Spatio-temporal Shared-Field Modeling of Beluga and Bowhead Whale Sightings Using a Joint Marked Log-Gaussian Cox Process

We analyze a decade of aerial survey whale sighting data (2010-2019) to model the spatio-temporal distributions and group sizes of beluga (Delphinapterus leucas) and bowhead (Balaena mysticetus) whales in the United States Arctic. To jointly model these species, we develop a multi-species Log-Gaussian Cox Process (LGCP) in which species specific intensity surfaces are linked through a shared latent spatial Gaussian field. This structure allows the model to capture broad spatial patterns common to both species while still accommodating species level responses to environmental covariates and seasonal variation. The latent field is represented using the Stochastic Partial Differential Equation (SPDE) approach with an anisotropic Matern covariance, implemented on an ocean constrained triangulated mesh so that spatial dependence aligns with marine geography. Whale group size is incorporated through a marked point process extension with species specific negative binomial marks, allowing occurrence and group sizes to be jointly analyzed within a unified framework. Inference is carried out using the Integrated Nested Laplace Approximation (INLA), enabling efficient model fitting over a decade of survey effort. The results highlight persistent multi-species hotspots and distinct environmental associations for each species, demonstrating the value of shared field LGCPs for joint species distribution modeling in data sparse and heterogeneous survey settings.