For a given population, a set of common SNPs and the method of calculating the genetic relationship matrix that we have used here, is a fixed quantity because it depends only on effective population size of the human populations [28]. We used , which was calculated from theory based upon an effective population size of 10,000. Variance in genetic relatedness (and therefore power of detection) can decrease by including many rare SNPs in calculating the GRM because adding more rare SNPs increases the effective population size reflecting recent population expansion. The variance in relatedness can also increase by sampling closer relatives (see below for more discussion) or, for example, by creating a relationship matrix based upon haplotype information. Modifying the GRM can also affect the variance of the off-diagonal elements. For example by applying a weighting of SNPs depending on linkage disequilibrium the variance in the estimates of genetic relationships will decrease so that the sampling variance of the estimate of SNP-based heritability will be increased [29]. Although we derive the theory and show the results based on the SNPs
