Using Multivariate Generalised Linear Mixed Models for Studying Roots Development: An Example Based on Minirhizotron Observations

The characterisation of the spatial and temporal distribution of the root system in a cultivated field depends on the soil volume occupied by the root systems (the scatter), and the local intensity of the root colonisation in the field (the intensity). We introduce a multivariate generalised linear mixed model for simultaneously describing the scatter and the intensity using data obtained with minirhizotrons (i.e., tubes with observation windows, which are inserted in the soil, enabling to observe the roots directly). The models presented allow studying intricate spatial and temporal dependence patterns using a graphical model to represent the dependence structure of latent random components. The scatter is described by a binomial mixed model (presence of roots in observation windows). The number of roots crossing the reference lines in the observational windows of the minirhizotron is used to estimate the intensity through a specially defined Poisson mixed model. We explore the fact that it is possible to construct multivariate extensions of generalised linear mixed models that allow to simultaneously represent patterns of dependency of the scatter and the intensity along with time and space. We present an example where the intensity and scatter are simultaneously determined at three different time points. A positive association between the intensity and scatter at each time point was found, suggesting that the plants are not compensating a reduced occupation of the soil by increasing the number of roots per volume of soil. Using the general properties of graphical models, we identify a first-order Markovian dependence pattern between successively observed scatters and intensities. This lack of memory indicates that no long-lasting temporal causal effects are affecting the roots' development. The two dependence patterns described above cannot be detected with univariate models.