Lipophilic hormones (soluble in lipids but not in water), such as steroid hormones, including testosterone, are transported in water-based blood plasma through specific and non-specific proteins. Fairer offers from test subjects with higher testosterone in the original study increase the likeliness of the offer being accepted by the negotiating partner, therefore decreasing the probability of both participants leaving without any money. Test subjects with an artificially enhanced testosterone level generally made better, fairer offers than those who received placebos, thus reducing the risk of a rejection of their offer to a minimum. Moreover, the conversion of testosterone to estradiol regulates male aggression in sparrows during breeding season. In one experiment, subjects who interacted with handguns showed higher testosterone levels and aggression than those who interacted with toys. The masculinization of the brain is not just mediated by testosterone levels at the adult stage, but also testosterone exposure in the womb. Here, adjusting for PCOS had negligible effects on MR results, suggesting these phenotypes are primarily dependent on direct androgen load, and not on metabolic disease (Supplementary Data 8). The MR Egger value in the x-axis corresponds to 1 SD increase in risk per 1 SD increase in T/free T. Case and control numbers for each endpoint are available from Supplementary Data 8. SHBG adjusted analyses further suggested these associations were androgen dependent (Supplementary Data 7 and Supplementary Fig. 8). These suggested that associations to metabolic traits were not primarily attributable to androgen action (Supplementary Data 7 and Supplementary Fig. 8). For T traits, we additionally compared the causality results of these models to estimates from CAUSE, a MR method similarly designed to distinguish pleiotropy from true causality (Supplementary Data 2)55. Therefore, given the vast polygenicity of the studied T traits, we chose latent causal variable (LCV)53 and MR-Egger54 as our primary causality analysis methods, designed to take into account pleiotropy-induced confounding. The second limitation (especially in the form of genetic pleiotropy) is harder to control when using a large number of SNPs as instrumental variables. The first assumption is partly controlled by using BOLT-LMM as our model in the primary GWAS analysis together with using PCs to control for population stratification. We performed power analyses on the Cox models using the powerEpiCont.default from powerSurvEpi package in R. Cox proportional hazards models were used for estimating hazard ratios (HRs) and 95% CIs, with age as the time scale and 10 first principal components of ancestry and genotyping batch as covariates. For PGS analyses, we used same variant weights (LDpred infinitesimal model) as for YFS, and calculated genome-wide PGSs for each individual with PLINK2 (v2.00a2.3LM). At near confluence, cells were washed with PBS and cultured in serum-free SFM4CHO medium (Thermo Scientific HyClone, Logan, UT) for four days before the SHBG-containing medium was harvested. For the expression of SHBG protein, wild type (corresponding to the C genotype of rs6258) and rs6258 (corresponding to the T genotype of rs6258) SHBG cDNAs in the pRC/CMV expression vector were transfected into CHO cells, and G418 was used for selection of stably transfected cells. The steroid-binding properties of SHBG in diluted serum samples or tissue culture medium were determined by Scatchard analysis . In experiments evaluating SHBG binding capacity, serum SHBG concentrations were determined by two-site immunofluorometric assay (PerkinElmer Life Sciences, Turku, Finland) , or by a steroid-binding capacity assay . Detailed description of the free testosterone fraction measurements is provided in Text S1. Each of the 12 genetic instruments described above was used as an exposure instrumental variable in our subsequent Mendelian Randomization analyses. For downstream analyses we produced genetic instruments using two approaches. Given the relatively small sizes of these replication studies, we used these data to validate genetic instruments in aggregate rather than as individual loci (Supplementary Table S28). Here, regression models were conducted on ventiles of the score, and were controlled for 10 genetic principal components, and additionally menopausal status in women (Figure ED2). Free testosterone fraction was measured by an equilibrium dialysis method in 87 subjects with the CC genotype and 32 subjects with the CT genotype of rs6258 (Figure 3D) . Since only two subjects in the replication cohorts had four risk alleles, individuals having three and four risk alleles were grouped into one category to obtain more reliable effect estimates during the subsequent analyses. Altogether, ∼2.5 million SNPs, imputed using the HapMapII CEU population, were tested for association with serum testosterone in the discovery stage.
