EFFECTS OF ASSORTATIVE MATING ON ESTIMATES OF SNP HERITABILITY

Background Mates are similar to one another across a large number of traits, including liabilities underlying psychiatric disorders. It has long been known that when such phenotypic similarity implies genetic similarity (hereafter, assortative mating), heritability estimates from family and twin studies can be biased. However, the effects of assortative mating, if any, on estimates of heritability from all SNPs in unrelated individuals (SNP-based heritability, h2SNP) have not been investigated to date. Methods We derived mathematically the expected behavior of estimates from Haseman-Elston regression and GREML, and assessed these predictions via simulation. We then assessed in the UK Biobank whether the predicted signatures of assortative mating on h2SNP were observed. Results We show analytically and via simulation that estimates of h2SNP from both GREML and Haseman-Elston regression are typically biased upwards in the presence of assortative mating. However, estimates from Haseman-Elston regression are roughly constant as a function of sample size and number of markers, whereas the ratio of sample size to number of markers strongly affects those from GREML. This difference in estimate behavior allows one to assess in real data whether assortative mating is affecting estimates of h2SNP. When we did this in the UK Biobank for height and IQ, we observed that h2SNP estimates for height that behaved as predicted, but not for h2SNP estimates for IQ. Discussion For many traits, the degree of bias in estimates of h2SNP is expected to be small, but it can be non-trivial for other traits, depending on the degree of assortative mating and the heritability of the traits. For example, based on spousal similarity, we predict that h2SNP estimates of height and IQ are ~25% greater than their true equilibrium values. That we did not observe the predicted pattern of h2SNP estimates for IQ may either suggest that spousal similarity for IQ occurs via mechanisms that do not lead to genetic similarity (e.g., social homogamy) or that the effects of assortative mating on the covariance between causal variants is counter-acted by the forces of natural selection.