Variance components analysis has emerged as a powerful tool in complex trait genetics, with applications ranging from heritability estimation to association mapping. While the application of these methods to large-scale genetic datasets can potentially reveal important insights into genetic architecture, existing methods for fitting variance components do not scale well to these datasets. Here, we present a new algorithm for variance components analysis that is accurate and highly efficient, capable of estimating one hundred variance components on a million individuals genotyped at a million SNPs in a few hours. We illustrate the utility of our method in estimating variation in a trait explained by genotyped SNPs (SNP heritability) as well in partitioning heritability across population and functional genomic annotations. Analyzing 22 diverse traits with genotypes from 300, 000 individuals across about 8 million common and low frequency SNPs (minor allele frequency > 0.1%), we observe that the allelic effect size increases with decreasing MAF (minor allele frequency) and LD (linkage disequilibrium) across the analyzed traits consistent with the action of negative selection. Partitioning heritability across 28 functional annotations, we observe enrichment of heritability in FANTOM5 enhancers in asthma, eczema, thyroid and autoimmune disorders. ### Competing Interest Statement The authors have declared no competing interest.
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