University of California

Phosphate fluxes in the soil-plant system: A computer simulation


K. R. Helyar
D. N. Munns

Authors Affiliations

K. R. Helyar was Research Assistant, Department of Soils and Plant Nutrition, University of California, Davis, California. Present address: Agricultural Research Centre, Wollongbar, New South Wales, 2480, Australia; D. N. Munns was Associate Professor of Soil Science, Department of Soils and Plant Nutrition, University of California, Davis.

Publication Information

Hilgardia 43(4):103-130. DOI:10.3733/hilg.v43n04p103. May 1975.

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The kinetics of phosphate reaction in soil were simulated by means of the computer language IBM S/360 continuous systems modeling program (CSMP). The model includes parameters of intensity, capacity, and buffer capacity. Predicted changes in solution phosphate concentration following addition of various levels of calcium phosphate agreed with experimentally determined changes.

A separate model segment simulating uptake by plants was interfaced with the CSMP soil model. This segment uses standard numerical integration techniques, prepared in Fortran. It takes into account the convection and diffusion of phosphate to the root, the extension rate and radius of roots, length of root hairs, effect of solution phosphate concentration and root age on absorption, variation in slope of the sorption isotherm with phosphate concentration, and diurnal variation in transpiration rate.

Simulations have been run with several parameters varied over their natural range as observed in experiments with clover or recorded in the literature. The output of these simulations indicates that root extension, the soil’s diffusion coefficient, and slope of the sorption isotherm have most influence, and that root hair length has less influence and root radius little. Convection contributed negligibly to computed uptake, but direct absorption from the root hair cylinder can be significant.

The most important assumptions which bear on the use of the model in its current state appear to be: i)

that within the root-hair cylinder neither diffusion nor desorption rates are limiting.


that uptake constants for the individual root segment decline as the segment ages in a characteristic manner (about which little is known).


that except by removing phosphate, the root does not significantly alter soil properties in the rhizosphere (including moisture content), so that diffusion coefficients and buffer capacities measured in bulk soil samples are applicable.


that the contribution of mycorrhizal associations to uptake is not important.

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Helyar K, Munns D. 1975. Phosphate fluxes in the soil-plant system: A computer simulation. Hilgardia 43(4):103-130. DOI:10.3733/hilg.v43n04p103
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