The rhizosphere is the influence-sphere of the root. It is a local ecosystem with complex functions that determine nutrient uptake, cycling of resources, and plant health. Mathematical models can quantitatively explain and help to understand rhizosphere complexity. To interpret model predictions and relevance of processes, we require understanding of the underlying concepts. Conceptualization of rhizosphere processes bridges mathematical modeling and experimental work and thus is key to understanding the rhizosphere.
We review concepts and assumptions foundational to the modeling of soil-plant-microorganism processes in the rhizosphere. Rhizosphere models are designed to simulate a plurality of components (solutes, substrates, and microorganisms). They specify components and interactions, drawing from the disciplines of soil science, botany, microbiology, and ecology. Solute transport models are applied to describe bioavailability in the rhizosphere. The root is typically a sink (e.g. nutrient uptake) or source (e.g. exudation) for one or more solutes. Microorganisms are usually described in time only, neglecting possible spatial movement. Interactions between components, e.g. chemical reactions and substrate-dependent bacterial growth rates, are usually described by coupling via reaction terms.
Rhizosphere models share concepts that we organized in a collective framework. This collective framework facilitates the development of new models. The interdisciplinary approach in which knowledge from soil ecology, botany, and soil physics are combined in rhizosphere models has proven fruitful for applications in plant and soil systems. We advocate multi-component-multi-interaction ecosystems around the root, with each component represented by an advection-diffusion-motility-reaction equation.