Spatio-temporal occupancy models with INLA

Modern methods for quantifying, predicting and mapping species distributions have played a crucial part in biodiversity conservation. Occupancy models have become a popular choice for analysing species occurrence data due to their ability to separate out the observational error induced by imperfect detection of a species, and the sources of bias affecting the occupancy process. However, the spatial and temporal variation in occupancy that is not accounted for by environmental covariates is often ignored or modelled through simple spatial structures as the computational costs of fitting explicit spatio-temporal models is too high. In this work, we demonstrate how Integrated Nested Laplace Approximation (INLA) may be used to fit complex spatio-temporal occupancy models and how the R-INLA package can provide a user-friendly interface to make such complex models available to users. We show how occupancy models, provided some simplification on the detection process is assumed, can be framed as latent Gaussian models and, as such, benefit from the powerful INLA framework. A large selection of complex modelling features, and random effect models, including spatio-temporal models, have already been implemented in R-INLA. These also become available for occupancy models, providing the user with an efficient, reliable and flexible toolbox. We illustrate how INLA provides a flexible and computationally efficient framework for developing and fitting complex occupancy models using two complex case studies. Through these, we show how different spatio-temporal models that include spatial-varying trends, smooth terms and spatio-temporal random effects can be fitted to aggregated detection/non-detection data. At the cost of limiting the complexity of the detection model structure, INLA can incorporate a range of rather complex structures in the ecological process of interest and hence, extend the functionality of occupancy models. The limitations of occupancy models in terms of scalability for large spatio-temporal data sets remain a challenge and an active area of research. INLA-based occupancy models provide an alternative inferential and computational framework to fit complex spatio-temporal occupancy models. The need for new and more flexible computationally efficient approaches to fit such models makes INLA an attractive option for addressing complex ecological problems, and a promising area of research.