Genome-wide scans for deviations from expected genotype frequencies, as determined by the Hardy–Weinberg equilibrium (HWE), are commonly applied to detect genotyping errors and deviations from random mating. In contrast to the autosomes, genotype frequencies on the X chromosome do not reach HWE within a single generation. Instead, if allele frequencies in males and females initially differ, they oscillate for a few generations toward equilibrium. Allele frequency differences between the sexes are expected in populations that have experienced recent sex-biased admixture, namely, their male and female founders differed in ancestry. Sex-biased admixture does not allow testing for HWE on X, because deviations are naturally expected, even under random mating (post admixture) and error-free genotyping. In this paper, we develop a likelihood ratio test and a χ2 test to detect deviations from expected genotype frequencies on X, beyond natural deviations due to sex-biased admixture. We demonstrate by simulations that our tests are powerful for detecting deviations due to non-random mating, while at the same time they do not reject the null under historical sex-biased admixture and random mating thereafter. We also demonstrate that when applied to 1000 Genomes project populations, our likelihood ratio test rejects fewer SNPs than other tests, but we describe limitations in the interpretation of the results.
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1000 Genomes Project Consortium, Auton A, Brooks LD, Durbin RM, Garrison EP, Kang HM et al. (2015) A global reference for human genetic variation. Nature 526:68–74
Anderson CA, Pettersson FH, Clarke GM, Cardon LR, Morris AP, Zondervan KT (2010) Data quality control in genetic case-control association studies. Nat Protoc 5:1564–1573
Ayres KL, Balding DJ (1998) Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient. Hered (Edinb) 80(Pt 6):769–777
Baharian S, Barakatt M, Gignoux CR, Shringarpure S, Errington J, Blot WJ et al. (2016) The great migration and African-American genomic diversity. PLoS Genet 12:e1006059
Bonnen PE, Lowe JK, Altshuler DM, Breslow JL, Stoffel M, Friedman JM et al. (2010) European admixture on the Micronesian island of Kosrae: lessons from complete genetic information. Eur J Hum Genet 18:309–316
Bourgain C, Abney M, Schneider D, Ober C, McPeek MS (2004) Testing for Hardy-Weinberg equilibrium in samples with related individuals. Genetics 168:2349–2361
Bryc K, Velez C, Karafet T, Moreno-Estrada A, Reynolds A, Auton A et al. (2010) Colloquium paper: genome-wide patterns of population structure and admixture among Hispanic/Latino populations. Proc Natl Acad Sci USA 107(Suppl 2):8954–8961
Bycroft C, Freeman C, Petkova D, Band G, Elliott LT, Sharp K et al. (2018) The UK Biobank resource with deep phenotyping and genomic data. Nature 562:203–209
Chang D, Gao F, Slavney A, Ma L, Waldman YY, Sams AJ et al. (2014) Accounting for eXentricities: analysis of the X chromosome in GWAS reveals X-linked genes implicated in autoimmune diseases. PLoS ONE 9:e113684
Emigh TH (1980) A comparison of tests for Hardy-Weinberg equilibrium. Biometrics 36:627–642
Gao F, Chang D, Biddanda A, Ma L, Guo Y, Zhou Z et al. (2015) XWAS: a software toolset for genetic data analysis and association studies of the X chromosome. J Hered 106:666–671
Graffelman J (2015) Exploring diallelic genetic markers: the Hardy-Weinberg Package. J Stat Softw 64:1
Graffelman J, Jain D, Weir B (2017) A genome-wide study of Hardy-Weinberg equilibrium with next generation sequence data. Hum Genet 136:727–741
Graffelman J, Sanchez M, Cook S, Moreno V (2013) Statistical inference for Hardy-Weinberg proportions in the presence of missing genotype information. PLoS ONE 8:e83316
Graffelman J, Weir BS (2016) Testing for Hardy-Weinberg equilibrium at biallelic genetic markers on the X chromosome. Hered (Edinb) 116:558–568
Graffelman J, Weir BS (2018) Multi-allelic exact tests for Hardy-Weinberg equilibrium that account for gender. Mol Ecol Resour 18:461–473
Gravel S (2012) Population genetics models of local ancestry. Genetics 191:607–619
Gravel S, Zakharia F, Moreno-Estrada A, Byrnes JK, Muzzio M, Rodriguez-Flores JL et al. (2013) Reconstructing native American migrations from whole-genome and whole-exome data. PLoS Genet 9:e1004023
Hao W, Storey JD (2017) Extending tests of Hardy-Weinberg equilibrium to structured populations. bioRxiv. https://doi.org/10.1101/240804
Hernandez JL, Weir BS (1989) A disequilibrium coefficient approach to Hardy-Weinberg testing. Biometrics 45:53–70
Jagadeesan A, Gunnarsdottir ED, Ebenesersdottir SS, Guethmundsdottir VB, Thordardottir EL, Einarsdottir MS et al. (2018) Reconstructing an African haploid genome from the 18th century. Nat Genet 50:199–205
Jennings HS (1916) The numerical results of diverse systems of breeding. Genetics 1:53–89
Khramtsova EA, Davis LK, Stranger BE (2019) The role of sex in the genomics of human complex traits. Nat Rev Genet. 20:173–190
Kim SK, Gignoux CR, Wall JD, Lum-Jones A, Wang H, Haiman CA et al. (2012) Population genetic structure and origins of native Hawaiians in the multiethnic cohort study. PLoS ONE 7:e47881
Kudelka MR, Hinrichs BH, Darby T, Moreno CS, Nishio H, Cutler CE et al. (2016) Cosmc is an X-linked inflammatory bowel disease risk gene that spatially regulates gut microbiota and contributes to sex-specific risk. Proc Natl Acad Sci USA 113:14787–14792
Kukurba KR, Parsana P, Balliu B, Smith KS, Zappala Z, Knowles DA et al. (2016) Impact of the X Chromosome and sex on regulatory variation. Genome Res 26:768–777
Laird NM, Lange C (2011) The fundamentals of modern statistical genetics. Springer-Verlag, New York
Laurie CC, Doheny KF, Mirel DB, Pugh EW, Bierut LJ, Bhangale T et al. (2010) Quality control and quality assurance in genotypic data for genome-wide association studies. Genet Epidemiol 34:591–602
Levene H (1949) On a matching problem arising in genetics. Ann Math Stat 20:91
Li YR, Li J, Zhao SD, Bradfield JP, Mentch FD, Maggadottir SM et al. (2015) Meta-analysis of shared genetic architecture across ten pediatric autoimmune diseases. Nat Med 21:1018–1027
Lie BA, Dupuy BM, Spurkland A, Fernandez-Vina MA, Hagelberg E, Thorsby E (2007) Molecular genetic studies of natives on Easter Island: evidence of an early European and Amerindian contribution to the Polynesian gene pool. Tissue Antigens 69:10–18
Lind JM, Hutcheson-Dilks HB, Williams SM, Moore JH, Essex M, Ruiz-Pesini E et al. (2007) Elevated male European and female African contributions to the genomes of African American individuals. Hum Genet 120:713–722
Mathias RA, Taub MA, Gignoux CR, Fu W, Musharoff S, O’Connor TD et al. (2016) A continuum of admixture in the Western Hemisphere revealed by the African Diaspora genome. Nat Commun 7:12522
Moreno-Estrada A, Gravel S, Zakharia F, McCauley JL, Byrnes JK, Gignoux CR et al. (2013) Reconstructing the population genetic history of the Caribbean. PLoS Genet 9:e1003925
Puig X, Ginebra J, Graffelman J (2017) A Bayesian test for Hardy-Weinberg equilibrium of biallelic X-chromosomal markers. Hered (Edinb) 119:226–236
Purcell S, Neale B, Todd-Brown K, Thomas L, Ferreira MA, Bender D et al. (2007) PLINK: a tool set for whole-genome association and population-based linkage analyses. Am J Hum Genet 81:559–575
Rohlfs RV, Weir BS (2008) Distributions of Hardy-Weinberg equilibrium test statistics. Genetics 180:1609–1616
Rosenberg NA (2016) Admixture models and the breeding systems of H. S. Jennings: A GENETICS Connection. Genetics 202:9–13
Scelsi MA, Khan RR, Lorenzi M, Christopher L, Greicius MD, Schott JM et al. (2018) Genetic study of multimodal imaging Alzheimer’s disease progression score implicates novel loci. Brain 141:2167–2180
Shriner D (2011) Approximate and exact tests of Hardy-Weinberg equilibrium using uncertain genotypes. Genet Epidemiol 35:632–637
Traglia M, Bseiso D, Gusev A, Adviento B, Park DS, Mefford JA et al. (2017) Genetic mechanisms leading to sex differences across common diseases and anthropometric traits. Genetics 205:979–992
Turner S, Armstrong LL, Bradford Y, Carlson CS, Crawford DC, Crenshaw AT et al. (2011) Quality control procedures for genome-wide association studies. Curr Protoc Hum Genet. 1–18. https://doi.org/10.1002/0471142905.hg0119s68
Wakefield J (2010) Bayesian methods for examining Hardy-Weinberg equilibrium. Biometrics 66:257–265
Wigginton JE, Cutler DJ, Abecasis GR (2005) A note on exact tests of Hardy-Weinberg equilibrium. Am J Hum Genet 76:887–893
Yap CX, Sidorenko J, Wu Y, Kemper KE, Yang J, Wray NR et al. (2018) Dissection of genetic variation and evidence for pleiotropy in male pattern baldness. Nat Commun 9:5407
You XP, Zou QL, Li JL, Zhou JY (2015) Likelihood ratio test for excess homozygosity at marker loci on X chromosome. PLoS ONE 10:e0145032
Yu C, Zhang S, Zhou C, Sile S (2009) A likelihood ratio test of population Hardy-Weinberg equilibrium for case-control studies. Genet Epidemiol 33:275–280
Zheng G, Joo J, Zhang C, Geller NL (2007) Testing association for markers on the X chromosome. Genet Epidemiol 31:834–843
We thank Alon Keinan for discussions. SC thanks the German–Israeli Foundation for Scientific Research and Development (GIF) grant I-2489-407.6/2017 and the Israel Science Foundation (ISF) grant 407/17.
Conflict of interest
The authors declare that they have no conflict of interest.
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