Modelling the contribution of arbuscular mycorrhizal fungi to plant phosphate uptake

• In this paper, we investigate the role of arbuscular mycorrhizal fungi in plant phosphorus nutrition. We develop a mathematical model which quantitatively assesses the contribution of external fungal hyphae to plant phosphate uptake. • We derive an equation for solute uptake by a growing fungal mycelium which we couple with a model for root uptake. We analyse the model using nondimensionalization and numerical simulations. • Simulations predict that removal of phosphate from soil is dominated by hyphal uptake as opposed to root uptake. Model analysis shows that the depletion zones around hyphae overlap within 8 h and that the transfer between fungus and root is a critical step for the behaviour of phosphorus within the mycelial phase. We also show that the volume fraction of mycelium is negligibly small in comparison to other soil phases. • This is the first model to quantify the contribution of mycorrhizal fungi to plant phosphate uptake. A full data set for model parametrization and validation is not currently available. Therefore, more complete sets of experimental measurements are necessary to make this model more applicable.