We consider three approaches to estimating heritability for a phenotype with a narrow-sense heritability of 80%. First, the classic approach to estimating heritability is to divide the phenotypic covariance of related individuals by the fraction of the genome they share IBD13. In this instance, the phenotypic covariance of pairs of related individuals will be 0.80 times the fraction of genome shared IBD (Figure 1a). The second approach, developed by Yang et al.10, is to estimate the genetic relationship of unrelated individuals over genotyped SNPs and applied a linear mixed model with the genetic relationship matrix to estimate phenotype. To illustrate this approach we simulated 2 million independent pairs of individuals, regressing their normalized genetic similarity over the product of their normalized phenotypes giving a regression coefficient of 0.79±0.014 (Figure 1b). This Haseman-Elston regression16 shows how genetic similarity of unrelated individuals can be used to estimate heritability of genotyped SNPs (hg2). In general, the heritability explained by genotyped SNPs is less than the total narrow-sense heritability (h2) since phenotypic variation determined by poorly tagged SNPs such as rare variants will not be captured10.
