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：在统计学文献中，缺乏允许非对称多元空间效应来建模复杂空间现象背后关系的方法。间作是此类现象之一。在这种古老的农业实践中，多种作物物种或品种在近距离内共同种植，并受到相互竞争的影响。为了正确分析这样的系统，有必要考虑地块内和地块间的效应，其中地块间的效应是非对称的。基于多元空间自回归模型和高斯图模型，所提出的方法考虑了非对称空间关系，从而消除了空间分析中的一些限制因素，并使研究人员能更好地了解空间关系的存在及其程度。使用贝叶斯估计框架，该模型在模拟研究中显示出有希望的结果。该模型被应用于包含比利时菊苣和甜菜的间作数据，以说明所提出方法的使用。包含所提出方法的R包可在https://CRAN.R-project.org/package=SAGM上找到。