Monitoring species occurrence is essential for understanding biodiversity change, informing conservation decisions, and assessing the impact of environmental pressures on ecosystems. Species occurrence data arise from different survey designs, and the statistical literature has developed distinct corresponding modelling approaches, namely occupancy models, species distribution models, and presence-only methods, whose fundamental connections have remained largely unrecognised. We argue that these are all special cases of a single hierarchical observation process. To make these connections explicit, we introduce a unified terminology centred on two data types: detection/non-detection data with T visits (DN-T) and detection-only data (DO), where DN-T with T>1 corresponds to traditional occupancy modelling, DN-1 to species distribution modelling, and DO to what the literature commonly, but we argue inaccurately, calls presence-only data. Within this framework, we study the identifiability of DO models and propose a novel hierarchical model for DO data that, for the first time, explicitly accounts for both false positive and false negative detection errors. Identifiability is achieved through prior distributions that express the natural belief that a species is more likely to be recorded where it is present than where it is absent. ...
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