A nonlinear mixed effects model to explain inter-individual variability in plant populations

It is common knowledge that the genetic variability of plants, even of the same variety, can be very important and, if we add locally varying climatic effects, the development of two neighboring similar plants could be highly different. This is one of the reasons why population-based methods for modeling plant growth are of great interest. A highly promising individual-based plant growth model is the GreenLab model [4] which was recently shown to have a good predictive capacity among competing models [1]. In this study, we extend the GreenLab formulation to the population level. In order to model the deviations from some fixed but unknown important biophysical and genetic parameters we introduce into the GreenLab model appropriate random effects. Under some assumptions, the resulting model can be cast into the framework of nonlinear mixed effects models. A stochastic variant of an EM-type algorithm (Expectation-Maximization) is generally needed to perform MLE for this type of incomplete data models and the interest is focused on the design of an efficient algorithm. In this direction, we propose a suitable Monte-Carlo EM (MCEM) algorithm for our model, where at each EM-iteration, MCMC is used to draw from the hidden states given the observed data. Data consist in organ mass measurements and are treated sequentially as first proposed in [11]. The performance of the algorithm is illustrated on simulated data from the sugar beet plant. Some possible extensions and improvements are also discussed.