When working with contemporary spatial ecological datasets, statistical modellers are often confronted by two major challenges: (I) the need for covariance models with the flexibility to accommodate directional patterns of anisotropy; and (II) the computational effort demanded by high-dimensional inverse and determinant problems involving the covariance matrix \(\vec {V}\). In the case of rectangular lattice data, the spatially separable covariogram is a longstanding but underused model that can reduce arithmetic complexity by orders of magnitude. We examine a class of covariograms for stationary data that extends the separable model through affine coordinate transformations, providing a far greater flexibility for handling anisotropy than that offered by the standard approach of using geometric anisotropy to extend an isotropic model. This motivates our development of an extremely fast estimator of the orientation of the axes of range anisotropy on spatial lattice data, and a powerful visual diagnostic for nonstationarity. In a case study, we demonstrate how these tools can be used to analyze and predict forest damage patterns caused by outbreaks of the mountain pine beetle.

在使用当代空间生态数据集时，统计建模人员通常面临两个主要挑战：（I）需要协方差模型并要灵活地适应各向异性的方向性模型；（II）涉及协方差矩阵\（\ vec {V} \）的高维逆和行列式问题所需的计算量。在矩形格数据的情况下，空间可分离的协方差图是一个长期存在但未充分利用的模型，可以将算术复杂度降低几个数量级。我们检查了一类用于固定数据的协方差图，该数据通过仿射坐标变换扩展了可分离模型，与使用几何各向异性扩展各向同性模型的标准方法相比，该方法为处理各向异性提供了更大的灵活性。这激发了我们对空间点阵数据上范围各向异性轴的方向的极快速估算器的发展，以及对非平稳性的强大视觉诊断的发展。在一个案例研究中，我们演示了如何使用这些工具来分析和预测由山松甲虫暴发引起的森林破坏模式。