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Analytical study of a stochastic plant growth model: Application to the GreenLab model

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  • Kang, M.Z.
  • Cournède, P.H.
  • de Reffye, P.
  • Auclair, D.
  • Hu, B.G.

Abstract

A stochastic functional–structural model simulating plant development and growth is presented. The number of organs (internodes, leaves and fruits) produced by the model is not only a key intermediate variable for biomass production computation, but also an indicator of model complexity. To obtain their mean and variance through simulation is time-consuming and the results are approximate. In this paper, based on the idea of substructure decomposition, the theoretical mean and variance of the number of organs in a plant structure from the model are computed recurrently by applying a compound law of generating functions. This analytical method provides fast and precise results, which facilitates model analysis as well as model calibration and validation with real plants. Furthermore, the mean and variance of the biomass production from the stochastic plant model are of special interest linked to the prediction of yield. In this paper, through differential statistics, their approximate results are computed in an analytical way for any plant age. A case study on sample trees from this functional–structural model shows the theoretical moments of the number of organs and the biomass production, as well as the computation efficiency of the analytical method compared to a Monte-Carlo simulation method. The advantages and the drawbacks of this stochastic model for agricultural applications are discussed.

Suggested Citation

  • Kang, M.Z. & Cournède, P.H. & de Reffye, P. & Auclair, D. & Hu, B.G., 2008. "Analytical study of a stochastic plant growth model: Application to the GreenLab model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(1), pages 57-75.
    • Handle: RePEc:eee:matcom:v:78:y:2008:i:1:p:57-75
    DOI: 10.1016/j.matcom.2007.06.003
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    References listed on IDEAS

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    1. Dayan, E. & Presnov, E. & Fuchs, M., 2004. "Prediction and calculation of morphological characteristics and distribution of assimilates in the ROSGRO model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(1), pages 101-116.
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    Cited by:

    1. Parsons, Russell A. & Mell, William E. & McCauley, Peter, 2011. "Linking 3D spatial models of fuels and fire: Effects of spatial heterogeneity on fire behavior," Ecological Modelling, Elsevier, vol. 222(3), pages 679-691.
    2. Wu, Lin & Le Dimet, François-Xavier & de Reffye, Philippe & Hu, Bao-Gang & Cournède, Paul-Henry & Kang, Meng-Zhen, 2012. "An optimal control methodology for plant growth—Case study of a water supply problem of sunflower," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 909-923.
    3. Trevezas, S. & Malefaki, S. & Cournède, P.-H., 2014. "Parameter estimation via stochastic variants of the ECM algorithm with applications to plant growth modeling," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 82-99.
    4. D. Logothetis & S. Malefaki & S. Trevezas & P.-H. Cournède, 2022. "Bayesian Estimation for the GreenLab Plant Growth Model with Deterministic Organogenesis," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 63-87, March.

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    2. Dayan, J & Dayan, E & Strassberg, Y & Presnov, E, 2004. "Simulation and control of ventilation rates in greenhouses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(1), pages 3-17.

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