Estimation of indirect genetic effects and heritability under assortative mating
Open accessAbstract
Both direct genetic effects (effects of alleles in an individual on that individual) and indirect genetic effects — effects of alleles in an individual (e.g. parents) on another individual (e.g. offspring) — can contribute to phenotypic variation and genotype-phenotype associations. Here, we consider a phenotype affected by direct and parental indirect genetic effects under assortative mating at equilibrium. We generalize classical theory to derive a decomposition of the equilibrium phenotypic variance in terms of direct and indirect genetic effect components. We extend this theory to show that popular methods for estimating indirect genetic effects or ‘genetic nurture’ through analysis of parental and offspring polygenic predictors (called polygenic indices or scores — PGIs or PGSs) are substantially biased by assortative mating. We propose an improved method for estimating indirect genetic effects while accounting for assortative mating that can also correct heritability estimates for bias due to assortative mating. We validate our method in simulations and apply it to PGIs for height and educational attainment (EA), estimating that the equilibrium heritability of height is 0.699 (S.E. = 0.075) and finding no evidence for indirect genetic effects on height. We estimate a very high correlation between parents’ underlying genetic components for EA, 0.755 (S.E. = 0.035), which is inconsistent with twin based estimates of the heritability of EA, possibly due to confounding in the EA PGI and/or in twin studies. We implement our method in the software package snipar , enabling researchers to apply the method to data including observed and/or imputed parental genotypes. We provide a theoretical framework for understanding the results of PGI analyses and a practical methodology for estimating heritability and indirect genetic effects while accounting for assortative mating.
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DGE-based SNP heritability estimates do not account for the increase in genetic variance due to AM-induced correlations between causal alleles, leading to a downward bias similar to other family-based heritability estimates.
“However, DGE-based SNP heritability estimates do not account for the increase in genetic variance due to AM-induced correlations between causal alleles, leading to a downward bias similar to other family-based heritability estimates such as classical twin designs and relatedness disequilibrium regression23,36.”
From Family-GWAS reveals effects of environment and mating on genetic associations (2024) · cites this paper as [23]
Even direct genetic effect PGIs may be correlated with genetic factors not directly captured by the PGI or environmental factors, leading to confounding in standard PGI analysis.
“Even DGE PGIs may be correlated with genetic factors not directly captured by the PGI or environmental factors, leading to confounding in standard PGI analysis23.”
From Family-GWAS reveals effects of environment and mating on genetic associations (2024) · cites this paper as [23]
Polygenic indices based on direct genetic effects from FGWAS have favorable properties due to the removal of confounding from PGI weights, making them suited to applications that are sensitive to confounding.
“Polygenic predictors (called polygenic indices, PGIs, or polygenic scores) based on DGE estimates from FGWAS – hereafter, DGE PGIs – have favorable properties due to the removal of confounding from PGI weights, making them suited to applications that are sensitive to confounding4,5,9,13,23.”
From Family-GWAS reveals effects of environment and mating on genetic associations (2024) · cites this paper as [23]
Such confounding is expected under assortative mating and thus likely affects height and education-related direct genetic effect PGIs when analyzing relevant outcomes.
“although such confounding is expected under AM and thus likely affects height and education-related DGE PGIs (when analyzing relevant outcomes)16,23.”
From Family-GWAS reveals effects of environment and mating on genetic associations (2024) · cites this paper as [23]
These factors include environmental factors and direct genetic effects of other variants with which the PGI is correlated due to non-random mating.
“These include environmental factors and DGEs of other variants with which the PGI is correlated due to non-random mating15,23.”
From Family-GWAS reveals effects of environment and mating on genetic associations (2024) · cites this paper as [23]
Some, but not all, methods using genome-wide summary statistics have been shown to be particularly vulnerable to biased inferences due to uncorrected population stratification confounding.
“Some, but not all, of these methods have been shown to be particularly vulnerable to biased inferences due to uncorrected population stratification confounding: for example, measuring the strength of AM23, assessing evidence for IGEs11,42,43, assessing evidence for polygenic selection using ancient and modern DNA4,5,9, and Mendelian Randomisation13.”
From Family-GWAS reveals effects of environment and mating on genetic associations (2024) · cites this paper as [23]
This finding is consistent with a greater contribution from confounding factors to the predictive power of population-effect-based educational attainment PGIs.
“This finding is consistent with a greater contribution from confounding factors to the predictive power of (standard-GWAS derived) population-effect-based EA PGIs17,23.”
From Family-GWAS reveals effects of environment and mating on genetic associations (2024) · cites this paper as [23]
At equilibrium, β=δ+(1+rpar)α, where rpar is the correlation between parents' PGIs.
“At equilibrium, β=δ+(1+rpar)α, where rpar is the correlation between parents’ PGIs23.”
From Family-GWAS reveals effects of environment and mating on genetic associations (2024) · cites this paper as [23]
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Okewole, A., Bourque, V.-R., Koko, M., Huguet, G., Børglum, A. D., Grove, J., Jacquemont, S., Baron‐Cohen, S., & Warrier, V. (2026) · Molecular Psychiatry · doi:10.1038/s41380-026-03880-1 · Cited by 1 · see citing works
Yengo, L., Liang, Y., 23andMe Research Team, Wang, X., Granka, J. M., Evans, D. M., Sidorenko, J., & Visscher, P. M. (2026) · Nature Human Behaviour · doi:10.1038/s41562-026-02599-x
Indirect Genetic Effects on Alcohol Use Disorder and Nicotine DependencePreprint
Luo, M., Pons, V. T., Zakharin, M., Pingault, J., Gillespie, N. A., & van Loo, H. M. (2026) · medRxiv · doi:10.64898/2026.04.17.26351089
Estimating uncertainty in family-based GWASPreprint
Miao, X., Edge, M. D., & Harpak, A. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.05.11.724392
Zhou, J., Ta, A. P., Yang, C., & El‐Shamy, A. (2026) · Biomedicines · doi:10.3390/biomedicines14081677
Malawsky, D., Hegemann, L., Wootton, O., Havdahl, A., Sunde, H., & Martin, H. (2026) · bioRxiv · doi:10.64898/2026.09.01.748516
Bazezew, M. M., Glaser, B. D., Hegemann, L., Askelund, A. D., Pingault, J., Wootton, R. E., Davies, N. M., Ask, H., Havdahl, A., & Hannigan, L. J. (2026) · European Child & Adolescent Psychiatry · doi:10.1007/s00787-026-03197-y
Morosoli, J. J., Orpwood, E., Morris, T. P., ter Kuile, A., Allegrini, A. G., & Pingault, J. (2026) · Nature Communications · doi:10.1038/s41467-026-78790-5
- Authors
- Young, A. S.
- Venue
- bioRxiv (Cold Spring Harbor Laboratory)
- Publisher
- openRxiv
- Published
- 2023-07-11
- PMC
- PMC10369881
- OpenAlex
- W4384038447
- Cited by
- 32
- References
- 53
- Citations by year
- 2026: 13 · 2025: 12 · 2024: 7
- Type
- posted content
- Language
- en
- Open access
- green
- doi.org
- Licence
- cc-by
- Locations
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
- PubMed (publishedVersion)
- PubMed Central (submittedVersion, cc-by)
- Funders
- Open Philanthropy Project (010623-00001 and 2019-198171, 010623-00001)
- National Institutes of Health (00001)
- University of California, Los Angeles
- National Institute on Aging (R24AG065184, R01AG042568)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic and phenotypic traits in livestock
- Social Sciences › Sociology and Political Science › Intergenerational and Educational Inequality Studies
- Keywords
- indirect genetic effects, assortative mating, heritability estimation, polygenic risk score, genetic nurture, educational attainment, height, bias correction
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