To investigate the origin of correlations between each pair of traits Y and Z, we portioned the bivariate correlation into an environmental correlation, ρe(Y,Z), and a genetic correlation, ρg(Y,Z), for each pair of traits. To do this, we fitted the base polygenic model to each pair of traits simultaneously, and set the cross-trait correlation to Cov(Yi,Zi) = ρe(Y,Z) + ρg(Y,Z) and the cross-trait, cross-individual correlation to Cov(Yi,Zj) = 2 ϕij ρg(Y,Z) . To summarize the results, we defined |1 − ρg(Y,Z)| as the distance between each pair of traits, and implemented a simple hierarchical clustering analysis [65], which successively connects the most similar traits using a greedy algorithm. This analysis was carried out in R, using the hclust() function and the “average” agglomeration method.
