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Methods WinBUGS code used for the Cannell and leaf datasets (both contained data on all four traits: r, l, M, and A). The WinBUGS code used for the Sonoran data is a slightly modified (or simplified) version of the following code because the Sonora data only included data on three traits (r, l, and M). model { # Loop through each observation i in the dataset: for(i in 1:N){ # Create data matrix by repeating observed data 6 times, for each of the six models. # The data are read-in in a file that contains the variables LogLength = log(l), LogMass = # log(M), and logArea = log(A). Put all data in the data vector Y, which is equivalent to the # observation vector for [log(l) log(M) log(A)] in eqn (2) in the main text. for(m in 1:6){ Y[i,m,1] - LogLength[i] Y[i,m,2] - LogMass[i] Y[i,m,3] - LogArea[i] } # The likelihood (sampling distribution for loglength, logmass, logarea) is a # multivariate normal distribution with mean mu and precision matrix Omega. # Note, the text refers to the covariance matrix, Sigma, but WinBUGS parameterizes # the normal distribution in terms of a precision matrix.The data are Y[,,1] = loglength; # Y[,,2] = logmass; Y[,,3] = logarea. Allow the mean and precision to vary by model m. # If models 1 (elastic) or 2 (stress), only use LogLength LogArea, Y[i,m,1:2] and use # the mean mu12 and precision matrix Omega12; for the other models, use all three # variables, Y[i,m,1:3], and use the mean mu and the precision matrix Omega for(m in 1:2){ # Multivariate normal likelihood for first 2 scaling models: Y[i,m,1:2] ~ dmnorm(mu12[i,m,1:2], Omega12[m,1:2,1:2]) # Define replicated data, Yrep12, for each model Yrep12[i,m,1:2] ~ dmnorm(mu12[i,m,1:2], Omega12[m,1:2,1:2]) for(k in 1:2){ # Compute squared difference (or squared error) for posterior # predictive loss calculation: sqdiff12[i,m,k] - pow(Yrep12[i,m,k] - Y[i,m,k],2) # Replicated data on regu