Spatial Gaussian fields for complex areas with application to marine megafauna conservation

Abstract

Spatial Gaussian fields (SGFs) are widely employed in modeling the distributions of marine megafauna, yet they traditionally rely on assumptions of isotropy and stationarity, conditions that often prove unrealistic in complex ecological environments featuring coastlines, islands, and depth gradients acting as partial movement barriers. Existing spatial models typically treat these barriers as either fully impermeable, completely blocking species movement and dispersal, or entirely absent, which inadequately represents most real-world scenarios. To address this limitation, we introduce the Zonal spatial Gaussian field model (Z-SPDE), an extension of spatial Gaussian fields that explicitly incorporates multiple zones with varying levels of permeability. The model assigns spatially varying range parameters to distinct zones, allowing ecological and geographical knowledge about zone permeability to directly inform model specifications. This approach maintains computational efficiency by utilizing the integrated nested Laplace approximation (INLA) framework combined with stochastic partial differential equations (SPDEs), ensuring efficient and feasible application even in large, complex spatial domains. We demonstrate the practical utility and flexibility of the Z-SPDE model through its application to dugong (Dugong dugon) distribution data from the Red Sea. This area is characterized by a heterogeneous spatial structure, influenced by coastlines, islands, and varying bathymetric depths. Our results indicate that the model effectively captures spatial dependencies and gradients of zonal permeability, significantly enhancing spatial inference accuracy. This methodological advancement offers ecologists and conservation planners a powerful and realistic tool for modeling species distributions, facilitating more informed decisions in marine conservation and spatial management across diverse ecological landscapes.