A flexible framework for N-mixture occupancy models: applications to breeding bird surveys

Estimating species abundance under imperfect detection is a key challenge in biodiversity conservation. The N-mixture model, widely recognized for its ability to distinguish between abundance and individual detection probability without marking individuals, is constrained by its stringent closure assumption, which leads to biased estimates when violated in real-world settings. To address this limitation, we propose an extended framework based on a development of the mixed Gamma-Poisson model, incorporating a community parameter that represents the proportion of individuals consistently present throughout the survey period. This flexible framework generalizes both the zero-inflated type occupancy model and the standard N-mixture model as special cases, corresponding to community parameter values of 0 and 1, respectively. The model's effectiveness is validated through simulations and applications to real-world datasets, specifically with 5 species from the North American Breeding Bird Survey and 46 species from the Swiss Breeding Bird Survey, demonstrating its improved accuracy and adaptability in settings where strict closure may not hold.