Interpretable Non-Separable Spatio-Temporal Interaction Cox Model for Diffusion Prediction in Invasive Species Management

Accurate prediction of invasive species diffusion is essential for effective management and ecological conservation. Existing spatio-temporal Cox process models face limitations due to the separability assumption, which fails to capture spatio-temporal coupling dynamics inherent in biological diffusion processes. This study proposes a Spatio-Temporal Interaction Kernel Cox (STIK-Cox) model that constructs a non-separable conditional intensity function integrating baseline intensity, spatial and temporal proximity kernels, seasonal fluctuation, and a spatio-temporal interaction term. The model employs maximum likelihood estimation with Limited-memory Broyden–Fletcher–Goldfarb–Shanno with Bounds (L-BFGS-B) optimisation and incorporates SHapley Additive exPlanations (SHAP) for interpretability analysis. Using the Vespa mandarinia (Hymenoptera, Vespidae) monitoring dataset from Washington State, the model achieves a comprehensive accuracy score of 0.957, a capture rate of 98.74% at a 0.5° threshold, and a mean prediction error of 0.0802°. K-function analysis confirms effective capture of spatial clustering patterns, while SHAP analysis reveals longitude as the primary predictive driver. The non-separable design outperforms conventional methods including inverse distance weighting and Poisson point processes. This framework demonstrates the potential of non-separable spatio-temporal point processes for invasive species early warning, providing a scientific basis for targeted monitoring and resource allocation in ecological management.