Abstract
The heritability of a trait (h 2) is the proportion of its population variance caused by genetic differences, and estimates of this parameter are important for interpreting the results of genome-wide association studies (GWAS). In recent years, researchers have adopted a novel method for estimating a lower bound on heritability directly from GWAS data that uses realized genetic similarities between nominally unrelated individuals. The quantity estimated by this method is purported to be the contribution to heritability that could in principle be recovered from association studies employing the given panel of SNPs (\(h_{\text{SNP}}^{2}\)). Thus far, the validity of this approach has mostly been tested empirically. Here, we provide a mathematical explication and show that the method should remain a robust means of obtaining \(h_{\text{SNP}}^{2}\) under circumstances wider than those under which it has so far been derived.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bell AE (1977) Heritability in retrospect. J Hered 68(5):297–300
Benjamin DJ, Cesarini D, Chabris CF, Glaeser EL, Laibson DI, Guonason V, Harris TB, Launer LJ, Purcell SM, Smith AV, Johannesson M, Magnusson PKE, Beauchamp JP, Christakis NA, Atwood CS, Hebert B, Freese J, Hauser RM, Hauser TS, Grankvist A, Hultman CM, Lichtenstein P (2012) The promises and pitfalls of genoeconomics. Annu Rev Econ 4:627–662. doi:10.1146/annurev-economics-080511-110939
Browning SR, Browning BL (2011) Population structure can inflate SNP-based heritability estimates. Am J Hum Genet 89:191–193. doi:10.1016/j.ajhg.2011.05.025
Browning SR, Browning BL (2013) Identity-by-descent-based heritability analysis in the Northern Finland Birth Cohort. Hum Genet 132:129–138. doi:10.1007/s00439-012-1230-y
Bulmer MG (1980) The mathematical theory of quantitative genetics. Oxford University Press, New York
Chabris CF, Lee JJ, Benjamin DJ, Beauchamp J, Glaeser EL, Borst G, Pinker S, Laibson D (2013) Why is it hard to find genes that are associated with social science traits? Theoretical and empirical considerations. Am J Public Health 103:S152–S166. doi:10.2105/AJPH.2013.301327
Crow JF, Kimura M (1970) An introduction to population genetics theory. Harper and Row, New York
Dickson SP, Wang K, Krantz I, Hakonarson HH, Goldstein DB (2010) Rare variants create synthetic genome-wide associations. PLoS Biol 8:e1000294. doi:10.1371/journal.pbio.1000294
Eyre-Walker A (2010) Genetic architecture of a complex trait and its implications for fitness and genome-wide association studies. Proc Natl Acad Sci USA 107:1752–1756. doi:10.1073/pnas.0906182107
Falconer DS (1960) Introduction to quantitative genetics, 1st edn. Oliver and Boyd, Edinburgh
Fisher RA (1918) The correlation between relatives on the supposition of Mendelian inheritance. Trans Roy Soc Edinburgh 52:399–433
Fisher RA (1941) Average excess and average effect of a gene substitution. Ann Eugen 11:53–63
Fisher RA (1973) Statistical methods and scientific inference, 3rd edn. Hafner, New York
Gibson G (2012) Rare and common variants: twenty arguments. Nat Rev Genet 13:135–145. doi:10.1038/nrg3118
Goddard ME, Lee SH, Yang J, Wray NR, Visscher PM (2011) Response to Browning and Browning. Am J Hum Genet 89:193–195. doi:10.1016/j.ajhg.2011.05.022
Hemani G, Knott S, Haley C (2013) An evolutionary perspective on epistasis and the missing heritability. PLoS Genet 9:e1003295. doi:10.1371/journal.pgen.1003295
Hill WG, Mackay TFC (2004) D. S. Falconer and introduction to quantitative genetics. Genetics 167:1529–1536
Janss L, de los Campos G, Sheehan N, Sorensen D (2012) Inferences from genomic models in stratified populations. Genetics 192:693–704. doi:10.1534/genetics.112.141143
Lande R (1977) The influence of the mating system on the maintenance of genetic variability in polygenic characters. Genetics 86:485–496
Lee JJ, Chow CC (2013) The causal meaning of Fisher’s average effect. Genet Res 95:89–109. doi:10.1017/S0016672313000074
Lee SH, Wray NR, Goddard ME, Visscher PM (2011) Estimating missing heritability for disease from genome-wide association studies. Am J Hum Genet 88:294–305. doi:10.1016/j.ajhg.2011.02.002
Lee SH, Yang J, Chen GB, Ripke S, Stahl EA, Hultman CM, Sklar P, Visscher PM, Sullivan PF, Goddard ME, Wray NR (2013) Estimation of SNP heritability from dense genotype data. Am J Hum Genet 93:1151–1155
Lynch M, Walsh B (1998) Genetics and the analysis of quantitative traits. Sinauer, Sunderland
Manolio TA, Collins FS, Cox NJ, Goldstein DB, Hindorff LA, Hunter DJ, Mc-Carthy MI, Ramos EM, Cardon LR, Chakravarti A, Cho JH, Guttmacher AE, Kong A, Kruglyak L, Mardis E, Rotimi CN, Slatkin M, Valle D, Whitte-more AS, Boehnke M, Clark AG, Eichler EE, Gibson G, Haines JL, Mackay TFC, McCarroll SA, Visscher PM (2009) Finding the missing heritability of complex diseases. Nature 461:747–753. doi:10.1038/nature08494
Park JH, Gail MH, Weinberg CR, Carroll RJ, Chung CC, Wang Z, Chanock SJ, Fraumeni JF, Chatterjee N (2011) Distribution of allele frequencies and effect sizes and their interrelationships for common genetic susceptibility variants. Proc Natl Acad Sci USA 108:18026–18031. doi:10.1073/pnas.1114759108
Powell JE, Visscher PM, Goddard ME (2010) Reconciling the analysis of IBD and IBS in complex trait studies. Nat Rev Genet 11:800–805. doi:10.1038/nrg2865
Speed D, Hemani G, Johnson MR, Balding DJ (2012) Improved heritability estimation from genome-wide SNPs. Am J Hum Genet 91:1011–1021. doi:10.1016/j.ajhg.2012.10.010
Speed D, Hemani G, Johnson MR, Balding DJ (2013) Response to Lee et al.: SNP-based heritability analysis with dense data. Am J Human Genet 93:1155–1157. doi:10.1016/j.ajhg.2013.10.016
Stahl EA, Wegmann D, Trynka G, Gutierrez-Achury J, Do R, Voight BF, Kraft P, Chen R, Kallberg HJ, Kurreeman FAS, Diabetes Genetics Replication and Meta-Analysis Consortium, Myocardial Infarction Genetics Consortium, Kathiresan S, Wijmenga C, Gregersen PK, Alfredsson L, Siminovitch KA, Worthington J, de Bakker PIW, Raychaudhuri S, Plenge RM (2012) Bayesian inference analyses of the polygenic architecture of rheumatoid arthritis. Nat Genet 44:483–489. doi:10.1038/ng.2232
Trzaskowski M, Davis OSP, DeFries JC, Yang J, Visscher PM, Plomin R (2013) DNA evidence for strong genome-wide pleiotropy of cognitive and learning abilities. Behav Genet 43:267–273. doi:10.1007/s10519-013-9594-x
Vattikuti S, Guo J, Chow CC (2012) Heritability and genetic correlations explained by common SNPs for metabolic syndrome traits. PLoS Genet 8:e1002637. doi:10.1371/journal.pgen.1002637
Visscher PM, Hill WG, Wray NR (2008) Heritability in the genomics era—concepts and misconceptions. Nat Rev Genet 9:255–266. doi:10.1038/nrg2322
Visscher PM, Yang J, Goddard ME (2010) A commentary on ‘Common SNPs explain a large proportion of the heritability for human height’ by Yang et al. (2010). Twin Res Hum Genet 13:517–524. doi:10.1375/twin.13.6.517
Wray NR, Purcell SM, Visscher PM (2011) Synthetic associations created by rare variants do not explain most GWAS results. PLoS Biol 9:e1000579. doi:10.1371/journal.pbio.1000579
Wright S (1921) Systems of mating. Genetics 144:111–178
Yang J, Benyamin B, McEvoy BP, Gordon S, Henders AK, Nyholt DR, Madden PA, Heath AC, Martin NG, Montgomery GW, Goddard ME, Visscher PM (2010) Common SNPs explain a large proportion of the heritability for human height. Nat Genet 42:565–569. doi:10.1038/ng.608
Yang J, Lee SH, Goddard ME, Visscher PM (2011a) GCTA: a tool for genome-wide complex trait analysis. Am J Hum Genet 88:76–82. doi:10.1016/j.ajhg.2010.11.011
Yang J, Manolio TA, Pasquale LR, Boerwinkle E, Caporaso N, Cunningham JM, de Andrade M, Feenstra B, Feingold E, Hayes MG, Hill WG, Landi MT, Alonso A, Lettre G, Lin P, Ling H, Lowe W, Mathias RA, Melbye M, Pugh E, Cornelis MC, Weir BS, Goddard ME, Visscher PM (2011b) Genome partitioning of genetic variation for complex traits using common SNPs. Nat Genet 43:519–525. doi:10.1038/ng.823
Zaitlen NA, Kraft P (2012) Heritability in the genome-wide association era. Hum Genet 131:1655–1664. doi:10.1007/s00439-012-1199-6
Zaitlen NA, Kraft P, Patterson N, Pasaniuc B, Bhatia G, Pollack S, Price AL (2013) Using extended genealogy to compute components of heritability for 23 quantitative and dichotomous traits. PLoS Genet 9:e1003520. doi:10.1371/journal.pgen.1003520
Zhou X, Carbonetto P, Stephens M (2013) Polygenic modeling with Bayesian sparse linear mixed models. PLoS Genet 9:e1003264. doi:10.1371/journal.pgen.1003264
Zuk O, Hechter E, Sunyaev SR, Lander ES (2012) The mystery of missing heritability: genetic interactions create phantom heritability. Proc Natl Acad Sci USA 109:1193–1198. doi:10.1073/pnas.1119675109
Acknowledgments
We thank Doug Speed and Xiang Zhou for answering our queries. This work was supported by the Intramural Program of the NIH, The National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK). Assistance with phenotype harmonization and genotype cleaning, as well as with general study coordination, was provided by the Gene Environment Association Studies, GENEVA Coordinating Center (U01 HG004446). Assistance with data cleaning was provided by the National Center for Biotechnology Information.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Lee, J.J., Chow, C.C. Conditions for the validity of SNP-based heritability estimation. Hum Genet 133, 1011–1022 (2014). https://doi.org/10.1007/s00439-014-1441-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00439-014-1441-5