Charlotte Baey

A non linear mixed effects model of plant growth and estimation via stochastic variants of the EM algorithm

ABSTRACT There is a strong genetic variability among plants, even of the same variety, which, combined with the locally varying environmental conditions in a given field, can lead to the development of highly different neighboring plants. This is one of the reasons why population-based methods for modeling plant growth are of great interest. GreenLab is a functional–structural plant growth model which has already been shown to be successful in describing plant growth dynamics primarily at individual level. In this study, we extend its formulation to the population level. In order to model the deviations from some fixed but unknown important biophysical and genetic parameters we introduce random effects. The resulting model can be cast into the framework of non linear mixed models, which can be seen as particular types of incomplete data models. A stochastic variant of an EM-type algorithm (expectation–maximization) is generally needed to perform maximum likelihood estimation for this type of models. Under some assumptions, the complete data distribution belongs to a subclass of the exponential family of distributions for which the M-step can be solved explicitly. In such cases, the interest is focused on the best approximation of the E-step by competing simulation methods. In this direction, we propose to compare two commonly used stochastic algorithms: the Monte-Carlo EM (MCEM) and the SAEM algorithm. The performances of both algorithms are compared on simulated data, and an application to real data from sugar beet plants is also given.

Evaluation of the predictive capacity of five plant growth models for sugar beet

A lot of plant growth models coexist, with different modelling approaches and levels of complexity. In the case of sugar beet, many of them are used as predictive tools, even when they were not originally designed for this purpose. We propose the evaluation and comparison of five plant growth models that rely on the same energetic production of biomass, but with different levels of description (per plant or per square meter) and different biomass repartition (empirical or via allocation): Greenlab, LNAS, CERES, PILOTE and STICS. The models were calibrated on a first set of data, and their predictive capacities were compared on an independent data set from the same variety and similar environmental conditions, using the root mean squared error of prediction (RMSEP) and modelling efficiency (EF) for the total dry matter production and the dry matter of root. All the models tended to overestimate both the total dry matter and the dry matter of root. Greenlab gave the best predictions for the root biomass, and CERES the best total biomass predictions. The overestimation was partly explained by a hail episode that caused a lot of damages to the leaves in the validation year. The five models also provided similar yield prediction errors.