Abstract

Multiscale modelling of plant nutrient uptake

In this talk I will present a mathematical model for plant nutrient uptake from the soil. As a starting point I will consider the Nye-Tinker-Barber model for nutrient uptake by a single bare cylindrical root. I will then present some of the analysis of this model culminating with the derivation of the analytic formula for nutrient flux into the root. The basic “bald root” model is then extended to include root hairs and mycorrhizae, which have been found experimentally to be very important for the uptake of immobile nutrients. Again, analytic expressions for nutrient uptake can be derived. The simplicity and clarity of the analytical formulae for the solution of the single root models allows the extension of these models to more realistic branched roots. These root system models can be used to show that the volume averaging of the branching structure, a commonly used technique for translating results from single root scale to root system scale, can lead to large errors. The next step in developing the modelling is to include water movement and uptake. The water uptake model that we have developed shows that the water saturation can develop pseudo-steadystate wet and dry zones in the rooting region of the soil. The dry zone is shown to stop the movement of nutrient from the top of the soil to the groundwater.