J. L. Araus and J. E. Cairns, Field high-throughput phenotyping: the new crop breeding frontier, Trends in Plant Science, vol.19, issue.1, 2014.
DOI : 10.1016/j.tplants.2013.09.008

A. Audebert, T. Ghneim, S. Roques, P. Thaunay, and J. P. Fleuriot, Development of a high-throughput system for phenotyping rice roots traits, 3rd International Rice Congress Proceedings (Hanoi), 2010.

C. Azcón-aguilar, I. Padilla, C. Encina, and R. Arcon, Arbuscular mycorrhizal inoculation enhances plant growth and changes root system morphology, Agron Sustain. Dev, vol.16, pp.647-652, 1996.

M. Balduzzi, B. M. Binder, A. Bucksch, C. Chang, L. Hong et al., Reshaping Plant Biology: Qualitative and Quantitative Descriptors for Plant Morphology, Frontiers in Plant Science, vol.167, issue.e0127657, p.117, 2017.
DOI : 10.1104/pp.114.251751

URL : https://hal.archives-ouvertes.fr/hal-01455754

J. G. Benjamin, L. R. Ahuja, A. , and R. R. , Modelling corn rooting patterns and their effects on water uptake and nitrate leaching, Plant and Soil, vol.27, issue.2, pp.223-232, 1996.
DOI : 10.1007/BF00009332

F. Biscarini, P. Cozzi, L. Casella, P. Riccardi, A. Vattari et al., Genome-Wide Association Study for Traits Related to Plant and Grain Morphology, and Root Architecture in Temperate Rice Accessions, PLOS ONE, vol.7, issue.1, 2016.
DOI : 10.1371/journal.pone.0155425.s006

A. Blum, Effective use of water (EUW) and not water-use efficiency (WUE) is the target of crop yield improvement under drought stress, Field Crops Research, vol.112, issue.2-3, 2009.
DOI : 10.1016/j.fcr.2009.03.009

F. Boudon, C. Pradal, T. Cokelaer, P. Prusinkiewicz, and C. Godin, L-Py: An L-System Simulation Framework for Modeling Plant Architecture Development Based on a Dynamic Language, Frontiers in Plant Science, vol.3, 2012.
DOI : 10.3389/fpls.2012.00076

URL : https://hal.archives-ouvertes.fr/cirad-00703085

A. Bucksch, J. Burridge, L. York, and A. Das, Image-Based High-Throughput Field Phenotyping of Crop Roots, PLANT PHYSIOLOGY, vol.166, issue.2, pp.470-486, 2014.
DOI : 10.1104/pp.114.243519

A. Bucksch, A. Das, H. Schneider, N. Merchant, and J. S. Weitz, Overcoming the Law of the Hidden in Cyberinfrastructures, Trends in Plant Science, vol.22, issue.2, pp.117-123, 2017.
DOI : 10.1016/j.tplants.2016.11.014

A. Carminati, A. B. Moradi, D. Vetterlein, P. Vontobel, E. Lehmann et al., Dynamics of soil water content in the rhizosphere, Plant and Soil, vol.130, issue.3, pp.163-176, 2010.
DOI : 10.1104/pp.106.1.179

Y. L. Chen, V. M. Dunbabin, J. A. Postma, A. J. Diggle, J. A. Palta et al., Phenotypic variability and modelling of root structure of wild Lupinus angustifolius genotypes, Plant and Soil, vol.37, issue.5977, pp.345-364, 2011.
DOI : 10.1071/FP09197

J. Chopard, 3D modelling of water transfers in soil and roots systems, Proc. 4th Int. Workshop on Functional-Structural Plant, 2004.

J. L. Chopart and P. Siband, Development and validation of a model to describe root length density of maize from root counts on soil profiles, Plant and Soil, vol.214, issue.1/2, pp.61-74, 1999.
DOI : 10.1023/A:1004658918388

J. Christopher, M. Christopher, R. Jennings, S. Jones, S. Fletcher et al., QTL for root angle and number in a population developed from bread wheats (Triticum aestivum) with contrasting adaptation to water-limited environments, Theoretical and Applied Genetics, vol.26, issue.6, pp.1563-1574, 2013.
DOI : 10.1007/s11032-009-9381-9

V. Clausnitzer and J. W. Hopmans, Simultaneous modeling of transient three-dimensional root growth and soil water flow, Plant and Soil, vol.56, issue.2, pp.299-314, 1994.
DOI : 10.1626/jcs.60.312

S. Cohen-boulakia, K. Belhajjame, O. Collin, J. Chopard, C. Froidevaux et al., Scientific workflows for computational reproducibility in the life sciences: Status, challenges and opportunities, Future Generation Computer Systems, vol.75, pp.284-298, 2017.
DOI : 10.1016/j.future.2017.01.012

URL : https://hal.archives-ouvertes.fr/hal-01516082

M. Colin-belgrand, H. Joannes, E. Dreyer, and L. Pagès, A new data processing system for root growth and ramifi- cation analysis: description of methods, Annales des Sciences Foresti??res, vol.46, issue.Supplement, pp.305-309, 1989.
DOI : 10.1051/forest:19890570

URL : https://hal.archives-ouvertes.fr/hal-00882560

C. Collet, M. Löf, and L. Pagès, Root system development of oak seedlings analysed using an architectural model, Effects Compet. Grass Plant Soil, vol.279, pp.367-383, 2006.

L. H. Comas, S. R. Becker, V. M. Cruz, P. F. Byrne, and D. A. Dierig, Root traits contributing to plant productivity under drought, Frontiers in Plant Science, vol.4, 2013.
DOI : 10.3389/fpls.2013.00442

URL : http://journal.frontiersin.org/article/10.3389/fpls.2013.00442/pdf

B. Courtois, N. Ahmadi, F. Khowaja, A. H. Price, J. F. Rami et al., Rice Root Genetic Architecture: Meta-analysis from a Drought QTL Database, Rice, vol.107, issue.1, pp.115-128, 2009.
DOI : 10.1007/BF00222910

B. Courtois, L. Shen, W. Petalcorin, S. Carandang, R. Mauleon et al., Locating QTLs controlling constitutive root traits in the rice population IAC 165 × Co39 A simple threedimensional macroscopic root water uptake model based on the hydraulic architecture approach, Euphytica Hydrol Earth Syst. Sci, vol.1345194, issue.16, pp.335-345, 2003.

F. Danjon, D. Bert, C. Godin, and P. Trichet, Structural root architecture of 5-year-old Pinus pinaster measured by 3D digitising and analysed with AMAPmod, Plant Soil, vol.217, pp.49-63, 1999.
DOI : 10.1007/978-94-017-3469-1_6

F. Danjon, T. Fourcaud, and D. Bert, Root architecture and wind-firmness of mature Pinus pinaster, New Phytologist, vol.4, issue.2, pp.387-400, 2005.
DOI : 10.1201/9780203909423.ch10

URL : https://hal.archives-ouvertes.fr/hal-00016510

F. Danjon, R. , and B. , Assessing and analyzing 3D architecture of woody root systems, a review of methods and applications in tree and soil stability, resource acquisition and allocation, Plant and Soil, vol.284, issue.Suppl, pp.1-34, 2008.
DOI : 10.1626/jcs.64.50

J. Dardanelli, J. Ritchie, and M. Calmon, An empirical model for root water uptake. Field Crop Res, 2004.
DOI : 10.1016/j.fcr.2003.09.008

J. Deans, E. Ford, S. De-dorlodot, P. Bertin, P. Baret et al., Modelling root structure and stability Scaling up quantitative phenotyping of root system architecture using a combination of aeroponics and image analysis, Tree Root Syst. Mycorrhizas Aspects Appl. Biol, vol.71, issue.73, pp.189-195, 1983.

T. M. Dejong, D. Silva, D. Vos, J. Escobar-gutierrez, A. J. Van-isterdael et al., Using functional-structural plant models to study, understand and integrate plant development and ecophysiology The roots of a new green revolution, Ann. Bot. Trends Plant Sci, vol.108, issue.15, pp.987-989, 2010.

A. Diggle, Rootmap: a root growth model, Mathematics and Computers in Simulation, vol.30, issue.1-2, pp.175-180, 1988.
DOI : 10.1016/0378-4754(88)90121-8

A. J. Diggle, ROOTMAP???a model in three-dimensional coordinates of the growth and structure of fibrous root systems, Plant and Soil, vol.27, issue.2, pp.169-178, 1988.
DOI : 10.1071/BI9720669

C. Doussan, Modelling of the Hydraulic Architecture of Root Systems: An Integrated Approach to Water Absorption???Model Description, Annals of Botany, vol.81, issue.2, pp.213-223, 1997.
DOI : 10.1006/anbo.1997.0540

C. Doussan, L. Pagès, and A. Pierret, Soil exploration and resource acquisition by plant roots: an architectural and modelling point of view, Agronomie, vol.23, pp.5-6, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00886193

C. Doussan, A. Pierret, E. Garrigues, L. C. Pagès, G. Vercambre et al., Modelling of the Hydraulic Architecture of Root Systems: An Integrated Approach to Water Absorption???Distribution of Axial and Radial Conductances in Maize, Annals of Botany, vol.81, issue.2, pp.225-2320541, 1997.
DOI : 10.1006/anbo.1997.0541

X. Draye, Y. Kim, G. Lobet, and M. Javaux, Model-assisted integration of physiological and environmental constraints affecting the dynamic and spatial patterns of root water uptake from soils, Journal of Experimental Botany, vol.61, issue.8, pp.2145-2155, 2010.
DOI : 10.1093/jxb/erq077

X. Draye and L. Pagès, CrossTalk: A Simulation Platform for the Linking of Existing Soil, Plant and Atmosphere Models, 2006 Second International Symposium on Plant Growth Modeling and Applications, 2006.
DOI : 10.1109/PMA.2006.49

V. Dunbabin, A. Diggle, Z. Rengel, and R. Van-hugten, Modelling the interactions between water and nutrient uptake and root growth, Plant and Soil, vol.239, issue.1, pp.19-38, 2002.
DOI : 10.1023/A:1014939512104

V. Dunbabin, J. Postma, and A. Schnepf, Modelling root???soil interactions using three???dimensional models of root growth, architecture and function, Plant and Soil, vol.192, issue.3, pp.93-124, 2013.
DOI : 10.1111/j.1469-8137.2011.03840.x

L. Dupuy, P. J. Gregory, A. G. Bengough, and J. Hoffmann, Root growth models: towards a new generation of continuous approaches, Journal of Experimental Botany, vol.61, issue.8, pp.2131-21433, 2010.
DOI : 10.1093/jxb/erp389

C. Ehlert, C. Maurel, F. Tardieu, and T. Simonneau, Aquaporin-Mediated Reduction in Maize Root Hydraulic Conductivity Impacts Cell Turgor and Leaf Elongation Even without Changing Transpiration, PLANT PHYSIOLOGY, vol.150, issue.2, pp.1093-1104, 2009.
DOI : 10.1104/pp.108.131458

URL : https://hal.archives-ouvertes.fr/hal-00408979

R. Feddes, Field test of a modified numerical model for water uptake by root systems, Water Resources Research, vol.34, issue.2, pp.1199-1206, 1974.
DOI : 10.2136/sssaj1970.03615995003400030013x

C. Fournier, C. Pradal, and G. Louarn, Building modular FSPM under OpenAlea: Concepts and applications, 6th workshop on Functional- Structural Plant Models, pp.109-112, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01192232

R. Furbank and M. Tester, Phenomics ??? technologies to relieve the phenotyping bottleneck, Trends in Plant Science, vol.16, issue.12, pp.635-644, 2011.
DOI : 10.1016/j.tplants.2011.09.005

W. Gardner, DYNAMIC ASPECTS OF WATER AVAILABILITY TO PLANTS, Soil Science, vol.89, issue.2, pp.63-73, 1960.
DOI : 10.1097/00010694-196002000-00001

G. Garin, C. Fournier, B. Andrieu, V. Houlès, C. Robert et al., A modelling framework to simulate foliar fungal epidemics using functional???structural plant models, Annals of Botany, vol.114, issue.4, pp.795-812, 2012.
DOI : 10.1093/aob/mcu101

URL : https://hal.archives-ouvertes.fr/hal-01025689

E. Garrigues, C. Doussan, and A. Pierret, Water Uptake by Plant Roots: I ??? Formation and Propagation of a Water Extraction Front in Mature Root Systems as Evidenced by 2D Light Transmission Imaging, Plant and Soil, vol.123, issue.1-2, pp.83-98, 2006.
DOI : 10.1007/978-1-4612-2894-3_1

URL : https://hal.archives-ouvertes.fr/hal-00009562

Z. Ge, G. Rubio, and J. Lynch, The importance of root gravitropism for inter-root competition and phosphorus acquisition efficiency: results from a geometric simulation model, Plant Soil, vol.218, pp.159-171, 2000.

S. Giuliani, M. C. Sanguineti, R. Tuberosa, M. Bellotti, S. Salvi et al., Root-ABA1, a major constitutive QTL, affects maize root architecture and leaf ABA concentration at different water regimes, Journal of Experimental Botany, vol.56, issue.422, pp.3061-3070, 2005.
DOI : 10.1093/jxb/eri303

C. Godin, Representing and encoding plant architecture: A review, Annals of Forest Science, vol.57, issue.5, pp.413-438, 2000.
DOI : 10.1051/forest:2000132

URL : https://hal.archives-ouvertes.fr/hal-00827475

C. Godin, C. , and Y. , A Multiscale Model of Plant Topological Structures, Journal of Theoretical Biology, vol.191, issue.1, pp.1-46, 1997.
DOI : 10.1006/jtbi.1997.0561

URL : https://hal.archives-ouvertes.fr/hal-00827484

C. Godin, E. Costes, C. , and Y. , Exploring plant topological structure with the AMAPmod software: an outline., Silva Fennica, vol.31, issue.3, pp.357-368, 1997.
DOI : 10.14214/sf.a8533

URL : http://doi.org/10.14214/sf.a8533

C. Godin, E. Costes, and H. Sinoquet, A Method for Describing Plant Architecture which Integrates Topology and Geometry, Annals of Botany, vol.84, issue.3, pp.343-357, 1999.
DOI : 10.1006/anbo.1999.0923

URL : https://hal.archives-ouvertes.fr/hal-00827477

C. Godin, E. Costes, and H. Sinoquet, Plant Architecture Modelling - Virtual Plants, Dynamic and Complex Systems, Turnbull, C. Plant architecture and its manipulation, 2005.
DOI : 10.1002/9781119312994.apr0171

URL : https://hal.archives-ouvertes.fr/hal-00019850

C. Godin, H. Sinoquet, C. Granier, and D. Vile, Functional-structural plant modelling Phenotyping and beyond: modelling the relationships between traits, New Phytol. Curr. Opin. Plant Biol, vol.166, issue.18, pp.705-708, 2005.

P. J. Gregory, Roots, rhizosphere and soil: the route to a better understanding of soil science?, European Journal of Soil Science, vol.3, issue.1, 2006.
DOI : 10.1023/A:1011972019617

S. Griffon and F. De-coligny, AMAPstudio: An editing and simulation software suite for plants architecture modelling, Ecological Modelling, vol.290, 2014.
DOI : 10.1016/j.ecolmodel.2013.10.037

URL : https://hal.archives-ouvertes.fr/hal-01268810

Y. Guédon, D. Barthélémy, Y. Caraglio, C. , and E. , Pattern Analysis in Branching and Axillary Flowering Sequences, Journal of Theoretical Biology, vol.212, issue.4, pp.481-520, 2001.
DOI : 10.1006/jtbi.2001.2392

G. L. Hammer, Z. S. Dong, G. Mclean, A. Doherty, C. Messina et al., Can Changes in Canopy and/or Root System Architecture Explain Historical Maize Yield Trends in the U.S. Corn Belt?, Crop Science, vol.49, issue.1, pp.299-312, 2009.
DOI : 10.2135/cropsci2008.03.0152

L. Han, E. Costes, F. Boudon, T. Cokelaer, C. Pradal et al., Investigating the influence of geometrical traits on light interception efficiency of apple trees: A modelling study with MAppleT, 2012 IEEE 4th International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications, pp.152-159, 2012.
DOI : 10.1109/PMA.2012.6524827

URL : https://hal.archives-ouvertes.fr/hal-00790650

M. Homaee, R. A. Feddes, and C. Dirksen, A Macroscopic Water Extraction Model for Nonuniform Transient Salinity and Water Stress, Soil Science Society of America Journal, vol.66, issue.6, 2002.
DOI : 10.2136/sssaj2002.1764

B. Hufnagel, S. M. De-sousa, L. Assis, C. T. Guimaraes, W. Leiser et al., Duplicate and Conquer: Multiple Homologs of PHOSPHORUS-STARVATION TOLERANCE1 Enhance Phosphorus Acquisition and Sorghum Performance on Low-Phosphorus Soils, PLANT PHYSIOLOGY, vol.166, issue.2, pp.659-677, 2014.
DOI : 10.1104/pp.114.243949

D. Hüsken, E. Steudle, and U. Zimmermann, Pressure Probe Technique for Measuring Water Relations of Cells in Higher Plants, PLANT PHYSIOLOGY, vol.61, issue.2, pp.158-163, 1978.
DOI : 10.1104/pp.61.2.158

C. Iversen, M. Murphy, A. , and M. , Advancing the use of minirhizotrons in wetlands, Plant and Soil, vol.160, issue.1-2, 2012.
DOI : 10.1046/j.1469-8137.2003.00903.x

H. Iwata, M. F. Minamikawa, H. Kajiya-kanegae, M. Ishimori, and T. Hayashi, Genomics-assisted breeding in fruit trees, Breeding Science, vol.66, issue.1, pp.100-115, 2016.
DOI : 10.1270/jsbbs.66.100

M. Javaux, T. Schröder, J. Vanderborght, and H. Vereecken, Use of a three-dimensional detailed modeling approach for predicting root water uptake. Vadose Zo, J, vol.7, pp.1079-1088, 2008.

R. Karwowski and P. Prusinkiewicz, Design and Implementation of the L+C Modeling Language, Electronic Notes in Theoretical Computer Science, vol.86, issue.2, pp.134-152, 2003.
DOI : 10.1016/S1571-0661(04)80680-7

J. Kashiwagi, L. Krishnamurthy, H. D. Upadhyaya, H. Krishna, S. Chandra et al., Genetic variability of drought-avoidance root traits in the mini-core germplasm collection of chickpea (Cicer arietinum L.)., Euphytica, vol.102, issue.3, pp.213-222, 2005.
DOI : 10.1007/978-94-017-2356-5_21

D. B. Kell, Breeding crop plants with deep roots: their role in sustainable carbon, nutrient and water sequestration, Annals of Botany, vol.108, issue.3, pp.407-418, 2011.
DOI : 10.1093/aob/mcr175

J. Kholová, C. T. Hash, P. L. Kumar, R. S. Yadav, Á. Koov et al., Terminal drought-tolerant pearl millet [Pennisetum glaucum (L.) R. Br.] have high leaf ABA and limit transpiration at high vapour pressure deficit Modelling the effect of plant water use traits on yield and stay-green expression in sorghum, J. Exp. Bot. Funct. Plant Biol, vol.61, issue.41, pp.1431-1440, 1071.

H. Khuder, A. Stokes, F. Danjon, K. Gouskou, and F. Lagane, Is it possible to manipulate root anchorage in young trees?, Plant and Soil, vol.34, issue.1-2, pp.87-102, 2007.
DOI : 10.1007/s00468-004-0396-x

URL : https://hal.archives-ouvertes.fr/hal-00174690

O. Kniemeyer and W. Kurth, The modelling platform GroIMP and the programming language XL, " in Applications of Graph Transformations with Industrial Relevance, AGTIVE LNCS, pp.570-572, 2007.

J. Knox, T. Hess, A. Daccache, W. , and T. , Climate change impacts on crop productivity in Africa and South Asia, Environmental Research Letters, vol.7, issue.3, pp.34032-34042, 2012.
DOI : 10.1088/1748-9326/7/3/034032

URL : http://iopscience.iop.org/article/10.1088/1748-9326/7/3/034032/pdf

N. Koebernick, U. Weller, K. Huber, S. Schlüter, H. J. Vogel et al., In Situ visualization and quantification of Three-dimensional root system architecture and growth using x-ray computed tomography. Vadose Zo, 2014.

R. C. Kuijken, F. A. Eeuwijk, . Van, L. F. Marcelis, H. J. Bouwmeester et al., Root phenotyping: from component trait in the lab to breeding: Table 1., Journal of Experimental Botany, vol.66, issue.18, pp.5389-5401, 2013.
DOI : 10.1093/jxb/erv239

R. Lee, The Outlook for Population Growth, Science, vol.42, issue.3, pp.569-573, 2011.
DOI : 10.1353/dem.2005.0021

D. Leitner, B. Felderer, P. Vontobel, and A. Schnepf, Recovering Root System Traits Using Image Analysis Exemplified by Two-Dimensional Neutron Radiography Images of Lupine, PLANT PHYSIOLOGY, vol.164, issue.1, pp.24-35, 2014.
DOI : 10.1104/pp.113.227892

D. Leitner, S. Klepsch, G. Bodner, and A. Schnepf, A dynamic root system growth model based on L-Systems, Plant and Soil, vol.58, issue.9, pp.177-192, 2010.
DOI : 10.2136/sssaj2003.3870

URL : https://link.springer.com/content/pdf/10.1007%2Fs11104-010-0284-7.pdf

D. Leitner, S. Klepsch, ß. Knie, A. Schnepf, and A. , The algorithmic beauty of plant roots ??? an L-System model for dynamic root growth simulation, Mathematical and Computer Modelling of Dynamical Systems, vol.83, issue.6, pp.575-587, 2010.
DOI : 10.2136/vzj2007.0115

D. Leitner, F. Meunier, G. Bodner, M. Javaux, and A. Schnepf, Impact of contrasted maize root traits at flowering on water stress tolerance ??? A simulation study, Field Crops Research, vol.165, pp.125-137, 2014.
DOI : 10.1016/j.fcr.2014.05.009

L. Marié and C. , Rhizoslides: paper-based growth system for non-destructive, high throughput phenotyping of root development by means of image analysis, Plant Methods, vol.10, issue.1, pp.13-23, 2014.
DOI : 10.1186/1746-4811-10-13

A. Lindenmayer, Mathematical models for cellular interactions in development II. Simple and branching filaments with two-sided inputs, Journal of Theoretical Biology, vol.18, issue.3, pp.300-315, 1968.
DOI : 10.1016/0022-5193(68)90080-5

D. B. Lobell, M. B. Burke, C. Tebaldi, M. D. Mastrandrea, W. P. Falcon et al., Prioritizing Climate Change Adaptation Needs for Food Security in 2030, Science, vol.45, issue.5863, pp.607-610, 2008.
DOI : 10.1023/A:1005669807945

D. B. Lobell and S. M. Gourdji, The Influence of Climate Change on Global Crop Productivity, PLANT PHYSIOLOGY, vol.160, issue.4, pp.1686-1697, 2012.
DOI : 10.1104/pp.112.208298

G. Lobet, X. Draye, and C. Périlleux, An online database for plant image analysis software tools, Plant Methods, vol.9, issue.1, pp.38-48, 2013.
DOI : 10.1104/pp.113.221531

G. Lobet, M. P. Pound, J. Diener, C. Pradal, X. Draye et al., Root System Markup Language: Toward a Unified Root Architecture Description Language, Plant Physiology, vol.167, issue.3, pp.617-627, 2015.
DOI : 10.1104/pp.114.253625

URL : https://hal.archives-ouvertes.fr/hal-01113767

M. Lucas, Y. Guédon, C. Jay-allemand, C. Godin, and L. Laplaze, An Auxin Transport-Based Model of Root Branching in Arabidopsis thaliana, PLoS ONE, vol.52, issue.11, 2008.
DOI : 10.1371/journal.pone.0003673.s004

URL : https://hal.archives-ouvertes.fr/hal-00831804

J. P. Lynch, Root Architecture and Plant Productivity, Plant Physiology, vol.109, issue.1, 1995.
DOI : 10.1104/pp.109.1.7

URL : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC157559/pdf

J. P. Lynch and J. P. Lynch, TURNER REVIEW No. 14. Roots of the Second Green Revolution, Australian Journal of Botany, vol.55, issue.5, pp.493-512, 2007.
DOI : 10.1071/BT06118

J. P. Lynch, Root phenes that reduce the metabolic costs of soil exploration: opportunities for 21st century agriculture, Plant, Cell & Environment, vol.14, issue.9, pp.1775-1784, 2015.
DOI : 10.1016/j.pbi.2011.03.020

J. P. Lynch, J. G. Chimungu, and K. M. Brown, Root anatomical phenes associated with water acquisition from drying soil: targets for crop improvement, Journal of Experimental Botany, vol.65, issue.21, pp.6155-6166, 1997.
DOI : 10.1093/jxb/eru162

Z. Ma, T. Walk, A. Marcus, and J. Lynch, Morphological synergism in root hair length, density, initiation and geometry for phosphorus acquisition in Arabidopsis thaliana: a modeling approach, Plant and Soil, vol.236, issue.2, pp.221-235, 2001.
DOI : 10.1023/A:1012728819326

E. S. Mace, V. Singh, E. J. Van-oosterom, G. L. Hammer, C. H. Hunt et al., QTL for nodal root angle in sorghum (Sorghum bicolor L. Moench) co-locate with QTL for traits associated with drought adaptation, Theoretical and Applied Genetics, vol.23, issue.1, pp.97-109, 2012.
DOI : 10.1093/bioinformatics/btm143

K. Macmillan, K. Emrich, H. P. Piepho, C. E. Mullins, and A. H. Price, Assessing the importance of genotype??????environment interaction for root traits in rice using a mapping population II: conventional QTL analysis, Theoretical and Applied Genetics, vol.107, issue.5, pp.953-964, 2006.
DOI : 10.2135/cropsci2002.0255

J. Maeght, B. Rewald, and A. Pierret, How to study deep roots???and why it matters, Frontiers in Plant Science, vol.4, 2013.
DOI : 10.3389/fpls.2013.00299

URL : http://journal.frontiersin.org/article/10.3389/fpls.2013.00299/pdf

S. Mairhofer and S. Zappala, Recovering complete plant root system architectures from soil via X-ray ??-Computed Tomography, Plant Methods, vol.9, issue.1, pp.1746-4811, 2013.
DOI : 10.1007/BF01275497

URL : https://plantmethods.biomedcentral.com/track/pdf/10.1186/1746-4811-9-8?site=plantmethods.biomedcentral.com

S. Mairhofer, S. Zappala, T. , and S. , RooTrak: Automated Recovery of Three-Dimensional Plant Root Architecture in Soil from X-Ray Microcomputed Tomography Images Using Visual Tracking, PLANT PHYSIOLOGY, vol.158, issue.2, pp.561-569, 2012.
DOI : 10.1104/pp.111.186221

Y. Mano and F. Omori, High-density linkage map around the root aerenchyma locus Qaer1.06 in the backcross populations of maize Mi29 ?? teosinte ???Zea nicaraguensis???, Breeding Science, vol.59, issue.4, pp.427-433, 2009.
DOI : 10.1270/jsbbs.59.427

URL : https://www.jstage.jst.go.jp/article/jsbbs/59/4/59_4_427/_pdf

A. M. Manschadi, J. T. Christopher, P. Peter-devoil, and G. L. Hammer, The role of root architectural traits in adaptation of wheat to water-limited environments, Functional Plant Biology, vol.33, issue.9, pp.823-837, 1071.
DOI : 10.1071/FP06055

L. Mathieu and G. Lobet, ???Rhizoponics???: a novel hydroponic rhizotron for root system analyses on mature Arabidopsis thaliana plants, Plant Methods, vol.11, issue.1, 2015.
DOI : 10.1104/pp.111.179895

R. Metzner, A. Eggert, D. Van-dusschoten, D. Pflugfelder, S. Gerth et al., Direct comparison of MRI and X-ray CT technologies for 3D imaging of root systems in soil: potential and challenges for root trait quantification, Plant Methods, vol.11, issue.1, p.17, 2015.
DOI : 10.1007/BF01386390

F. Meunier, V. Couvreur, X. Draye, J. Vanderborght, and M. Javaux, Towards quantitative root hydraulic phenotyping: novel mathematical functions to calculate plant-scale hydraulic parameters from root system functional and structural traits, Journal of Mathematical Biology, vol.21, issue.4, pp.1133-1170, 2017.
DOI : 10.1007/s00344-003-0008-9

URL : http://doi.org/10.1007/s00285-017-1111-z

F. Molz, Models of water transport in the soil-plant system: A review, Water Resources Research, vol.6, issue.1, pp.1245-1260, 1981.
DOI : 10.1016/S0065-2296(08)60329-8

S. J. Mooney, T. P. Pridmore, J. Helliwell, and M. J. Bennett, Developing X-ray Computed Tomography to non-invasively image 3-D root systems architecture in soil, Plant and Soil, vol.61, issue.1-2, pp.1-22, 2011.
DOI : 10.1016/S0167-1987(01)00188-X

A. B. Moradi, A. Carminati, D. Vetterlein, P. Vontobel, E. Lehmann et al., Three-dimensional visualization and quantification of water content in the rhizosphere, New Phytologist, vol.130, issue.3, pp.653-663, 2011.
DOI : 10.1111/j.1469-8137.1995.tb01823.x

H. S. Neufeld, D. M. Durall, P. M. Rich, and D. T. Tingey, A rootbox for quantitative observations on intact entire root systems, Plant and Soil, vol.72, issue.2, pp.295-298, 1989.
DOI : 10.1093/treephys/3.4.393

K. Nielsen, J. Lynch, Y. Ong, K. Streit, M. Henke et al., Carbon cost of root systems: an architectural approach, Plant and Soil, vol.151, issue.6, pp.161-169, 1994.
DOI : 10.1016/B978-0-12-546805-3.50015-1

B. Orman-ligeza, R. Civava, S. De-dorlodot, and X. Draye, Root Engineering (A Morte and A Varma, 2014.

H. Ozier-lafontaine, F. Lecompte, and J. F. Sillon, Fractal analysis of the root architecture of Gliricidia sepium for the spatial prediction of root branching, size and mass: model development and evaluation in agroforestry, Plant and Soil, vol.209, issue.2, pp.167-179, 1999.
DOI : 10.1023/A:1004461130561

A. Paez-garcia, C. Motes, W. Scheible, R. Chen, E. Blancaflor et al., Root Traits and Phenotyping Strategies for Plant Improvement, Plants, vol.109, issue.2, pp.334-355, 2015.
DOI : 10.1007/s11104-012-1483-1

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4844329

E. Page and A. L. Gerwitz, Mathematical models, based on diffusion equations, to describe root systems of isolated plants, row crops, and swards, Plant and Soil, vol.217, issue.2, pp.243-254, 1974.
DOI : 10.1007/BF00017252

L. Pagès, M. O. Jordan, D. Picard, L. Pagès, G. Vercambre et al., A simulation model of the three-dimensional architecture of the maize root system, Plant and Soil, vol.39, issue.1, pp.147-154, 1989.
DOI : 10.1111/j.1469-8137.1987.tb04683.x

J. Palta, X. Chen, and S. Milroy, Large root systems: are they useful in adapting wheat to dry environments?, Functional Plant Biology, vol.38, issue.5, pp.347-354, 2011.
DOI : 10.1071/FP11031

B. Péret, G. Li, J. Zhao, L. R. Band, U. Voß et al., Auxin regulates aquaporin function to facilitate lateral root emergence, Nature Cell Biology, vol.144, issue.10, pp.991-998, 1038.
DOI : 10.1104/pp.107.101337

B. Péret, A. M. Middleton, A. P. French, A. Larrieu, A. Bishopp et al., Sequential induction of auxin efflux and influx carriers regulates lateral root emergence, Molecular Systems Biology, vol.20, issue.1, 2013.
DOI : 10.1105/tpc.108.061143

J. S. Perret, M. E. Belushi, and M. Deadman, Non-destructive visualization and quantification of roots using computed tomography, Soil Biology and Biochemistry, vol.39, issue.2, 2007.
DOI : 10.1016/j.soilbio.2006.07.018

A. Pierret, C. Doussan, Y. Capowiez, F. Bastardie, and L. Pagès, Root Functional Architecture: A Framework for Modeling the Interplay between Roots and Soil, Vadose Zone Journal, vol.6, issue.2, 2007.
DOI : 10.2136/vzj2006.0067

URL : https://hal.archives-ouvertes.fr/ird-00190010

A. Pohlmeier, A. Oros-peusquens, M. Javaux, M. I. Menzel, J. Vanderborght et al., Changes in soil water content resulting from root uptake monitored by magnetic resonance imaging. Vadose Zo, 2008.

J. Postma, J. Lynch, J. Postma, and J. Lynch, Theoretical evidence for the functional benefit of root cortical aerenchyma in soils with low phosphorus availability Root cortical aerenchyma enhances the growth of maize on soils with suboptimal availability of nitrogen, phosphorus, and potassium, Ann. Bot. Plant Physiol, vol.107, issue.56, pp.829-841, 2010.

C. Pradal, S. Artzet, J. Chopard, D. Dupuis, C. Fournier et al., InfraPhenoGrid: A scientific workflow infrastructure for plant phenomics on the Grid, Future Generation Computer Systems, vol.67, pp.341-353, 2017.
DOI : 10.1016/j.future.2016.06.002

URL : https://hal.archives-ouvertes.fr/hal-01336655

C. Pradal, S. Dufour-kowalski, F. Boudon, C. Fournier, and C. Godin, OpenAlea, Proceedings of the 27th International Conference on Scientific and Statistical Database Management, SSDBM '15, pp.751-760, 1071.
DOI : 10.1007/978-3-642-13818-8_33

URL : https://hal.archives-ouvertes.fr/hal-00831801

C. Pradal, C. Fournier, P. Valduriez, and S. Cohen-boulakia, OpenAlea, Proceedings of the 27th International Conference on Scientific and Statistical Database Management, SSDBM '15, 2015.
DOI : 10.1007/978-3-642-13818-8_33

URL : https://hal.archives-ouvertes.fr/hal-00831801

A. H. Price, K. A. Steele, B. J. Moore, and R. G. Jones, Upland rice grown in soil-filled chambers and exposed to contrasting water-deficit regimes, Field Crops Research, vol.76, issue.1, pp.25-43, 2002.
DOI : 10.1016/S0378-4290(02)00010-2

P. Prusinkiewicz, Modeling plant growth and development, Current Opinion in Plant Biology, vol.7, issue.1, pp.79-83, 2004.
DOI : 10.1016/j.pbi.2003.11.007

P. Prusinkiewicz and R. Karwowski, L-Studio/cpfg: A Software System for Modeling Plants, 1999.
DOI : 10.1007/3-540-45104-8_38

P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, 1990.
DOI : 10.1007/978-1-4613-8476-2

R. Rellán-Álvarez, G. Lobet, H. Lindner, P. L. Pradier, J. Sebastian et al., GLO-Roots: an imaging platform enabling multidimensional characterization of soil-grown root systems, 2015.

C. Richard and L. Hickey, High-throughput phenotyping of seminal root traits in wheat, Plant Methods, vol.11, issue.1, 2015.
DOI : 10.1093/biomet/58.3.545

R. A. Richards and J. B. Passioura, A breeding program to reduce the diameter of the major xylem vessel in the seminal roots of wheat and its effect on grain yield in rain-fed environments, Australian Journal of Agricultural Research, vol.40, issue.5, pp.943-950, 1071.
DOI : 10.1071/AR9890943

T. Roose and A. C. Fowler, A model for water uptake by plant roots, Journal of Theoretical Biology, vol.228, issue.2, 2004.
DOI : 10.1016/j.jtbi.2003.12.012

T. Roose and A. C. Fowler, A mathematical model for water and nutrient uptake by plant root systems, Journal of Theoretical Biology, vol.228, issue.2, 2004.
DOI : 10.1016/j.jtbi.2003.12.013

T. Roose, S. D. Keyes, K. R. Daly, A. Carminati, W. Otten et al., Challenges in imaging and predictive modeling of rhizosphere processes, Plant and Soil, vol.192, issue.1-2, pp.9-10, 2016.
DOI : 10.1111/j.1469-8137.2011.03840.x

R. Sayar, H. Khemira, and M. Kharrat, Inheritance of deeper root length and grain yield in half-diallel durum wheat (Triticum durum) crosses, Annals of Applied Biology, vol.3, issue.2, 2007.
DOI : 10.2134/agronj1942.00021962003400100008x

. Appl, J. Schmidhuber, and F. N. Tubiello, Global food security under climate change, Proc. Natl. Acad. Sci. U.S.A, vol.151, issue.104, 2007.

A. Schnepf, D. Leitner, S. A. Klepsch, D. Leitner, and S. Klepsch, Modelling Phosphorus Dynamics in the Soil???Plant System, Soil Biol, vol.26, pp.113-133, 2011.
DOI : 10.1007/978-3-642-15271-9_5

S. Sharma, S. Xu, B. Ehdaie, A. Hoops, T. J. Close et al., Dissection of QTL effects for root traits using a chromosome arm-specific mapping population in bread wheat, Theoretical and Applied Genetics, vol.43, issue.4, pp.759-769, 2011.
DOI : 10.1139/gen-43-1-53

V. Singh, E. J. Van-oosterom, D. R. Jordan, and G. L. Hammer, Genetic control of nodal root angle in sorghum and its implications on water extraction Europ, J. Agronomy, vol.42, 2012.

V. Singh, E. J. Van-oosterom, D. R. Jordan, C. D. Messina, M. Cooper et al., Morphological and architectural development of root systems in sorghum and maize, Plant and Soil, vol.56, issue.1-2, pp.287-299, 2010.
DOI : 10.1111/j.1438-8677.1995.tb00852.x

F. Somma, V. Clausnitzer, and J. Hopmans, Transient three-dimensional modeling of soil water and solute transport with simultaneous root growth, root water and nutrient uptake, Plant and Soil, vol.202, issue.2, pp.281-291, 1998.
DOI : 10.1023/A:1004378602378

J. S. Sperry, Hydraulics of vascular water transport What plant hydraulics can tell us about plant responses to climate-change droughts, Signalling and Communication in Plants: Mechanical Integration of Plant Cells and Plants, ed P. Wojtaszek, pp.303-327, 2011.

J. S. Sperry, V. Stiller, and U. G. Hacke, Soil water uptake and water transport through root systems, Plant Roots: The Hidden Half, pp.663-681, 2002.

J. S. Sperry, Y. Wang, B. T. Wolfe, D. S. Mackay, W. R. Anderegg et al., Pragmatic hydraulic theory predicts stomatal responses to climatic water deficits, New Phytologist, vol.19, issue.3, pp.577-589, 2016.
DOI : 10.1111/nph.14087

J. Spindel, H. Begum, D. Akdemir, P. Virk, B. Collard et al., Genomic selection and association mapping in rice (Oryza sativa): effect of trait genetic architecture, training population composition, marker number and statistical model on accuracy of rice genomic selection in elite, tropical rice breeding lines, PLoS Genet, 2015.

E. Steudle, Pressure probe techniques: basic principles and application to studies of water and solute relations at the cell, tissue, and organ level, Water Deficits: Plant Responses from Cell to Community, pp.5-36, 1993.

E. Steudle, Water uptake by plant roots: an integration of views, Plant Soil, vol.226, p.1026439226716, 2000.
DOI : 10.1007/978-94-017-2858-4_9

L. Stingaciu, H. Schulz, A. Pohlmeier, S. Behnke, H. Zilken et al., In situ root system architecture extraction from magnetic resonance imaging for water uptake modeling. Vadose Zo, 2013.

D. L. Strayer, M. E. Power, W. F. Fagan, S. T. Pickett, and J. Belnap, A Classification of Ecological Boundaries, BioScience, vol.53, issue.8, pp.10-1641, 2003.
DOI : 10.1641/0006-3568(2003)053[0723:ACOEB]2.0.CO;2

B. Sultan, P. Roudier, P. Quirion, A. Alhassane, B. Muller et al., Assessing climate change impacts on sorghum and millet yields in the Sudanian and Sahelian savannas of West Africa, Environmental Research Letters, vol.8, issue.1, pp.14040-14050, 2013.
DOI : 10.1088/1748-9326/8/1/014040

URL : https://hal.archives-ouvertes.fr/hal-00857331

F. Tardieu, S. Trachsel, S. Kaeppler, K. Brown, and J. Lynch, Any trait or trait-related allele can confer drought tolerance: just design the right drought scenario, Journal of Experimental Botany, vol.63, issue.1, pp.25-31, 2011.
DOI : 10.1093/jxb/err269

URL : https://academic.oup.com/jxb/article-pdf/63/1/25/1479743/err269.pdf

S. Tron, G. Bodner, F. Laio, L. Ridolfi, and D. Leitner, Can diversity in root architecture explain plant water use efficiency? A modeling study, Ecological Modelling, vol.312, pp.200-210, 2015.
DOI : 10.1016/j.ecolmodel.2015.05.028

R. Tuberosa, S. Salvi, M. C. Sanguineti, P. Landi, M. Maccaferri et al., Mapping QTLS regulating morpho-physiological traits and yield: case studies, shortcomings and perspectives in drought-stressed maize Identification of QTLs for root characteristics in maize grown in hydroponics and analysis of their overlap with QTLs for grain yield in the field at two water regimes, Ann. Bot. Plant Mol. Biol, vol.89, issue.48, pp.941-963, 1023.

Y. Uga, K. Okuno, and M. Yano, QTLs underlying natural variation in stele and xylem structures of rice root, Breeding Science, vol.58, issue.1, pp.7-14, 2008.
DOI : 10.1270/jsbbs.58.7

V. Vadez, Root hydraulics: The forgotten side of roots in drought adaptation, Field Crops Research, vol.165, pp.15-24, 2014.
DOI : 10.1016/j.fcr.2014.03.017

V. Vadez, J. Kholova, S. Medina, K. Aparna, H. V. Anderberg et al., Transpiration efficiency: new insights into an old story, Journal of Experimental Botany, vol.65, issue.21, pp.6141-6153, 2013.
DOI : 10.1093/jxb/eru040

V. Vadez, L. Krishnamurthy, C. T. Hash, H. D. Upadhyaya, and A. K. Borrell, Yield, transpiration efficiency, and water use variations and their relationships in the sorghum reference collection, Crop Pasture Sci, vol.62, pp.1-11, 1071.

V. Vadez, A. Soltani, L. Krishnamurthy, T. R. Sinclair, T. H. Honert et al., Modelling possible benefit of root related traits to enhance terminal drought adaption of chickpea. Field Crops Res Water transport in plants as a catenary process Functional branch analysis as tool for fractal scaling above-and belowground trees for their additive and nonadditive properties, Discuss. Faraday Soc. Ecol. Modell, vol.137, issue.14901, pp.108-115, 1016.

R. K. Varshney, M. Thudi, S. N. Nayak, P. M. Gaur, J. Kashiwagi et al., Genetic dissection of drought tolerance in chickpea (Cicer??arietinum L.), Theoretical and Applied Genetics, vol.38, issue.11, pp.445-462, 2014.
DOI : 10.1071/FP10244

J. Vos, J. B. Evers, G. H. Buck-sorlin, B. Andrieu, M. Chelle et al., Functional-structural plant modelling: a new versatile tool in crop science Functional-Structural plant modelling in crop production: adding a dimension, J. Exp. Bot. Frontis, vol.61, issue.22, pp.1-12, 2007.

T. Walk, R. Jaramillo, and J. Lynch, Architectural Tradeoffs between Adventitious and Basal Roots for Phosphorus Acquisition, Plant and Soil, vol.31, issue.1-2, pp.347-357, 2006.
DOI : 10.1007/s11104-005-0389-6

A. P. Wasson, R. A. Richards, R. Chatrath, S. C. Misra, S. V. Prasad et al., Traits and selection strategies to improve root systems and water uptake in water-limited wheat crops, Journal of Experimental Botany, vol.63, issue.9, pp.3485-3498, 2012.
DOI : 10.1093/jxb/ers111

L. Xu, M. Henke, J. Zhu, W. Krth, G. M. Buck-sorlin et al., A functional???structural model of rice linking quantitative genetic information with morphological development and physiological processes, Annals of Botany, vol.107, issue.5, pp.817-828, 2011.
DOI : 10.1093/aob/mcq264

URL : https://hal.archives-ouvertes.fr/hal-01132289

M. Zarebanadkouki, Y. X. Kim, and A. Carminati, Where do roots take up water? Neutron radiography of water flow into the roots of transpiring plants growing in soil, New Phytologist, vol.21, issue.4, pp.1034-1044, 2013.
DOI : 10.1007/s00344-003-0008-9

A. Zhan, H. Schneider, and J. P. Lynch, Reduced Lateral Root Branching Density Improves Drought Tolerance in Maize, Plant Physiology, vol.168, issue.4, pp.1603-1885, 2015.
DOI : 10.1104/pp.15.00187

H. G. Zheng, R. C. Babu, M. S. Pathan, L. Ali, N. Huang et al., Quantitative trait loci for root-penetration ability and root thickness in rice: Comparison of genetic backgrounds, Genome, vol.43, issue.1, pp.53-61, 2000.
DOI : 10.1139/g99-065

M. H. Zimmermann, Hydraulic architecture of some diffuse-porous trees, Canadian Journal of Botany, vol.56, issue.18, pp.2286-2295, 1978.
DOI : 10.1139/b78-274