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Oscillations in Functional Structural Plant Growth Models

Published online by Cambridge University Press:  12 December 2012

A. Mathieu ,
V. Letort ,
P.H. Cournède ,
B.G. Zhang ,
P. Heuret  and
P. de Reffye
A. Mathieu*
Affiliation:
AgroParisTech, UMR EGC (1091), Grignon, France
V. Letort
Affiliation:
Ecole Centrale Paris, MAS, Châtenay-Malabry, France
P.H. Cournède
Affiliation:
Ecole Centrale Paris, MAS, Châtenay-Malabry, France
B.G. Zhang
Affiliation:
China Agricultural University, College of Resources and Environmental Sciences, Beijing, China
P. Heuret
Affiliation:
INRA, UMR EcoFoG (745), French Guyana, Kourou, French Guyana
P. de Reffye
Affiliation:
CIRAD, UMR AMAP, Montpellier, France
*
⋆ Corresponding author. E-mail: amelie.mathieu@agroparistech.fr
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Abstract

The dynamic model of plant growth GreenLab describes plant architecture and functional growth at the level of individual organs. Structural development is controlled by formal grammars and empirical equations compute the amount of biomass produced by the plant, and its partitioning among the growing organs, such as leaves, stems and fruits. The number of organs initiated at each time step depends on the trophic state of the plant, which is evaluated by the ratio of biomass available in plant to the demand of all the organs. The control of the plant organogenesis by this variable induces oscillations in the simulated plant behaviour. The mathematical framework of the GreenLab model allows to compute the conditions for the generation of oscillations and the value of the period according to the set of parameters. Two case-studies are presented, corresponding to emergence of oscillations associated to fructification and branching.

Similar alternating patterns are commonly reported by botanists. In this article, two examples were selected: alternate patterns of fruits in cucumber plants and alternate appearances of branches in Cecropia trees. The model was calibrated from experimental data collected on these plants. It shows that a simple feedback hypothesis of trophic control on plant structure allows the emergence of cyclic patterns corresponding to the observed ones.

Keywords

dynamic system of plant growthfunctional-structural plant modelsGreenLabcucumber plantCecropia trees
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 6: Biological oscillations , 2012 , pp. 47 - 66
Copyright
© EDP Sciences, 2012

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References

Références

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
C.C. Berg, P. Franco, Flora neotropica monograph 94. Cecropia. Organization for Flora Neotropica. 2005. New York Botanical Garden Press, Bronx, New York, USA.
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. Nat. Phenom, 6(2) (2011), 133–159. CrossRefGoogle Scholar
Evers, J., Vos, J., Yin, X., Romero, P., van der Putten, P.E.L., Struik, P.C.. Simulation of wheat growth and development based on organ-level photosynthesis and assimilate allocation. Journal of Experimental Botany, 61 (2010), 2203–2216 doi:10.1093/jxb/erq025. CrossRefGoogle Scholar
Evers, J., van der Krol, A., Vos, J., Struik, P.C.. Understanding shoot branching by modelling form and function. Trends in Plant Science, 16 (2011), 464–467. CrossRefGoogle ScholarPubMed
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 ScholarPubMed
Godin, C.. Representing and encoding plant architecture: a review. Annals of Forest Science, 57 (2000), 413–438. CrossRefGoogle Scholar
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
Heuvelink, E.. Dry Matter Partitioning in Tomato: Validation of a Dynamic Simulation Model. Annals of Botany, 77 (1996), 71–80. 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
Heuret, P., Barthélémy, D., Guédon, Y., Coulmier, X., Tancre, J.. Synchronization of growth, branching and flowering processes in the south american tropical tree Cecropia obtusa (Cecropiaceae). American Journal of Botany, 89 (2002), No. 7, 1180–1187. CrossRefGoogle Scholar
F. Hallé, R.A.A. Oldeman. Essai sur l’architecture et la dynamique de croissance des arbres tropicaux. Masson, Paris, 1970.
Kirkpatrick, S., Gelatt, C., Vecchi, M.. Optimization by simulated annealing. Science, 220 (1983), 671–680. doi: 10.1126/science.220.4598.671 CrossRefGoogle ScholarPubMed
Kitajima, K., Mulkey, S., Samaniego, M., and Wright, J.. Decline of photosynthetic capacity with leaf age and position in two tropical pioneer species. American Journal of Botany, 89 (2002), No. 12, 1925–1932.
V. Letort, P. Heuret, P.C. Zalamea, E. Nicolini, P. de Reffye. Analysis of Cecropia sciadophylla Morphogenesis Based on a Sink-Source Dynamic Model. International Symposium on Plant Growth Modeling and Applications (PMA09), IEEE Computer Society, Los Alamitos, CA, USA. (2009), 10–17.
Letort, V., Heuret, P., Zalamea, P.C., Nicolini, E., de Reffye, P.. Analysing the effects of local environment on the source-sink balance of Cecropia sciadophylla: a methodological approach based on model inversion. Annals of Forest Science, 69 (2012), 167–180. CrossRefGoogle Scholar
Luquet, D., Dingkuhn, M., Kim, H.K., 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 (2006), 309–323. doi: 10.1071/FP05266 CrossRefGoogle Scholar
Ma, Y.T., Wubs, A.M., Mathieu, A., Heuvelink, E., Zhu, J.Y., Hu, B.G., Cournède, P.-H., deReffye, P.. Simulation of fruit-set and trophic competition and optimization of yield advantages in six Capsicum cultivars using functional-structural plant modelling. Annals of Botany, 107 (2011), 793–803. CrossRefGoogle Scholar
Marcelis, L.F.M.. A Simulation Model for Dry Matter Partitioning in Cucumber. Annals of Botany, 74 (1994), 43–52. CrossRefGoogle Scholar
Marcelis, L.F.M., Heuvelink, E., Baan Hofman-Eijer, L., Den Bakker, J., Xue, L.B.. Flower and fruit abortion in sweet pepper in relation to source and sink strength. Journal of Experimental Botany, 55 (2004), 22-1–2268. CrossRefGoogle ScholarPubMed
A. Mathieu, P.-H. Cournède, D. Barthélémy, P. de Reffye. Conditions for the Generation of Rhythms in a Discrete Dynamic System. Case of a Functional Structural Plant Growth Model. 2nd International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA06), IEEE Computer Society, Los Alamitos, CA, USA. (2007), 26–33.
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.
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
Mathieu, A., Cournède, P.-H., Barthélémy, D., de Reffye, P.. Rhythms and alternating patterns in plants as emergent properties of a model of interaction between development and functioning. Annals of Botany, 101 (2008), No. 8, 1233–1242. CrossRefGoogle Scholar
Mickelbart, M.V., Bender, G.S., Witney, G.W., Adams, C., Arpaia, M.L.. Effects of clonal rootstocks on ’Hass’ avocado yield components, alternate bearing, and nutrition. Journal of Horticultural Science and Biotechnology, 82 (2007), 460–466. CrossRefGoogle Scholar
Monselise, S.P., Goldschmidt, E.E.. Alternate bearing in fruit trees. Horticultural Reviews. 4 (1982), 128–173. Google Scholar
P. de Reffye, M. Goursat, J.-P. Quadrat, and B.G. Hu. The Dynamic Equations of the Tree Morphogenesis Greenlab Model. Technical Report 4877, INRIA, (2003).
Sabatier, S., Barthélémy, D.. Growth dynamics and morphology of annual shoots according to their architectural position in young Cedrus atlantica (Endl.) Manetti ex Carrière (pinaceae). Annals of Botany, 84 (1999), 387–392. CrossRefGoogle Scholar
Schapendonk, A., Brouwer, P.. Fruit growth of cucumber in relation to assimilate supply and sink activity. Scientia Horticulturae 23 (1984), 21-33. CrossRefGoogle Scholar
J. Schupp. Alternate Bearing in Fruit Crops. PennState Technical Report, 2011: http://extension.psu.edu/fruit-times/news/2011/alternate-bearing-in-fruit-crops
Shinozaki, K., Yoda, K., Hozumi, K., Kira, T.. A quantitative analysis of plant form - the pipe model theory i. basic analysis. Japanese Journal of Ecology., 14 (1964), 97–105. Google Scholar
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
U. Van Meeteren, H. Van Gelder. Role of flower buds in flower bud abscission in Hibiscus. Acta Horticulturae (1995), 284-289.
Verreynne, J.S., Lovatt, C.J.. The Effect of Crop Load on Budbreak Influences Return Bloom in Alternate Bearing ’Pixie’ Mandarin. Journal of the American Society for Horticultural Science, 134 (2009), 299–307. Google Scholar
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, pp. 77–123.
Zalamea, P.C., Stevenson, P.R., Madrinan, S., Aubert, P.M., Heuret, P.. Growth pattern and age determination for Cecropia sciadophylla (Urticaceae). American Journal of Botany, 95 (2008), 263–271. CrossRefGoogle Scholar