Assortative Mating Biases Marker-based Heritability Estimators

Many complex traits are subject to assortative mating (AM), with recent molecular genetic findings confirming longstanding theoretical predictions that AM alters genetic architecture by inducing long range dependence across causal variants. However, all marker-based heritability estimators assume mating is random. We provide mathematical and simulation-based evidence demonstrating that both method-of-moments estimators and likelihood-based estimators produce biased estimates in the presence of AM and that common approaches to account for population structure fail to mitigate this bias. Then, examining height and educational attainment in the UK Biobank, we demonstrate that these biases affect real world traits. Finally, we derive corrected heritability estimators for traits under equilibrium AM.