The methods of using SNP data to estimate genetic variance in unrelated individuals have been detailed elsewhere [3], [13]. In brief, given GWAS data, we can model the phenotype as(1)where y is an N×1 vector of phenotypes with N being the sample size, g is an N×1 vector with each of its elements being the total genetic effect of an individual captured by all SNPs, and e is an N×1 vector of residuals. We have and , where is the genetic variance captured by all SNPs, A is the genetic relationship matrix (GRM) estimated from SNPs [3], is the residuals variance and I is an identity matrix. The genetic relationships, also known as ‘genomic relationships’ or ‘genetic similarity relationships’, are referenced to the current population, and so can be negative as they are distributed about a mean of zero. Equation (1) is a typical mixed linear model with , in which the variance components can be estimated using a restricted maximum likelihood (REML) approach [13], [14]. The proportion of variance explained by all SNPs (SNP heritability) is defined as .
