Free Standard AU & NZ Shipping For All Book Orders Over $80!
Register      Login
Functional Plant Biology Functional Plant Biology Society
Plant function and evolutionary biology
Shopping Cart: ( empty )
You are here: Home > Journals > FP > FP08065
RESEARCH ARTICLE
Contents Vol 35(10)

Parametric identification of a functional–structural tree growth model and application to beech trees (Fagus sylvatica)

Véronique Letort A D , Paul-Henry Cournède A , Amélie Mathieu A , Philippe de Reffye B and Thiéry Constant C
+ Author Affiliations
- Author Affiliations

A Ecole Centrale of Paris, Laboratoire de Mathématiques Appliquées aux Systèmes, F-92295 Châtenay-Malabry cedex, France.

B Cirad-Amis, UMR AMAP, TA 40/01 Avenue Agropolis, F-34398 Montpellier cedex 5, France and INRIA-Saclay, Parc Orsay Université, F-91893 Orsay cedex, France.

C LERFOB UMR INRA-ENGREF No. 1092, Wood Quality Research Team, INRA Research Centre of Nancy, F-54280 Champenoux, France.

D Corresponding author. Email: letort@mas.ecp.fr

This paper originates from a presentation at the 5th International Workshop on Functional–Structural Plant Models, Napier, New Zealand, November 2007.

Functional Plant Biology 35(10) 951-963 https://doi.org/10.1071/FP08065
Submitted: 8 March 2008  Accepted: 22 September 2008   Published: 11 November 2008

Abstract

Functional–structural models provide detailed representations of tree growth and their application to forestry seems full of prospects. However, owing to the complexity of tree architecture, parametric identification of such models remains a critical issue. We present the GreenLab approach for modelling tree growth. It simulates tree growth plasticity in response to changes of their internal level of trophic competition, especially topological development and cambial growth. The model includes a simplified representation of tree architecture, based on a species-specific description of branching patterns. We study whether those simplifications allow enough flexibility to reproduce with the same set of parameters the growth of two observed understorey beech trees (Fagus sylvatica L.) of different ages in different environmental conditions. The parametric identification of the model is global, i.e. all parameters are estimated simultaneously, potentially providing a better description of interactions between sub-processes. As a result, the source–sink dynamics throughout tree development is retrieved. Simulated and measured trees were compared for their trunk profiles (fresh masses and dimensions of every growth units, ring diameters at different heights) and compartment masses of their order 2 branches. Possible improvements of this method by including topological criteria are discussed.

Additional keywords: architectural development, carbon allocation, parameter estimation, plasticity.


Acknowledgement

Data were collected with the support of the LERFOB Wood Quality research team. We particularly thank Claude Houssement, Emmanuel Cornu and Alain Mercanti for their help in the measurement process. This research is partly supported by the Cap Digital Business Cluster Terra Numerica project.


References


Allen MT, Prusinkiewicz P, DeJong TM (2005) Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH model. New Phytologist 166, 869–880.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Balandier P, Lacointe A, Le Roux X, Sinoquet H, Cruziat P, Le Dizès S (2000) SIMWAL: a structural-functional model simulating single walnut tree growth in response to climate and pruning. Annals of Forest Science 57, 571–585.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Barna M (2004) Adaptation of european beech (Fagus sylvatica L.) to different ecological conditions: leaf size variations. Polish Journal of Ecology 52, 34–45. open url image1

Barthélémy D, Caraglio Y (2007) Plant architecture: a dynamic, multilevel and comprehensive approach to plant form, structure and ontogeny. Annals of Botany 99, 375–407.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Barthélémy D , Caraglio Y , Costes E (1997) Architecture, gradients morphogénétiques et âge physiologique chez les végétaux. In ‘Modélisation et simulation de l’architecture des végétaux’. (Ed. J Bouchon) pp. 89–136. (INRA: France) [In French]

Beaudet M, Messier C (1998) Growth and morphological responses of yellow birch, sugar maple and beech seedlings growing under a natural light gradient. Canadian Journal of Forest Research 28, 1007–1015.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Collet C, Lanter O, Pardos M (2001) Effect of canopy opening on height and diameter growth in naturally regenerated beech seedlings. Annals of Forest Science 58, 127–134.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Comps B, Thiébaut B, Barrière G, Letouzey J (1994) Répartition de la biomasse entre organs végétatifs et reproducteurs chez le hêtre européen (Fagus sylvatica L.), selon le secteur de la couronne et l’âge des arbres. Annals of Forest Science [In French] 51, 11–26.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Costes E , Smith C , Favreau R , Guédon Y , DeJong T (2007) Linking carbon economy and architectural development of peach trees by integrating markovian models into L-PEACH. In ‘Proceedings of the 5th international workshop on functional–structural plant models’. (Eds P Prunsinkiewicz, J Hanan, B Lane) pp. 39-1–39-3. (HortResearch: Napier, New Zealand)

Cournède P-H, Kang M, Mathieu A, Yan H, Hu B, de Reffye P (2006) Structural factorization of plants to compute their functional and architectural growth. Simulation 82, 427–438.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Cournède P-H, Mathieu A, Houllier F, Barthélémy D, De Reffye P (2008) 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, 1207–1219.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Deleuze C, Houllier F (2002) A flexible radial increment taper equation derived from a process-based carbon partitioning model. Annals of Forest Science 59, 141–154.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Dingkuhn M, Luquet D, Kim HK, Tambour L, Clément-Vidal A (2006) Ecomeristem, a model of morphogenesis and competition among sinks in rice. 2. Simulating genotype responses to phosphorus deficiency. Functional Plant Biology 33, 325–337.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Duff GH, Nolan NJ (1953) Growth and morphogenesis in the Canadian forest species. Canadian Journal of Botany 31, 471–513.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Durand J-B, Guédon Y, Caraglio Y, Costes E (2005) Analysis of the plant architecture via tree-structured statistical models: the hidden Markov tree models. New Phytologist 166, 813–825.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Ferraro P, Godin C (2000) A distance measure between plant architectures. Annals of Forest Science 57, 445–461.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Godin C, Caraglio Y (1998) A multiscale model of plant topological structures. Journal of Theoretical Biology 191, 1–46.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Grossman YL, DeJong TM (1994) PEACH: a model of reproductive and vegetative growth in peach trees. Tree Physiology 14, 329–345.
| PubMed |
open url image1

Guédon Y, Barthélémy D, Caraglio Y, Costes E (2001) Pattern analysis in branching and axillary flowering sequences. Tree Physiology 14, 329–345. open url image1

Guo Y, Ma Y, Zhan Z, Li B, Dingkuhn M, Luquet D, De Reffye P (2006) Parameter optimization and field validation of the functional-structural model GreenLab for maize. Annals of Botany 97, 217–230.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Guo H , Letort V , Hong L , Fourcaud T , Cournède P-H , Lu Y , De Reffye P (2008) Adapatation of the GreenLab model for analyzing source–sink relationships in Chinese pine saplings. In ‘Plant growth modelling, simulation, visualization and their applications’. (Eds T Fourcaud, XP Zhang) pp. 236–243. (IEEE Computer Society: Los Alamitos, CA, USA)

Hallé F , Oldemann R (1970) ‘Essai sur l’architecture et la dynamique de croissance des arbres tropicaux.’ (Masson: Paris)

Kirkpatrick S, Gelatt C, Vecchi M (1983) Optimization by simulated annealing. Science 220, 671–680.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Lanner RM (1985) On the insensivity of height growth to spacing. Forest Ecology and Management 13, 143–148.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Le Roux X, Lacointe A, Escobar-Gutiérrez A, Le Dizès S (2001) Carbon-based models of individual tree growth: a critical appraisal. Annals of Forest Science 58, 469–506.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Louarn G , Dong Q , Wang Y , Barczi JF , De Reffye P (2008) Parameter stability of the functional-structural model GreenLab-tomato as affected by plant density and biomass acquisition. In ‘Plant growth modelling, simulation, visualization and their applications’. (Eds T Fourcaud, XP Zhang) pp. 142–148. (IEEE Computer Society: Los Alamitos, CA, USA)

Luquet D, Dingkuhn M, Kim HK, Tambour L, Clément-Vidal A (2006) Ecomeristem, a model of morphogenesis and competition among sinks in rice. 1. Concept, validation and sensitivity analysis. Functional Plant Biology 33, 309–323.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Luquet D, Song YH, Elbelt S, This D, Clément-Vidal A, Périn C, Fabre D, Dingkuhn M (2007) Model-assisted physiological analysis of Phyllo, a rice architectural mutant. Functional Plant Biology 34, 11–23.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Mathieu A (2006) Essai sur la modélisation des interactions entre la croissance et le développement d’une plante: cas du modèle GreenLab. PhD thesis, Ecole Centrale de Paris. [In French]

Nicolini E (1997) Approche morphologique du développement du hêtre (Fagus sylvatica L.). PhD thesis, University of Montpellier II, France. [In French]

Nicolini E (1998) Architecture et gradients morphogénétiques chez de jeunes hêtres (Fagus sylvatica L.) en milieu forestier. Canadian Journal of Botany [In French] 76, 1232–1244.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Nicolini E, Chanson B (1999) La pousse courte, un indicateur du degree de maturation chez le hêtre (Fagus sylvatica L.). Canadian Journal of Botany [In French] 77, 1539–1550.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Nicolini E, Chanson B, Bonne F (2001) Stem growth and epicormic branch formation in understorey beech trees (Fagus sylvatica L.). Annals of Botany 87, 737–750.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Perttunen J, Sievänen R (2005) Incorporating Lindenmayer systems for architectural development in a functional-structural tree model. Ecological Modelling 181, 479–491.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Perttunen J, Sievänen R, Nikinmaa E, Salminen H, Saarenmaa H, Vakeva J (1996) LIGNUM: a tree model based on simple structural units. Annals of Botany 77, 87–98.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Perttunen J, Nikinmaa E, Lechowicz MJ, Sievänen R, Messier C (2001) Application of the functional-structural tree model LIGNUM to sugar maple sapling (Acer saccharum Marsh) growing in forest gaps. Annals of Botany 88, 471–481.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Pouderoux S, Dhote JF, Deleuze C (2001) Analysis of crown efficiency in a common beech thinning trial using a process-based model. Annals of Forest Science 58, 261–275.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Pretzsch H, Biber P, Ďurský J (2002) The single tree-based stand simulator SILVA: construction, application and validationevaluation. Forest Ecology and Management 162, 3–21.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Prusinkiewicz P (2004) Modeling plant growth and development. Current Opinion in Plant Biology 7, 79–83.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Rauscher HM, Isebrands JG, Host GE, Dickson RE, Dickmann DI, Crow TR, Michael DA (1990) ECOPHYS: an ecophysiological growth process model for juvenile poplar. Tree Physiology 7, 255–281.
| PubMed |
open url image1

Rostand-Mathieu A, Cournède P-H, De Reffye P (2006) A dynamical model of plant growth with full retroaction between organogenesis and photosynthesis. ARIMA 4, 101–107. open url image1

Sabatier S, Barthélémy D (1999) 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, 387–392.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Sarijeva G, Knapp M, Lichtenthaler H (2007) Differences in photosynthetic activity, chlorophyll and carotenoid levels, and in chlorophyll fluorescence parameters in green sun and shade leaves of Ginkgo and Fagus. Journal of Plant Physiology 164, 950–955.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Shinozaki K, Yoda K, Hozumi K, Kira T (1964) A quantitative analysis of plant form – the pipe model theory. I Basic analysis. Japanese Journal of Ecology 14, 97–105. open url image1

Sievänen R, Nikinmaa E, Nygren P, Ozier-Lafontaine H, Perttunen J, Hakula H (2000) Components of functional–structural tree models. Annals of Forest Science 57, 399–412.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Sinoquet H, Sonohat G, Phattaralerphong J, Godin C (2005) Foliage randomness and light interception in 3-D digitized trees: an analysis from multiscale discretization of the canopy. Plant, Cell & Environment 28, 1158–1170.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Sterck FJ, Schieving F (2007) 3-D growth patterns of trees: effects of carbon economy, meristem activity and selection. Ecological Monographs 77, 405–420.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Sterck FJ, Schieving F, Lemmens A, Pons TL (2005) Performance of trees in forest canopies: explorations with a bottom-up functional–structural plant growth model. New Phytologist 166, 827–843.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Thiébaut B, Puech S (1984) Développement du hêtre commun, morphologie et architecture de l’arbre. Revue Forestière française [In French] 56, 45–58. open url image1

Walter E , Pronzato L (1994) ‘Identification de modèles paramétriques à partir de données expérimentales.’ (Masson: Paris)

Wang YP (2003) A comparison of three different canopy radiation models commonly used in plant modelling. Functional Plant Biology 30, 143–152.
| Crossref | GoogleScholarGoogle Scholar | open url image1

White DA (1993) Relationships between foliar number and the cross-sectional areas of sapwood and annual rigns in red oak (Quercus rubra) crowns. Canadian Journal of Forest Research 23, 1245–1251.
| Crossref | GoogleScholarGoogle Scholar | open url image1

Yan H-P, Kang MZ, de Reffye P, Dingkuhn M (2004) A dynamic, architectural plant model simulating resource-dependent growth. Annals of Botany 93, 591–602.
| Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Zhang Y, Reed DD, Cattelino PJ, Gale MR, Jones EA, Liechty HO, Mroz GD (1994) A process-based growth model for young red pine. Forest Ecology and Management 69, 21–40.
| Crossref | GoogleScholarGoogle Scholar | open url image1