Winfried Kurth

MORPHOLOGICAL MODELS OF PLANT GROWTH : POSSIBILITIES AND ECOLOGICAL RELEVANCE

Abstract Three-dimensional models of plant architecture and growth, based on botanical knowledge, have direct applications in simulations of photosynthetically active radiation transfer in forest stands and in models of water conduction and transpiration. Furthermore, they can serve as a basis for future tree models which have to integrate the aspects of light interception, hydraulics, mechanical stability, gas exchange and carbon allocation. Models which reflect the genetically fixed aspect of plant architecture have already reached a high level, with a combination of Lindenmayer systems and stochastic processes as a theoretical basis. The AMAP approach (de Reffye et al., CIRAD, Montpellier, France) is the most elaborated one and has also led to excellent graphical results. Further potential lies in the parameterisation of the underlying grammars and distributions, which allows the full inclusion of external growth factors like light and water availability, of mechanical obstacles, and of physiological constraints. Some preliminary graphical results are shown which were produced by a program executing a simple form of stochastic growth grammars.

A functional–structural model of rice linking quantitative genetic information with morphological development and physiological processes

BACKGROUND AND AIMS Although quantitative trait loci (QTL) analysis of yield-related traits for rice has developed rapidly, crop models using genotype information have been proposed only relatively recently. As a first step towards a generic genotype-phenotype model, we present here a three-dimensional functional-structural plant model (FSPM) of rice, in which some model parameters are controlled by functions describing the effect of main-effect and epistatic QTLs. METHODS The model simulates the growth and development of rice based on selected ecophysiological processes, such as photosynthesis (source process) and organ formation, growth and extension (sink processes). It was devised using GroIMP, an interactive modelling platform based on the Relational Growth Grammar formalism (RGG). RGG rules describe the course of organ initiation and extension resulting in final morphology. The link between the phenotype (as represented by the simulated rice plant) and the QTL genotype was implemented via a data interface between the rice FSPM and the QTLNetwork software, which computes predictions of QTLs from map data and measured trait data. KEY RESULTS Using plant height and grain yield, it is shown how QTL information for a given trait can be used in an FSPM, computing and visualizing the phenotypes of different lines of a mapping population. Furthermore, we demonstrate how modification of a particular trait feeds back on the entire plant phenotype via the physiological processes considered. CONCLUSIONS We linked a rice FSPM to a quantitative genetic model, thereby employing QTL information to refine model parameters and visualizing the dynamics of development of the entire phenotype as a result of ecophysiological processes, including the trait(s) for which genetic information is available. Possibilities for further extension of the model, for example for the purposes of ideotype breeding, are discussed.

Relational growth grammars – a graph rewriting approach to dynamical systems with a dynamical structure

Relational growth grammars (RGG) are a graph rewriting formalism which extends the notations and semantics of Lindenmayer systems and which allows the specification of dynamical processes on dynamical structures, particularly in biological and chemical applications. RGG were embedded in the language XL, combining rule-based and conventional object-oriented constructions. Key features of RGG and of the software GroIMP (Growth grammar related Interactive Modelling Platform) are listed. Five simple examples are shown which demonstrate the essential ideas and possibilities of RGG: signal propagation in a network, cellular automata, globally-sensitive growth of a plant, a chemical prime number generator, and a polymerisation model using a simple mass-spring kinetics.

The Modelling Platform GroIMP and the Programming Language XL

We present the open-source modelling platform GroIMP and the rule-based programming language XL. The underlying representation of data within GroIMP is a graph, which can be transformed by rules specified in XL. The principal field of application is modelling of virtual plants, but the system can also be used for a lot of other applications.

Relational Growth Grammars --- A Parallel Graph Transformation Approach with Applications in Biology and Architecture

We present the formalism of relational growth grammars. They are a variant of graph grammars with a principal application for plant modelling, where they extend the well-established, but limited formalism of L-systems. The main property is the application of rules in parallel, motivated by the fact that life is fundamentally parallel. A further speciality is the dynamic creation of right-hand sides on rule application. Relational growth grammars have been successfully used not only for plant modelling, but also to model general 3D structures or systems of Artificial Life. We illustrate these applications at several examples, all being implemented using our programming language XL which extends Java and provides an implementation of relational growth grammars.

A Rule-Based Functional-Structural Model of Rice Considering Source and Sink Functions

As a first step towards a generic genotype-phenotype model of rice, we present here a model of the growth and morphology of rice in combination with ecophysiological processes using the technique of functional-structural plant modelling (FSPM) and the interactive modelling platform GroIMP along with the graph-based Relational Growth Grammar formalism. The model constitutes a simple yet functionally coherent phenotype model of rice, consisting of a set of morphogenetic RGG rules describing an “average” developmental course and final morphology, partially linking yield traits to processes (tiller and grain number, stem length, grain filling rate, grain weight).

Representation of Genotype and Phenotype in a Coherent Framework Based on Extended L-Systems

A formal language approach for the specification of ALife models is presented. “Relational Growth Grammars” incorporate rule-based, procedural and object-oriented concepts. By enabling parametric Lindenmayer systems to rewrite multiscaled graphs, it becomes possible to represent genes, plant organs and populations as well as developmental aspects of these entities in a common formal framework. Genetic operators (mutation, crossing-over, selection) take the form of simple graph rewrite rules. This is illustrated using Richard Dawkins’ “biomorphs”, whereas other applications are briefly sketched. The formalism is implemented as part of an interactive software platform.

Exploring root developmental plasticity to nitrogen with a three-dimensional architectural model

Background and aimsRoot plasticity is a key process affecting the root system foraging capacity while itself being affected by the nutrient availability around the root environment. Root system architecture is determined by three types of plastic responses: chemotropism, spacing of lateral roots, hierarchy between laterals and their mother root.MethodsWe attempt a systematic comparison of the effect of each mechanism on the whole root plasticity when the root is grown under four distinct nutrient distribution scenarios using a functional-structural root model. Nutrient distributions included i) a completely random distribution, ii) a layered distribution, iii) a patch distribution, and iv) a gradient distribution. Root length, volume, total uptake, uptake efficiency as well as the soil profiles are given as model outputs.ResultsRoot uptake was more efficient in a soil with a gradient nutrient distribution and less so in a patch distribution for all mechanisms. In terms of mechanisms uptake was more efficient for the spacing (elongation) mechanism than the hierarchy (branching) mechanism.ConclusionsRoot mechanisms play a different role in the foraging of the root with chemotropism being a global tracking mechanism, whereas spacing and hierarchy are ways to proliferate in a zone with locally available nutrients.

A graph model and grammar for multi-scale modelling using XL

A graph formalism and grammar suitable for multi-scale modelling is introduced in this paper. Existing rule-based rewriting mechanisms related to L-systems do not take scales into account or rely on string-based mechanisms. This poses difficulties to develop multi-scale models using rule-based graph approaches. Using a type graph to capture scale relationships and accounting for scales using an additional edge type, we introduce a technique to overcome these problems. Syntax for expressing multi-scale graphs allows the construction of models in the language XL coupled with existing rule-based functionality.

FSPM-P: towards a general functional-structural plant model for robust and comprehensive model development

In the last decade, functional-structural plant modelling (FSPM) has become a more widely accepted paradigm in crop and tree production, as 3D models for the most important crops have been proposed. Given the wider portfolio of available models, it is now appropriate to enter the next level in FSPM development, by introducing more efficient methods for model development. This includes the consideration of model reuse (by modularisation), combination and comparison, and the enhancement of existing models. To facilitate this process, standards for design and communication need to be defined and established. We present a first step towards an efficient and general, i.e., not speciesspecific FSPM, presently restricted to annual or bi-annual plants, but with the potential for extension and further generalization.Model structure is hierarchical and object-oriented, with plant organs being the base-level objects and plant individual and canopy the higher-level objects. Modules for the majority of physiological processes are incorporated, more than in other platforms that have a similar aim (e.g., photosynthesis, organ formation and growth). Simulation runs with several general parameter sets adopted from the literature show that the present prototypewas able to reproduce a plausible output range for different crops (rapeseed, barley, etc.) in terms of both the dynamics and final values (at harvest time) of model state variables such as assimilate production, organ biomass, leaf area and architecture.