Mean square error (MSE) for the occupancy estimator in the hierarchical/naïve models, and their ratio, obtained from simulations of three “abundance” scenarios: (a) Scenario B1 from [14], (b) Scenario B2 and (c) Scenario B3.

Simulations were run for a range of sample sizes, with S sites and K replicate surveys per site (5000 simulations per case). When , the naïve model was fitted to the data resulting from collapsing the detection/non-detection history into a single record per site (1 if species detected at least once, 0 otherwise). The hierarchical model outperforms the naïve model, being clearly superior in the third example.