Average semivariance yields accurate estimates of the fraction of marker-associated genetic variance and heritability in complex trait analyses

The development of genome-informed methods for identifying quantitative trait loci (QTL) and studying the genetic basis of quantitative variation in natural and experimental populations has been driven by advances in high-throughput genotyping. For many complex traits, the underlying genetic variation is caused by the segregation of one or more ‘large-effect’ loci, in addition to an unknown number of loci with effects below the threshold of statistical detection. The large-effect loci segregating in populations are often necessary but not sufficient for predicting quantitative phenotypes. They are, nevertheless, important enough to warrant deeper study and direct modelling in genomic prediction problems. We explored the accuracy of statistical methods for estimating the fraction of marker-associated genetic variance (p) and heritability (H M 2) for large-effect loci underlying complex phenotypes. We found that commonly used statistical methods overestimate p and H M 2. The source of the upward bias was traced to inequalities between the expected values of variance components in the numerators and denominators of these parameters. Algebraic solutions for bias-correcting estimates of p and H M 2 were found that only depend on the degrees of freedom and are constant for a given study design. We discovered that average semivariance methods, which have heretofore not been used in complex trait analyses, yielded unbiased estimates of p and H M 2, in addition to best linear unbiased predictors of the additive and dominance effects of the underlying loci. The cryptic bias problem described here is unrelated to selection bias, although both cause the overestimation of p and H M 2. The solutions we described are predicted to more accurately describe the contributions of large-effect loci to the genetic variation underlying complex traits of medical, biological, and agricultural importance.Author summary: The contributions of individual genes to the phenotypic variation observed for genetically complex traits has been an ongoing and important challenge in biology, medicine, and agriculture. While many genes have statistically undetectable effects, those with large effects often warrant in-depth study and can be important predictors of complex phenotypes such as disease risk in humans or disease resistance in domesticated plants and animals. The genes identified through associations with genetic markers in complex trait analyses typically account for a fraction of the heritable variation, a genetic parameter we called ‘marker heritability’. We discovered that textbook statistical methods systematically overestimate marker heritability and thus overestimate the contributions of specific genes to the phenotypic variation observed for complex traits in natural and experimental populations. We describe the source of the upward bias, validate our findings through computer simulation, describe methods for bias-correcting estimates of marker heritability, and illustrate their application through empirical examples. The statistical methods we describe supply investigators with more accurate estimates of the contributions of specific genes or networks of interacting genes to the heritable variation observed in complex trait studies.