Bayesian spatio-temporal modelling of anchovy abundance through the SPDE Approach

The Peruvian anchovy is an important species from an ecological and economical perspective. Some important features to evaluate fisheries management are the relationship between the anchovy presence/abundance and covariates with spatial and temporal dependencies accounted for, the nature of the behaviour of anchovy throughout space and time, and available spatio-temporal predictions. With these challenges in mind, we propose to use flexible Bayesian hierarchical spatio-temporal models for zero-inflated positive continuous data. These models are able to capture the spatial and temporal distribution of the anchovies, to make spatial predictions within the temporal range of the data and predictions about the near future. To make our modelling computationally feasible we use the stochastic partial differential equations (SPDE) approach combined with the integrated nested Laplace approximation (INLA) method. After balancing goodness of fit, interpretations of spatial effects across years, prediction ability, and computational costs, we suggest to use a model with a spatio-temporal structure. Our model provides a novel method to investigate the Peruvian anchovy dynamics across years, giving solid statistical support to many descriptive ecological studies.