N_c-mixture occupancy model
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A class of occupancy models for detection/non-detection data is proposed to relax the closure assumption of N-mixture models. We introduce a community parameter c, ranging from 0 to 1, which characterizes a certain portion of individuals being fixed across multiple visits. As a result, when c equals 1, the model reduces to the N-mixture model; this reduced model is shown to overestimate abundance when the closure assumption is not fully satisfied. Additionally, by including a zero-inflated component, the proposed model can bridge the standard occupancy model (c=0) and the zero-inflated N-mixture model (c=1). We then study the behavior of the estimators for the two extreme models as c varies from 0 to 1. An interesting finding is that the zero-inflated N-mixture model can consistently estimate the zero-inflated probability (occupancy) as c approaches 0, but the bias can be positive, negative, or unbiased when c>0 depending on other parameters. We also demonstrate these results through simulation studies and data analysis.
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