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

Abstract

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.

Accounting for spatially biased sampling effort in presence‐only species distribution modelling

“…Bayesian approaches (Eddy, 2004) incorporating collection activity in species distribution model estimates have also been investigated. Latimer et al (2006) and Royle et al (2007) demonstrated a hierarchical framework incorporating spatially explicit details such as the complexity of irregular sampling intensity (termed 'spatial coverage bias' by Royle et al, 2007) (see also Gelfand et al, 2003;Arg aez et al, 2005;Latimer et al, 2006;Ward et al, 2009;Di Lorenzo et al, 2011;Hui et al, 2011;Golini, 2012). Bias correction features are available in Maxent, the widely used, machine learning approach to species distribution modelling that uses presence/background data to generate model estimates (Dud ık et al, , 2007Phillips et al, 2004Phillips et al, , 2006.…”

Inferring model‐based probability of occurrence from preferentially sampled data with uncertain absences using expert knowledge

“…Secondly, if the false absences occur randomly in space (no preferential sampling), several methods are available (Ward et al . ; Warton & Shepherd ; Di Lorenzo & Farcomeni ) in addition to BIR. In this context, there is currently a debate regarding whether the probability of occurrence can be inferred from presence‐only data sets.…”

A MANOVA test for multivariate lognormal observations with a spike at zero, with application to ecological niches of South Africa

“…(). These kind of data are now common in ecology (Scarnati et al., ; Di Lorenzo et al., ; and references therein) and the focus may be on prediction, interpretation, or both. In fact, researchers are usually interested in predicting an area of suitability for each species of interest, or to relate the abundance with predictors such as level of humidity, median temperature in the summer, etc.…”

“…More details on the measurements in the NIAPS, which were later converted to abundance measures and linked by us to environmental covariates, can be obtained from Kotzé et al (2010). These kind of data are now common in ecology (Scarnati et al, 2009;Di Lorenzo et al, 2011;and references 167 .144 .239 .290 .886 .988 .163 .165 .219 .214 .829 .952 .156 .146 .189 .197 .760 .874 .143 .094 .162 .121 .615 .643 therein) and the focus may be on prediction, interpretation, or both. In fact, researchers are usually interested in predicting an area of suitability for each species of interest, or to relate the abundance with predictors such as level of humidity, median temperature in the summer, etc.…”