Mean square error (MSE) for the occupancy estimator in the hierarchical/naïve models, and their ratio, obtained from simulations of (a) Scenario A1 and (b) Scenario A2 (see Table 1 for details).

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). In the majority of these cases the performance of the hierarchical model was either comparable or considerably superior to that of the naïve model. A ratio <1 indicates that the MSE of the hierarchical model is smaller than in the naïve model.