For most human complex diseases and traits, SNPs identified by genome-wide association studies (GWAS) explain only a small fraction of the heritability. Here we report a user-friendly software tool called genome-wide complex trait analysis (GCTA), which was developed based on a method we recently developed to address the "missing heritability" problem. GCTA estimates the variance explained by all the SNPs on a chromosome or on the whole genome for a complex trait rather than testing the association of any particular SNP to the trait. We introduce GCTA's five main functions: data management, estimation of the genetic relationships from SNPs, mixed linear model analysis of variance explained by the SNPs, estimation of the linkage disequilibrium structure, and GWAS simulation. We focus on the function of estimating the variance explained by all the SNPs on the X chromosome and testing the hypotheses of dosage compensation. The GCTA software is a versatile tool to estimate and partition complex trait variation with large GWAS data sets.

Genome-wide association studies have identified hundreds of genetic variants associated with complex human diseases and traits, and have provided valuable insights into their genetic architecture. Most variants identified so far confer relatively small increments in risk, and explain only a small proportion of familial clustering, leading many to question how the remaining, 'missing' heritability can be explained. Here we examine potential sources of missing heritability and propose research strategies, including and extending beyond current genome-wide association approaches, to illuminate the genetics of complex diseases and enhance its potential to enable effective disease prevention or treatment.Many common human diseases and traits are known to cluster in families and are believed to be influenced by several genetic and environmental factors, but until recently the identification of genetic variants contributing to these 'complex diseases' has been slow and arduous 1 . Genome-wide association studies (GWAS), in which several hundred thousand to more than a million single nucleotide polymorphisms (SNPs) are assayed in thousands of individuals, represent a powerful new tool for investigating the genetic architecture of complex diseases 1, 2. In the past few years, these studies have identified hundreds of genetic variants associated with such conditions and have provided valuable insights into the complexities of their genetic architecture3 , 4.The genome-wide association (GWA) method represents an important advance compared to 'candidate gene' studies, in which sample sizes are generally smaller and the variants assayed are limited to a selected few, often on the basis of imperfect understanding of biological pathways and often yielding associations that are difficult to replicate 5,6. GWAS are also an important step beyond family-based linkage studies, in which inheritance patterns are related to several hundreds to thousands of genomic markers. Despite many clear successes in singlegene 'Mendelian' disorders7 , 8, the limited success of linkage studies in complex diseases has been attributed to their low power and resolution for variants of modest effect 9-11 .The underlying rationale for GWAS is the 'common disease, common variant' hypothesis, positing that common diseases are attributable in part to allelic variants present in more than 1-5% of the population12 -14. They have been facilitated by the development of commercial 'SNP chips' or arrays that capture most, although not all, common variation in the genome. Although the allelic architecture of some conditions, notably age-related macular degeneration, for the most part reflects the contributions of several variants of large effect (defined loosely here as those increasing disease risk by twofold or more), most common variants individually or in combination confer relatively small increments in risk (1.1-1.5-fold) and explain only a small proportion of heritability-the portion of phenotypic variance in a population attributable to additive ...

Single nucleotide polymorphisms (SNPs) discovered by genome-wide association studies (GWASs) account for only a small fraction of the genetic variation of complex traits in human populations. Where is the remaining heritability? We estimated the proportion of variance for human height explained by 294,831 SNPs genotyped on 3,925 unrelated individuals using a linear model analysis, and validated the estimation method by simulations based upon the observed genotype data. We show that 45% of variance can be explained by considering all SNPs simultaneously. Thus, most of the heritability is not missing but has not previously been detected because the individual effects are too small to pass stringent significance tests. We provide evidence that the remaining heritability is due to incomplete linkage disequilibrium (LD) between causal variants and genotyped SNPs, exacerbated by causal variants having lower minor allele frequency (MAF) than the SNPs explored to date.

Obesity is globally prevalent and highly heritable, but the underlying genetic factors remain largely elusive. To identify genetic loci for obesity-susceptibility, we examined associations between body mass index (BMI) and ~2.8 million SNPs in up to 123,865 individuals, with targeted follow-up of 42 SNPs in up to 125,931 additional individuals. We confirmed 14 known obesity-susceptibility loci and identified 18 new loci associated with BMI (P<5×10−8), one of which includes a copy number variant near GPRC5B. Some loci (MC4R, POMC, SH2B1, BDNF) map near key hypothalamic regulators of energy balance, and one is near GIPR, an incretin receptor. Furthermore, genes in other newly-associated loci may provide novel insights into human body weight regulation.

Here we conducted a large-scale genetic association analysis of educational attainment in a sample of approximately 1.1 million individuals and identify 1,271 independent genome-wide-significant SNPs. For the SNPs taken together, we found evidence of heterogeneous effects across environments. The SNPs implicate genes involved in brain-development processes and neuron-to-neuron communication. In a separate analysis of the X chromosome, we identify 10 independent genome-wide-significant SNPs and estimate a SNP heritability of around 0.3% in both men and women, consistent with partial dosage compensation. A joint (multi-phenotype) analysis of educational attainment and three related cognitive phenotypes generates polygenic scores that explain 11-13% of the variance in educational attainment and 7-10% of the variance in cognitive performance. This prediction accuracy substantially increases the utility of polygenic scores as tools in research.