Simulation of carbon allocation and organ growth variability in apple tree by connecting architectural and source-sink models.

BACKGROUND AND AIMS Plant growth depends on carbon availability and allocation among organs. QualiTree has been designed to simulate carbon allocation and partitioning in the peach tree (Prunus persica), whereas MappleT is dedicated to the simulation of apple tree (Malus × domestica) architecture. The objective of this study was to couple both models and adapt QualiTree to apple trees to simulate organ growth traits and their within-tree variability. METHODS MappleT was used to generate architectures corresponding to the 'Fuji' cultivar, accounting for the variability within and among individuals. These architectures were input into QualiTree to simulate shoot and fruit growth during a growth cycle. We modified QualiTree to account for the observed shoot polymorphism in apple trees, i.e. different classes (long, medium and short) that were characterized by different growth function parameters. Model outputs were compared with observed 3D tree geometries, considering shoot and final fruit size and growth dynamics. KEY RESULTS The modelling approach connecting MappleT and QualiTree was appropriate to the simulation of growth and architectural characteristics at the tree scale (plant leaf area, shoot number and types, fruit weight at harvest). At the shoot scale, mean fruit weight and its variability within trees was accurately simulated, whereas the model tended to overestimate individual shoot leaf area and underestimate its variability for each shoot type. Varying the parameter related to the intensity of carbon exchange between shoots revealed that behaviour intermediate between shoot autonomy and a common assimilate pool was required to properly simulate within-tree fruit growth variability. Moreover, the model correctly dealt with the crop load effect on organ growth. CONCLUSIONS This study provides understanding of the integration of shoot ontogenetic properties, carbon supply and transport between entities for simulating organ growth in trees. Further improvements regarding the integration of retroaction loops between carbon allocation and the resulting plant architecture are expected to allow multi-year simulations.

[1]  Kathy Steppe,et al.  Tree girdling responses simulated by a water and carbon transport model. , 2011, Annals of botany.

[2]  L C Ho,et al.  Metabolism and Compartmentation of Imported Sugars in Sink Organs in Relation to Sink Strength , 1988 .

[3]  Przemyslaw Prusinkiewicz,et al.  L-Py: An L-System Simulation Framework for Modeling Plant Architecture Development Based on a Dynamic Language , 2012, Front. Plant Sci..

[4]  Christophe Godin,et al.  Similarities and gradients in growth unit branching patterns during ontogeny in "Fuji" apple trees: a stochastic approach. , 2006, Journal of experimental botany.

[5]  Przemyslaw Prusinkiewicz,et al.  Towards aspect-oriented functional--structural plant modelling. , 2011, Annals of botany.

[6]  Gerhard Buck-Sorlin,et al.  The rule-based language XL and the modelling environment GroIMP illustrated with simulated tree competition. , 2008, Functional plant biology : FPB.

[7]  S. Drake,et al.  Canopy Position and Light Effects on Spur, Leaf, and Fruit Characteristics of ‘Delicious’ Apple , 1987, HortScience.

[8]  Damien Sellier,et al.  Phloem transport in trees: A generic surface model , 2014 .

[9]  B. Iooss,et al.  A Review on Global Sensitivity Analysis Methods , 2014, 1404.2405.

[10]  Evelyne Costes,et al.  Light interception efficiency of apple trees: A multiscale computational study based on MAppleT , 2014 .

[11]  Sébastien Griffon,et al.  AMAPstudio: an editing and simulation software suite for plants architecture modelling , 2014 .

[12]  Romeo Favreau,et al.  Linking water stress effects on carbon partitioning by introducing a xylem circuit into L-PEACH. , 2011, Annals of botany.

[13]  André Lacointe,et al.  Carbon allocation among tree organs: A review of basic processes and representation in functional-structural tree models , 2000 .

[14]  J. Racskó.  Crop Load, Fruit Thinning and their Effects on Fruit Quality of Apple (Malus domestica Borkh.) , 2006 .

[15]  P. Cournède,et al.  SUNLAB: A functional-structural model for genotypic and phenotypic characterization of the sunflower crop , 2012, 2012 IEEE 4th International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications.

[16]  Hervé Sinoquet,et al.  SIMWAL: A structural-functional model simulating single walnut tree growth in response to climate and pruning , 2000 .

[17]  A. Naor,et al.  Irrigation and crop load interactions in relation to apple yield and fruit size distribution , 1997 .

[18]  P. de Reffye,et al.  A Functional and Structural Mongolian Scots Pine (Pinus sylvestris var. mongolica) Model Integrating Architecture, Biomass and Effects of Precipitation , 2012, PloS one.

[19]  Przemyslaw Prusinkiewicz,et al.  Integrating simulation of architectural development and source-sink behaviour of peach trees by incorporating Markov chains and physiological organ function submodels into L-PEACH. , 2008, Functional plant biology : FPB.

[20]  Jim Hanan,et al.  A functional-structural kiwifruit vine model integrating architecture, carbon dynamics and effects of the environment. , 2011, Annals of botany.

[21]  H. Sinoquet,et al.  Does variability in shoot carbon assimilation within the tree crown explain variability in peach fruit growth? , 2004, Tree physiology.

[22]  Pierre-Eric Lauri,et al.  Genotype of Apple Trees Affects Growth and Fruiting Responses to Shoot Bending at Various Times of Year , 2001 .

[23]  P. Reich,et al.  Biomass allocation to leaves, stems and roots: meta-analyses of interspecific variation and environmental control. , 2012, The New phytologist.

[24]  P E H Minchin,et al.  New understanding on phloem physiology and possible consequences for modelling long-distance carbon transport. , 2005, The New phytologist.

[25]  M. Génard,et al.  Modelling the size and composition of fruit, grain and seed by process-based simulation models. , 2011, The New phytologist.

[26]  John W. Palmer,et al.  Effects of crop load on fruiting and gas-exchange characteristics of 'Braeburn'/M.26 apple trees at full canopy. , 2000 .

[27]  E. F. Bradley,et al.  Collection and processing of field data. , 1967 .

[28]  T. Bohr,et al.  Modeling the Hydrodynamics of Phloem Sieve Plates , 2012, Front. Plant Sci..

[29]  Godin,et al.  A multiscale model of plant topological structures , 1998, Journal of theoretical biology.

[30]  M. R. Thorpe,et al.  Modelling phloem transport within a pruned dwarf bean: a 2-source-3-sink system. , 2011, Functional plant biology : FPB.

[31]  Jan Vos,et al.  Using functional–structural plant models to study, understand and integrate plant development and ecophysiology. , 2011, Annals of botany.

[32]  Y. L. Grossman,et al.  Maximum Vegetative Growth Potential and Seasonal Patterns of Resource Dynamics during Peach Growth , 1995 .

[33]  M. Vandame,et al.  Testing the branch autonomy theory: a 13C/14C double-labelling experiment on differentially shaded branches , 2004 .

[34]  M. Blanke,et al.  Effect of fruiting on carbon budgets of apple tree canopies , 1993, Trees.

[35]  E. Costes,et al.  3D digitizing based on tree topology: application to study the variability of apple quality within the canopy , 1999 .

[36]  Carlo Meloni,et al.  Uncertainty Management in Simulation-Optimization of Complex Systems : Algorithms and Applications , 2015 .

[37]  J. Lecoeur,et al.  Are the common assimilate pool and trophic relationships appropriate for dealing with the observed plasticity of grapevine development? , 2010, Annals of botany.

[38]  P. de Reffye,et al.  Parameter optimization and field validation of the functional-structural model GREENLAB for maize. , 2006, Annals of botany.

[39]  Ep Heuvelink,et al.  Dry matter partitioning in a tomato plant: one common assimilate pool? , 1995 .

[40]  J. Palmer,et al.  Effect of crop load on fruiting and leaf photosynthesis of 'Braeburn'/M.26 apple trees. , 1997, Tree physiology.

[41]  Escobar-Gutierrez,et al.  Modelling of allocation and balance of carbon in walnut (Juglans regia L.) seedlings during heterotrophy-autotrophy transition , 1998, Journal of theoretical biology.

[42]  D. Barthélémy,et al.  A dynamic model of plant growth with interactions between development and functional mechanisms to study plant structural plasticity related to trophic competition. , 2009, Annals of botany.

[43]  Michel Génard,et al.  QualiTree, a virtual fruit tree to study the management of fruit quality. II. Parameterisation for peach, analysis of growth-related processes and agronomic scenarios , 2011, Trees.

[44]  E Costes,et al.  Winter bud content according to position in 3-year-old branching systems of 'Granny Smith' apple. , 2003, Annals of botany.

[45]  P. Millard,et al.  The Effect of the Autumn Senescence of Leaves on the Internal Cycling of Nitrogen for the Spring Growth of Apple Trees , 1989 .

[46]  A. Novoplansky.  Hierarchy establishment among potentially similar buds , 1996 .

[47]  E. F. Walton,et al.  Estimation of the bioenergetic costs of fruit and other organ synthesis in apple , 1999 .

[48]  P. Hansen.  14C‐Studies on Apple Trees. VII. The Early Seasonal Growth in Leaves, Flowers and Shoots as Dependent upon Current Photosynthates and Existing Reserves , 1971 .

[49]  C. Fournier,et al.  OpenAlea: a visual programming and component-based software platform for plant modelling. , 2008, Functional plant biology : FPB.

[50]  R. O. Sharples,et al.  The influence of shade and within-tree position on apple fruit size, colour and storage quality , 1971 .

[51]  D. L. Abbott.  The Apple Tree: Physiology and Management , 1984 .

[52]  T. G. Thorp,et al.  Apple dwarfing rootstocks and interstocks affect the type of growth units produced during the annual growth cycle: precocious transition to flowering affects the composition and vigour of annual shoots. , 2008, Annals of botany.

[53]  Robert Faivre,et al.  Influence of the variation of geometrical and topological traits on light interception efficiency of apple trees: sensitivity analysis and metamodelling for ideotype definition , 2014, Annals of botany.

[54]  Thomas M. Hinckley,et al.  THE THEORY AND PRACTICE OF BRANCH AUTONOMY , 1991 .

[55]  Przemyslaw Prusinkiewicz,et al.  MAppleT: simulation of apple tree development using mixed stochastic and biomechanical models. , 2008, Functional plant biology : FPB.

[56]  L. C. Grappadelli,et al.  An expolinear model of the growth pattern of the apple fruit , 1995 .

[57]  O. Leyser,et al.  Canalization: what the flux? , 2014, Trends in genetics : TIG.

[58]  H Sinoquet,et al.  Exploring within-tree architectural development of two apple tree cultivars over 6 years. , 2003, Annals of botany.

[59]  Michael Henke,et al.  PART OF A SPECIAL ISSUE ON FUNCTIONAL -STRUCTURAL PLANT MODELLING An approach to multiscale modelling with graph grammars , 2014 .

[60]  E. Lötze,et al.  Early prediction of harvest fruit size distribution of an apple and pear cultivar , 2004 .

[61]  D. Gianelle,et al.  Maximum Growth Potential and Periods of Resource Limitation in Apple Tree , 2016, Front. Plant Sci..

[62]  A. J. Greaves,et al.  Sensitivity of Floral Shoot Growth, Fruit Set and Early Fruit Size inActinidia deliciosato Local Carbon Supply☆ , 1998 .

[63]  Catherine Massonnet,et al.  Variabilité architecturale et fonctionnelle du système aérien chez le pommier (Malus domestica Borkh.): comparaison de quatre cultivars par une approche de modélisation structure-fonction , 2004 .

[64]  R. Bendel,et al.  Comparative gas exchange characteristics of potted, glasshouse-grown almond, apple, fig, grape, olive, peach and Asian pear , 1992 .

[65]  Przemyslaw Prusinkiewicz,et al.  The L-system-based plant-modeling environment L-studio 4.0 , 2004 .

[66]  M. Génard.  Influence du nombre de feuilles et de la répartition des fruits sur la production et la qualité des pêches , 1992 .

[67]  H. Sinoquet,et al.  Assessment of the three-dimensional architecture of walnut trees using digitising , 1997 .

[68]  M. Génard,et al.  Assessment of the water stress effects on peach fruit quality and size using a fruit tree model, QualiTree , 2013 .

[69]  Jim Hanan,et al.  Models of long-distance transport: how is carrier-dependent auxin transport regulated in the stem? , 2012, The New phytologist.

[70]  A. Granier,et al.  Modelling carbon and water cycles in a beech forest: Part I: Model description and uncertainty analysis on modelled NEE , 2005 .

[71]  B. Andrieu,et al.  Functional-structural plant modelling: a new versatile tool in crop science. , 2010, Journal of experimental botany.

[72]  Przemyslaw Prusinkiewicz,et al.  Control of bud activation by an auxin transport switch , 2009, Proceedings of the National Academy of Sciences.

[73]  T. Dejong,et al.  Source- and Sink-limited Growth Periods of Developing Peach Fruits Indicated by Relative Growth Rate Analysis , 1993 .

[74]  Michel Génard,et al.  QualiTree, a virtual fruit tree to study the management of fruit quality. I. Model development , 2011, Trees.

[75]  T. Sachs.  Pattern Formation in Plant Tissues , 1991 .

[76]  L. C. Grappadelli,et al.  Early Season Patterns of Carbohydrate Partitioning in Exposed and Shaded Apple Branches , 1994 .

[77]  Michel Génard,et al.  A virtual peach fruit model simulating changes in fruit quality during the final stage of fruit growth. , 2005, Tree physiology.

[78]  P. Prusinkiewicz,et al.  Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH model. , 2005, The New phytologist.

[79]  Françoise Lescourret,et al.  A simulation model of growth at the shoot-bearing fruit level: I. Description and parameterization for peach , 1998 .

[80]  J. Goudriaan,et al.  Modelling Potential Crop Growth Processes , 1994, Current Issues in Production Ecology.

[81]  Gerhard Buck-Sorlin,et al.  The role of branch architecture in assimilate production and partitioning: the example of apple (Malus domestica) , 2014, Front. Plant Sci..