Understanding the impact of roots and rhizosphere traits on plant resource efficiency is important, in particular in the light of upcoming shortages of mineral fertilizers and climate change with increasing frequency of droughts. We developed a modular approach to root growth and architecture modelling with a special focus on soil root interactions. The dynamic three-dimensional model is based on L-Systems, rewriting systems well-known in plant architecture modelling. We implemented the model in Matlab in a way that simplifies introducing new features as required. Different kinds of tropisms were implemented as stochastic processes that determine the position of the different roots in space. A simulation study was presented for phosphate uptake by a maize root system in a pot experiment. Different sink terms were derived from the root architecture, and the effects of gravitropism and chemotropism were demonstrated. This root system model is an open and flexible tool which can easily be coupled to different kinds of soil models.

Summary• Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but quantitative understanding of their role in this is weak. This limits, for example, the breeding of more nutrient-efficient crop genotypes.• We developed a mathematical model of nutrient transport and uptake in the root hair zone of single roots growing in soil or solution culture. Accounting for root hair geometry explicitly, we derived effective equations for the cumulative effect of root hair surfaces on uptake using the method of homogenization.• Analysis of the model shows that, depending on the morphological and physiological properties of the root hairs, one of three different effective models applies. They describe situations where: (1) a concentration gradient dynamically develops within the root hair zone; (2) the effect of root hair uptake is negligibly small; or (3) phosphate in the root hair zone is taken up instantaneously. Furthermore, we show that the influence of root hairs on rates of phosphate uptake is one order of magnitude greater in soil than solution culture.• The model provides a basis for quantifying the importance of root hair morphological and physiological properties in overall uptake, in order to design and interpret experiments in different circumstances.

Mathema cal modeling is an important tool in rhizosphere research. Considering that root system and rhizosphere traits govern plant resource effi ciency, accurate modeling of nutrient uptake is an important challenge in the light of upcoming shortages of mineral ferlizers 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 infl uences 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 specifi c scales are considered. On the single root scale, we derive a model that describes the transport and compe ve sorp on 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 simula on case study where the P uptake of a young oilseed rape (Brassica napus L. subsp. napus) root system growing in a rhizotron as eff ected by root exuda on is inves gated. Results suggest that young parts of the root system are responsible for most of the P uptake a er 16 d. Thus the eff ect of exuda on on P uptake is strongly dependent on the age distribu on of the root system. By mathema cal modeling we hope to increase insight into underlying processes and to provide a fl exible tool for experimental design. A. Schnepf, BOKU-Univ. of Natural Resources and Life Sciences Vienna, Dep. of Water, Air and Environment, Ins tute of Hydraulics and Rural Water Management, Muthgasse 18, A-1190 Vienna, Austria and BOKU-Univ. of Natural Resources and Life Sciences Vienna, Dep. of Forest and Soil Sciences, Ins t u t e o f S o i l R e s e a r c h , P e t e r J o r d a n S t r . 8 2 ,