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

Published online by Cambridge University Press:  10 July 2013

P.-H. Cournède ,
Y. Chen ,
Q. Wu ,
C. Baey  and
B. Bayol
P.-H. Cournède*
Affiliation:
Ecole Centrale Paris, Laboratoire MAS, Digiplante - 92290 Châtenay Malabry, France
Y. Chen
Affiliation:
Ecole Centrale Paris, Laboratoire MAS, Digiplante - 92290 Châtenay Malabry, France
Q. Wu
Affiliation:
Ecole Centrale Paris, Laboratoire MAS, Digiplante - 92290 Châtenay Malabry, France
C. Baey
Affiliation:
Ecole Centrale Paris, Laboratoire MAS, Digiplante - 92290 Châtenay Malabry, France
B. Bayol
Affiliation:
Ecole Centrale Paris, Laboratoire MAS, Digiplante - 92290 Châtenay Malabry, France
*
⋆ Corresponding author. E-mail: [email protected]
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Abstract

Mathematical models of plant growth are generally characterized by a large number ofinteracting processes, a large number of model parameters and costly experimental dataacquisition. Such complexities make model parameterization a difficult process. Moreover,there is a large variety of models that coexist in the literature with generally anabsence of benchmarking between the different approaches and insufficient modelevaluation. In this context, this paper aims at enhancing good modelling practices in theplant growth modelling community and at increasing model design efficiency. It gives anoverview of the different steps in modelling and specify them in the case of plant growthmodels specifically regarding their above mentioned characteristics.

Different methods allowing to perform these steps are implemented in a dedicated platformPYGMALION (Plant Growth Model Analysis, Identification and Optimization). Some of thesemethods are original. The C++ platform proposes a framework in which stochastic ordeterministic discrete dynamic models can be implemented, and several efficient methodsfor sensitivity analysis, uncertainty analysis, parameter estimation, model selection ordata 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 toillustrate 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 realdata and is shown to have interesting predictive capacities when coupled with dataassimilation techniques.

Keywords

good modelling practicesensitivity analysisuncertainty analysisparameter estimationparticle filteringdata assimilationplant growth modelsLNAS model
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 4: Plant growth modelling , 2013 , pp. 112 - 130
Copyright
© EDP Sciences, 2013

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References

D.R. Anderson. Model based inference in the life sciences. Springer, 2008.
C. Baey, A. Didier, S. Li, S. Lemaire, F. Maupas, P.-H. Cournède. Evaluation of the predictive capacity of five plant growth models for sugar beet. 4th international symposium on Plant Growth and Applications (PMA12), Shanghai, China, IEEE, 2012.
Baey, C., Didier, A., Lemaire, S., Maupas, F., Cournède, P.-H.. Modelling the interindividual variability of organogenesis in sugar beet populations using a hierarchical segmented model. Ecological Modelling, 263 (2013), 56–63. CrossRefGoogle Scholar
Bertheloot, J., Cournède, P.-H., Andrieu, B.. NEMA, a functional-structural model of N economy within wheat culms after flowering: I. Model description. Annals of Botany, 108 (2011), No. 6, 1085–1096. CrossRefGoogle ScholarPubMed
B.M. Bolker. Ecological models and data in R. Princeton University Press, 2008.
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
Brukkin, V., Morozova, N.. Plant growth and development - basic knowledge and current views. Mathematical Modelling of Natural Phenomena, 6 (2011), No. 2, 1–53. CrossRefGoogle Scholar
K.P. Burnham, D.R. Anderson. Model selection and multimodel inference: a practical information-theoretic approach. 2nd edition, Springer Verlag, 2002.
Campbell, K., McKay, M.D., and Williams, B.J.. Sensitivity analysis when model outputs are functions. Reliability Engineering and System Safety, 91 (2006), No. 10-11, 1468–1472. CrossRefGoogle Scholar
Campillo, F., Rossi, V.. Convolution particle filter for parameter estimation in general state-space models. IEEE Transactions on Aerospace and Electronic Systems, 45 (2009), No. 3, 1063–1072. CrossRefGoogle Scholar
Campolongo, F., Cariboni, J., Saltelli, A.. An effective screening design for sensitivity analysis of large models. Environmental Modelling and Software, 22 (2007), 1509–518. CrossRefGoogle Scholar
O. Cappé, E. Moulines, T. Rydén. Inference in hidden Markov models, Springer, New York, 2005.
Cariboni, J., Gatelli, D., Liska, R., Saltelli, A.. The role of sensitivity analysis in ecological modelling. Ecological Modelling, 203 (2007), 167–182. CrossRefGoogle Scholar
E.R. Carson, C. Cobelli. Modelling methodology for physiology and medicine. Academic Press, San Diego (US), 2001.
Y. Chen, B. Bayol, C. Loi, S. Trevezas, P.-H. Cournède. Filtrage par noyaux de convolution itératif. Actes des 44èmes Journées de Statistique, JDS2012, Bruxelles 21-25 Mai 2012.
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., Letort, V., Mathieu, A., Kang, M.Z., Lemaire, S., Trevezas, S., Houllier, F., de Reffye, P.. Some parameter estimation issues in functional-structural plant modelling. Math. Model. Natural Phenom., 6 (2011), No. 2, 133–159. CrossRefGoogle Scholar
Cox, D.C., Baybutt, P.. Methods for uncertainty analysis: a comparative survey. Risk Analysis, 1 (1981), No. 4, 251–258. CrossRefGoogle Scholar
Dente, L., Satalino, G., Mattia, F., Rinaldi, M.. Assimilation of leaf area index derived from ASAR and MERIS data into CERES-wheat model to map wheat yield. Remote Sensing of Environment, 112 (2008), No. 4, 1395–1407. 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, pp. 2824–2837.
B. Efron, R.J. Tibshirani. An introduction to the bootstrap. Chapman & Hall / CRC Monographs on Statistics and Applied Probability, 1994.
G. Evensen. Data assimilation: The ensemble Kalman filter. Springer, 2009.
G.C. Goodwin, R.L. Payne. Dynamic system identification: Experiment design and data analysis. Academic Press, New York, 1977.
Guérif, M., Duke, C.. Calibration of the sucros emergence and early growth module for sugar beet using optical remote sensing data assimilation. European Journal of Agronomy, 9 (1998), 127–136. CrossRefGoogle Scholar
Guérif, M., Duke, C.. Adjustment procedures of a crop model to the site specific characteristics of soil and crop using remote sensing data assimilation. Agriculture, Ecosystems and Environment, 81 (2000), No. 1, 57–69. CrossRefGoogle Scholar
Helton, J.C., Johnson, J.D., Salaberry, C.J., Storlie, C.B.. Survey of sampling based methods for uncertainty and sensitivity analysis. Reliability Engineering and System Safety, 91 (2006), 1175–1209. CrossRefGoogle Scholar
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 Scholar
Guo, Y., Fourcaud, T., Jaeger, M., Zhang, X.P., Li, B.G.. Plant growth and architectural modelling and its applications. Annals of Botany, 107 (2011), 723–727. CrossRefGoogle ScholarPubMed
Hemmerling, R., Kniemeyer, O., Lanwert, D., Buck-Sorlin, G., Kurth, W.. The rule based language XL and the modeling environment GroIMP illustrated with simulated tree competition. Functional Plant Biology 35 (2008), No. 10, 739–750. CrossRefGoogle Scholar
Homma, T., Saltelli, A.. Importance measures in global sensitivity analysis of nonlinear models. Reliability Engineering and System Safety, 52 (1996), 1–17. 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
Keating, B.A., Carberry, P.S., Hammer, G.L., Probert, M.E., Robertson, M.J., Holzworth, D., Huth, N.I., Hargreaves, J.N.G., Meinke, H., Hochman, Z., McLean, G., Verburg, K., Snow, V., Dimes, J.P., Silburn, M., Wang, E., Brown, S., Bristow, K.L., Asseng, S., Chapman, S., McCown, R.L., Freebairn, D.M., Smith, C.J.. An overview of APSIM, a model designed for farming systems simulation. European Journal of Agronomy, 18 (2003), No. 3-4, 267–288. CrossRefGoogle Scholar
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.. Optimization by Simulated Annealing. Science, 220 (1983), No. 4598, 671–680. CrossRefGoogle ScholarPubMed
Kitagawa, G.. Monte Carlo filter and smoother for non-gaussian nonlinear state space models. Journal of Computational and Graphical Statistics, 5 (1996), No. 1, 1–25. Google Scholar
Kuhn, E., Lavielle, M.. Maximum likelihood estimation in nonlinear mixed effects models. Computational Statistics and Data Analysis, 49 (2005), No. 4, 1020–1038. CrossRefGoogle Scholar
Lamboni, M., Monod, H., Makowski, D.. Multivariate global sensitivity analysis for dynamic crop models. Field Crops Research, 113 (2009), 312–320. CrossRefGoogle Scholar
Launay, M., Guérif, M.. Assimilating remote sensing data into a crop model to improve predictive performance for spatial applications. Agriculture, ecosystems and environment, 111 (2005), 321–339. CrossRefGoogle Scholar
Lecoeur, J., Poiré-Lassus, R., Christophe, A., Pallas, B., Casadebaig, P., Debaeke, P., Vear, F., Guilioni, L.. Quantifying physiological determinants of genetic variation for yield potential in sunflower. SUNFLO: a model-based analysis. Functional Plant Biology, 38 (2011), 246–259. CrossRefGoogle Scholar
F. Legland, C. Musso, N. Oudjane. An analysis of regularized interacting particle methods for nonlinear filtering. 3rd IEEE Workshop on Computer-Intensive Methods in Control and Data Processing, Prague, 1998.
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, pp 116–129.
S. Lemaire, F. Maupas, P.-H. Cournède, J.-M. Allirand, P. de Reffye, B. Ney. Analysis of the density effects on the source-sink dynamics in sugar-beet growth. 3rd international symposium on Plant Growth and Applications(PMA09), Beijing, China (B.-G. Li, M. Jaeger, Y. Guo, eds.), IEEE Computer Society (Los Alamitos, California), Novem. 9-12 2009.
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.
Ma, Y., Wen, M.P., Guo, Y., Li, B.G., Cournède, P.-H., de Reffye, P.. Parameter optimization and field validation of the functional-structural model GreenLab for maize at different population densities. Annals of Bot., 101 (2008), 1185–1194. CrossRefGoogle ScholarPubMed
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
H. Monod, C. Naud, D. Makowski. Uncertainty and sensitivity analysis for crop models. Working with Dynamic Crop Models (D. Wallach, D. Makowski, J.W. Jones, eds.), Elsevier, 2006, pp. 55–100.
M.G. Morgan, M. Henrion, M. Small. Uncertainty. Cambridge University Press, 1990.
Morris, M.D.. Factorial sampling plans for preliminary computational experiments. Technometrics, 33 (1991), 161–174. CrossRefGoogle Scholar
Nilson, T.. A theoretical analysis of the frequency of gaps in plant stands. Agricult. and Forest Meteorol., 8 (1971), 25–38. CrossRefGoogle Scholar
A. O’Hagan, J.J. Forster. Kendall’s advanced theory of statistics: Bayesian inference. Arnold, London, 2nd edit., 2004,
Perttunen, J., Sievänen, R., Nikinmaa, E., Salminen, H., Saarenmaa, H., Vakeva, J.. Incorporating Lindenmayer systems for architectural development in a functional-structural tree model. Ecological Modelling, 181 (2005), 479–491. CrossRefGoogle Scholar
Pradal, C., Dufour-Kowalski, S., Boudon, F., Fournier, C., Godin, C.. OpenAlea: a visual programming and component-based software platform for plant modelling. Functional Plant Biology, 35 (2008), No. 10, 751–760. CrossRefGoogle Scholar
Rossi, V., Vila, J.-P.. Nonlinear filtering in discrete time: A particle convolution approach. Annales de l’Institut de Statistique de l’Université de Paris, 50 (2006), No. 3, 71–102. Google Scholar
Ruget, F., Brisson, N., Delécolle, R., Faivre, R.. Sensitivity analysis of a crop simulation model, STICS, in order to choose the main parameters to be estimated. Agronomie, 22 (2002), 133–158. CrossRefGoogle Scholar
A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, S. Tarantola. Global sensitivity analysis. The primer ed., John Wiley&Sons, 2008.
Y.H. Shi, R. Eberhart. A modified particle swarm optimizer. Evolutionary Computation Proceedings (IEEE World Congress on Computational Intelligence) (K.R. Belew, L.B. Booker, eds.), Morgan Kaufmann, 1998, pp. 69–73.
Sobol, I.. Sensitivity analysis for non-linear mathematical models. Math. Model. Comput. Experim., 1 (1993), 407–414. Google Scholar
Trevezas, S., Cournède, P.-H.. A sequential Monte Carlo approach for MLE in a plant growth model. Journal of Agricultural, Biological, and Environmental Statistics, 18 (2013), No. 2, 250–270. Google Scholar
Taylor, W.. Small sample properties of a class of two-stage Aitken estimator. Econometrica, 45 (1977), No. 2, 497–508. CrossRefGoogle Scholar
R.H. Van Waveren, S. Groot, H. Scholten, F. Van Geer, H. Wosten, R. Koeze, J. Noort. Good modelling practice handbook. Tech. Report 99-05, STOWA, Utrecht, RWS-RIZA, Lelystad, The Netherlands, 1999.
Varella, H., Buis, S., Launay, M., and Guérif, M.. Global sensitivity analysis for choosing the main soil parameters of a crop model to be determined. Agricultural Sciences, 3 (2012), 949–961. CrossRefGoogle Scholar
Vos, J., Evers, J.B., Buck-Sorlin, G.H., Andrieu, B., Chelle, M., de Visser, P.H.B.. Functional-structural plant modelling: a new versatile tool in crop science. Journal of Experimental Botany, 61 (2010), No. 8, 2101–2115. CrossRefGoogle ScholarPubMed
Wallach, D., Goffinet, B.. Mean Squared Error of Prediction in Models for Studying Ecological and Agronomic Systems. Biometrics, 43 (1987), No. 3, 561–573. CrossRefGoogle Scholar
Wallach, D., Goffinet, B., Bergez, J.-E., Debaeke, P., Leenhardt, D., Aubertot, J.-N.. The effect of parameter uncertainty on a model with adjusted parameters. Agronomie, 22 (2002), 159–170. CrossRefGoogle Scholar
Wallach, D., Buis, S., Lecharpentier, P., Bourges, J., Clastre, P., Launay, M., Bergez, J.-E., Guérif, M., Soudais, J., Justes, E.. A package of parameter estimation methods and implementation for the STICS crop-soil model. Environmental Modelling and Software, 26 (2011), 386–394. CrossRefGoogle Scholar
E. Walter, L. Pronzato. Identification de modèles paramétriques. Masson, Paris, 2006.
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.
Wu, Q., Cournède, P.-H., Mathieu, A.. An efficient computational method for global sensitivity analysis and its application to tree growth modelling Reliability Engineering and System Safety, 107 (2012), 35–43. CrossRefGoogle Scholar
Q. Wu, P.-H. Cournède. A comprehensive methodology of global sensitivity analysis for complex mechanistic models: An application to plant growth. Submitted, (2013).
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 ScholarPubMed