Assortative mating biases marker-based heritability estimators

Richard Border,Teresa de Candia,Matt Jones,Matthew C. Keller,Loic Yengo,Michael E. Goddard,Peter M. Visscher,Sean O’Rourke

doi:10.1038/s41467-022-28294-9

Abstract

Many traits are subject to assortative mating, with recent molecular genetic findings confirming longstanding theoretical predictions that assortative mating induces long range dependence across causal variants. However, all marker-based heritability estimators implicitly assume mating is random. We provide mathematical and simulation-based evidence demonstrating that both method-of-moments and likelihood-based estimators are biased in the presence of assortative mating and derive corrected heritability estimators for traits subject to assortment. Finally, we demonstrate that the empirical patterns of estimates across methods and sample sizes for real traits subject to assortative mating are congruent with expected assortative mating-induced biases. For example, marker-based heritability estimates for height are 14% – 23% higher than corrected estimates using UK Biobank data.

Highlights

To assess the scenario wherein a nontrivial fraction of causal variants are missing from Z, we estimated HE regression and REML models after removing 50 or 75% of simulated SNPs at random (Fig. 4b)
We randomly selected ten mutually exclusive subsamples of nsmall = 16,000 individuals for each trait and compared HE and REML estimates in each subsample to the non-overlapping complementary subsample comprised of the remaining nlarge 1⁄4 n−16,000 individuals, controlling for sex, age, genotyping batch, testing center, and the first ten genomic ancestry PCs
Further information on research design is available in the Nature Research Reporting Summary linked to this article

Summary

Results

Our theoretical results depend on several key parameters: r denotes the phenotypic correlation between mates on an additive phenotype y with a heritable component Zu; h20 denotes the panmictic heritability, what the narrow-sense heritability of the phenotype would be in the absence of AM; h21 denotes the equilibrium narrow-sense heritability approached under multiple generations of AM; and Z denotes the nm matrix of n unrelated individuals’ standardized genotypes at m causal loci with effects vector u. The rows of Z (individuals’ genotypes) are independent random vectors with mm covariance matrix Υ, which quantifies the correlation between loci. As the elements of Υ1 agree in sign with the corresponding elements of uuT (i.e., trait increasing alleles are positively correlated), the equilibrium additive genetic variance under AM, σ2g;1, is considerably greater than the panmictic additive genetic variance, σ 2g ;0

Discussion

Methods

Code availability