Mathematical modeling is an important tool in rhizosphere research. Considering that root system and rhizosphere traits govern plant resource efficiency, accurate modeling of nutrient uptake is an important challenge in the light of upcoming shortages of mineral fertilizers and climate change. We present a three-dimensional model for phosphate uptake by a growing and exuding root system. The model is able to predict the influences of gravitropism under geometrical constraints like in pot or rhizotron experiments. In this way it is possible to directly compare the simulated case study to the real experiment. Two specific scales are considered. On the single root scale, we derive a model that describes the transport and competitive sorption of P and citrate in soil. On the whole root system scale, we use this model together with a root growth model to calculate a sink term for P uptake by a growing root system in three dimensions. We show a simulation case study where the P uptake of a young oilseed rape (Brassica napus L. subsp. napus) root system growing in a rhizotron as effected by root exudation is investigated. Results suggest that young parts of the root system are responsible for most of the P uptake after 16 d. Thus the effect of exudation on P uptake is strongly dependent on the age distribution of the root system. By mathematical modeling we hope to increase insight into underlying processes and to provide a flexible tool for experimental design.

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