All analyses we have performed are univariate, i.e. a single phenotype at a time. However, multivariate models fit easily in the same analysis framework and the only limitation is computational. As an example, we approximated a full bivariate analysis of height and weight by using logarithms of the phenotypes, exploiting the relationship log(BMI) = log(Weight) − 2log(Height), so that from three univariate analyses we can estimate the genetic correlation between log(Weight) and log(Height). We estimated a genetic correlation of 0.45 (s.e. = 0.17) between log(Weight) and log(Height) (Supplementary Table 12). Although this is on the logarithm scale, the estimate on the observed scale is unlikely to be very different. This estimate indicates that for genetic variation tagged by common SNPs there is a substantial overlap in genome-wide additive factors for height and weight.
