Mixed linear model methods are useful to control for population structure in GWAS21,22. Population structure in the data causes correlations of SNPs on different chromosomes. Consequently, fitting only one chromosome in the model (separate analysis) also captures some of the variance due to other chromosomes, so that the estimate of variance explained by each chromosome from the separate analysis ( hC2(sep)) is biased upwards (Online Methods). The joint analysis has the advantage of protecting against such inter-chromosomal correlations because the estimate of each hC2 is conditional on the other chromosomes in the model so that the estimates of variance explained by different chromosomes are independent of each other. We therefore can calculate the variance attributable to population structure by comparing the estimates between hC2(sep) and hC2. The inter-chromosomal SNP correlations occur for two reasons: 1) cryptic relatedness (e.g. unexpected cousins) because closely related individuals will share SNPs identical by descent on more than one chromosome; 2) systematic difference in allele frequencies between subpopulations (population stratification). We modelled the variance attributed to these two forms of population structure as hC2(sep)−hC2=b0+b1LC+ε, where
