Acock, B., and Y.A. Pachepsky. 1996. Convective-diffusive model of two-dimen-sional root growth and proliferation. Plant Soil 180:231-240. doi:10.1007/BF00015306.
Ahmadi, S.H., F. Plauborg, M.N. Andersen, A.R. Sepaskhah, C.R. Jensen, and S. Hansen. 2011. Effects of irrigation strategies and soils on field grown pota-toes: Root distribution. Agric. Water Manage. 98:1280-1290. doi:10.1016/j.agwat.2011.03.013.
Amato, M., and J.T. Ritchie. 2002. Spatial distribution of roots and water up-take of maize (Zea mays L.) as affected by soil structure. ETATS-UNIS. CSSA, Madison, WI.
Angadi, S.V., and M.H. Entz. 2002. Root system and water use patierns of dif-ferent height sunflower cultivars. Agron. J. 94:136-145. doi:10.2134/agronj2002.0136.
Böhm, W. 1979. Methods for studying root systems. Springer-Verlag, Berlin.
Burch, G.J. 1978. Agronomic and physiological responses of soybean and sor-ghum crops to water deficits ii. Crop evaporation, soil water depletion and root distribution. Aust. J. Plant Physiol. 5:169. doi:10.1071/PP9780169.
Camposeo, S., and P. Rubino. 2003. Effect of irrigation frequency on root water up-take in sugar beet. Plant Soil 253:301-309. doi:10.1023/A:1024801312711.
Clausnitzer, V., and J.W. Hopmans. 1994. Simultaneous modelling of transient three dimensional root growth and soil water flow. Plant Soil 164:299-314. doi:10.1007/BF00010082.
Coelho, E.F., and D. Or. 1999. Root distribution and water uptake patierns of corn under surface and subsurface drip irrigation. Plant Soil 206:123. doi:10.1023/A:1004325219804.
de Willigen, P., M. Heinen, A. Mollier, and M. Van Noordwijk. 2002. Two-dimen-sional growth of a root system modelled as a diffusion process. I. Analytical solutions. Plant Soil 240:225-234. doi:10.1023/A:1015744529454.
Ditimer, H.J. 1937. A quantitative study of the roots and root hairs of a winter rye plant (Secale cereale). Am. J. Bot. 24:417-420. doi:10.2307/2436424.
Dupuy, L., P.J. Gregory, and A.G. Bengough. 2010. Root growth models: Towards a new generation of continuous approaches. J. Exp. Bot. 61:2131-2143. doi:10.1093/jxb/erp389.
Gale, M.R., and D.F. Grigal. 1987. Vertical root distributions of northern tree species in relation to successional status. Can. J. For. Res. 17:829-834. doi:10.1139/x87-131.
Gao, Y., A. Duan, X. Qiu, Z. Liu, J. Sun, J. Zhang, and H. Wang. 2010. Distribution of roots and root length density in a maize/soybean strip intercropping sys-tem. Agric. Water Manage. 98:199-212. doi:10.1016/j.agwat.2010.08.021.
Gerwitz, A., and E.R. Page. 1974. An empirical mathematical model to describe plant root systems. J. Appl. Ecol. 11:773-781. doi:10.2307/2402227.
Grabarnik, P., L. Pagès, and A.G. Bengough. 1998. Geometrical properties of simulated maize root systems: Consequences for length density and inter-section density. Plant Soil 200:157-167. doi:10.1023/A:1004382531671.
Husson, F., S. Lê, and J. Pagès. 2009. Analyse de données avec R. Pratique de la statistique, Presses Univ. de Rennes, France.
Jackson, R.B., J. Canadell, J.R. Ehleringer, H.A. Mooney, O.E. Sala, and E.D. Schulze. 1996. A global analysis of root distributions for terrestrial biomes. Oecologia 108:389-411. doi:10.1007/BF00333714.
Katayama, K. 2000. Analysis of relationship between root length density and water uptake by roots of five crops using minirhizotron in the semi-arid tropics. Jpn. Agric. Res. Q. 34:81.
Kirkham, M.B., S.J. Grecu, and E.T. Kanemasu. 1998. Comparison of minirhi-zotrons and the soil-water-depletion method to determine maize and soybean root length and depth. Eur. J. Agron. 8:117-125. doi:10.1016/S1161-0301(97)00019-1.
Lampurlanés, J., P. Angás, and C. Cantero-Martinez. 2001. Root growth, soil water content and yield of barley under different tillage systems on two soils in semiarid conditions. Field Crops Res. 69:27-40. doi:10.1016/S0378-4290(00)00130-1.
Leitner, D., S. Klepsch, G. Bodner, and A. Schnepf. 2010. A dynamic root system growth model based on L-Systems. Plant Soil 332:177-192. doi:10.1007/s11104-010-0284-7.
Liu, L.P., Y.T. Gan, R. Bueckert, and K. Van Rees. 2011. Rooting systems of oil-seed and pulse crops. II: Vertical distribution patierns across the soil profile. Field Crops Res. 122:248-255. doi:10.1016/j.fcr.2011.04.003.
Lopez-Zamora, I., N. Falcão, N.B. Comerford, and N.F. Barros. 2002. Root isotropy and an evaluation of a method for measuring root distribution in soil trenches. For. Ecol. Manage. 166:303-310. doi:10.1016/S0378-1127(01)00679-X.
Moroke, T.S., R.C. Schwartz, K.W. Brown, and A.S.R. Juo. 2005. Soil water de-pletion and root distribution of three dryland crops. Soil Sci. Soc. Am. J. 69:197-205. doi:10.2136/sssaj2005.0197.
Moroni, M.T., D. Worledge, and C.L. Beadle. 2003. Root distribution of Eucalyp-tus nitens and E. globulus in irrigated and droughted soil. For. Ecol. Manage. 177:399-407. doi:10.1016/s0378-1127(02)00410-3.
Neukirchen, D., M. Himken, J. Lammel, U. Czypionka-Krause, and H.W. Olfs. 1999. Spatial and temporal distribution of the root system and root nutri-ent content of an established miscanthus crop. Eur. J. Agron. 11:301-309. doi:10.1016/S1161-0301(99)00031-3.
Oikeh, S.O., J.G. Kling, W.J. Horst, V.O. Chude, and R.J. Carsky. 1999. Growth and distribution of maize roots under nitrogen fertilization in plinthite soil. Field Crops Res. 62:1-13. doi:10.1016/S0378-4290(98)00169-5.
Page, E.R., and A. Gerwitz. 1974. Mathematical models based on diffusion equations, to describe root systems of isolated plants, row crops and swards. Plant Soil 41:243-254. doi:10.1007/BF00017252.
Pagès, L. 2012. Links between root developmental traits and foraging performance. Plant Cell Environ. 34:1749-1760. doi:10.1111/j.1365-3040.2011.02371.x.
Pagès, L., and F. Aries. 1988. SARAH: Modèle de simulation de la croissance, du développement et de l'architecture des systèmes racinaires. Agronomie 8:889-896. doi:10.1051/agro:19881008.
Pavlychenko, T.K. 1937. Quantitative study of the entire root systems of weed and crop plant under field conditions. Ecology 18:62-79. doi:10.2307/1932703.
Pohl, M., R. Strude, A. Butiler, and C. Rixen. 2011. Functional traits and root morphology of alpine plants. Ann. Bot. (Lond.) 108:537-545. doi:10.1093/aob/mcr169.
R Development Core Team. 2011. R: A language and environment for statistical computing. version 2.14.1. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org (accessed 3 Oct. 2011).
Radersma, S., and C.K. Ong. 2004. Spatial distribution of root length density and soil water of linear agroforestry systems in sub-humid kenya: Implica-tions for agroforestry models. For. Ecol. Manage. 188:77-89. doi:10.1016/j.foreco.2003.07.021.
Saltelli, A., K. Chan, and E.M. Scott. 2000. Sensitivity analysis, John Wiley and Sons, New York.
Schenk, H.J. 2008. The shallowest possible water extraction profile: A null mod-el for global root distributions. Vadose Zone J. 7:1119-1124. doi:10.2136/vzj2007.0119.
Sharp, R.E., and W.J. Davies. 1985. Root growth and water uptake by maize plants in drying soil. J. Exp. Bot. 36:1441-1456. doi:10.1093/jxb/36.9.1441.
Varadhan, R., and P. Gilbert. 2009. An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional non-linear ob-jective function. J. Stat. Softw. 32:1-26.
Zhang, X. 2004. Root growth and soil water utilization of winter wheat in the north china plain. Hydrol. Processes 18:2275. doi:10.1002/hyp.5533.
Zotarelli, L., J.M. Scholberg, M.D. Dukes, R. Muñoz-Carpena, and J. Icerman. 2009. Tomato yield, biomass accumulation, root distribution and irriga-tion water use efficiency on a sandy soil, as affected by nitrogen rate and irrigation scheduling. Agric. Water Manage. 96:23-34. doi:10.1016/j.ag-wat.2008.06.007.
