Spatial statistical models for complex regions: the distribution of a crustacean species in the North-Western Ionian Sea

In order to evaluate the spatio-temporal fluctuations of an aquatic population in relation to anthropogenic and environmental factors, we consider density, biomass and size of a crustacean species particularly diffused in the North-Western Ionian Sea: Parapenaeus longirostris (Lucas, 1846). Data from twelve trawl surveys (1995-2006) were analyzed by two different spatio-temporal statistical models accounting for a complex region comprised between the coastline and a specified depth contour. First generalized additive models (GAM’s) were used with soap film smoothers (Wood et al., 2008). While conventional smoothing performs badly when used over complicated regions, soap film smoothing avoids errors across boundaries, using a set of basis functions for the interior region and another one for the boundary. These smoothers, that can be represented in terms of a low rank basis and one or two quadratic penalties, employ a global tuning parameter and one for each boundary and are estimated by penalized likelihood maximization with smoothing degree given by generalized cross validation minimization. Covariates that proved to be significant within the GAM’s were used in a Bayesian implementation combining the Stochastic Partial Differential Equation (SPDE) representation of a Gaussian process with the Integrated Nested Laplace Approximation (INLA). The SPDE approach approximates a Gaussian Markov Random Field substituting the spatio-temporal covariance function and the corresponding dense covariance matrix with a sparse precision matrix for a neighbourhood structure. With respect to MCMC methods INLA provides more accurate deterministic approximations to posterior marginal distributions and a more computational efficient algorithm for Bayesian inference.