A Bayesian Model for Presence-Only Semicontinuous Data, With Application to Prediction of Abundance of Taxus Baccata in Two Italian Regions

In studies about the potential distribution of ecological niches, only the presence of the species of interest is usually recorded. Pseudo-absences are sampled from the study area in order to avoid biased estimates and predictions. For cases in which, instead of the mere presence, a continuous abundance index is recorded, we derive a two-part model for semicontinuous (i.e., positive with excess zeros) data which explicitly takes into account uncertainty about the sampled zeros. Our model is a direct extension of the one of Ward et al. (Biometrics 65, 554-563, 2009). It is fit in a Bayesian framework, which has many advantages over the maximum likelihood approach of Ward et al. (2009), the most important of which is that the prevalence of the species does not need to be known in advance. We illustrate our approach with real data arising from an original study aiming at the prediction of the potential distribution of the Taxus baccata in two central Italian regions. Supplemental materials giving detailed proofs of propositions, tables and code are available online.