When does sampling uncertainty matter in matrix population models? Evidence from published projection matrices

Owen Russell Jones, Emily Simmonds

1. The collation of thousands of population projection matrices in the COM(P)ADRE Matrix Databases has enabled large-scale comparative analyses in ecology, evolution, and demography. A persistent challenge is that transition rates are estimated from finite samples, yet the resulting sampling uncertainty is rarely reported and typically ignored in downstream analyses. Although sampling uncertainty is well recognised, it remains unclear when it affects demographic inference.
2. Using a subset of studies from the COMPADRE Plant Matrix Database for which transition-specific sample sizes could be obtained, we reconstructed sampling distributions for transition rates and derived demographic parameters, and conducted three related analyses: a comparative analysis, a within-species time-series analysis, and a multi-site extension of the climate-demography analysis, each fit with and without explicit sampling uncertainty.
3. The effects of sampling uncertainty were strongly trait-dependent. It had little influence on integrated demographic metrics such as population growth rate, but accounted for a substantial fraction of the total variation in traits related to mortality trajectories, particularly the shape of the mortality distribution. In these cases, point estimates were often systematically displaced from their underlying sampling distributions due to boundary estimates of stage-specific survival (i.e. survival probabilities near 0 or 1), which are common in published matrices. By contrast, inference in a within-species analysis of weather effects on vital rates was largely unaffected.
4. Together, these analyses show that ignoring sampling uncertainty does not universally compromise inference from published projection matrices, but can yield fragile or biased conclusions for certain demographic traits. We identify structural features of MPMs and analyses that may indicate heightened sensitivity to sampling uncertainty, and discuss implications for researchers using compiled demographic databases.