In a fractai branching pattern the same rules govern branching at each subsequent level. The initial size (diameter) and the essential branching rules thus contain the information required to construct the whole pattern. If root branching patterns have fractal characteristics, measurement of the proximal root diameter at the stem base and the branching rules as observed anywhere in the root system, would be enough to predict total root length, root diameter distribution and root length per unit dry weight (specific root length).A 'pipe stem' model is used to derive algebraic relations between total root size and proximal root diameter for two classes of branching patterns, determinate and proportionate. To predict total root length from the proximal root diameter, at least information is needed on the minimum root diameter, the average length of internal and external links (segments) and the proportionality factor between total cross sectional areas before and after branching. For the length of the longest root or the specific root length further information on the branching rules is needed, as it is highest for determinate and proportionate branching rules, respectively. Abbreviations:CSA -cross sectional area.

Soils under intensive livestock farming and heavily fertilized with animal manure may have elevated soil phosphorus (P) contents. We determined P desorption kinetics in batch experiments using soils from a pot experiment where grass was cropped on a P‐rich noncalcareous sandy soil without P addition, to lower the soil P content. A diffusion model was used to describe P desorption kinetics from a spherical aggregate. The model was calibrated with data from the batch experiments. Simulation results show that in the pot experiment, P desorption from the solid phase of the inner layers was initially far from equilibrium with the rest of the aggregate, but desorption came closer to equilibrium as the soil P content decreased further. A simple tool is presented, referred to as the dynamic bioavailability index (DBI), to determine whether kinetics of P desorption limits plant uptake. This tool is the dimensionless ratio of the modeled maximal diffusive flux from soil aggregates to solution and the plant uptake rate measured in the pot experiment. The DBI was initially much larger than one; the maximal possible P desorption rate exceeded the uptake rate, so uptake was not limited by desorption. The DBI stabilized at a value somewhat larger than one after a while, due to soil transport limitations. This decrease coincided with a large decrease of the P content in the grass to a value (far) below what is considered as optimal; the supply rate of P from soil to the root cannot meet the demand needed for optimal P uptake. The DBI could be seen as a promising onset to a new dynamic approach of bioavailability.

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We compared four root water uptake (RWU) models of diff erent complexity that are all embedded in greater soil water fl ow models. The soil models used were SWAP (one-dimensional), FUSSIM2 (two-dimensional), and RSWMS (three-dimensional). Within SWAP, two RWU func ons were u lized (SWAP-macro and SWAP-micro). The complexity of the processes considered in RWU increases from SWAP-macro, to SWAP-micro, to FUSSIM2, to RSWMS. The objec ve of our study was to determine to what extent the RWU models diff ered when tested under extreme condi ons: low root length density, high transpira on rate, and low water content. Comparison 1 looked at the results of the models for a scenario of transpira on and uptake and Comparison 2 studied compensa on mechanisms of water uptake. The uptake scenario pertained to a long dry period with constant transpiraon and a single rainfall event. As could be expected, the models yielded diff erent results in Comparison 1, but the diff erences in cumula ve transpira on were modest due to various feedback mechanisms. In Comparison 2, the cumula ve eff ect of diff erent feedback processes were studied. Redistribu on of water due to soil pressure head gradients generated by water uptake led to an increase in cumula ve transpira on of 32%, and the inclusion of compensa on in uptake by the roots resulted in a further increase of 10%. Going from one-to three-dimensional modeling, the horizontal gradients in the soil and root system increased, which reduced the actual transpira on. The analysis showed that both soil physical and root physiological factors are important for proper determinis c modeling of RWU.Abbrevia ons: RWU, root water uptake.

A mathematical model was developed to describe carbon (C) and nitrogen (N) cycling in different soil types, e.g. clay and sandy soils. Transformation rates were described by first-order kinetics. Soil organic matter is divided into four fractions (including microbial biomass pool) and three fractions of residues. The fraction of active soil organic matter was assumed to be affected by the extent of physical protection within the soil, as was the soil microbial biomass. The extent of protection influenced the steady state level of the model, and, hence, the mineralization rates. The mineralization rate in fine-textured soils is lower than in coarse-textured soils; in fine-textured soils a larger proportion of the soil organic matter may be physically protected. The availability of organic materials as a substrate for microorganisms is not only determined by their chemical composition, but also by their spatial distribution in the soil. (Abstract retrieved from CAB Abstracts by CABI’s permission)