Root architecture modelling in heterogeneous soils How do root systems respond to environmental stresses Since the 1950s crops were bred for high-input agroecosystems which led to extensive use of fertilizers. This resulted in environmental problems and high production costs. Nowadays, breeding crops with high plant productivity, but also minimizing the impacts on the sustainability of low-input agroecosystems becomes increasingly important. In such breeding programmes the root architecture is crucial for the selection process, since architectural, morphological, anatomical and physiological root traits influence plant nutrient and water uptake. A deeper knowledge of the growing root system and its dynamic rhizosphere will enable us to determine suitable root system traits as selection criteria in crop breeding. In this project we will focus on water and phosphate uptake under different environmental stresses. This major inputs for crop productivity will gain even more significance considering the higher frequencies of droughts due to climate change and increased fertilizer costs due a upcoming phosphate crisis. We will focus on the following research questions: (1) In which way does the root system adapt to water and phosphate availability, and how can root architecture models be extended to implement integral root system responses? (3) How can this be integrated into the soil environment, and how can appropriate sink terms be developed? (4) Can root uptake and resource efficiency be understood as an optimization process? The project will be conducted in close collaboration between mathematical modellers and experts for rhizosphere processes, water management and plant breeding. Mathematical modelling will enhance the general understanding of rhizosphere processes, including root growth dynamics. We will systematically analyse root traits in heterogeneous soil environments using mathematical modelling supported by experimental observations. The mathematical modelling will be initially done on single root scale where relevant processes are described in a mechanistic way using partial differential equations. In a second step root system models are developed from the single root scale using up-scaling techniques such as homogenisation and averaging. Experiments will include X-ray computer microtomographic imaging to gain insight in three dimensional root system architecture development. The new root architecture model will be combined with a sub-model simulating aboveground demand (leaf gas exchange, P-demand). The complete model will be validated using soil column experiments. The project will be beneficial for managing plant nutrition and irrigation and will facilitate the integration of root research methods into the frame of breeding programs. Thereby project findings will encourage the use of root architecture traits in future crop improvement efforts.