A mathematical modeling of plant nutrient uptake
T. Roose (University of Oxford, UK)
In this talk I will present a hierarchy of models that enable the evaluation of the levels of nutrient and water uptake by branched root systems from partially saturated soil. In particular, the models take into account the simultaneous on uptake of highly buffered nutrients and water from the soil. First I will present a model for nutrient uptake by a single cylindrical root that will be non-dimensionalised and solved analytically (Roose et al. 2001). The second stage model treats water uptake and transport by the different subbranches in the root system (Roose&Fowler, 2004a). The main finding of the analysis is that some subbranches are less effective at taking up water and transporting to the shoots than main tap roots due to their anatomical structure. Finally, the root water uptake models will be combined with nutrient uptake models in order to evaluate nutrient concentration gradients in the soil (Roose&Fowler, 2004b). Using this final model I will show that previous models by Barber, Tinker and Nye can systematically underestimate the phosphate uptake, due to their oversimplified approach in dealing with root branching structure. I will show how this discrepancy can be remedied without the need for extensive three dimensional computer simulations. In particular, I will discuss how the rigorous application of the method of spatial averaging can give better estimates for phosphate uptake by field crops. Whilst the spatial averaging presented in Roose&Fowler (2004b) does introduce approximations, it does so without neglecting any necessary root structural effects.
ROOSE, T., FOWLER, A. C. & DARRAH, P. R. (2001) Mathematical model of plan nutrient uptake. Journal of Mathematical Biology 42, 347-360.
ROOSE, T. & FOWLER, A. C. (2004a) A model for water uptake by plants. Journal of Theoretical Biology 228, 155-171.
ROOSE, T. & FOWLER, A. C. (2004b) A mathematical model for water and nutrient uptake by roots. Journal of Theoretical Biology 228, 173-184.