A mathematical model of plant nutrient uptake

Abstract. The classical model of plant root nutrient uptake due to Nye, Tinker and Barber is developed and extended. We provide an explicit closed formula for the uptake by a single cylindrical root for all cases of practical interest by solving the absorption-diffusion equation for the soil nutrient concentration asymptotically in the limit of large time. We then use this single root model as a building block to construct a model which allows for root size distribution in a more realistic plant root system, and we include the effects of root branching and growth. The results are compared with previous theoretical and experimental studies.

[1]  F. Molz.  Potential Distributions in the Soil-Root System1 , 1975 .

[2]  P. Thorne.  Fate of explosives in plant tissues contaminated during phytoremediation , 1999 .

[3]  M. Canny,et al.  The Branch Roots of Zea. I. First Order Branches, Their Number, Sizes and Division Into Classes , 1991 .

[4]  K. Okada,et al.  Signalling in cell type specification. , 1999, Seminars in cell & developmental biology.

[5]  C. Hackett,et al.  A Model of the Extension and Branching of a Seminal Root of Barley, and Its Use in Studying Relations Between Root Dimensions I the Model , 1972 .

[6]  B. Scheres,et al.  Cellular organisation of the Arabidopsis thaliana root. , 1993, Development.

[7]  F. Magdoff,et al.  Nutrient cycling, transformations, and flows: implications for a more sustainable agriculture , 1997 .

[8]  De Chen,et al.  Two-dimensional model of water transport in the root zone and plant for container-grown chrysanthemum , 1992 .

[9]  C. Hackett,et al.  A model of the Extension and Branching of a Seminal Root of Barley, and Its Use in Studying Relations Between Root Dimensions II. Results and Inferences From Manipulation of the Model , 1972 .

[10]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[11]  C. Marschner.  Mineral Nutrition of Higher Plants, 2nd edition, H. Marschner. Academic Press, London (1995), 889, (ISBN 0-12-473543-6). Price: 29.95 Pound Sterling , 1996 .

[12]  Claude Doussan,et al.  Modelling of the Hydraulic Architecture of Root Systems: An Integrated Approach to Water Absorption—Distribution of Axial and Radial Conductances in Maize , 1998 .

[13]  Z. Kabala,et al.  Water Transport in an Unsaturated Medium to Roots with Differing Local Geometries , 1992 .

[14]  François Tardieu,et al.  Modeling root water potential and soil-root water transport. I. Model presentation , 1991 .

[15]  P. B. Tinker,et al.  Solute Movement in the Soil-Root System. , 1978 .

[16]  M. Canny,et al.  The branch roots of Zea , 1994 .

[17]  R. H. Ritchie,et al.  Asymptotic Expansions of Solutions of the Heat Conduction Equation in Internally Bounded Cylindrical Geometry , 1956 .

[18]  M. N. Nimah,et al.  Model for Estimating Soil Water, Plant, and Atmospheric Interrelations: I. Description and Sensitivity , 1973 .

[19]  B. Scheres,et al.  Root pattern: shooting in the dark? , 1998, Seminars in cell & developmental biology.

[20]  H. Marschner.  Mineral Nutrition of Higher Plants , 1988 .

[21]  P. Nye.  Towards the quantitative control of crop production and quality , 1992 .

[22]  J. Thornley.  Modelling Water in Crops and Plant Ecosystems , 1996 .

[23]  M. Canny,et al.  Rates of water uptake into the mature root system of maize plants , 1993 .

[24]  M. Loreau,et al.  Phenotypic diversity and stability of ecosystem processes. , 1999, Theoretical population biology.

[25]  E. George.  Contribution of mycorrhizal hyphal to nutrient and water uptake of plants , 1992 .

[26]  Bengough.  Modelling Rooting Depth and Soil Strength in a Drying Soil Profile , 1997, Journal of theoretical biology.

[27]  D. Robinson.  The responses of plants to non-uniform supplies of nutrients. , 1994, The New phytologist.

[28]  A. Mclaren,et al.  TEMPORAL AND VECTORIAL REACTIONS OF NITROGEN IN SOIL: A REVIEW , 1970 .

[29]  Fred J. Molz,et al.  Models of water transport in the soil‐plant system: A review , 1981 .

[30]  M. Kaufmann,et al.  An interpretation of some whole plant water transport phenomena. , 1983, Plant physiology.

[31]  P. Tinker.  Transport of Water to Plant Roots in Soil , 1976 .

[32]  E. Steudle,et al.  How does water get through roots , 1998 .

[33]  J. Bear,et al.  Modeling groundwater flow and pollution , 1987 .

[34]  Hinch.  Perturbation Methods , 1991 .

[35]  E. Steudle,et al.  Axial and Radial Hydraulic Resistance to Roots of Maize (Zea mays L.). , 1989, Plant physiology.

[36]  S. A. Barber,et al.  Phosphate Uptake by Corn as Affected by Soil Characteristics and Root Morphology 1 , 1979 .

[37]  I. Jakobsen,et al.  External hyphae of vesicular arbuscular mycorrhizal fungi associated with trifolium subterraneum l. 1. spread of hyphae and phosphorus inflow into roots , 1992 .

[38]  Joe Landsberg,et al.  Water Movement Through Plant Roots , 1978 .

[39]  M. Muir.  Physical Chemistry , 1888, Nature.

[40]  H. Weitzner,et al.  Perturbation Methods in Applied Mathematics , 1969 .

[41]  H. M. Taylor,et al.  WATER UPTAKE BY COTTON ROOT SYSTEMS: AN EXAMINATION OF ASSUMPTIONS IN THE SINGLE ROOT MODEL , 1975 .

[42]  Frank C. Hoppensteadt,et al.  Mathematical methods of population biology , 1982 .

[43]  Loïc Pagès,et al.  MODELLING OF THE HYDRAULIC ARCHITECTURE OF ROOT SYSTEMS : AN INTEGRATED APPROACH TO WATER ABSORPTION : MODEL DESCRIPTION , 1998 .

[44]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[45]  Ross M. Welch,et al.  A new paradigm for world agriculture: meeting human needs: Productive, sustainable, nutritious , 1999 .

[46]  P. B. Tinker,et al.  Solute Movement in the Rhizosphere , 2000 .

[47]  P. Nobel,et al.  Radial Hydraulic Conductivity of Individual Root Tissues of Opuntia ficus-indica (L.) Miller as Soil Moisture Varies , 1996 .

[48]  R. Burton.  A MECHANISTIC APPROACH , 1990 .

[49]  Abhishek Gupta,et al.  Recurrent acute respiratory tract infections in areas with high nitrate concentrations in drinking water. , 2000, Environmental health perspectives.

[50]  D. Miller.  Studies of Root Function in Zea mays: IV. Effects of Applied Pressure on the Hydraulic Conductivity and Volume Flow through the Excised Root. , 1985, Plant physiology.

[51]  L. Saker,et al.  Nutrient Supply and the Growth of the Seminal Root System in Barley III. COMPENSATORY INCREASES IN GROWTH OF LATERAL ROOTS, AND IN RATES OF PHOSPHATE UPTAKE, IN RESPONSE TO A LOCALIZED SUPPLY OF PHOSPHATE , 1978 .

[52]  S. A. Barber,et al.  Soil Nutrient Bioavailability: A Mechanistic Approach , 1984 .

[53]  D. Goolsby.  Mississippi Basin nitrogen flux believed to cause Gulf hypoxia , 2000 .

[54]  Andrew C. Fowler,et al.  Mathematical Models in the Applied Sciences , 1997 .

[55]  Jan W. Hopmans,et al.  Parameter uncertainty analysis of common infiltration models , 1998 .

[56]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[57]  A. ALLSOPP,et al.  Plant Anatomy , 1966, Nature.

[58]  N. Claassen,et al.  Ion Diffusion in the Soil–Root System , 1997 .

[59]  P. Reich,et al.  Effects of plant species richness on invasion dynamics, disease outbreaks, insect abundances and diversity. , 1999, Ecology letters.

[60]  W. R. Gardner.  Relation of Root Distribution to Water Uptake and Availability1 , 1964 .

[61]  P. Tinker,et al.  THE DEVELOPMENT OF ENDOMYCORRHIZAL ROOT SYSTEMS: I. SPREAD OF INFECTION AND GROWTH‐PROMOTING EFFECTS WITH FOUR SPECIES OF VESICULAR‐ARBUSCULAR ENDOPHYTE , 1977 .

[62]  T. Jamieson.  ON ROOT HAIRS. , 1893, Science.

[63]  D. Miller.  Studies of root function in Zea mays. II. Dimensions of the root system , 1981 .

[64]  E. Joner,et al.  Growth and extracellular phosphatase activity of arbuscular mycorrhizal hyphae as influenced by soil organic matter , 1995 .

[65]  P. Nye.  Towards the quantitative control of crop production and quality. II. The scientific basis for guiding fertilizer and management practice, particularly in poorer countries , 1992 .

[66]  Toshio Tabuchi,et al.  Soil-Water Interactions , 2020 .

[67]  Yakov A. Pachepsky,et al.  A modular soil and root process simulator , 1997 .

[68]  Stan D. Wullschleger,et al.  Modeling the belowground response of plants and soil biota to edaphic and climatic change — What can we expect to gain? , 1994 .

[69]  A. Vallejo,et al.  Water and Solute Movement under Conventional Corn in Central Spain. II. Salt Leaching , 1996 .

[70]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[71]  D. R. Nielsen,et al.  Nitrogen Transformations During Continuous Leaching 1 , 1974 .

[72]  D. Tennant,et al.  A test of a modified line intersect method of estimating root length , 1975 .

[73]  W. R. Gardner,et al.  Some Observations on the Movement of Water to Plant Roots1 , 1962 .

[74]  E. Newman.  Water Movement Through Root Systems , 1976 .

[75]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[76]  A. Hershey,et al.  Transformation of a Tundra River from Heterotrophy to Autotrophy by Addition of Phosphorus , 1985, Science.

[77]  François Tardieu,et al.  Modeling Root Water Potential and Soil‐Root Water Transport: II. Field Comparisons , 1991 .

[78]  E. J. Kamprath,et al.  Soil Nutrient Bioavailability—A Mechanistic Approach , 1985 .

[79]  R. Meagher,et al.  Phytoremediation of toxic elemental and organic pollutants. , 2000, Current opinion in plant biology.

[80]  L. A. Mackie-Dawson,et al.  Methodology for the study of roots in field experiments and the interpretation of results. , 1991 .

[81]  P. Weerathaworn,et al.  Anatomy of Seedling Roots of Tropical Maize (Zea mays L.) Cultivars at Low Water Supply , 1992 .

[82]  Peter J. Gregory,et al.  Water and crop growth. , 1988 .

[83]  F. Moreno,et al.  Reducing Fertilization for Maize in Southwest Spain , 1998 .

[84]  G. Ellis,et al.  Nitrite and nitrate analyses: a clinical biochemistry perspective. , 1998, Clinical biochemistry.

[85]  R. Simcock,et al.  Harvesting a crop of gold in plants , 1998, Nature.

[86]  J. Ritchie,et al.  Resistance to water flow in the sorghum plant. , 1980, Plant physiology.

[87]  J. H. Manwaring,et al.  Rapid physiological adjustment of roots to localized soil enrichment , 1990, Nature.

[88]  J. Passioura,et al.  Water Transport in and to Roots , 1988 .

[89]  S. A. Barber,et al.  Root Characteristics of Corn Genotypes as Related to P Uptake1 , 1979 .

[90]  S. A. Barber,et al.  A Method for Characterizing the Relation between Nutrient Concentration and Flux into Roots of Intact Plants. , 1974, Plant physiology.

[91]  M. Caldwell,et al.  Competition for Phosphorus: Differential Uptake from Dual-Isotope—Labeled Soil Interspaces Between Shrub and Grass , 1985, Science.

[92]  D. Miller,et al.  Studies of Root Function in Zea mays: III. Xylem Sap Composition at Maximum Root Pressure Provides Evidence of Active Transport into the Xylem and a Measurement of the Reflection Coefficient of the Root. , 1985, Plant physiology.

[93]  P. Nye.  The Effect of Root Shrinkage on Soil Water Inflow , 1994 .

[94]  I. Jakobsen,et al.  External hyphae of vesicular–arbuscular mycorrhizal fungi associated with Trifolium subterraneum L. , 1992 .

[95]  D. J. Greenwood,et al.  Dynamic model for the effects of K‐fertilizer on crop growth, K‐uptake and soil‐K in arable cropping. 1. Description of the model , 1997 .

[96]  Kristian Borch,et al.  Ethylene: a regulator of root architectural responses to soil phosphorus availability , 1999 .

[97]  D. Bowling,et al.  Uptake of Ions by Plant Roots , 1976 .

[98]  H. Lee Allen,et al.  Water quality impacts of forest fertilization with nitrogen and phosphorus , 1999 .

[99]  C. Davis.  Absorption of Soil Moisture by Maize Roots , 1940, Botanical Gazette.

[100]  Abhishek Gupta,et al.  Methaemoglobinaemia in areas with high nitrate concentration in drinking water. , 2000, The National medical journal of India.

[101]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[102]  W. Davies,et al.  Pressure –Flow Relationships, Xylem Solutes and Root Hydraulic Conductance in Flooded Tomato Plants , 1996 .