Uncovering the Genetic Architectures of Quantitative Traits

Abstract

The aim of a genome-wide association study (GWAS) is to identify loci in the human genome affecting a phenotype of interest. This review summarizes some recent work on conceptual and methodological aspects of GWAS. The average effect of gene substitution at a given causal site in the genome is the key estimand in GWAS, and we argue for its fundamental importance. Implicit in the definition of average effect is a linear model relating genotype to phenotype. The fraction of the phenotypic variance ascribable to polymorphic sites with nonzero average effects in this linear model is called the heritability, and we describe methods for estimating this quantity from GWAS data. Finally, we show that the theory of compressed sensing can be used to provide a sharp estimate of the sample size required to identify essentially all sites contributing to the heritability of a given phenotype.

Keywords: Average effect of gene substitution; Compressed sensing; GWAS; Heritability; Population genetics; Quantitative genetics; Review; Statistical genetics.

Fig. 1

Breeding (additive genetic) values and dominance deviations at a biallelic locus. The frequency of allele ${\mathcal{A}}_2$ is 0.6, and the causal effects of ${\mathcal{A}}_1{\mathcal{A}}_1$ → ${\mathcal{A}}_1{\mathcal{A}}_2$ and ${\mathcal{A}}_1{\mathcal{A}}_2$ → ${\mathcal{A}}_2{\mathcal{A}}_2$ are 3 and − 2 respectively. The genotype frequencies are in Hardy–Weinberg equilibrium. The phenotypic mean of each genotype is equal to the sum of its breeding value (α_ij) and genetic residual (δ_ij); in this case of nonlinearity within a locus, the genetic residuals are called dominance deviations. The phenotypic means are represented by the blue points, and the corresponding breeding values by the red points. The slope of the linear function giving the breeding values is the average effect of gene substitution.