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.

翻译：本研究分析了十年间（2010-2019）的航空调查鲸类目击数据，以建模美国北极地区白鲸（Delphinapterus leucas）与弓头鲸（Balaena mysticetus）的时空分布及群体规模。为联合建模这两种物种，我们构建了一个多物种对数高斯Cox过程（LGCP）模型，其中物种特异性强度曲面通过共享的潜空间高斯场相互关联。该结构使模型能够捕捉两物种共有的宏观空间格局，同时兼顾物种对环境协变量与季节变化的特异性响应。潜空间场采用随机偏微分方程（SPDE）方法结合各向异性Matern协方差函数进行表征，并在受海洋地理约束的三角网格上实现，以确保空间依赖性与海洋地理特征一致。鲸类群体规模通过标记点过程扩展纳入模型，采用物种特异性负二项分布标记，使得物种出现概率与群体规模能在统一框架下联合分析。基于集成嵌套拉普拉斯近似（INLA）进行统计推断，实现了对十年调查数据的高效模型拟合。结果揭示了持续存在的多物种聚集热点及各物种独特的环境关联性，证明了共享场LGCP模型在数据稀疏且异质性调查场景中用于联合物种分布建模的价值。