Quantifying patterns of temporal trends in species assemblages is an important analytical challenge in community ecology. We describe methods of analysis that can be applied to a matrix of counts of individuals that is organized by species (rows) and time-ordered sampling periods (columns). We first developed a bootstrapping procedure to test the null hypothesis of random sampling from a stationary species abundance distribution with temporally varying sampling probabilities. This procedure can be modified to account for undetected species. We next developed a hierarchical model to estimate species-specific trends in abundance while accounting for species-specific probabilities of detection. We analysed two long-term datasets on stream fishes and grassland insects to demonstrate these methods. For both assemblages, the bootstrap test indicated that temporal trends in abundance were more heterogeneous than expected under the null model. We used the hierarchical model to estimate trends in abundance and identified sets of species in each assemblage that were steadily increasing, decreasing or remaining constant in abundance over more than a decade of standardized annual surveys. Our methods of analysis are broadly applicable to other ecological datasets, and they represent an advance over most existing procedures, which do not incorporate effects of incomplete sampling and imperfect detection.
