Optimal experimental designs for dynamic monitoring the growth of plants foliage

Modelling canopy growth is an important question in plant biology. A myriad of models has already been proposed for describing the dynamics of plant foliage in the field. The monitoring of the canopy during the growing period is central for selecting and validating the models. However, the design of data collection in the field is often empirical and sometimes, unfortunately, unsuitable for estimating parameters and discriminating models.

The question ”when collecting canopy data so one can accurately estimate model parameters and discriminate models” can be addressed by using methods from the Optimal Design of Experiments.

This field of statistics provides methods for designing experiments (e.g. size of the experiment, times of observation, number of replicates) that optimize the information on the processes. It can be helpful to reduce the costs of experiments by providing as much information as possible with minimal experimental effort.

The experimental designs problem consists, most often, of finding factors that minimize the variance of the estimators of model parameters. Several existing criteria based on the Fisher information matrix, which measures the amount of information that an observable random variable carries on unknown parameters. For example, the A-optimality aims to minimize the trace of the inverse of the information matrix, and the E-optimality aims to maximize the minimum eigenvalue of the information matrix. In our case, D-optimality, T-optimality, and DT-optimality are specifically studied. Their definitions and uses will be explained.

In this study, we addressed the question of field monitoring using the Optimal Design of Experiments framework. We first introduced D, T, and DT optimal designs for non-linear models. Then, by using two simple growth models we illustrated how they can be used to find optimal monitoring designs of plant growth.”