What Secrets Do Beluga and Bowhead Whales Hide in the Arctic?

Over the past ten years aircraft have flown over the U.S. Arctic, recording sightings of beluga and bowhead whales. Researchers turned these data into a dynamic map using a statistical model called the Log‑Gaussian Cox Process (LGCP). Imagine two intensity surfaces—one for each species—linked by a shared spatial field. This field captures common hotspots, like food‑rich waters, while still showing species‑specific environmental differences. To make the model realistic, they employed a stochastic partial differential equation (SPDE) on a triangulated mesh that follows the shape of the ocean. This way spatial dependence respects coastlines and natural barriers. Whale group sizes were added as negative‑binomial marks, allowing joint study of where whales are and how many gather. The whole procedure was computed with INLA, a fast algorithm that avoids lengthy calculations. Results reveal hot areas where both species meet each year, as well as zones where only one appears, linked to temperature, depth, and plankton availability. This knowledge helps protect the most vulnerable habitats and guides future research in scarcely explored regions.

The Log‑Gaussian Cox Process (LGCP) is a point‑process model where the occurrence intensity is a log‑normal random field. In practice, the logarithm of intensity follows a Gaussian field, allowing capture of complex spatial dependencies. To model two species simultaneously, the authors introduced a shared latent field η(s) that influences both intensities λ₁(s)=exp[β₁X₁(s)+η(s)] and λ₂(s)=exp[β₂X₂(s)+η(s)]. Here X₁ and X₂ are species‑specific environmental covariates (e.g., surface temperature, depth), while β₁ and β₂ weight their effects. The field η(s) is built with the SPDE approach, which approximates a Gaussian field with Matérn covariance via a finite‑element mesh. Anisotropy is introduced by modifying the diffusion matrix, so correlation can vary directionally, reflecting ocean currents or underwater ridges. The triangulated mesh is constrained to the marine coastline, preventing the model from extending dependence beyond land. To incorporate group sizes, a marked point process is used: each sighting carries a mark following a negative‑binomial distribution, parameterized by μᵢ(s) and dispersion κᵢ. This enables joint modeling of sighting frequency and group‑size variability while preserving statistical coherence. Inference is performed with Integrated Nested Laplace Approximation (INLA), which provides approximate maximum‑likelihood estimates for complex hierarchical models without costly Monte Carlo simulations. INLA exploits the sparsity of the SPDE precision matrix, dramatically reducing computation time. Results reveal shared hotspots, highlighted by high η(s) values, and species‑specific environmental associations captured by β₁ and β₂. For instance, belugas show a strong positive response to sea‑ice cover, whereas bowheads are more sensitive to seafloor depth. This joint approach is especially valuable in data‑sparse settings, as the shared field “borrows” information across species, improving estimate precision. Moreover, the marked structure allows assessment of climate‑change impacts not only on presence but also on group size, offering crucial insights for conservation management. Finally, the model’s flexibility permits extension to additional species or finer temporal covariates, paving the way for a new generation of marine species distribution models.