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 on the whole genome, our approximation theories are also applicable in analyses using a subset of SNPs, e.g. SNPs from a single chromosome. In that case, used in the approximation equations should be either observed empirically from data or derived from theory [28] based on the subset of SNPs.