Genetic correlations of psychiatric traits with body composition and glycemic traits are sex- and age-dependent

Body composition is often altered in psychiatric disorders. Using genome-wide common genetic variation data, we calculate sex-specific genetic correlations amongst body fat %, fat mass, fat-free mass, physical activity, glycemic traits and 17 psychiatric traits (up to N = 217,568). Two patterns emerge: (1) anorexia nervosa, schizophrenia, obsessive-compulsive disorder, and education years are negatively genetically correlated with body fat % and fat-free mass, whereas (2) attention-deficit/hyperactivity disorder (ADHD), alcohol dependence, insomnia, and heavy smoking are positively correlated. Anorexia nervosa shows a stronger genetic correlation with body fat % in females, whereas education years is more strongly correlated with fat mass in males. Education years and ADHD show genetic overlap with childhood obesity. Mendelian randomization identifies schizophrenia, anorexia nervosa, and higher education as causal for decreased fat mass, with higher body fat % possibly being a causal risk factor for ADHD and heavy smoking. These results suggest new possibilities for targeted preventive strategies.

P sychiatric disorders are complex traits influenced by thousands of genetic variants that act in concert with environmental factors 1,2 . Genome-wide association studies (GWASs) of psychiatric disorders have identified more than 300 independent genomic loci 3,4 , informed biological follow-up studies 5 and may deliver promising targets for drug discovery and repurposing [6][7][8] . Genome-wide summary statistics generated by GWASs can be used in several different ways 9 , including estimating single-nucleotide polymorphism-based heritability (h 2 SNP ), which is the phenotypic variance explained by common genomic variants. Values of h 2 SNP range from 10 to 30% for psychiatric disorders and typically capture around a third of the heritability estimated by twin studies 10 . Additionally, genetic correlations can be calculated using GWAS summary statistics via bivariate linkage disequilibrium score regression (LDSC), which estimates the genetic overlap (i.e. the shared genetic effects) between two traits 11,12 . Such GWAS-based genetic correlation analyses have shown substantial genetic overlap among psychiatric disorders 13 , providing evidence for an underlying "p factor" representing general liability for psychiatric illness 14,15 . For instance, genomic structural equation modelling 16 of GWAS summary statistics for schizophrenia, bipolar disorder, major depressive disorder, posttraumatic stress disorder and anxiety showed that they load onto one shared latent factor with loading estimates between 0.29 and 0.86 16 . However, marked differences in the clinical presentation of psychiatric disorders exist for psychotic experiences or dysfunctional reward systems, suggesting the existence of additional disorder-specific genetic effects 13,14,16 .
Clinically, many psychiatric disorders are accompanied by disturbances in appetite regulation, eating behaviour and altered physical activity. These disturbances can alter body composition and result in comorbid overweight or underweight 17 , most prominently observed in eating disorders, such as binge-eating disorder and anorexia nervosa 18 . Such severe weight dysregulation typically reduces patients' quality of life and is associated with excess morbidity and mortality 19 . Body composition traits, including body fat % (BF%) and fat-free mass (FFM), are also complex, with substantial twin heritabilities of~70% 20,21 . Body mass index (BMI) is the most commonly studied body composition phenotype and its associated genetic variants have been found to be significantly overrepresented in genes and genomic regions active in brain cell types 22 , suggesting it may be a partially behavioural trait. Several studies have also shown negative genetic correlations of BMI with anorexia nervosa and schizophrenia 12,[23][24][25] and positive genetic correlations of BMI with attention-deficit/hyperactivity disorder (ADHD) and major depressive disorder 26,27 . These observations suggest that an in-depth investigation of the shared genomics between psychiatric and body composition traits is needed.
In addition, both extreme overweight and extreme underweight show a clear sex difference: females are not only disproportionately affected by anorexia nervosa (with ratios up to 15:1) but also by obesity (≥30 kg/m 2 ) [28][29][30] . Sex differences are not limited to body composition: major depressive disorder 31 and anxiety 32 are more common in females, whereas ADHD 33 and autism spectrum disorder 34 occur more often in males. Sex differences in body composition, psychiatry and their interplay are not fully understood. Hormones and sex chromosomes have clearly been demonstrated to play a role 35 , but are insufficient to fully explain the sex differences 36 .
In this study, our primary aim is to identify pairs of traits with shared genetic factors by calculating sex-specific genetic correlations. To do so, we calculate sex-specific genetic correlations for GWASs of 12 psychiatric disorders mostly supplied by the Psychiatric Genomics Consortium (URLs) and five behavioural traits with sex-specific GWASs of body composition traits derived from a healthy and medication-free subsample of the UK Biobank (URLs; Supplementary Tables 1, 2). These include BMI, BF%, absolute fat mass (FM) and FFM, as well as body compositionrelated traits, such as objectively measured physical activity from the UK Biobank (URLs) and glycaemic traits from MAGIC (URLs; Supplementary Data 1). We apply trait-specific illness and medication filtering to obtain genomic variants that are associated with body composition traits independent of the confounding effects of somatic diseases, such as diabetes or endocrine illnesses and addiction-related behaviours, including smoking and alcohol consumption, as well as psychiatric disorders. Where possible, putative causality is examined using generalized summary databased Mendelian randomization (GSMR) 37 in females and males separately. As a secondary aim, we use GWASs of BMI and FFM from different stages of life, including childhood, adolescence, young adulthood and late adulthood, to identify the developmental stages in which the sharing of body composition genomic factors with genetic liability for psychiatric disorders occurs.
Here, we show that the genomic overlap between body composition traits and psychiatric disorders is evident only in later adulthood, whereas childhood and young adulthood GWASs of BMI do not correlate significantly with psychiatric traits. Accelerometer-measured physical activity shows genetic correlations with obsessive compulsive disorder (OCD) and anorexia nervosa, but with no other psychiatric disorder. In addition, glycaemic traits show significant genetic correlations only with anorexia nervosa and years of education, which positions anorexia nervosa as unique among the psychiatric disorders we investigate. These findings encourage a deeper investigation of metabolic pathways that may be implicated in psychiatric disorders to identify potential targets for preventive strategies.

Results
Genetic overlap between the sexes. Body composition and physical activity showed substantial heritability explained by common genetic variation ranging from 28-51% (standard error (s.e.) = 0.4-0.8%, LDSC; Supplementary Table 3) and sexdependent sets of genomic variation at p Bonferroni = 0.05/28 = 0.002. We detected a genetic correlation between males and females in BF% that was significantly different from 1 (r g = 0.89, s.e. = 0.03; p ≠1 = 4.7 × 10 −4 , LDSC). Sensitivity analyses using Haseman-Elston regression 38 confirmed these results (Supplementary Table 3) and suggest that specific sets of genomic variation associated with BF% may be differentially active in females and males. The genetic correlations between females and males for the remaining traits are presented in Supplementary Table 4. Detailed results for the body composition and physical activity GWASs, including significant hits and Manhattan plots, are presented on Functional Mapping and Annotation (FUMA; URLs) entry 20-22 and 38-41.
Genetic overlap of psychiatric and body composition traits. In the genetic correlations of the psychiatric disorders and behavioural traits with body composition and physical activity, distinct patterns emerged resulting in two groups (Table 1). In the first group, anorexia nervosa, education years, OCD and schizophrenia were significantly negatively associated with BF%, while anorexia nervosa and schizophrenia were also significantly negatively associated with FFM (see Fig. 1 and Supplementary Data 2 for full results). By contrast, in the second group, ADHD, heavy smoking, alcohol dependence and insomnia were significantly positively associated with BF%, while only ADHD and heavy smoking were also significantly positively associated with FFM ( Table 1). The p value threshold for the genetic correlations with body composition traits was p Bonferroni = 0.05/190 = 2.6 × 10 −4 using matrix decomposition of the genetic correlation matrix to identify the number of independent tests to adjust the threshold using Bonferroni correction 39 .
Putative causal relationships. GSMR revealed evidence consistent with putative causal relationships between psychiatric traits and body composition. The effects on continuous traits are expressed as β coefficients (Fig. 2a-c, e, Supplementary Fig. 1), whereas the effects on binary traits are presented as odds ratios (ORs; Fig. 2d). Estimates with binary exposures were converted to the liability scale 40 . The Bonferroni-corrected p value was 0.05/ 190 = 2.6 × 10 −4 for the GSMR analyses (Supplementary Data 4,5). In the first group, GSMR showed evidence for a 1.8 kg decrease in FM per standard deviation of liability to anorexia nervosa (p = 2.3 × 10 −8 , GSMR) that was more pronounced in females (β AN→FM = −2.14, p = 1.9 × 10 −5 , GSMR) than in males (β AN→FM = −1.3, p = 4.9 × 10 −4 , GSMR). This mirrored the observed genetic correlations. Additionally, GSMR showed evidence for a 3. Genetic correlations with glycaemic traits. Our investigation into whether the relationships of the psychiatric traits with body composition are mirrored in their relationships with glycaemic traits (Fig. 3) showed that anorexia nervosa (r g = −0.28; p = 1.8 × 10 −7 , LDSC) and education years (r g = −0.28, p = 1.0 × 10 −12 , LDSC) correlated genetically negatively with fasting insulin concentrations. Accordingly, anorexia nervosa (r g = −0.29, p = 2.8 × 10 −5 , LDSC) and education years (r g = −0.33, p = 9.2 × 10 −6 , LDSC) also showed negative genetic correlations with insulin resistance. In addition, education years showed a negative genetic correlation with fasting glucose concentrations (r g = −0.14; p =      Age-dependent genetic correlations. As a secondary aim, we explored the developmental dependence of genetic correlations of BMI and FFM at different ages with psychiatric disorders and behavioural traits (Fig. 4). We used BMI as a proxy measure of BF% as no GWAS of BF% in childhood or adolescence were available. To test if the sets of genetic variants affecting body composition at different stages of life differentially correlate with psychiatric disorders and behavioural traits, we estimated the following genetic BMI correlations and tested if they were significantly different from one 41 : between childhood and adolescence/young adulthood (r g = 1.00, s.e. = 0.07, LDSC), between childhood and later adulthood (r g = 0.66, s.e. = 0.04, LDSC) and between adolescence and later adulthood (r g = 0.80, s.e. = 0.05, LDSC). The genetic correlation of FFM between childhood and adulthood was also significantly different from one (r g = 0.30, s.e. = 0.04, LDSC). As above, multiple psychiatric disorders and traits showed significant positive and negative genetic correlations with adult BMI and FFM. However, neither BMI in childhood, adolescence or young adulthood, nor FFM in childhood, showed significant genetic correlations with any of the psychiatric disorders or behavioural traits (Supplementary Data 8). To additionally test an extreme phenotype, we calculated genetic correlations between psychiatric traits and obesity in childhood.
In the second group, ADHD was the only psychiatric disorder that showed a significant positive genetic correlation with obesity in childhood (r g = 0.22, s.e. = 0.05, LDSC). GSMR analyses gave evidence for a 1.42-fold increase for ADHD per kg/m 2 increase in childhood BMI (p = 1.26 × 10 −8 , GSMR).

Discussion
Symptomatically, psychiatric disorders are often accompanied by alterations in energy intake, energy expenditure and body composition. Recent genetic analyses of BMI found an important role for genes expressed in the brain and specific brain cell types 22 , suggesting that BMI may be a metabo-behavioural trait. This spurred our in-depth investigation of the shared genetics of psychiatric traits and body composition. We were able to show that five psychiatric disorders-anorexia nervosa, OCD, schizophrenia, ADHD and alcohol dependence-as well as three behavioural traits-education years, insomnia and heavy smoking -show significant genetic correlations (i.e. shared genetics) with body composition in two distinct patterns. The first group of psychiatric disorders and behavioural traits included anorexia nervosa, OCD, schizophrenia and education years, and was characterized by genetic correlations with genomic variants predisposing to lower BF% and FFM. The second group comprised ADHD, alcohol dependence, heavy smoking and insomnia, and had genetic correlations with genomic variants predisposing to higher BF% and FFM. Our Mendelian randomization analyses used significant genetic variants as instrumental variables and found that anorexia nervosa, schizophrenia and education years showed evidence consistent with a negative causal effect on FM and, in the reverse direction, higher BF% appeared to be a risk factor for both ADHD and heavy smoking. Our results also suggested that the overweight seen in individuals with schizophrenia in epidemiological studies 42 is likely to represent medication effects 43 given our observations of a putative causal effect of schizophrenia on lower FM and FFM. This finding reiterates the pressing need for the development of new antipsychotic medications with more favourable weight-related side effect profiles.
In our analysis, anorexia nervosa showed a stronger correlation with BF% in females than in males. This phenomenon was not observed for other traits genetically associated with anorexia nervosa, such as neuroticism, anxiety, major depressive disorder, OCD or schizophrenia 41 . These findings suggest that anorexia nervosa and BF% may share a sex-dependent set of genomic variants potentially contributing to the marked sex bias in the prevalence of anorexia nervosa. Education years showed a stronger genetic correlation with FM in males than in females. However, the GSMR analysis showed a more pronounced protective effect of education years on FM in females than in males in line with a large epidemiological study 44 . This suggests that the stronger genetic association between education years and FM in males may be driven by a set of pleiotropic variants.
From a developmental perspective, it is striking that GWASs of body composition across ages do not genetically correlate perfectly with each other. These varying genetic effects across the lifespan 41,45 have been termed "genetic innovation" 46 and represent the effects of partially different, age-dependent sets of genomic variants on body composition regulation at certain periods of life 41,45 . Some of the psychiatric disorders, such as ADHD and anorexia nervosa, typically have their onset in childhood or adolescence with preceding symptoms or behaviours that implicate neurodevelopmental components. We used the available life-stage GWASs of body composition and did not find genetic overlap between childhood or adolescence/young adulthood BMI with psychiatric disorders, but instead found significant genetic correlations of psychiatric disorders with later adult BMI and BF%. Our analyses also show that genetic variants associated with obesity before the age of ten were positively correlated only with ADHD and negatively only with education years. The relatively specific positive genetic correlation of childhood obesity with ADHD recapitulates a large body of clinical evidence of high phenotypic comorbidity 47 , also shown in family studies 48 . Overweight may represent a difficult but potentially intervenable risk factor at a young age.
Our finding of a genetic overlap between ADHD and obesity in childhood may implicate shared biological pathways between both traits. Given our other results, it appears that this shared component is unlikely to be related to physical activity or glycaemic traits. Instead, speculatively, a central nervous system pathway that is dysregulated by increased body mass in childhood may increase the liability to develop ADHD.
We also investigated body composition-related traits, including physical activity, fasting insulin and fasting glucose concentrations. Physical activity showed a positive genetic correlation with anorexia nervosa and OCD, which themselves were negatively genetically correlated with BF%. Carrying genetic variants that predispose to higher physical activity may be associated with the relationship between lower BF% and psychiatric traits. Higher physical activity, therefore, should be carefully assessed in the treatment of patients with compulsive psychiatric disorders like anorexia nervosa and OCD as it may be a genetically mediated behaviour, as indicated by our analysis.
Contrary to our expectations, ADHD did not show a genetic correlation with physical activity. This suggests that hyperactivity in ADHD may not originate from biological liability for higher accelerometer-measured physical activity 49 and is likely to have an alternative cause, such as insufficient inhibitory control as observed in paediatric clinical samples with ADHD 50 , healthy adult population samples 51 , and in a large longitudinal developmental cohort study 52 .
Our analyses showed that anorexia nervosa and education years have a negative genetic correlation with fasting insulin concentrations and insulin resistance, positioning anorexia nervosa as a special case within the psychiatric disorders and potentially differentiating it from OCD. These negative correlations with fasting insulin concentrations mirrored the negative   genetic correlations between anorexia nervosa, education years and BF%. The potential involvement of metabolic hormones like insulin in anorexia nervosa underscores the relationship of brain and body and their reciprocal regulation 53 , opening an avenue for deeper investigation of metabolic components in psychiatric disorders. The genetic correlations of ADHD with glycaemic traits were not significant, implying that these traits play a smaller role in ADHD than in anorexia nervosa, given the comparable sample size of the GWASs on both psychiatric disorders 25,26 . Genetic associations of physical activity and glycaemic traits with body composition and psychiatric traits in plausible directions render them interesting candidates for formal mediation analyses as they may be actionable targets 54 .
Our study represents the largest investigation of sex-and agedependent effects in the genomic overlap of body composition and psychiatric traits. Although our analyses drew on the largest available GWASs, some phenotypes still had relatively small sample sizes for genomic investigations of common variants in complex traits, especially for our sex-specific analyses. These should be repeated when sample sizes have increased, especially for OCD as its currently available GWAS sample size is particularly modest. All Mendelian randomization analyses, using GSMR 37 , with body composition or glycaemic traits, ADHD, education years, schizophrenia or heavy smoking as exposure were sufficiently powered; however, the analyses with anorexia nervosa, insomnia or OCD as exposures should be regarded as exploratory in nature because p value thresholds were lowered to include at least 10 single-nucleotide polymorphisms (SNPs) in the instrument variable.
Finally, the age-dependent genetic influences we observed between psychiatric traits and body composition suggests that future research could focus on a developmental approach to GWAS analyses of body composition, to capture age-and sexdependent differences. These differences have already been suggested by larger twin studies 55,56 and two molecular genetic studies 41,45 , which enabled our examination of their relationship with psychiatric traits. Most importantly, shared biological pathways and common environmental factors influencing both body composition and behavioural traits should be studied as potential targets for interventions.
Methods UK Biobank subsample. We performed GWASs on an unrelated (KING relatedness metric >0.044, equivalent to a relatedness value of 0.088; n related = 7765) European subsample (defined by 4-means clustering of the genetic principal components) 57 of the genotyped UK Biobank participants (n = 155,961, 45% female, 32% of the genotyped participants, Supplementary Table 1) 58,59 . The UK Biobank (URLs) is a prospective cohort sampled from the general population between 2006 and 2010. All participants were between 40 and 69 years old, were registered with a general practitioner through the United Kingdom's National Health Service, and lived within travelling distance of one of the assessment centres.
Ethics. The UK Biobank is approved by the North West Multi-centre Research Ethics Committee. All procedures performed in studies involving human participants were in accordance with the ethical standards of the North West Multi-centre Research Ethics Committee and with the 1964 Declaration of Helsinki and its later amendments or comparable ethical standards. All participants provided written informed consent to participate in the study. This study has been completed under UK Biobank approved study application 27546.
Power calculations of the GWASs. We conducted power calculations for the female and male GWASs using the Genetic Power Calculator 60 . A minimum of 39,580 individuals is required to detect a SNP that accounts for 0.1% of trait variance at 80% power at a genome-wide significance threshold of p ≤ 5 × 10 −8 and a minor allele frequency of 0.20. According to these results, the female and the male GWASs were sufficiently powered to detect genome-wide significant loci with 70,700 females and 85,261 males. With these parameters, the female GWAS had a power of 99.8% and the male GWAS of 99.9%.
GWASs on body composition traits in the UK Biobank. The continuous body composition traits-BF%, FM, FFM and BMI-were measured using the validated bioelectrical impedance analyser Tanita BC-418 MA (Tanita Corporation, Arlington Height, IL) at every assessment centre 61,62 for every participant across the UK. We applied trait-specific medication and illness filtering to exclude participants with compromised hydration status and medications or illnesses known to affect body composition to identify genetic variation associated with body composition phenotypes that is not confounded by illnesses and their downstream effects or metabolism-changing medication. We applied stringent exclusion criteria and covaried for addictive behaviour-related phenotypes, including smoking and alcohol consumption (for exclusion criteria, see Supplementary Table 2). We regressed the body composition traits on factors related to assessment centre, genotyping batch, smoking status, alcohol consumption, menopause and continuous measures of age, and socioeconomic status (SES) measured by the Townsend Deprivation Index 63 as independent variables. We took the residuals from these regressions as our phenotypes for the GWASs. We included 7,794,483 SNPs and insertion-deletion variants (hereafter referred to as SNPs) with a minor allele frequency >1%, imputation quality scores >0.8, and that were genotyped, or present in the HRC reference panel 64 and used an additive model on the imputed dosage data provided by UK Biobank, using BGENIE v1.2 65 . We accounted for underlying population stratification by including the first six principal components, calculated on the genotypes of our European subsample using FlashPCA2 66 . We performed GWASs including incremental numbers of principal components and checked each GWAS for inflation by calculating its LDSC intercept. We identified six principal components as the optimal number to adjust for population stratification within the European subsample and to not overcorrect the analysis retaining the greatest signal. Additionally, we included assessment centre as a covariate to adjust for population stratification. We then meta-analysed the sex-specific GWASs using METAL 67 (URLs) applying an inverse variance-weighted model with a fixed effect, to obtain sex-combined results.
Clumping and genome-wide significant loci. Significantly associated SNPs (p < 5 × 10 −8 ) were considered as potential index SNPs. SNPs in LD (r 2 > 0.2) with a more strongly associated SNP within 3000 kb were assigned to the same locus using FUMA (URLs) 68 . Overlapping clumps were merged with a second clumping procedure in FUMA, merging all lead SNPs with r 2 = 0.1 to genomic loci. After clumping, independent genome-wide significant loci (5 × 10 −8 ) were compared with entries in the NHGRI-EBI GWAS catalogue 69 , using FUMA 68 .
Heritability estimation and investigation of sex differences. To ensure the robustness of our results, we applied multiple approaches to calculate heritability estimates and genetic correlations. We used BOLT-LMM 70 , LDSC 11 and GREML 71 implemented in GCTA 72 to calculate common variant h 2 SNP (URLs). Additionally, we calculated the genetic correlation between females and males using LDSC 11 and Haseman-Elston regression 38 implemented in GCTA 72 to estimate sex differences in the genetic architecture of the body composition, glycaemic traits and physical activity. Haseman-Elston regression uses the cross-product of phenotypes for pairwise individuals and a genetic relatedness matrix to calculate heritability and genetic correlations 73 . All other statistics were calculated in R 3.4.1 if not otherwise stated (URLs).
GWASs of psychiatric disorders and behavioural traits. All of the following traits were used for the sex-specific and age-dependent analyses (Supplementary Data 1). The sex-specific summary statistics for the psychiatric disorders, including major depressive disorder 27 , schizophrenia 3 , anorexia nervosa 25 88,89 by International Headache Genetics Consortium (IHGC). Glycaemic traits' 90 summary statistics were provided by the Meta-Analyses of Glucose and Insulin-related traits Consortium (MAGIC), whereas childhood obesity 91 results were provided by the Early Growth Genetics (EGG, URLs) Consortium, BMI in young adulthood by Graff et al. 92 and physical activity by our group 41 .
Genetic correlations. Using an analytic extension of LDSC 11 , we calculated SNPbased bivariate genetic correlations (r g ) to examine the genetic overlap of body composition and glycaemic traits with psychiatric and behavioural traits and disorders in a sex-specific manner. Differences in genetic correlations were calculated and their s.e.'s were calculated using a block jackknife approach as previously described 41 . Generalized summary data-based Mendelian randomization. We investigated putative causal bidirectional relationships between these traits using GSMR 37 . Mendelian randomization is a method that uses genetic variants as instrumental variables, which are expected to be independent of confounding factors, to test for causative associations between an exposure and an outcome 93 . Mendelian randomization can be used to infer credible causal associations when randomizedcontrolled trials are not feasible or are unethical 93 . GSMR performs a multi-SNP Mendelian randomization analysis using summary statistics. Let z be a genetic variant (e.g. SNP), x be the exposure (e.g. psychiatric disorder) and y be the outcome (e.g. body composition trait). First, GSMR is based on the premise that several nearly independent SNPs (z) are associated with the exposure (x). Second, it assumes that the exposure (x) has an causal effect on y. If both assumptions hold true, the SNPs that are associated with the exposure (x) will exert an effect on the outcome (y) via the exposure (x). If in this instance no pleiotropy is present, the estimate (b xy ) at any of the SNPs that are associated with the exposure (x) should be highly similar, because each effect of all SNPs on the outcome (y) will be mediated through the exposure (x). With the help of a generalized least squares (GLS) model, the estimates of b xy of each SNP that is associated with the exposure (x) can be combined, resulting in higher statistical power 37,94 . The GSMR method essentially implements summary data-based Mendelian randomization analysis for each SNP instrument individually, and integrates the b xy estimates of all the SNP instruments by GLS, accounting for the sampling variance in both b zx and b yz for each SNP and the LD among SNPs. We used individual-level genotype data from a subsample of the anorexia nervosa GWAS to approximate the underlying LD structure to account for LD between the variants in the multi-SNP instrument. Pleiotropy is an important potential confounding factor that could bias the estimate and often results in an inflated test statistic in Mendelian randomization analysis. We also removed potentially pleiotropic SNPs (i.e. SNPs that have effects on both risk factor and outcome) from this analysis using the heterogeneity in dependent instruments outlier method 37,95 that detects pleiotropic SNPs at which the estimates of b xy are significantly different from expected under a causal model. The power of detecting a pleiotropic SNP depends on the sample sizes of the GWAS data sets and the deviation of b xy estimated at the pleiotropic SNP from the causal model. Based on this, the overall b xy can be estimated from all the instruments remaining using a GLS approach that takes the LD between the variants and the correlations between their effect sizes into account by modelling them in a covariance matrix. Additionally, GSMR uses the intercept of the bivariate LD score regression to account for potential sample overlap between the GWASs used as instruments for the exposure or outcome 12 . Estimates with binary exposures were converted to the liability scale 40 . Some of these analyses are exploratory because a few utilised GWASs were underpowered (i.e. did not detect ≥10 genome-wide significant independent loci at a p value level of 5 × 10 −8 ) and we therefore lowered the p value threshold for inclusion, in order to include at least 10 independent SNP instruments as previously recommended 37 .
Correction for multiple testing. We calculated the number of independent traits by matrix decomposition (i.e. number of principal components accounting for 99.5% of variance explained) and adjusted our p value threshold accordingly. The first matrix of the main analysis contained all 17 psychiatric traits, all four body composition traits, physical activity and childhood obesity (Supplementary Data 2). All sex-specific correlations were entered when available. The second matrix comprised all 17 psychiatric traits and all glycaemic traits listed in Supplementary Data 6, including their sex-specific correlations. The family-wise Bonferroni-corrected p value threshold for the main analysis, including the genetic correlations with body composition traits and physical activity, was p Bonferroni = 0.05/190 = 2.6 × 10 −4 and the family-wise p value threshold for the genetic correlations with glycaemic traits was p Bonferroni = 0.05/231 = 2.2 × 10 −4 .
Reporting summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability
Supplementary Data 1 contains all information on data availability, including download links for summary statistics. Summary statistics for the body composition GWASs are available at www.topherhuebel.com/GWAS and the GWAS catalogue (www.ebi.ac.uk/ gwas/). All sex-combined summary statistics for the psychiatric disorders are available at www.med.unc.edu/pgc/results-and-downloads/ and for glycaemic traits at https://www. magicinvestigators.org/. Sex-specific summary statistics of the psychiatric disorders can be requested from each working group of the Psychiatric Genomics Consortium by submitting a secondary analysis proposal. The data that support the findings of this study are available from UK Biobank (www.ukbiobank.ac.uk). Restrictions apply to the availability of these data, which were used under license for the current study (Project ID: 27546). Data are available for bona fide researchers upon application to the UK Biobank.