A hierarchical, multivariate meta-analysis approach to synthesising global change experiments

Meta-analyses enable synthesis of results from globally distributed experiments to draw general conclusions about the impacts of global change factors on ecosystem function. Traditional meta-analyses, however, are challenged by the complexity and diversity of experimental results. We illustrate how several key issues can be addressed by a multivariate, hierarchical Bayesian meta-analysis (MHBM) approach applied to information extracted from published studies. We applied an MHBM to log-response ratios for aboveground biomass (AB, n = 300), belowground biomass (BB, n = 205) and soil CO₂ exchange (SCE, n = 544), representing 100 studies. The MHBM accounted for study duration, climate effects and covariation among the AB, BB and SCE responses to elevated CO₂ (eCO₂) and/or warming. The MHBM revealed significant among-study covariation in the AB and BB responses to experimental treatments. The MHBM imputed missing duration (4.2%) and climate (6%) data, and revealed that climate context governs how eCO₂ and warming impact ecosystem function. Predictions identified biomes that may be particularly sensitive to eCO₂ or warming, but that are under-represented in global change experiments. The MHBM approach offers a flexible and powerful tool for synthesising disparate experimental results reported across multiple studies, sites and response variables.