Presentation: A Marriage of Models and Maps: Multivariate Spatio-Temporal Models for Ocean Community Dynamics
Speaker: James Thorson, PhD, Operations Research Analyst, Fishery Resource Analysis and Monitoring Division, Northwest Fisheries Science Center, National Marine Fisheries Service, NOAA
Abstract: Theoretical mechanisms for species coexistence (in fishes, plants, plankton, etc.) typically involve understanding variation over time in abundance for multiple species at many different sites. These ecological models can increasingly be fitted using spatio-temporal statistical methods. However, these models involve four “big-N” problems: covariation among a large number of sites, years, species, and an asymmetric matrix representing species interactions. In this talk, I discuss recent progress in using automatic differentiation software (Template Model Builder) combined with the Laplace approximation to overcome all four big-N problems. In particular, I fit multivariate spatio-temporal models to fish sampling data using a sparse spatial precision matrix, combined with a factor-model for covariation among species and a separable space-time parameterization of abundance. I also introduce a rank-reduced parameterization of species interactions inspired by co-integration models from econometrics. Throughout, I demonstrate models using multidecadal surveys of fish populations worldwide, including an analysis of recovering grey seals in the Gulf of St. Lawrence. I conclude with research recommendations for using statistical methods to resolve fundamental questions regarding species coexistence mechanisms for natural communities.