B. Acock and P. Yaa, Convective-diffusive model of two-dimensional root growth and proliferation, Plant and Soil, vol.56, issue.2, pp.231-240, 1996.
DOI : 10.1007/BF00015306

T. Addiscott and A. Whitemore, Computer simulation of changes in soil mineral nitrogen and crop nitrogen during autumn, winter and spring, The Journal of Agricultural Science, vol.106, issue.01, pp.141-157, 1987.
DOI : 10.1111/j.1365-2389.1979.tb00978.x

J. Arvo and D. Kirk, Modelling plants with environmentsensitive automata, Proceedings of Ausgraph, pp.27-33, 1988.

S. Asseng, C. Richter, and G. Wessolek, Modelling root growth of wheat as the linkage between crop and soil, Plant and Soil, vol.190, issue.2, pp.267-277, 1997.
DOI : 10.1023/A:1004228201299

P. Balandier, A. Lacointe, L. Roux, X. Sinoquet, H. Cruziat et al., SIMWAL: A structural-functional model simulating single walnut tree growth in response to climate and pruning, Annals of Forest Science, vol.57, issue.5, pp.571-585, 2000.
DOI : 10.1051/forest:2000143
URL : https://hal.archives-ouvertes.fr/hal-00883362

J. Bayala, L. Heng, M. Van-noordwijk, and S. Ouedraogo, Hydraulic redistribution study in two native tree species of agroforestry parklands of West African dry savanna, Acta Oecologica, vol.34, issue.3, pp.370-378, 2008.
DOI : 10.1016/j.actao.2008.06.010

C. Birch and M. Hutchings, Exploitation of Patchily Distributed Soil Resources by the Clonal Herb Glechoma Hederacea, The Journal of Ecology, vol.82, issue.3, pp.653-664, 1994.
DOI : 10.2307/2261272

G. Boswell, H. Jacobs, K. Ritz, G. Gadd, and F. Davidson, The Development of Fungal Networks in Complex Environments, Bulletin of Mathematical Biology, vol.67, issue.2, pp.605-634, 2007.
DOI : 10.1007/s11538-005-9056-6

R. Brugge and J. Thornley, A Growth Model of Root Mass and Vertical Distribution, Dependent on Carbon Substrate from Photosynthesis and with Non-limiting Soil Conditions, Annals of Botany, vol.55, issue.4, pp.563-577, 1985.
DOI : 10.1093/oxfordjournals.aob.a086931

V. Clausnitzer and J. 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 : 10.1007/BF00010082

M. Coutts, C. Nielsen, and B. Nicoll, The development of symmetry, rigidity and anchorage in the structural root system of conifers, Plant Soil, vol.217, pp.1-15, 1999.
DOI : 10.1007/978-94-017-3469-1_1

D. Jager and A. , Response of plants to a localized nutrient supply, p.137, 1985.

P. De-willigen, M. Heinen, A. Mollier, and M. Van-noordwijk, Two-dimensional growth of a root system modelled as a diffusion process. I. Analytical solutions, Plant and Soil, vol.240, issue.2, pp.225-234, 2002.
DOI : 10.1023/A:1015744529454

A. 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 : 10.1007/BF02376780

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, issue.5-6, pp.419-431, 2003.
DOI : 10.1051/agro:2003027
URL : https://hal.archives-ouvertes.fr/hal-00886193

V. Dunbabin, A. Diggle, Z. Rengel, and R. Van-hungten, 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, A. Diggle, and Z. Rengel, Simulation of field data by a basic three-dimensional model of interactive root growth, Plant and Soil, vol.239, issue.1, pp.39-54, 2002.
DOI : 10.1023/A:1014952728942

A. Fitter, A. Hodge, R. D. Hutchings, M. John, and E. , Plant response to patchy soils The ecological consequences of environmental heterogeneity, pp.71-90, 2000.

R. Grant, Simulation of Carbon Assimilation and Partitioning in Maize, Agronomy Journal, vol.81, issue.4, pp.563-571, 1989.
DOI : 10.2134/agronj1989.00021962008100040004x

N. Greene, Voxel space automata: modeling with stochastic growth processes in voxel space, ACM SIGGRAPH Computer Graphics, vol.23, issue.3, pp.175-184, 1989.
DOI : 10.1145/74334.74351

N. Greene, Detailing tree skeletons with voxel automata. Siggraph course notes for photorealistic volume modelling and rendering technique, pp.1-15, 1991.

H. Hayhoe, ANALYSIS OF A DIFFUSION MODEL FOR PLANT ROOT GROWTH AND AN APPLICATION TO PLANT SOIL-WATER UPTAKE, Soil Science, vol.131, issue.6, pp.334-343, 1981.
DOI : 10.1097/00010694-198106000-00002

M. Heinen, A. Mollier, and P. De-willigen, Growth of a root system described as diffusion. II. Numerical model and application, Plant and Soil, vol.252, issue.2, pp.251-265, 2003.
DOI : 10.1023/A:1024749022761

D. Hillel and H. Talpaz, NOTE SIMULATION OF ROOT GROWTH AND ITS EFFECT ON THE PATTERN OF SOIL WATER UPTAKE BY A NONUNIFORM ROOT SYSTEM, Soil Science, vol.121, issue.5, pp.307-312, 1976.
DOI : 10.1097/00010694-197605000-00008

M. Hutchings and E. John, The Effects of Environmental Heterogeneity on Root Growth and Root/Shoot Partitioning, Annals of Botany, vol.94, issue.1, pp.1-8, 2004.
DOI : 10.1093/aob/mch111

C. Jones, W. Bland, J. Ritchie, and J. Williams, Simulation of root growth (eds) Modelling plant and soil systems, Madison: Agronomy Monograph, vol.31, pp.91-124, 1991.

A. Lacointe, Carbon allocation among tree organs: A review of basic processes and representation in functional-structural tree models, Annals of Forest Science, vol.57, issue.5, pp.521-533, 2000.
DOI : 10.1051/forest:2000139
URL : https://hal.archives-ouvertes.fr/hal-01191058

A. Lacointe, J. Isebrands, and G. Host, A new way to account for the effect of source-sink spatial relationships in whole plant carbon allocation models, Canadian Journal of Forest Research, vol.32, issue.10, pp.1838-1848, 2002.
DOI : 10.1139/x02-101
URL : https://hal.archives-ouvertes.fr/hal-01190855

L. Roux, X. Lacointe, A. Escobar-gutiérrez, A. , L. Dizès et al., Carbon-based models of individual tree growth: A critical appraisal, Annals of Forest Science, vol.58, issue.5, pp.469-506, 2001.
DOI : 10.1051/forest:2001140
URL : https://hal.archives-ouvertes.fr/hal-00964753

E. Malézieux, Y. Crozat, C. Dupraz, M. Laurans, D. Makowski et al., Mixing plant species in cropping systems: concepts, tools and models. A review, Agron Sustain Dev, vol.28, pp.1-20, 2008.

D. Mobbs, G. Lawson, A. Friend, N. Crout, J. Arah et al., HyPAR: Model for agroforestry systems. Technical manual. Model description for version 3.0, pp.44-45, 1999.

R. Mulia, 3D modelling of the growth of plant root systems in heterogeneous soils with voxel automata approach?Modelling concept and application with agroforestry trees, p.87, 2005.

R. Mulia and C. Dupraz, Unusual Fine Root Distributions of Two Deciduous Tree Species in Southern France: What Consequences for Modelling of Tree Root Dynamics?, Plant and Soil, vol.95, issue.4, pp.71-85, 2006.
DOI : 10.1007/s11104-005-3770-6

E. Page and A. 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, S. Asseng, S. Pellerin, A. Diggle, A. Smit et al., Modelling Root System Growth and Architecture, pp.113-146, 2000.
DOI : 10.1007/978-3-662-04188-8_4

V. Reddy and P. Yaa, Testing a Convective-dispersive Model of Two-dimensional Root Growth and Proliferation in a Greenhouse Experiment with Maize Plants, Annals of Botany, vol.87, issue.6, pp.759-768, 2001.
DOI : 10.1006/anbo.2001.1409

D. Robinson, The responses of plants to non-uniform supplies of nutrients, New Phytologist, vol.48, issue.4, pp.635-674, 1994.
DOI : 10.1016/0016-7061(93)90116-3

R. Singh, C. Ong, and N. Saharan, Above and below ground interactions in alley-cropping in semi-arid India, Agroforestry Systems, vol.17, issue.3, pp.259-274, 1989.
DOI : 10.1007/BF00141088

F. Somma, J. Hopmans, and V. Clausnitzer, Transient threedimensional modelling of soil water and solute transport with simultaneous root growth, root water, and nutrient uptake, Plant and Soil, vol.202, issue.2, pp.281-293, 1998.
DOI : 10.1023/A:1004378602378

A. Sullivan and I. Knight, A hybrid cellular automata/ semi-physical model of fire growth, Proc Conf Complex Systems, pp.64-73, 2004.

M. Van-noordwijk, D. Willigen, and P. , Quantitative root ecology as element of soil fertility theory, Neth J Agric Sci, vol.34, pp.273-281, 1986.

M. Van-noordwijk and G. Brouwer, Review of Quantitative Root Length Data in Agriculture, pp.515-525, 1991.
DOI : 10.1016/B978-0-444-89104-4.50071-2

M. Van-noordwijk and B. Lusiana, Background on a model of water, nutrient, and light capture in agroforestry systems, ICRAF, pp.54-55, 2000.

M. Van-noordwijk and G. Cadisch, Access and excess problems in plant nutrition, Plant Soil, vol.247, pp.25-39, 2002.
DOI : 10.1007/978-94-017-2789-1_2

M. Van-noordwijk and R. Mulia, Functional branch analysis as tool for fractal scaling above- and belowground trees for their additive and non-additive properties, Ecological Modelling, vol.149, issue.1-2, pp.41-51, 2002.
DOI : 10.1016/S0304-3800(01)00513-0

M. Van-noordwijk, G. Lawson, A. Soumaré, J. Groot, and K. Hairiah, Root distribution of trees and crops: competition and/or complementarity., pp.319-364, 1996.
DOI : 10.1079/9781780645117.0221

M. Van-noordwijk, P. Martikainen, P. Bottner, E. Cuevas, C. Rouland et al., Global change and root function, Global Change Biology, vol.151, issue.1157, pp.759-772, 1998.
DOI : 10.1046/j.1365-2486.1998.00194.x

M. Van-noordwijk, S. Rahayu, S. Williams, K. Hairiah, N. Khasanah et al., Crop and tree rootsystem dynamics, Belowground interactions in tropical agroecosystems . CAB International, pp.83-107, 2004.

P. Von-carlowitz and G. Wolf, Open-pit sunken planting: a tree establishment technique for dry environments, Agroforestry Systems, vol.15, issue.1, pp.17-29, 1991.
DOI : 10.1007/BF00046276

O. Wilderotter, An adaptive numerical method for the Richards equation with root growth, Plant and Soil, vol.251, issue.2, pp.255-267, 2003.
DOI : 10.1023/A:1023031924963

F. Woodward and C. Osborne, The representation of root processes in models addressing the responses of vegetation to global change, New Phytologist, vol.147, issue.1, pp.223-232, 2000.
DOI : 10.1046/j.1469-8137.2000.00691.x