Improved Heritability Estimation from Genome-wide SNPs Doug Speed, Gibran Hemani, Michael R. Johnson, David J. Balding  The American Journal of Human Genetics  Volume 91, Issue 6, Pages 1011-1021 (December 2012) DOI: 10.1016/j.ajhg.2012.10.010 Copyright © 2012 The American Society of Human Genetics Terms and Conditions

Figure 1 Investigation of the Robustness of hˆ2 to Assumptions of Polygeneity (A) The distribution of hˆ2 for different numbers of causal variants, from one up to “ALL” (all 81,327 SNPs), with the use of the standard kinship matrix A (left) and the weighted kinship matrix A∗ (right). Boxes indicate interquartile ranges, colors correspond to simulated h2 (red, 0.5; green, 0.8), and whiskers span the full range except for outliers, indicated with circles. (B) The layout matches that of (A), but now the boxes correspond to the REML SD estimates calculated by GCTA, and the purple lines mark the empirical SD estimates based on the 50 replicates. The American Journal of Human Genetics 2012 91, 1011-1021DOI: (10.1016/j.ajhg.2012.10.010) Copyright © 2012 The American Society of Human Genetics Terms and Conditions

Figure 2 Investigation of the Robustness of hˆ2 to Assumptions of the Relationship between Effect-Size Variance and MAF Phenotypes were simulated with each of four models (indexed by α1) for the relationship between effect-size variance and MAF (Equation 5). Analysis was performed with each of the same four models (indexed by α2) when allele counts were standardized. Boxes indicate interquartile ranges of hˆ2. Colors correspond to simulated h2 (red, 0.5; green, 0.8), and gray boxes indicate that the analysis model matches the simulation model (α1 = α2). The American Journal of Human Genetics 2012 91, 1011-1021DOI: (10.1016/j.ajhg.2012.10.010) Copyright © 2012 The American Society of Human Genetics Terms and Conditions

Figure 3 Distributions of hˆ2 with and without Adjustment for LD The x axis indicates the relative levels of tagging of the causal variants. The boxes indicate interquartile ranges of hˆ2 under SNP-based mixed-model analysis using A (left) or A∗ (right). Colors correspond to simulated h2 (red, 0.5; green, 0.8), and gray boxes indicate that causal variants were chosen at random without regard to tagging. The American Journal of Human Genetics 2012 91, 1011-1021DOI: (10.1016/j.ajhg.2012.10.010) Copyright © 2012 The American Society of Human Genetics Terms and Conditions