*Ecological Archives* E096-096-A4

Chris H. Wilson, T. Trevor Caughlin, David J. Civitello, and S. Luke Flory. 2015. Combining mesocosm and filed experiments to predict invasive plant performance: a hierarchical Bayesian approach. *Ecology* 96:1084–1092. http://dx.doi.org/10.1890/14-0797.1

Appendix D. Cross-validated posterior predictive distribution for the gamma-gamma hierarchical biomass model.

We fitted the biomass model 21 times, each time holding out one of the 21 sites, and then predicting its mean response by drawing from the estimated parameters of the Michaelis-Menten function and the site-level variance (i.e., predicting a "new" site given the same light level). The predictions include a 50% confidence (credible) interval (solid black bars), and a 95% confidence interval (dashed lines). Approximately half of the sites fall outside the 50% prediction intervals, which is around the expected number if the model is true. Essentially, this cross-validation ensures that the model is not overly sensitive to the exclusion of the site being predicted, and is an approximation of how well our model should hold up under future replications.

Fig. D1. Cross-validated posterior predictive distribution for the mean biomass/plant (g) at each site, compared to the observed mean (red x's).