Methodological approaches for modelling fish species occurrence patterns have been lately proposed. The presence/absence of species can be modeled with a hierarchical Bayesian model using the geographical and environmental characteristics of each sampling locations. Maps of predicted probabilities of presence can be generated using Bayesian kriging. Our interest here is to describe how to use the integrated nested Laplace approximation (INLA) (Rue et al., 2009) jointly with the Stochastic Partial Differential Equation (SPDE) approach (Lindgren et al. 2011) to perform fast inference and prediction in such models. A particular example related to the presence of the Mediterranean mackerel is here presented. Moreover, our interest is also to show that our approach can be adapted to be used in situations where sampling is likely to be preferential. Preferential sampling arises when the process that determines the data locations and the process being modeled are stochastically dependent. Commercial fishery is a clear example of this situation: fishermen go to fish in the area where they presume that can take the target species. To show how to perform preferential sampling we also present an example about the abundance of a target species (hake) in the Western Mediterranean.

Joint work with  A. López-Quílez, F. Muñoz, J. Illian, D. Simpson, M. G. Pennino and J.M. Bellido