State-Space Estimation of Spatially Explicit Assessment Models Using Gaussian Random Fields and Template Model Builder

Stock assessments typically involve a workflow where spatially referenced data are pre-processed to estimate spatially aggregated measures of a population (i.e. indices of abundance, composition summaries), and these aggregate measures are then used to estimate parameters for a non-spatial population model.  However, improvements in statistical and computational methods allow population dynamcis to be estimated using spatiotemporal models, which replace variables representing total abundance with random fields representing population densities over the population’s range.  We provide a brief introduction to spatiotemporal methods, including their estimation using Template Model Builder, while demonstrating a new state-space spatiotemporal model involving Gompertz-form density dependence.  We use simulation experiments and data for three rockfishes in the California Current to contrast spatial and non-spatial state-space models, and results indicate that non-spatial models can result in biased estimates of both population abundance and the strength of density dependence.  We conclude by discussing future prospects for this rich vein of research regarding spatial population-dynamics models.