Abstract. The development of functional-structural plant models has opened interesting perspectives for a better understanding of plant growth as well as for potential applications in breeding or decision aid in farm management. Parameterization of such models is however a difficult issue due to the complexity of the involved biological processes and the interactions between these processes. The estimation of parameters from experimental data by inverse methods is thus a crucial step. This paper presents some results and discussions as first steps towards the construction of a general framework for the parametric estimation of functional-structural plant models. A general family of models of Carbon allocation formalized as dynamic systems serves as the basis for our study. An adaptation of the 2-stage Aitken estimator to this family of model is introduced as well as its numerical implementation, and applied in two different situations: first a morphogenetic model of sugar beet growth with simple plant structure, multi-stage and detailed observations, and second a tree growth model characterized by sparse observations and strong interactions between functioning and organogenesis. The proposed estimation method appears robust, easy to adapt to a wide variety of models, and generally provides a satisfactory goodness-of-fit. However, it does * Corresponding author. E-mail: paul-henry.cournede@ecp. Some parameter estimation issues in plant growth modelling not allow a proper evaluation of estimation uncertainty. Finally some perspectives opened by the theory of hidden models are discussed.

This article concerns maximum likelihood estimation for discrete time homogeneous nonparametric semi-Markov models with finite state space. In particular, we present the exact maximum likelihood estimator of the semi-Markov kernel which governs the evolution of the semi-Markov chain. We study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of the observation tends to infinity, and (ii) for parallel observations of independent copies of a semi-Markov chain censored at a fixed time, when the number of copies tends to infinity. In both cases, we obtain strong consistency, asymptotic normality, and asymptotic efficiency for every finite dimensional vector of this estimator. Finally, we obtain explicit forms for the covariance matrices of the asymptotic distributions.

Cournède. A nonlinear mixed effects model of plant growth and estimation via stochastic variants of the EM algorithm.. Communications in Statistics -Theory and Methods, 2015, pp. AbstractThere 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 nonlinear 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.