How Close to the Mark Might Published Heritability Estimates Be?


  • Michael Maraun Department of Psychology, Simon Fraser University, Burnaby, B.C., Canada
  • Moritz Heene Department Psychology, Ludwig Maximilian Universität München
  • Philipp Sckopke Department of Psychology, Ludwig Maximilian University, Munich, Germany



Heritability, heritability estimation, standard biometric model, quantitative genetics, , structural equation modeling, random forest


The behavioural scientist who requires an estimate of narrow heritability, h2, will conduct a twin study, and input the resulting estimated covariance matrices into a particular mode of estimation, the latter derived under supposition of the standard biometric model (SBM). It is known that the standard biometric model can be expected to misrepresent the phenotypic (genetic) architecture of human traits. The impact of this misrepresentation on the accuracy of h2 estimation is unknown. We aimed to shed some light on this general issue, by undertaking three simulation studies. In each, we investigated the parameter recovery performance of five modes- Falconer’s coefficient and the SEM models, ACDE, ADE, ACE, and AE- when they encountered a constructed, non-SBM, architecture, under a particular informational input. In study 1, the architecture was single-locus with dominance effects and genetic-environment covariance, and the input was a set of population covariance matrices yielded under the four twin designs, monozygotic-reared together, monozygotic-reared apart, dizygotic-reared together, and dizygotic-reared apart; in study 2, the architecture was identical to that of study 1, but the informational input was monozygotic-reared together and dizygotic-reared together; and in study 3, the architecture was multi-locus with dominance effects, genetic-environment covariance, and epistatic interactions. The informational input was the same as in study 1. The results suggest that conclusions regarding the coverage of h2 must be drawn conditional on a) the general class of generating architecture in play; b) specifics of the architecture’s parametric instantiations; c) the informational input into a mode of estimation; and d) the particular mode of estimation
employed. The results showed that the more complicated the generating architecture, the poorer a mode’s h2 recovery performance. Random forest analyses furthermore revealed that, depending on the genetic architecture, h2, the dominance and locus additive parameter, and proportions of alleles were involved in complex interaction effects impacting on h2 parameter recovery performance of a mode of estimation. Data and materials:


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Afifi, T. O., Asmundson, G. J., Taylor, S., & Jang, K. L. (2010). The role of genes and environment on trauma exposure and posttraumatic stress disorder symptoms: A review of twin studies. Clinical Psychology Review, 30(1), 101–112.

Benyamin, B., Pourcain, B., Davis, O. S., Davies, G., Hansell, N. K., Brion, M.-J., Kirkpatrick, R. M., Cents, R. A., Frani ́c, S., & Miller, M. B. (2014). Childhood intelligence is heritable, highly polygenic and associated with FNBP1L. Molecular Psychiatry, 19(2), 253–258.

Bischl, B., Lang, M., Kotthoff, L., Schiffner, J., Richter, J., Jones, Z., Casalicchio, G., Gallo, M., Bossek, J., Studerus, E., Judt, L., Kuehn, T., Kerschke, P., Fendt, F., Probst, P., Sun, X., Thomas, J., Vieira, B., Beggel, L., . . . Coors, S. (2017). Mlr: Machine Learning in R. Retrieved May 15, 2017, from

Bowles, S., Gintis, H., et al. (2001). The inheritance of economic status: Education, class and genetics [Publisher: Oxford University Press New York]. International encyclopedia of the social and behavioral sciences: Genetics, behavior and society, 6, 4132–141.

Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32.

Bronfenbrenner, U. (1999). Nature with nurture: A reinterpretation of the evidence [Publisher: Oxford University Press New York]. Race and IQ, 153–183.

Calaway, R., Analytics, R., & Weston, S. (2015). Foreach: Provides Foreach Looping Construct for R. Retrieved May 15, 2017, from

Chen, X., Kuja-Halkola, R., Rahman, I., Arpegård, J., Viktorin, A., Karlsson, R., Hägg, S., Svensson, P., Pedersen, N. L., & Magnusson, P. K. E. (2015). Dominant Genetic Variation and Missing Heritability for Human Complex Traits: Insights from Twin versus Genome-wide Common SNP Models. The American Journal of Human Genetics, 97(5), 708–714.

Cliff, N. (1983). Some cautions concerning the application of causal modeling methods. Multivariate Behavioral Research, 18(1), 115–126.

Dowle, M., Srinivasan, A., Gorecki, J., Short, T., Lianoglou, S., & Antonyan, E. (2017). Data.table: Extension of ’data.frame’. Retrieved May 15, 2017, from

Eaves, L., & Erkanli, A. (2003). Markov Chain Monte Carlo Approaches to Analysis of Genetic and Environmental Components of Human Developmental Change and G × E Interaction. Behavior Genetics, 33(3), 279–299.

Eichler, E. E., Flint, J., Gibson, G., Kong, A., Leal, S. M., Moore, J. H., & Nadeau, J. H. (2010). Missing heritability and strategies for finding the underlying causes of complex disease. Nature Reviews Genetics, 11, 446.

Evans, D. M. (2011). Gene-Gene Interaction and Epistasis. In Analysis of Complex Disease Association Studies (pp. 197–213). Elsevier.

Evans, D. M., Gillespie, N. A., & Martin, N. G. (2002). Biometrical genetics. Biological Psychology, 61(1-2), 33–51.

Evans, L. M., Tahmasbi, R., Vrieze, S. I., Abecasis, G. R., Das, S., Gazal, S., Bjelland, D. W., De Candia, T. R., Goddard, M. E., Neale, B. M., Yang, J., Visscher, P. M., & Keller, M. C. (2018). Comparison of methods that use whole genome data to estimate the heritability and genetic architecture of complex traits. Nature Genetics, 50(5), 737–745.

Falconer, D. S. (1960). Introduction to quantitative genetics. Pearson Education Limited.

Fedko, I. O., Hottenga, J.-J., Helmer, Q., Mbarek, H., Huider, F., Amin, N., Beulens, J. W., Bremmer, M. A., Elders, P. J., Galesloot, T. E., Kiemeney, L. A., Van Loo, H. M., Picavet, H. S. J., Rutters, F., Van Der Spek, A., Van De Wiel, A. M., Van Duijn, C., De Geus, E. J. C., Feskens, E. J. M., . . . Bot, M. (2021). Measurement and genetic architecture of lifetime depression in the Netherlands as assessed by LIDAS (Lifetime Depression Assessment Self-report). Psychological Medicine, 51(8), 1345–1354.

Fisher, R. A. (1919). XV.—The Correlation between Relatives on the Supposition of Mendelian Inheritance. Transactions of the Royal Society of Edinburgh, 52(2), 399–433.

Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. The Annals of Statistics, 29(5).

Goldstein, A., Kapelner, A., Bleich, J., & Pitkin, E. (2015). Peeking inside the black box: Visualizing statistical learning with plots of individual conditional expectation. Journal of Computational and Graphical Statistics, 24(1), 44–65.

Gregersen, J. W., Kranc, K. R., Ke, X., Svendsen, P., Madsen, L. S., Thomsen, A. R., Cardon, L. R., Bell, J. I., & Fugger, L. (2006). Functional epistasis on a common MHC haplotype associated with multiple sclerosis. Nature, 443(7111), 574–577.

Grotzinger, A. D., Rhemtulla, M., De Vlaming, R., Ritchie, S. J., Mallard, T. T., Hill, W. D., Ip, H. F., Marioni, R. E., McIntosh, A. M., Deary, I. J., Koellinger, P. D., Harden, K. P., Nivard, M. G., & Tucker-Drob, E. M. (2019). Genomic structural equation modelling provides insights into the multivariate genetic architecture of complex traits. Nature Human Behaviour, 3(5), 513–525.

Hare, R. D. (1991). The Hare psychopathy checklist-revised: Manual. Multi-Health Systems, Incorporated.

Hare, R. D. (1996). Psychopathy: A Clinical Construct Whose Time Has Come. Criminal Justice and Behavior, 23(1), 25–54.

He, L., Sillanpää, M. J., Silventoinen, K., Kaprio, J., & Pitkäniemi, J. (2016). Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models. Genetics, 202(4), 1313–1328.

Heath, A. C., Neale, M. C., Hewitt, J. K., Eaves, L. J., & Fulker, D. W. (1989). Testing structural equation models for twin data using LISREL. Behavior Genetics, 19(1), 9–35.

Herzig, A. F., Nutile, T., Ruggiero, D., Ciullo, M., Perdry, H., & Leutenegger, A.-L. (2018). Detecting the dominance component of heritability in isolated and outbred human populations. Scientific Reports, 8(1), 18048.

Hill, W. D., Harris, S. E., & Deary, I. J. (2019). What genome-wide association studies reveal about the association between intelligence and mental health. Current Opinion in Psychology, 27, 25–30.

Hill, W. G., Goddard, M. E., & Visscher, P. M. (2008). Data and Theory Point to Mainly Additive Genetic Variance for Complex Traits. PLOS Genetics, 4(2), e1000008.

Hohman, T. J., Koran, M. E., Thornton-Wells, T., & for the Alzheimer’s Neuroimaging Initiative. (2013). Epistatic Genetic Effects among Alzheimer’s Candidate Genes. PLoS ONE, 8(11), e80839.

Holzinger, K. J. (1929). The relative effect of nature and nurture influences on twin differences. Journal of Educational Psychology, 20(4), 241–248.

Hsu, S. D. (2014). On the genetic architecture of intelligence and other quantitative traits. arXiv preprint arXiv:1408.3421.

Hu, L.-t., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1–55.

Jinks, J. L., & Fulker, D. W. (1970). Comparison of the biometrical genetical, MAVA, and classical approaches to the analysis of human behavior. Psychological Bulletin, 73(5), 311–349.

Keller, M. C., & Coventry, W. L. (2005). Quantifying and Addressing Parameter Indeterminacy in the Classical Twin Design. Twin Research and Human Genetics, 8(3), 201–213.

Keller, M. C., Medland, S. E., & Duncan, L. E. (2010). Are Extended Twin Family Designs Worth the Trouble? A Comparison of the Bias, Precision, and Accuracy of Parameters Estimated in Four Twin Family Models. Behavior Genetics, 40(3), 377–393.

Kempthorne, O. (1978). A Biometrics Invited Paper: Logical, Epistemological and Statistical Aspects of Nature-Nurture Data Interpretation. Biometrics, 34(1), 1–23.

Long, J. S. (1981). Estimation and hypothesis testing in linear models containing measurement error: A review of Jöreskog’s model for the analysis of covariance structures. In P. V. Marsden (Ed.), Linear models in social research (pp. 209–256). Sage.

Lynch, M., & Walsh, B. (1998). Genetics and analysis of quantitative traits. Sinauer.

MacCallum, R. C., Wegener, D. T., Uchino, B. N., & Fabrigar, L. R. (1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin, 114(1), 185–199.

Marchini, J., Donnelly, P., & Cardon, L. R. (2005). Genome-wide strategies for detecting multiple loci that influence complex diseases. Nature genetics, 37(4), 413.

Neale, M., & Maes, H. (2004). Methodology for genetic studies of twins and families. Virginia Commonwealth University, Department of Psychiatry.

Nichols, R. C. (1965). The national merit twin study. Methods and goals in human behavior genetic, 231–244.

Nikolas, M. A., & Burt, S. A. (2010). Genetic and environmental influences on ADHD symptom dimensions of inattention and hyperactivity: A meta-analysis. Journal of Abnormal Psychology, 119(1), 1–17.

Nolte, I. M., Van Der Most, P. J., Alizadeh, B. Z., De Bakker, P. I., Boezen, H. M., Bruinenberg, M., Franke, L., Van Der Harst, P., Navis, G., Postma, D. S., Rots, M. G., Stolk, R. P., Swertz, M. A., Wolffenbuttel, B. H., Wijmenga, C., & Snieder, H. (2017). Missing heritability: Is the gap closing? An analysis of 32 complex traits in the Lifelines Cohort Study. European Journal of Human Genetics, 25(7), 877–885.

Polderman, T. J. C., Benyamin, B., de Leeuw, C. A., Sullivan, P. F., van Bochoven, A., Visscher, P. M., & Posthuma, D. (2015). Meta-analysis of the heritability of human traits based on fifty years of twin studies. Nature Genetics, 47(7), 702–709.

Revelle, W. (2016). psych: Procedures for Personality and Psychological Research. Northwestern University. Evanston, Illinois, USA. Retrieved from

Revolution Analytics & Weston, S. (2022). doMC: Foreach Parallel Adaptor for ’parallel’.

Rijsdijk, F. V. (2002). Analytic approaches to twin data using structural equation models. Briefings in Bioinformatics, 3(2), 119–133.

Ritchie, M. D., Hahn, L. W., Roodi, N., Bailey, L. R., Dupont, W. D., Parl, F. F., & Moore, J. H. (2001). Multifactor-Dimensionality Reduction Reveals High-Order Interactions among Estrogen-Metabolism Genes in Sporadic Breast Cancer. The American Journal of Human Genetics, 69(1), 138–147.

Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1–36.

Schönemann, P. H. (1989). New questions about old heritability estimates. Bulletin of the Psychonomic Society, 27(2), 175–178.

Schönemann, P. H. (1997). On models and muddles of heritability. Genetica, 99(2), 97–108.

Schwabe, I., Janss, L., & Van Den Berg, S. M. (2017). Can We Validate the Results of Twin Studies? A Census-Based Study on the Heritability of Educational Achievement. Frontiers in Genetics, 8, 160.

Shalizi, C. (2007). Yet More on the Heritability and Malleability of IQ. [Retrieved September 27, 2007].

Sniekers, S., Stringer, S., Watanabe, K., Jansen, P. R., Coleman, J. R. I., Krapohl, E., Taskesen, E., Hammerschlag, A. R., Okbay, A., Zabaneh, D., Amin, N., Breen, G., Cesarini, D., Chabris, C. F., Iacono, W. G., Ikram, M. A., Johannesson, M., Koellinger, P., Lee, J. J., . . . Posthuma, D. (2017). Genome-wide association meta-analysis of 78,308 individuals identifies new loci and genes influencing human intelligence. Nature Genetics, 49(7), 1107–1112.

Strange, A., Capon, F., Donnelly, P., & Trembath, R. (2010). A genome-wide association study identifies new psoriasis susceptibility loci and an interaction between HLA-C and ERAP1. Nature Genetics, 42, 985–990.

Strobl, C., Boulesteix, A.-L., Kneib, T., Augustin, T., & Zeileis, A. (2008). Conditional variable importance for random forests. BMC Bioinformatics, 9(1), 307.

Tomarken, A. J., & Waller, N. G. (2003). Potential problems with "well fitting" models. Journal of Abnormal Psychology, 112(4), 578–598.

Van Houtem, C., Laine, M., Boomsma, D., Ligthart, L., Van Wijk, A., & De Jongh, A. (2013). A review and meta-analysis of the heritability of specific phobia subtypes and corresponding fears. Journal of Anxiety Disorders, 27(4), 379–388.

Visscher, P. M., Wray, N. R., Zhang, Q., Sklar, P., McCarthy, M. I., Brown, M. A., & Yang, J. (2017). 10 Years of GWAS Discovery: Biology, Function, and Translation. The American Journal of Human Genetics, 101(1), 5–22.

Vitzthum, V. J. (2003). A number no greater than the sum of its parts: The use and abuse of heritability. Human Biology, 75(4), 539–558.

Wei, W.-H., Hemani, G., & Haley, C. S. (2014). Detecting epistasis in human complex traits. Nature Reviews Genetics, 15(11), 722–733.

Wickham, H., François, R., Henry, L., Müller, K., & Vaughan, D. (2023). dplyr: A grammar of data manipulation.

Wright, M. N., & Ziegler, A. (2017). ranger: A fast implementation of random forests for high dimensional data in C++ and R. Journal of Statistical Software, 77(1), 1–17.

Wright, S. (1921). Systems of mating. I. The biometric relations between parent and offspring. Genetics, 6(2), 111–123.

Zhu, Z., Bakshi, A., Vinkhuyzen, A. A., Hemani, G., Lee, S. H., Nolte, I. M., van Vliet-Ostaptchouk, J. V., Snieder, H., Esko, T., & Milani, L. (2015). Dominance genetic variation contributes little to the missing heritability for human complex traits. The American Journal of Human Genetics, 96(3), 377–385.

Zuk, O., Hechter, E., Sunyaev, S. R., & Lander, E. S. (2012). The mystery of missing heritability: Genetic interactions create phantom heritability. Proceedings of the National Academy of Sciences, 109(4), 1193–1198.






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