Using copula graphical models to detect the impact of drought stress on maize and wheat yield

Abstract Improving crop yields is one of the main goals of agronomy. However, yield is determined by a complex interplay between Genotypic, Environmental and Management factors (G$\times$E$\times$M), which varies across time and space. Therefore, identifying the fundamental relations underlying yield variation is a principal aim of agricultural research. A narrow, and not necessarily appropriate, set of statistical methods tends to be used in the study of such relations, which is why we aim to introduce a diverse audience of agronomists, production ecologists, plant breeders and others interested in explaining yield variation to the use of graphical models. More specifically, we wish to demonstrate the usefulness of copula graphical models for heterogeneous mixed data. This new statistical learning technique provides a graphical representation of conditional independence relationships within data that is not necessarily normally distributed and consists of multiple groups for environments, management decisions, genotypes or abiotic stresses such as drought. This article introduces some basic graphical model terminology and theory, followed by an application on Ethiopian maize and wheat yield undergoing drought stress. The proposed method is accompanied with the R package heteromixgm cran.r-project.org.