ROOTMAP—a model in three-dimensional coordinates of the growth and structure of fibrous root systems

A model is described which simulates the growth of fibrous root systems. The root growth is specified in terms of growing time, numbers of axes, initiation times of axes, growth rates and branching characteristics of the roots, and characteristics governing the direction of root growth. The model generates a representation of the root system in which the locations of all branches and root tips are recorded in three-dimensional coordinates, and updates this representation in discrete time steps until the specified growing time is reached. Data are presented from a simulation of wheat root growth by the model. The simulated root system is represented pictorially and also graphically in the form of root length and root tip number profiles which are stratified by branching order class. The pictorial representations produced by the model are much more realistic than any which have been produced by past root growth models, and the graphical representations show trends in root length and root tip numbers which are the same as those commonly observed in real roots.     

Growth and development of root systems: Geometrical and structural aspects

The agronomist who wants to study the nutrient and water uptake of roots needs a quantitative three-dimensional dynamic model of the structure of root systems.The model presented takes into account current knowledge about the morphogenesis of root systems. It describes the root system as a set of root axes, characterised by their orders. The morphogenetic properties of root axes differ according to their order. The axes of order 1 are directly inserted on the stem, the axes of order 2 are inserted on axes of order 1, and so on. They tend to be more plagiotropec and to have less vascular bundles as the order increases.The evolution of the simulated structure is achieved by three processes: emission of new root axes from the shoot, growth and branching of existing root axes. The elongation of an axis depends on its order and on local growing conditions. Branches appear acropetally at a specified distance from the apex and from former branches, along ranks facing xylem poles, with a branching angle specific of their order.From the three-dimensional branched structures simulated by the model, various outputs, such as kinetics of growth and development, root profiles or cross-section maps can be computed, compared to observed data and used as inputs in uptake models. Some examples of such possible outputs are presented.

---

Résumé L'agronome qui veut étudier l'absorption hydrique et minérale des racines a besoin d'un modèle dynamique tri-dimensionnel de la structure du système racinaire.Le modèle présentd est fondé sur les connaissances actuelles sur la morphogenèse racinaire. Le système racinaire y est représenté comme un ensemble d'axes caractérisés par leur ordre. En effet, les propriétés morphogénétiques des racines varient d'un ordre d l'autre. Les axes d'ordre 1 sont insérés directement sur la tige, les axes d'ordre 2 sur les axes d'ordre 1, et ainsi de suite. Les axes tendent à être de plus en plus plagiotropes et à avoir de moins en moins de faisceaux vasculaires quand l'ordre augmente.Trois processus interviennent pour faire évoluer la structure racinaire simulée au cours du temps: l'émission de nouveaux axes racinaires à partir des tiges, la croissance, et la ramification des axes

     

Why are laterals less affected than main axes by homogeneous unfavourable physical conditions? A model-based hypothesis

When plants develop in strong soils, growth of the root system is generally depressed. However, branching and elongation of branches are often less affected than growth of the main axes, whenever the whole root system encounters even-impeded conditions. On the basis of a model simulating root growth and architecture as related to assimilate availability, we propose a simple hypothesis to explain such behaviour. In the model, growth of each root depends on its own elongation potential, which is estimated by its apical diameter. The potential elongation rate–apical diameter relationship is the same for all the roots of the system and is described by a monomolecular function. Our hypothesis is that the effect of soil strength can be simulated by introducing an impedance factor in the definition of root maximum potential elongation rate, common to the whole root system. When such impedance factor is applied, it affects more the potential of larger roots (main axes) than that of thinner roots (secondary and tertiary branches). Simulations provided in high impedance conditions led to root systems characterised by short taproots, whereas growth of secondary roots was unaffected and growth of tertiary roots was enhanced. Actual branching density was also higher, although branching rules have been unchanged. Such simulated systems where similar to that observed in strong soils. Friction laws or pore size can be involved in the larger reduction of the potential growth of main axes. Moreover, when growth of main axes is restricted, assimilate availability becomes higher for branches and that could explain that their growth could be increased in a homogeneous strong soil. This revised version was published online in June 2006 with corrections to the Cover Date.     

Architectural analysis and modelling of the branching process of the young oil-palm root system

An architectural analysis of the root system of young oil-palm (Elaeis guineensis Jacq.) seedlings was made. In this analysis, root branching was modelled by a Markov chain (discrete-time, discrete-state space stochastic process). This study has been realized on radicles of young oil-palm seedlings which were considered as main axes which branch. We defined an elementary length unit as the smallest length between two successive lateral roots. The model was based on the analysis of a sequence of events, each event being indexed by the rank of the elementary length unit on the main axis. An event was defined as the state of the length unit, chosen between unbranched state and three branched-state categories. The branching process of the oil-palm radicle was modelled by a four-state first-order Markov chain. Consequently, the state of an elementary length unit depended only on the state of the previous one. The Markov chain was homogeneous, i.e. the transition probabilities did not depend on the rank of the elementary length unit.This study allowed us to identify a probabilistic model of root branching which was the first step in the elaboration of a stochastic model of the architecture of the oil-palm root system.     

Fractal analysis of the root architecture of Gliricidia sepium for the spatial prediction of root branching,size and mass: model development and evaluation in agroforestry

Based on fractal and pipe model assumptions, a static three-dimensional model of the Gliricidia sepium root system was developed, in order to provide a basis for the prediction of root branching, size and mass in an alley cropping system. The model was built from observations about the topology, branching rules, link length and diameter, and root orientation, provided by in situ and extracted root systems. Evaluation tests were carried out at the plant level and at the field level. These tests principally concerned coefficients α and q –- the proportionality factor α between total cross-sectional area of a root before and after branching, and allocation parameter q that defines the partitioning of biomass between the new links after a branching event –- that could be considered as key variables of this fractal approach. Although independent of root diameter, these coefficients showed a certain variability that may affect the precision of the predictions. When calibrated, however, the model provided suitable predictions of root dry matter, total root length and root diameter at the plant level. At the field level, the simulation of 2D root maps was accurate for root distribution patterns, but the number of simulated root dots was underestimated in the surface layers. Hence recommendations were made to improve the model with regard to α and q. This static approach appeared to be well suited to study the root system of adult trees. Compared with explicit models, the main advantage of the fractal approach is its plasticity and ease of use. This revised version was published online in June 2006 with corrections to the Cover Date.     

A density-based approach for the modelling of root architecture: application to Maritime pine (Pinus pinaster Ait.) root systems

Root morphology influences strongly plant/soil interactions. However, the complexity of root architecture is a major barrier when analysing many phenomena, e.g. anchorage, water or nutrient uptake. Therefore, we have developed a new approach for the representation and modelling of root architecture based on branching density. A general root branching density in a space of finite dimension was used and enabled us to consider various morphological properties. A root system model was then constructed which minimizes the difference between measured and simulated root systems, expressed with functions which map root density in the soil. The model was tested in 2D using data from Maritime pine Pinus pinaster Ait. structural roots as input. We showed that simulated and real root systems had similar root distributions in terms of radial distance, depth, branching angle and branching order. These results indicate that general density functions are not only a powerful basis for constructing models of architecture, but can also be used to represent such structures when considering root/soil interaction. These models are particularly useful in that they provide a local morphological characterization which is aggregated in a given unit of soil volume.     

Evaluation in field conditions of a three-dimensional architectural model of the maize root system: Comparison of simulated and observed horizontal root maps

Most existing water and nutrient uptake models are based on the assumption that roots are evenly distributed in the soil volume. This assumption is not realistic for field conditions, and significantly alters water or nutrient uptake calculations. Therefore, development of models of root system growth that account for the spatial distribution of roots is necessary.The objective of this work was to test a three dimensional architectural model of the maize root system by comparing simulated horizontal root maps with observed root maps obtained from the field. The model was built using the current knowledge on maize root system morphogenesis and parameters obtained under field conditions. Simulated root maps (0.45 × 0.75 m) of horizontal cross sections at 3 depths and 3 dates were obtained by using the model for a plant population. Actual root maps were obtained in a deep, barrier-free clay-loamy soil by digging pits, preparing selected horizontal planes and recording root contacts on plastic sheets.Results showed that both the number of cross-sections of axile roots, and their spatial distribution characterized with the R-index value of Clark and Evans (1954), were correctly accounted for by the model at all dates and depths. The number of cross-sections of laterals was also correctly predicted. However, laterals were more clustered around axile roots on simulated root maps than on observed root maps. Although slight discrepancies appeared between simulated and observed root maps in this respect, it was concluded that the model correctly accounted for the general colonization pattern of the soil volume by roots under a maize crop.     

Fine root architecture, morphology, and biomass of different branch orders of two Chinese temperate tree species

We have limited understanding of architecture and morphology of fine root systems in large woody trees. This study investigated architecture, morphology, and biomass of different fine root branch orders of two temperate tree species from Northeastern China—Larix gmelinii Rupr and Fraxinus mandshurica Rupr —by sampling up to five fine root branch orders three times during the 2003 growing season from two soil depths (i.e., 0–10 and.10–20 cm). Branching ratio (R _b) differed with the level of branching: R _b values from the fifth to the second order of branching were approximately three in both species, but markedly higher for the first two orders of branching, reaching a value of 10.4 for L. gmelinii and 18.6 for F. mandshurica. Fine root diameter, length, SRL and root length density not only had systematic changes with root order, but also varied significantly with season and soil depth. Total biomass per order did not change systematically with branch order. Compared to the second, third and/or fourth order, the first order roots exhibited higher biomass throughout the growing season and soil depths, a pattern related to consistently higher R _b values for the first two orders of branching than the other levels of branching. Moreover, the differences in architecture and morphology across order, season, and soil depth between the two species were consistent with the morphological disparity between gymnosperms and angiosperms reported previously. The results of this study suggest that root architecture and morphology, especially those of the first order roots, should be important for understanding the complexity and multi-functionality of tree fine roots with respect to root nutrient and water uptake, and fine root dynamics in forest ecosystems.     

Root System Development of Oak Seedlings Analysed using an Architectural Model. Effects of Competition with Grass

A dynamic 3D model of root system development was adapted to young sessile oak seedlings, in order to evaluate the effects of grass competition on seedling root system development. The model is based on a root typology and the implementation of a series of developmental processes (axial and radial growth, branching, reiteration, decay and abscission). Parameters describing the different processes are estimated for each root type. Young oak seedlings were grown for 4 years in bare soil or with grass competition and were periodically excavated for root system observation and measurements (topology of the root system, length and diameter of all roots with a diameter greater than 0.3 mm). In the fourth year, 40 cm×20 cm×20 cm soil monoliths were excavated for fine root measurement (root density and root length). Root spatial development was analysed on a sub-sample of roots selected on four seedlings. The model was a guideline that provided a complete and consistent set of parameters to represent root system development. It gave a comprehensive view of the root systems and made it possible to quantify the effects of competition on the different root growth processes. The same root typology was used to describe the seedlings in bare soil and in grass. Five root types were defined, from large tap roots to fine roots. Root system size was considerably reduced by grass competition. Branching density was not affected but the branch roots were always smaller for the seedlings grown in competition. Reiteration capacity was also reduced by competition. Cross sectional areas before and after branching were linearly related with a scaling coefficient close to 1, as predicted by the pipe model theory. This relationship was not affected by grass competition.     

The position and growth of lateral roots on cultured root axes of tomato,Lycopersicon esculentum (Solanaceae)

Root axes of tomato (Lycopersicon esculentum) were cultured in vitro in three different concentrations of sucrose in order to vary their growth rate. Lateral root growth and the initiation of lateral root primordia were studied on each group of axes. Various aspects of primordium initiation, positioning, and emergence were quantified with a view to discovering variable and constant features of these processes. Variable parameters were the rate and frequency of root primordium emergence. Constant parameters, at least under the prevailing conditions, were the spacing between successive laterals and primordia, and the position of the primordia in relation to the vascular system. A model of primordium initiation is presented which combines controls determined by the divisional history of the potential primordium cell and by the vascular pattern.Dedicated with great respect to Prof. DrElisabeth Tschermak-Woess on the occasion of her 70th birthday in recognition of her distinguished contributions to cytology.     

A comparative study between two citrus rootstocks: Effect of nitrate on the root morpho-topology and net nitrate uptake

Root morpho-topology and net nitrate uptake of two citrus seedlings, Volkamer Lemon and Carrizo Citrange, grown at two nitrogen supplies (NO₃-N 5 M and 1000 M, respectively) were studied. Root morphological and topological parameters were gauged by an image-specific analysis system (WinRHIZO). Net nitrate uptake was estimated using the nitrate depletion method. The main findings showed that Carrizo seedlings had a dichotomous branching root system characterized by high root tip numbers and long 2^nd order lateral roots. Conversely, Volkamer root systems had a herringbone structure with a long tap root and 1^st order lateral root. Nitrate treatment did not seem to affect the pattern of the two genotypes, except for the 2^nd order lateral roots (Carrizo more than Volkamer) and root/shoot ratio and root mass ratio (Volkamer more than Carrizo) that were significantly different at low nitrate supply. Nitrate treatments induced a diverse net nitrate uptake regulation between citrus rootstocks. Indeed, at low nitrate supply, Carrizo showed a more efficient nitrate acquisition process in terms of: 1) higher net nitrate uptake maximum of the inducible high affinity transport system or full induction (A), (2) higher cumulative nitrate uptake (A_t) and (3) lower t₁ parameter defined as the half time of the net nitrate uptake rate of the inducible transport system during the induction phase, compared to Volkamer. Conversely, at the high nitrate level, only the genotypical difference of the t₁ parameter was maintained. The results suggested that, at the low nitrate level, the morphological root traits such as higher 2^nd order lateral roots and greater root tip numbers of the Carrizo compared with Volkamer seedlings, enhance the capacity to absorb nitrate from nutrient solution.     

Comparing different approaches to calculate the effects of heterogeneous root distribution on nutrient uptake: a case study on subsoil nitrate uptake by a barley root system

Simulation models of nutrient uptake of root systems starting with one-dimensional single root approaches up to complex three-dimensional models are increasingly used for examining the interacting of root distribution and nutrient uptake. However, their accuracy was seldom systematically tested. The objective of the study is to compare one-dimensional and two-dimensional modelling approaches and to test their applicability for simulation of nutrient uptake of heterogeneously distributed root systems giving particular attention to the impact of spatial resolution. Therefore, a field experiment was carried out with spring barley (Hordeum vulgare L. cv. Barke) in order to obtain data of in situ root distribution patterns as model input. Results indicate that a comparable coarse spatial resolution can be used with sufficient modelling results when a steady state approximation is applied to the sink cells of the two-dimensional model. Furthermore, the accuracy of the model was clearly improved compared to a simple zero sink approach assuming both near zero concentrations within the sink cell and a linear gradient between the sink cell and its adjacent neighbours. However, for modelling nitrate uptake of a heterogeneous root system a minimum number of grid cells is still necessary. The tested single root approach provided a computational efficient opportunity to simulate nitrate uptake of an irregular distributed root system. Nevertheless, two-dimensional models are better suited for a number of applications (e.g. surveys made on the impact of soil heterogeneity on plant nutrient uptake). Different settings for the suggested modelling techniques are discussed.     

Transient three-dimensional modeling of soil water and solute transport with simultaneous root growth,root water and nutrient uptake

A three-dimensional solute transport model was developed and linked to a three-dimensional transient model for soil water flow and root growth. The simulation domain is discretized into a grid of finite elements by which the soil physical properties are spatially distributed. Solute transport modeling includes passive and active nutrient uptake by roots as well as zero- and first-order source/sink terms. Root water uptake modeling accounts for matric and osmotic potential effects on water and passive nutrient uptake. Root age effects on root water and nutrient uptake activity have been included, as well as the influence of nutrient deficiency and ion toxicity on root growth. Examples illustrate simulations with different levels of model complexity, depending on the amount of information available to the user. At the simplest level, root growth is simulated as a function of mechanical soil strength only. Application of the intermediate level with root water and nutrient uptake simulates the influence of timing and amount of NO3 application on leaching. The most comprehensive level includes simulation of root and shoot growth as influenced by soil water and nutrient status, temperature, and dynamic allocation of assimilate to root and shoot.     

Modelling the interactions between water and nutrient uptake and root growth

A model of three-dimensional root growth has been developed to simulate the interactions between root systems, water and nitrate in the rooting environment. This interactive behaviour was achieved by using an external-supply/internal-demand regulation system for the allocation of endogenous plant resources. Data from pot experiments on lupins heterogeneously supplied with nitrate were used to test and parameterise the model for future simulation work. The model reproduced the experimental results well (R ² = 0.98), simulating both the root proliferation and enhanced nitrate uptake responses of the lupins to differential nitrate supply. These results support the use of the supply/demand regulation system for modelling nitrate uptake by lupins. Further simulation work investigated the local uptake response of lupins when nitrate was supplied to a decreasing fraction of the root system. The model predicted that the nitrate uptake activity of lupin roots will increase as the fraction of root system with access to nitrate decreases, but is limited to an increase of around twice that of a uniformly supplied control. This work is the first example of a modelled root system responding plastically to external nutrient supply. This model will have a broad range of applications in the study of the interactions between root systems and their spatially and temporally heterogeneous environment.     

Consequences of root growth kinetics and vascular structure on the distribution of lateral roots

It has been proposed that the acropetal initiation of lateral roots is a built‐in process specified as part of the general process of cell division and differentiation in the parent root tip. Conversely, it is commonly reported that root branching is essentially a variable feature. In the present study, the interlateral distance along the parent root has been investigated using three banana varieties (Musa spp.) grown in two substrates. The pattern of lateral root initiation was obscured by variations of root growth patterns and vascular structure among roots, genotypes and substrates. A framework model is formulated showing the influence of growth pattern and vascular structure on branching density. The model raises a distinction between growth components which should not affect the branching density (i.e. rate of cell division) and which may affect it (i.e. size of mature cells and number of transverse divisions performed by cells executing their trajectory in the meristem). It appears also that lateral root density and root growth rate might be independently modulated by appropriate changes of root growth patterns, in banana and presumably many other taxa.     

SimRoot: Modelling and visualization of root systems

SimRoot, a geometric simulation model of plant root systems, is described. This model employs a data structure titled the Extensible Tree, which is well suited to the type of data required to model root systems. As implemented on Silicon Graphics workstations, the data structure and visualization code provides for continuous viewing of the simulated root system during growth. SimRoot differs from existing models in the explicit treatment of spatial heterogeneity of physiological processes in the root system, and by inclusion of a kinematic treatment of root axes. Examples are provided of the utility of the model in estimating the fractal geometry of simulated root systems in 1, 2, and 3 dimensional space. We envision continued development of the model to incorporate competition from neighboring root systems, linkage with crop simulation models to simulate root-shoot interactions, explicit treatment of soil heterogeneity, and plasticity of root responses to soil factors such as presence of mycorrhizal associations.     

Geometrical properties of simulated maize root systems: consequences for length density and intersection density

The spatial distribution of root length density (RLD) is important because it affects water and nutrient uptake. It is difficult to obtain reliable estimates of RLD because root systems are very variable and heterogeneous. We identified systematic trends, clustering, and anisotropy as geometrical properties of root systems, and studied their consequences for the sampling and observation of roots. We determined the degree of clustering by comparing the coefficient of variation of a simulated root system with that of a Boolean model. We also present an alternative theoretical derivation of the relation between RLD and root intersection density (RID) based on the theory of random processes of fibres. We show how systematic trends, clustering and anisotropy affect the theoretical relation between RLD and RID, and the consequences this has for measurement of RID in the field. We simulated the root systems of one hundred maize crops grown for a thermal time of 600 K d, and analysed the distribution of RLD and root intersection density RID on regular grids of locations throughout the simulated root systems. Systematic trends were most important in the surface layers, decreasing with depth. Clustering and anisotropy both increased with depth. Roots at depth had a bimodal distribution of root orientation, causing changes in the ratio of RLD/RID. The close proximity of the emerging lateral roots and the parent axis caused clustering which increased the coefficient of variation.     

Modelling minirhizotron observations to test experimental procedures

In order to help design experiments with minirhizotrons or interpret data from such experiments, a modelling approach is a valuable tool to complement empirical approaches. The general principle of this modelling approach is to calculate and to study the part of a theoretical root system that is intersected by passes through a virtual minirhizotron tube (modelled here as a cylinder). Various outputs can be calculated from this part of the root system, and related to the surrounding root system which is perfectly known, since it has been simulated and stored in a data structure. Therefore, the method involves two levels of modelling that are presented and discussed: the root system architecture of a crop, and the observations that can be achieved with minirhizotron tubes. Illustrations of the method are presented to study the effect of several factors on the rooting depth curves, and to show how images may be calculated to mimic what can actually be viewed from inside the tube. These first results show that the maximum rooting depth curves, as virtually observed in the minirhizotron tube, present large variations and strongly underestimate the maximum rooting depth of the modelled root system (up to 60 cm in average). The underestimation is still more critical when the radius of the tube is lower than 3 cm, and when the tube is close to the vertical (angle lower than 0.2 rad). The use of the 0.9 quantile instead of the average value, for each of the observation dates, leads to a better estimation of the maximum rooting depth.     

A mathematical model for water and nutrient uptake by plant root systems

This article deals with modelling the simultaneous uptake of water and highly buffered nutrient, such as phosphate, by root branching structures from partially saturated soil. We use the simultaneous water and nutrient uptake model to investigate the effect that water movement has on nutrient uptake. With the aid of this model we are also able to show that the previous models by Barber and Tinker and Nye systematically underestimated the phosphate uptake, due to the oversimplified approach in dealing with root branching structure. In this article we show how this discrepancy can be remedied and the root branching structure included in the models of plant nutrient uptake. We will also discuss the differences in the results for continuous and spot fertilization combined with variable rainfall.     

Modelling zinc uptake by rice crop using a Barber-Cushman approach

The Barber-Cushman mechanistic nutrient uptake model which has been utilized extensively to describe and predict nutrient uptake by crop plants at different stages of crop growth was evaluated for its ability to predict the Zn uptake by rice seedlings. Uptake of the nutrient is, therefore, determined by the rate of nutrient supply to the root surface by mass flow and diffusion. Inter root competition and time dependent root density are accounted for by soil volume that delivers nutrients. The radii of these cylinders decline with increasing density. Since mass flow and diffusion each supply zinc to the root, the process can be described mathematically using the model of Barber-Cushman (1984). The 11 parameters of the model for the uptake by rice cultivars were measured by established experimental techniques. Zinc uptake at different growth stages predicted by the model was compared to measured zinc uptake by rice cultivars grown on sandy loam soil in a green house. Predicted zinc uptake was significantly correlated with observed uptake r ²=0.99^**. Sensitivity analysis was also used to investigate the impact of changes in soil nutrient supply, root morphological and root uptake kinetic parameters on simulated nutrient uptake. Overall results of sensitivity analysis indicate that the half distance between root axes, rate of root growth and water flux affect the uptake of zinc particularly at their higher values rather than at lower values and DaZn is the most sensitive parameter for zinc uptake at its lower values.