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The genetic architecture of complex human traits remains largely unknown. The distribution of heritability across the minor allele frequency (MAF) spectrum for a trait will be a function of the MAF of its causal variants and their effect sizes. Assumptions about these relationships underpin the tools used to estimate heritability. We examine the performance of two widely used tools, Haseman-Elston (HE) Regression and genomic-relatedness-based restricted maximum-likelihood (GREML). Our simulations show that HE is less biased than GREML under a wide variety of models and that the estimated standard error for HE tends to be substantially overestimated. We then applied HE Regression to infer the heritability of 72 quantitative biomedical traits from up to 50,000 individuals with genotype and imputation data from the UK Biobank. We found that adding each individuals’ geolocation as covariates corrected for population stratification that could not be accounted for by principal components alone (particularly for rare variants). The biomedical traits we analyzed had an average heritability of 0.27, with low frequency variants (MAF≤0.05) explaining an average of 47.7% of the total heritability (and lower frequency variants with MAF≤0.02 explaining a majority of our increased heritability over previous estimates). Variants in regions of low linkage disequilibrium (LD) accounted for 3.3-fold more heritability than the variants in regions of high LD, an effect primarily driven by low frequency variants. These findings suggest a moderate action of negative selection on the causal variants of these traits.