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Abstract Plant growth and high yields are secured by intensive use of nitrogen (N) fertilizer, which, however, pollutes the environment, especially when N is in the form of nitrate. Ammonium is oxidized to nitrate by nitrifiers, but roots can release biological nitrification inhibitors (BNIs). Under what conditions does root-exudation of BNIs facilitate nitrogen N uptake and reduce pollution by N loss to the environment? We modeled the spatial–temporal dynamics of nitrifiers, ammonium, nitrate, and BNIs around a root and simulated root N uptake and net rhizosphere N loss over the plant’s life cycle. We determined the sensitivity of N uptake and loss to variations in the parameter values, testing a broad range of soil–plant-microbial conditions, including concentrations, diffusion, sorption, nitrification, population growth, and uptake kinetics. An increase in BNI exudation reduces net N loss and, under most conditions, increases plant N uptake. BNIs decrease uptake in the case of (1) low ammonium concentrations, (2) high ammonium adsorption to the soil, (3) rapid nitrate- or slow ammonium uptake by the plant, and (4) a slowly growing or (5) fast-declining nitrifier population. Bactericidal inhibitors facilitate uptake more than bacteriostatic ones. Some nitrification, however, is necessary to maximize uptake by both ammonium and nitrate transporter systems. An increase in BNI exudation should be co-selected with improved ammonium uptake. BNIs can reduce N uptake, which may explain why not all species exude BNIs but have a generally positive effect on the environment by increasing rhizosphere N retention.

Considering the rhizosphere microbes easily affected by the environmental factors, we formulate a three-dimensional diffusion model of the rhizosphere microbes with the impulsive feedback control to describe the complex degradation and movement by introducing beneficial microbes into the plant rhizosphere. The sufficient conditions for existence of the order-1 periodic solution are obtained by using the geometrical theory of the impulsive semi-dynamical system. We show the impulsive control system tends to an order-1 periodic solution if the control measures are achieved. Furthermore, we investigate the stability of the order-1 periodic solution by means of a novel method introduced in the literature [Y. Ye, The Theory of the Limit Cycle, Shanghai Science and Technology Press, 1984.]. Finally, mathematical results are justified by some numerical simulations.

In models of water flow in soil and roots, differences in the soil hydraulic properties of the rhizosphere and the bulk soil are usually neglected. There is, however, strong experimental evidence that rhizosphere and bulk soil hydraulic properties differ significantly from each other due to various root-soil interaction processes. Two such processes, which can also influence each other, are rhizosphere loosening or compaction and mucilage deposition. In this work, we identified realistic gradients in rhizosphere bulk density and mucilage concentration using X-ray CT imaging, respectively, model simulation for two different soil types and soil bulk densities and related them to soil hydraulic parameters. Using a 1D-single-root model, we then evaluated both the individual and combined effects of these gradients on soil water dynamics using scenario simulations. We showed that during soil drying, a lower rhizosphere bulk density leads to an earlier onset of water stress and to a reduced root water uptake that is sustained longer. The presence of mucilage led to a faster reduction of root water uptake. This is due to the stronger effect of mucilage viscosity on hydraulic conductivity compared to the mucilage- induced increase in water retention. Root water uptake was rapidly reduced when both mucilage and rhizosphere bulk density gradients were considered. The intensity of the effect of gradients in rhizosphere bulk density and mucilage concentration depended strongly on the interplay between initial soil hydraulic conditions, soil type and soil bulk densities. Both gradients in rhizosphere bulk density and mucilage concentration appear as a measure to sustain transpiration at a lower level and to avoid fast dehydration.

Considering the rhizosphere microbes easily affected by the environmental factors, we formulate a three-dimensional diffusion model of the rhizosphere microbes with the impulsive feedback control to describe the complex degradation and movement by introducing beneficial microbes into the plant rhizosphere. The sufficient conditions for existence of the order-1 periodic solution are obtained by using the geometrical theory of the impulsive semi-dynamical system. We show the impulsive control system tends to an order-1 periodic solution if the control measures are achieved. Furthermore, we investigate the stability of the order-1 periodic solution by means of a novel method introduced in the literature [Y. Ye, The Theory of the Limit Cycle, Shanghai Science and Technology Press, 1984.]. Finally, mathematical results are justified by some numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: One of the main problems when introducing beneficial microbes to the plant rhizosphere is that the plant growth promoting rhizobacteria (PGPR) do not survive or do not execute their specific function. The goal of our research was to evaluate microbial inoculant survival in rhizospheres, using mathematical modeling and computer-based simulations. We tested several abiotic factors effects on PGPR survival: the availability of soluble organic compounds and molecular oxygen, and the concentration of mineral nitrogen in soil. The principal biotic factors considered were the direct and indirect interactions between PGPR and resident microorganisms, protozoan predation, and bacterial parasitism. A model system of four non-linear ordinary differential equations was developed to simulate the growth of PGPR populations in the rhizosphere. Simulation results indicated that the competition for limiting resources between the introduced population and the resident microorganisms was the most important factor determining PGPR survival. The most effective PGPR inoculation was expected in organic and mineral poor soils or stressed soils, when development of the resident microflora was inhibited. Another important factor for PGPR survival was compatibility between the composition of the host plant root exudates, and ability of the PGPR to utilize those compounds. [Copyright &y& Elsevier]

ECOPHYS, an individual-based process model for poplar, requires a three-dimensional soil water redistribution model to simulate soil water dynamics, plant uptake, and root growth. SOILPSI is a potential-driven water redistribution model based on the RHIZOS rhizosphere simulator. It expands on RHIZOS by calculating water flux based on water potential, and has a macropore flow mode to allow rapid drainage of the soil. SOILPSI simulates water flux in three dimensions and accounts for slope. SOILPSI was evaluated by comparing model output to soil moisture data collected under bare soil conditions. AMMI analysis of a date×depth matrix of differences between simulated and observed soil moisture content showed that excluding the two shallowest soil layers resulted in a difference matrix that conformed to an additive model. The grand mean predicted values were within 2% of the observed values, and 50 of 56 predicted values were within 5% of the observed values. Better agreements between simulated and observed soil moisture content were observed deeper in the soil profile and later in the season. Agreement between SOILPSI and field conditions was consistently more accurate than RHIZOS. Improving simulation of evaporative flux at the soil surface would improve simulation accuracy in the upper horizons. [Copyright &y& Elsevier]