Modelling the interindividual variability of organogenesis in sugar beet populations using a hierarchical segmented model

Baey, Charlotte; Didier, Anne; Lemaire, Sébastien; Maupas, Fabienne; Cournède, Paul-Henry

doi:10.1016/j.ecolmodel.2013.04.013

Cited by 8 publications

(6 citation statements)

References 41 publications

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“…In terms of parameter estimation, a more general approach to maximum likelihood estimation is also developed based on a stochastic variant of a generalized EM (Expectation-Maximization) algorithm as described in [59]. An objective is also to be able to handle mixed-effects models in order to describe plant populations and estimate the interindividual variability as illustrated in [3]. Stochastic EM algorithms can also be used for this purpose [37].…”

Section: Discussionmentioning

confidence: 99%

Development and Evaluation of Plant Growth Models: Methodology and Implementation in the PYGMALION platform

Cournède

Chen

et al. 2013

Math. Model. Nat. Phenom.

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Abstract. Mathematical models of plant growth are generally characterized by a large number of interacting processes, a large number of model parameters and costly experimental data acquisition. Such complexities make model parameterization a difficult process. Moreover, there is a large variety of models that coexist in the literature with generally an absence of benchmarking between the different approaches and insufficient model evaluation. In this context, this paper aims at enhancing good modelling practices in the plant growth modeling community and at increasing model design efficiency. It gives an overview of the different steps in modelling and specify them in the case of plant growth models specifically regarding their above mentioned characteristics.Different methods allowing to perform these steps are implemented in a dedicated platform PYGMALION (Plant Growth Model Analysis, Identification and Optimization). Some of these methods are original. The C++ platform proposes a framework in which stochastic or deterministic discrete dynamic models can be implemented, and several efficient methods for sensitivity analysis, uncertainty analysis, parameter estimation, model selection or data assimilation can be used for model design, evaluation or application.Finally, a new model, the LNAS model for sugar beet growth, is presented and serves to illustrate how the different methods in PYGMALION can be used for its parameterization, its evaluation and its application to yield prediction. The model is evaluated from real data and is shown to have interesting predictive capacities when coupled with data assimilation techniques.

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Section: Discussionmentioning

confidence: 99%

Development and Evaluation of Plant Growth Models: Methodology and Implementation in the PYGMALION platform

Cournède

Chen

et al. 2013

Math. Model. Nat. Phenom.

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“…Around this overall behavior, important variations of growth rate can be noticed from one individual to another. A piecewise linear growth can be a good approximation of the dynamics, similarly to the model adopted in [4]. The objective is to design a model that reproduces this overall dynamics and takes into account this inter-individual variability.…”

Section: A Experimental Conditions and Observed Variabilitymentioning

confidence: 99%

“…Heterogeneity was studied in a sugar beet population in [4] for the organogenesis and in [5] for a full FSPM model. The approach is based on the identification of non-linear mixed effect models with the Stochastic Approximation Expectation Maximization (SAEM) algorithm as proposed by [6].…”

Section: Introductionmentioning

confidence: 99%

Modeling the inter-individual variability of single-stemmed plant development

Noce

Letort

Hansart

et al. 2016

2016 IEEE International Conference on Functional-Structural Plant Growth Modeling, Simulation, Visualization and Applications (

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Modeling the development of single-stemmed plants is classically done by expressing the number of phytomers in the main axis as a function of the thermal time. In many cases, a strong inter-individual variability is encountered, that cannot be straightforwardly associated to any environmental or microenvironmental factors. We propose a methodological framework to describe the heterogeneity of individual responses in a population by hierarchical or mixed-effect models : some regression parameters are random variables identically distributed in the population. The method is illustrated using experimental data collected on young Acacia erioloba plants, grown in CEREEP greenhouse, for which two piecewise-linear models of organogenesis are identified using Expectation-Maximization (EM) algorithm and compared according to their adequacy to the data. The Estep and the M-step of the algorithm are analytic as long as the dependence is linear with respect to the individual parameters, i.e. the latent variables of the mixed-effect model. In the general case, the posterior distribution of the individual parameters cannot be analytically determined. Monte-Carlo Markov Chains are generated with Metropolis-Hasting during the E-step to estimate the distribution. Alternatively, a Laplace approximation of the posterior distribution appeared to be quite relevant in our case. Such framework will be adapted to the identification of a complete FSPM of Acacia growth combining organogenesis and functioning.

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“…A global sensitivity analysis of Sobol type (Wu et al, 2012) was applied to the Greenlab model in (Baey et al, 2013). The results revealed that the three most influential parameters are µ, s pr and a r , with high total-order indices.…”

Section: Simulated Datamentioning

confidence: 99%

“…Nevertheless, these results suggest that the method based on the Fisher Information Matrix is very promising and gives satisfactory results. Baey et al (2013).…”

Section: Simulated Datamentioning

confidence: 99%

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

Baey¹,

Trevezas²,

Cournède³

2015

Communications in Statistics - Theory and Methods

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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.

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Modelling the interindividual variability of organogenesis in sugar beet populations using a hierarchical segmented model

Cited by 8 publications

References 41 publications

Development and Evaluation of Plant Growth Models: Methodology and Implementation in the PYGMALION platform

Development and Evaluation of Plant Growth Models: Methodology and Implementation in the PYGMALION platform

Modeling the inter-individual variability of single-stemmed plant development

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

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