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In this paper we present a mathematical model for estimating external mycelium growth of arbuscular mycorrhizal fungi and its effect on root uptake of phosphate (P). The model describes P transport in soil and P uptake by both root and fungi on the single root scale. We investigate differences in soil P depletion and overall P influx into a mycorrhizal root by assuming that different spatial regions of mycelia are active in P uptake. When all external hyphae contribute to P uptake, overall uptake is dominated by the fungus and the most effective growth pattern appears to be the one using a high level of anastomosis. The same is true when only the proportion of external hyphae assumed to be active contributes to uptake. When uptake is restricted to the tips, hyphal contribution to overall P uptake is less dominant; the most effective growth pattern appears to be the one characterised by nonlinear branching where branching stops at a given maximal hyphal tip density. Comparison to measured P depletion in the literature suggests that the scenario where active hyphae are contributing to P uptake is likely to fit the data best. These quantitative predictions promote our understanding of the mycorrhizal symbiosis and its role in plant P nutrition.

Impact of growth and uptake patterns of arbuscular mycorrhizal fungi on plant phosphorus uptake—a modelling study