Using Delta Generalized Additive Models to Produce Distribution Maps for Spatially Explicit Ecosystem Models

Spatial ecosystem models, such as OSMOSE, have become integral tools in achieving ecosystem-based management for their ability to thoroughly describe predator–prey dynamics in a spatially explicit context. Distribution maps, which define the initial spatial allocation of functional groups abundance, can have a large effect on the predator–prey dynamics that spatially explicit ecosystem models simulate. Here, we introduce the delta GAM approach we developed to be able to produce distribution maps for an OSMOSE model of the West Florida Shelf (Gulf of Mexico), OSMOSE-WFS. This delta GAM approach predicts the spatial distribution of different life stages of the multiple functional groups represented in OSMOSE-WFS (‘life-stage groups’) at different seasons, over the entire Gulf of Mexico (GOM) shelf including areas where abundance estimates do not exist, using different research survey datasets and regional environmental and habitat features. Our delta GAM approach consists of fitting two independent models, a binomial GAM and a quasi-Poisson GAM, whose predictions are then combined using the delta method to yield spatial abundance estimates. To validate delta GAMs, bootstraps are used and Spearman\u27s correlation coefficients (Spearman\u27s ρ’s) between predicted and observed abundance values are estimated and tested to be significantly different from zero. We use pink shrimp (Farfantepenaeus duorarum) to demonstrate our delta GAM approach by predicting the summer distribution of this species over the GOM shelf and the West Florida Shelf. Predictions of the delta GAM reflect existing empirical research related to pink shrimp habitat preferences and predictions of a negative binomial GAM previously designed for the GOM. We find that using a delta rather than a negative binomial GAM saves significant computation time at the expense of a slight reduction in GAM performance. A positive and highly significant Spearman\u27s ρ between observed and predicted abundance values indicates that our delta GAM can reliably be used to predict pink shrimp spatial distribution. Spearman\u27s ρ was also positive and highly significant in every life-stage group represented in OSMOSE-WFS and season, though often low. Therefore, delta GAMs fitted for the different life-stage groups and seasons correctly predict qualitative differences between low- and high-abundance areas and are deemed appropriate for generating distribution maps for OSMOSE-WFS. The delta GAM approach we developed is a simple, convenient method to create distribution maps to be fed into spatially explicit ecosystem models, where wide spatial and taxonomic coverage is desired while benefits of high precision estimates are lost at run-time