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

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.