Abstract
Mechanistic models of nutrient uptake are essential to the study of plant-soil interactions. In these models, uptake rates depend on the supply of the nutrient through the soil and the uptake capacity of the roots. The behaviour of the models is complex, although only six to ten parameters are used. Our goal was to demonstrate a comprehensive and efficient method of exploring a steady-state uptake model with variation in parameters across a range of values described in the literature. We employed two analytical techniques: the first a statistical analysis of variance, and the second a graphical representation of the simulated response surface. The quantitative statistical technique allows objective comparison of parameter and interaction sensitivity. The graphical technique uses a judicious arrangement of figures to present the shape of the response surface in five dimensions. We found that the most important parameters controlling uptake per unit length of root are the average dissolved nutrient concentration and the maximal rate of nutrient uptake. Root radius is influential if rates are expressed per unit root length; on a surface area basis, this parameter is less important. The next most important parameter is the effective diffusion coefficient, especially in the uptake of phosphorus. The interactions of parameters were extremely important and included three and four dimensional effects. For example, limitation by maximal nutrient influx rate is approached more rapidly with increasing nutrient solution concentration when the effective diffusion coefficient is high. We also note the ecological implications of the response surface. For example, in nutrient-limited conditions, the rate of uptake is best augmented by extending root length; when nutrients are plentiful increasing uptake kinetics will have greater effect.
Similar content being viewed by others
References
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.
Barber S A and Cushman J H 1981 Nitrogen uptake model for agronomic crops. In Modeling wastewater renovation-land treatment. Ed. I R Iskandar. pp 382–409. Wiley-Interscience, New York, USA.
Barber S A and Ernani P O 1992 Use of a mechanistic uptake model for evaluating phosphate fertilizer materials. J. Plant Nutr. 15, 1047–1053.
Chapin F SIII 1980 The mineral nutrition of wild plants. Ann. Rev. Ecol. Sys. 11, 233–260.
Classen N and Barber S A 1976 Simulation model for nutrient uptake from soil by a growing plant root system. Agron. J. 68, 961–964.
Cushman J H 1979 An analytical solution to solute transport near root surfaces for low initial concentration: I. Equations development. Soil Sci. Soc. Am. J. 43, 1087–1095.
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.
Gardner R H, O'Neill R V, Mankin J B and Carney J H 1981 A comparison of sensitivity analysis and error analysis based on a stream ecosystems model. Ecol. Model. 12, 173–190.
Gillespie A R and Pope P E 1990 Rhizosphere acidification increases phosphorus recovery of black locust: I. Induced acidification and soil response. Soil Sci. Soc. Am. J. 54, 533–537.
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.
Kimmins J P, Binkley D, Chatarpaul L and de Catanzaro J 1985 Biogeochemistry of temperate forest ecosystems; literature on investories and dynamics of biomass and nutrients. Petawawa National Forestry Institute, Report PI-X-47E/F. Canadian Forestry Service, Ottawa, Canada.
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.
Nye P H and Spiers J A 1964 Simultaneous diffusion and mass flow to plant roots. Trans. Int. Congr. Soil Sci. 8th. 31 Aug.–9 Sept. 1964. pp 535–541. Rompresfilatelia, Bucharest, Hungary.
Nye P H and Tinker P B 1977 Solute movement in the soil-root system. Blackwell Scientific, Oxford, UK.
Olsen S R, Kemper W D and Jackson R D 1962 Phosphate diffusion to plant roots. Soil Sci. Soc. Am. Proc. 26, 222–227.
Rastetter E B and Shaver G R 1992 A model of multiple-elelment limitation for acclimating vegetation. Ecol. 73, 1157–1174.
Rengel Z 1993 Mechanistic simulation models of nutrient uptake: a review. Plant and Soil 152, 161–173.
Rengel Z and Robinson D L 1990 Modeling magnesium uptake from an acid soil: I. Nutrient relationships at the soil-root interface. Soil Sci. Soc. Am. J. 54, 785–791.
Sanders F E, Tinker P B and Nye P H 1970 Uptake of solutes by multiple root systems from soil. I. An electrical analogue of diffusion to root systems. Plant and Soil 34, 453–466.
Schenk M K and Barber S A 1979 Phosphate uptake by corn as affected by soil characteristics and root morphology. Soil Sci. Soc. Am. J. 43, 880–883.
Seeling B and Claassen N 1990 A method for determining Michaelis-Menten kinetic parameters of nutrient uptake for plants growing in soil. Z. Pflanzenernahr. Bodenkd. 153, 301–303.
Silberbush M and Barber S A 1983 Sensitivity analysis of parameters used in simulating K uptake with a mechanistic mathematical model. Agron. J. 75, 851–854.
Smethurst P J, Comerford N B and Neary D G 1993 Predicting the effects of weeds on K and P uptake by young slash pine on a Spodosol. For. Ecol. Manage. 60, 27–39.
Van Heerden C and Yanai R D 1995 Effects of stresses on forest growth in models applied to the Solling spuce site. Ecol. Model. 83, 273–282.
Van Rees K C J and Comerford N B 1990 The role of woody roots of slash pine seedlings in water and potassium absorption. Can. J. For. Res. 20, 1183–1191.
Yanai R D 1991 Soil solution phosphorus dynamics in a whole-tree-harvested northern hardwood forest. Soil Sci. Soc. Am. J. 55, 1746–1752.
Yanai R D 1994 A steady-state model of nutrient uptake accounting for newly grown roots. Soil Sci. Soc. Am. J. 58, 1562–1571.
Yanai R D, Fahey T J and Miller S L 1995 Efficiency of nutrient acquisition by fine roots and mycorrhizae. In Resource physiology of conifers. Eds. W K Smith and T M Hinckley. pp 75–103. Academic Press, New York, USA.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Williams, M., Yanai, R.D. Multi-dimensional sensitivity analysis and ecological implications of a nutrient uptake model. Plant Soil 180, 311–324 (1996). https://doi.org/10.1007/BF00015315
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00015315