Modeling Benthic Animals in Space and Time Using Bayesian Point Process With Cross Validation: The Case of Holoturians

Holothurian populations in the Mediterranean are relatively understudied, with limited knowledge of their spatial distribution, habitat preferences, and ecological dynamics, making their monitoring a key challenge for ecosystem assessment and sustainable management. However, species distribution modeling is often complicated by the presence-only nature of the data and hetero- geneous sampling designs. This study develops a spatio-temporal framework based on Log-Gaussian Cox Processes to analyze Holothurians’ positions collected across nine survey campaigns conducted from 2022 to 2024 near Giglio Island, Italy. The sur- veys combined high-resolution photogrammetry with diver-based visual censuses, leading to varying detection probabilities across habitats, especially within Posidonia oceanica meadows. We adopt a model with a shared spatial Gaussian process component to accommodate this complexity, accounting for habitat structure, environmental covariates, and temporal variability. Model estima- tion is performed using Integrated Nested Laplace Approximation. We evaluate the predictive performances of alternative model specifications through a novel k-fold cross-validation strategy for point processes, using the Continuous Ranked Probability Score. Results highlight the influence of habitat-type covariates, strong variability across campaigns, and a locally structured spatial field capturing residual spatial heterogeneity. Our approach provides a flexible and computationally efficient framework for integrating heterogeneous presence-only data in marine ecology and comparing the predictive ability of alternative models.