Beyond SNP Heritability: Polygenicity and Discoverability of Phenotypes Estimated with a Univariate Gaussian Mixture Model

Abstract

Of signal interest in the genetics of traits are estimating the proportion, π 1 , of causally associated single nucleotide polymorphisms (SNPs), and their effect size variance, σ 2 β , which are components of the mean heritabilities captured by the causal SNP. Here we present the first model, using detailed linkage disequilibrium structure, to estimate these quantities from genome-wide association studies (GWAS) summary statistics, assuming a Gaussian distribution of SNP effect sizes, β. We apply the model to three diverse phenotypes -schizophrenia, putamen volume, and educational attainment -and validate it with extensive simulations. We find that schizophrenia is highly polygenic, with ≃ 5 × 10 4 causal SNPs distributed with small effect size variance, σ 2 β = 3.5 × 10 −5 (in units where the phenotype variance is normalized to 1), requiring a GWAS study with more than 1/2-million samples in each arm for full discovery. In contrast, putamen volume involves only ≃ 3 × 10 2 causal SNPs, but with σ 2 β = 1.2 × 10 −3 , indicating a much larger proportion of the causal SNPs that are strongly associated. Educational attainment has similar polygenicity to schizophrenia, but with effects that are substantially weaker, σ 2 β = 5 × 10 −6 , leading to much lower heritability. Thus the model is able to describe the broad genetic architecture of phenotypes where both polygenicity and effect size variance range over several orders of magnitude, shows why only small proportions of heritability have been explained for discovered SNPs, and provides a roadmap for future GWAS discoveries.

Localizing components of shared transethnic genetic architecture of complex traits from GWAS summary data

“…Across the 9 traits, the estimated proportions of common causal SNPs in each population (the sum of the 293 numbers of population-specific and shared causal SNPs) are consistent with previously reported estimates 294 of polygenicity in single populations 7,8,55,75,76 . For example, we estimate that approximately 10% of common 295…”

Mapping causal pathways from genetics to neuropsychiatric disorders using genome‐wide imaging genetics: Current status and future directions

“…93 Measuring the effect size differences at an individual locus for two different traits determines whether the maximum effect of a variant is higher in one trait than another. Recent studies [94][95][96] have asked a broader question: Are effect size distributions of common variants across the genome in general stronger for neuroimaging traits than they are for neuropsychiatric disorders? Effect size distributions can be estimated by clustering the effect sizes of linkage disequilibrium (LD)-independent SNPs across the genomes into one of two general categories: (i) susceptibility SNPs, which show some level of nonzero effect sizes (although do not necessarily survive genome-wide significance); and (ii) SNPs that have signals so low they cannot be distinguished from no effect.…”

“…Genetic variants impacting psychiatric disorders are amongst the most polygenic studied with an estimated 10 000-50 000 susceptibility SNPs, 94 indicating that many genetic variants, each of exceedingly small effect size, impact risk for these disorders. 94,95 In comparison, ulcerative colitis and asthma are estimated to have only 1000-2000 susceptibility SNPs. 94 Within the realm of imaging genetics, the degree of polygenicity of the putamen is over 30-fold less than that of schizophrenia, again indicating a higher effect size distribution of a brain structure trait as compared to a disorder.…”

Annotation-Informed Causal Mixture Modeling (AI-MiXeR) reveals phenotype-specific differences in polygenicity and effect size distribution across functional annotation categories

“…For example, they are agnostic about the number of genetic variants influencing a 18 phenotype and their effect sizes [4]. Both of these quantities can vary and still result in the same 19heritability, which is proportional to their product [5,6]. 20Recently, we developed a model which allows the breakdown of SNP-heritability into the number of 21 variants influencing a given phenotype (non-null variants) and the distribution of their effect sizes using 22 summary statistics from GWAS and detailed population-specific linkage disequilibrium (LD) structure [5, 23 6].…”

“…It was shown that, in the framework of the infinitesimal model, 0 2 has 14 the same mathematical meaning as the intercept term in the LDSC model [6]. The last unknown factor in 15 (5), , is modeled as a random variable with point-normal mixture distribution, where the variance is 16 allowed to differ between different variant annotation categories: 17…”