A mathematical model of plant nutrient uptake

Abstract

This thesis deals with the mathematical modelling of nutrient uptake by plant roots. It starts with the Nye-Tinker-Barber model for nutrient uptake by a single bare cylindrical root. The model is treated using matched asymptotic expansion and an analytic formula for the rate of nutrient uptake is derived for the first time. The basic 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 are 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 models clearly show that the "volume averaging of branching structure" technique commonly used to extend the Nye-Tinker-Barber with experiments can lead to large errors. The same models also indicate that in the absence of large-scale water movement, due to rainfall, fertiliser fails to penetrate into the soil. This motivates us to build a model for water movement and uptake by branched root structures. This model considers the simultaneous flow of water in the soil, uptake by the roots, and flow within the root branching network to the stems of the plant. The water uptake model 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. Finally we present a model for the simultaneous movement and uptake of both nutrients and water. This is discussed as a new tool for interpreting available experimental results and designing future experiments. The parallels between evolution and mathematical optimisation are also discussed.

Recovering Root System Traits Using Image Analysis Exemplified by Two-Dimensional Neutron Radiography Images of Lupine

“…Thus, the node points assigned in this area are questionable. Second, the algorithm does not (Roose et al, 2001), and this has been confirmed by our analysis. The resulting root system has a maximum root order of four; however, most of the roots belong to orders zero to three.…”

Modeling Phosphorus Capture by Plants Growing in a Multispecies Riparian Buffer

“…These observations are consistent with the findings from several studies, as summarized by Hinsinger et al [10], which attribute the formation of similar gradients to the relatively slow diffusion rate of P through the soil to the root surface with little or no contribution attributable to mass flow. However, Roose et al [31] suggest that the numerical solution used in the NST 3.0 model has limitations when describing more complex roots systems. To address this concern, Roose and Kirk [32] explored the use of a simplified analytical solution that would more fully allow for both convection and diffusion.…”

Modelling Nutrient Uptake by Individual Hyphae of Arbuscular Mycorrhizal Fungi: Temporal and Spatial Scales for an Experimental Design

“…On the other hand, if the hypha were growing in a (soil) matrix with pores much smaller than the hyphal radius, the model would reduce to the situation of a continuum soil which is mostly the case for plant roots. For this situation, there exists an approximate analytical solution as detailed in Roose et al (2001). However, this model is based on the following assumptions that represent simplification of the real soil system:…”