Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-24T12:45:28.761Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Parameter Estimation Issues in Functional-Structural Plant Modelling

Published online by Cambridge University Press:  01 March 2011

P.-H. Cournède ,
V. Letort ,
A. Mathieu ,
M. Z. Kang ,
S. Lemaire ,
S. Trevezas ,
F. Houllier  and
P. de Reffye
P.-H. Cournède*
Affiliation:
Ecole Centrale Paris, MAS, Châtenay-Malabry, France INRIA Saclay - Île-de-France, EPI Digiplante, Orsay, France
V. Letort
Affiliation:
Ecole Centrale Paris, MAS, Châtenay-Malabry, France INRIA Saclay - Île-de-France, EPI Digiplante, Orsay, France
A. Mathieu
Affiliation:
AgroParisTech, UMR EGC, Grignon, France
M. Z. Kang
Affiliation:
CASIA, LIAMA, Beijing, China
S. Lemaire
Affiliation:
ITB, Paris, France
S. Trevezas
Affiliation:
INRIA Saclay - Île-de-France, EPI Digiplante, Orsay, France
F. Houllier
Affiliation:
INRA, UMR AMAP, Montpellier, France
P. de Reffye
Affiliation:
INRIA Saclay - Île-de-France, EPI Digiplante, Orsay, France CIRAD, UMR AMAP, Montpellier, France
*
⋆ Corresponding author. E-mail: paul-henry.cournede@ecp.fr
Get access

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

Keywords

functional-structural plant modelscarbon allocationGreenLabmaximum likelihood estimatorAitken Estimatorhidden models
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 2: Modelling of plant growth , 2011 , pp. 133 - 159
Copyright
© EDP Sciences, 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

Allen, M.T., Prusinkiewicz, P., Dejong, T.M.. Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees, the L-peach model. New Phytologist, 166 (2005), 869–880. CrossRefGoogle ScholarPubMed
E. Assmann. The principles of forest yield study. Perfamon Press Ltd., Oxford, 1970.
D. Barthélémy, Y. Caraglio, E. Costes. Architecture, gradients morphogénétiques et âge physiologique chez les végétaux. Modélisation et simulation de l’architecture des végétaux, (J. Bouchon, ed.), Sciences Update, INRA, 1997, 89–136.
Barthélémy, D., Caraglio, Y.. Plant architecture: a dynamic, multilevel and comprehensive approach to plant form, structure and ontogeny. Annals of Botany, 99 (2007), No. 3, 375–407. CrossRefGoogle ScholarPubMed
Brisson, N., Gary, C., Justes, E., Roche, R., Mary, B., Ripoche, D., Zimmer, D., Sierra, J., Bertuzzi, P., Burger, P., Bussière, F., Cabidoche, Y.M., Cellier, P., Debaeke, P., Gaudillère, J.P., Hénault, C., Maraux, F., Seguin, B., Sinoquet, H.. An overview of the crop model STICS. European Journal of Agronomy, 18 (2003), 309–332. CrossRefGoogle Scholar
O. Cappé, E. Moulines, T. Rydén. Inference in hidden Markov models, Springer, New York, 2005.
Christophe, A., Letort, V., Hummel, I., Cournède, P.-H., de Reffye, P., Lecoeur, J.. A model based analysis of the dynamics of carbon balance at the whole plant level in Arabidopsis Thaliana. Functional Plant Biology, 35(11) (2008), 1147–1162. CrossRefGoogle Scholar
P.-H. Cournède. Dynamic system of plant growth. HDR Thesis, University of Montpellier II, 2009.
Cournède, P.-H., Kang, M.Z., Mathieu, A., Barczi, J.-F., Yan, H.P., Hu, B.G., de Reffye, P., Structural factorization of plants to compute their functional and architectural growth. Simulation, 82 (2006), No. 7, 427–438. CrossRefGoogle Scholar
Cournède, P.-H., Mathieu, A., Houllier, F., Barthélémy, D., de Reffye, P.. Computing competition for light in the GreenLab model of plant growth: a contribution to the study of the effects of density on resource acquisition and architectural development. Annals of Botany, 101 (2008), No. 8, 1207–1219. CrossRefGoogle ScholarPubMed
H. Cramer. Mathematical methods of statistics. Princeton University Press, Princeton, 1946.
de Reffye, P., Blaise, F., Chemouny, S., Fourcaud, T., Houllier, F.. Calibration of hydraulic growth model on the architecture of cotton plants. Agronomie, 19 (1999), 265–280. CrossRefGoogle Scholar
de Reffye, P., Elguero, E., Costes, E.. Growth units construction in trees: a stochastic approach. Acta Biotheoretica, 39 (1991), 325–342. CrossRefGoogle Scholar
P. de Reffye, E. Heuvelink, D. Barthélémy, P.-H. Cournède. Plant growth models. Ecological Models, Vol. 4 of Encyclopedia of Ecology (5 volumes) (S.E. Jorgensen and B. Fath, eds.), Elsevier, Oxford, 2008, 2824–2837.
P. de Reffye, S. Lemaire, N. Srivastava, F. Maupas, P.-H. Cournède. Modeling inter-individual variability in sugar beet populations. 3rd international symposium on Plant Growth and Applications(PMA09), Beijing, China (B.G. Li, M. Jaeger, Y. Guo, eds.), IEEE, November 9-12 2009.
Dempster, A.P., Laird, N.M., Rubin, D.B.. Maximum Likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 39 (1977), 1–38. Google Scholar
A. Doucet, A.M. Johansen. A tutorial on particle filtering and smoothing: fifteen years later. Tech. report, Department of Statistics, University of British Columbia, 2008.
Drouet, J.-L., Pagès, L.. GRAAL: a model of GRowth Architecture and carbon ALlocation during the vegetative phase of the whole maize plant, model description and parameterisation. Ecological Modelling, 165 (2003), 147–173. CrossRefGoogle Scholar
Eschenbach, C.. Emergent properties modelled with the functional structural tree growth model almis: Computer experiments on resource gain and use. Ecological Modelling, 186 (2005), No. 4, 470 – 488. CrossRefGoogle Scholar
Farrar, J.F.. Sink strength: What is it and how do we measure it? A summary. Plant, Cell and Environment, 16 (1993), No. 9, 1045–1046. Google Scholar
Fourcaud, T., Zhang, X.P., Stokes, A., Lambers, H., Körner, C.. Plant growth modelling and applications: The increasing importance of plant architecture in growth models. Annals of Botany, 101 (2008), No. 8, 1053–1063. CrossRefGoogle Scholar
Gaucherel, C., Campillo, F., Misson, L., Guiot, J., Boreux, J.-J.. Parameterization of a process-based tree-growth model: Comparison of optimization, MCMC and particle filtering algorithms. Environmental Modelling and Software, 23 (2008), No. 10-11, 1280 – 1288. CrossRefGoogle Scholar
Godin, C., Sinoquet, H.. Functional-strucutural plant modelling. New Phytologist, 166 (2005), 705–708. CrossRefGoogle ScholarPubMed
G.C. Goodwin, R.L. Payne. Dynamic system identification: Experiment design and data analysis. Academic Press, New York, 1977.
Guédon, Y., Barthélémy, D., Caraglio, Y., Costes, E.. Pattern analysis in branching and axillary flowering sequences. Journal of Theoretical Biology, 212 (2001), 481–520. CrossRefGoogle ScholarPubMed
H. Guo, V. Letort, L. Hong, T. Fourcaud, P.-H. Cournède, Y. Lu, P. de Reffye. Adaptation of the Greenlab model for analyzing sink-source relationships in Chinese pine saplings. Plant growth Modeling, simulation, visualization and their Applications (PMA06). (T. Fourcaud and XP. Zhang, eds.), IEEE Computer Society, Los Alamitos, California, 2007.
Guo, Y., Ma, Y.T., Zhan, Z.G., Li, B.G., Dingkuhn, M., Luquet, D., de Reffye, P.. Parameter optimization and field validation of the functional-structural model Greenlab for Maize. Annals of Botany, 97 (2006), 217–230. CrossRefGoogle ScholarPubMed
F. Hallé, R.A.A. Oldeman. Essai sur l’architecture et la dynamique de croissance des arbres tropicaux. Masson, Paris, 1970.
Hammer, G., Cooper, M., Tardieu, F., Welch, S., Walsh, B., Van Eeuwijk, F., Chapman, S., Podlich, D.. Models for navigating biological complexity in breeding improved crop plants. Trends in Plant Science, 11 (2006), No. 12, 587–593. CrossRefGoogle Scholar
Heuvelink, E.. Evaluation of a dynamic simulation model for tomato crop growth and development. Annals of Botany, 83 (1999), 413–422. CrossRefGoogle Scholar
C.A. Jones, J.R. Kiniry. Ceres - Maize : A simulation model of Maize growth and development. Texas A&M University Press, 1986.
Julier, S., Uhlmann, J., Durrant-Whyte, H.F.. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control, 45 (2000), No. 3, 477–482. CrossRefGoogle Scholar
Kang, M.Z., Cournède, P.-H., de Reffye, P., Auclair, D., Hu, B.G.. Analytical study of a stochastic plant growth model: application to the Greenlab model. Mathematics and Computers in Simulation, 78 (2008), No. 1, 57–75. CrossRefGoogle Scholar
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.. Optimization by Simulated Annealing. Science, 220 (1983), No. 4598, 671–680. CrossRefGoogle Scholar
Lacointe, A.. Carbon allocation among tree organs : A review of basic processes and representation in functional-structural models. Annals of Forest Sciences, 57 (2000), 521–533. CrossRefGoogle Scholar
S. Lemaire, F. Maupas, P.-H. Cournède, P. de Reffye. A morphogenetic crop model for sugar-beet (Beta Vulgaris l.). Crop Modeling and Decision Support, (W. Cao, J. White, E. Wang, eds.), Springer, 2009, 116–129.
V. Letort. Multi-scale analysis of source-sink relationships in plant growth models for parameter identification. Case of the Greenlab model. Ph.D. thesis, Ecole Centrale Paris, 2008.
Letort, V., Cournède, P.-H., Mathieu, A., de Reffye, P., Constant, T.. Parametric identification of a functional-structural tree growth model and application to beech trees (Fagus Sylvatica). Functional Plant Biology, 35 (2008), No. 10, 1243–1254. CrossRefGoogle Scholar
Letort, V., Mahe, P., Cournède, P.-H., de Reffye, P., Courtois, B.. Quantitative genetics and functional-structural plant growth models: Simulation of quantitative trait loci detection for model parameters and application to potential yield optimization. Annals of Botany, 101 (2008), No. 8, 951–963. Google ScholarPubMed
Ljung, L.. Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems. IEEE Trans. Autom. Control, 20 (1979), No. 5, 643–652. CrossRefGoogle Scholar
L. Ljung. System identification: Theory for the user. Prentice-Hall, New Jersey, 1999.
L. Ljung, T. Söderström. Theory and practice of recursive identification. MIT Press, Cambridge, MA, 1983.
C. Loi, P.-H. Cournède. Generating functions of stochastic L-systems and application to models of plant development. Discrete Mathematics and Theoretical Computer Science Proceedings, AI (2008), 325–338.
C. Loi, P.-H. Cournède, J. Françon. A symbolic method to analyse patterns in plant structure. Journal of Computer Science and Technology, In Press (2011).
Luquet, D., Dingkuhn, M., Kim, H., Tambour, L., Clément-Vidal, A.. Ecomeristem, a model of morphogenesis and competition among sinks in rice. 1. concept, validation and sensitivity analysis. Functional Plant Biology, 33 (2007), No. 4, 309–323. CrossRefGoogle Scholar
Y.T. Ma, M.P. Wen, B.G. Li, P.-H. Cournède, P. de Reffye. Calibration of Greenlab model for Maize with sparse experimental data. The Second International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA06) (T. Fourcaud and X.P. Zhang, eds.), IEEE, Los Alamitos, California, 2007.
D. Makowski, J. Hillier, D. Wallach, B. Andrieu, M.-H. Jeuffroy. Parameter estimation for crop models. Working with Dynamic Crop Models, (D. Wallach, D. Makowski, J.W. Jones, eds.), Elsevier, 2006, 55–100.
Mathieu, A., Cournède, P.-H., Letort, V., Barthélémy, D., de Reffye, P.. A dynamic model of plant growth with interactions between development and functional mechanisms to study plant structural plasticity related to trophic competition. Annals of Botany, 103 (2009), 1173–1186. CrossRefGoogle ScholarPubMed
A. Mathieu, B.G. Zhang, E. Heuvelink, S.J. Liu, P.-H. Cournède, P. de Reffye. Calibration of fruit cyclic patterns in cucumber plants as a function of source-sink ratio with the Greenlab model. Proceedings of the 5th international workshop on FSPM (P. Prusinkiewicz, J. Hanan, eds.), November 2007.
Nicolini, E., Chanson, B., Bonne, F.. Stem growth and epicormic branch formation in understorey beech trees (Fagus Sylvatica l.). Annals of Botany, 87 (2001), 737–750. CrossRefGoogle Scholar
Olsson, J., Cappé, O., Douc, R., Moulines, E.. Sequential Monte Carlo smoothing with application to parameter estimation in nonlinear state space models. Bernoulli, 14 (2008), No. 1, 155–179. CrossRefGoogle Scholar
Pallas, B., Christophe, A., Cournède, P.-H., Lecoeur, J.. Using a mathematical model to evaluate the trophic and non-trophic determinants of axis development in Grapevine (Vitis Vinifera l.). Functional Plant Biology, 36 (2009), No. 2, 156–170. CrossRefGoogle Scholar
Prusinkiewicz, P.. Modeling plant growth and development. Current Opinion in Plant Biology, 7 (2004), No. 1, 79–84. CrossRefGoogle Scholar
Quach, M., Brunel, N., d’Alché Buc, F.. Estimating parameters and hidden variables in non-linear state-space models based on ODEs for biological networks inference. Bioinformatics, 23 (2007), No. 23, 3209–3216. CrossRefGoogle Scholar
Rabiner, L.R.. A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE, 77 (1989), 257–284. CrossRefGoogle Scholar
O. Schabenberger, F. Pierce. Contemporary statistical models for the plant and soil sciences. Addison-Wesley, 2001.
Sievänen, R., Nikinmaa, E., Nygren, P., Ozier-Lafontaine, H., Perttunen, J., Hakula, H.. Components of a functional-structural tree model. Annals of Forest Sciences, 57 (2000), 399–412. CrossRefGoogle Scholar
Taylor, W.. Small sample properties of a class of two-stage Aitken estimator. Econometrica, 45 (1977), No. 2, 497–508. CrossRefGoogle Scholar
Thiébaut, B, Puech, S.. Développement du hêtre commun. Morphologie et architecture de l’arbre. Revue Forestière Française, 56 (1984), No. 1, 45–58. CrossRefGoogle Scholar
E. Walter, L. Pronzato. Identification de modèles paramétriques. Masson, Paris, 2006.
F. Wang, M.Z. Kang, Q. Lu, H. Han, V. Letort, Y. Guo, P. de Reffye, B. Li. Simulation of the structure and function of young Mongolian scots pine trees using the stochastic Greenlab model. Annals of Botany, In press (2010).
J. Warren-Wilson. Ecological data on dry matter production by plants and plant communities. The collection and processing of field data (E.F. Bradley, O.T. Denmead, eds.), Interscience Publishers, New York, 1967, 77–123.
P. Wernecke, J. Müller, T. Dornbusch, A. Wernecke, W. Diepenbrock. The virtual crop modelling system VICA specified for Barley. Functional-structural plant modelling in crop production, (J. Vos, L.F.M. Marcelis, P.H.B. de Visser, P.C. Struik, J.B. Evers, eds.), Springer, 2007, 58–69.
Q. Wu, J. Bertheloot, A. Mathieu, B. Andrieu, P.-H. Cournède. Assessment of non-linearity in functional-structural plant models. 6th international workshop on Functional-Structural Plant Models (FSPM10), Davis, USA (T. De Jong, J. Vos, A. Escobar, eds.), November 9-12 2010.
Q. Wu, P.-H. Cournède. Sensitivity analysis of Greenlab model for Maize. 3rd international symposium on Plant Growth and Applications(PMA09), Beijing, China (B.G. Li, M. Jaeger, Y. Guo, eds.), IEEE, November 9-12 2009.
Yan, H.P., Kang, M.Z., de Reffye, P., Dingkuhn, M.. A dynamic, architectural plant model simulating resource-dependent growth. Annals of Botany, 93 (2004), 591–602. CrossRefGoogle Scholar
Z.G. Zhan, P. de Reffye, F. Houllier, B.G. Hu. Fitting a structural-functional model with plant architectural data. Plant Growth Models and Applications (B.G. Hu, M. Jaeger, eds.), Tsinghua University Press and Springer (Beijing, China), 2003, 236–249.
W. Zucchini, I.L. MacDonald. Hidden Markov models for time series - An introduction using R. Chapman and Hall, 2009.