Within the statistical literature, there is a lack of methods that allow for asymmetric multivariate spatial effects to model relations underlying complex spatial phenomena. Intercropping is one such phenomenon. In this ancient agricultural practice multiple crop species or varieties are cultivated together in close proximity and are subject to mutual competition. To properly analyse such a system, it is necessary to account for both within- and between-plot effects, where between-plot effects are asymmetric. Building on the multivariate spatial autoregressive model and the Gaussian graphical model, the proposed method takes asymmetric spatial relations into account, thereby removing some of the limiting factors of spatial analyses and giving researchers a better indication of the existence and extend of spatial relationships. Using a Bayesian-estimation framework, the model shows promising results in the simulation study. The model is applied on intercropping data consisting of Belgian endive and beetroot, illustrating the usage of the proposed methodology. An R package containing the proposed methodology can be found on https:// CRAN.R-project.org/package=SAGM.

翻译：在统计文献中，缺乏允许非对称多变量空间效应来建模复杂空间现象背后关系的方法。间作便是这样一种现象。在这种古老的农业实践中，多种作物种类或品种在近距离内共同种植，并相互竞争。为正确分析此类系统，必须同时考虑地块内效应和地块间效应，其中地块间效应是非对称的。基于多变量空间自回归模型和高斯图模型，所提出的方法将非对称空间关系纳入考量，从而消除了空间分析中的部分限制因素，使研究者能够更准确地了解空间关系的存在及其程度。采用贝叶斯估计框架，该模型在模拟研究中显示出有前景的结果。该模型应用于包含比利时菊苣和甜菜的间作数据，展示了所提出方法的使用。包含该方法的R包可在https://CRAN.R-project.org/package=SAGM上获取。