Fitting complex ecological point process models with integrated nested Laplace approximation

We highlight an emerging statistical method, integrated nested Laplace approximation (INLA), which is ideally suited for fitting complex models to many of the rich spatial data sets that ecologists wish to analyse. INLA is an approximation method that nevertheless provides very exact estimates. In this article, we describe the INLA methodology highlighting where it offers opportunities for drawing inference from (spatial) ecological data that would previously have been too complex to make practical model fitting feasible. We use INLA to fit a complex joint model to the spatial pattern formed by a plant species, Thymus carnosus, as well as to the health status of each individual. The key ecological result revealed by our spatial analysis of these data, relates to the distance-to-water covariate. We find that T. carnosus plants are generally healthier when they are further away from the water. We suggest that this may be the result of a combination of (1) plants having alternative rooting strategies depending on how close to water they grow and (2) the rooting strategy determining how well the plants were able to tolerate an unusually dry summer. We anticipate INLA becoming widely used within spatial ecological analysis over the next decade and suggest that both ecologists and statisticians will benefit greatly from working collaboratively to further develop and apply these emerging statistical methods.