Common SNPs explain a large proportion of the heritability for human height

Abstract

SNPs discovered by genome-wide association studies (GWASs) account for only a small fraction of the genetic variation of complex traits in human populations. Where is the remaining heritability? We estimated the proportion of variance for human height explained by 294,831 SNPs genotyped on 3,925 unrelated individuals using a linear model analysis, and validated the estimation method with simulations based on the observed genotype data. We show that 45% of variance can be explained by considering all SNPs simultaneously. Thus, most of the heritability is not missing but has not previously been detected because the individual effects are too small to pass stringent significance tests. We provide evidence that the remaining heritability is due to incomplete linkage disequilibrium between causal variants and genotyped SNPs, exacerbated by causal variants having lower minor allele frequency than the SNPs explored to date.

Figure 1

Prediction error of genetic relationship. The genetic relationship at unobserved causal loci is predicted, with error, from the relationship estimated from genotyped SNPs. The prediction error is calibrated by comparing the relationship at causal loci (mimicked by a set of random SNPs with MAF ≤ θ) to that estimated from another set of random SNPs. Values plotted on y-axis are (1−β) var(A_jk) (see Online Methods for the notations) calculated from different numbers of random SNPs (N) in both adult and adolescent datasets. The slope of each line is equal to 1.0, with R² = 1.0. The intercept (c) is constant for a certain MAF threshold θ, and c = 6.2 × 10⁻⁶ (p-value = 2 × 10⁻¹⁴), 3.4 × 10⁻⁶ (p-value = 9 × 10⁻¹²), 1.8 × 10⁻⁶ (p-value = 4 × 10⁻¹⁰), 7.8 × 10⁻⁷ (p-value = 2 × 10⁻⁷) and 9.2 × 10⁻⁹ (p-value = 0.87, not significant) for θ = 0.1, 0.2, 0.3, 0.4 and 0.5, respectively.

Figure 2

Estimates of variance explained by genome-wide SNPs from adjusted estimates of genetic relationships are unbiased. Results are shown as estimates of variance explained by different proportions of SNPs randomly selected from all the SNPs in the combined set. For each group of SNPs, the variance explained by genome-wide SNPs is estimated using both raw estimates of genetic relationships and adjusted estimates of genetic relationships correcting for prediction error (assuming c = 0). Error bars denote s.e. of the estimate of variance explained by genome-wide SNPs. The log-likelihood ratio test (LRT) statistic is calculated as twice the difference in log-likelihood between the full (h² ≠ 0) and reduced (h² = 0) models.

Figure 3

All pairwise comparisons contribute to the estimate of genetic variance. Shown are the squared z-score differences between individuals ( $\mathrm{\Delta }{y}_{jk}^2$) plotted against the adjusted estimates of genetic relationship ( $A_{jk}^{\ast }$). The blue line is the linear regression line of $\mathrm{\Delta }{y}_{jk}^2$ on $A_{jk}^{\ast }$. The intercept and regression coefficient are estimates of twice the phenotypic variance and minus twice the genetic variances, respectively. The intercept is 1.98 (s.e. = 0.001) and the regression coefficient is −1.01 (s.e = 0.27), consistent with estimates of the phenotypic and additive genetic variance of 0.990 and 0.505, respectively, and a proportion of variance explained by all SNPs of 0.51.