Estimating the occupancy rate of spatially rare or hard to detect species: a conditional approach

We consider the problem of estimating the occupancy rate of a target species in a region divided in spatial units (called quadrats); this quantity being defined as the proportion of quadrats occupied by this species. We mainly focus on spatially rare or hard to detect species that are typically detected in very few quadrats, and for which estimating the occupancy rate (with an acceptable precision) is problematic. We develop a conditional approach for estimating the quantity of interest; we condition on the presence of the target species in the region of study. We show that conditioning makes identifiable the occurrence and detectability parameters, regardless of the number of visits made in the sampled quadrats. Compared with an unconditional approach, it proves to be complementary, in that this allows us to deal with biological questions that cannot be addressed by the former. Two Bayesian analyses of the data are performed: one is noninformative, and the other takes advantage of the fact that some prior information on detectability is available. It emerges that taking such a prior into account significantly improves the precision of the estimate when the target species has been detected in few quadrats and is known to be easily detectable.