, and education[END_REF][START_REF] Ree | Predicting job performance: Not much more than g[END_REF][START_REF] Richardson | Does IQ Really Predict Job Performance[END_REF]Schmidt & Hunter, 2004;[START_REF] Sorokin | Social and Cultural Mobility[END_REF]Strenze, 2007;[START_REF] Von Stumm | Childhood intelligence, locus of control and behaviour disturbance as determinants of intergenerational social mobility: British Cohort Study 1970[END_REF]. For instance, intelligence scores generally increase with occupational level and the correlation between intelligence and job performance appears to be greater than the correlation between job experience (i.e., length of experience in a given occupation) and job performance (Schmidt & Hunter, 2004). In light of the extensive literature reporting the effect of multiple predictors (e.g., parental SES, childhood behaviors…) on SES mobility and occupational outcomes, researchers started modeling these associations with Structural Equation Modelling (SEM).

SEM is a multivariate technique that tests the direct and indirect effects of specified causal models with multiple predictors (Staff et al., 2017). For instance, using SEM, von Stumm and colleagues (2009) found that while education mediates the effects of intelligence, parental social class, and teacher and mother ratings of childhood behavior, these predictors all also directly influence social mobility at age 30.

Higher intelligence is also associated with healthier behaviors and lower rates of chronic illnesses and mortality [START_REF] Calvin | Intelligence in youth and all-cause-mortality: Systematic review with metaanalysis[END_REF](Calvin et al., , 2017;;[START_REF] Čukić | Childhood IQ and survival to 79: Follow-up of 94% of the Scottish Mental Survey 1947[END_REF][START_REF] Wraw | Intelligence in youth and mental health at age 50[END_REF]Wraw et al., , 2018)).

For instance, individuals with an IQ score of 1 SD over the mean early in life were 1.14 times more likely to have good, very good, or excellent health compared to fair or poor health around 50 years old after controlling for age, sex, and childhood SES (measured by income, education, and occupation; [START_REF] Wraw | Intelligence in youth and mental health at age 50[END_REF]. When examining the associations between intelligence and physical activity, diet, smoking, and drinking habits, the association between intelligence and these habits prevailed, even after correcting for childhood or adulthood SES (Wraw et al., 2018).

The association between mental health disorders and intelligence is less clear. While some report that high intelligence is a protective factor for several mental and somatic disorders [START_REF] Burdick | The role of general intelligence as an intermediate phenotype for neuropsychiatric disorders[END_REF]Ghaffari, Abbaskhanian, & Jalili, 2014;Ghaffari, Abbaskhanian, Jalili, et al., 2014;Koenen et al., 2009;[START_REF] Sjölund | IQ and Level of Alcohol Consumption-Findings from a National Survey of Swedish Conscripts[END_REF], others suggest that high intelligence is a risk factor for these phenotypes [START_REF] Benbow | Intellectually gifted students also suffer from immune disorders[END_REF][START_REF] Benbow | Physiological correlates of extreme intellectual precocity[END_REF][START_REF] Kanazawa | Intelligence and Substance Use: Review of General Psychology[END_REF]Karpinski et al., 2018;[START_REF] Lancon | Comorbidités psychiatriques et qualité de vie chez les sujets adultes à haut potentiel intellectuel: Relations avec l'estime de soi[END_REF]D. J. Smith et al., 2015;[START_REF] White | Intelligence across childhood in relation to illegal drug use in adulthood: 1970 British Cohort Study[END_REF]; K. M. Williams et al., 2017). The majority of studies reporting a negative effect of intelligence on mental and somatic health, however, often suffer from sampling bias, the lack of a control group, or insufficient sample size (Gauvrit, 2014;Martin et al., 2010). Thus, studies addressing these caveats are necessary to robustly examine when intelligence serves as a protective or risk factor for mental health.

In light of the impact of intelligence on important life and health outcomes, researchers are interested in explaining individual differences in intelligence by examining the genetic and environmental (including social) etiologies of intelligence and its biological basis in the brain.

1.3.General Psychopathology Measures

Although mental health disorders have traditionally been viewed as distinct categorical conditions, there is strong comorbidity across disorders [START_REF] Caspi | Longitudinal Assessment of Mental Health Disorders and Comorbidities Across 4 Decades Among Participants in the Dunedin Birth Cohort Study[END_REF][START_REF] Kessler | Prevalence, Severity, and Comorbidity of 12-Month DSM-IV Disorders in the National Comorbidity Survey Replication[END_REF][START_REF] Merikangas | Lifetime Prevalence of Mental Disorders in U.S. Adolescents: Results from the National Comorbidity Survey Replication-Adolescent Supplement (NCS-A)[END_REF]. Diagnoses are typically given using international (International Classification of Diseases, ICD) or national (e.g., Diagnostic and Statistical Manual of Mental Disorders, DSM) diagnostic tools that are regularly updated (the latest versions are . A nationally representative survey of about 9,000 Americans over 18 years old found that 55% of individuals had a single diagnosis, 22% had 2 diagnoses, and 23% had 3 or more diagnoses from the DSM-IV [START_REF] Kessler | Prevalence, Severity, and Comorbidity of 12-Month DSM-IV Disorders in the National Comorbidity Survey Replication[END_REF]. Comorbidity is also linked to severity: About 9.6% of individuals with 1 disorder, 25.5% with 2 disorders, and 49.9% with 3 or more disorders were diagnosed as having a severe disorder, preventing them from carrying out their daily activities due to mental health issues or addiction [START_REF] Kessler | Prevalence, Severity, and Comorbidity of 12-Month DSM-IV Disorders in the National Comorbidity Survey Replication[END_REF]. In light of the comorbidity and positive correlation between comorbidity and severity, Krueger and colleagues (1998) hypothesized that there may be a more parsimonious structure to psychopathology than the current nosology.

In fact, [START_REF] Achenbach | Behavioral Problems and Competencies Reported by Parents of Normal and Disturbed Children Aged Four Through Sixteen[END_REF] reported that childhood disorders could be divided into two dimensions: an Internalizing dimension, including anxiety and depression symptoms, and an Externalizing dimension, including aggressive, delinquent, and hyperactivity symptoms. Krueger andMarkon (2006, 2011) replicated these dimensions in their adult studies and proposed that psychiatric disorders in adulthood could be divided into an Internalizing dimension, reflecting the liability to experience mood and anxiety disorders (major depression, generalized anxiety disorder (GAD), panic disorder, and social phobia), and an Externalizing dimension, indicating liability to experience substance use disorders and antisocial disorders. The Internalizing and Externalizing-factors are thought to be robust across ages (Lahey et al., 2018;Martel et al., 2017), sex [START_REF] Kendler | The structure of genetic and environmental risk factors for common psychiatric and substance use disorders in men and women[END_REF][START_REF] Kramer | The role of internalizing and externalizing liability factors in accounting for gender differences in the prevalence of common psychopathological syndromes[END_REF], countries [START_REF] Slade | The structure of common DSM-IV and ICD-10 mental disorders in the Australian general population[END_REF], and less common mental disorders [START_REF] Forbush | The structure of common and uncommon mental disorders[END_REF].

The psychopathology model later accommodated a third dimension. Prior studies on psychopathology focused on mental health disorders that were common in the general population and did not include schizophrenia or psychosis in their psychopathology models because the diagnosis criteria for these disorders were too specific: They required the presence of both positive and negative symptoms of psychosis (e.g., hallucinations and affective flattening, respectively; [START_REF] Carpenter | The psychoses: Cluster 3 of the proposed meta-structure for DSM-V and ICD-11: Paper 4 of 7 of the thematic section: 'A proposal for a meta-structure for DSM-V and ICD-11[END_REF], which prevented an accurate estimation of the disorder prevalence until the creation of the psychosis spectrum (van Os et al., 2009). While some argued that these symptoms and disorders could load on the internalizing-factor [START_REF] Verona | Suicide Attempts Associated With Externalizing Psychopathology in an Epidemiological Sample[END_REF], others suggested that schizophrenia and schizotypal personality disorder made up their own dimension [START_REF] Kendler | The structure of genetic and environmental risk factors for common psychiatric and substance use disorders in men and women[END_REF][START_REF] Wolf | Associations among major psychiatric diagnoses[END_REF]. When Kotov and colleagues (2011) included individuals with schizophrenia and schizotypal personality disorder in their analyses of psychopathology, they found that these disorders indeed loaded on a separate from externalizing and internalizing behaviors. This new dimension captured the common variance across psychotic experiences, including dissociations, hallucinations, disorganized thoughts, and so forth, reflecting a person's liability to psychotic symptoms. Access to recent large scaled datasets enabled the inclusion of a fourth dimension to models of psychopathology: Instead of having Attention Deficit Hyperactivity Disorder (ADHD) load onto the externalizing factor and Autism Spectrum Disorder (ASD) onto the thought disorder factor [START_REF] Lahey | A Hierarchical Causal Taxonomy of Psychopathology across the Life Span[END_REF] these disorders made up their own neurodevelopmental dimension, with other neurodevelopmental disorders (Grotzinger et al., 2022;[START_REF] Rietz | Overlap between attention-deficit hyperactivity disorder and neurodevelopmental, externalising and internalising disorders: Separating unique from general psychopathology effects[END_REF].

The three-factor model of psychopathology is now known as the Correlated Factors Model (Figure 1B): where highly correlated disorders can be reduced into either an internalizing, an externalizing, or a psychosis (or thought disorder) factor (although a fourth neurodevelopmental dimension could be added if researchers had access to neurodevelopmental data). Yet, in light of the high correlations between these three dimensions [START_REF] Wright | The Structure of Psychopathology: Toward an Expanded Quantitative Empirical Model[END_REF], the comorbidity of disorders across dimensions [START_REF] Costello | Prevalence and development of psychiatric disorders in childhood and adolescence[END_REF][START_REF] Lahey | Patterns of Heterotypic Continuity Associated With the Cross-Sectional Correlational Structure of Prevalent Mental Disorders in Adults[END_REF], and the fact that parental psychopathology is linked to kin with little specificity [START_REF] Dean | The impact of parental mental illness across the full diagnostic spectrum on externalising and internalising vulnerabilities in young offspring[END_REF]McLaughlin, Gadermann, et al., 2012), researchers proposed that these dimensions could be further reduced into a general psychopathology or p-factor (Caspi et al., 2014;Lahey et al., 2012). This p-factor reflects an individual's propensity to psychopathology as the g-factor would for general intelligence. And just like the g-factor, it would explain why individuals with one disorder would be more likely to have other disorders.

The integration of a general p-factor can be captured by several statistical psychopathology models. The p-factor model allows for all mental health disorders to simultaneously be reduced to a single dimension, capturing common variance across mental health disorders (Figure 1A).

In the hierarchical p-factor model (Figure 1D), mental health disorders are first reduced to three dimensions (e.g., externalizing, internalizing, and thought disorders) and correlations across dimensions are captured by a p-factor. Finally, the bifactor model has a general p-factor that captures the common variance across mental health disorders and then specific dimensions which capture the remaining (residual) variance across subsets of disorders (Figure 1C). Note, that although the subsets of dimensions in the bifactor model have similar names to the correlated factors and the hierarchical dimensions, they do not capture the same things. The Internalizing dimension of the correlated or hierarchical factor model corresponds to the common variance across mood and affective disorders, which may also be partially shared with disorders from other dimensions. In contrast, the internalizing dimension from the bifactor model captures the common variance across mood and affective disorders that is shared between these disorders relative to the p-factor (e.g., [START_REF] Lahey | A Hierarchical Causal Taxonomy of Psychopathology across the Life Span[END_REF]. Although the most popular psychopathology factor model is currently the bifactor model (Harden, Engelhardt, et al., 2020;Lahey et al., 2021;McElroy et al., 2018), it has been widely criticized. Some researchers have shown that the model fit indices of factor analyses are biased in favor of the bifactor model, which has a higher fit propensity and overfits the data (Greene et al., 2019;Morgan et al., 2015;Watts et al., 2020). Others found that different models of psychopathology, which have different interpretations (e.g., hierarchical and bifactor models), can be statistically equivalent to each other. For instance, the bifactor model is hard to distinguish from the correlated factors model (Bonifay et al., 2017;Watts et al., 2019) , and the p-factor scores from the bifactor model are highly correlated (r = 0.97) to those from the hierarchical p-factor (Conway et al., 2019).

What model accurately portrays the underlying structure of psychopathology is subject to debate: The presence of a general p-factor appears to be a mathematical necessity of the positive manifold, and the proposed models of psychopathology, which have different theoretical implications, are mathematically equivalent (van Bork et al., 2019). Therefore, arguing for a "true" structure of psychopathology seems improbable. Researchers may instead want to select the psychopathology model and the dimensions that best fit their research question.

Finally, the conceptual nature of the psychopathology factors is subject to debate. Some proposed that psychopathology factors reflect "severity or general dysfunction, or general liability for psychopathology through shared environmental and genetic factors, or disordered thought processes, or trait-like attributes, such as negative emotionality (Caspi & Moffitt, 2018;Lahey et al., 2021) " (Fried et al., 2021). However, if the p-factor reflects liability it is unclear why models are estimated based on symptoms instead of environmental and biological risk factors (Fried et al., 2021). Using data from over 70,000 participants, Fried and colleagues (2021) examined the extent to which factor scores extracted from the bifactor, hierarchical, and correlated factors model were correlated with their respective sum of indicators. They found high correlations across scores, implying these psychopathology factors reflect severity or comorbidity instead of liability, which could be then be linked to genetic and environmental predispositions.

1.4.Why study general psychopathology?

Although the nature of the p-factor is unclear and some criticize the mechanisms behind the p-factor for being unfalsifiable (Lahey et al., 2021;for review Watts et al., 2019for review Watts et al., , 2020)), there is evidence for the criterion validity of the p-factor (e.g., Allegrini et al., 2020;Lahey et al., 2015).

The p-factor reflects the global severity of mental health disorders (Fried et al., 2021) and is also associated with a variety of outcomes such as lower intelligence, executive function, school functioning, income, and higher levels of aggression, peer delinquency, self-harm (Abbott et al., 2018;Lahey et al., 2015;Martel et al., 2017;[START_REF] Pettersson | Criterion Validity and Utility of the General Factor of Psychopathology in Childhood: Predictive Associations With Independently Measured Severe Adverse Mental Health Outcomes in Adolescence[END_REF][START_REF] Sallis | General psychopathology, internalising and externalising in children and functional outcomes in late adolescence[END_REF]. For instance, Sallis and colleagues (2019) [START_REF] Sallis | General psychopathology, internalising and externalising in children and functional outcomes in late adolescence[END_REF]. Similar internalizing estimates across models suggest that the shared variance across internalizing disorders that is not shared with other disorders predicts individual differences in well-being, whereas a decrease in the externalizing estimate suggests that the shared variance across all disorders is a better predictor of English performance at age 16 than the shared variance that is specific to externalizing disorders.

Considering that some of the above associations decreased or were no longer significant when adding the general factor of psychopathology in the model, Sallis and colleagues (2019) proposed that the general psychopathology factor may be a more relevant predictor of life outcomes. This is consistent with a longitudinal Swedish twins' study (N = 16,806) reporting that the childhood general p-factor was a better predictor of adverse clinical and social outcomes during adolescence than the internalizing and externalizing-factors [START_REF] Pettersson | Criterion Validity and Utility of the General Factor of Psychopathology in Childhood: Predictive Associations With Independently Measured Severe Adverse Mental Health Outcomes in Adolescence[END_REF].

In light of the predictive power of psychopathology factors on life outcomes, it is important to understand the etiology of psychopathology factors. Studying the associations between psychopathology factors and environmental and genetic effects may help identify common risk factors and biomarkers across mental health disorders.

Genetic effects On Cognition and Psychopathology

2.1.Nurture without Nature

Numerous epidemiological studies have looked at the environmental predictors of cognition and psychopathology. The strongest predictor of intelligence is parental SES (Flensborg-Madsen et al., 2020;Flensborg-Madsen & Mortensen, 2017). For instance, parental SES between 1 and 3 years old explained 16% of the variance in adult IQ (between 26 and 29 years old) in the Copenhagen Perinatal Cohort, whereas the model with all predictors (parental SES, head circumference, 3-year milestones, etc.) explained 22-24% in the variance in adult IQ (Flensborg-Madsen & Mortensen, 2017). Parental SES also predicts mental health: Children from low-SES families have a 68-115% higher risk of having a mental disorder, even if SES indicators are more strongly related to behavior problems than depression or anxiety [START_REF] Peverill | Socioeconomic status and child psychopathology in the United States: A meta-analysis of population-based studies[END_REF].

Environmental measures during adulthood may mediate the effects of early life factors, such as parental SES, on behavioral outcomes in adulthood (Figure 2). A study found that adult SES partially mediated this association between early intelligence and parental SES on several health outcomes (e.g., hypertension) at 50 years old [START_REF] Wraw | Intelligence in youth and mental health at age 50[END_REF]. For some outcomes, such as depression, sleep difficulty, and mental health status, their association with early intelligence was no longer significant after adjusting for adult SES. The authors proposed that the association between early intelligence and life outcomes may therefore depend on the stress levels experienced across social class [START_REF] Wraw | Intelligence in youth and mental health at age 50[END_REF], as more intelligent individuals, who have a greater SES, experience less stress [START_REF] Sapolsky | The influence of social hierarchy on primate health[END_REF].

Figure 2. Proximal and Distal Factors Influence Adult

Outcomes. The association between childhood intelligence and certain life outcomes can disappear when adjusting for adulthood socioeconomic status, suggesting that adulthood socioeconomic status mediates the effect of early intelligence on some later life outcomes.

Trauma and life stressors also predict intelligence and psychopathology. Meta-analyses suggest that individuals exposed to childhood trauma are 2-3 times more likely to develop psychosis [START_REF] Dam | Childhood bullying and the association with psychosis in non-clinical and clinical samples: A review and meta-analysis[END_REF][START_REF] Trotta | The impact of childhood adversity on the persistence of psychotic symptoms: A systematic review and meta-analysis[END_REF]. Individuals with depression commonly report exposure to stressful life events and childhood trauma. One study examining whether childhood intelligence, anxiety disorders, and conduct problems predict PTSD risk and exposure to traumatic events found that higher intelligence (IQ >= 115) served as a protective factor (OR= 0.3) for trauma exposure and the subsequent risk of developing PTSD [START_REF] Breslau | Intelligence and Other Predisposing Factors in Exposure to Trauma and Posttraumatic Stress Disorder: A Follow-up Study at Age 17 Years[END_REF]. However, trauma exposure is also linked to a decrease in IQ score, as children exposed to interpersonal trauma during the first 2 years of life appear to have an IQ score of 1.5 SD lower than their non-exposed peers (Enlow et al., 2012). Trauma exposure is positively correlated with a range of psychiatric disorders: a research review on the effects of childhood trauma on adulthood found that physical abuse, sexual abuse, and unspecified neglect were associated with mood disorders and anxiety disorders; emotional abuse with personality disorders and schizophrenia; and physical neglect with personality disorders (Carr et al., 2013).

Trauma and early life stress exposure can lead to a wide range of biological and brain changes in childhood and adulthood that can have lasting effects on psychopathology and other life outcomes (Dye, 2018;Lupien et al., 2009).

As exemplified with SES and trauma -some of the largest and most studied environmental predictors of cognition and mental health, associations between environmental factors and intelligence and psychopathology are complex and bidirectional. Although researchers attempt to model causal effects by using early predictors on later life outcomes and consider a variety of predictors and their relationships to accurately estimate an effect, studies that do not use genetically informed designs tend to overestimate or spuriously attribute environmental effects to behavioral outcomes [START_REF] Lemery | Genetically Informative Designs for the Study of Behavioural Development[END_REF][START_REF] Liu | Using Genetically Informed Designs to Understand the Environment: The Importance of Family-Based Approaches[END_REF]. Spurious associations arise in the presence of gene-environment correlations (rGE) when a person's genotype is associated with their exposure to a particular environment (Box 2). In most cases, the association between an environment and a trait is confounded or initiated by a genotype. Thus, in addition to studying environmental predictors of cognition and psychopathology, genetic influences must be considered to accurately identify protective and risk factors as targets of future public policies and behavioral interventions.

[ Box 2] The association between environmental and genetic effects can be quantified with correlations.

There are several types of gene-environment correlations (rGE; examples in Figure B2).

1. Passive rGEs refer to the association between a child's genotype, which they inherit from their parents, and their environment. Both the child's genotype and the child's living environment influence an outcome. Omitting the genotype 2. Evocative rGEs refer to an individual indirectly shaping their environment by evoking a response.

Active rGEs occur when an individual's genotype shapes their choice of environment

Considering that a person's environment may depend on their genes' effects, people's genotypes must be taken into account to accurately identify the exposures that should be targeted by preventive medicine or interventions.

Please note that gene-environment correlations (rGE) differ from gene-by-environment interactions: "GE correlation refers to genetic mediation of associations between environments and traits, whereas GE interaction involves genetic moderation of these associations" [START_REF] Plomin | Genotype-Environment Correlation in the Era of DNA[END_REF]. [End of Box]

Figure B2. Examples of the Three types of Gene by Environment Correlations (rGE)

2.2.Proof of Nature: Heritability of Cognitive Behaviors and Psychopathology

All traits are heritable (Tukerheimer, 2000). In other words, individual differences (or variance) observed across traits, such as cognitive ability, are in part explained by individual differences (or variance) in the genetic makeup of these individuals. Heritability corresponds to the proportion of phenotypic variance (Vp) that is explained by the total genetic variance (Vg). Heritability is calculated as: H 2 = Vg / Vp, where Vp = Vg + Ve (Ve , environmental variance). Therefore, if there are large environmental differences between individuals, Ve increases and reduces the heritability estimate, while Vg remains unchanged. Whereas broadsense heritability reflects additive, dominant/recessive, and peristatic genetic effects, narrowsense (h 2 ) reflects the proportion of genetic variance attributable to additive genetic effects and is often used as an indicator of broad-sense heritability because it is easier to measure.

Historically, studies on heritability relied on twin studies, where researchers compared the prevalence of a trait between mono-and di-zygotic twin pairs to evaluate the degree of genetic and environmental influences on a specific trait (Bartels et al., 2002;Bishop et al., 1995;de Zeeuw et al., 2015;Polderman et al., 2015). If monozygotic twins are more similar on a trait than dizygotic twin pairs, genetics must have a large influence on the trait, since monozygotic twin pairs share almost 100% of their genome and dizygotic around 50% of their genome. In contrast, if monozygotic and dizygotic twins have the same prevalence for a trait, it suggests that the environment is more influential. A recent review of 50 twin studies over 17,000 traits found that the average trait heritability was 49% (Polderman et al., 2015). Other studies used adoption at birth, comparing trait prevalence between monozygotic twins reared in different environments, and more generally, trait correlations between relatives of varying genetic and environmental similarity (Bouchard & McGue, 1981;Loehlin, 1989;Plomin et al., 1997).

Along came the post-genomic era, which started after the completion of the Human Genome Project. This project took over a decade to sequence the human genome for around 3 billion dollars. Since then, whole-genome sequencing cost has declined to about 1,000 dollars a person (Harden, 2021) and led to the discovery that even if we share 99.5% of our genetic information, instances where we genetically differ significantly contribute to individual differences across traits.

The most common type of genetic variation is single nucleotide polymorphisms (SNPs).

SNPs reflect 90% of the genetic variations across individuals and are regions in the genome where a Deoxyribonucleic acid (DNA) base pair (i.e., adenine (A), cytosine (C), guanine (G), or thymine (T)) varies in at least 1% of the general population. There are approximately 5 million known SNPs. Although changes in SNPs do not necessarily change the amino acid sequence of a protein, they can influence gene expression, messenger ribonucleic acid (mRNA) stability, and the localization of mRNA and/or proteins that may have a downstream effect on a trait or disease [START_REF] Shastry | SNPs: Impact on gene function and phenotype[END_REF].

Examining SNP differences between individuals is now easy and cheap: it requires noninvasive saliva samples and 60 dollars a person to sequence a subset of the genome. Therefore, massive amounts of genetic data have been collected by national biobanks, such as the UK Biobank and the Million Veterans Program, as well as by direct-to-consumer genetic companies, such as 23andMe© or Ancestry.com. Although private companies have genetic data for millions of individuals, the UK Biobank, with genetic data from 500,000 individuals, is a primary source for large-scale genomic data due to its size, straightforward access procedures, and its rich data for health and life outcomes (Harden, 2021).

The extent to which each SNP is associated with a particular trait is quantified by largescaled studies on individuals with genetic and trait data known as Genome-Wide Association Studies (GWASs; Box 3). GWAS results can be used to estimate trait heritability based on measures of genetic relatedness [START_REF] Visscher | Assumption-Free Estimation of Heritability from Genome-Wide Identity-by-Descent Sharing between Full Siblings[END_REF]. For instance, heritability can be quantified by examining whether pairs of unrelated individuals that are more genetically similar are also more phenotypically similar [START_REF] Yang | Common SNPs explain a large proportion of the heritability for human height[END_REF]. Another way to estimate heritability is by examining whether sibling pairs that are less genetically related are more similar phenotypically than sibling pairs that are genetically closer [START_REF] Visscher | Assumption-Free Estimation of Heritability from Genome-Wide Identity-by-Descent Sharing between Full Siblings[END_REF].

Across all cognitive traits, heritability has typically been found to lie between 20 and 80% [START_REF] Plomin | The genetic basis of complex human behaviors[END_REF]Polderman et al., 2015). While twin studies report that general cognitive function has a heritability of more than 50% from adolescence through adulthood to older age (Haworth et al., 2010;[START_REF] Plomin | Genetics and intelligence differences: Five special findings[END_REF][START_REF] Tucker-Drob | Genetic and Environmental Influences on Cognition Across Development and Context[END_REF], SNP-based estimates of heritability for general cognitive function are about 20-30% (Table 1 in Davies et al., 2018). This is also true for mental health disorders, with the SNP heritability at 0.26 for Schizophrenia and 0.11 for major depression disorder and twin heritability at 0.77 for Schizophrenia and 0.45 for multiple depression disorder (see Table 1 from Smoller et al., 2019). As for the psychopathology factors, studies using different samples and factoring methods to extract general psychopathology measures report SNP heritability ranging from 16 to 38% [START_REF] Alnaes | Association of Heritable Cognitive Ability and Psychopathology With White Matter Properties in Children and Adolescents[END_REF][START_REF] Mollon | Genetic influences on externalizing psychopathology overlap with cognitive functioning and show developmental variation[END_REF][START_REF] Neumann | Single Nucleotide Polymorphism Heritability of a General Psychopathology Factor in Children[END_REF], although the SNP heritability was only significant for the general psychopathology factor of the hierarchical but not the bifactor model [START_REF] Mollon | Genetic influences on externalizing psychopathology overlap with cognitive functioning and show developmental variation[END_REF].

Heritability estimates from twin studies are systematically larger than those from DNAbased methods. This is known as the missing heritability problem and the reasons behind this missingness have been widely discussed for diverse phenotypes [START_REF] Manolio | Finding the missing heritability of complex diseases[END_REF][START_REF] Owen | Explaining the missing heritability of psychiatric disorders[END_REF][START_REF] Young | Solving the missing heritability problem[END_REF][START_REF] Young | Discovering missing heritability in whole-genome sequencing data[END_REF]. In brief, it may be (1) that GWAS studies are not sufficiently powered to detect variants with weak genetic effects, (2) that genotyping tools do not capture the rare variants that contribute to heritability, or that (3) twin and family studies, which consider additive genetic effects and shared and non-shared environmental effects overestimate heritability by omitting genetic interactions, gene by environment interactions or through the violation of environmental assumptions (Harden, 2021). Whether heritability is missing or hiding in rare variants that are not typically measured [START_REF] Wainschtein | Assessing the contribution of rare variants to complex trait heritability from whole-genome sequence data[END_REF] or in the heterogeneity of effects across populations [START_REF] Tropf | Hidden heritability due to heterogeneity across seven populations[END_REF], is still subject to debate.

Most traits are nonetheless heritable, with twin and family studies providing the upper bound and DNA-based methods the lower bounds of heritability.

[ Box 3] Genome-wide association studies (GWASs) identify common variants (i.e., single nucleotide polymorphisms, SNPs) that contribute to the inherited variation of common traits and diseases. However, a significant association between a SNP and a trait (p< 5*10 -8 ) does not prove that the SNP has a causal effect on the phenotype. It could be that the SNP is structurally correlated with a causal variant that is not measured, or because it is correlated with an environmental factor that varies across human populations, which is known as population stratification [START_REF] Hamer | Beware the chopsticks gene[END_REF]. To partially correct for population stratification (see the last paragraph), researchers restrict their analyses to individuals of the same ancestry, used mixed models, and adjust for the 10 to 100 first genetic principal components that capture broad patterns of genomic similarity within a sample [START_REF] Shin | A mixed model reduces spurious genetic associations produced by population stratification in genome-wide association studies[END_REF]. The results (the summary statistics) of a GWAS, therefore, correspond to the output of a series of linear regression for each SNP, typically, with age, sex, and genetic principal components as covariates.

Unlike mendelian studies, where a single mutation may have high penetrance (effect size), like the autosomal dominant polymorphism of the FOXP2 genetic mutation associated with verbal dyspraxia, GWAS results have shown that a variety of traits (e.g., height, intelligence, depression…) are highly polygenic. This means that these traits are associated with many genetic variants, each of which has a small effect (r2 < 0.1; [START_REF] Chabris | The Fourth Law of Behavior Genetics[END_REF].

Because these effects are small, the larger the sample the more likely you can find robust associations between genetic variants and a trait.

GWASs were an important advancement from candidate gene studies, which focused on examining the association of one or several variants of a known gene with a phenotype in a small sample. Apart from the APOE ε4 polymorphism associated with an increased risk of Alzheimer's disease [START_REF] Abondio | The Genetic Variability of APOE in Different Human Populations and Its Implications for Longevity[END_REF], the majority of candidate genes results did not replicate [START_REF] Border | No Support for Historical Candidate Gene or Candidate Gene-by-Interaction Hypotheses for Major Depression Across Multiple Large Samples[END_REF][START_REF] Hirschhorn | A comprehensive review of genetic association studies[END_REF][START_REF] Todd | Statistical false positive or true disease pathway?[END_REF]. This is because the majority of genetic variants do not have high penetrance, requiring the use of large-scale GWAS studies.

In general, most efforts lie in identifying associations with characteristics shown within diagonal dotted lines in Figure B3. However, GWASs can only identify a subset of risk variants, which could in part explain the missing heritability problem. Another major problem with GWASs, which also applies to all genetic studies, is that it examines associations and can be used to measure heritability in a given population at a given time. Therefore, findings from GWAS on European ancestry can differ from findings in other ancestries. For instance, the SNP association or the SNP itself may not be associated with a trait across different ancestries.

Finally, GWAS are biased by demographic (population stratification and assortative mating) and indirect (genetic nurture) genetic effects (Figure 1 from Howe et al., 2021). Even though researchers use linear mixed model methods when examining SNP effects and control for the top 10-100 principal components of the genotyped data, these steps do not completely control for fine-scale population structure. Family-based designs, such as within-sibship GWASs, are now being used to address these biases (Howe et al., 2021).

[End of Box]

2.3.Nature and Nurture

In light of the small effect of each SNP across traits, Wray and colleagues (2007) proposed that the multiple-risk alleles throughout the genome be simultaneously considered to better estimate individual genetic predisposition for a trait or disorder. These researchers created polygenic scores (PGSs), also known as Polygenic Risk Scores (PRSs), as an estimate of someone's genetic liability to a trait or disease, calculated according to their genotype profile and GWAS results for the trait or disease in question [ Box 4]. PGSs have been calculated for a variety of traits, including Educational Attainment (EA, years of completed education, or level of completed education), Cognitive Performance (as measured by general or fluid intelligence; Davies et al., 2018;Lee et al., 2018), non-cognitive skills (Demange et al., 2021), depression [START_REF] Wray | Genome-wide association analyses identify 44 risk variants and refine the genetic architecture of major depression[END_REF], schizophrenia [START_REF] Lam | Comparative genetic architectures of schizophrenia in East Asian and European populations[END_REF][START_REF] Pardiñas | Common schizophrenia alleles are enriched in mutation-intolerant genes and in regions under strong background selection[END_REF], mood disorders [START_REF] Coleman | Bipolar Disorder Working Group of the Psychiatric Genomics Consortium, Major Depressive Disorder Working Group of the Psychiatric Genomics Consortium[END_REF], and many other disorders.

Genetic research on intelligence heavily relies on Educational Attainment (EA) [START_REF] Plomin | The new genetics of intelligence[END_REF] because it is easy to measure, recorded by a majority of studies and cohorts, and is phenotypically (r = 0.50) and genetically (rg = 0.65) highly correlated with intelligence [START_REF] Rietveld | GWAS of 126,559 individuals identifies genetic variants associated with educational attainment[END_REF]. In 2018, Lee and colleagues (2018) ran a discovery GWAS on over 1.1 million individuals (EA3), which lead to the discovery of 1,271 independent genome-wide significant SNPs associated with EA. The discovery GWAS summary statistics were used to create a EA PGSs in independent samples, the Health and Retirement Study (HRS) and the Add Health Study, to obtain unbiased genetic predisposition estimates of EA.

The EA PGSs for these samples accounted for 11-13% of the variance in EA, after adjusting for age, sex, and population stratification with the first 10 genetic principal components (Lee et al., 2018). Although a GWAS of EA was recently conducted on 3 million individuals, yielding a PGS that explained 12-16% of the variance in EA [START_REF] Okbay | Polygenic prediction of educational attainment within and between families from genome-wide association analyses in 3 million individuals[END_REF], the summary statistics are not publicly available as they require permission from 23andme.

Over the last decade, the creation of PGSs has been a turning point for research in intelligence [START_REF] Plomin | The new genetics of intelligence[END_REF] and psychopathology [START_REF] Andlauer | Polygenic scores for psychiatric disease: From research tool to clinical application[END_REF], with the hopes of using PGSs as early predictors of general cognition or psychopathology. For instance, a recent study examined the extent to which PGSs of specific disorders predict the factors of a bifactor model in children. The associations between the PGSs of specific disorders and the general psychopathology factor suggested that there are shared variants across all disorders and the associations between the PGSs of specific disorders and the subfactors of the bifactor model suggested that there are shared variants that are specific to a subset of disorders, which supports the validity of the bifactor model to describe psychopathology [START_REF] Neumann | Combined polygenic risk scores of different psychiatric traits predict general and specific psychopathology in childhood[END_REF]. PGSs have many other applications: they can be used to control for genetic influences in their studies [START_REF] Rietveld | GWAS of 126,559 individuals identifies genetic variants associated with educational attainment[END_REF]Stumm et al., 2020), to investigate gene by environment interactions (e.g., Harden et al., 2020;[START_REF] Os | Replicated evidence that endophenotypic expression of schizophrenia polygenic risk is greater in healthy siblings of patients compared to controls, suggesting gene-environment interaction. The EUGEI study[END_REF]Rimfeld et al., 2018), study environmental factors mediating the effects of genes on the outcome of interest (e.g., [START_REF] He | A Gene-Environment Interaction Study of Polygenic Scores and Maltreatment on Childhood ADHD[END_REF][START_REF] Pat | Motivation and Cognitive Abilities as Mediators Between Polygenic Scores and Psychopathology in Children[END_REF][START_REF] Wertz | Genetics of nurture: A test of the hypothesis that parents' genetics predict their observed caregiving[END_REF], and disentangle intergenerational genetic effects from environmental factors (e.g., [START_REF] Ayorech | Genetic Influence on Intergenerational Educational Attainment[END_REF][START_REF] Pingault | Identifying intergenerational risk factors for ADHD symptoms using polygenic scores in the Norwegian Mother[END_REF].

Several studies suggest that SES and the PGS for EA (or general intelligence) are the largest predictors of EA (or general intelligence; [START_REF] Allegrini | Genomic prediction of cognitive traits in childhood and adolescence[END_REF]Lee et al., 2018;[START_REF] Sirin | Socioeconomic Status and Academic Achievement: A Meta-Analytic Review of Research[END_REF]Strenze, 2007). For instance, one study found that the EA PGS predicted 14% of the variance in educational attainment, whereas SES at age 16 predicted 23% of the variance in educational attainment (von Stumm et al., 2020). Another study reported that the general intelligence PGS (β = 0.26) had more influence on general cognitive ability than parental SES (β = 0.20) and that, together, they explained 24% of the variance in general cognitive ability [START_REF] Paul | Childhood Socioeconomic Status and Polygenic Scores for Cognition Have Independent Associations with Cognitive Performance During Middle Childhood[END_REF].

Studies reported that SES, intelligence, and education are phenotypically and genotypically associated with mental health, even if their effects vary by mental health disorder (Box 2; e.g., [START_REF] Keyes | Fluid intelligence and psychiatric disorders in a population representative sample of US adolescents[END_REF]McLaughlin et al., 2012;[START_REF] Pasman | Substance use: Interplay between polygenic risk and neighborhood environment[END_REF]. Mental Health disorders are negatively associated with SES [START_REF] Hudson | Socioeconomic status and mental illness: Tests of the social causation and selection hypotheses[END_REF][START_REF] Reiss | Socioeconomic inequalities and mental health problems in children and adolescents: A systematic review[END_REF][START_REF] Reiss | Socioeconomic status, stressful life situations and mental health problems in children and adolescents: Results of the German BELLA cohort-study[END_REF], intelligence [START_REF] Melby | Is there an association between full IQ score and mental health problems in young adults? A study with a convenience sample[END_REF][START_REF] Wraw | Intelligence in youth and mental health at age 50[END_REF], and educational attainment [START_REF] Lereya | Mental health difficulties, attainment and attendance: A cross-sectional study[END_REF]. Genetic correlations between the general psychopathology factor and intelligence (e.g., rg= -0.74; [START_REF] Alnaes | Association of Heritable Cognitive Ability and Psychopathology With White Matter Properties in Children and Adolescents[END_REF] and between mental health disorders and SES are also negative [START_REF] Marees | Genetic correlates of socioeconomic status influence the pattern of shared heritability across mental health traits[END_REF]. Although educational attainment and intelligence have a high genetic correlation of 0.70 (Hill, Marioni, et al., 2019), the genetic correlations of mental health disorders with intelligence or EA can differ in magnitude, suggesting that different genetic variants are also at play in the genetic predisposition to mental health disorders (Figure 1. b in [START_REF] Hill | What genome-wide association studies reveal about the association between intelligence and mental health[END_REF].

In light of the importance of these predictors and the complex relationships between them, more recent studies attempt to simultaneously model these influences to better understand the etiology of intelligence and psychopathology disorders. Associations between these variables can be studied in numerous ways depending on the question at hand. For instance, some were interested in uncovering whether shared genetic variants between EA and depression are mediated by SES [START_REF] Avinun | Cognitive ability, Socioeconomic Status, and Depressive Symptoms: A Gene-Environment-Trait Correlation[END_REF], while others focused on assessing the Depression PGS' prediction of depression after adjusting for additional psychosocial measures, such as parental history and SES [START_REF] Agerbo | Risk of Early-Onset Depression Associated With Polygenic Liability, Parental Psychiatric History, and Socioeconomic Status[END_REF]. Due to the complexity of the design and the availability of variables across data sets, very few studies can examine associations between cognition, psychopathology, genetics, trauma exposure, and SES. One of these few studies examined the environmental (childhood trauma and parental education, the latter serving as a proxy of SES), psychopathological (depression diagnosis), and genetic variables predicting cognitive functioning in adults. They found that while all variables independently predicted cognitive functioning even when controlling for each other, most of the variance in the association was explained by depression and parental education [START_REF] Goltermann | Childhood maltreatment and cognitive functioning: The role of depression, parental education, and polygenic predisposition[END_REF].

However, similar analyses could be performed to quantify environmental, cognitive, and genetic effects on adult psychopathology. As done for cognitive dysfunction by Goltermann and colleagues (2021), future large-scaled cohort studies with rich datasets should focus on identifying variables that might be subject to interventions for psychopathology.

[ Box 4] Polygenic scores correspond to a weighted average of all or a subset of SNPs associated with a trait or disorder. GWAS results from a discovery sample are used to determine which of the two alleles of a SNP is positively associated with a trait (increasing allele, e.g., Adenine

or Thymine and Guanine or Cytosine) and are used to quantify the association (weight)

between increasing allele and the trait or disorder. In an independent target sample, a person's increasing allele count at each SNP (0, 1, or 2) is multiplied by the SNP weight. The weighted SNP counts are then summed providing a unique polygenic score for each individual. Once the scores for each individual are created, researchers can examine the extent to which the PGS predicts a specific trait using linear regression.

The accuracy of the PGS increases with the heritability of the trait and the size of the GWAS sample and decreases with the increase in polygenicity of a trait and variation in the genetic architecture of a trait across environments [START_REF] Dudbridge | Power and Predictive Accuracy of Polygenic Risk Scores[END_REF]. Although larger datasets have increased the predictive power of the PGS (Davies et al., 2018;Lee et al., 2018;[START_REF] Okbay | Genome-wide association study identifies 74 loci associated with educational attainment[END_REF][START_REF] Rietveld | GWAS of 126,559 individuals identifies genetic variants associated with educational attainment[END_REF][START_REF] Yengo | Meta-analysis of genomewide association studies for height and body mass index in ∼700000 individuals of European ancestry[END_REF], the current PGS for behavioral outcomes cannot accurately predict outcomes for specific individuals. The PGS for Educational Attainment (EA) accounts for 11% of the variance in EA, after adjusting for age, sex, and population stratification with the first 10 genetic principal components. And yet, for any value of PGS, almost every value of EA is observed.

PGSs are nonetheless useful tools for social science (Harden, 2021;[START_REF] Harden | Using genetics for social science[END_REF][START_REF] Raffington | Polygenic Scores in Developmental Psychology: Invite Genetics In, Leave Biodeterminism Behind[END_REF], allowing, for instance, for researchers to control for genetic influences in their experiments [START_REF] Rietveld | GWAS of 126,559 individuals identifies genetic variants associated with educational attainment[END_REF], to investigate gene by environment interactions [START_REF] Barcellos | Education can reduce health differences related to genetic risk of obesity[END_REF], and study environmental factors mediating the effects of genes on the outcome of interest [START_REF] Wertz | Genetics of nurture: A test of the hypothesis that parents' genetics predict their observed caregiving[END_REF].

However, considering that the PGS created from summary statistics from a specific ancestry group will have lower predictive power in another ancestry group, it is necessary to run more discovery GWASs on non-European samples to increase the PGS in non-European individuals, even if there are new methods that attempt to combine summary statistics across ancestry groups to boost predictive power of PGSs in non-European samples [START_REF] Ruan | Improving Polygenic Prediction in Ancestrally Diverse Populations[END_REF].

[End Box 3]

Brain Correlates of Intelligence and Psychopathology

While there are reliable associations between genetic, environmental factors, and cognitive abilities and disorders, the causal chains are long and indirect, and the effect sizes are small. A better understanding of the mechanisms behind phenotypic diversity can be achieved by considering more proximal factors, or intermediate phenotypes, in large population samples.

Obvious candidates lie within the brain, which collects both genetic and environmental influences and is the biological basis for cognition and behavior.

2.4.Intelligence and the Brain

The largest cerebral predictor of general intelligence is Total Brain Volume (r = 0.24; Pietschnig et al., n.d.). Although there are substantial differences in TBV between sexes (Ritchie et al., 2018;C. M. Williams et al., 2021), there are little to no sex differences in mean intelligence [START_REF] Deary | Brother-sister differences in the g factor in intelligence: Analysis of full, opposite-sex siblings from the NLSY1979[END_REF][START_REF] Johnson | Sex Differences in Variability in General Intelligence: A New Look at the Old Question[END_REF] and the correlation between intelligence and TBV are similar across sexes (Cox et al., 2019a;Ritchie et al., 2018).

It could be that differences in brain size are compensated by differences in regional size and structure, function, or connectivity (Deary et al., 2021).

Studies have decomposed the brain into its tissue types and loci to identify the brain measures associated with interindividual differences in intelligence. One of the most wellknown neurological models of intelligence is the Parietal Frontal Integration Theory (P-FIT; (Jung & Haier, 2007). This theory is based on anatomical, functional, and diffusion neuroimaging studies and proposes that intelligence recruits regions in the dorsolateral prefrontal cortex, the inferior and parietal lobule, the anterior cingulate, and a few regions in the temporal and occipital lobes. Since then, several studies examining the associations between intelligence and cortical volumes, thicknesses, surface areas, fractional anisotropy 1 , mean diffusivity 2 , and brain lesions across children, adolescents, and middle-aged to older adults generally provide support for the P-FIT theory (for review see Figure 3 from Deary et al., 2021), although some studies report conflicting findings (e.g., [START_REF] Aggleton | Hippocampal-anterior thalamic pathways for memory: Uncovering a network of direct and indirect actions[END_REF][START_REF] Grazioplene | Subcortical intelligence: Caudate volume predicts IQ in healthy adults[END_REF][START_REF] Nomi | Structural Connections of Functionally Defined Human Insular Subdivisions[END_REF][START_REF] Rhein | Neuroanatomical Correlates of Intelligence in Healthy Young Adults: The Role of Basal Ganglia Volume[END_REF]Ritchie et al., 2018), or additional regional associations with intelligence (Basten et al., 2015;Cox et al., 2019b), such as with the thalamus volume (r = 0.25, Cox et al., 2019b). Other models, known as the Multiple Demand Network or the frontoparietal network [START_REF] Camilleri | Definition and characterization of an extended multipledemand network[END_REF][START_REF] Duncan | The multiple-demand (MD) system of the primate brain: Mental programs for intelligent behaviour[END_REF], which describe the association between the brain and executive functions, indirectly contribute to brain correlates of intelligence by reporting overlapping regions with the P-FIT model (Deary et al., 2021).

Few studies have simultaneously examined the effect of cortical and subcortical volumes as well as micro-and macro-white matter measures on intelligence using SEM models [START_REF] Penke | Brain white matter tract integrity as a neural foundation for general intelligence[END_REF][START_REF] Ritchie | Beyond a bigger brain: Multivariable structural brain imaging and intelligence[END_REF]Ritchie et al., , 2018)). A study examining the association between latent factors of white matter microstructure (e.g., general Fractional Anisotropy, FA) and intelligence found that latent factors accounted for 10% of the variance in intelligence in 73 years old participants (N = 420; [START_REF] Penke | Brain white matter tract integrity as a neural foundation for general intelligence[END_REF]. In contrast, other studies simultaneously examining the effects of different tissue types found that the general factor of FA did not significantly predict the gfactor and that grey matter volumes were the largest predictor of the g-factor, followed by white matter hyperintensity volume. These global measures explained 5.4 -18% of the variance in the g-factor, depending on age (Cox et al., 2019a;[START_REF] Ritchie | Beyond a bigger brain: Multivariable structural brain imaging and intelligence[END_REF].

Other studies examined the extent to which regional measures account for individual differences in intelligence. For instance, a study found that the frontopolar prefrontal cortex volume and the FA in the forceps minor were associated with intelligence when simultaneously examining multivariate cross-tissue contributions of grey matter regions and white matter pathways previously associated with intelligence [START_REF] Kievit | Distinct aspects of frontal lobe structure mediate age-related differences in fluid intelligence and multitasking[END_REF]. Therefore, future studies that simultaneously consider global and regional measures are necessary to pinpoint the relative contributions of different brain measures on intelligence.

Several studies focused on structural and functional connectomes to better test network theories (e.g., P-FIT). Although these studies are not without limitations [START_REF] Buchanan | The effect of network thresholding and weighting on structural brain networks in the UK Biobank[END_REF], a recent study (N = 884) reported that they could predict 20% of the variance in intelligence with several connectivity networks from an hour of resting-state functional MRI when using a leave-one-family-out cross-validation scheme. When they removed or 'lesioned' a network, the prediction only slightly declined, suggesting that there is no single network or structure associated with intelligence. Intelligence instead appears to rely on distributed and redundant information in functional connectivity patterns across brain regions [START_REF] Dubois | A distributed brain network predicts general intelligence from resting-state human neuroimaging data[END_REF]. Another study created morphometric similarity networks that are based on inter-regional similarity across cellular, molecular, and functional features in the brain. The authors found that differences in the degree of morphometric similarity between nodes across the brain predicted 40% of the variance in verbal numerical and matrix reasoning [START_REF] Seidlitz | Morphometric Similarity Networks Detect Microscale Cortical Organization and Predict Inter-Individual Cognitive Variation[END_REF].

Although these studies provide good predictive models of variation in intelligence, future studies choose to focus on the relative contribution specific cerebral regions and measures to explain differences in intelligence.

2.5.Intelligence, Brain, Environment, and Genetics

The extent to which the genetic variants associated with intelligence are also associated with brain volumes varies across brain regions and measures. For instance, intelligence is genetically correlated with TBV (rg = 0.23), grey matter volumes (rg = 0.08; Davies et al., 2018), with the FA of some white matter tracts (|rg| = 0.15 to 0.18), including the superior frontal-occipital fasciculus, and the corpus callosum [START_REF] Zhao | Common genetic variation influencing human white matter microstructure[END_REF], and with regional grey matter volumes, such as the left posterior cingulate cortex (rg = 0.23; [START_REF] Zhao | Genome-wide association analysis of 19,629 individuals identifies variants influencing regional brain volumes and refines their genetic co-architecture with cognitive and mental health traits[END_REF].

Variations in SNPs associated with differences in intelligence are associated with tissuespecific gene expression in the brain [START_REF] Coleman | Biological annotation of genetic loci associated with intelligence in a meta-analysis of 87,740 individuals[END_REF][START_REF] Hill | What genome-wide association studies reveal about the association between intelligence and mental health[END_REF]Savage et al., 2018). For instance, some genes associated with intelligence are thought to play a role in neurogenesis as well as synapse, neuron, and oligodendrocyte differentiation (Hill, Marioni, et al., 2019).

In light of the genetic and intelligence and brain to intelligence associations, researchers have recently started to simultaneously examine genetic and neural effects on intelligence to examine the extent to which various cerebral regions or networks mediate genetic effect on intelligence (Loughnan et al., 2021). For instance, one study used the summary statistic from the intelligence GWAS conducted by Davis and colleagues (2018) to create PGSs for intelligence that predicted 3% (IntegraMooDS N = 742) to 5.1% (IMAGEN N = 1651) of the variance in the g-factor. Using vertex-wise and cortex-wise analyses, the authors found that the surface area and cortical thickness of the prefrontal anterior cingulate, insula, and medial temporal cortices mediated the effect of the g-factor PGS on the g-factor across cohorts and that the mediation pathway explained 0.75% to 0.77% of the variance in the g-factor (Lett et al., 2020). Although these mediation paths currently only explain less than 1% of the variance in intelligence, the amount of predictive power of these pathways may increase with the quality of the intelligence PGS. Additional studies examining a larger set of brain correlates are required to replicate and deepen our understanding of the strongest cerebral mediators of genetic predisposition to intelligence.

There are currently only a few studies that simultaneously integrate brain, genetic, and Their findings suggest that although both SES and the EA PGS influence brain size, inequalities in SES influence global changes in cortical development [START_REF] Judd | Cognitive and brain development is independently influenced by socioeconomic status and polygenic scores for educational attainment[END_REF]. However, such studies, integrating behavioral, brain, genetic, and environmental data, remain rare. This can generally be explained by the fact that these studies require a cohort (i) with genetic data, (ii) the behavioral, brain, and environmental variables of interest, (iii) a large enough sample to examine the small associations described above, and (iv) that has not been included in the GWASs on the trait of interest. The latter is a major limitation when using the UK Biobank, which is consistently included in the majority of GWAS due to its rich behavioral and genetic data on up to 500,000 participants.

2.6.Psychopathology and the Brain

Numerous studies attempted to identify biomarkers that may be specific to a mental health disorder (e.g., [START_REF] Abi-Dargham | The search for imaging biomarkers in psychiatric disorders[END_REF][START_REF] Gray | Multimodal Abnormalities of Brain Structure and Function in Major Depressive Disorder: A Meta-Analysis of Neuroimaging Studies[END_REF][START_REF] Grimm | Transdiagnostic neuroimaging of reward system phenotypes in ADHD and comorbid disorders[END_REF]. However, in light of the high comorbidity across mental health disorders and the difficulty in identifying specific biomarkers (for review [START_REF] Dalgleish | Transdiagnostic approaches to mental health problems: Current status and future directions[END_REF][START_REF] Sprooten | Addressing reverse inference in psychiatric neuroimaging: Meta-analyses of task-related brain activation in common mental disorders[END_REF] efforts have been made to identify common biomarkers across disorders [START_REF] Goodkind | Identification of a common neurobiological substrate for mental illness[END_REF][START_REF] Janiri | Shared Neural Phenotypes for Mood and Anxiety Disorders: A Meta-analysis of 226 Task-Related Functional Imaging Studies[END_REF][START_REF] Mcteague | Identification of Common Neural Circuit Disruptions in Cognitive Control Across Psychiatric Disorders[END_REF][START_REF] Sha | Common Dysfunction of Large-Scale Neurocognitive Networks Across Psychiatric Disorders[END_REF][START_REF] Wise | Common and distinct patterns of grey-matter volume alteration in major depression and bipolar disorder: Evidence from voxel-based meta-analysis[END_REF]. For instance, a meta-analysis of 193 studies and 15,892 found that volumes associated with cognitive control and attention, the dorsal anterior cingulate cortex and left and right anterior insulae volumes, were reduced in individuals with addiction, anxiety, bipolar disorder, depression, obsessive-compulsive disorder (OCD), or schizophrenia [START_REF] Goodkind | Identification of a common neurobiological substrate for mental illness[END_REF]. Activity in these regions also varied between controls and individuals with either anxiety, bipolar disorder, depression, or PTSD, suggesting impairments in inhibitory control and salience processing may be common across these disorders [START_REF] Janiri | Shared Neural Phenotypes for Mood and Anxiety Disorders: A Meta-analysis of 226 Task-Related Functional Imaging Studies[END_REF]. Other neuroimaging studies report that prefrontal cortical and limbic circuits, which play a role in the regulation of emotions, the integration of emotional responses, and the selection of motivated behaviors, are prominently associated with many types of psychopathology [START_REF] Kalin | Prefrontal Cortical and Limbic Circuit Alterations in Psychopathology[END_REF].

The phenotypic psychopathology factors are associated with a range of neural phenotypes [START_REF] Elliott | A Connectome-wide Functional Signature of Transdiagnostic Risk for Mental Illness[END_REF][START_REF] Romer | Structural alterations within cerebellar circuitry are associated with general liability for common mental disorders[END_REF][START_REF] Romer | Replicability of structural brain alterations associated with general psychopathology: Evidence from a population-representative birth cohort[END_REF][START_REF] Snyder | Distinct patterns of reduced prefrontal and limbic grey matter volume in childhood general and internalizing psychopathology[END_REF][START_REF] Sripada | Widespread attenuating changes in brain connectivity associated with the general factor of psychopathology in 9-and 10-year olds[END_REF]. The general psychopathology factor from a bifactor model is associated with a general reduction in grey matter volume (Kaczkurkin et al., 2019;[START_REF] Snyder | Distinct patterns of reduced prefrontal and limbic grey matter volume in childhood general and internalizing psychopathology[END_REF]. As for cortical thickness and surface area, a study of 875 adults with a bifactor model of psychopathology reported that the general psychopathology factor was negatively associated with the neocortex and that there were few unique cerebral associations with the residual thought disorder, externalizing, and internalizing factors [START_REF] Romer | Pervasively Thinner Neocortex as a Transdiagnostic Feature of General Psychopathology[END_REF]. In contrast, a white matter study on 410 young adults with a bifactor model of psychopathology found that specific microstructural variations were associated with the general psychopathology factor and with the residual internalizing and externalizing factors [START_REF] Hinton | White matter microstructure correlates of general and specific second-order factors of psychopathology[END_REF].

2.7.Psychopathology, Brain, Environment, and Genetics

Although there is an extensive literature linking trauma and life stressors to psychopathology (Carr et al., 2013;[START_REF] Green | Childhood Adversities and Adult Psychiatric Disorders in the National Comorbidity Survey Replication I: Associations With First Onset of DSM-IV Disorders[END_REF][START_REF] Haidl | The non-specific nature of mental health and structural brain outcomes following childhood trauma[END_REF][START_REF] Kessler | Childhood adversities and adult psychopathology in the WHO World Mental Health Surveys[END_REF][START_REF] Mclaughlin | Childhood adversities and posttraumatic stress disorder: Evidence for stress sensitisation in the World Mental Health Surveys[END_REF][START_REF] Roffman | Association of adverse prenatal exposure burden with child psychopathology in the Adolescent Brain Cognitive Development (ABCD) Study[END_REF][START_REF] Trotta | The impact of childhood adversity on the persistence of psychotic symptoms: A systematic review and meta-analysis[END_REF], there are still few largescale neuroimaging studies examining the cerebral correlates of trauma. One UK Biobank study on about 6,000 older adults found that individuals reporting that they felt hated by a family member as a child had smaller cerebellar and ventral striatum volumes (although these effects were small, ηp 2 < 0.01; [START_REF] Gheorghe | Associations of perceived adverse lifetime experiences with brain structure in UK Biobank participants[END_REF]. A study on 9-and 10-year-old children from the Adolescent Brain Cognitive Development (ABCD) study (N= 4,447 -7,662) derived dimensions of psychopathology from the Child Behavior Checklist (e.g., attention problems, thought problems, anxious/depressed symptoms). The authors examined the extent to which a mental health disorder polygenic risk score (e.g., depression PGS, Bipolar Disorder PGS), a family history variable (e.g., family history of depression, alcohol problem), or a brain measure (i.e., global, lobar, and subcortical measures and functional connectivities) predicted each dimension of psychopathology after adjusting for various covariates. Global or lobar cerebral measures were not associated with any of the dimensions except for the right nucleus accumbens, which had a negative effect on somatic complaints (d = -0.10). Several family history indicators, the PGS of depression, the PGS of ADHD, and some connectivity networks were associated with several psychopathology factors [START_REF] Wainberg | Cannabis, schizophrenia genetic risk, and psychotic experiences: A cross-sectional study of 109,308 participants from the UK Biobank[END_REF]. Although this study provides evidence for a non-specific influence of brain, environmental, and genetic factors on a range of pathological factors, further studies are needed to examine (i) additional cerebral correlates of psychopathology and (ii) the extent to which cerebral markers mediate the influence that PGSs have on psychopathology.

To our knowledge, the only large-scale study exploring the brain's mediating effects of trauma on psychopathology in adulthood focused on childhood trauma and functional connectivity in 19,535 individuals. Functional connectivities of the temporal cortex, precuneus, medial frontal cortex, and prefrontal cortex were negatively associated with a child's traumatic event score. Using the mean strength of these functional connectivities as mediators, mediation pathways explained 0.5% (self-harm) to 1.9% (addiction) of the variance in mental health disorders and the mean strength of the significant functional connectivities mediated the effects of childhood maltreatment on general mental health. The authors additionally reported that the association matrix between childhood trauma exposure and functional connectivity was similar with and without adjusting for the Townsend Index, which measures neighborhood deprivation in the UK [START_REF] Wan | Brain functional connectivities that mediate the association between childhood traumatic events, and adult mental health and cognition[END_REF]. In light of the Townsend Index's weak (but significant) correlation of 0.08 with childhood maltreatment [START_REF] Wan | Brain functional connectivities that mediate the association between childhood traumatic events, and adult mental health and cognition[END_REF], better indicators may be necessary to accurately control for adult SES. As few studies examine the associations between environmental, brain, and psychopathology and their mediation effects, these findings must be replicated to be judged as robust and extended to include structural brain regions and additional environmental measures.

2.8.Explaining the Gap

Numerous reviews emphasize the importance of environmental, genetic, and biological data to understand the etiology of intelligence and psychopathology (e.g., Abdellaoui & Verweij, 2021;Deary et al., 2021, p. 202; J. R. [START_REF] Gray | Neurobiology of intelligence: Science and ethics[END_REF][START_REF] Hyde | Understanding risk for psychopathology through imaging gene-environment interactions[END_REF]Sprooten et al., 2021;[START_REF] Thapar | The contribution of gene-environment interaction to psychopathology[END_REF]. And yet, until recently, most studies were constrained to studying two types of data, such as behavioral and neuroimaging data or genetic and behavioral data. Although this can be explained by the absence of sufficiently rich and large datasets to test more numerous and complex associations between variables, the replicability of studies examining binary associations has also been quite low (e.g., behavioral and neuroimaging studies), motivating researchers to continue testing these associations. For instance, the hippocampus was a major candidate for depression [START_REF] Videbech | Hippocampal volume and depression: A meta-analysis of MRI studies[END_REF], whereby depressive patients had smaller hippocampal volumes. However, a recent large-scaled ENIGMA study reported that this effect was specifically driven by patients with recurrent major depressive disorder (d=-0.17; N cases = 1,119) and absent when examining first-episode patients and controls [START_REF] Schmaal | Subcortical brain alterations in major depressive disorder: Findings from the ENIGMA Major Depressive Disorder working group[END_REF], which could partly explain the absence of this association in UK Biobank studies with over 15,000 participants [START_REF] Harris | Structural neuroimaging measures and lifetime depression across levels of phenotyping in UK biobank[END_REF]. As for the cerebral correlates of intelligence, the P-FIT theory was created based on a meta-analytic review by Jung and Haier (2007) of 37 underpowered functional and structural studies. While more recent meta-analytic results support the P-FIT model, a meta-analysis found less functional support for the role of temporal and occipital sensory regions on intelligence and did not find an association between intelligence and the grey matter of regions within the parietal lobe (Basten et al., 2015).

Although meta-analyses exist to establish the magnitude of an effect and its significance across numerous studies, they may be influenced by publication bias and may be biased by underpowered studies, which tend to report inaccurate effect sizes. In some cases, such as for studies linking differences in general psychopathology to variations in the brain, investigations are too recent for there to be replications and meta-analyses (Sprooten et al., 2021).

Discrepancies in the reported results are not only due to small sample size, but may also stem from differences in terms of MRI acquisition parameters, segmentation software, brain atlases, sample age range, phenotypic measures, and included covariates. Recent reviews recommend thousands of participants for reliable results, considering that most effect sizes are below 0.2 [START_REF] Marek | Towards Reproducible Brain-Wide Association Studies[END_REF][START_REF] Marek | Reproducible brain-wide association studies require thousands of individuals[END_REF]. In light of these limitations, the creation of birth cohorts, biobank studies, and international consortiums has been a real game-changer for the field, as they address the limitation of sample size and, sometimes, additional caveats as well.

The limitations of neuroimaging studies go beyond the literature on cognition and psychopathology. Until 2019, the number of sufficiently powered studies appropriately examining normative neuroanatomical differences was small and the extent to which cerebral measures are influenced by brain size, age, sex, and handedness was not well established [START_REF] Eliot | Dump the "dimorphism": Comprehensive synthesis of human brain studies reveals few male-female differences beyond size[END_REF][START_REF] Gao | A review on neuroimaging studies of genetic and environmental influences on early brain development[END_REF][START_REF] Guadalupe | Human subcortical brain asymmetries in 15,847 people worldwide reveal effects of age and sex[END_REF][START_REF] Kong | Mapping cortical brain asymmetry in 17,141 healthy individuals worldwide via the ENIGMA Consortium[END_REF][START_REF] Reardon | Normative brain size variation and brain shape diversity in humans[END_REF].

As a result, these findings require replication and supplementary investigation for future research interested in linking neuroanatomical data to genetic and environmental predictors of cognition and mental health disorders.

2.9.The Goal

The goal of the dissertation was to identify the neuroanatomical measures that mediate genetic and environmental effects on the general intelligence and psychopathology.

To do so, we first identified how to adjust for global cerebral measures when reporting regional cerebral effects independently of brain size. We additionally addressed the gap in the literature regarding normative neuroanatomical measures by examining the effect of age, sex, and global measures on over 620 cerebral measures (paper 1) and 306 brain asymmetries (paper 2) in the UK Biobank. These analyses included cortical, subcortical, and cerebellar grey matter volumes, and cortical thicknesses and surface areas. The first two papers reveal how brain size should be accounted for when examining the associations between regional cerebral measures and cognition or psychopathology in papers 5 and 6.

We then created phenotypic and genetic measures of cognition and psychopathology for the mediation models. In paper 3, we created an age-standardized g-factor relative to the UK population and a g-factor PGS for individuals with neuroimaging data. We calculated the gfactor PGS using the summary statistics from the GWAS we ran on individuals in the UK Biobank with a g-factor measure of good quality and without neuroimaging data. In paper 4, we created phenotypic psychopathology factors (e.g., general psychopathology factor, internalizing-factor, etc.) from 10 binary mental health disorders for over 400,000 individuals by combining probable diagnoses from the online questionnaire, self-reported medical diagnoses during visits, and hospital diagnoses in the UK Biobank. In paper 5, we ran factor analyses on these 10 binary mental health diagnoses to obtain phenotypic models of psychopathology. We ran a GWAS on each mental health disorder, excluding participants with neuroimaging data. We meta-analyzed our GWAS results with publicly available summary statistics for similar disorders that excluded the UK Biobank. Using Genomic SEM, we applied the phenotypic psychopathology model structure to the meta-analyzed genetic data and extracted SNP effects for each of the genetic psychopathology factors (e.g., Internalizingfactor). Finally, we created psychopathology factors PGSs for UK Biobank individuals with neuroimaging data and examined whether TBV mediated (i) the effect of the psychopathology factors PGSs on their respective phenotypic psychopathology factors (e.g., Internalizing PGS' effect on the Internalizing factor) on and (ii) the effect of childhood adversity on each phenotypic psychopathology factor.

In paper 6, we identified the global and regional cerebral measures mediating the g-factor PGS' effect on the g-factor and if the same regions mediated the effect of childhood adversity on the g-factor.

Finally, we discuss our main findings and major limitations, before providing guidelines for future studies interested in examining the complex associations between the brain, genes, the environment, cognition, and psychopathology.

Part 1 : Studying Regional Measures

Independently of Global Brain Size

Paper 1 -Studying Regional Volumes, Mean Thicknesses, and Surface Areas Independently of Global Brain Size We responded to a review by Eliot and colleagues (2021) light of a recent review stating that all sex differences were reduced to body size. Using the results from the first paper and additional analyses and figures, we show that sex differences in the brain cannot be reduced to body size. been of great interest to researchers in epidemiology, neuroscience, and genetics as it predicts a wide array of educational, health, and social outcomes (e.g., Calvin et al., 2017;Deary et al., 2007;Strenze, 2007). Given the numerous genetic, neural, and environmental factors that may contribute to intelligence, large-scale studies are needed to identify the respective contribution of these factors and their potential interactions on intelligence (for review see Deary et al., 2019Deary et al., , 2021)).

The UK Biobank is an ideal database to study the causes and consequences of intelligence, with its cognitive, brain imaging, genetic, health, and environmental data on more than 500,000 British middle-aged and older adults. Yet, numerous factors make the use of the assessment center on a touchscreen or autonomously online, with one's device.

To maximize the number of participants included in their studies on intelligence in the UK Biobank, some researchers estimated intelligence with a single test, either a Verbal Numerical Reasoning (aka Fluid Intelligence, FI) score or a reaction time score [START_REF] Davies | Genome-wide association study of cognitive functions and educational attainment in UK Biobank (N=112 151)[END_REF][START_REF] Kievit | The neural determinants of age-related changes in fluid intelligence: A pre-registered, longitudinal analysis in UK Biobank[END_REF]Lee et al., 2018;Savage et al., 2018;[START_REF] Sniekers | Genome-wide association meta-analysis of 78,308 individuals identifies new loci and genes influencing human intelligence[END_REF]. Others created a general intelligence (g) factor from 3 to 7 cognitive variables using Principal Component Analysis (PCA) or Confirmatory Factor Analysis (CFA; Cox et al., 2019;[START_REF] Hepsomali | Diet and general cognitive ability in the UK Biobank dataset[END_REF][START_REF] Lyall | Cognitive Test Scores in UK Biobank: Data Reduction in 480,416 Participants and Longitudinal Stability in 20,346 Participants[END_REF][START_REF] Navrady | Intelligence and neuroticism in relation to depression and psychological distress: Evidence from two large population cohorts[END_REF][START_REF] De La Fuente | A general dimension of genetic sharing across diverse cognitive traits inferred from[END_REF]. Furthermore, most studies used test scores that were neither adjusted for age nor standardized relative to a representative sample of the general population, despite the acknowledged lack of representativeness of the UK Biobank sample (Fry et al., 2017). As the UK Biobank continues to accrue data and attract new researchers, access to a standardized general factor of intelligence for most UK Biobank participants will benefit future studies that consider intelligence as a variable of interest or as a confounder.

Intelligence is moderate to highly heritable (Davies et al., 2018;Polderman et al., 2015) and individual differences in intelligence are associated with a variety of brain measures (Basten et al., 2015;Deary et al., 2010;Jung & Haier, 2007). Because intelligence is highly polygenic, a person's genetic liability to being more intelligent can be quantified with a polygenic score (PGS). PGSs are calculated using a person's genotype profile and the association between each SNP and a trait quantified by Genome-Wide Association Studies (GWASs). PGS of intelligence is thought to predict 4-10.6% of the variance in intelligence (Davies et al., 2018;Hill et al., 2019;Lee et al., 2018). However, few studies examined the extent to which cerebral measures mediate the effects that intelligence PGS or the environment has on intelligence (Lett et al., 2020;Loughnan et al., 2021) because such analyses require rich datasets and Genome-Wide Association Study (GWAS) results that exclude the target sample.

Since the UK Biobank is consistently included in GWASs of intelligence, researchers are unable to examine the associations between intelligence PGSs and neuroanatomical, environmental, and behavioral data in the UK Biobank.

Therefore, our first aim was to create a standardized general intelligence (g factor) score

for each UK Biobank participant with at least one cognitive test that is relative to the UK population given the participant's age, sex, and occupation. Our second aim was to create a general intelligence polygenic score (g PGS) for individuals with neuroimaging data in the UK Biobank, to be used by future studies aiming to link genes, brain, and intelligence.

We first standardized 8 cognitive test scores relative to the UK population and then extracted a g factor score with CFA from the cognitive tests for individuals that at least completed one cognitive test. We estimated the quality of the g factor scores of participants with missing data. We then conducted a genome-wide association study (GWAS) of the g factor score on the UK Biobank participants with a g factor of good quality and without neuroimaging data (N = 187,288), and we assessed its predictive validity in the participants with neuroimaging data (N = 39,131). We assessed the external validity of our g factor by examining the correlation between our g factor and life outcomes.

This study provides cognitive measures that are partially adjusted for sampling bias in the UK Biobank and a PGS for future UK Biobank studies interested in examining the genetic associations of intelligence with neuroimaging, behavioral, and environmental measures.

Methods

All analyses were performed in R (R Core Team, 2022). Supplemental Information, supplemental data, and code are anonymously available on the Open Science Framework (OSF): https://osf.io/49scv/?view_only=29e0ee6a1420461d81d234d94d549751 .

The standardization of cognitive test and g factor scores relative to the UK population are summarized in Figure 1. Boxes represent produced norms and models. Arrows represent computations.

UK Biobank dataset and participants

The The UK Biobank participants differ from the general UK population: they tend to be healthier and to have a higher socioeconomic status (e.g., more likely to own property; Fry et al., 2017;Keyes & Westreich, 2019), women are overrepresented and the distribution across ages differs from the general population (ages 50-59 in 2001 overrepresented, while 30-39 are underrepresented). Therefore, we used public Census data to compensate for differences between UK Biobank participants and the UK population.

Census data

The UK 2001 census data (Office for National Statistics, 2011) was obtained from Casweb (casweb.mimas.ac.uk). We selected tables ST033 and ST034, which provide occupation categories for people currently in employment (ST033) and unemployed or economically inactive (ST034), between 16 and 74 (ST033) or 64 (ST034) years of age by sex.

We adjusted for sampling bias using the Occupational Classification in the 2001 census because occupation is correlated with intelligence (Schmidt & Hunter, 2004), the data was publicly available by age, sex, and country, and job codes were similar to the UK Biobank (Standard Occupational Classification 2000 -SOC2000; Office for National Statistics, 2000).

We did not use the 2011 census because occupation was coded using SOC2010, which differs notably from SOC2000, with no easy correspondence. We matched participants to census characteristics using their age, country, and occupation on the day the census was conducted (April 29, 2001; Supplemental Section 1.1). We did not use the level of qualification because it was not publicly available by age, country, and sex in the 2001 or 2011 UK Census. We examined the distribution of standardized and age-adjusted test scores with cNorm (Section 2.3.4.) at the center (Figure S1) and online (Figure S2) across job codes. We used 8 cognitive tests to create the g factor (bolded tests in Table 1). Some participants completed some tests several times. We only considered the first occurrence of each test to best reflect the stable part of general intelligence, before aging and cognitive decline. To obtain a raw score for each test, we had to select between variables when several measures were provided for a test and/or transform these measures. We excluded participants with abnormal results (e.g., too many errors in the Symbol digit substitution test, indicating noncompliance with the test instructions) or who did not finish the test. Retained measures, transformations, and exclusion criteria are described in Table 2. 2) to provide a test score relative to the UK population (Figure 1). We created a common norming model for males and females. We simultaneously performed two adjustments:

1. An age adjustment by using the semiparametric continuous norming method was proposed by Lenhard and colleagues (2016). With this method, raw scores are modeled as a function of both standard scores and an explanatory variable, age when taking the test in this case.

2. A socio-demographic adjustment: by using standardization samples and computing weights to apply to participants, to compensate for the socio-demographic differences between the UK Biobank population and the complete UK population.

To do so, we first created standardization samples for each test and location (online/center), with about 32,000 to 497,000 participants. Details regarding the standardization sample creation and the number of participants in each sample are in Supplemental Section 1.2.

We then used cell weighting to adjust measures from the standardization samples to reflect the UK population characteristics: For each standardization sample, we computed the proportion of participants for each possible combination of country, sex, age range at census, occupation status, and occupation SOC group. We compared the proportion of UK Biobank participants in each cell to the 2001 census and created weights for each cell by dividing the census proportion by the UK Biobank proportion. See Supplemental section 1.3. for details and an example. We used the cNorm package [START_REF] Lenhard | CNORM -Generating Continuous Test Norms[END_REF] to compute norming models on the standardization samples with census weights, using the semiparametric continuous norming method. We modeled raw scores as a function of standard scores (percentiles) and age at test completion. Age at test completion is provided in field 21003 for tests taken at the assessment center and in fields 20134 to 20138 for tests taken online. This age differs from the age used to compute census weighting factors, which is the participant's age on the day of the 2001 census.

We applied the norming models to the whole dataset and obtained standardized test scores for all participants on the tests they took (Figure 1).

G factor

We created a g factor score for all participants who completed at least one of the eight cognitive tests using confirmatory factor analysis (CFA). The g factor was standardized relative to the UK population. We also evaluated the impact of missing test scores on the quality of the g factor.

CFA Parameters

We performed a CFA with one-factor loading on the eight cognitive tests. We estimated the CFA model with the lavaan R package (Rosseel, 2012). We used the full information maximum likelihood (FIML) estimator to make use of all data points even for cases with missing values, estimated the mean structure, and set the variance of the latent variable to 1 to estimate each observed variable loading. Model fit was assessed using commonly used model fit indices: the Tucker Lewis Index (TLI), the Comparative Fit Index (CFI), Standardized Root Mean Square Residual (SRMR), and the Root Mean Square Error of Approximation (RMSEA).

Good fit was established with a CFI and TLI > 0.95, a RMSEA < 0.06 and a SRMR < 0.08 (Hu & Bentler, 1999). See Supplemental Section 1.4. for a discussion on the choice of factor analysis.

G Factor Score Standardization

We created a standardization sample with 496,990 participants who had data for the census variables: sex, age on census day, and occupation on census day (countries were merged, see Supplement Section 1.3), to compute census weighting factors for these participants (Figure 1). We computed factor scores using the regression estimation method, which maximizes validity (DiStefano et al., 2009). We then computed the weighted mean and weighted standard deviation of these scores, using the census weighting factors. We subtracted the weighted sample mean from the raw factor scores and divided the result by the weighted sample standard deviation, to obtain factor scores with a general population mean of 0 and a standard deviation of 1.

Evaluation of the g Factor Score Quality in the Presence of Missing Data

We examined how well a g factor score computed using a subset of tests (called partial factor score) correlates with the factor score that would have been obtained from the full set of eight tests (called full factor score) by looking at the correlation between the full and the partial factor scores for each the 80 subsets of tests present in the data, in the 30,471 participants who completed all the tests.

Analyses

In the following analyses, we included participants whose combination of cognitive tests allowed for a correlation with the complete g factor of 0.70 or higher (N = 261,701). This threshold was chosen to maximize the robustness of the factor as well as the number of participants for which we would generate a g factor.

Testing Validity: Correlations with Alternative estimates of g and Life outcomes

To examine the external validity of our g measure by examining correlations in complete cases between our g factor and FI, life and health outcomes expected to correlate with intelligence (e.g., educational attainment, income, deprivation indices, etc., life and health outcomes described in Supplemental Data S8). In brief, we selected well-being, household income before taxes, highest qualification as well as the Townsend deprivation score -a deprivation score of an individual's postal code from the census data -and the index of multiple deprivations that regroups several deprivation indices which vary by country. The latter include subindices such as health, income, education, employment, and housing. The index of multiple deprivations and its subindices come from a UK government qualitative study of deprived areas in British local councils and are calculated separately for England, Wales, and Scotland.

Common multiple deprivation scores across countries were combined into a single variable for the correlation matrix (Supplemental Data S8). We adjusted each measure for sex and age at which the measure was reported.

Genetic Analyses

We conducted genetic analyses to create polygenic scores (PGS) for individuals with neuroimaging data for future UK Biobank studies. A detailed overview of the genetic analyses is available in Supplemental Section 1.6.

Main Analyses

In brief, we conducted a g factor GWAS on 187,288 individuals without neuroimaging data or twins/siblings with neuroimaging data (No Neuroimaging GWAS). We removed participants with neuroimaging data and their siblings to maintain the independence of predictions and prevent overfitting. We controlled for sex, center, chip, birth year, and the first 40 principal components (PCs) of the genotyped data. All GWASs were conducted on 5,319,661 variants with a linear mixed model-based association analysis using a sparse genetic relationship matrix to control for relatedness (fastGWA; [START_REF] Jiang | A resource-efficient tool for mixed model association analysis of large-scale data[END_REF] from the Genomewide Complex Trait Analysis (GCTA) package [START_REF] Yang | GCTA-GREML accounts for linkage disequilibrium when estimating genetic variance from genomewide SNPs[END_REF].

Using sBayesR (Lloyd-Jones et al., 2019), we created PGSs from the summary statistics of the No Neuroimaging GWAS for individuals with either neuroimaging data or siblings with neuroimaging data to assess the predictive power of genetic variance from the no Neuroimaging GWAS on the g factor (for details see Supplemental Section 1.6.5.1). After excluding individuals from non-British ancestry, first or second-degree cousins, and parentoffsprings, we adjusted the g factor PGS for sex, birth year, and the first 40 PCs and then examined its association with g.

Additional Analyses

We conducted additional analyses to answer the following questions.

Does the g factor PGS explain more variance in g than the Fluid Intelligence (FI)

PGS? Using the GWAS and PGS procedures described above, we ran a GWAS of FI on 180,722 individuals without neuroimaging data or twins/siblings with neuroimaging data (FI GWAS) and calculated FI PGS for individuals with neuroimaging data with the GWAS and PGS parameters described above. After excluding individuals from non-British ancestry, first or second-degree cousins, and parent-offsprings and adjusting the FI PGS for sex, birth year, and the first 40 PCs, we examined the percentage of variance explained in g and FI, separately.

Once you control for between-family factors, what proportion of variance in g does the g PGS predict?

To quantify to what extent the polygenic signal captures genetic effects that pass through the environment (indirect genetic effects or genetic nurture; Howe et al., 2021), we conducted family fixed-effects analyses. To do so, we first ran a g factor GWAS on the sample from the No Neuroimaging GWAS without siblings (No Family, No Neuroimaging GWAS). We used the summary statistics from this GWAS to create polygenic scores for individuals with siblings. After excluding individuals from non-British ancestry, first or second-degree cousins, we adjusted the PGS for sex, birth year, and the first 40 PCs. Finally, we ran the family fixed effects model with and without including sibship as a random effect and reported the change in explained variance of the PGS on the g factor when adjusting or not for sibling pairs (for details see Supplemental Section 1.6.5.2).

Do our g factor and FI measures have similar genetic correlations and heritabilities as the Cognitive Performance and Educational Attainment (EA) measures from Lee and colleagues (2018)?

We examined whether the genetic influences underlying our g factor and FI measure were similar to the genetic influences underlying the EA (i.e., years of education, or achieved educational level) and Cognitive Performance (i.e., measured as FI in the UK Biobank and with a g factor in the COGENT and CHARGE consortiums) reported by Lee and colleagues (2018). We compared our findings to the Lee and colleagues (2018) results because this is the largest genetic study of cognition to date and results are publicly available. To do so, we calculated the genetic correlations between our g-factor GWAS summary statistics, our FI GWAS summary statistics, and the publicly available Educational Attainment (EA) and g factor summary statistics. We additionally calculated the heritability estimates of each summary statistics file to examine whether our g factor was more heritable than our FI measure, previous g factor measures, and EA. These analyses were conducted with linkage disequilibrium score regression using the ldsc function from the GSEM package (Grotzinger et al., 2019). We conducted additional correlational analyses on a subset of participants that had neuroimaging data and PGSs. We examined correlations on complete cases between our g factor and alternative measures of intelligence for the UK Biobank (FI alone, g factor with 4 tests…), life and health outcomes expected to correlate with intelligence (e.g., educational attainment, income, deprivation indices, etc., life and health outcomes in Supplemental Data S8 on OSF), Total Brain Volume (TBV; Williams et al., 2021), and the FI and g factor PGS in individuals with neuroimaging data.

We compared our g factor score to alternate measures of intelligence by transforming the cognitive variables and extracting the g factor as done by Cox and colleagues (2019) and de Nooij and colleagues (2020), which used a different combination of cognitive tests and factoring methods with a similar sample to the one we used to calculate PGSs. The authors used cognitive tests completed at the center during the neuroimaging visit (Instance 2) and included tests that were not initially available at the first center visit. Cox and colleagues (2019) created a latent factor using CFA from the MAT, the SDS, the FI, and the TMTB cognitive tests, and de Nooij and colleagues (2020) extracted the first principal component of the numerical memory, the FI, the SDS, the TMTB, the MAT, and the TWR cognitive tests.

Since our g factor is adjusted for age, we created alternative g factors that are adjusted for age in the CFA or after extracting the first PC. We additionally similarly controlled for sex to examine whether differences between our g factor and the g alternatives could be explained by sex differences.

Results

Cognitive Tests

We compared the distribution of the standard test scores before and after adjusting for the difference between the UK Biobank population and the general UK population (Figure 2).

After adjusting for age and census weights, the distribution of the scores shifted to the right, indicating a relatively higher score in the UK Biobank relative to the UK norm (Supplemental Section 2.1.1). In some cases, the distribution was not normal because of its categorical nature (e.g., MEMN) or because of threshold effects (e.g., MEMS). Correlations between standard scores ranged from 0.07 (MEMN and RT) to 0.50 (TMT and SDS). TMT and FI had the highest correlation coefficients with other cognitive tests (Figure S3; Supplemental Section 2.1.2).

Distribution of the g factor before and after census correction

We compared the distribution of the g factor scores before (M = -0.004, SD = 0.993) and after (M = 0.086, SD = 1.001) adjusting for the difference between the UK Biobank population and the general UK population (d = 0.09). After adjusting, the factor score distribution shifted to the right, indicating a relatively higher score in the UK Biobank relative to the UK norm (Figure 4; g distribution by job category in Supplemental Section 2.1.5).

G Factor Quality

The quality of the g factor and the number of individuals for each possible combination of completed tests are available in Supplemental Section 2.1.6. For example, if we select participants with any of the first 73 cognitive test combinations observed in the UK Biobank, the worst factor scores of these participants would have a correlation of 0.70 with the ideal, 8tests factor scores, and the number of available participants will be over 261,701. We examined the external validity of our g measure by examining the association in complete cases between our g factor measure, FI (which is often used as a proxy of g in most studies), and life outcomes collected at the first center visit or online to estimate correlation coefficients on a larger number of participants (Figure 5).

Figure 5. Correlation between age and sex-adjusted g factor Scores and Health and Life

Outcomes. Pearson correlation coefficients were estimated on 181,327 individuals without missing data. All measures are adjusted for age at which the measure was taken and sex. G corresponds to the g factor of individuals with a combination of cognitive tests that allowed for a correlation of 0.70 or higher between their actual g factor and what their g factor would have been if they had completed all tests. FI: Fluid Intelligence.

Genetic Analyses

Main Results

We identified 100 approximately independent SNPs attaining genome-wide significance in the No Neuroimaging Sample GWAS (h2 = 0.197, SE = 0.008). There were 84 genomic risk loci with the g factor in the No Neuroimaging GWAS (P < 5×10 -8 ; Table S8; Supplemental Data S1-S2 on OSF). See Figure S5 for the Manhattan and QQ-plots.

We created g factor PGS for 38,866 individuals and a FI PGS for 38,642 individuals who either had neuroimaging data or siblings with neuroimaging data and g factor quality greater than r >= 0.70. Of the 39,866 individuals with neuroimaging data, 23,689 had a g factor quality of r = 1 (Table S9).

After excluding individuals from non-British ancestry and first or second-degree cousins and parent-offspring, we adjusted the g and FI values for sex, year of birth, and the first 40 genetic PCs. The g factor PGS created from the No Neuroimaging GWAS explained 7.6% of the variance in the g factor of 26,082 individuals with neuroimaging data and 1,092 twins or siblings without neuroimaging data (N = 27,174). The FI created from the No Neuroimaging GWAS explained 6.6% of the variance in FI of individuals with either neuroimaging data or siblings with neuroimaging data (N = 26,360; Supplemental Section 2.2.5).

Additional Analyses

Does the g factor PGS explain more variance in g than the FI PGS?

The g factor PGS created from the No Neuroimaging GWAS explained 1.6% more variance in g than the FI PGS created from the No Neuroimaging GWAS, which explained 6.0% of the variance in the g factor (N=26,360). The g factor PGS created from the No Neuroimaging GWAS explained 5.8% of the variance in FI (N=26,360).

Once you control for between-family factors, what proportion of variance in g does the g PGS predict?

After excluding individuals from non-British ancestry and first or second-degree cousins and correcting for sex, year of birth, and the first 40 genetic PCs, the family fixed-effect analysis on the g factor PGS from the No Family GWAS summary statistics showed a decrease in explained variance 7.5% from to 4.2% and a reduction of 10% in the effect size (N = 14,601). See Supplemental Section 2.2.4. for additional PGS analyses.

Do our g factor and FI measures have similar genetic correlations and heritabilities as the g factor and Educational Attainment (EA) measures from Lee and colleagues (2018)?

The SNP heritability of the present g factor was similar to the heritability of Lee's g factor (h2 = 0.199, SE = 0.008) and greater than Lee's EA (h2 = 0.151, SE = 0.004; Table 3 andS11). Lee's g factor was highly correlated to our various estimates of the g factor 0.92-0.93, suggesting that they capture common genetic influences (Figure S10).

Measures

We conducted separate correlation analyses on our g factor with the alternative g factors, neuroimaging, and PGSs because these data were only available for participants who visited the center for the neuroimaging visit.

The alternative g factors were created from cognitive test scores from their neuroimaging visit and cognitive tests that were only available at the second visit. The correlation between our study's g factor (adjusted for age, not sex) and the cognitive tests ranged from 0.25 (RT) to 0.84 (TMT), whereas the age-adjusted g factors from previous studies ranged from about 0.16 (RT) to 0.71 (MAT; Figure S13).

Correlation coefficients between our study's g factor and alternative g factors were high (0.85 to 0.89; Figure S13). The alternative g factor measures were more correlated to the highest qualification achieved (r = 0.26-0.29 vs. r = 0.24) and income (r = 0.18-0.19 vs. r = 0.16) than the present g factor because the cognitive tests included in the alternative g factors were the cognitive tests with the highest correlations with highest qualification and income (Figure S15).

The g factor from the present study and the g factors calculated as done by previous studies were highly correlated after adjusting for the age of test completion and sex. The g factors positively correlated with the PGS, highest qualifications, income before tax, overall health, and total brain volume, and negatively with the deprivation indices (Figure 6). We also looked at the correlation coefficients of the g factors with well-being and additional deprivation indices, which reflect the degree of housing, employment, education, etc. deprivation in an area. However, these correlations were small and therefore reported in Figure S16.

Discussion

We aimed to create an age-standardized g factor measure that is relative to the UK population and provide a PGS for UK Biobank participants with neuroimaging data. Unlike previous studies on the g factor in the UK Biobank, we partially adjust for sampling bias on the g factor in the UK Biobank, we provide an estimation of the g factor's quality for each participant with missing data, and we perform a g factor GWAS excluding participants with neuroimaging data to allow future studies on the genetic, environmental, and neural correlates of intelligence in the UK Biobank. Our g factor was highly correlated with alternative g factor measures of intelligence in the UK Biobank and their correlations with life and health outcomes were similar. The g factor PGS of 26,082 UK Biobank individuals with neuroimaging data and 1,092 siblings without neuroimaging data explained 7.6% of the variance in the intelligence score.

The g factor from the present study and alternative g factor measures were similarly correlated to life outcomes, such as household income before tax or highest qualification (i.e., level of education) when adjusting for age and sex. The slightly higher correlations between the alternative g factor measures and the highest qualification achieved compared to our g factor could be explained by the tests used to create the alternative g factors, which correlated the most with the highest qualification. Therefore, some outcomes, such as the highest qualification, may not be as highly correlated to general intelligence as previously thought but may be more correlated with specific cognitive tests.

We report a negative correlation between our g factor and the Townsend Index, an SES measure that reflects a person's material deprivation based on unemployment rates, non-car ownership, non-homeownership, and household overcrowding in their postal code. This negative correlation coincides with the negative correlation between neighborhood deprivation and educational attainment [START_REF] Garner | Neighborhood Effects on Educational Attainment: A Multilevel Analysis[END_REF], as well as previous findings that childhood IQ remains stable across old age (Deary et al., 2000), predicts later SES outcomes [START_REF] Deary | Intergenerational social mobility and mid-life status attainment: Influences of childhood intelligence, childhood social factors, and education[END_REF]. We additionally found a negative correlation between our g factor and the index of multiple deprivation of the area where a person resides, which was largely explained by the negative correlation between the g factor and the education deprivation index of the area where a person resides. The education deprivation index was measured by a score reflecting child and adolescent school performance (e.g., English, math, and science exams Stage 3 exams) and adult skills (e.g., the proportion of adults with no or low qualifications) in a given geographical area.

The g PGS created from the No Neuroimaging GWAS summary statistics explained 7.7% of the variance in the g factor of individuals with neuroimaging data and siblings with neuroimaging data. The largest GWAS study of cognition to date (Lee et al., 2018) The FI PGS explained 1.6% less variance in g than the PGS of the g factor, suggesting that the g PGS is a better genetic predictor of g. The genetic correlations between FI and the g factor were high, suggesting that FI and g have very similar genetic influences. The g factor and FI PGSs also similarly correlated with total brain volume, the most correlated brain measure to intelligence (Deary et al., 2021). Taken together, our findings suggest that a common genetic component to FI and the g factor may explain the genetic association between intelligence and TBV. Although the FI PGS may be sufficient when investigating global brain size associations with intelligence, the g factor PGS still explains a larger range of variance in general intelligence than FI and its use should be favored when controlling for the genetic components of intelligence.

The present study has several limitations. First, the selection of cognitive tests currently available in the UK Biobank severely underrepresents verbal ability. Only 2 of the 8 cognitive tests included in this study were verbal: the FI test (verbal-numerical reasoning) and the numeric memory test (digit span). The UK Biobank is currently in the process of adding verbal tests to the cognitive assessment (e.g., picture vocabulary and word production), which would justify the calculation of a new g factor once they are completed by a sufficient number of participants.

The underrepresentation of verbal skills may partly explain why women had a slightly lower g factor than men (d = -0.13). Another non-exclusive explanation may be that male and female UK populations are unequally sampled in the UK Biobank, with women representing 54.4% of the entire sample. Thus, women with lower general intelligence may have been oversampled compared to men with lower intelligence. Finally, participants were born between 1934 and 1971 (median: 1950), a period when women in the UK may have had inferior educational opportunities, preventing them from reaching their intellectual potential. The UK Biobank may thus not be suitable to reliably estimate sex differences in cognitive abilities and other phenotypes associated with cognitive ability.

Second, although the loadings of the present study correspond to those previously reported by UK Biobank studies (Cox et al., 2019;[START_REF] De La Fuente | A general dimension of genetic sharing across diverse cognitive traits inferred from[END_REF], the highest loadings on the g factor in the UK Biobank differ from those reported across studies using psychometric tests to measure intelligence. Specifically, the Raven's Progressive Matrices test is expected to have the highest loading on g across psychometric tests around 0.7 [START_REF] Gignac | Raven's is not a pure measure of general intelligence: Implications for g factor theory and the brief measurement of g[END_REF][START_REF] Gignac | Bifactor Modeling and the Estimation of Model-Based Reliability in the WAIS-IV[END_REF]. And yet, we and other UK Biobank studies report the highest loading for trail-making and FI (Cox et al., 2019;[START_REF] De La Fuente | A general dimension of genetic sharing across diverse cognitive traits inferred from[END_REF] and a loading of around 0.5 for the matrices. One study examined the concurrent validity of each UK Biobank cognitive test by reporting the correlation between each UK biobank cognitive test and one to several well-validated standard cognitive tests of the same cognitive domain (reference tests).

The authors found that the UK Biobank TMT B strongly correlated at 0.66 with the reference TMT B test and that the UK Biobank Matrices correlated at 0.57 with the reference matrices test. Overall, they concluded that the UK Biobank tests load strongly on general cognitive ability. They additionally measured test-retest reliability after a mean of 28 days and report that the test-retest reliability was greater than 0.5 but that the mean performance on some tests, such as FI increased at Time 2. Considering that we took the first instance of test completion, our g factor should not be prone to repeat testing effects (Fawns-Ritchie & Deary, 2020).

We were limited when correcting for the socio-demographic imbalance in the UK Biobank. Due to occupation coding constraints, we had to use the 2001 census data, instead of the 2011 census data, and we only determined the occupation on census day of 71.5% of participants. Moreover, we were limited by the number of variables on which we adjusted the UK Biobank sample as we did not have access to the qualification data by age, sex, and country.

Although further variables should be adjusted to provide a g factor that is perfectly relative to the UK population, we nonetheless provide cognitive test scores and a g factor measure that are age-standardized and, to some extent, adjusted for sampling bias in the UK Biobank.

Finally, the g factor score was calculated from different subsets of tests and although we took the first instance of a test, some tests were taken at different ages. Therefore, although we attempted to provide a g factor measure of pre-aging adult intelligence, some test scores may already be influenced by cognitive decline. However, one study examining test-retest reliability over a period of 4 years, which may reflect cognitive decline, reported that most UK Biobank cognitive tests show reasonable stability except for the visual memory task (pairs-matching; [START_REF] Lyall | Cognitive Test Scores in UK Biobank: Data Reduction in 480,416 Participants and Longitudinal Stability in 20,346 Participants[END_REF] and another study found declines in cognitive abilities before 65 years of age were small [START_REF] Cornelis | Age and cognitive decline in the UK Biobank[END_REF]. Therefore, considering that the majority of participants were 64 years or younger and that the median age was 60, our g factor measure likely reflects pre-cognitive-decline intelligence scores.

The present study provides cognitive test scores and a g factor score for UK Biobank participants that are adjusted for age and partially adjusted for sampling bias as well as a g PGS for UK Biobank individuals with neuroimaging data that explained 7.6% of the variance in the g factor. The behavioral and genetic scores from this study will enable the simultaneous investigation of the associations between the brain, genes, and intelligence, which are currently rare in the present literature (Deary et al., 2021). Taken together, the present study offers robust measures of intelligence that will foster homogeneity in intelligence research within the UK

Prevalence between High and Average G-factor Groups

Although the aims of this paper are not directly in line with the aim of the dissertation, we created mental health disorder diagnoses in this paper that were then used to create general measures of psychopathology in paper 5 and we make use of the g-factor created in paper 3. 1) -is associated with greater physical health and longevity (2).

And yet, some researchers report that highly intelligent individuals are at a higher risk of developing mental health and somatic disorders (3). The majority of studies that report a negative effect of intelligence on mental and somatic health, however, often suffer from sampling bias, the lack of a control group, or insufficient sample size (4,[START_REF] Martin | Mental Disorders Among Gifted and Nongifted Youth: A Selected Review of the Epidemiologic Literature[END_REF]. The present paper addresses these caveats by examining the difference in the prevalence of health and somatic disorders and other traits between the highly intelligent (2 SD above mean) and averagely intelligent (within 2 SD of the mean) individuals of the UK Biobank (N ≃ 261,500).

The notion of general intelligence (g) stems from the positive correlation in performance across most cognitive tests (6). It is formally defined as the common source of variance underlying performance across a wide range of tests and is usually computed using factor analysis. Intelligence Quotient (IQ) reflects a person's average performance across cognitive tests relative to a representative sample of the same-age national population.

Henceforth, IQ and g will be used interchangeably and as shortcuts for general intelligence scores.

Over the last decades, intelligence has proved to be a strong predictor of education [START_REF] Deary | Intelligence and educational achievement[END_REF], socio-economic success [START_REF] Strenze | Intelligence and socioeconomic success: A meta-analytic review of longitudinal research[END_REF], and health outcomes [START_REF] Wraw | Intelligence in youth and health behaviours in middle age[END_REF]. For instance, having a childhood IQ one standard deviation (SD) above the mean decreases one's risk of accidents and developing heart, respiratory, and digestive disease by 20-25% [START_REF] Wraw | Intelligence in youth and health behaviours in middle age[END_REF][START_REF] Wrulich | Forty years on: childhood intelligence predicts health in middle adulthood[END_REF]. And yet, whether intelligence also serves as a protective factor for mental health disorders is still subject to debate. While some postulate that high intelligence serves as a protective factor for several mental and somatic disorders (11,[START_REF] Ghaffari | IQ Score of Children with Persistent or Perennial Allergic Rhinitis: A Comparison with Healthy Children[END_REF], others suggest that high intelligence is a risk factor for these phenotypes (3,[START_REF] Smith | Childhood IQ and risk of bipolar disorder in adulthood: prospective birth cohort study[END_REF].

The most recent study examining the prevalence of mental health and somatic (i.e., allergies, asthma, immunodeficiencies) disorders in highly intelligent individuals reported that high IQ was a risk factor for affective disorders, neurodevelopmental disorders, and diseases related to the immune system(3). However, the study suffers from sampling bias because participants were recruited from the American Mensa Ltd.

-a society open to individuals that at some point scored in the top 2% on a verified intelligence test (N = 3,715). Since IQ tests are typically administered to children when parents or teachers notice behavioral problems or by individuals experiencing stereotypical characteristics associated with IQ, selecting individuals from a sample of individuals who actively decided to take an IQ test or become members of a highly intelligent society may exacerbate the correlation between having a high IQ and mental health disorders and/or behavioral problems (4,[START_REF] Martin | Mental Disorders Among Gifted and Nongifted Youth: A Selected Review of the Epidemiologic Literature[END_REF]. The present paper thus aims to address these limitations.

We investigated the difference in prevalence between individuals with high (2 SD above the population mean) and average (within 2 SD from the population mean) general intelligence scores (g-factor scores( 14)) in the UK Biobank across mental health disorders, somatic disorders, and certain traits. We examined group differences in the prevalence of available mental health and somatic disorders in the UK Biobank, as well as phenotypes that are thought to differ in prevalence in highly intelligent individuals, such as subjective wellbeing phenotypes (e.g., well-being, social isolation [START_REF] Li | Country roads, take me home… to my friends: How intelligence, population density, and friendship affect modern happiness[END_REF][START_REF] Zettergren | Adolescents With High IQ and Their Adjustment in Adolescence and Midlife[END_REF]), myopia [START_REF] Czepita | Are children with myopia more intelligent? A literature review[END_REF], chronotype [START_REF] Ujma | The relationship between chronotype and intelligence: the importance of work timing[END_REF], and trauma [START_REF] Mcguire | The Role of Trauma Type and Age in the Relation Between Trauma Exposure and Intelligence[END_REF]. Finally, we included sexual behaviors because studies have shown heterogeneous results concerning the relation between sexual behaviors and IQ [START_REF] Rahman | Gender nonconformity, intelligence, and sexual orientation[END_REF]21). As a point of comparison, we report differences in prevalence across phenotypes between the average and low (2 SD under the population mean) g-factor groups in the exploratory analyses.

Methods

The preregistration, code, and supplemental tables and files are available here: https://osf.io/cywd6/?view_only=fa9f5091de124d96be3eb1a55a4e7f01. We estimated the quality of the g-factor based on the combination of completed tests, and we selected participants who had a sufficiently reliable estimate of g (correlation with full g factor > 0.7; N= 261,701 participants; details in Section S1.1). Participants were excluded when there was a mismatch between the self-reported (field 31) and genetic sex (field 22001).

Self-reported sex was coded -0.5 for males and 0.5 for females.

G-factor Groups

We created 3 g-factor groups: a high g-factor group (g-factor 2 SD above the population mean), a low g-factor group (g-factor 2 SD below the population mean), and an average gfactor group (g-factor within 2 SD from the population mean). About 90% of individuals were in the average g-factor group (236,273/261,701), 6.2% in the high g-factor group As the age of onset of disorders was not available for all participants and/or measures, we took into account the maximum age at which an individual provided the most recent measure of a disorder to approximate lifetime prevalence (Section S1.4).

Statistical Analyses

To reduce the number of statistical tests performed when examining group differences in each phenotype, we first examined age and sex effects and interactions on each phenotype (Section S1.5.1). If age and sex's main effects or interactions did not significantly predict a phenotype (p > 0.05), they were excluded from the g-factor group analyses. Equation 1corresponds to the model with all possible predictors.

To be included in the group comparison of a phenotype, participants had to have a g factor measure. They had to have answered all of the questions used to create that phenotype, except when the same question was asked several times (Section S1.5.2).

We used logistic regression for binary phenotypes, multinomial regressions for ordinal phenotypes, and linear regressions for continuous phenotypes. Age was mean-centered in ordinal and binary regressions, while age and continuous phenotypes were men-centered and divided by 1sd in linear regressions to report standardized betas. 2). Since the analyses on the low g-factor group were exploratory, we applied the same multiple comparison correction as for the high g-factor group (e.g., 0.05/ (6*32) for equation 2).

Results

Differences in the Prevalence of Phenotypes between Participants with High and

Average CA Sex and age effects across phenotypes are described in Supplemental Section 2.1. and in Supplemental Tables S3. The prevalence of each disorder by g-factor group is available in Supplemental Tables S4 and regression results are reported in Supplemental Tables S5. supplemental tables standard error (SE) for p-value thresholds for multiple comparison corrections. High g-factor: participants with a g-factor score 2SD above the mean. Low gfactor: participants with a g-factor score 2SD under the mean. Average g-factor: participants with a g-factor score between + or -2SD from the mean. Compared to individuals in the average g-factor group, the odds of having some type of allergy increased by 13% for individuals in the high g-factor group (OR=1.13). This was explained by their greater propensity to having eczema and other allergies (e.g., food; respectively 1.25 and 1.33 times more likely), which were included in the general allergy diagnosis (Table 2). The odds of being myopic increased by 93% in the high g-factor group (OR = 1.93) and this remained significant when controlling for educational attainment (OR = 1.75; Supplemental Section 2.2).

Trauma

Compared to individuals in the average g-factor group, the odds of experiencing catastrophic trauma, adulthood stressors, childhood abuse, and childhood stressors decreased by 10% (OR=0.90), 31% (OR = 0.69), 38% (OR = 0.62), and 24% (OR = 0.76; Table 2) in the high g-factor group, respectively.

Traits

Compared to individuals in the average g-factor group, the odds of feeling more socially isolated decreased by 15% in the high g-factor group (OR=0.85), whereas the odds of having an evening-like chronotype, ever engaging in same-sex behavior, and ever using cannabis increased by 15% (OR = 1.15), 23% (OR = 1.23), and 25% (OR=1.25) respectively in the high g-factor group. Fig S4 shows that there are more individuals with a higher-than-average gfactor that have used cannabis 1 to 100 times and that over 100 times there are no group differences. The high g-factor group had a lower neuroticism score than individuals in the average g-factor group (β = -0.12; Table 2).

3.2. Phenotypes with group differences between both the high and average and the low and average g-factor groups

Childhood stressors, childhood abuse, adulthood stressors, PTSD, and social isolation were more prevalent in the low g-factor group compared to the average g-factor group (Table S2) and were more prevalent in the average g-factor group compared to the high g-factor group (Table 2), suggesting that the prevalence of these phenotypes decreases with an increasing gfactor. The low g-factor group had a higher neuroticism score than the average g-factor group, which had a higher neuroticism score than the high g-factor group. The odds of ever trying cannabis and having an evening-like chronotype respectively decreased by 41% (OR = 0.59) and 14% (OR = 0.86) in the low g-factor group compared to the average g-factor group.

Discussion

We examined differences in the prevalence of mental health disorders, somatic and certain traits between individuals with high (2 SD above mean) and average g-factor scores (within 2 SD of the mean) in the UK Biobank (N ≃ 7,266 -252,249). We contrasted these results with differences observed between individuals with low and average g-factor scores.

We found that the high g-factor group did not have more mental health disorders than the average g-factor group in general and that they were less likely to have general anxiety and PTSD. Individuals with higher intelligence were also less likely to have experienced trauma and stressors, except for adulthood abuse, which may be part of the explanation for the previous finding. The high g-factor group was also less neurotic and felt less socially isolated. In contrast, the low g-factor group was more neurotic, felt more socially isolated, and had a greater prevalence of trauma, stressors, and PTSD than the average g-factor group, suggesting that the prevalence of these phenotypes decreases with increasing intelligence. Among the few somatic disorders that were examined, we found that individuals with high intelligence were more myopic and had more allergies, although they had a lower prevalence of hay fever rhinitis, and asthma. Individuals with high intelligence were also more likely to present certain traits, such as having an afternoon-evening chronotype, ever tried cannabis, and ever engaged in same-sex behavior, whereas the low g-factor group was less likely to have ever tried cannabis and engaged in same-sex behavior than the average g-factor group. There were no differences between groups in the prevalence of insomnia.

The result of the present study contradicts several studies that reported an increased risk for various psychiatric disorders in individuals with high intelligence (3,[START_REF] Smith | Childhood IQ and risk of bipolar disorder in adulthood: prospective birth cohort study[END_REF]. As noted in the introduction, these studies were generally based on small samples and suffered from major sampling bias or a lack of a control group (4,[START_REF] Martin | Mental Disorders Among Gifted and Nongifted Youth: A Selected Review of the Epidemiologic Literature[END_REF]. Our results suggest that high intelligence is not a risk factor for psychiatric disorders and even a protective factor for general anxiety. We find that increasing intelligence is associated with a decrease in trauma exposure, and consequently PTSD. This is consistent with previous findings [START_REF] Mcguire | The Role of Trauma Type and Age in the Relation Between Trauma Exposure and Intelligence[END_REF] and with the association of childhood trauma with lower intelligence [START_REF] Enlow | Interpersonal trauma exposure and cognitive development in children to age 8 years: a longitudinal study[END_REF].

With regards to somatic disorders, we replicate the increased risk of allergies in individuals with high intelligence(3). One possible explanation for this association is that allergies and intelligence share neural correlates [START_REF] Takeuchi | Allergic tendencies are associated with larger gray matter volumes[END_REF]. Another possibility is that more intelligent individuals with a higher g-factor live in more urban areas [START_REF] Jokela | Flow of cognitive capital across rural and urban United States[END_REF], where allergies are more prevalent [START_REF] Schröder | The rural-urban enigma of allergy: What can we learn from studies around the world?[END_REF], or that individuals with high intelligence are more aware of allergic symptoms and have better access to health care. However, the prevalence between groups did not differ across all allergies (e.g., Asthma, Hay Fever Rhinitis).

In line with a previous literature review [START_REF] Czepita | Are children with myopia more intelligent? A literature review[END_REF], the risk of myopia was greater for individuals with high intelligence. While near-work activities (e.g., reading and computer use) seem to be a risk factor for myopia, this association appears to be distinct from that of higher intelligence and education level [START_REF] Mutti | Parental Myopia, Near Work, School Achievement, and Children's Refractive Error[END_REF]. Although additional years of education contribute to an increase in the risk of developing myopia [START_REF] Mountjoy | Education and myopia: assessing the direction of causality by mendelian randomisation[END_REF], most of the evidence points toward shared genetic factors between intelligence and myopia [START_REF] Williams | Phenotypic and genotypic correlation between myopia and intelligence[END_REF], which is consistent with our observation that the risk of myopia associated with a high g-factor only slightly decreased when adjusting for educational attainment.

Our results indicate more afternoon-evening chronotypes in individuals with high intelligence than in individuals with average intelligence, which could be explained by differences in the work schedules of the different g-factor groups [START_REF] Ujma | The relationship between chronotype and intelligence: the importance of work timing[END_REF]. In line with a previous study [START_REF] Rahman | Gender nonconformity, intelligence, and sexual orientation[END_REF], we find that individuals with high intelligence are more likely to ever have engaged in same-sex behavior. We note that this measure may not reflect sexual orientation, but sexual exploration. We also found an association between ever trying cannabis and intelligence, but this was only true when looking at individuals who consumed cannabis less than 101 times in their lifetime, not for more intensive consumption. Therefore, this measure may reflect a tendency to explore rather than a substance abuse disorder. One possibility is that individuals with higher intelligence, which is positively correlated with the "Openness to Experience" personality trait (r = 0.30 ( 30)), may be more likely to seek out new experiences and explore alternative behaviors than the average.

First, as most neurodevelopmental and some psychotic disorders were not available or had too few cases in the UK Biobank, our results do not allow us to conclude on these psychiatric disorders. Second, UK Biobank has a "healthy volunteer" selection bias [START_REF] Fry | Comparison of Sociodemographic and Health-Related Characteristics of UK Biobank Participants With Those of the General Population[END_REF].

Although the prevalence of psychiatric disorders and traits differ from the general population, this should not affect the validity of the group comparisons because the phenotypes were designed with the same criterion between high and average IQ groups. Finally, the prevalence of psychiatric disorders and traits between g-factor groups may differ across the lifespan.

However, here, we were interested in lifetime prevalence, which makes the UK Biobank, a prospective aging study, a good candidate for the question at hand.

High intelligence is not a risk factor for psychiatric disorders and is a protective factor for general anxiety and PTSD. Our results reinforce the idea that higher intelligence is an advantage. This does not imply that general intelligence is irrelevant for psychiatric evaluation: 1 indeed, it may affect the presentation of symptoms, and the available resources for recovery. 2Paper 5 (in prep.) -Creating Phenotypic and Genetic

Measures of General Psychopathology: Preliminary Mediation Analyses

The following section reflects on-going work. The following analyses are presented in a single paper and this is subject to change, as we plan to conduct additional analyses to examine:

(1) the biological utility of the psychopathology factors (i.e., Are the SNPs associated with the P-factor operating through the p-factor? Do downstream bioinformatic analyses of the correlated factors models show robust and distinct biological signals with minimal overlap?), ( 2) the utility of each polygenic score (i.e., Does the P-factor PGS explain more variance in Internalizing Disorders than the Internalizing PGS? Does the P-factor PGS explain more variance than all of the subfactor PGSs combined?), and ( 3) the global and regional neuroanatomical measures that mediate genetic and environmental effects on general psychopathology. (Caspi et al., 2014;Caspi & Moffitt, 2018;[START_REF] Lahey | Using Confirmatory Factor Analysis to Measure Contemporaneous Activation of Defined Neuronal Networks in Functional Magnetic Resonance Imaging[END_REF][START_REF] Markon | Bifactor and Hierarchical Models: Specification, Inference, and Interpretation[END_REF]. In line with this finding, MHDs are influenced by shared genetic, neural, and environmental risk factors (for review Sprooten et al., 2021). And yet, there is little research simultaneously examining the respective contribution of these influences on psychopathology. The UK Biobank, which includes phenotypic, environmental, genetic, and neuroimaging data, is an ideal candidate for this research. However, polygenic scores (PGSs) for UK Biobank participants cannot be created from public MHDs summary statistics because they include the UK Biobank data. In light of our goal to examine the genetic, environmental, and neural correlates of psychopathology in the UK Biobank, we first examined the phenotypic and genetic structure of psychopathology in the UK Biobank and then created psychopathology PGSs for individuals with neuroimaging data before investigating whether global cerebral markers (e.g., Total Brain Volume, TBV) mediate genetic (PGSs) and environmental (childhood adversity) effects on psychopathology.

p-factor models are typically created using Structural Equation Modelling (SEM) to capture the common variance across MHDs (Caspi & Moffitt, 2018;[START_REF] Markon | Bifactor and Hierarchical Models: Specification, Inference, and Interpretation[END_REF], although some studies have used principal component analysis (Allegrini et al., 2020). Currently, the most popular SEM model of the p-factor is the bifactor model [START_REF] Gluschkoff | The General Psychopathology Factor: Structural Stability and Generalizability to Within-Individual Changes[END_REF]Harden et al., 2020;Lahey et al., 2021;McElroy et al., 2018), where all MHDs on load on one hand Another popular model is the Hierarchical Taxonomy of Psychopathology (HiTOP; [START_REF] Kotov | The Hierarchical Taxonomy of Psychopathology (HiTOP): A dimensional alternative to traditional nosologies[END_REF]. It is the most extensive hierarchical model of psychopathology (Caspi & Moffitt, 2018;[START_REF] Kotov | The Hierarchical Taxonomy of Psychopathology (HiTOP): A dimensional alternative to traditional nosologies[END_REF]Lahey, Applegate, et al., 2012;Lahey et al., 2021) and includes several levels with correlated factors mapped using the bass-ackward approach [START_REF] Goldberg | Doing it all Bass-Ackwards: The development of hierarchical factor structures from the top down[END_REF]; a common method in psychopathology and personality research [START_REF] Michelini | Delineating and validating higher-order dimensions of psychopathology in the Adolescent Brain Cognitive Development (ABCD) study[END_REF][START_REF] Wright | The hierarchical structure of DSM-5 pathological personality traits[END_REF]). In the HiTOP model, spectra factors (e.g., Internalizing) that load onto the p-factor are divided into subfactors (e.g., Distress), which are further separated into syndromes or disorders (e.g., Major Depression Disorder), and are then split into specific symptoms.

Some argue against the bifactor model, since model fit indices are biased in favor of the bifactor model (Greene et al., 2019;Morgan et al., 2015) and because models with different interpretations can be statistically equivalent to each other [START_REF] Van Bork | What is the p-factor of psychopathology? Some risks of general factor modeling[END_REF](van Bork et al., , 2019)). For instance, the bifactor model is hard to mathematically distinguish from the correlated factors model-a model without a p-factor but with correlated Externalizing, Internalizing, and Thought Disorders factors (Bonifay et al., 2017;Watts et al., 2019), even though their interpretations are drastically different. The bifactor p-factor is also highly correlated (r = 0.97) to the hierarchical p-factor (Conway et al., 2019). Therefore, although correlations across MHDs are consistently described in the literature with a general measure of psychopathology and Internalizing, Externalizing, and Thought Disorders factors, the underlying structure of psychopathology is subject to debate.

MHDs are heritable (Smoller et al., 2019) and individuals who have parents with s are more likely to develop any type of (McLaughlin et al., 2012). MHDs are genetically correlated, suggesting that similar genetic factors may in part explain the phenotypic overlap across MHDs. Several twin and genomic studies support the presence of a genetic psychopathology factor across ages (Allegrini et al., 2020;[START_REF] Selzam | A polygenic p factor for major psychiatric disorders[END_REF]. For instance, Grotzinger et al., (2019) found that the common genetic variance across MHDs could be captured by a single genetic psychopathology factor. Other researchers have since then examined more complex psychopathology models of genetic data (e.g., the bifactor model) and reported shared genetic influences across subsets of s (Grotzinger et al., 2022;Mallard et al., 2022).

Exposure to early life stressors is associated with an increased risk of developing several forms of psychopathology (for review [START_REF] Mclaughlin | Early life stress and psychopathology[END_REF]. For instance, a research review on the effects of childhood trauma on adulthood found that physical abuse, sexual abuse, and unspecified neglect were associated with mood disorders and anxiety disorders;

emotional abuse with personality disorders and schizophrenia; and physical neglect with personality disorders (Carr et al., 2013). Others report that physical abuse with onset in middle childhood and that sexual abuse with onset in middle childhood or adolescence were associated with all forms of psychopathology, and physical abuse onset at any time was uniquely linked with PTSD (Adams et al., 2018). Finally, the influence of trauma and stress exposure on psychopathology and other life outcomes is accompanied by a range of biological and brain changes in childhood and adulthood that can have lasting effects [START_REF] Smith | Early life stress and development: Potential mechanisms for adverse outcomes[END_REF].

Therefore, we not only aimed to (i) examine the phenotypic and genetic structure of psychopathology in the UK Biobank and (ii) provide polygenic scores of psychopathology factors for UK Biobank participants with neuroimaging data (N = 26,610), but also (iii) to examine the extent to which global cerebral measures mediate the effects of childhood adversity and the psychopathology PGSs on their respective psychopathology factors. Given the size and richness of the UK Biobank, the phenotypic and genetic measures of psychopathology will be used as an index of mental health by future studies, will help identify pleiotropic genetic effects on MHDs, and will further contribute to our understanding of the association between psychopathology and variations in brain structure.

Childhood Adversity

To confirm that childhood adversity was the most predictive early life factor available in the UK Biobank, we created a childhood adversity score from the childhood stressors and abuse questions on the online mental health questionnaire. We calculated a childhood adversity score by conducting a Principal Component Analysis (PCA) and extracting the first PC with the stats package (Supplemental Information 1.1; Figure 1). Childhood adversity score was

Phenotypic Analyses

Mental health Disorders

We report sex and age (linear and quadratic) effects and their interactions on each binary MHD with logistic regressions (p < 0.05/(5*10), with 5 corresponding to the number of coefficients of interest per disorder and 10 to the number of investigated disorders) in Supplemental Information 2.1 and Supplemental Table C. Sex was coded -0.5 for males and 0.5 for females. Since the age at diagnosis was generally not available, we calculated age as the maximum age at which an individual provided the most recent measure of a disorder to approximate lifetime prevalence.

Exploratory Factor Analyses (EFAs)

We excluded participants with neuroimaging data and their siblings yielding 465,858 participants (254,181 women) in the EFA and CFA analyses (Table 1). We randomly selected 50% of the sample as the training sample. In the training sample with and without missing data, we calculated the terachoric correlation matrix of our binary MHDs (mixedCor function), which we then used as input for the EFAs (fa function; mixedCor and fa functions form the psych package; [START_REF] Revelle | psych: Procedures for Psychological, Psychometric, and Personality Research[END_REF]. Since the indicators are categorical and some loadings are under 0.5, we used the difference in the Root Mean Square Error Approximation (ΔRMSEA) with a 0.015 cut-value to determine the number of factors to retain [START_REF] Finch | Using Fit Statistic Differences to Determine the Optimal Number of Factors to Retain in an Exploratory Factor Analysis[END_REF]. We first examined the ΔRMSEA across EFAs with 1-4 factors. We applied the most common factoring methods: principal axis factoring (PAF) and maximum likelihood (ML), although PAF is more appropriate for non-normal data than ML [START_REF] Fabrigar | Evaluating the use of exploratory factor analysis in psychological research[END_REF]. We applied oblimin (oblique), varimax, and bifactor (orthogonal) rotations and explored a hierarchical structure with an omega hierarchical estimation (McDonald, 2014).

Confirmatory Factor Analyses (CFAs)

We ran CFAs on the test sample (remaining 50% of the sample) with the cfa function from the lavaan package (Rosseel, 2012) on the test sample with and without missing data with the Diagonally Weighted Least Squares (DWLS) estimator and pairwise missing cases for missing data because our observed variables were binary (Figure 1). We Since the Tucker Lewis Index (TLI), the Comparative Fit Index (CFI), and RMSEA are overestimated with the DWLS estimator [START_REF] Savalei | Improving Fit Indices in Structural Equation Modeling with Categorical Data[END_REF][START_REF] Shi | The Effect of Estimation Methods on SEM Fit Indices[END_REF][START_REF] Xia | RMSEA, CFI, and TLI in structural equation modeling with ordered categorical data: The story they tell depends on the estimation methods[END_REF] and because the appropriate CFI, TLI, and RMSEA fit indices for DWLS estimation [START_REF] Savalei | Improving Fit Indices in Structural Equation Modeling with Categorical Data[END_REF] have not yet been implemented in lavaan, we relied on the Standardized Root Mean Square Residual (SRMR) cut-off of 0.08 to establish good model fit (Hu & Bentler, 1999;[START_REF] Savalei | Improving Fit Indices in Structural Equation Modeling with Categorical Data[END_REF].

Childhood Adversity

We compared the regression estimate of childhood adversity on our latent psychopathology factors to regression estimates of other early life factors (e.g., Breastfed? yes or no) on our latent psychopathology factors in the lavaan framework (Figure 1). We ran additional analyses to examine the predictive power of intelligence and socio-economic measures on each of the psychopathology latent factors (Supplemental Information 1.1) and simultaneously estimated the effect of these predictors on each of the psychopathology latent factors in the lavaan framework. We controlled for sex (0: males, 1: females).

Genetic Analyses

Although the primary goal was to create PGS for the phenotypic psychopathology factors, we additionally examined the genetic structure of psychopathology.

GWASs and GWAS Meta-analyses

In brief, we first conducted a GWAS of each MHD in the UK Biobank on 5,319,661 variants with ultra-fast generalized linear mixed model-based association analysis for binary traits using a sparse GRM (fastGWA-GLMM) from the Genome-wide Complex Trait Analysis (GCTA) package [START_REF] Jiang | A generalized linear mixed model association tool for biobank-scale data[END_REF] on individuals of British ancestry without neuroimaging data or siblings with neuroimaging data (Figure 1). We controlled for relatedness, sex (0: males, 1: females), center, genotyping chip, birth year, and the first 40 PCs of the PCA on the genotyped data to adjust for population stratification (Table 1; Table S1; Supplemental Information 1.2.1-1.2.2).

Since some MHDs had few cases in the UK Biobank, we meta-analyzed the summary statistics from the above GWASs with publicly available summary statistics of similar phenotypes that excluded the UK Biobank using METAL [START_REF] Willer | METAL: Fast and efficient meta-analysis of genomewide association scans[END_REF]; Table 1; Table S1; Figure S1; Supplemental Information 1.2.3). [START_REF] Bulik-Sullivan | LD Score regression distinguishes confounding from polygenicity in genome-wide association studies[END_REF]. Observed heritability (h2). Genomic inflation factor (λGC). Ratio(SE) : (intercept - 1)/(mean χ2 - 1). Neff=4*(SamplePrev*(1-SamplePrev)).

2

outcome. We ran one model per PGS to report an R 2 by latent factor. Model fit in the CFA models with the DWLS estimator was assessed using the SRMR cut-off of 0.08 or below indicating a good fit (Hu & Bentler, 1999;[START_REF] Savalei | Improving Fit Indices in Structural Equation Modeling with Categorical Data[END_REF].

Genetic Correlations with External Variables

As previously done to examine convergent and discriminant validity (Mallard et al., 2022), we calculated the genetic correlation of each latent variable with each exogenous variable within the Genomic SEM framework. We used genetic summary statistics used in previous papers (Grotzinger et al., 2022;[START_REF] Karlsson Linnér | Multivariate analysis of 1.5 million people identifies genetic associations with traits related to self-regulation and addiction[END_REF]Mallard et al., 2022), while removing phenotypes that were redundant with the investigated latent factor (e.g., we excluded Schizophrenia summary statistics when examining genetic correlations with the Thought Disorder factor).

Cerebral mediators of PGSs' effects on phenotypic psychopathology factors

Within the lavaan framework, we first examined the extent to which TBV predicted each latent factor while adjusting for several covariates: sex, age, age 2 , sex by age, sex by age 2 , and Scanner Site.

If TBV was a significant predictor of a latent factor (p < 0.05), we included TBV as a mediator of the residualized PGS's effect on the latent factor. The residualized PGSs were PGSs adjusted for birth year and the first 40 PC of the genotyped data. In the lavaan framework, the latent factor and the global measures were adjusted for sex, age, age 2 , sex by age, sex by age 2 , and Scanner Site.

Finally, to examine the extent to which TBV mediated genetic and environmental effects on general psychopathology factors, we added childhood adversity as exposure and examined whether the effect of childhood adversity was mediated by TBV. Model fit in the CFA models with the DWLS estimator was assessed using the SRMR cut-off of 0.08 indicating a good fit (Hu & Bentler, 1999;[START_REF] Savalei | Improving Fit Indices in Structural Equation Modeling with Categorical Data[END_REF].

To examine the extent to which global cerebral measures mediate genetic and environmental effects on general psychopathology measures, we will conduct the above analyses with the global measures that make up TBV instead of TBV (Figure 1). In the global regressions analyses, we applied a multiple comparison correction of p < 0.05/7, with 7 the number of global measures.

Results

Phenotypic analysis

EFA

The training sample consisted of 232,470 participants (Nmissing = 459). We report results from the PAF method and oblimin rotation on the training sample with missing data in text because the model fit and amount of variance explained across psychiatric disorders by the latent factors were similar across factoring methods, rotation methods, and samples (File S1-S2). The ΔRMSEA was 0.017 between the 2 and 3-factor models and 0.010 between the 3 and 4-factor models, suggesting that 3 factors are sufficient. Depression, Anxiety, OCD, Self-Harm, and PTSD loaded onto a factor that we refer to as the Internalizing Factor. The Hazardous Alcohol use or dependence and the Other Hazardous Substance use or dependence variables loaded on the same factor, which we named the Hazardous Substance Use or Dependence factor. Finally, bipolar disorder and schizophrenia loaded on a factor we refer to as the Thought Disorder factor. The omega hierarchical solution yielded a similar structure to the three factor EFA.

CFA

We ran CFAs on a test sample (50%, N = 232,929 participants, Nmissing = 416). Since the model fit and parameters of the test sample were similar to those from the entire sample with and without missing data (Files S3), we report the model fit and parameters from the models on the full dataset with missing variables.

The single p-factor model fit was good but explained the least amount of variance in psychopathology (43%; Figure 2). We ran bifactor models with modified latent variable variances and loadings and added constraints when the solution was not found (Table S2). We applied loading constraints to solve Heywood cases, which can be due to latent variables with only 2 indicators [START_REF] Kolenikov | Testing Negative Error Variances: Is a Heywood Case a Symptom of Misspecification[END_REF]. The correlated factors model, the hierarchical model, and the bifactor model with constrained loadings for the Hazardous Substance Use or Dependence factor and the Thought Disorders factor fit the data well and respectively explained 55%, 55%, and 58% of the variance across psychopathology measures (Figure 2). All MHDs positively loaded onto the latent factors across models, except for self-harm which negatively loaded onto the residualized Internalizing factor of the constrained bifactor model.

The constrained bifactor model also had non-significant loadings: the PTSD and eating disorder loadings on the residualized Internalizing factor were close to 0 (Figure 2; Supplemental Tables D).

Genetic analysis

Phenotypically Informed Models on Genetic Data

Genomic SEM Models

We applied the phenotypic model structure of the Correlated Factors, the Hierarchical, and the Bifactor Models to individuals with genetic data and without neuroimaging data. The genetic and phenotypic Correlated Factors Models were the most parsimonious model that generally best fit the data (Figure 2; Files S4; Supplemental Tables F).

SNP Effects

We extracted the SNP effects on the latent variables of the phenotypically informed Correlated Factors Model. The LDSC statistics and Q-Q Plots (Table S3; Figure S3) indicated that the GWASs for the Internalizing and the Thought Disorders factors were adequately powered and of good quality, but that the Hazardous Substance Use or Dependence GWAS was underpowered and may be biased by confounding, poor quality control, or other artifacts (Lee et al., 2018).

We only found genome-wide significant SNPs at p < 5e-8 for the Internalizing and the Thought Disorders factors (Figure S3; Supplemental Information 2.5). Using FUMA, we identified 25 lead SNPs and 19 genomic loci for the Internalizing factor and 116 lead SNPs and 97 genomic loci for the Thought Disorders factor.

Genetic Correlations

We examined the convergent and discriminant validity of our factors with 82 genetic correlations for the Internalizing factor, 89 genetic correlations for the Thought Disorders

PGS Prediction

We created Internalizing, Thought Disorders, and Hazardous Substance Use or Dependence PGSs for individuals with neuroimaging data and their siblings (N = 26,610) that were not related to individuals in the discovery multivariate GWASs. The Internalizing PGS explained 2.6% of the variance of the Internalizing factor, the Thought Disorders PGS explained 2.3% of the variance of the Thought Disorders factor, and the Hazardous Substance Use or Dependence PGS explained 0.3% of the variance in the Hazardous Substance Use or Dependence factor (Supplemental Information 2.7; Supplemental Tables H).

Genetically informed CFA Models

The EFA on odd SNPs yielded a 3-factor structure that differed from the phenotypic structure (File S5): instead of loading on the Internalizing factor, OCD and eating disorders loaded on their own factor, which we refer to as the compulsive disorders factor. Both the alcohol and the other substance hazardous use or dependence variables loaded on the Internalizing factor with general anxiety, PTSD, depression, and self-harm thought or action.

We applied the genetically informed 3-factor model structure from the EFA to even SNPs using CFA. The CFI (0.97) suggested good fit and the SRMR fit was acceptable (0.09).

The residual correlations of the CFA model on even SNPs suggested that the residual correlation between AUD and OCD be added to achieve a good fit (CFI = 0.97; SRMR = 0.08).

Since the goal was to extract all SNP effects on the genetically informed latent variables, we also ran the genetically informed 3-factor model structure on all SNPs. The model without the residual correlation between AUD and OCD fit the data well (CFI = 0.97; SRMR = 0.08).

Considering that the residual correlations of the model on all SNPs suggested that we include the residual correlation between AUD and SCZ instead of the one between AUD and OCD to improve fit, we did not include additional residual correlations (File S6; Figure 5; Supplemental Tables I).

Mediation Models with Global Cerebral Measures

TBV was a significant negative predictor of the Hazardous Substance Use or Dependence factor but not the Internalizing or the Thought Disorders factor from the correlated factors model (b = -0.09, SE=0.03, p = 1.67E-04, std.lv = -0.09; Supplemental Section 2.8;

Figure S11; Supplemental Table J). TBV did not mediate the effect of the Hazardous Substance Use or Dependence factor PGS's effect on the Hazardous Substance Use or Dependence factor but did mediate 0.9% of the effect of childhood adversity on the Hazardous Substance Use or Dependence factor (Figure 6). The Hazardous Substance Use or Dependence factor PGS, TBV, and the covariates explained 8% of the variance in the Hazardous Substance Use or Dependence factor. Adding Childhood Adversity increased the variance explained to 16% (Supplemental Section 2.9; Supplemental Tables J).

When breaking down TBV into its subcomponents, the Hazardous Substance Use or Dependence factor was positively predicted by TSA and the brain stem volume and negatively predicted by total MCT and cerebellar and cerebral WMVs. Although TBV did not predict the Internalizing or the Thought Disorders factors, Internalizing disorders were negatively predicted by Cerebellum GMV and the Thought Disorder factor was positively predicted by the brainstem volume and negatively by cerebellar and cerebral WMVs. However, the Thought Disorder predictors were no longer significant after multiple comparison corrections (SRMR = 0.07; Supplemental Tables J). We plan on examining whether these global measures mediate the effects of the PGSs of psychopathology and childhood adversity on psychopathology.

Discussion

The paper (i) examined the phenotypic and genetic structure of psychopathology in the UK Biobank, (ii) provides phenotypic and genetic psychopathology measures for future UK biobank studies interested in studying or adjusting for specific and general psychopathology measures, and (iii) examined the extent to which TBV (and later, global cerebral measures) mediates the effects of childhood adversity and genetic predispositions on general psychopathology measures in the UK Biobank.

The most popular psychopathology structure is the bifactor model, although the exact structure varies across studies (e.g., number of factors other than the p-factor, presence of correlations, loadings...; [START_REF] Carragher | The structure of adolescent psychopathology: A symptom-level analysis[END_REF]Caspi et al., 2014;Lahey, Applegate, et al., 2012;Lahey et al., 2018;Watts et al., 2020). In our phenotypic analyses, it was the most difficult to fit and required that we constrain the loadings of the variables making up the Thought Disorders factor and the Hazardous Substance Use or Dependence factor to equality.

Eating disorders and PTSD significantly loaded on the p-factor but not on the residual Internalizing factor, suggesting that their shared variance is fully captured by the p-factor. Therefore, eating disorders and PTSD did not both load on a general factor and on a subfactor, as is expected in a bifactor model. We found that the correlated factors model and the hierarchical model had a better fit than the bifactor and p-factor models. This is inconsistent with previous reports that the bifactor model has a higher fit propensity and tends to overfit the data [START_REF] Bornovalova | Appropriate Use of Bifactor Analysis in Psychopathology Research: Appreciating Benefits and Limitations[END_REF]Watts et al., 2020), including nonsensical patterns (Bonifay et al., 2017). Some argue that the correlated factors model is more parsimonious (Murray et al., 2016, p. 20;Watts et al., 2019) and, in line with previous studies, we found that including a p-factor in the correlated factors model did not explain any extra variance (Watts et al., 2019). In general, the Internalizing, Externalizing (in our case, Hazardous Substance Use or Dependence), and Thought Disorder dimensions are widely supported by both binary and symptomatic data, including dimensional scoring of symptom dimensions assessed with standardized psychiatric interviews [START_REF] Kotov | The structure and short-term stability of the emotional disorders: A dimensional approach[END_REF][START_REF] Markon | Modeling psychopathology structure: A symptom-level analysis of Axis I and II disorders[END_REF][START_REF] Wright | The hierarchical structure of DSM-5 pathological personality traits[END_REF].

Although the nature of the p-factor is undetermined (Lahey et al., 2021) and some criticize the mechanisms behind the p-factor for being unfalsifiable (Watts et al., 2020), the pfactor reflects the global severity across MHDs (Fried et al., 2021). In line with previous studies reporting lower intelligence, executive function, school functioning, income, and higher levels of aggression, peer delinquency, and self-harm with general measures of psychopathology (Abbott et al., 2018;Harden et al., 2020;Lahey et al., 2015;Martel et al., 2017), we find that there is a negative association between several measures of psychopathology and intelligence, income, and a positive one with the Townsend deprivation index (a socio-economic variable). Therefore, while the correlated factors model is the most parsimonious model of psychopathology, researchers may nonetheless want to study a p-factor depending on the question at hand. We replicate recent findings suggesting that psychopathology's phenotypic and genetic factor structures differ (Grotzinger et al., 2022;Mallard et al., 2022). Although previous studies suggested that genetic indicators may serve as proxies for their respective phenotypes, we add to the literature against the ''phenotypic null hypothesis'' [START_REF] Turkheimer | A phenotypic null hypothesis for the genetics of personality[END_REF], which states the phenotypic and genetic factor structures converge. These results suggest while there are common underlying genetic factors between disorders, environmental influences likely contribute to correlations across disorders at the phenotypic level. Therefore, studying both environmental and genetic effects is crucial to understanding the factors and mechanisms underlying general psychopathology.

We did not find genome-wide significant SNP effects for the Hazardous Substance Use or Dependence factor and the SNPs only explained 0.3% of the variance in the Hazardous Substance Use or Dependence factor. Our analyses suggest that our GWAS is underpowered and that our findings may be biased. Therefore, it may be advantageous to create a p-factor PGS to serve as a proxy for genetic predispositions to the Hazardous Substance Use or Dependence factor. Although the signal captured by the p-factor PGS will be less specific to Hazardous Substance Use or Dependence, it will be better powered and therefore a potentially better predictor of Hazardous Substance Use or Dependence. Recent studies, however, suggest that the p-factor provides limited insight into the biology associated with psychopathology even if the hierarchical and bifactor specifications both fit the data well (Grotzinger et al., 2022) and that a p-factor captures a heterogeneous signal that is difficult to parse (Grotzinger et al., 2022;Mallard et al., 2022). Therefore, we plan on conducting additional analyses to examine (i) whether the p-factor with our model structure is biologically relevant and (ii) whether the p- There was a positive genetic correlation between educational attainment and the Thought Disorders factor and a negative correlation between educational attainment and the Internalizing factor. This is consistent with a previous study reporting positive genetic correlations for educational attainment with schizophrenia and with bipolar disorder and negative ones for major depressive disorder (the variable loading the most onto the Internalizing factor). When separating educational attainment into its cognitive and noncognitive genetic components, cognitive effects are negatively correlated with schizophrenia and with bipolar disorders, whereas non-cognitive effects remain positively correlated (Demange et al., 2021). Considering that the phenotypic correlation of the Thought Disorders factor with educational attainment was positive, this association may be partially mediated by genetic effects. We additionally found a positive phenotypic correlation between educational attainment and our psychopathology factors but a negative one for intelligence and our psychopathology factors. Since the genetic correlation between educational attainment and the Internalizing factor was negative, the positive phenotypic correlation between educational attainment and the Internalizing factor may be driven by environmental factors.

Although TBV was a negative predictor of the Hazardous Substance Use or Dependence factor, it was not associated with Thought Disorders or Internalizing Disorders.

However, when looking at the associations between these factors and the global measures making up TBV, we found that TSA and the brain stem volume positively predicted and total MCT and cerebellar and cerebral WMVs negatively predicted the Hazardous Substance Use or Dependence factor. Although TBV was not associated with Internalizing disorders, Cerebellum GMV negatively predicted Internalizing disorders. In upcoming analyses, we will examine whether these global measures mediate genetic and environmental effects on our general measures of psychopathology.

The effect of the Hazardous Substance Use or Dependence PGS on the Hazardous Substance Use or Dependence factor was not mediated by TBV and only 0.9% of the effect of childhood adversity on the Hazardous Substance Use or Dependence factor was mediated by TBV. Although the effects of the psychopathology PGSs on their respective psychopathology factors were not mediated by TBV, they may still be mediated by other global or regional brain measures. Based on previous findings, we expect regional brain measures to correlate with our measures of psychopathology [START_REF] Parkes | Transdiagnostic dimensions of psychopathology explain individuals' unique deviations from normative neurodevelopment in brain structure[END_REF]. However, given previous reports that neuroanatomical alone have low predictive power for some MHDs (Traut et al., 2022), it is unlikely that these regions will mediate a large proportion of the effect.

The present study has several limitations. First, the UK Biobank is limited in its available phenotypic measures: although we have some inpatient data, diagnoses are mostly self-reported and diagnoses are mostly binary and do not capture the complexity of symptoms within a disorder. A previous study suggested that using self-report data may produce GWAS signals of low specificity (Cai et al., 2020). However, excluding self-report measures, did not significantly change the GWAS results of a recent study examining the genetic structure of psychopathology across 11 s (Grotzinger et al., 2022). Another recent study bypassed the limitations of the binary UK Biobank measures by modeling lifetime depression, mania, and psychosis self-reported symptoms with Bayesian item response theory and linear mixed models and found that (i) the genetic factor structure differed from the phenotypic factor structure, that (ii) the s, which we aggregated, such as Bipolar Disorder I and Bipolar Disorder II, actually load on different factors, and (iii) that these transdiagnostic factors have divergent genetic architectures (Mallard et al., 2022). Therefore, studying symptoms and or subdomains within s may provide additional biological insight into shared mechanisms across disorders. Second, we selected MHDs available for a large number of participants and, in turn, could not include developmental disorders (e.g., autism spectrum disorder). Even with a liberal diagnosis criterion, the prevalence of MHDs such as OCD and Schizophrenia was lower in the UK Biobank than in the general population. This is consistent with previous findings that the UK Biobank tends to be healthier than the general population (Fry et al., 2017) and may partially be explained by the fact that certain diagnoses are less frequent for people of this age.

Third, although age and sex are often regressed out of MHDs before generating the pfactor (Allegrini et al., 2020;Harden et al., 2020), the residuals of the binary MHDs would be difficult to interpret. While age is associated with psychopathology, we omitted age because it was not available for a majority of diagnoses. However, this should not drastically influence our results, since we examined adults between 50 and 70 years old -at a time when a majority of disorders have already been identified [START_REF] Solmi | Age at onset of mental disorders worldwide: Large-scale meta-analysis of 192 epidemiological studies[END_REF]. Moreover, past studies examining age effects on psychopathology factors generally report that the general psychopathology factor and externalizing and internalizing factors are consistent across ages (Caspi et al., 2014;Caspi & Moffitt, 2018;Krueger & Markon, 2006;Lahey, Applegate, et al., 2012;[START_REF] Michelini | Delineating and validating higher-order dimensions of psychopathology in the Adolescent Brain Cognitive Development (ABCD) study[END_REF].

Introduction

The positive correlation in performance across cognitive tests can be reduced to a single dimension: the general intelligence factor (g-factor), which reflects a person's general cognitive performance. Although several studies examined the genetic and neurological basis of intelligence separately, there are relatively few studies investigating how genetic, environmental, and neurological factors simultaneously influence intelligence due to the lack of sufficiently rich and large datasets (for review Deary et al., 2021). Thus, this paper aims to capitalize on the richness of the UK Biobank -a large-scale prospective study with neural, genetic, environmental, and behavioral data -and identify the neuroanatomical measures (e.g., brain volumes) mediating the effect of genetic and environmental factors on intelligence in the UK Biobank.

Intelligence is heritable, with genetic differences accounting for about 50% of the differences in intelligence (Haworth et al., 2010;Polderman et al., 2015). Genome-Wide Association Studies (GWASs) are used to identify genetic differences linked to variations in intelligence by pinpointing the Single-Nucleotide Polymorphisms (SNPs) that contribute to differences in intelligence. SNPs that vary with intelligence scores are typically associated to brain-expressed genes [START_REF] Johnson | Systems genetics identifies a convergent gene network for cognition and neurodevelopmental disease[END_REF]Lee et al., 2018) that are linked to a range of neuronal classes and processes, such as synaptic and neuron differentiation (Hill et al., 2019).

SNP variations may therefore be associated to differences at the macroscopic cerebral level. SNP variations can be summarized into a single score: a polygenic score (PGS), which predicts an individual's phenotype given their genetic predisposition. A PGS is derived from the sum of the effect allele at each SNP that is weighted by the SNP's effect on a trait (estimated in a GWAS). The PGS of Cognitive Performance (i.e., Fluid Intelligence in the UK Biobank and g-factor in COGENT and CHARGE consortiums) predicted up to 10.6% of the variance in cognitive performance in an independent sample (Lee et al., 2018). Although PGSs do not currently explain enough variance in intelligence to accurately predict individual intelligence scores [START_REF] Morris | Can education be personalised using pupils' genetic data?[END_REF], PGSs are valuable measures of genetic factors at the population level. Educational attainment and cognitive performance PGSs are increasingly being used to disentangle environmental from genetic effects on educational and life outcomes [START_REF] Bates | The Nature of Nurture: Using a Virtual-Parent Design to Test Parenting Effects on Children's Educational Attainment in Genotyped Families[END_REF]Rimfeld et al., 2018;[START_REF] Saarentaus | Polygenic burden has broader impact on health, cognition, and socioeconomic outcomes than most rare and high-risk copy number variants[END_REF]Stumm et al., 2020).

Since genetic and environmental effects act on intelligence via the brain, numerous studies investigated the neural correlates of intelligence. The most well-replicated association is the positive correlation of Total Brain Volume (TBV) with intelligence scores, ranging from r = 0.24 to 0.31 (Cox et al., 2019;[START_REF] Gignac | Brain volume and intelligence: The moderating role of intelligence measurement quality[END_REF][START_REF] Pietschnig | Meta-analysis of associations between human brain volume and intelligence differences: How strong are they and what do they mean?[END_REF]. Beyond overall brain size, the Parieto-Frontal Integration Theory (Jung & Haier, 2007) is the most supported theory on the regional correlates of intelligence. Although studies report additional or fewer regions than those predicted by the P-Fit, structural (grey and white matter volumes), diffusion, and functional studies find that intelligence scores are associated with the lateral and medial frontal, parietal, lateral temporal, and lateral occipital cortex, and their underlying white matter connectivity (e.g., arcuate fasciculus; for review Deary et al., 2021;Jung & Haier, 2007).

Previous UK Biobank studies examined the brain correlates of intelligence [START_REF] Cox | Ageing and brain white matter structure in 3,513 UK Biobank participants[END_REF](Cox et al., , 2019)). The authors reported consistent associations with the P-FIT theory, such as stronger associations in the frontal pole, and the paracingulate, as well as less consistent associations with the P-FIT theory, such as weak associations in inferior frontal and superior parietal areas. They also found associations in the insula and precuneus/posterior cingulate volumes, which were only recently implicated in general intelligence (Basten et al., 2015). As for subcortical volumes, they found that the thalamic volumes were the most associated with verbal numerical reasoning (β= 0.23). Finally, they reported that many of these regions still predicted intelligence when adjusting for Total Brain Volume (TBV), suggesting that some regions make a unique contribution to intelligence that goes beyond TBV.

Although genetic and brain correlates of general intelligence (g-factor) have largely been studied, only two studies, to our knowledge, examined the extent to which neural measures mediate the effect of the g-factor polygenic score (gPGS) on the phenotypic g-factor.

One study using vertex-wise mediation analyses of cortical thickness and surface areas reported that the association between the gPGS and the phenotypic g-factor was mediated by brain cortical thickness and surface area of the anterior cingulate cortex, the prefrontal cortex, the insula, the medial temporal cortex, and inferior parietal cortex up to 0.75% in IMAGEN (N= 1,651) and 0.77% in IntegraMooDS (N= 742; Lett et al., 2020). In other words, these regions explained 20-40% of the variance explained by the gPGS on the g-factor (3-5%). A preprint on 550 adults, which used the same summary statistics of intelligence (Savage et al., 2018) as the above study to create their gPGSs, found that two intraparietal areas and the posterior temporal cortex surface areas mediated the effect of the gPGS on the g-factor [START_REF] Genç | Structural architecture and brain network efficiency links polygenic scores to intelligence[END_REF]. These mediation studies suggest that specific cortical regions mediate the effect of the gPGS on the phenotypic g-factor.

However, the extent to which additional regions, such as subcortical and cerebellar volumes, mediate the effect of the gPGS on intelligence has yet to be investigated. Moreover, the associations between cortical regions, genetics, and intelligence have not been investigated using the finer-grained segmentations of the Destrieux atlas. Therefore, our first aim was to examine whether subcortical volumes, cerebellar volumes, cortical volumes, cortical thicknesses, and cortical surface areas mediate the effects of the gPGS and the phenotypic gfactor with a more predictive gPGS in the UK Biobank.

Since early adversity is associated with a decrease in intelligence and cognitive function later in life (Enlow et al., 2012;McGuire & Jackson, 2020) and may have lasting biological and cerebral effects changes in childhood and adulthood (Dye, 2018;Lupien et al., 2009), our second aim was to examine whether the regions that mediate the gPGS's effect on the g-factor also mediate childhood adversity's effect on the g-factor. Taken together, these analyses will shed a light on the neuroanatomical measures that mediate the genetic (gPGS) and early environmental (childhood adversity) effects on intelligence (g-factor) in the UK Biobank. on which it was created. Max N: maximum number of participants included in the analyses.

Corresponds to N for TBV but will be reduced when including other brain measures when data for a region is missing.

Imaged derived Phenotypes

We used the same 10 global and 620 regional imaging phenotypes examined by Williams and colleagues (2021). The global phenotypes include TBV, total Mean Cortical Thickness (MCT), Total Surface Area (TSA), subcortical Grey Matter Volume (GMV), cortical GMV, cerebral White Matter Volume (WMV), cerebellar GMV, cerebellar WMV, the brainstem volume, and cerebral spinal fluid (CSF), whereas the regional phenotypes include: Freesurfer subcortical segmentations for the caudate, putamen, accumbens, and pallidum were used instead of the preregistered FIRST volumes, for segmentation consistency with the other subcortical and cortical volumes which were segmented from Freesurfer.

Although we did not preregister that we would examine the effects of the left and right measure of the whole thalamus, hippocampus, and amygdala because we focused the association of their subsegmentations with the g-factor, we ran these exploratory analyses to facilitate result comparison with previous studies and examine whether associations at the subcortical sub-segmentation level manifested at the global level.

Childhood Adversity Score

A childhood adversity score was created from questions in the UK Biobank on childhood abuse and social stressors. Childhood abuse was measured with data fields 20488 "When I was growing up... People in my family hit me so hard that it left me with bruises or marks") and 20490 ("When I was growing up... Someone molested me (sexually)") and childhood stressors

were measured with data fields 20487 ("When I was growing up... I felt that someone in my family hated me"), 20489 ("When I was growing up... I felt loved"), and 20491 ("When I was growing up... There was someone to take me to the doctor if I needed it"). All questions are rated from 0 (Never True) to 4 (Very Often True). So that all indicators are in the same direction, we subtracted data field 20489 and data field 20491 responses from 4 (reverse coding). We conducted a PCA on the scores from these questions and extracted the first principal component (PC1) as our measure of childhood adversity, which captured 42% of the variance across questions (Table 2). For all mediation models described in the present study, indirect effects were calculated using the product method. We estimated direct paths (exposure to an outcome) and indirect paths (exposure to mediators to outcomes) and adjusted the mediators and outcome for age (linear and quadratic), sex, and their interactions in the lavaan framework.

We set a lenient p-value threshold to 0.05 and a stricter one to p < 0.05/N (N: the number of regional and global measures included in the model of interest). Good fit was established with a CFI > 0.95, a RMSEA < 0.06 and a SRMR < 0.08 (Hu & Bentler, 1999).

Do global measures mediate the g-PGS' and Childhood Adversity's effects on the g-factor?

We applied the same mediation models as in section 2.5.2. except that we added Childhood Adversity as an additional exposure and estimated its direct and indirect paths through the global measure(s) to the g-factor. Lavaan considers correlations between predictors without estimating them.

What regional measures predict the g-factor?

The aim was to identify the regions that contribute more to the g-factor than what is predicted given their size: this includes (1) regions that significantly predict the g-factor after adjusting for brain size and are positive with or without adjusting for global brain size and (2) regions that significantly predict the g-factor after adjusting for brain size and are negative with or without adjusting for global brain size.

To do so, we ran equations 3 and 4 (i refers to an individual, the regional measure N corresponds to a regional volume, thickness, or surface, and the global measure to TBV for volumes, Total MCT for mean thicknesses, and TSA for surface areas). The significance threshold was set to p < 0.05/N (N: the number of coefficients of interest, which was 148 for surfaces, 148 for thicknesses, and 311 for volumes).

We additionally plan on examining the concordance between the regions that significantly predict the g-factor in our study and the P-Fit Theory. We will map the P-Fit Theory Broadman Areas to the Destrieux segmentations and examine whether the P-Fit regions have the largest effect size with and without global adjustment. Equation 3g-factori = Intercept + Regional Measure N i + Sexi + Agei + Age 2 i+ Age*Sexi + Age 2 *Sexi + e Equation 4g-factori = Intercept + Regional Measure N i + Global Measure N i + Sexi + Agei + Age 2 i+ Age*Sexi + Age 2 *Sexi + e 2.5.5. Do the Regional Measures that predict the g-factor independently from brain size still predict the g-factor when entered in the same model?

Based on equations 3 and 4, we selected the regions that still significantly and positively or negatively predicted the g-factor after adjusting for brain size. Because brain regions are correlated, their effect on the g-factor may be shared across regions even if they are independent of global brain size. Therefore, to avoid redundancy, we examined whether these regions still predicted the g-factor when simultaneously entered in a regression model predicting the g-factor (Equation 5, where N refers to a region, i to an individual, and the global measure to TBV for volumes, Total MCT for mean thicknesses, and TSA for surface areas).

The significance threshold was set to p < 0.05/N (N: the number of regional measures included in the model of interest). Equation 5g-factori = Intercept + Regional Measure 1 i + Regional Measure 2 i ….

+ Regional Measure N i + Global Measure N i + Sexi + Agei + Age 2 i+ Age*Sexi + Age 2 *Sexi + e 2.5.6. Do Regional Measures mediate the g-PGS' effects on the g-factor?

For volumes, thicknesses, and surface areas separately, we examined the simultaneous mediation of the global measure and the significant regional measures from equation 5 with the sem function from the lavaan package (Rosseel, 2012). The gPGS was the exposure, global and regional measures were the mediators, and the g-factor served as the outcome.

2.5.7. Do Regional Measures mediate the g-PGS' and Childhood Adversity's effects on the g-factor?

We applied the same mediation models as in section 2.5.6. except that we added Childhood Adversity as additional exposure and estimated its direct and indirect paths through regional and global measures to g-factor.

3.4.What regional measures predict the g-factor?

Regression results are available in Supplemental Tables B (full models) and C (regional estimates). Figure 2 shows the g-factor estimate by volume, surface area, or thickness estimate when including or excluding the global measure in the regression model. Figures of the estimate by region for each type of possible change in significance or estimate (Table 3) are available in Files S1-3. There were 242 out of 311 volumes, 130 out of 148 surface areas, and 6 out of 148 mean thicknesses, that were no longer significant after adjusting for global brain size, suggesting that they contribute to the g-factor through global brain size (Table 3; Supplemental B3-4 & C1-3;

Files S1-3).

There were 40 volumes (mainly cerebellar GMVs, subcortical thalamic and hippocampal nuclei, and a few cortical volumes), 12 cortical surface areas (mostly frontal), and 21 cortical mean thicknesses (mostly temporal; Table 3; Supplemental B5-6 & C1-3; Files S1-3) that were significant and had positive estimates after adjusting for brain size, suggesting that they contribute more (positively) to the g-factor than what is expected given their size.

There were 2 ventricular volumes and 7 cortical mean thicknesses (the left and right pericallosal sulci, the left and right anterior cingulate gyri and sulci, right occipital pole, left suborbital sulcus, and the right frontal marginal gyrus and sulcus; Table 3; Supplemental B5-6 & C1-3; Files S1-3) that were significant and had negative estimates after adjusting for brain size, suggesting that they contribute more (negative) to the g-factor than what is expected given their size.

There were 18 volumes and 6 surface areas that were still significant but had their estimates switch from positive to negative, suggesting that they contribute less to the g-factor than what is expected given their contribution to global brain size. For volumes, these regions included the right and left caudate, the right and left lingual gyrus, left and right pericallosal sulci, the right posterior-ventral part of the cingulate gyrus (isthmus), the right occipital pole, the right superior parietal gyrus, the hippocampal tail, and several subthalamic nuclei. As for surfaces, these regions included the left and right postcentral sulci, the left paracentral gyrus and sulcus, the middle anterior cingulate gyrus sand sulcus, the left lingual gyrus, and the left posteriorventral part of the cingulate gyrus (isthmus).

Finally, there were 10 mean thicknesses, 3 ventricular volumes, and 1 subthalamic nuclei volume that became significant and negative after adjusting for brain size, suggesting that they contribute less to the g-factor than what is expected given their size. For mean thicknesses, regions include left and right transverse frontopolar gyri and sulci, the right lingual gyrus, right suborbital sulcus, the right superior frontal gyrus, the right cuneus gyrus, the right occipital superior gyrus, the right posterior-ventral part of the cingulate gyrus (isthmus), and left occipital pole and left posterior transverse collateral sulcus.

3.5.Do the Regional Measures that predict the g-factor independently from brain size still predict the g-factor when entered in the same model?

We then examined whether regions that significantly and positively or negatively predicted the g-factor after adjusting for brain size do so independently from each other. We found that there were 4 Volumes, 3 Surface Areas, and 12 Mean Thicknesses that still significantly predicted the g-factor independently from each other and global brain size (Supplemental B9-11).

3.6. Do Regional Measures mediate the g-PGS' effects on the g-factor?

Volumes

Based on the previous analyses in section 3.5, we included the right olfactory bulb, the left subcallosal gyrus, and the Right Mediodorsal Medial Magnocellular Thalamic Nuclei volumes in the regional and global volumetric mediation model. We did not include the 3 rd ventricle volume even if it was significant because we do not expect ventricular volumes to mediate genetic effects on intelligence.

The indirect path from the gPGS to the g-factor was significant for TBV and the right olfactory bulb volume after multiple comparison corrections and for left subcallosal gyrus volume at the p < 0.05 threshold. TBV mediated 5.07% of the gPGS' effect on the g-factor, whereas the right olfactory bulb volume mediated 0.46% and left subcallosal gyrus volume 0.31% of the gPGS' effect on the g-factor (Figure 3; Supplemental Table D3).

Surface Areas

Based on the previous analyses in section 3.5, we included TSA, the right orbital part of the inferior frontal gyrus surface area, the left subcallosal gyrus surface area, and the Left Anterior Transverse Collateral Sulcus surface area in the regional and global surface area mediation model.

Total Surface Area mediated 3.99%, the Left Anterior Transverse Collateral Sulcus surface area 0.41%, the left subcallosal gyrus 0.30%, and the Right Orbital Part of the Inferior Frontal Gyrus surface area 0.35% of the effect of the gPGS on the g-factor at the p < 0.05/4 threshold (Figure 3; Supplemental Table D4).

Mean Thicknesses

Based on the previous analyses in section 3.5, we included Total MCT, the Right anterior part of the cingulate gyrus and sulcus, the left anterior part of the cingulate gyrus and sulcus, the left planum polare of the superior temporal gyrus, the left inferior segment of the circular sulcus of the insula, the right Pericallosal sulcus, the left Short Insular gyrus, the Right Postcentral Sulcus, the Right Superior Segment of Circular Insula Sulcus, the Right Superior Temporal Sulcus, the Right Precentral Gyrus, the Left Subcallosal Gyrus, and the Left Pericallosal sulcus mean thicknesses in the regional and global mean thickness mediation model.

Total MCT did not mediate the effects of the gPGS or Childhood Adversity on the gfactor. The right anterior part of the cingulate gyrus and sulcus mean thickness mediated 0.27% of the effect of the gPGS on the g-factor at p < 0.05. The left anterior part of the cingulate gyrus mediated 0.14%, the left short insular gyrus mean thickness 0.18%, left planum polare of the superior temporal gyrus mean thickness 0.16%, the right pericallosal sulcus mean thickness mediated 0.12%, the left inferior segment of the circular sulcus of the insula mean thickness mediated 0.18%, and the right pericallosal sulcus mediated 0.27% of the effect of the gPGS on the g-factor at p < 0.05 (Figure 3; Supplemental Table D5).

3.7. Do Regional Measures mediate the g-PGS' and Childhood Adversity's effects on the g-factor?

Volumes

In the volumetric mediation models, TBV mediated 4.15% of the gPGS' effect on the gfactor and the right olfactory bulb volume mediated 0.37% of the gPGS' effect on the g-factor at p < 0.05/4, whereas right mediodorsal medial magnocellular thalamic nuclei volume 0.32% of the gPGS' effect on the g-factor at p < 0.05. Therefore, the left subcallosal gyrus volume was no longer significant when adding Childhood Adversity in the mediation model and the indirect path through the Right Mediodorsal Medial Magnocellular Thalamic Nuclei became significance at p < 0.05. TBV mediated 1.41% of Childhood Adversity's effect on the g-factor, whereas the right olfactory bulb volume mediated 0.14% of Childhood Adversity's effect on the g-factor at p < 0.05 (Figure 3; Supplemental Table E3).

Surface Areas

Total Surface Area mediated 3.37%, the left anterior transverse Collateral Sulcus 0.34%, and the Right Orbital Part of the Inferior Frontal Gyrus surface area 0.29% of the effect of the gPGS on the g-factor at the p < 0.05/4 threshold (Supplemental Table D4). Total Surface Area mediated 1.11% and the Left Anterior Transverse Collateral Sulcus surface area 0.16% of Childhood Adversity's effect on the g-factor (Figure 3; Supplemental Table E4).

Mean Thicknesses

Total MCT did not mediate the effects of the gPGS or Childhood Adversity on the gfactor. The right anterior part of the cingulate gyrus and sulcus mean thickness still mediated 0.27% of the effect of the gPGS on the g-factor at p < 0.05. The right pericallosal sulcus mean thickness mediated 0.12%, the left short insular gyrus mean thickness 13%, and the left planum polare of the superior temporal gyrus mean thickness 0.15% of the effect of the gPGS on the g-factor at p < 0.05. However, the left inferior segment of the circular sulcus of the insula mean thickness and the left anterior part of the cingulate gyrus and sulcus mean thickness no longer mediated the gPGS' effect on the g-factor. Instead, a new region mediated the gPGS' effect on the g-factor: the left subcallosal gyrus mean thickness (0.17%), which also mediated the effect of Childhood Adversity's effect on the g-factor (0.10%; Figure 3; Supplemental Table C5).

Discussion

This paper capitalized on the richness of the UK Biobank data to examine the extent to which neuroanatomical measures (e.g., brain volumes) mediate the effect of genetic and environmental factors on intelligence in the UK Biobank. Using a g-factor measure and the gPGS created in a previous paper (Williams et al., 2022), we first examined the association between the g-factor and neuroanatomical measures in the UK Biobank on about 30,000 individuals. We then identified the neuroanatomical measures mediating the gPGS' effect on the g-factor and whether the same regions mediated childhood adversity's effect on the gfactor. Although volumetric and surface global measures were the main mediators of the gPGS' effect on the g-factor, global measures mediated less than 10% of the gPGS' effect on the gfactor and less than 3% of Childhood Adversity's effect on the g-factor, suggesting that mediation by neuroanatomical measures only explains a small fraction of the total effect of the gPGS and Childhood Adversity on the g-factor.

Most associations between the g-factor and volumes (78%) or surface areas (88%) disappeared after adjusting for global brain size, suggesting that the majority of volumes and surfaces contribute to intelligence through their contribution to global cerebral effects. In contrast, only 4% of mean thicknesses were no longer significant after adjusting for global brain size and 26% of mean thicknesses still predicted the g-factor after adjusting for Total MCT. Therefore, mean thicknesses appear to influence the g-factor through region-specific effects rather than global effects. This can be explained by the small associations between regional mean thicknesses and Total MCT (mean β = 0.03) compared to those of regional volumes with TBV (mean β = 0.30) as well as the small association between Total MCT and the g-factor (β = 0.04). Therefore, adjusting for Total MCT captures little variance between regional mean cortical thicknesses and the g-factor.

Regions that contribute the most to the g-factor not only correspond to regions that significantly predict the g-factor after adjusting for brain size but also maintain the direction of their effect with or without adjusting for global measures. We found that cerebellar volumes, subcortical nuclei volumes, a few cortical volumes, frontal surface areas, and temporal mean thicknesses contributed more positively to the g-factor than what is expected given their size.

In contrast, a few distributed mean thicknesses and ventricular volumes contributed more negatively to the g-factor than what is expected given their size. Negative and positive associations between cortical thickness and intelligence have been reported across the cortex [START_REF] Karama | Childhood cognitive ability accounts for associations between cognitive ability and brain cortical thickness in old age[END_REF] and are thought to depend on the measure of the intelligence [START_REF] Goriounova | Genes, Cells and Brain Areas of Intelligence[END_REF]: Greater crystallized intelligence is associated with cortical thinning whereas fluid intelligence does not appear to be related with cortical thickness [START_REF] Tadayon | Differential Contribution of Cortical Thickness, Surface Area, and Gyrification to Fluid and Crystallized Intelligence[END_REF]. Studies looking at age-related changes in performance on the cognitive tests of the UK Biobank found that performance on the verbal numerical UK Biobank test (also known as the fluid intelligence test) does not decrease as expected with age [START_REF] Hagenaars | Shared genetic aetiology between cognitive functions and physical and mental health in UK Biobank (N=112 151) and 24 GWAS consortia[END_REF]. Instead, the performance stagnates as would be expected with crystallized intelligence [START_REF] Cavanaugh | Adult development and aging[END_REF]. Therefore, our g-factor measure, on which the fluid intelligence test loads highly (0.62), likely captures both crystallized and fluid intelligence and may explain why we find distributed positive and negative associations between mean thicknesses and intelligence. Therefore, future studies may want to explore the associations between brain regions and subdomains of intelligence to obtain a better understanding of the associations between general intelligence, cognitive abilities, and the cortex (Jung & Haier, 2007).

Although we find frontal and temporal-parietal associations with general intelligence, we will conduct further analyses to see whether our findings support the P-Fit theory (for review Deary et al., 2010Deary et al., , 2021)). Specifically, we will match the Destrieux segmentations to the Broadman Areas and will examine whether these cortical Destrieux segmentations areas are associated to the g-factor with and without adjustment for global measures. As for regions influencing the g-factor that are not in P-Fit, a previous UK Biobank study reported a significant association between the g-factor and the whole hippocampal or thalamic volumes after adjusting for brain size (Cox et al., 2019). Yet, we found no such associations. Instead, we report novel associations between the g-factor and subcortical subsegmentations as well as cerebellar subsegmentations.

We find that regional measures independently explained a small portion of the effect of the gPGS on the g-factor and that the gPGS' effect on the g-factor is mediated by several cortical surface areas, volumes, and mean thickness. Although we used different segmentation and samples from Lett and colleagues (2020), we similarly find that the gPGS' effect on the gfactor is mediated by the anterior cingulate cortex, prefrontal, insular, medial temporal, and inferior parietal mean thicknesses and surface areas. However, we find that our regional measures mediate a smaller percentage of the gPGS' effect on the g-factor (around 0.30% instead of 0.75%), which may be due to the difference in age between cohorts or to their larger such as connectivity, white matter tracts, or functional activation, to better understand the extent to which cerebral measures mediate the environmental and genetic factors on the gfactor.

The present study is limited in its ability to generalize to all UK Biobank participants since individuals with neuroimaging data are different from UK Biobank participants without neuroimaging data [START_REF] Lyall | Quantifying bias in psychological and physical health in the UK Biobank imaging sub-sample[END_REF] and the UK population (Fry et al., 2017). Moreover, our analyses were restrained to individuals of British ancestry, suggesting that further research is needed to examine whether genetic factors on intelligence are mediated by the same cerebral regions across ancestries. The polygenic score also only predicted 7.9% of the variance in the g-factor, suggesting that additional regions may be found when using a more predictive polygenic score. Finally, not including the most important environmental predictor of intelligence, parental or childhood socioeconomic status (SES; Flensborg-Madsen et al., 2020;

Flensborg-Madsen & Mortensen, 2017), is a major limitation of our study. Since childhood SES was not available in the UKBiobank, we focused on childhood adversity, which is strongly associated with intelligence (McGuire & Jackson, 2020), although less so than parental SES.

Although we could have computed a measure of adult SES as done by previous studies (e.g., [START_REF] Kweon | Human brain anatomy reflects separable genetic and environmental components of socioeconomic status[END_REF] to serve as a proxy of childhood SES, the bidirectional influences between adulthood SES and intelligence would have compromised the interpretation mediation model given.

The present paper provides the largest study of the neuroanatomical measures mediating genetic (gPGS) and early environmental (childhood adversity) effects on intelligence (g-factor). We replicate and extend previous findings and highlight the importance of adding environmental data to better understand the mechanisms by which genetic and environmental factors influence general intelligence. In light of the strong evidence for genetic and environmental factors contributing to individual differences in intelligence (for review Deary et al., 2021;Harden, 2021), we urge future studies to simultaneously investigate the genetic, environmental, and cerebral effects on intelligence by examining a variety of cerebral properties, from the macro to the micro, to understand discrepancies in intelligence (for review Deary et al., 2021), and, in turn, later health, educational, and social outcomes (Calvin et al., 2017;Schmidt & Hunter, 2004;Strenze, 2007;Twig et al., 2018).

Discussion

Cognition and psychopathology predict a variety of health, educational, and social outcomes (e.g., Calvin et al., 2017;Schmidt & Hunter, 2004;Strenze, 2007;Twig et al., 2018).

Although both genetic and environmental factors influence cognition and psychopathology (for review Deary et al., 2021;Harden, 2021;Sprooten et al., 2021), the causal chains linking To set the stage for the mediation analyses, I first conducted a series of analyses described in papers 1 to 5: In papers 1 and 2, we identified the methods that should be used to tease apart regional from global cerebral effects and we controlled for typical confounds (i.e., sex, age). In papers 3, 4, and 5, we created phenotypic and genetic measures of general cognition and psychopathology. At the end of paper 5 and in paper 6, we examined the extent to which cerebral measures mediate additive genetic and environmental effects on psychopathology and general cognition, respectively.

After going over the major contributions of these individual studies, I provide future directions for studies interested in understanding what and how environmental, genetic, and neural factors influence general cognition and psychopathology.

Factors influencing Brain Anatomy

In papers 1 and 2, we examined how global brain size should be taken into account when investigating regional cerebral effects. Studying regional effects without adjusting for global measures provides insights into the regions associated with a trait but does not tell us whether this association is due to global versus region-specific effects. By adjusting for global effects, we test whether a region contributes to a trait independently of global brain size.

We specifically tested how different types of adjustment techniques influence the significance and magnitude of reported group differences. By taking the case of sex differences and examining other factors known to influence brain size, such as age, we also shed a light on the debated sex and age differences across regional measures in the brain.

1.1.Individual Differences in Global Brain Size

Paper 1 further supports that brain allometry is an inherent property of the brain [START_REF] Mankiw | Allometric Analysis Detects Brain Size-Independent Effects of Sex and Sex Chromosome Complement on Human Cerebellar Organization[END_REF][START_REF] Reardon | Normative brain size variation and brain shape diversity in humans[END_REF][START_REF] Toro | Brain volumes and Val66Met polymorphism of the BDNF gene: Local or global effects?[END_REF]. In line with previous studies [START_REF] Reardon | An Allometric Analysis of Sex and Sex Chromosome Dosage Effects on Subcortical Anatomy in Humans[END_REF][START_REF] Sanchis-Segura | Sex differences in gray matter volume: How many and how large are they really?[END_REF][START_REF] Williams | Adjusting for allometric scaling in ABIDE I challenges subcortical volume differences in autism spectrum disorder[END_REF], there were some differences in the reported magnitude and size of the group differences when omitting brain allometry. However, adjusting for global brain size by adding the global measure as covariate in linear regression models did not have a large impact on the significance and magnitude of reported sex and age effects or interactions. In contrast, the proportion method, where a region is divided by its global measure to create an adjusted regional measure, did not sufficiently adjust for global brain size: It led to erroneous group differences in regional structure by ignoring the intercept of the relationship between regional and global brain size. Although there are other, less common, methods of global brain size adjustments that we did not explore [START_REF] Sanchis-Segura | Sex differences in gray matter volume: How many and how large are they really?[END_REF], our findings extend to some of these methods: If these methods consider the intercept and slope of the association between a region and its global measure, they should yield similar results to the linear covariate and allometric adjustment.

1.2.Sex and Age Effects

While it is widely accepted that adjusting for differences in body size, and by proxy TBV, attenuates and sometimes even cancels out observed sex differences across brain regions (for review [START_REF] Eliot | Dump the "dimorphism": Comprehensive synthesis of human brain studies reveals few male-female differences beyond size[END_REF], the regions that significantly differ between sexes after controlling for brain size are still debated. Conflicting results stem from a variety of reasons, including limited sample size, differences in MRI acquisition parameters, segmentation atlases, sample age, and adjustments for brain size (as highlighted by the previous section).

A recent literature review of the cerebral sex differences across anatomical and connectivity studies concluded that most sex differences were attributable to differences in body size [START_REF] Eliot | Dump the "dimorphism": Comprehensive synthesis of human brain studies reveals few male-female differences beyond size[END_REF]. In light of our findings in the first paper, we replied with a commentary and argued the contrary: Sex differences are not merely attributable to differences in body size because TBV differed between men and women after controlling for weight and height, and regional measures differed between sexes after controlling for global brain size.

Although the review correctly points out that current results are largely inconsistent, it is not sufficient to say that sex differences in brain regions are reduced to body size. Considering that the conclusions were largely based on underpowered studies, that only the significance of the regions was compared, and that comparisons were done across studies using different segmentation techniques, we believe that the authors of the review did not have sufficient evidence to claim that sex differences are an artifact of variations in body size.

Papers 1 and 2 are not the only large-scale studies reporting sex differences. When comparing our results to previous studies [START_REF] Peyre | Neuroanatomy of dyslexia: An allometric approach[END_REF]Ritchie et al., 2018;[START_REF] Sanchis-Segura | Sex differences in gray matter volume: How many and how large are they really?[END_REF] and conducting similar analyses on different segmentations to remove the bias of using different segmentations, we find some largely consistent patterns even when using different segmentations, sampling age range, and adjustments for global measures. However, the cross-sectional nature of our study implies that some age-related changes and sex differences we report may be specific to our sample. Age-related changes in cerebral measures can be better measured using longitudinal data and growth curve modeling, which explicitly models changes over time and quantifies both group-level and individual-level differences [START_REF] Curran | Twelve Frequently Asked Questions About Growth Curve Modeling[END_REF].

Finally, regions exhibiting sex differences may in part explain sex differences in cognition or pathology. Although sex differences in cognition only occur on subtests and tend to be small [START_REF] Jäncke | Sex/gender differences in cognition, neurophysiology, and neuroanatomy[END_REF], one study found that about 99% of the modest sex difference in verbal numerical reasoning was mediated by volumetric and surface brain measures and that cortical thickness had a trivial mediating effect (Ritchie et al., 2018). As for psychopathology, there are marked sex differences in the prevalence and clinical manifestations of mental health disorders [START_REF] Mccarthy | Neuroimmunology and neuroepigenetics in the establishment of sex differences in the brain[END_REF] and there is evidence that differential risk for psychiatric disorders between sexes likely stems from sex differences in maturing brain circuitry (for review Kaczkurkin et al., 2019). Yet, there are still conflicting results regarding the association between sex differences in the brain and sex differences in cognition and psychopathology.

Therefore, more research on the regions associated with sex differences in behavior is needed to better understand the mechanisms underlying sex differences in behavior.

Creating an Index of General Intelligence: Purpose and Limitations

In chapter 3, we created a general intelligence measure (g-factor) for UK Biobank participants that is in part adjusted for sampling bias using UK National 2001 Census data.

Although past studies also created a g-factor for the UK Biobank and looked at the genetic effects underlying the g-factor, the creation of the g-factor was done with two goals in mind.

The first goal was to create a g-factor PGS for individuals in the UK Biobank with neuroimaging data. Since previous intelligence or cognitive performance GWAS results included UK Biobank participants, we had to create a g-factor and performed our own g-factor GWAS that excluded our target population (individuals with neuroimaging data) to obtain unbiased PGSs.

The second goal was to create an intelligence measure that is relative to the UK population to accurately classify UK Biobank individuals as having an average versus a high IQ. This was done because the UK Biobank sample tends to have better occupations, higher SES, and thus, in turn, have a higher IQ. We note that our adjustment using occupational status was only partial, as we did not have access to the safeguarded census qualification data by age group, sex, and country.

In the future, we could test the efficiency of our adjustment technique by comparing the intelligence score we created to an intelligence score adjusted for sampling bias using recently created weights [START_REF] Alten | Reweighting the UK Biobank to reflect its underlying sampling population substantially reduces pervasive selection bias due to volunteering[END_REF] that exploited multiple social and economic variables available both in the UK Biobank and safeguarded census data. However, this study's weights

have not yet been returned to the UK Biobank and their code requires the geographical coordinates of the UK Biobank participants, which were not available to us. Although imperfect, our current adjustment shows that 6% of UK Biobank participants have a reliable gfactor in the high IQ group, which is much higher than the expected 2% in the population, suggesting that the adjustment was efficient even if it was only partial.

The g-factor PGS created from the No Neuroanatomy GWAS explained 7.6% of the variance in the g-factor. Although it is less than the 10% reported by Lee and colleagues (2018), who had a larger discovery sample and used MTAG, our PGS remains a good predictor of the g-factor. The decrease from 7.5% to 4.2% after controlling for family effects (Full GWAS vs.

No Family Full GWAS) is consistent with previous studies showing that phenotypes that are sensitive to demographic and indirect genetic effects, such as educational attainment, have more biased estimates in population-based studies than in family-based studies. This particularly true for phenotypes that are more sensitive to demographic and indirect genetic effects (Howe et al., 2021). One way to control for demography and indirect effects is to conduct within-family GWAS -where mean genotype across a sibship is added as a covariate that reflects the association between the genotype and the outcome that is due to parents.

However, in light of the limited availability of family data and homozygosity within families, population GWAS samples of unrelated individuals currently remain the optimal solution to maximize statistical power for the discovery of trait and genetic associations (Howe et al., 2021).

Creating Indices of General Psychopathology: Purpose and Limitations

We combined ordinal, continuous, and binary measures collected at different time points, that were either hospital diagnoses, self-report professional diagnoses, or probable diagnoses from mental health questionnaires in the UK Biobank to create binary mental health disorder diagnoses for a maximum number of participants in the UK Biobank. This was done (i) to examine the difference in prevalence between Average and High IQ groups across mental health disorders and (ii) to increase the power of the discovery GWASs of mental health disorders used to derive PGSs of psychopathology.

In paper 4, we examined differences in the prevalence of mental health disorders between individuals with a high (g-factor 2 SD above mean) versus average IQ (g-factor 2 SD within mean). We found that high intelligence is not a risk factor for mental health disorders. If anything, individuals with a high IQ had a lower risk of experiencing anxiety disorders, PTSD, and trauma compared to individuals with an average IQ. Because the UK Biobank tends to be healthier than the general population (Fry et al., 2017), the prevalence and odds ratios reported in the UK biobank may differ from the UK population (Keyes & Westreich, 2019). However, this should not affect our estimations of the difference in prevalence between high and average IQ groups since the phenotypes were created with the same criterion for the high and average IQ groups.

In paper 5, we examined the genetic and phenotypic structure of psychopathology and created phenotypic and genetic general psychopathology factors for UK Biobank participants.

The phenotypic and genetic analyses suggest that the correlated factors model and the hierarchical model were the best fitting models. We calculated PGSs for the latent variables of the Correlated Factors model instead of latent variables of the hierarchical model because the former was the most parsimonious model and because the utility of the P-factor is debated (Grotzinger et al., 2022;Mallard et al., 2022).

The Internalizing Disorder PGS and the Thought Disorder PGS predicted 2.7% and 2.6%

of the variance of their respective latent factors. In contrast, the Hazardous Substance Use or Dependence PGS only explained 0.3% of the variance in Hazardous Substance Use or Dependence because the GWAS for this factor was largely underpowered. Although a previous study found that the genetic P-factor has a heterogeneous signal (i.e., very few SNPs operated via the P-factor; Grotzinger et al., 2022), the P-factor PGS may be a better predictor of the Hazardous Substance Use or Dependence factor than its respective PGS for two reasons: First, the P-factor PGS would be derived from a well-powered GWAS and second, it is not a given that our P-factor would also have a heterogenous signal since the psychopathology model structure we applied to our genetic data differs from previous genetic studies. Finally, our exploratory factor analyses on the genetic data add to the emerging literature (Grotzinger et al., 2022;Mallard et al., 2022) reporting that the phenotypic model structure differs from the genetic structure of psychopathology.

By using minimal phenotyping (such as self-report symptoms, or medical diagnoses) to create our mental health disorder diagnoses and performing GWAS on these diagnoses, our UK Biobank GWASs' signal may have low specificity (Cai et al., 2020). To address this issue, we meta-analyzed our GWAS results with those from previous studies using clinical diagnoses by mental health professionals when possible. Although our signal may be biased compared to studies using clinical diagnoses or symptomatology scales, sensitivity analyses of a recent large-scale study examining the underlying genetic structure of psychopathology across 11 mental health phenotypes revealed that excluding GWASs that used self-report cohorts led to minimal changes in discovery (Grotzinger et al., 2022).

Mediation Models: Current Conclusions

In the 6 th paper, we find that the effects of the g-factor PGS and childhood adversity on the g-factor were mainly mediated by global brain volume and surface area: The percentage mediated by global volumes and total surface area was 10-15 times larger than that of regional volumes, surface areas, or mean thicknesses. Although larger brains are considered to have more neurons [START_REF] Hou | Age-related degeneration of corpus callosum in the 90+ years measured with stereology[END_REF] and differences in cortical thickness can lead to variations in neural density or columnar arrangement [START_REF] La Fougère | Where in-vivo imaging meets cytoarchitectonics: The relationship between cortical thickness and neuronal density measured with high-resolution [18F]flumazenil-PET[END_REF], macroscopic properties are limited in their ability to inform on microstructural changes in the brain.

Therefore, large-scale studies with out-of-sample predictions and new methods linking micro to macro-structure are needed to understand how brain anatomy is associated with intelligence (for recommendations see Deary et al., 2021).

At the end of the 5 th paper, we run preliminary mediation analyses with TBV to exemplify the utility of our phenotypic and genotypic measures of psychopathology in the UK Biobank The mediation analyses revealed that TBV mediated about 1% of the effect of childhood adversity on Hazardous Substance Use or Dependence. In line with previous research, childhood adversity was a major predictor of Hazardous Substance Use or Dependence (Adams et al., 2018;[START_REF] Copeland | Association of Childhood Trauma Exposure With Adult Psychiatric Disorders and Functional Outcomes[END_REF], explaining on its own 8% of the variance in Hazardous Substance Use or Dependence. To better understand how childhood adversity predicts pathology, we plan on identifying the global and regional measures mediating the effects of childhood adversity on Hazardous Substance Use or Dependence as well as those associated with Internalizing and Thought Disorders.

Although TBV mediated genetic or environmental predictors of intelligence and psychopathology, TBV only mediated 7% of the g-factor PGS's effect on the g-factor and only mediated 1% of childhood adversity's effect on Hazardous Substance Use or Dependence.

These results suggest that about 93% of the g-factor PGS's effect on the g-factor and 99% of childhood adversity's effect on Hazardous Substance Use or Dependence remains to be explained. Therefore, future studies should include additional cerebral measures to better understand the underlying mechanisms by which environmental and genetic influences act on intelligence and psychopathology.

Future Directions

Throughout the dissertation, we focused on structural measures because neuroanatomical measures that reflect early brain organization are more likely to be closer to genes in the causal chains than functional activation. However, we only examined volumes, mean thicknesses, and surface areas as potential mediators of genetic and environmental effects on general intelligence and psychopathology. Since studies report that cerebral asymmetries are associated with intelligence [START_REF] Moodie | Fluctuating asymmetry in brain structure and general intelligence in 73-year-olds[END_REF] or with some [START_REF] Cao | Mapping cortical and subcortical asymmetries in substance dependence: Findings from the ENIGMA Addiction Working Group[END_REF][START_REF] Schijven | Large-scale analysis of structural brain asymmetries in schizophrenia via the ENIGMA consortium[END_REF] but not all (de Kovel et al., 2019) mental health disorders, future studies should examine whether brain asymmetries mediate environmental and genetic effects on general intelligence and on some general measures of psychopathology. In light of studies reporting an association between white matter measures and general intelligence (Cox et al., 2019b) or general measures of psychopathology [START_REF] Hinton | White matter microstructure correlates of general and specific second-order factors of psychopathology[END_REF], white matter connectivity between regions should also be included in future mediation studies. Both grey matter volumes and white matter indices, such as fractional anisotropy, could be combined in different networks of functional significance (e.g., P-FIT Network, default-mode Network; [START_REF] Madole | Aging-Sensitive Networks Within the Human Structural Connectome Are Implicated in Late-Life Cognitive Declines[END_REF], enabling the study of brain-cognition and brain-psychopathology associations at the structural network level.

Other studies have used resting-state or task-based functional MRI data to study individual differences in cognition [START_REF] Dubois | A distributed brain network predicts general intelligence from resting-state human neuroimaging data[END_REF][START_REF] Lohmann | Predicting intelligence from fMRI data of the human brain in a few minutes of scan time[END_REF][START_REF] Saxe | Brain entropy and human intelligence: A resting-state fMRI study[END_REF] and psychopathology [START_REF] Alnaes | Patterns of sociocognitive stratification and perinatal risk in the child brain[END_REF][START_REF] Smith | A positivenegative mode of population covariation links brain connectivity, demographics and behavior[END_REF]. For instance, a recent study in the Adolescent Brain Cognitive Development (ABCD) study examining the association between the p-factor and functional-connectivity patterns across the whole connectome of 9-and 10-year-old kids. The authors found that the p-factor is associated with altered connectivity patterns in the networks associated with the generation of spontaneous thought (e.g., defaultmode network) and in those associated with cognitive control (e.g., frontoparietal network, cingulo-opercular network; [START_REF] Sripada | Widespread attenuating changes in brain connectivity associated with the general factor of psychopathology in 9-and 10-year olds[END_REF]. Ideally, future models should include both functional and structural connectivity because their correspondence is not perfect: at best functional and structural connectivity are correlated at 0.5 [START_REF] Honey | Predicting human resting-state functional connectivity from structural connectivity[END_REF]for review Suárez et al., 2020;[START_REF] Zimmermann | Unique Mapping of Structural and Functional Connectivity on Cognition[END_REF].

However, combining structural and functional data does not always increase outcome prediction. A recent study using functional and structural neuroimaging data to predict Autism Spectrum Disorder (ASD) found that functional MRI was more important for prediction accuracy than structure and that adding structural measures, age and sex barely increased prediction (Traut et al., 2022). To understand whether this trend is specific to ASD or extends to general cognition and psychopathology, future research should examine the relative and combined contribution of structural and functional data to cognition and psychopathology. This research will shed a light on the brain measures that should be included in mediation models with genetic and environmental effects and has implications for creating biomarkers of cognitive deficits or psychopathology (Traut et al., 2022).

Although macroscopic level data reveals the regions and connectivities associated with a trait, numerous efforts are being made to understand how these associations translate at the cytoarchitectonic, molecular, and synaptic levels. For instance, GWAS results provide some insight into the biological mechanisms of intelligence and psychopathology. SNP associations with intelligence have been linked to genes expressed in specific classes of neurons across cerebral regions, such as pyramidal cells in the CA1 of the hippocampus [START_REF] Coleman | Biological annotation of genetic loci associated with intelligence in a meta-analysis of 87,740 individuals[END_REF][START_REF] Hill | What genome-wide association studies reveal about the association between intelligence and mental health[END_REF]Savage et al., 2018). Animal models can also be used to identify how environmental and genetic factors act on the architecture of the brain and lead to behavioral changes. For example, early life stressors are thought to influence anxiety-like behaviors by modifying the cytoarchitecture and transcriptome of the prefrontal cortex in adolescent mice [START_REF] Usui | Early Life Stress Alters Gene Expression and Cytoarchitecture in the Prefrontal Cortex Leading to Social Impairment and Increased Anxiety[END_REF]. Moreover, novel brain network techniques integrating multi-modal imaging data have been shown to capture known cortical cytoarchitecture and related gene expression, and individual differences in these networks have been linked to individual differences in intelligence [START_REF] Seidlitz | Morphometric Similarity Networks Detect Microscale Cortical Organization and Predict Inter-Individual Cognitive Variation[END_REF]. To understand the factors and the complex mechanisms underlying general cognition and psychopathology, researchers must not only integrate multimodal imaging techniques, obtain better genetic measures, and include more environmental predictors, but also must integrate epigenetic, transcriptomic, proteomic, and histological results (for review with intelligence Deary et al., 2021).

Conclusion

The goal of this dissertation was to examine the neuroanatomical mediators of genetic and environmental effects on cognition and mental health disorders. We find that the g-factor PGS and childhood adversity's effect on the g-factor are mainly mediated by global neuroanatomical measures and that childhood adversity's effects on the Hazardous Substance Use or Dependence factor are slightly) mediated by TBV. However, these global cerebral measures explain less than 10% of the PGSs' on the g-factor and less than 1-3% of Childhood Adversity's effect on cognitive and psychopathology factors. Therefore, future studies must consider additional cerebral measures, as mediators of genetic and environmental effects on general intelligence and psychopathology measures, as well as better genetic and environmental predictors.

The present dissertation also highlights, with each of its papers, the complex steps required to conduct multi-disciplinary analyses aimed at understanding the neural, genetic, and environmental effects on general cognition and psychopathology. With the present dissertation and my future work, I hope to significantly contribute to our understanding of the complex effects and interactions of environmental, genetic, and neural factors on cognition and psychopathology.

Figure B1 .

 B1 Figure B1. Principal Component Analysis and Confirmatory Factor Analysis. F: Latent Factor. Y: Observed variable. W: weight. b: regression or correlation coefficient. U: variance in Y not captured by the latent factor. [End of Box]

Figure 1 .

 1 Figure 1. Psychopathology Factor Models. Circles: Latent Variables. Square: Observed variables. Lines can correspond to raw or standardized estimates.

  examined the predictive power of the psychopathology factors between 4 and 8 years old (N= 3,654 to 6,201) on English and Math GCSE scores at age 16, depression and anxiety at age 18, and well-being, criminal activity, and alcohol use at age 21. The general psychopathology factor of a bifactor model in young children was associated with developing depressive disorders (β = 0.12), lower wellbeing (β = -0.06), and failing in mathematics or English GCSE at 16 years (β = -0.24, β = -0.26, respectively). The internalizing factor from the correlated factors model and the bifactor model were similarly negatively associated with well-being (β = -0.10 and β = -0.09, respectively), whereas the externalizing factors from the correlated factors model and the bifactor model were negatively associated with English GCSE at 16 years (β = -0.38 and β = -0.08, respectively;

  Figure B2. Examples of the Three types of Gene by Environment Correlations (rGE).Figure and examples adapted from Jaffee & Price (2007) and Knafo & Jaffee (2013).

Figure B3. 1 .

 1 Figure B3.1. Identification of genetic variants as a function of the strength of the genetic effect and risk allele frequency. Effect Size: Odds ratio. Adapted from Figure 1. of Manolio and colleagues (2009).

  environmental data. One longitudinal study of 551 adolescents used SES and the EA PGS to disentangle the genetic and environmental associations with brain development and cognition. They found that while SES and the EA PGS predicted global surface area (SES β= 0.18, PGS β =0.12) and working memory performance (SES β = 0.23, PGS β =0.11) at 14 years old, only SES predicted the change in global surface area between 14 and 19 years old (β = -0.15) and only the EA PGS explained the change in WM between 14 and 19 years old (β =-0.27).

  ability to learn, reason and solve problems(Arvey et al., 1994) -has

  cognitive tests in the UK Biobank difficult. First, not all participants completed the same number of tests and more recent tests have fewer participants (e.g., word production) because only a subset of participants returned to the test centers or participated in the online follow-up questionnaire to complete more tests when asked. Second, those who completed the same number of tests did not necessarily complete the same combination of tests. Across 501,650 participants with data on at least one of the eight cognitive tests, we counted 80 different combinations of tests, with only 30,471 participants having usable data on all eight tests. Third, the age at which a test was completed varies by test and participant, with some participants completing a test as early as 38 years old and as late as 82 years old. Fourth, some participants completed certain tests several times. Finally, some tests or similar tests with slight variations (e.g., 14 instead of 13 questions for Fluid Intelligence) were completed at different locations:

Figure 1 .

 1 Figure 1. G factor Creation Pipeline. Cylinders represent datasets; inputs are UK Biobank and UK Census data (2001); blue cylinders are subsets of data (standardization samples).

  could complete several cognitive tests every time they visited the UK Biobank assessment centers (category 100026) and during the online follow-up (category 116).

4 .

 4 If we include participants with a poor g factor measure (r < .7), are the genetic correlation and heritabilities similar? Using the GWAS described above, we conducted a GWAS on 307,009 individuals with a g factor measure and without neuroimaging data or twins/siblings with neuroimaging data (Low Quality No Neuroimaging g factor GWAS). If the genetic correlation and heritabilities were similar or better for this Low g Quality GWAS compared to the No Neuroimaging GWAS, we should be able to use this larger sample size to obtain more lead SNPs and better polygenic predictions. 2.5.3. Testing Validity: Correlations with Alternative estimates of g, Life outcomes, Neuroimaging, and Genetic Measures

Figure 2 .

 2 Figure 2. The Distribution of Cognitive Tests Before (blue) and After (orange) correcting for Sociodemographic Differences between the UK Biobank Population and the UK Population (2001 Census). FI: Fluid Intelligence. RT: Reaction Time. MAT: Matrix Pattern Completion. TWR: Tower Rearranging. MEMN: Numeric Memory. MEMS: Pair Matching. SDS: Symbol Digit Substitution. TMT: Trail Making.

  fit on 501,650 participants[START_REF] Stankov | Low Correlations between Intelligence and Big Five Personality Traits: Need to Broaden the Domain of Personality[END_REF]307 with complete data; N Women = 272,955; N Men = 228,695) was good (CFI = 0.955, TLI = 0.938, RMSEA = 0.024, SRMR = 0.028). The g factor accounted for 29% of the variance across cognitive tests and the loadings ranged from 0.77 (TMT) to 0.277 (RT) (Figure3; Supplemental Section 2.1.3). Sex differences in cognitive and g factor scores are available in Supplemental Section 2.1.4.

Figure 3 .

 3 Figure 3. Confirmatory Factor Analysis of UK Biobank Cognitive Tests. Analyses were conducted with full information maximum likelihood with the lavaan package (Rosseel et al., 2021). Explained variance: 29%. FI: Fluid Intelligence. MAT: Matrix Pattern Completion. TWR: Tower Rearranging. MEMN: Numeric Memory. MEMS: Pair Matching. SDS: Symbol Digit Substitution. TMT: Trail Making. Loadings from completely standardized solutions (i.e., standardized observed and latent variables).

Figure 4 .

 4 Figure 4. The Distribution of the g Factor Scores Before and After Census Correction for All Participants (left) and a Subset of Participants (right). The subset of participants had a g factor score from a combination of subtests that allowed for a minimum correlation of 0.70 between the partial g factor score and the full g factor score.

3. 3 .

 3 Analysis of Individuals with a g Factor Quality over 0.70 3.3.1. Correlations: Alternative g factors and Life outcomes

4 .

 4 Do participants with a low-quality g factor estimate (r < .7) impact the results? We found that the heritability of the Low-Quality No Neuroimaging GWAS (h2 = 0.127, SE = 0.005) was much lower than the heritability of the No Neuroimaging GWAS (h2 = 0.197, SE = 0.008; TableS10) and that the genetic correlation between the Low-Quality No Neuroimaging GWAS and the No Neuroimaging GWAS was of 0.98 (FigureS10), suggesting that although both GWASs are measuring overlapping genetic effects, the Low-Quality No Neuroimaging GWAS has more measurement error. The genetic correlations of the Low-Quality No Neuroimaging GWAS were lower with Lee's g factor (0.87 vs. 0.93) and EA (0.5 vs. 0.55), suggesting that doubling the sample size by including g factor estimates of lower quality is counterproductive for the GWAS. 3.3.3. Correlations: Alternative g factors, Life outcomes, Neuroimaging, and Genetic

Figure 6 .

 6 Figure 6. Correlation between age and sex-adjusted G Factor Scores, selected Life and Health Outcomes, Total Brain Volume (TBV), and sex and year of birth adjusted Polygenic Scores (PGSs). Pearson correlation coefficients were estimated on 13,085 British individuals without missing data without first-or second-degree cousins and parent offspring. We included all life and health variables with an r > or = 0.1 with g except for the Townsend Deprivation Index. CFA: Confirmatory Factor Analysis. PC1: 1st Principal Component. G: General Factor for intelligence. G corresponds to the g factor of individuals with a combination of cognitive tests that allowed for a correlation of 0.70 or higher between their actual g factor and what their g factor would have been if they had completed all tests. FI: Fluid Intelligence. Income: Income before tax. PGSs were adjusted for sex and birth year (yr birth).

  similarly found that their Cognitive Performance PGS explained 7% of the variance in Cognitive Performance for individuals in the Wisconsin Longitudinal Study, a study that used cognitive tests with similar properties to their discovery GWAS. However, they found that the Cognitive Performance PGS from the summary statistics of their multi-trait analysis GWAS (MTAG) of CP yielded more significant SNPs and thus, explained 9.7% of the variance in CP for individuals in the Wisconsin Longitudinal Study. Although the MTAG summary statistics may explain more variance in g, these summary statistics cannot be applied to the UK Biobank individuals with neuroimaging data because they were included in the discovery GWAS.

  In a previous paper[START_REF] Williams | A General Cognitive Ability Factor for the UK Biobank[END_REF], we calculated g-factor scores for individuals in the UK Biobank who completed at least one of the following tests: Fluid Intelligence, Matrix Pattern Completion, Tower Rearranging, Numeric Memory, Pairs Matching, Symbol Digit Substitution, Reaction Time, and Trail Making. Cognitive tests were adjusted for age and standardized using the occupational data from the 2001 census to obtain a g-Factor score relative to the general population in the UK.

Equation 1 :

 1 𝑃𝑃ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 = 𝛽𝛽0 + 𝛽𝛽1 * 𝑎𝑎𝑎𝑎𝑒𝑒 + 𝛽𝛽2 * 𝑎𝑎𝑎𝑎𝑒𝑒 2 + 𝛽𝛽3 * 𝑠𝑠𝑒𝑒𝑠𝑠 + 𝛽𝛽4 * 𝐶𝐶𝐶𝐶 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 + 𝛽𝛽5 * 𝑎𝑎𝑎𝑎𝑒𝑒 * 𝑠𝑠𝑒𝑒𝑠𝑠 + 𝛽𝛽6 * 𝑎𝑎𝑎𝑎𝑒𝑒 2 * 𝑠𝑠𝑒𝑒𝑠𝑠 + 𝛽𝛽7 * 𝑠𝑠𝑒𝑒𝑠𝑠 * 𝐶𝐶𝐶𝐶 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 + 𝛽𝛽8 * 𝑎𝑎𝑎𝑎𝑒𝑒 * 𝐶𝐶𝐶𝐶 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 + 𝛽𝛽9 * 𝑎𝑎𝑎𝑎𝑒𝑒 2 * 𝐶𝐶𝐶𝐶 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 + 𝛽𝛽10 * 𝑎𝑎𝑎𝑎𝑒𝑒 * 𝑠𝑠𝑒𝑒𝑠𝑠 * 𝐶𝐶𝐶𝐶 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 + 𝛽𝛽11 * 𝑎𝑎𝑎𝑎𝑒𝑒 2 * 𝑠𝑠𝑒𝑒𝑠𝑠 * 𝐶𝐶𝐶𝐶 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 We report results with the g-factor group predictor that survived a Bonferroni correction of 0.05 divided by the number of coefficients in the equation with the g-factor group term times the number of coefficients of interest times the number of investigated phenotypes (e.g., 0.05/ (6*32) for equation

Fig 1 .

 1 Fig 1. Group Differences in Prevalence between High and Average and Low and Average gfactor Groups across Phenotypes and Scores. OCD: Obsessive-Compulsive Disorder; PTSD: Post-Traumatic Stress Disorder. Correction for multiple comparisons varies by phenotype. See

  on a general psychopathology factor -capturing common variance across all MHDs -and on the other hand on several orthogonal latent factors -capturing variance specific to a subset of MHDs. These latter factors are typically referred to as residualized Internalizing, Externalizing, and Thought Disorders factors. Substance use disorders, antisocial disorders, and personality disorders tend to load on the Externalizing factor, whereas depression, anxiety, and eating disorders load on the Internalizing factor, and schizophrenia and bipolar disorder load on the Thought Disorders factor.

  Figure 1. Methods Flowchart. Numbers under the boxes correspond to their respective methods section in the text. SNP: Single Nucleotide Polymorphism. SEM: Structural Equation Modelling. PC1: 1st principal component. CFA: Confirmatory Factor Analysis. EFA: Exploratory Factor Analysis. MHD: Mental Health Disorders. GWAS: Genome-Wide Association Study. PGS: Polygenic Score. UKB: UK Biobank. R packages used for the analyses are in italics.

  fitted 4 CFA models based on the EFA results: (1) a model where all MHDs loaded on a single p-factor, (2) a bifactor model where the p-factor, Internalizing, Hazardous Substance Use or Dependence (our Externalizing factor), and Thought Disorders factors were orthogonal, (3) a hierarchical model where MHDs loaded onto either Internalizing, Externalizing, and Thought Disorders Factors, which then loaded onto the p-factor, and (4) a correlated factors model where MHDs either loaded on the Internalizing, the Hazardous Substance Use or Dependence or the Thought Disorders factor, which were correlated.

Figure 2 .

 2 Figure 2. Phenotypic and Genetic Psychopathology Models across 10 Mental Health Disorders. Haz. Use or Dep.: Hazardous Use or Dependence. OCD: Obsessive-Compulsive Disorder. PTSD: Post-traumatic stress disorder.

  factor, and 84 genetic correlations for the Hazardous Substance Use or Dependence factor (Figure 4; Figures S4-9 for all phenotypes; Supplemental Tables G). All factors were genetically correlated with the psychiatric cross-disorder summary statistics after correction for multiple comparisons (p < 0.05/N, the number of genetic correlations investigated by factor). The Hazardous Substance Use or Dependence factor genetically correlated positively with Cannabis Use Disorder at p < 0.001 but not after multiple comparison corrections and the internalizing factor genetically correlated positively with Neuroticism (convergent validity). The Internalizing and the Thought Disorders factors were not correlated with the Cannabis use disorder (iPsych) traits, and the Thought Disorders factor weakly correlated with the Neuroticism trait (discriminant validity).

Figure 4 .

 4 Figure 4. Genetic correlations (rg) estimates between the Internalizing Disorders, Hazardous Substance (Haz.) Use or Dependence (Dep.), and Thought Disorders factors and a Subset of Phenotypes selected to establish Convergent and Discriminant Validity. Error bars represent 95% confidence intervals (CIs) centered on the rg estimate, computed as 1.96 times the s.e. ** significant after adjusting for multiple comparisons: p <0.05/82 for internalizing, p < 0.05/84 for Sub Haz. Use Dep, and p < 0.05/89 for Thought Disorders. * p < 0.001.

Figure 5 .

 5 Figure 5. Genetically Informed Correlated Factors Model of Psychopathology across 10 Mental Health Disorders. Haz. Use or Dep.: Hazardous Use or Dependence. OCD: Obsessive-Compulsive Disorder. PTSD: Post-traumatic stress disorder. Estimates when latent variables are standardized.

Figure 6 .

 6 Figure 6. Mediation Models with the Hazardous Substance (Haz.) Use or Dependence (Dep.) Polygenic Score (PGS), Total Brian Volume (TBV) on the Hazardous Substance Use or Dependence factor from the Phenotypic Model without (A) and with (B) Childhood Adversity. ***p < 0.001, **p<0.01, *p<0.05. Red: Mediation path is significant at p < 0.01. Covariate coefficients are not shown for clarity but are available in Supplemental Tables J.

  factor PGS, the three PGSs from the Correlated Factors Model, or the Hazardous Substance Use or Dependence PGS, explain the most variance in the Hazardous Substance Use or Dependence factor. Nonetheless, the genetic correlations indicate that the Hazardous Substance Use or Dependence factor captures genetic variance expected to correlate with external phenotypes associated with substance use.

  This preliminary study aimed to (i) examine the phenotypic and genetic structure of psychopathology in the UK Biobank, (ii) provide polygenic scores of psychopathology factors for UK Biobank participants with neuroimaging data (N = 26,610), and also (iii) examine the extent to which global cerebral measures (TBV for now) mediate genetic (PGS) and environmental (childhood adversity) effects on psychopathology. By providing phenotypic and genetic psychopathology measures in the UK Biobank, we contribute to the understanding of Part 3: Mediators of Environmental and Genetic factors on General Cognition

  444 cortical regions (148 volumes, 148 surface areas, and 148 cortical thicknesses) from the Freesurfer a2009s segmentations (Destrieux Atlas, data-field 197), 116 whole segmentations and subsegmentations of the amygdala, hippocampus, and thalamus and subsegmentations of the brainstem (Freesurfer subsegmentations, data-field 191), 28 cerebellum GMV segmentations from the FAST segmentations (data-field 1101), and 32 subcortical, white matter, and ventricle volumes from the Freesurfer ASEG segmentations (data-field 190).

Figure 1 .

 1 Figure 1. Meditating effect of global cerebral measures on the g-factor PGS's effect on the gfactor with and without including Childhood Adversity. g-factor: general intelligence factor. PGS: polygenetic scores. Coefficients correspond to direct effects. Fit of TBV Models: CFI = 1.00, SRMR= 0.00, RMSEA = 0.00. Fit of Global Measures Model: CFI = 1.00, SRMR= 0.01, RMSEA = 0.03. The PGS is adjusted for birth year and the 1 st 40 principal components of the genotyped data. Cerebral measures and the g-factor are adjusted for sex, age, age 2 , age by sex, age 2 by sex, and scanner site.

Figure 2 .

 2 Figure 2. Standardized (Std) Estimate of a Region's association with the g-factor with (pink) and without (blue) adjusting for a Global Measure. Each point corresponds to a region. Region names are not shown for clarity. Global Measure: Total Brain Volume for volumes. Total Surface Area for surface areas. Total Mean Cortical Thickness for thicknesses.

Figure 3 .

 3 Figure 3. Meditating effect of regional cerebral measures on the g-factor PGS's effect on the g-factor with and without including Childhood Adversity. g-factor: general intelligence factor. PGS: polygenetic scores. Coefficients correspond to direct effects. Fit of volume and surface area models: CFI = 1.00, SRMR= 0.00, RMSEA = 0.00. Fit of mean thickness model without Childhood Adversity: CFI = 0.95, SRMR= 0.05, RMSEA = 0.15, and with CFI = 0.95, SRMR= 0.05, RMSEA = 0.14. The PGS is adjusted for birth year and the 1 st 40 principal components of the genotyped data. Cerebral measures and the g-factor are adjusted for sex, age, age 2 , age by sex, age 2 by sex, and scanner site.

  genetic and environmental factors to behavior are long, indirect, and effect sizes are small. More proximal factors, such as the brain, collect both genetic and environmental influences and contribute to individual differences in cognition and psychopathology. Therefore, studying the causes and mechanisms by which these genetic and environmental factors influence the brain should in fine shed a light on interindividual differences in life outcomes. And yet, few studies have simultaneously examined the effects of neural, environmental, and genetic factors on cognition or psychopathology. The aim of this dissertation was therefore to examine the extent to which neuroanatomical measures mediate the effects that genes and the environment have on cognition and psychopathology in the UK Biobank.

  to study neural, genetic, and environmental influences on psychopathology. Although TBV was associated with the Hazardous Substance Use or Dependence factor but not Internalizing or Thought Disorder factors, TBV was not a significant mediator of the Hazardous Substance Use or Dependence PGS's effect on the Hazardous Substance Use or Dependence. In other words, the little effect (0.3%) of the Hazardous Substance Use or Dependence PGS on Hazardous Substance Use or Dependence does not act on brain size. Although TBV could mediate the effect of a more predictive PGS on Hazardous Substance Use or Dependence, reports of a null genetic correlation between brain size and alcoholic drinks per week[START_REF] Jansen | Genome-wide meta-analysis of brain volume identifies genomic loci and genes shared with intelligence[END_REF] suggest that genetic predispositions for Hazardous Substance Use or Dependence may not influence global brain size but may act on other cerebral properties.

  UK Biobank is an open-access large prospective study with phenotypic, genotypic, and neuroimaging data from more than 500,000 participants. Participants were recruited between 2006 and 2010, from the vicinity of 22 assessment centers in England, Wales, and

	Scotland, with an age range for inclusion of 40-69 years (Sudlow et al., 2015). Data collection
	continues up to date. All participants provided informed consent ("Resources tab" at
	https://biobank.ctsu.ox.ac.uk/crystal/field.cgi?id=200). The UK Biobank received ethical
	approval from the Research Ethics Committee (reference 11/NW/0382) and the present study
	was conducted based on application 46007.
	Participants performed a variety of cognitive tests, either when visiting a UK Biobank

assessment center, or online during the online follow-up. Participants who did not complete any of the cognitive tests retained for this study were excluded, yielding 501,650 participants (excluded 843 participants).

Table 1 .

 1 UK Biobank Cognitive Tests Considered for this Study. 1

	Test		UKB links	Description	Number of	Included
	(Included		(C: center,		participants	or
	tests in bold)	O: Online)			Excluded
	FI -Fluid	C	Under a time limit of 2 minutes,	C=205,333	Included
	intelligence		O 118	answer a set of 13 (center) or 14	O=123,613
				(online) numerical and verbal
				reasoning questions.
	MAT	-	C 501	Select the element that best	C=33,657	Included
	Matrix			completes matrix pattern blocks.
	pattern			15 puzzles.
	completion
	TWR	-	C 503	Looking at an illustration of three	C=33,381	Included
	Tower			pegs (towers), on which three
	rearranging			differently-colored hoops have
				been placed, find how many
				moves it would take to rearrange
				the hoops into another specific
				position.18 puzzles.
	MEMN	-	C 100029	memorize 2 digits displayed on	C=82,865	Included
	Numeric		O 120	the screen. After they disappear	O=111,062
	memory			for 3 seconds, enter them. Every
				time a sequence is correctly
				remembered, the next sequence is
				made one digit longer, up to a
				maximum of 12 digits.
	MEMS	-	C 100030	memorize the position of	C=498,730	Included
	Pairs		O 117	matching pairs of cards. Once the	O=118,528
	matching			cards are turned face down, find
				as many pairs as possible in the
				fewest tries. Up to 3 rounds, with
				an increasing number of pairs (3,
				6, 8).
	MEMW	-	C 506	memorize 12 pairs of words	C=34,045	Excluded:
	Paired			shown for 30 seconds in total.		ceiling
	associate			After an interval (different test),		effect
	learning			see the first word of 10 of these
				pairs and select the matching
				second word from 4 alternatives.
	MEMP	-	C 100031	Early in the test session, the	C=211,952	Excluded:
	Prospective			participant is shown "At the end		only	1
	memory			of the games we will show you		question
				four colored shapes and ask you

Table 2 .

 2 Raw scores Transformations for the Included Cognitive Tests 1

	Test		Measures used	Raw score computation
	FI -Fluid	Number of correct answers [0-14]	Measure unchanged
	intelligence		Fields 20016 (center) & 20191
			(online)
	MAT -Matrix	Number of correct answers [0-15]	Measure unchanged
	pattern		Field 6373 (center only)
	completion
	TWR -Tower	Number of correct answers [0-18]	Measure unchanged
	rearranging		Field 21004 (center only)
	MEMN	-	Maximum number of digits	Measure unchanged
	Numeric		remembered correctly [0-12]
	memory		Fields 4282 (center) & 20240
			(online)
	MEMS -Pairs	Numbers of correct and incorrect	Score computed as follows:
	matching		matches in each round. The test has	-Each correct pair earns 2 points in
			up to 3 rounds, with increasing	rounds 1 and 2, 1 point in round 3
			difficulty (more pairs to remember).	-Each incorrect pair loses 1 point
			Access to a round is subject to a high	-Within each round, negative scores
			score in the previous round.	are brought back to zero
			Fields 10136/398 (center) & 20131
			(online)
			Fields 10137/399 (center) & 20132
			(online)
	SDS -Symbol	Number of correct matches and	Score = the number of correct
	digit		number of attempts	matches
	substitution		Fields 23324 (center) & 20159	Exclusion criteria: scores with more
			(online) Fields 23323 (center) &	than 35 attempts and less than 65%
			20195 (online)	correct matches (participants likely
				did not follow test instructions, for
				example by repeatedly entering the
				same digit). These outlier limits
				were computed as ±3sd from the
				mean.
	RT -Reaction	Mean time to correctly identify	Score = -log(mean time to correctly
	time		matches	identify matches)
			Field 20023 (center only)	Higher scores represent better
				performance
				No exclusion criteria because
				response times out of the 50ms to
				2000ms range were already
				excluded.

Table of Contents 1. Introduction 126 2. Methods 128 2

 of .1. Participants .................................................................................................................. 128 2.2. G-factor Groups .......................................................................................................... 128 2.4. Phenotypes .................................................................................................................. 129 2.5. Age .............................................................................................................................. 131 2.6. Statistical Analyses ..................................................................................................... 132 Differences in the Prevalence of Phenotypes between Participants with High and Average CA ......................................................................................................................

	1. Introduction
	Is being intellectually gifted a strength or a handicap? Intelligence -the ability to learn,
	reason, and solve problems(
	3. Results	131
	3.1. . 131
	3.1.1. Mental Health Disorders	132
	3.1.2. Somatic Phenotypes	135
	3.1.3. Trauma	135
	3.1.4. Traits	135
	4. Discussion	136

3.2. Phenotypes with group differences between both the high and average and low and average CA groups ............................................................................................................. 135

Table 1 .

 1 Phenotypic Prevalence in the UK Biobank 1

	Type	Phenotype

Table 2 .

 2 Phenotypes that differ in Prevalence betweenAverage and High General Intelligence Groups.

	Average g-Factor	High g-Factor

E: Evening, M: Morning. Cannabis Use: never used versus used at least once 3.1.2. Somatic Phenotypes

Table of Contents

 of Participants .................................................................................................................. 149 2.2. Phenotypes .................................................................................................................Phenotypic Analyses ..................................................................................................Mediation Models with Global Cerebral Measures .................................................... 162

	Introduction
	Mental health disorders (MHDs) co-occur within individuals to such a degree that
	comorbidity might be considered the norm. Factor analyses suggest that this overlap can be
	Abstract explained by broad factors of psychopathology, including a transdiagnostic p-factor 145
	1. Introduction 2. Methods representing general psychopathology risk	146 149
	2.1. . 149
	2.2.1. Mental Health Disorders	149
	2.2.2. Global Cerebral Measures	149
	2.2.3. Childhood Adversity	150
	2.3. . 152
	2.3.1. Exploratory Factor Analyses (EFAs)	152
	2.3.2. Confirmatory Factor Analyses (CFAs)	152
	2.3.3. Childhood Adversity	153
	2.4. . 153
	2.4.1. GWASs and GWAS Meta-analyses	153
	2.4.2. Genomic SEM	155
	2.4.3. Polygenic Scores	155
	2.4.4. Genetic Correlations with External Variables	156
		. 157
	3.1.1. EFA	157
	3.1.2. CFA	157
	3.1.3. Childhood Adversity	159
		. 160
	3.2.1. Phenotypically Informed Models on Genetic Data	160
	3.2.1.1. Genomic SEM Models	160
	3.2.1.2. SNP Effects	160
	3.2.1.2. Genetic Correlations	160
	3.2.1.3. PGS Prediction	161
	3.2.2. Genetically informed CFA Models	161
	3.3. 4. Discussion	165
	5. References	170

Genetic Analyses .......................................................................................................2.5. Cerebral mediators of PGSs' effects on phenotypic psychopathology factors ........... 156 3. Results 157 3.1. Phenotypic analysis ....................................................................................................3.2. Genetic analysis .........................................................................................................

Table 1 .

 1 Summary of the 10 Psychopathology Measures with GWAS summary statistics 1

	Phenotypic Analyses

Table 1 .

 1 Descriptive Statistics of the variables included in Each Analysis g-factor: general intelligence score. G-factor is scaled for the regressions. PGS: Polygenic Score. PGS is scaled before being residualized for birth year and the 1 st 40 principal components of the genotyped data. Childhood Adversity scale on the sample (N about 150,000)

	Analyses	Max N Variable	Mean SD	Median
	Regressions	39,131	Age (years) g-factor	64.05 7.52 64.50 0.00 1.00 -0.01
	Mediation Models with g-factor PGS	28,917	Age (years) g-factor PGS g-factor	64.04 7.46 64.50 0.00 1.00 0.00 0.20 1.05 0.18
	Mediation Models with g-factor PGS & Childhood Adversity	19,956	Age (years) g-factor PGS g-factor Childhood Adversity -0.03 1.39 -0.50 64.08 7.42 64.58 0.03 0.99 0.02 0.27 1.03 0.26
	N.B.

Table 2 .

 2 Principal Component (PC) Loadings of Childhood Abuse and Stressor Variables

	Variable

Table 3 .

 3 Number of Volumes, Surface Areas, and Mean Thicknesses by types of Change in Significance and Estimate between Models without and with Global Brain Size

	Volumes	Surface Areas Mean Thicknesses

Acknowledgments

Acknowledgments This work received support under the program "Investissements d'Avenir" launched by the French Government and implemented by l'Agence Nationale de la recherche (ANR) with the reference ANR-17-EURE-0017 and ANR-10-IDEX-0001-02 PSL. This research has been conducted using the UK Biobank Resource. Declarations of interest: none. Acknowledgments This work received support under the program "Investissements d'Avenir" launched by the French Government and implemented by l'Agence Nationale de la recherche (ANR) with the references ANR-17-EURE-0017 and ANR-10-IDEX-0001-02 PSL. This research has been conducted using the UK Biobank Resource. Declarations of interest: none. Acknowledgments This work received support under the program "Investissements d'Avenir" launched by the French Government and implemented by l'Agence Nationale de la recherche (ANR) with the references ANR-17-EURE-0017 and ANR-10-IDEX-0001-02 PSL. This research has been conducted using the UK Biobank Resource. Declarations of interest: none. Acknowledgments This work received support under the program "Investissements d'Avenir" launched by the French Government and implemented by l'Agence Nationale de la recherche (ANR) with the references ANR-17-EURE-0017 and ANR-10-IDEX-0001-02 PSL. This research has been conducted using the UK Biobank Resource. Declarations of interest: none.

Data/Code Availability -This research has been conducted using data from UK Biobank, a major biomedical database (http://www.ukbiobank.ac.uk/). Restrictions apply to the availability of these data, which were used under license for this study: application 46007.

Supplements and code available on OSF: https://osf.io/49scv/?view_only=29e0ee6a1420461d81d234d94d549751 Data/Code Availability -This research has been conducted using data from UK Biobank, a major biomedical database (http://www.ukbiobank.ac.uk/). Restrictions apply to the availability of these data, which were used under license for this study: application 46007.

Preregistration, code, and supplemental tables and data are available on OSF: https://osf.io/cywd6/?view_only=fa9f5091de124d96be3eb1a55a4e7f01 Data/Code Availability -This research has been conducted using data from UK Biobank (http://www.ukbiobank.ac.uk/). Restrictions apply to the availability of these data, which were used under license for this study: application 46007. Code will be available on OSF once the paper is ready. Supplemental Information, Tables, and Files are available here: https://osf.io/unkym/?view_only=eea9ecdd47324c65b0e9b494925a1783 Data/Code Availability -This research has been conducted using data from UK Biobank (http://www.ukbiobank.ac.uk/). Restrictions apply to the availability of these data, which were used under license for this study: application 46007. Preregistration, supplemental tables and supplemental files are available here:

https://osf.io/ec97u/?view_only=4b366bd7ed2442a1a9f64bfcc2fe0946. Code will be available on OSF when the paper is ready to be submitted as a preprint.

Conflict of interest -On behalf of all authors, the corresponding author states that there is no conflict of interest.

Ethics Approval Statement-All participants provided informed consent ("Resources tab" at https://biobank.ctsu.ox.ac.uk/crystal/field.cgi?id=200). The UK Biobank received ethical approval from the Research Ethics Committee (reference 11/NW/0382) and the present study was conducted based on application 46 007.

Conflict of interest -On behalf of all authors, the corresponding author states that there is no conflict of interest.

Ethics Approval Statement-All participants provided informed consent ("Resources tab" at https://biobank.ctsu.ox.ac.uk/crystal/field.cgi?id=200). The authors assert that all procedures contributing to this work comply with the ethical standards of the relevant national and institutional committees on human experimentation and with the Helsinki Declaration of 1975, as revised in 2008. All procedures involving human subjects/patients were approved by the Research Ethics Committee (reference 11/NW/0382) and the present study was conducted based on application 46 007. (16,137/261,701), and 3.6 % in the low g-factor group (9,291/261,701; sex differences in Section S1.2).

Phenotypes

To maximize the number of participants with a diagnosis, each phenotype was created from a combination of questions on diagnoses by mental health professionals, self-reported diagnoses by professionals, and probable diagnoses obtained from previous studies 43-45 using the UK Biobank questionnaires (Tables SA,Section 1.3). We examined 32 phenotypes using one or several binary, ordinal, or continuous variables (Table 1; Table SB1-B2).

Across the 32 phenotypes, the prevalence differed between the high g-factor and average g-factor groups in 15 phenotypes (47%) and between the low g-factor and average g-factor groups in 12 phenotypes (38%; Fig 1). Phenotypic differences between the Low and Average g-factor are discussed in Supplemental Section 2.3. There were no significant interactions in the analyses comparing the average to the high g-factor groups. Low-powered phenotypes are discussed in Supplemental Section 2.4.

Mental Health Disorders

Compared to individuals in the average g-factor group, there was a 33% decrease in the odds of suffering from Post-Traumatic Stress Disorder (OR = 0.67) and a 31% decrease in the odds of having general anxiety (OR = 0.69) in the high g-factor group (Table 2). There was no significant difference across other mental health disorders (Fig 1).

Title: Phenotypic and Genetic Psychopathology Factors for the UK Biobank

Authors: Camille M. Williams 1 , Travis Mallard 2 , Tobias Wolfram 3 , Franck Ramus 1 , & Hugo Peyre 1,4,5 Running Title: Psychopathology Factors in the UK Biobank Conflict of interest -On behalf of all authors, the corresponding author states that there is no conflict of interest.

Ethics Approval Statement-All participants provided informed consent ("Resources tab" at https://biobank.ctsu.ox.ac.uk/crystal/field.cgi?id=200). The UK Biobank received ethical approval from the Research Ethics Committee (reference 11/NW/0382) and the present study was conducted based on application 46 007.

Abstract

Although the UK Biobank is ideal to examine the genetic, neural, and environmental causes and mechanisms underlying comorbidity in mental health, it is included in most genome-wide association studies (GWASs) of mental health disorders, making it difficult to calculate unbiased polygenic scores (PGSs) for its participants. Here, we provide PGSs of psychopathology factors for UK Biobank participants with neuroimaging data to examine whether cerebral measures mediate genetic (PGSs) and environmental (childhood adversity) effects on measures of general psychopathology.

In individuals without neuroimaging data, we first performed factor analyses on 10 binary mental health disorders. We then applied the phenotypic psychopathology model to the meta-analyzed genetic data for the same mental health disorders and conducted a multivariate GWAS. We calculated PGSs scores for individuals with neuroimaging data (N = 26,610) and finally examined whether Total Brain Volume (TBV) mediated the effects of psychopathology This preliminary paper provides phenotypic and genetic measures of psychopathology and exemplifies how these measures can be used to examine the genetic, neural, and environmental causes and mechanisms underlying comorbidity in mental health.

Methods

All analyses were conducted in R (R Core Team, 2022) and the Supplemental Information, Tables, and Files are available here: https://osf.io/unkym/?view_only=eea9ecdd47324c65b0e9b494925a1783

Participants

The UK Biobank has phenotypic, genotypic, and imaging data from more than 500,000 participants. Participants were recruited between 2006 and 2010 across 22 assessment centers in England, Wales, and Scotland, between the ages of 40 to 69 years old (Sudlow et al., 2015).

Participants

provided informed consent (https://biobank.ctsu.ox.ac.uk/crystal/field.cgi?id=200) and the UK Biobank received ethical approval from the Research Ethics Committee (reference 11/NW/0382). This study was conducted based on application 46007.

Phenotypes

Mental Health Disorders

We generated in a previous study (Williams et al., 2022) by combining self-reported measures and patient diagnoses (Supplemental Tables A). If a participant reported having an MHD during any of their visits to the center or the online follow-up, they were identified as a case for that disorder. There were 502,120 individuals with data on at least 1 of the Matter Volume (WMV), cerebellar GMV, cerebellar WMV, and the brainstem volume.

Genomic SEM

To create PGSs for the phenotypic psychopathology factors, we applied the phenotypic model structure to the MHD summary statistics from Table 1 using Genomic SEM (Grotzinger et al., 2019; Figure 1). These models will be referred to as phenotypically informed genetic models. We estimated the SNP effects of the latent factors of the most parsimonious and bestfitting genetic and phenotypic model (Supplemental Section 1.2.4.1). Although these analyses

were not yet performed, we plan on examining the extent to which each SNP plausibly operates via the latent factor by calculating a Q heterogeneity index for each SNP (for details see Grotzinger et al., 2022).

To examine the genetic structure of psychopathology, we first ran an EFA using odd SNPs (training sample) and then ran a CFA with the model structure from the EFA on the even SNPs (test sample). We used the genetic covariance matrix estimated by the Genomic SEM ldsc function as the input for the EFA (Supplemental Section 1.2.4.2; Figure 1). Finally, if the phenotypic and genetic structures differed, we planned on running a CFA on both odd and even SNPs before calculating the SNP effects for each latent variable from the genetically informed model and creating PGSs for these latent variables.

Genomic SEM fit was assessed using the CFI > 0.95 for good and > 0.90 for acceptable fit and SRMR < 0.08 for good fit (Grotzinger et al., 2019).

We conducted functional mapping and annotation analyses on the multivariate GWAS summary statistics of the latent factors using FUMA default parameters [START_REF] Watanabe | Functional mapping and annotation of genetic associations with FUMA[END_REF] to report the number of lead SNPs and genomic loci.

Title: Neuroanatomical Mediators of Environmental and Genetic factors and Intelligence

Authors: Camille M. Williams 1 , Hugo Peyre

Abstract

Although several studies suggest that genetic and environmental factors influence general intelligence (g-factor) by acting on the brain, there are few studies examining the extent to which cerebral measures mediate environmental and genetic effects on intelligence.

Therefore, we examined the brain volumes, cortical mean thicknesses, and cortical surface areas that mediate the g-factor polygenic score's (gPGS) and childhood adversity's effects on the g-factor in the UK Biobank.

We used a phenotypic g-factor and g-factor PGS from a previous study for individuals with neuroimaging data in the UK Biobank (N= 26,610) and created a measure of childhood adversity from questions related to childhood stressors and abuse.

To identify the regions to include in the mediation models, we first examined the global and regional measures predicting the g-factor in individuals with neuroimaging data (N=39,000). We then ran mediation models for global measures, regional volumes, mean thicknesses, and surface areas, separately, with and without childhood adversity to examine whether the effect of childhood adversity on the g-factor is mediated by the same cerebral measures as the gPGS.

We found that the percentage mediated by global volumes and surfaces of the gPGS and childhood adversity's effects were 10-15% times greater than that of regional volumes, surfaces, and mean thicknesses. Considering that Total Brain Volume only mediated 7.04% of the gPGS' effect on the g-factor and 2.50% of Childhood Adversity's effect on the g-factor, mediation models using alternative cerebral measures may shed more light on the underlying mechanisms by which environmental and genetic factors influence intelligence.

Methods

Analyses were run on R (R Core Team, 2022) and the preregistration, Supplemental Files and Tables are available here:

https://osf.io/ec97u/?view_only=4b366bd7ed2442a1a9f64bfcc2fe0946

Participants

The UK Biobank is a large prospective study with phenotypic, genotypic, and neuroimaging data from more than 500,000 participants. We included participants whose combination of cognitive tests allowed for a correlation with the complete g-factor of 0.70 or higher (N=261,701; Williams et al., 2022). This threshold was used to maximize the robustness of the factor and the number of participants with a gfactor.

In a previous paper, we analyzed the Image-Derived Phenotypes from the first Magnetic Imaging Resonance (MRI) visit generated by an image-processing pipeline developed and run by the UK Biobank Imaging team (Alfaro-Almagro et al., 2018;Miller et al., 2016) and reported 40,028 individuals with sex, age at MRI, and TBV data after excluding outliers (Williams et al., 2021). From here on, age at the first MRI visit will be referred to as age. From the 40,028 individuals with neuroimaging data, there were 39,131 participants with a g-factor of good quality (Table 1).

Statistical Analyses

We refer to the phenotypic g-factor as the g-factor and the g-factor PGS as the gPGS.

A residualized gPGS was created by adjusting the gPGS for birth year and the first 40 principal components of the genotyped data and is referred to as the gPGS from here on out. All continuous variables were mean-centered and divided by 1SD. Females were coded 0.5 and Males -0.5 in the regression analyses.

What global measures predict the phenotypic g-factor?

We first estimated the effect of TBV and the CSF on the phenotypic g-factor, while adjusting for Sex, Age (quadratic and linear), their interactions, and Scanner Site (Equation 1,

where i refers to an individual). Equation 1g-factori = Intercept + TBVi + CSFi + Sexi + Agei + Age 2 i+ Age*Sexi + Age 2 *Sexi + e

To identify the global measures driving the predictive effect of TBV on the g-factor, we simultaneously estimated the effect of total MCT, TSA, subcortical GMV cortical GMV, cerebral WMV, cerebellar GMV, cerebellar WMV, the brainstem volume, and CSF on the phenotypic g-factor, while adjusting for Sex, Age (quadratic and linear), their interactions, and Scanner Site (Equation 2, where i refers to an individual). Equation 2g-factori = Intercept + Total Mean Cortical Thicknessi + Total Surface Areai + Cerebral WMVi

We considered that a regional measure significantly predicts the g-factor when p < 0.05/N, N: the number of coefficients of interest, which was 2 for equation 1 and 8 for equation 2.

What global measures mediate the g-PGS' effects on the g-factor?

We ran two mediation models using the sem function in the lavaan package (Rosseel, 2012): one with the significant predictors of the g-factor from equation 1 and one with those segmentations. We additionally report volumes that mediate the gPGS' effect, and most notably the Right Mediodorsal Medial Magnocellular Thalamic Nuclei, a region thought to be implicated in executive functions (e.g., cognitive control and decision making) in light of its interconnectivity with the prefrontal cortex [START_REF] Ouhaz | Cognitive Functions and Neurodevelopmental Disorders Involving the Prefrontal Cortex and Mediodorsal Thalamus[END_REF].

When adding childhood adversity to the model, the percentage mediated by regional and global effects decreased to various extents across regions. For instance, adding childhood adversity to the mediation models did not impact the percentage mediated by the mean thickness of the right anterior part of the cingulate gyrus and sulcus. However, the surface area and volume of the left subcallosal gyrus and the mean thicknesses of the left inferior segment of the circular sulcus of the insula and the left anterior part of the cingulate gyrus and sulcus no longer mediated the gPGS' effect on the g-factor when adding childhood adversity to the model. Considering that childhood adversity significantly and negatively predicted these regions, the association between these non-longer mediating regions may be due to the correlation between childhood adversity and the gPGS: Part of the variance previously attributed to the g-PGS may have shifted from the gPGS to childhood adversity. Finally, when adding childhood adversity to the mean thickness mediation model, a new region mediated both the gPGS' effect and childhood adversity's effect on the g-factor: the left subcallosal gyrus mean thickness. The latter highlights the importance of including environmental measures to better understand the complex relationship between environmental and genetic effects on general intelligence.

Although we find that specific regions mediate the g-factor's and Childhood Adversity's effects independently from global brain size and regional associations, the mediation of global brain size was 10-20 times larger than the mediation of specific regions when examining volumes and surface areas. TBV explained 2.3% and the regional volumes included in the mediation models explained 0.3% of the variance in the g-factor, whereas TSA explained 1.8% and the regional surface areas included in the mediation models explained 0.2% of the variance in the g-factor. These findings are consistent with previous studies suggesting that general intelligence may be more related to global than region-specific differences in the grey matter volume [START_REF] Hilger | Predicting intelligence from brain gray matter volume[END_REF] and that adding regional effects on the g-factor does not substantially predict more variance in the g-factor than TBV alone (Cox et al., 2019). However, TBV only mediated 7.04% of the gPGS' effect on the g-factor and 2.50% of Childhood Adversity's effect on the g-factor, leaving 93% of the gPGS' effect on the g-factor, and 97.5% of Childhood Adversity's effect on the g-factor to be explained by other cerebral measures. Therefore, future research should include additional cerebral measures,