The science of complex systems is increasingly asked to forecast the consequences of climate change. As a result, scientists are now engaged in making predictions about an uncertain future, which entails the efficient communication of this uncertainty. Here we show the benefits of hierarchically decomposing the uncertainty in predicted changes in animal population size into its components due to structural uncertainty in climate scenarios (greenhouse gas emissions and global circulation models), structural uncertainty in the demographic model, climatic stochasticity, environmental stochasticity unexplained by climate–demographic trait relationships, and sampling variance in demographic parameter estimates. We quantify components of uncertainty surrounding the future abundance of a migratory bird, the greater snow goose (Chen caeruslescens atlantica), using a process-based demographic model covering their full annual cycle. Our model predicts a slow population increase but with a large prediction uncertainty. As expected from theoretical variance decomposition rules, the contribution of sampling variance to prediction uncertainty rapidly overcomes that of process variance and dominates. Among the sources of process variance, uncertainty in the climate scenarios contributed less than 3% of the total prediction variance over a 40-year period, much less than environmental stochasticity. Our study exemplifies opportunities to improve the forecasting of complex systems using long-term studies and the challenges inherent to predicting the future of stochastic systems.