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Common single-nucleotide polymorphisms (SNPs) are predicted to collectively explain 40-50% of phenotypic variation in human height, but identifying the specific variants and associated regions requires huge sample sizes1. Here, using data from a genome-wide association study of 5.4 million individuals of diverse ancestries, we show that 12,111 independent SNPs that are significantly associated with height account for nearly all of the common SNP-based heritability. These SNPs are clustered within 7,209 non-overlapping genomic segments with a mean size of around 90 kb, covering about 21% of the genome. The density of independent associations varies across the genome and the regions of increased density are enriched for biologically relevant genes. In out-of-sample estimation and prediction, the 12,111 SNPs (or all SNPs in the HapMap 3 panel2) account for 40% (45%) of phenotypic variance in populations of European ancestry but only around 10-20% (14-24%) in populations of other ancestries. Effect sizes, associated regions and gene prioritization are similar across ancestries, indicating that reduced prediction accuracy is likely to be explained by linkage disequilibrium and differences in allele frequency within associated regions. Finally, we show that the relevant biological pathways are detectable with smaller sample sizes than are needed to implicate causal genes and variants. Overall, this study provides a comprehensive map of specific genomic regions that contain the vast majority of common height-associated variants. Although this map is saturated for populations of European ancestry, further research is needed to achieve equivalent saturation in other ancestries.

A Teichmüller curve is an algebraic and isometric immersion of an algebraic curve into the moduli space of Riemann surfaces. We give the first explicit algebraic models of Teichmüller curves of positive genus. Our methods are based on the study of certain Hilbert modular forms and the use of Ahlfors's variational formula to identify eigenforms for real multiplication on genus two Jacobians. We also present evidence that Teichmüller curves admit a rich arithmetic geometry by exhibiting examples with small primes of bad reduction and notable divisors supported at their cusps. [ABSTRACT FROM AUTHOR]

Expansions and contractions of tandem DNA repeats are a source of genetic variation in human populations and in human tissues: some expanded repeats cause inherited disorders, and some are also somatically unstable. We analyzed DNA sequence data, derived from the blood cells of >700,000 participants in UK Biobank and the All of Us Research Program, and developed new computational approaches to recognize, measure and learn from DNA-repeat instability at 15 highly polymorphic CAG-repeat loci. We found that expansion and contraction rates varied widely across these 15 loci, even for alleles of the same length; repeats at different loci also exhibited widely variable relative propensities to mutate in the germline versus the blood. The high somatic instability of TCF4 repeats enabled a genome-wide association analysis that identified seven loci at which inherited variants modulate TCF4 repeat instability in blood cells. Three of the implicated loci contained genes ( MSH3 , FAN1 , and PMS2 ) that also modulate Huntington's disease age-at-onset as well as somatic instability of the HTT repeat in blood; however, the specific genetic variants and their effects (instability-increasing or-decreasing) appeared to be tissue-specific and repeat-specific, suggesting that somatic mutation in different tissues-or of different repeats in the same tissue-proceeds independently and under the control of substantially different genetic variation. Additional modifier loci included DNA damage response genes ATAD5 and GADD45A . Analyzing DNA repeat expansions together with clinical data showed that inherited repeats in the 5' UTR of the glutaminase ( GLS) gene are associated with stage 5 chronic kidney disease (OR=14.0 [5.7-34.3]) and liver diseases (OR=3.0 [1.5-5.9]). These and other results point to the dynamics of DNA repeats in human populations and across the human lifespan.

Structural variants (SVs) comprise the largest genetic variants, altering from 50 base pairs to megabases of DNA. However, SVs have not been effectively ascertained in most genetic association studies, leaving a key gap in our understanding of human complex trait genetics. We ascertained protein-altering SVs from UK Biobank whole-exome sequencing data ( n =468,570) using haplotype-informed methods capable of detecting sub-exonic SVs and variation within segmental duplications. Incorporating SVs into analyses of rare variants predicted to cause gene loss-of-function (pLoF) identified 100 associations of pLoF variants with 41 quantitative traits. A low-frequency partial deletion of RGL3 exon 6 appeared to confer one of the strongest protective effects of gene LoF on hypertension risk (OR = 0.86 [0.82-0.90]). Protein-coding variation in rapidly-evolving gene families within segmental duplications-previously invisible to most analysis methods-appeared to generate some of the human genome's largest contributions to variation in type 2 diabetes risk, chronotype, and blood cell traits. These results illustrate the potential for new genetic insights from genomic variation that has escaped large-scale analysis to date., Competing Interests: Declaration of Interests The authors declare no competing interests.

Hundreds of the proteins encoded in human genomes contain domains that vary in size or copy number due to variable numbers of tandem repeats (VNTRs) in protein-coding exons. VNTRs have eluded analysis by the molecular methods-SNP arrays and high-throughput sequencing-used in large-scale human genetic studies to date; thus, the relationships of VNTRs to most human phenotypes are unknown. We developed ways to estimate VNTR lengths from whole-exome sequencing data, identify the SNP haplotypes on which VNTR alleles reside, and use imputation to project these haplotypes into abundant SNP data. We analyzed 118 protein-altering VNTRs in 415,280 UK Biobank participants for association with 791 phenotypes. Analysis revealed some of the strongest associations of common variants with human phenotypes including height, hair morphology, and biomarkers of human health; for example, a VNTR encoding 13-44 copies of a 19-amino-acid repeat in the chondroitin sulfate domain of aggrecan (ACAN) associated with height variation of 3.4 centimeters (s.e. 0.3 cm). Incorporating large-effect VNTRs into analysis also made it possible to map many additional effects at the same loci: for the blood biomarker lipoprotein(a), for example, analysis of the kringle IV-2 VNTR within the LPA gene revealed that 18 coding SNPs and the VNTR in LPA explained 90% of lipoprotein(a) heritability in Europeans, enabling insights about population differences and epidemiological significance of this clinical biomarker. These results point to strong, cryptic effects of highly polymorphic common structural variants that have largely eluded molecular analyses to date.