Abstract
Simulations of crop productivity and environmental quality depend strongly on the root activity model used. Flexible, generic root system models are needed that can easily be coupled to various process-based soil models and can easily be modified to test various hypotheses about how roots respond to their environment. In this paper, we develop a convective-diffusive model of root growth and proliferation, and use it to test some of these hypotheses with data on the growth of roots on potted chrysanthemum cuttings. The proliferation of roots is viewed as a result of a diffusion-like gradient-driven propagation in all directions and convection-like propagation downwards caused by geotropism. The finite element method was used to solve the boundary problem for the convective-diffusive equation. To test hypotheses, we wrote modules in a way that caused a test parameter to be zero, should the hypothesis be rejected. These modules were added or removed to test each hypothesis in turn and in various combinations. The model explained 92% of the variation in the experimental data of Chen and Lieth (1993) on root growth of potted chrysanthemum cuttings. For this dataset the following hypotheses were accepted: (1) root diffusivity (colonization of new soil) did not depend on root density, (2) there was no geotropic trend in root development, (3) potential root growth increased linearly with root density, (4) there were (at least) two classes of roots with different rates of growth and proliferation, and (5) potential root growth rate decreased with distance from the plant stem base.
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Acock B, Reddy V R, Whisler F D, Baker D N, McKinion J M, Hodges H F and Boote K J 1983 The soybean crop simulator GLYCIM. Number 002 in series: Responses of vegetation to carbon dioxide, U.S. Dept. of Energy and Dept. of Agric. USA.
Ares J and Singh J S 1974 A model of the root biomass dynamics of a short grass prairie dominated by blue grama (Bouteloua Gracilis), J. Appl. Ecol. 11, 727–743.
Bar-Yosef B, Lambert J R and Baker D N 1982 Rhizos: a simulation of root growth and soil processes, sensitivity analysis and validation for cotton. Trans. ASAE 25, 1268–1273 and 1281.
Bengough A G, Mackenzie C J and Diggle A J 1992 Relations between root length densities and root intersections with horizontal and vertical planes using root growth modelling in 3-dimensions. Plant and Soil 145, 245–252.
Boyer J S 1971 Resistances to water transport in soybean, bean and sunflower. Crop Sci. 11, 403–407.
Brouwer R 1965 Water movement across the root. In The State and Movement of Water in living Organisms. Ed. C E Fogg. pp 131–149. Cambridge Univ. Press, Cambridge, UK.
Brugge R 1985 A mechanistic model of grass root growth and development dependent upon photosynthesis and nitrogen uptake. J. Theor. Biol. 116, 443–467.
Brugge R and Thornley J H M 1985 A growth model of root mass and vertical distribution, dependent on carbon substrate from photosynthesis and with nonlimiting soil conditions. Ann. Bot. 55, 563–577.
Clausnitzer V and Hopmans J W 1994 Simultaneous modelling of transient three dimensional root growth and soil water flow. Plant and Soil 164, 299–314.
Chen De-Xing and Lieth J H 1993 A two-dimensional, dynamic model for root growth distribution of potted plants. J. Am. Soc. Hort. Sci. 118, 181–187.
Chopart J L and Vauclin M 1990 Water balance estimation model: field test and sensitivity analysis. Soil Sci. Soc. Am. J. 54, 1377–1384.
Diggle A J 1988 ROOTMAP-a model in three-dimensional coordinates of the growth and structure of fibrous root systems. Plant and Soil 105, 169–178.
Gerwitz A and Page E R 1974 An empirical mathematical model to describe plant root systems. J. Appl. Ecol. 11, 773–781.
Grant R F 1989 Simulation of carbon assimilation and partitioning in maize. Agron. J. 81, 563–571.
Grant R F 1993 Simulation model of soil compaction and root growth: I. model structure. Plant and Soil 150, 1–14.
Hanks R J 1974 Model for predicting plant yield as influenced by water use. Agron. J. 66, 660–665.
Hansen G K 1975 A dynamic continuous simulation model of water state and transportation in the soil-plant-atmosphere system. I. The model and its sensitivity. Acta Agric. Scand. 25, 129–149.
Hayhoe H 1981 Analysis of a diffusion model for plant root growth and an application to plant soil-water uptake. Soil Sci. 131, 334–343.
Hillel D and Talpaz H 1976 Simulation of root growth and its effect on the pattern of soil water uptake by a nonuniform root system. Soil Sci. 121, 307–312.
Hoogenboom G and Huck M G 1986 ROOTSIMU V.4.0-a dynamic simulation of root growth, water uptake, and biomass partitioning in a soil-plant-atmosphere continuum: Update and documentation. Alabama Agric. Exp. Stn. Agronomy and Soils Dep. Ser. 109.
Hoogenboom G, Huck M G and Peterson C M 1988 Predicting root growth and water uptake under different soil water regimes. Agric. Systems 26, 263–290.
Huck M G and Hillel D 1983 A model of root growth and water uptake accounting for photosynthesis, respiration, transpiration and soil hydraulics. In Advances in Irrigation, Vol. 2. Ed. D Hillel. pp 273–333. Academic Press, New York, USA.
Jaffe M J, Takahashi H and Biro R L 1985 A pea mutant for the study of hydrotropism in roots. Science 230, 445–447,
Jones C A, Bland W L, Ritchie J T and Williams J R 1990 Simulation of root growth. In Modelling Plant and Soil Systems. Eds. J Y Ritchie and R J Hanks. pp 91–123. American Society of Agronomy, Madison, WI, USA.
Johnson I R and Thornley J H M 1985 Dynamic model of the response of a vegetative grass crop to light, temperature and nitrogen. Plant Cell Environ. 8, 485–499.
Klepper B and Rickman R W 1990 Modelling crop root growth and function. Adv. Agron. 44, 113–132.
Marani A, Cardon G E and Phene C J 1992 CALGOS, a version of GOSSYM adapted for irrigated cotton. I. Drip irrigation, soil water transport and root growth. 1992 Beltwide Cotton Conference Proc., pp 1352–1357. National Cotton Council, Memphis, USA.
Narda K N and Curry R B 1981 SOYROOT-A, dynamic model of soybean root growth and water uptake. Trans. ASAE 24, 651–656.
Pages L, Jordan M O and Picard D 1989 A simulation model of the three-dimensional architecture of the maize root system. Plant and Soil 119, 147–154.
Page E R and Gerwitz A 1974 Mathematical models based on diffusion equations, to describe root systems of isolated plants, row crops and swards. Plant and Soil 41, 243–254.
Pollard J T 1977 A Handbook of numerical and statistical Techniques with Examples mainly from the life Sciences. Cambridge Univ. Press, Cambridge, UK.
Porter J R, Klepper B and Belford R K 1986 A, model (WHTROOT) which sychronizes root growth and development with shoot development for winter wheat. Plant and Soil 92, 133–145.
Robertson M J, Fukai S, Hammer G L and Ludlow M M 1993 Modelling root growth of grain sorghum using the CERES approach. Field Crops Res. 33, 113–130.
Rose D A 1983 The description of the growth of root systems. Plant and Soil 75, 405–415.
Shein E V and Pachepsky Ya A 1995 Influence of root density on the critical soil water potential. Plant and Soil 171, 351–357.
Shibusawa S 1992 Hierarchical modelling of a branching root system based on L-system. Acta Hortic. 319, 659–664.
Silk W K and Ericson R O 1979 Kinematics of plant growth. J. Theor. Biol. 76, 481–501.
Subbaiah R and Rao K A 1993 Root growth simulation model under specified environment. J. Irrig. Drainage Eng. 119, 898–904.
Timlin D J, Heatmann G C and Ahuja L R 1992 Solute leaching in crop row vs. interrow zones. Soil Sci. Soc. Am. J. 56, 384–392.
Timlin J D, Pachepsky Ya A and Acock B 1996 A design for a modular generic soil simulator to interface with plant models. Agron. J. (In press).
Van Genuchten M Th 1981 Non-equilibrium transport parameters from miscible displacementexperiments. Research Res. No. 119. US Salinity Laboratory, USDA-SEA-ARS, Riverside, CA, USA.
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Acock, B., Pachepsky, Y.A. Convective-diffusive model of two-dimensional root growth and proliferation. Plant Soil 180, 231–240 (1996). https://doi.org/10.1007/BF00015306
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DOI: https://doi.org/10.1007/BF00015306