Daniel Leitner

Modelling root–soil interactions using three–dimensional models of root growth, architecture and function

BackgroundThree–dimensional root architectural models emerged in the late 1980s, providing an opportunity to conceptualise and investigate that all important part of plants that is typically hidden and difficult to measure and study. These models have progressed from representing pre–defined root architectural arrangements, to simulating root growth in response to heterogeneous soil environments. This was done through incorporating soil properties and more complete descriptions of plant function, moving into the realm of functional-structural plant modelling. Modelling studies are often designed to investigate the relationship between root architectural traits and root distribution in soil, and the spatio–temporal variability of resource supply. Modelling root systems presents an opportunity to investigate functional tradeoffs between foraging strategies (i.e. shallow vs deep rooting) for contrasting resources (immobile versus mobile resources), and their dependence on soil type, rainfall and other environmental conditions. The complexity of the interactions between root traits and environment emphasises the need for models in which traits and environmental conditions can be independently manipulated, unlike in the real world.ScopeWe provide an overview of the development of three–dimensional root architectural models from their origins, to their place today in the world of functional–structural plant modelling. The uses and capability of root architectural models to represent virtual plants and soil environment are addressed. We compare features of six current models, RootTyp, SimRoot, ROOTMAP, SPACSYS, R-SWMS, and RootBox, and discuss the future development of functional-structural root architectural modelling.ConclusionFunctional-structural root architectural models are being used to investigate numerous root–soil interactions, over a range of spatial scales. They are not only providing insights into the relationships between architecture, morphology and functional efficiency, but are also developing into tools that aid in the design of agricultural management schemes and in the selection of root traits for improving plant performance in specific environments.

A dynamic root system growth model based on L-Systems Tropisms and coupling to nutrient uptake from soil

Understanding the impact of roots and rhizosphere traits on plant resource efficiency is important, in particular in the light of upcoming shortages of mineral fertilizers and climate change with increasing frequency of droughts. We developed a modular approach to root growth and architecture modelling with a special focus on soil root interactions. The dynamic three-dimensional model is based on L-Systems, rewriting systems well-known in plant architecture modelling. We implemented the model in Matlab in a way that simplifies introducing new features as required. Different kinds of tropisms were implemented as stochastic processes that determine the position of the different roots in space. A simulation study was presented for phosphate uptake by a maize root system in a pot experiment. Different sink terms were derived from the root architecture, and the effects of gravitropism and chemotropism were demonstrated. This root system model is an open and flexible tool which can easily be coupled to different kinds of soil models.

A dynamic model of nutrient uptake by root hairs.

Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but quantitative understanding of their role in this is weak. This limits, for example, the breeding of more nutrient-efficient crop genotypes. We developed a mathematical model of nutrient transport and uptake in the root hair zone of single roots growing in soil or solution culture. Accounting for root hair geometry explicitly, we derived effective equations for the cumulative effect of root hair surfaces on uptake using the method of homogenization. Analysis of the model shows that, depending on the morphological and physiological properties of the root hairs, one of three different effective models applies. They describe situations where: (1) a concentration gradient dynamically develops within the root hair zone; (2) the effect of root hair uptake is negligibly small; or (3) phosphate in the root hair zone is taken up instantaneously. Furthermore, we show that the influence of root hairs on rates of phosphate uptake is one order of magnitude greater in soil than solution culture. The model provides a basis for quantifying the importance of root hair morphological and physiological properties in overall uptake, in order to design and interpret experiments in different circumstances.

Recovering Root System Traits Using Image Analysis Exemplified by Two-Dimensional Neutron Radiography Images of Lupine

Image-based parameterization of root architectural models is advanced by a new approach for the analysis of image sequences of plant root systems. Root system traits are important in view of current challenges such as sustainable crop production with reduced fertilizer input or in resource-limited environments. We present a novel approach for recovering root architectural parameters based on image-analysis techniques. It is based on a graph representation of the segmented and skeletonized image of the root system, where individual roots are tracked in a fully automated way. Using a dynamic root architecture model for deciding whether a specific path in the graph is likely to represent a root helps to distinguish root overlaps from branches and favors the analysis of root development over a sequence of images. After the root tracking step, global traits such as topological characteristics as well as root architectural parameters are computed. Analysis of neutron radiographic root system images of lupine (Lupinus albus) grown in mesocosms filled with sandy soil results in a set of root architectural parameters. They are used to simulate the dynamic development of the root system and to compute the corresponding root length densities in the mesocosm. The graph representation of the root system provides global information about connectivity inside the graph. The underlying root growth model helps to determine which path inside the graph is most likely for a given root. This facilitates the systematic investigation of root architectural traits, in particular with respect to the parameterization of dynamic root architecture models.

Root System Markup Language: toward a unified root architecture description language

Portability of root architecture data with the Root System Markup Language paves the way for central root phenotype repositories. The number of image analysis tools supporting the extraction of architectural features of root systems has increased in recent years. These tools offer a handy set of complementary facilities, yet it is widely accepted that none of these software tools is able to extract in an efficient way the growing array of static and dynamic features for different types of images and species. We describe the Root System Markup Language (RSML), which has been designed to overcome two major challenges: (1) to enable portability of root architecture data between different software tools in an easy and interoperable manner, allowing seamless collaborative work; and (2) to provide a standard format upon which to base central repositories that will soon arise following the expanding worldwide root phenotyping effort. RSML follows the XML standard to store two- or three-dimensional image metadata, plant and root properties and geometries, continuous functions along individual root paths, and a suite of annotations at the image, plant, or root scale at one or several time points. Plant ontologies are used to describe botanical entities that are relevant at the scale of root system architecture. An XML schema describes the features and constraints of RSML, and open-source packages have been developed in several languages (R, Excel, Java, Python, and C#) to enable researchers to integrate RSML files into popular research workflow.

A statistical approach to root system classification

Plant root systems have a key role in ecology and agronomy. In spite of fast increase in root studies, still there is no classification that allows distinguishing among distinctive characteristics within the diversity of rooting strategies. Our hypothesis is that a multivariate approach for “plant functional type” identification in ecology can be applied to the classification of root systems. The classification method presented is based on a data-defined statistical procedure without a priori decision on the classifiers. The study demonstrates that principal component based rooting types provide efficient and meaningful multi-trait classifiers. The classification method is exemplified with simulated root architectures and morphological field data. Simulated root architectures showed that morphological attributes with spatial distribution parameters capture most distinctive features within root system diversity. While developmental type (tap vs. shoot-borne systems) is a strong, but coarse classifier, topological traits provide the most detailed differentiation among distinctive groups. Adequacy of commonly available morphologic traits for classification is supported by field data. Rooting types emerging from measured data, mainly distinguished by diameter/weight and density dominated types. Similarity of root systems within distinctive groups was the joint result of phylogenetic relation and environmental as well as human selection pressure. We concluded that the data-define classification is appropriate for integration of knowledge obtained with different root measurement methods and at various scales. Currently root morphology is the most promising basis for classification due to widely used common measurement protocols. To capture details of root diversity efforts in architectural measurement techniques are essential.

The algorithmic beauty of plant roots – an L-System model for dynamic root growth simulation

Understanding the impact of root architecture on plant resource efficiency is important, in particular, in the light of upcoming shortages of mineral fertilizers and changed environmental conditions. In the 1950s, a great number of root systems of European cultivated plants were excavated and studied by L. Kutschera (1960). Her work gave enormous insight into the variety of root system architectures and helped to realize the importance of belowground processes to plant productivity. We analysed the resulting hand drawings by using mathematical modelling and found root system parameters for a newly developed parametric L-System model. In this way we were able to first reproduce the illustrations, second computationally analyse root system traits and finally access the dynamic root architecture development.

Modelling Phosphorus Dynamics in the Soil–Plant System

The large number of models for P dynamics in soil–plant systems focus on different scales and have different purposes. This chapter provides an overview of existing models and illustrates the scope and potential of current modelling techniques by using three case studies. We focus on plant traits that enhance plant phosphate uptake from soil. The first case study presents a model for phosphate uptake by mycorrhizal roots, the second study is based on a root system scale model that includes root plasticity, and the third presents a model for crop response to soil phosphate supply.

Comparison of nutrient uptake between three‐dimensional simulation and an averaged root system model

Abstract We present a new numerical approach describing nutrient uptake in three dimensions. Dynamic boundary conditions are considered at the individual root surfaces within a root system. As an example, we compare the three‐dimensional simulation results of phosphate uptake by a young maize root system to the corresponding effective solution. We show that the two solutions are similar concerning phosphate uptake and the size of the depletion zones. The presented approach makes it possible to verify simplifications that are made in the development of effective models. Furthermore, it is possible to extend existing models by including spatial heterogeneities that will increase our understanding of rhizosphere processes.

CRootBox: a structural–functional modelling framework for root systems

Background and Aims Root architecture development determines the sites in soil where roots provide input of carbon and take up water and solutes. However, root architecture is difficult to determine experimentally when grown in opaque soil. Thus, root architecture models have been widely used and been further developed into functional-structural models that simulate the fate of water and solutes in the soil-root system. The root architecture model CRootBox presented here is a flexible framework to model root architecture and its interactions with static and dynamic soil environments. Methods CRootBox is a C++-based root architecture model with Python binding, so that CRootBox can be included via a shared library into any Python code. Output formats include VTP, DGF, RSML and a plain text file containing coordinates of root nodes. Furthermore, a database of published root architecture parameters was created. The capabilities of CRootBox for the unconfined growth of single root systems, as well as the different parameter sets, are highlighted in a freely available web application. Key results The capabilities of CRootBox are demonstrated through five different cases: (1) free growth of individual root systems; (2) growth of root systems in containers as a way to mimic experimental setups; (3) field-scale simulation; (4) root growth as affected by heterogeneous, static soil conditions; and (5) coupling CRootBox with code from the book Soil physics with Python to dynamically compute water flow in soil, root water uptake and water flow inside roots. Conclusions CRootBox is a fast and flexible functional-structural root model that is based on state-of-the-art computational science methods. Its aim is to facilitate modelling of root responses to environmental conditions as well as the impact of roots on soil. In the future, this approach will be extended to the above-ground part of the plant.