Bayesian Estimation for the GreenLab Plant Growth Model with Deterministic Organogenesis

Plant growth modeling has attracted a lot of attention due to its potential applications. Many scientific disciplines are involved, and a lot of research effort and intensive computer methods were needed to understand better the complex mechanisms underlying plant evolution. Among the numerous challenges, one can cite mathematical modeling, parameterization, estimation and prediction. One of the most promising models that have been proposed in the literature is the GreenLab functional–structural plant growth model. In this study, we focus only on one of its versions, named GreenLab-1, particularly adapted to a certain class of plants with known organogenesis, such as sugar beet, maize, rapeseed and other crop plants. The parameters of the model are related to plant functioning, and the vector of observations consists of organ masses measured only once at a given observation time. Previous efforts for parameter estimation in GreenLab-1 include Kalman-type filters, stochastic variants of EM and/or ECM algorithms, and hybrid sequential importance sampling algorithms with Bayesian estimation only for the functional parameters of the model. In this paper, the first purely Bayesian approach for parameter estimation of the GreenLab-1 model is proposed. This approach has much more flexibility in handling complex structures, thus providing a useful tool for analyzing such types of models. In order to sample from the posterior distribution an MCMC algorithm is used and its implementation issues are also discussed. The performance of this method is illustrated on a simulated and a real dataset from the sugar beet plant, and a comparison is made with the MLE approach. © 2021, International Biometric Society

Mixed-Effects Estimation in Dynamic Models of Plant Growth for the Assessment of Inter-individual Variability

Modeling inter-individual variability in plant populations is a key issue to understand crop heterogeneity and its variations in response to the environment. Being able to describe the interactions among plants and explain the variability observed in the population could provide useful information on how to control it and improve global plant growth. We propose here a method to model plant variability within a field, by extending the so-called GreenLab functional-structural plant model from the individual to the population scale via nonlinear mixed-effects modeling. Parameter estimation of the population model is achieved using the stochastic approximation expectation maximization algorithm, implemented in the platform for plant growth modeling and analysis PyGMAlion. The method is first applied on a set of simulated data and then on a real dataset from a population of 34 winter oilseed rape plants at the rosette stage. Results show that our method allows for a good characterization of the variability in the population with only a limited number of parameters, which is a key point for plant models. Results on simulated data show that parameters associated with a low sensitivity index are inaccurately estimated by the algorithm when considered as random effects, but a good stability of the results can be obtained by considering them as fixed effects. These results open new ways for the analysis of inter-plant variability within a population and the study of plant–plant competition.Supplementary materials accompanying this paper appear online. © 2018, International Biometric Society

Bayesian Estimation for the GreenLab Plant Growth Model with Deterministic Organogenesis

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Some parameter estimation issues in functional-structural plant modelling

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 not allow a proper evaluation of estimation uncertainty. Finally some perspectives opened by the theory of hidden models are discussed