Hierarchical models for smoothed population indices: the importance of considering variations in trends of count data among sites

Population indices quantify changes in relative population sizes, which underpin much of basic ecology and conservation science. However, temporal changes in population counts may vary among survey sites for both ecological and artificial reasons, confounding existing population indices estimated without accounting for such variations. We created a smoothed hierarchical model, and compared its performance against the conventional approaches (generalized linear models and generalized additive models) and a non-smoothed hierarchical model using simulation data with a known nonlinear trend. The smoothed hierarchical model always estimated population indices with the best accuracy and precision; the performance of other models deteriorated substantially with increasing variation in trends of population counts among sites, causing inaccurate estimation of population growth rates. The estimated variations in trends of population counts among sites for 233 out of 518 North American breeding bird species were larger than the value used in the simulation where there was a considerable difference in the performance between hierarchical models and the conventional approaches. These estimated variations in trends of population counts among sites were particularly large in gregarious waterbirds. These results suggest that the smoothed hierarchical model developed in this study should play an important role in accurately assessing population indices, particularly for gregarious waterbirds, using count data from large-scale, long-term surveys in the field.