Exploring the spatial distribution patterns of South African Cape hakes using generalised additive models

We developed delta generalised additive models (GAMs) to predict the spatial distribution of different size classes of South African hakes, <i>Merluccius capensis</i> and <i>M. paradoxus</i>, using demersal trawl survey data and geographical (latitude and longitude) and environmental features (depth, temperature, bottom dissolved oxygen and sediment type). Our approach consists of fitting, for each hake size class, two independent models, a binomial GAM and a quasi-Poisson GAM, whose predictions are then combined using the delta method. Delta GAMs were validated using an iterative cross-validation procedure, and their predictions were then employed to produce distribution maps for the southern Benguela. Delta GAM predictions confirmed existing knowledge about the spatial distribution patterns of South African hakes, and brought new insights into the factors influencing the presence/absence and abundance of these species. Our GAM approach can be used to produce distribution maps for spatially explicit ecosystem models of the southern Benguela in a rigorous and objective way. Ecosystem models are critical features of the ecosystem approach to fisheries, and distribution maps constructed using our GAM approach will enable a reliable allocation of species biomasses in spatially explicit ecosystem models, which will increase trust in the spatial overlaps and, therefore, the trophic interactions predicted by these models.