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Within the statistical literature, there is a lack of methods that allow forasymmetric multivariate spatial effects to model relations underlying complexspatial phenomena. Intercropping is one such phenomenon. In this ancientagricultural practice multiple crop species or varieties are cultivatedtogether in close proximity and are subject to mutual competition. To properlyanalyse such a system, it is necessary to account for both within- andbetween-plot effects, where between-plot effects are asymmetric. Building onthe multivariate spatial autoregressive model and the Gaussian graphical model,the proposed method takes asymmetric spatial relations into account, therebyremoving some of the limiting factors of spatial analyses and givingresearchers a better indication of the existence and extend of spatialrelationships. Using a Bayesian-estimation framework, the model shows promisingresults in the simulation study. The model is applied on intercropping dataconsisting of Belgian endive and beetroot, illustrating the usage of theproposed methodology. An R package containing the proposed methodology can befound on https:// CRAN.R-project.org/package=SAGM.

A Spatial Autoregressive Graphical Model with Applications in Intercropping