Supporting Information 5

Following Aguirre et al. (2013), we generated randomised G-matrices by estimating the marginal posterior distribution of G-matrices for the ten populations. Second, for each MCMC sample, we calculate posterior predictive breeding values for individuals by taking draws from a multivariate normal distribution with a mean of zero and a variance of the i^th MCMC sample of the j^th G-matrix. Then, breeding values are assigned using the pedigree corresponding to each population. Finally, individuals were randomly assigned to one of ten dummy populations and G-matrices were constructed from the vectors of breeding values.

The distribution of explained variance for each eigentensor was then compared with a distribution of the explained variance generated from the null model, where the variation among matrices is due to sampling variation, not biologically meaningful differences.