### Summary

- Top of page
- Summary
- Introduction
- Models
- Methods
- Results
- Discussion
- Concluding remarks
- Acknowledgements
- References
- Supporting Information

** 1. ** One of the greatest challenges in ecology is to develop tools that can give reliable projections of future population fluctuations as well as to quantity uncertainties. The population prediction interval (PPI), i.e. the stochastic interval that includes a given population size with a certain probability, is affected by changes in expected population size, e.g. due to density regulation, fluctuations in population size because of demographic and environmental stochasticity, uncertainties and biases in parameter estimates, and observation error in estimates of population size.

** 2. ** The aim of this study was to examine how PPI can be used to obtain reliable projections of future population fluctuations. Our approach is to split long time series into two parts: the first part is used for parameter estimation and the second part is used for comparing population predictions with actual population sizes after a certain period of time.

** 3. ** Here we use the Common Birds Census – data from the UK for several species of passerines. Unbiased predictions will give a uniform distribution of the recorded population sizes across the PPI when transformed to a scale defined by the quantiles of the PPI. However, deviations from a uniform distribution reveal biases in the predictions. For instance, if there is a predominance of recorded population sizes in the upper quantiles of the PPI, this shows that our predictions underestimate future population sizes.

** 4. ** Unbiased predictions required models that included both partitioning of stochastic influences into demographic and environmental stochasticity as well as observation error.

** 5. ** Precision in the population predictions was improved when including observation error as well as density dependence.

** 6. ** We recommend that predictions of future fluctuations of small passerine populations are based on models that include density dependence as well as observation error and estimates of the demographic variance that is obtained from individual-based demographic data or based on species-specific life-history characteristics.

** 7. ** These results show that constructing PPI by stochastic simulations may be a useful tool for obtaining reliable population projections.