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.

Abstract. This review will outline a number of illustrative mathematical models describing the growth of avascular tumors. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modeling of avascular tumor development are outlined together with a list of key questions.

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Background and aimRecycled sources of phosphorus (P), such as struvite extracted from wastewater, have potential to substitute for more soluble manufactured fertilisers and help reduce the long-term threat to food security from dwindling finite reserves of phosphate rock (PR). This study aimed to determine whether struvite could be a component of a sustainable P fertiliser management strategy for arable crops.MethodsA combination of laboratory experiments, pot trials and mathematical modelling of the root system examined the P release properties of commercial fertiliser-grade struvite and patterns of P uptake from a low-P sandy soil by two different crop types, in comparison to more soluble inorganic P fertilisers (di-ammonium phosphate (DAP) and triple super phosphate (TSP)).ResultsStruvite had greatly enhanced solubility in the presence of organic acid anions; buckwheat, which exudes a high level of organic acids, was more effective at mobilising struvite P than the low level exuder, spring wheat. Struvite granules placed with the seed did not provide the same rate of P supply as placed DAP granules for early growth of spring wheat, but gave equivalent rates of P uptake, yield and apparent fertiliser recovery at harvest, even though only 26 % of struvite granules completely dissolved. Fertiliser mixes containing struvite and DAP applied to spring wheat have potential to provide both optimal early and late season P uptake and improve overall P use efficiency.ConclusionsWe conclude that the potential resource savings and potential efficiency benefits of utilising a recycled slow release fertiliser like struvite offers a more sustainable alternative to only using conventional, high solubility, PR-based fertilisers.Electronic supplementary materialThe online version of this article (doi:10.1007/s11104-015-2747-3) contains supplementary material, which is available to authorized users.