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Mechanistic simulation models of nutrient uptake: A review

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Abstract

Mechanistic models of nutrient uptake consider diffusion and mass flow acting simultaneously to supply nutrients to the sorbing root surface. Plant parameters that determine nutrient uptake include those describing changes in root geometry and size due to root growth and others describing kinetics of the nutrient uptake process. Mechanistic models generally assume that nutrient uptake occurs evenly along the roots that are uniformly distributed in homogeneous and isotropic soil having no temporal and spatial gradients in volumetric moisture content. Uptake of immobile nutrients (like P and K) is mainly determined by the soil-supply parameters and is well predicted by the simulation models. In contrast, uptake of mobile nutrients (e.g. Ca and Mg) that usually accumulate at the root surface is determined mainly by the plant-uptake parameters; prediction of uptake of those nutrients is subject to a much wider error due to uncertainties of applying kinetic parameters measured on hydroponically-grown plants to soil-grown plants. Comparison of model-predicted and experimentally-observed uptake values should be done by calculating the mean squares of deviates instead of performing regression analysis, especially if data that encompass a relatively wide range in root length are considered. Complementary-ion effects occurring at the soil-root interface raise the need for developing a multi-nutrient uptake model that will simultaneously calculate uptake of several essential nutrients taking into account interactions among them.

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References

  • Abbott M L and Fraley L Jr 1991 A review: Radiotracer methods to determine root distribution. Env. Exp. Bot. 31, 1–10.

    Article  Google Scholar 

  • Amacher M C 1984 Determination of ionic activities in soil solutions and suspensions: Principal limitations. Soil Sci. Soc. Am. J. 48, 519–524.

    Google Scholar 

  • Aramrattana P and Scott B I H 1987 Potassium flux studies in intact portions of the root of Oryza sativa. Aust. J. Plant Physiol. 14, 91–115.

    Google Scholar 

  • Baldwin J P, Nye P H and Tinker P B 1973 Uptake of solutes by multiple root systems from soil. III. A model for calculating the solute uptake by a randomly dispersed root system developing in a finite volume of soil. Plant and Soil 38, 621–635.

    Google Scholar 

  • Barber S A 1962 A diffusion and mass-flow concept of soil nutrient availability. Soil Sci. 93, 39–49.

    Google Scholar 

  • Barber S A 1984 Soil Nutrient Bioavailability: A Mechanistic Approach. Wiley-Interscience, New York.

    Google Scholar 

  • Barber S A and Cushman J H 1981 Nitrogen uptake model for agronomic crops. In Modeling Waste Water Renovation-Land Treatment. Ed. I K Iskandar. pp 382–409. Wiley-Interscience, New York.

    Google Scholar 

  • Bar-Yosef B, Kafkafi U and Bresler E 1972 Uptake of phosphorus by plants growing under field conditions. I. Theoretical model and experimental determination of its parameters. Soil Sci. Soc. Am. Proc. 36, 783–788.

    Google Scholar 

  • Bernston G M 1992 A computer program for characterizing root system branching patterns. Plant and Soil 140, 145–149.

    Google Scholar 

  • Borg G Ch, Jansson P-E and Linden B 1990 Simulated and measured nitrogen conditions in a manured and fertilised soil. Plant and Soil 121, 251–267.

    Google Scholar 

  • Bouldin D R 1989 A multiple ion uptake model. J. Soil Sci. 40, 309–319.

    Google Scholar 

  • Bouldin D R, Miyasaka S C and Grunes D L 1992 Cation accumulation by winter wheat forage. II. Correlation with multi-ion model. J. Plant Nutr. 15, 1081–1097.

    Google Scholar 

  • Bowling D J E 1976 Uptake of Ions by Plant Roots. Academic Press, London-New York.

    Google Scholar 

  • Bray R H 1954 A nutrient mobility concept of soil-plant relationships. Soil Sci. 78, 9–22.

    Google Scholar 

  • Brewster J L, Bhat K K S and Nye P H 1975 The possibility of predicting solute uptake and plant growth response from independently measured soil and plant characteristics. III. The growth and uptake of onions in a soil fertilized to different initial levels of phosphate and a comparison of the results with model predictions. Plant and Soil 42, 197–226.

    Google Scholar 

  • Brewster J L, Bhat K K S and Nye P H 1976 The possibility of predicting solute uptake and plant growth response from independently measured soil and plant characteristics. V. The growth and phosphorus uptake of rape in soil at a range of phosphorus concentrations and a comparison of results with the predictions of a simulation model. Plant and Soil 44, 295–328.

    Article  Google Scholar 

  • Chanter D O 1981 The use and misuse of linear regression methods in crop modelling. In Mathematics and Plant Physiology. Eds. D A Rose and D A Charles-Edwards. pp 253–267. Academic Press, London.

    Google Scholar 

  • Charles-Edwards D A 1981 The Mathematics of Photosynthesis and Productivity. Academic Press, London.

    Google Scholar 

  • Checkai R T, Corey R B and Helmke P A 1987 Effects of ionic and complexed metal concentrations on plant uptake of cadmium and micronutrient metals from solution. Plant and Soil 99, 335–345.

    Google Scholar 

  • Chen J-H and Barber S A 1990a Soil pH and phosphorus and potassium uptake by maize evaluated with an uptake model. Soil Sci. Soc. Am. J. 54, 1032–1036.

    Google Scholar 

  • Chen J-H and Barber S A 1990b Effect of liming and adding phosphate on predicted phosphorus uptake by maize on acid soils of three soil orders. Soil Sci. 150, 844–850.

    Google Scholar 

  • Claassen N and Barber S A 1976 Simulation model for nutrient uptake from soil by a growing plant root system. Agron. J. 68, 961–964.

    Google Scholar 

  • Claassen N, Syring K M and Jungk A 1986 Verification of a mathematical model by simulating potassium uptake from soil. Plant and Soil 95, 209–220.

    Google Scholar 

  • Clarke A L and Barley K P 1968 The uptake of nitrogen from soils in relation to solute diffusion. Aust. J. Soil Res. 6, 75–92.

    Google Scholar 

  • Corey R B, King L D, Lue-Hing C, Fanning D S, Street J J and Walker J M 1987 Effects of sludge properties on accumulation of trace elements by crops. In Land Application of Sludge. Food Chain Implications. Eds. A L Page, T J Logan and J A Ryan. pp 25–51. Lewis Publishers, Inc., Chelsea, MI.

    Google Scholar 

  • Cushman J H 1979 An analytical solution to solute transport near root surfaces for low initial concentration. I. Equation's development. Soil Sci. Soc. Am. J. 43, 1087–1090.

    Google Scholar 

  • Cushman J H 1984 Nutrient transport inside and outside the root rhizosphere: Generalized model. Soil Sci. 138, 164–171.

    Google Scholar 

  • Darrah P R 1991 Models of the rhizosphere. I. Microbial population dynamics around a root releasing soluble and insoluble carbon. Plant and Soil 133, 187–199.

    Google Scholar 

  • Denison R F 1992 Mathematical modeling of oxygen diffusion and separation in legume root nodules. Plant Physiol. 98, 901–907.

    Google Scholar 

  • Drew M C, Nye P H and Vaidyanathan L V 1966 The supply of nutrient ions by diffusion to plant roots in soil. I. Absorption of potassium by cylindrical roots of onion and leek. Plant and Soil 30, 252–270.

    Google Scholar 

  • Dunham R J and Nye P H 1974 The influence of soil water content on the uptake of ions by roots. III. Phosphate, potassium, calcium and magnesium uptake and concentration gradients in soil. J. Appl. Ecol. 13, 967–984.

    Google Scholar 

  • Evangelou V P and Wagner G J 1987 Effects of ion activity and sugar polyalcohol osmotica on ion uptake. J. Exp. Bot. 38, 1637–1651.

    Google Scholar 

  • Faber B A, Zasoski R J, Burau R G and Uriu K 1990 Zinc uptake by corn as affected by vesicular-arbuscular mycorrhizae. Plant and Soil 129, 121–130.

    Google Scholar 

  • Föhse D, Claassen N and Jungk A 1991 Phosphorus efficiency of plants. II. Significance of root radius, root hairs and cation-anion balance for phosphorus influx in seven plant species. Plant and Soil 132, 261–272.

    Google Scholar 

  • Fontes P C R, Barber S A and Wilcox G E 1986 Prediction of phosphorus uptake by two tomato cultivars growing under insufficient and sufficient phosphorus soil conditions using a mechanistic mathematical model. Plant and Soil 94, 87–97.

    Google Scholar 

  • Gahoonia T S and Nielsen N E 1992 Control of pH at the soil-root interface. Plant and Soil 140, 49–54.

    Google Scholar 

  • Gardiner D T, Christensen N W and Myrold D D 1990 A comparison of methods for estimating phosphorus uptake kinetics under steady-state conditions. J. Plant Nutr. 13, 1079–1093.

    Google Scholar 

  • Gessa C and Deiana S 1992 Ca-polygalacturonate as a model for a soil-root interface. II. Fibrillar structure and comparison with natural root mucilage. Plant and Soil 140, 1–13.

    Google Scholar 

  • Goudriaan J and Monteith J L 1990 A mathematical function for crop growth based on light interception and leaf area expansion. Ann. Bot. 66, 695–701.

    Google Scholar 

  • Greenwood D J, Verstraeten L M J, Draycott A and Sutherland R A 1987 Response of winter wheat to N-fertiliser: Dynamic model. Fert, I. Res. 12, 139–156.

    Google Scholar 

  • Hahn B D 1987 A mathematical model of photorespiration and photosynthesis. Ann. Bot. 60, 157–169.

    Google Scholar 

  • Hetrick B A D, Wilson G W T and Leslie J F 1991 Root architecture of warm- and cool-season grasses: Relationship to mycorrhizal dependence. Can. J. Bot. 69, 112–118.

    Google Scholar 

  • Hettiaratchi D R P 1990 Soil compaction and plant root growth. Phil. Trans. R. Soc. London (B) 329, 343–355.

    Google Scholar 

  • Hoffland E 1992 Quantitative evaluation of the role of organic acid exudation in the mobilization of rock phosphate by rape. Plant and Soil 140, 279–289.

    Google Scholar 

  • Hoffland E, Bloemhof H S, Leffelaar P A, Findenegg G R and Nelemans J A 1990a Simulation of nutrient uptake by a growing root system considering increasing root density and inter-root competition. In Plant Nutrition — Physiology and Applications. Ed. M Lvan Beusichem. pp 9–15. Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Google Scholar 

  • Hoffland E, Findenegg G R, Leffelaar P A and Nelemans J A 1990b Use of a simulation model to quantify the amount of phosphate released from rock phosphate by rape. Trans. 14th Int. Congress Soil Sci. (Kyoto) II, 170–175.

    Google Scholar 

  • Hunt R 1973 A method of estimating root efficiency. J. Appl. Ecol. 10, 157–164.

    Google Scholar 

  • Ingestad T and Ågren G I 1992 Theories and methods on plant nutrition and growth. Physiol. Plant. 84, 177–184.

    Article  Google Scholar 

  • Itoh S and Barber S A 1983a A numerical solution of whole plant nutrient uptake for soil-root systems with root hairs. Plant and Soil 70, 403–413.

    Google Scholar 

  • Itoh S and Barber S A 1983b Phosphorus uptake by six plant species as related to root hairs. Agron. J. 75, 457–461.

    Google Scholar 

  • Johnsson H, Bergstrom L, Jansson P E and Paustian K 1987 Simulated nitrogen dynamics and losses in a layered agricultural soil. Agric. Ecosystems Environ. 18, 333–356.

    Article  Google Scholar 

  • Jungk A and Claassen N 1989 Availability in soil and acquisition by plants as the basis for phosphorus and potassium supply to plants. Z. Pflanzenernaehr. Bodenkd. 152, 151–157.

    Google Scholar 

  • Kelly J M, Barber S A and Edwards G S 1992 Modeling magnesium, phosphorus and potassium uptake by loblolly pine seedlings using a Barber-Cushman approach. Plant and Soil 139, 209–218.

    Google Scholar 

  • Kothari S K, Marschner H and Römheld V 1991 Effect of a vesicular-arbuscular mycorrhizal fungus and rhizosphere micro-organisms on manganese reduction in the rhizosphere and manganese concentrations in maize (Zea mays L.) New Phytol. 117, 649–655.

    Google Scholar 

  • Kovar J L and Barber S A 1990 Potassium supply characteristics of thirty-three soils as influenced by seven rates of potassium. Soil. Sci. Soc. Am. J. 54, 1356–1361.

    Google Scholar 

  • Laurie S H, Tancock N P, McGrath S P and Sanders J R 1991 Influence of complexation on the uptake by plants of iron, manganese, copper and zinc. II. Effect of DTPA in a multi-metal and computer simulation study. J. Exp. Bot. 42, 515–519.

    Google Scholar 

  • Lewis D G and Quirk J P 1967 Phosphate diffusion in soil and uptake by plants. III. 31P movement and uptake by plants as indicated by 32P autoradiography. Plant and Soil 26, 445–453.

    Google Scholar 

  • Li X-L, Marschner H and George E 1991 Acquisition of phosphorus and copper by VA-mycorrhizal hyphae and root-to-shoot transport in white clover. Plant and Soil 136, 49–57.

    Google Scholar 

  • Li Y and Barber S A 1990 Calculating changes of legume rhizosphere soil pH and soil solution phosphorus from phosphorus uptake. Agron. Abstr., p 273. ASA, Madison, WI.

    Google Scholar 

  • Linehan D J, Sinclair A H and Mitchell M C 1989 Seasonal changes in Cu, Mn, Zn and Co concentrations in soil in the rootzone of barley (Hordeum vulgare L.). J. Soil Sci. 40, 103–115.

    Google Scholar 

  • Meharg A A and Killham K 1991 A novel method of quantifying root exudation in the presence of soil microflora. Plant and Soil 133, 111–116.

    Google Scholar 

  • Michalov J 1986 The feasibility of utilizing a mathematical model in studying nonlinear transport processes in living systems. Biol. Plant. 28, 329–337.

    Google Scholar 

  • Moldrup P, Rolston D E, Hansen J A A and Yamaguchi T 1992 A simple, mechanistic model for soil resistance to plant water uptake. Soil Sci. 153, 87–93.

    Google Scholar 

  • Mullins G L and Edwards J H 1989 A comparison of two methods for measuring potassium influx kinetics by intact corn seedlings. J. Plant Nutr. 12, 485–496.

    Google Scholar 

  • Mullins G L, Sommers L E and Barber S A 1986 Modeling the plant uptake of cadmium and zinc from soil treated with sewage sludge. Soil Sci. Soc. Am. J. 50, 1245–1250.

    Google Scholar 

  • Nissen P 1989 Multiphasic uptake of potassium by corn roots: No linear component. Plant Physiol. 89, 231–237.

    Google Scholar 

  • Nye P H 1966 The effect of nutrient intensity and buffering power of a soil, and the absorbing power, size and root-hairs of a root, on nutrient absorption by diffusion. Plant and Soil 25, 81–105.

    Google Scholar 

  • Nye P H 1984a On estimating the uptake of nutrients solubilized near roots or other surfaces. J. Soil Sci. 35, 439–466.

    Google Scholar 

  • Nye P H 1984b pH changes and phosphate solubilization near roots—An example of coupled diffusion processes. In Roots, Nutrient and Water Influx, and Plant Growth. Eds. S A Barber and D R Bouldin. pp 89–100. ASA Spec. Publ. 49. ASA, CSSA, and SSSA, Madison, WI.

    Google Scholar 

  • Nye P H and Marriott F H C 1969 A theoretical study of the distribution of substances around roots resulting from simultaneous diffusion and mass flow. Plant and Soil 30, 459–472.

    Google Scholar 

  • Nye P H and Tinker P B 1977 Solute Movement in the Soil-Root System. Blackwell Science Publishers, Oxford, UK.

    Google Scholar 

  • Nye P H, Brewster J L and Bhat K K S 1975 The possibility of predicting solute uptake and plant growth response from independently measured soil and plant characteristics. I. The theoretical basis of the experiments. Plant and Soil 42, 161–170.

    Google Scholar 

  • Parker D R, Aguilera J J and Thomason D N 1992 Zincphosphorus interactions in two cultivars of tomato (Lycopersicon esculentum L.) grown in chelator-buffered nutrient solutions. Plant and Soil 143, 163–177.

    Google Scholar 

  • Passioura J B 1963 A mathematical model for the uptake of ions from the soil solution. Plant and Soil 18, 225–238.

    Google Scholar 

  • Passioura J B 1973 Sense and nonsense in crop simulation. J. Aust. Inst. Agric. Sci. 39, 181–183.

    Google Scholar 

  • Pate J S, Layzell D B and McNeil D L 1979 Modelling the transport and utilization of carbon and nitrogen in a nodulated legume. Plant Physiol. 63, 730–737.

    Google Scholar 

  • Philip J R 1991 Soils, natural science and models. Soil Sci. 151, 91–98.

    Google Scholar 

  • Rengel Z 1991 Modeling magnesium uptake from an acid soil. III. Determination of root magnesium concentration. Soil Sci. Soc. Am. J. 55, 1612–1615.

    Google Scholar 

  • Rengel Z 1992 Modeling magnesium uptake from an acid soil. IV. Depletion of magnesium, calcium, and potassium from soluble and exchangeable phase. Commun. Soil Sci. Plant Anal. 23, 165–174.

    Google Scholar 

  • Rengel Z and Robinson D L 1989 Competititive Al3+ inhibition of net Mg2+ uptake by intact Lolium multiflorum roots. I. Kinetics. Plant Physiol. 91, 1407–1413.

    Google Scholar 

  • Rengel Z and Robinson D L 1990a Modeling magnesium uptake from an acid soil. I. Nutrient relationships at the soil-root interface. Soil Sci. Soc. Am. J. 54, 785–791.

    Google Scholar 

  • Rengel Z and Robinson D L 1990b Modeling magnesium uptake from an acid soil. II. Barber-Cushman model. Soil Sci. Soc. Am. J. 54, 791–795.

    Google Scholar 

  • Robinson D 1986 Limits to nutrient inflow rates in roots and root systems. Physiol. Plant. 68, 551–559.

    Google Scholar 

  • Robinson D L, Linehan D J and Caul S 1991 What limits nitrate uptake from soil? Plant Cell Environ. 14, 75–85.

    Google Scholar 

  • Römheld V 1990 The soil-root interface in relation to mineral nutrition. Symbiosis 9, 19–27.

    Google Scholar 

  • Ross G J S 1981 The use of non-linear regression methods in crop modelling. In Mathematics and Plant Physiology. Eds. D A Rose and D A Charles-Edwards. pp 269–282. Academic Press, London.

    Google Scholar 

  • Russell R S 1977 Plant Root Systems: Their Function and Interaction with the Soil. McGraw-Hill, London.

    Google Scholar 

  • Sanders F E and Tinker P B 1973 Phosphate flow into mycorrhizal roots. Pestic. Sci. 4, 385–395.

    Google Scholar 

  • Sattelmacher B, Klotz F and Marschner H 1990 Influence of the nitrogen level on root growth and morphology of two potato varieties differing in nitrogen acquisition. Plant and Soil 123, 131–137.

    Google Scholar 

  • Schenk M K and Barber S A 1979 Root characteristics of corn genotypes as related to P uptake. Agron. J. 71, 921–924.

    Google Scholar 

  • Schenk M K and Barber S A 1980 Potassium and phosphorus uptake by corn genotypes grown in the field as influenced by root characteristics. Plant and Soil 54, 65–76.

    Google Scholar 

  • Seeling B and Claassen N 1990 A method for determing Michaelis-Menten kinetic parameters of nutrient uptake for plants growing in soil. Z. Pflanzenernaehr. Bodenk. 153, 301–303.

    Google Scholar 

  • Shaw J K, Stivers R K and Barber S A 1983 Evaluation of differences in potassium availability in soils of the same exchangeable potassium level. Commun. Soil Sci. Plant Anal. 14, 1035–1049.

    Google Scholar 

  • Silberbush M and Barber S A 1983a Prediction of phosphorus and potassium uptake by soybeans with a mechanistic mathematical model. Soil Sci. Soc. Am. J. 47, 262–265.

    Google Scholar 

  • Silberbush M and Barber S A 1983b Sensitivity analysis of parameters used in simulating potassium uptake with a mechanistic mathematical model. Agron. J. 75, 851–854.

    Google Scholar 

  • Silberbush M and Barber S A 1984 Phosphorus and potassium uptake of field grown soybeans predicted by a simulation model. Soil Sci. Soc. Am. J. 48, 592–596.

    Google Scholar 

  • Silberbush M, Hallmark W B and Barber S A 1983 Simulation of effects of soil bulk density and P addition on K uptake by soybeans. Commun. Soil Sci. Plant Anal. 14, 287–296.

    Google Scholar 

  • Sinclair A H, Mackie-Dawson L A and Linehan D J 1990 Micronutrient inflow rates and mobilisation into soil solution in the root zone of winter wheat (Triticum aestivum L.). Plant and Soil 122, 143–146.

    Google Scholar 

  • Skogley E O, Georgitis S J, Yang J E and Schaff B E 1990 The phytoavailability soil test—PST. Commun. Soil Sci. Plant Anal. 21, 1229–1243.

    Google Scholar 

  • Teo Y H, Beyrouty C A and Gbur E E 1992 Nitrogen, phosphorus, and potassium influx kinetic parameters of three rice cultivars. J. Plant Nutr. 15, 435–444.

    Google Scholar 

  • Tinker P B 1969 A steady state method for determing diffusion coefficients in soil. J. Soil Sci. 20, 336–345.

    Google Scholar 

  • Uren N C and Reisenauer H M 1988 The role of root exudates in nutrient acquisition. Adv. Plant Nutr. 3, 79–114.

    Google Scholar 

  • Van Noordwijk M, de Willigen P, Ehlert P A I and Chardon W J 1990 A simple model of P uptake by crops as a possible basis for P fertilizer recommendations. Neth. J. Agric. Sci. 38, 317–332.

    Google Scholar 

  • Van Rees K C J, Comerford N B and McFee W W 1990a Modeling potassium uptake by slash pine seedlings from low-potassium-supplying soils. Soil Sci. Soc. Am. J. 54, 1413–1421.

    Google Scholar 

  • Van Rees K C J, Comerford N B and Rao P S C 1990b Defining soil buffer power: Implications for ion diffusion and nutrient uptake modeling. Soil Sci. Soc. Am. J. 54, 1505–1507.

    Google Scholar 

  • Wallach D and Goffinet B 1987 Evaluation of simulation models: A predictive accuracy criterion. Agron. Abstr., p 18. ASA, Madison, WI.

    Google Scholar 

  • Wellings N P, Warring A H and Thompson J P 1991 Vesicular-arbuscular mycorrhizae (VAM) improve phosphorus and zinc nutrition and growth of pigeonpea in a Vertisol. Aust. J. Agric. Res. 42, 835–845.

    Google Scholar 

  • Wild A, Woodhouse P H and Hooper M J 1979 A comparison between the uptake of potassium by plants from solutions of constant potassium concentration and during depletion. J. Exp. Bot. 30, 697–704.

    Google Scholar 

  • Wolf J, de Wit C T and Van Keulen H 1989 Modeling long-term crop response to fertilizer and soil nitrogen. I. Model description and application. Plant and Soil 120, 11–22.

    Google Scholar 

  • Yang J E and Skogley E O 1992 Diffusion kinetics of multinutrient accumulation by mixed-bed ion-exchange resin. Soil Sci. Soc. Am. J. 56, 408–414.

    Google Scholar 

  • Yerokun O A and Christenson D R 1990 Relating high soil test phosphorus concentrations to plant phosphorus uptake. Soil Sci. Soc. Am. J. 54, 796–799.

    Google Scholar 

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Rengel, Z. Mechanistic simulation models of nutrient uptake: A review. Plant Soil 152, 161–173 (1993). https://doi.org/10.1007/BF00029086

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