The remarkable complexity of soil and its importance to a wide range of ecosystem services presents major challenges to the modeling of soil processes. Although major progress in soil models has occurred in the last decades, models of soil processes remain disjointed between disciplines or ecosystem services, with considerable uncertainty remaining in the quality of predictions and several challenges that remain yet to be addressed. First, there is a need to improve exchange of knowledge and experience among the different disciplines in soil science and to reach out to other Earth science communities. Second, the community needs to develop a new generation of soil models based on a systemic approach comprising relevant physical, chemical, and biological processes to address critical knowledge gaps in our understanding of soil processes and their interactions. Overcoming these challenges will facilitate exchanges between soil modeling and climate, plant, and social science modeling communities. It will allow us to contribute to preserve and improve our assessment of ecosystem services and advance our understanding of climate-change feedback mechanisms, among others, thereby facilitating and strengthening communication among scientific disciplines and society. We review the role of modeling soil processes in quantifying key soil processes that shape ecosystem services, with a focus on provisioning and regulating services. We then identify key challenges in modeling soil processes, including the systematic incorporation of heterogeneity and uncertainty, the integration of data and models, and strategies for effective integration of knowledge on physical, chemical, and biological soil processes. We discuss how the soil modeling community could best interface with modern modeling activities in other disciplines, such as climate, ecology, and plant research, and how to weave novel observation and measurement techniques into soil models. We propose the establishment of an international soil modeling consortium to coherently advance soil modeling activities and foster communication with other Earth science disciplines. Such a consortium should promote soil modeling platforms and data repository for model development, calibration and intercomparison essential for addressing contemporary challenges.

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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.

CRootBox is a fast and flexible functional-structural root model that is based on state-of-the-art computational science methods. Its aim is to facilitate modelling of root responses to environmental conditions as well as the impact of roots on soil. In the future, this approach will be extended to the above-ground part of the plant.

Diversity in phosphorus (P) acquisition strategies was assessed among three species of arbuscular mycorrhizal fungi (AMF) isolated from a single field in Switzerland. Medicago truncatula was used as a test plant. It was grown in a compartmented system with root and root-free zones separated by a fine mesh. Dual radioisotope labeling ( 32 P and 33 P) was employed in the root-free zone as follows: 33 P labeling determined hyphal P uptake from different distances from roots over the entire growth period, whereas 32 P labeling investigated hyphal P uptake close to the roots over the 48 hours immediately prior to harvest. Glomus intraradices, Glomus claroideum and Gigaspora margarita were able to take up and deliver P to the plants from maximal distances of 10, 6 and 1 cm from the roots, respectively. Glomus intraradices most rapidly colonized the available substrate and transported significant amounts of P towards the roots, but provided the same growth benefit as compared to Glomus claroideum, whose Plant Soil (2011) 339:231-245 mycelium was less efficient in soil exploration and in P uptake and delivery to the roots. These differences are probably related to different carbon requirements by these different Glomus species. Gigaspora margarita provided low P benefits to the plants and formed dense mycelium networks close to the roots where P was probably transiently immobilized. Numerical modeling identified possible mechanisms underlying the observed differences in patterns of mycelium growth. High external hyphal production at the rootfungus interface together with rapid hyphal turnover were pointed out as important factors governing hyphal network development by Gigaspora, whereas nonlinearity in apical branching and hyphal anastomoses were key features for G. intraradices and G. claroideum, respectively.

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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.

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