MAppleT: simulation of apple tree development using mixed stochastic and biomechanical models
Evelyne Costes A F , Colin Smith A , Michael Renton D , Yann Guédon B C , Przemyslaw Prusinkiewicz E and Christophe Godin B CA INRA, UMR 1098 CIRAD-INRA-Montpellier SupAgro-UM2, 2 Place Viala, F-34060 Montpellier, France.
B CIRAD, UMR 1098 CIRAD-INRA- Montpellier SupAgro-UM2, Avenue Agropolis, TA A96/02, F-34398 Montpellier, France.
C INRIA, Equipe Virtual Plants, Avenue Agropolis, TA A96/02, F-34398 Montpellier, France.
D School of Plant Biology, Faculty of Natural and Agricultural Sciences, The University of Western Australia, Crawley, WA 6009, Australia.
E Department of Computer Science, University of Calgary, Alberta, T2N 1N4, Canada.
F Corresponding author. Email: costes@supagro.inra.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) 936-950 https://doi.org/10.1071/FP08081
Submitted: 17 March 2008 Accepted: 4 August 2008 Published: 11 November 2008
Abstract
Construction of tree architectural databases over years is time consuming and cannot easily capture event dynamics, especially when both tree topology and geometry are considered. The present project aimed to bring together models of topology and geometry in a single simulation such that the architecture of an apple tree may emerge from process interactions. This integration was performed using L-systems. A mixed approach was developed based on stochastic models to simulate plant topology and mechanistic model for the geometry. The succession of growth units (GUs) along axes and their branching structure were jointly modelled by a hierarchical hidden Markov model. A biomechanical model, derived from previous studies, was used to calculate stem form at the metamer scale, taking into account the intra-year dynamics of primary, secondary and fruit growth. Outputs consist of 3-D mock-ups – geometric models representing the progression of tree form over time. To asses these models, a sensitivity analysis was performed and descriptors were compared between simulated and digitised trees, including the total number of GUs in the entire tree, descriptors of shoot geometry (basal diameter, length), and descriptors of axis geometry (inclination, curvature). In conclusion, despite some limitations, MAppleT constitutes a useful tool for simulating development of apple trees in interaction with gravity.
Additional keywords: biomechanics, functional–structural plant model, Malus × domestica, Markov model, tree simulation.
Acknowledgements
We thank Julia Taylor-Hell for kindly making her model of branch bending in poplar trees available. We also thank Fredéric Boudon for his assistance on the Geom module from PlantGL, Jean-Jacques Kelner and Jean-Luc Regnard for allowing us to use their observations of apple trees. This research was supported in part by the Natural Sciences and Engineering Research Council of Canada Discovery Grant RGPIN 130084–2008 to PP. The postdoctoral positions of C Smith and M Renton were granted by the INRA Department of Genetics and Plant Breeding.
Allen M,
Prusinkiewicz P, Dejong T
(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 |
[Verified 2 September 2008]
Prusinkiewicz P
(1998) Modeling of spatial structure and development of plants. Scientia Horticulturae 74, 113–149.
| Crossref | GoogleScholarGoogle Scholar |
Prusinkiewicz P,
Mündermann L,
Karwowski R, Lane B
(2001) The use of positional information in the modeling of plants. Proceedings of the 28th Annual Conference on Computer Graphics And Interactive Techniques 20, 289–300.
| Crossref | GoogleScholarGoogle Scholar |
Renton M,
Kaitaniemi P, Hanan J
(2005a) Functional–structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function. Ecological Modelling 184, 277–298.
| Crossref | GoogleScholarGoogle Scholar |
Renton M,
Hanan J, Burrage K
(2005b) Using the canonical modelling approach to simplify the simulation of function in functional-structural plant models. New Phytologist 166, 845–857.
| Crossref | GoogleScholarGoogle Scholar | PubMed |
Renton M,
Guédon Y,
Godin C, Costes E
(2006) Similarities and gradients in growth unit branching patterns during tree ontogeny based on a stochastic approach in ‘Fuji’ apple trees. Journal of Experimental Botany 57, 3131–3143.
| Crossref | GoogleScholarGoogle Scholar | PubMed |
Segura V,
Denancé C,
Durel CE, Costes E
(2007) Wide range QTL analysis for complex architectural traits in a 1-year-old apple progeny. Genome 50, 159–171.
| Crossref | GoogleScholarGoogle Scholar | PubMed |
Shinozaki K,
Yoda K,
Hozumi K, Tira T
(1964) A quantitative analysis of plant form – the pipe model theory. (i) Basic analyses. Japanese Journal of Ecology 14, 97–105.
Sinoquet H,
Rivet P, Godin C
(1997) Assessment of the three-dimensional architecture of walnut trees using digitising. Silva Fennica 31, 265–273.
Suzuki M, Hiura T
(2000) Allometric differences between current-year shoots and large branches of deciduous broad-leaved tree species. Tree Physiology 20, 203–209.
| PubMed |
Thornby D,
Renton M, Hanan J
(2003) Using computational plant science tools to investigate morphological aspects of compensatory growth. Computational Science – ICCS 2003 2660/2003, 708–717.
| Crossref | GoogleScholarGoogle Scholar |
Wang R,
Hua W,
Dong Z,
Peng Q, Bao H
(2006) Synthesizing trees by plantons. The Visual Computer 22, 238–248.
| Crossref | GoogleScholarGoogle Scholar |
White J
(1979) The plant as a metapopulation. Annual Review of Ecology and Systematics 10, 109–145.
| Crossref | GoogleScholarGoogle Scholar |
Wilson BF, Archer RR
(1977) Reaction wood: induction and mechanical action. Annual Review of Plant Physiology 28, 23–43.
| Crossref | GoogleScholarGoogle Scholar |
