Evaluating and improving heritability models using summary statistics

There is currently much debate regarding the best model for how heritability varies across the genome. The authors of GCTA recommend the GCTA-LDMS-I model, the authors of LD Score Regression recommend the Baseline LD model, and we have recommended the LDAK model. Here we provide a statistical framework for assessing heritability models using summary statistics from genome-wide association studies. Based on 31 studies of complex human traits (average sample size 136,000), we show that the Baseline LD model is more realistic than other existing heritability models, but that it can be improved by incorporating features from the LDAK model. Our framework also provides a method for estimating the selection-related parameter α from summary statistics. We find strong evidence (P < 1 × 10^-6) of negative genome-wide selection for traits, including height, systolic blood pressure and college education, and that the impact of selection is stronger inside functional categories, such as coding SNPs and promoter regions.